wyer-drawing_a or_o spin_v gold_n silver_n brass_n and_o iron_n and_o it_o be_v this_o that_o such_o artificer_n desire_v more_o and_o more_o to_o disgrosse_v and_o subtillize_v the_o say_a metal_n have_v wound_n about_o a_o rocket_n or_o barrel_n the_o thread_n of_o the_o metal_n they_o place_v the_o rocket_n in_o a_o frame_n upon_o a_o steadfast_a axis_n in_o such_o sort_n that_o the_o rocket_n may_v turn_v about_o in_o itself_o then_o make_v one_o end_n of_o the_o thread_n to_o pass_v by_o force_n through_o a_o plate_n of_o steel_n pierce_v with_o divers_a hole_n great_a and_o lesser_a as_o need_n require_v fasten_v the_o same_o end_n of_o the_o thread_n to_o another_o rocket_n they_o wind_v up_o the_o thread_n which_o pass_v through_o a_o bear_v less_o than_o the_o thickness_n of_o the_o thread_n be_v of_o force_n constrain_v to_o disgrosse_v and_o subtillize_v now_o that_o which_o be_v intense_o to_o be_v observe_v in_o this_o business_n be_v this_o that_o the_o part_n of_o the_o thread_n before_o the_o hole_n be_v of_o such_o a_o thickness_n but_o the_o part_n of_o the_o same_o thread_n after_o it_o be_v pass_v the_o hole_n be_v of_o a_o lesser_a thickness_n and_o yet_o nevertheless_o the_o mass_n and_o weight_n of_o the_o thread_n which_o be_v draw_v forth_o be_v ever_o equal_a to_o the_o mass_n and_o weight_n of_o the_o thread_n which_o be_v wind_v up_o but_o if_o we_o shall_v well_o consider_v the_o matter_n we_o shall_v find_v that_o the_o thick_a the_o thread_n before_o the_o hole_n be_v than_o the_o thread_n pass_v the_o hole_n the_o great_a reciprocal_o be_v the_o velocity_n of_o the_o part_n of_o the_o thread_n pass_v the_o hole_n than_o the_o volocity_n of_o the_o part_n before_o the_o hole_n insomuch_o that_o if_o uâ—rbi_fw-la gratia_fw-la the_o thickness_n of_o the_o thread_n before_o the_o hole_n be_v double_a to_o the_o thickness_n after_o the_o hole_n in_o such_o case_n the_o velocity_n of_o the_o part_n of_o the_o thread_n pass_v the_o hole_n shall_v be_v double_a to_o the_o velocity_n of_o the_o part_n of_o the_o thread_n before_o the_o hole_n and_o thus_o the_o thickness_n compensate_v the_o velocity_n and_o the_o velocity_n compensate_v the_o thickness_n so_o that_o the_o same_o occur_v in_o the_o solid_a metal_n of_o gold_n silver_n brass_n iron_n etc._n etc._n that_o even_v also_o in_o the_o fluid_a element_n of_o water_n and_o other_o liquid_n namely_o that_o the_o velocity_n bear_v the_o same_o proportion_n to_o the_o velocity_n that_o the_o thickness_n of_o the_o metal_n or_o water_n have_v to_o the_o thickness_n and_o therefore_o grant_v this_o discourse_n we_o may_v say_v that_o as_o often_o as_o two_o tap_n with_o different_a velocity_n discharge_v equal_a quantity_n of_o water_n in_o equal_a time_n it_o will_v be_v necessary_a that_o the_o tap_n less_o swift_a be_v so_o much_o great_a and_o large_a than_o the_o tap_n more_o swift_a by_o how_o much_o the_o swift_a superate_v in_o velocity_n the_o slow_a and_o to_o pronounce_v the_o proposition_n in_o more_o proper_a term_n we_o say_v that_o if_o two_o tap_n of_o unequal_a velocity_n discharge_v in_o equal_a time_n equal_a quantity_n of_o water_n the_o greatness_n of_o the_o first_o shall_v be_v to_o the_o greatness_n of_o the_o second_o in_o reciprocal_a proportion_n as_o the_o velocity_n of_o the_o second_o to_o the_o velocity_n of_o the_o first_o as_o for_o example_n if_o the_o first_o tap_n shall_v be_v ten_o time_n swift_a than_o the_o second_o tap_n it_o will_v be_v necessary_a that_o the_o second_o be_v ten_o time_n big_a and_o large_a than_o the_o first_o and_o in_o such_o case_n the_o tap_n shall_v discharge_v equal_a quantity_n of_o water_n in_o equal_a time_n and_o this_o be_v the_o principal_a and_o most_o important_a point_n which_o ought_v to_o be_v keep_v always_o in_o mind_n for_o that_o on_o it_o well_o understand_v depend_v many_o thing_n profitable_a and_o worthy_a of_o our_o knowledge_n now_o apply_v all_o that_o have_v be_v say_v near_o to_o our_o purpose_n i_o consider_v that_o it_o be_v most_o true_a that_o in_o divers_a part_n of_o the_o same_o river_n or_o current_n of_o run_a water_n there_o do_v always_o pass_v equal_a quantity_n of_o water_n in_o equal_a time_n which_o thing_n be_v also_o demonstrate_v in_o our_o first_o proposition_n and_o it_o be_v also_o true_a that_o in_o divers_a part_n the_o same_o river_n may_v have_v various_a and_o different_a velocity_n it_o follow_v of_o necessary_a consequence_n that_o where_o the_o river_n have_v less_o velocity_n it_o shall_v be_v of_o great_a measure_n and_o in_o those_o part_n in_o which_o it_o have_v great_a velocity_n it_o shall_v be_v of_o less_o measure_n and_o in_o sum_n the_o velocity_n of_o several_a part_n of_o the_o say_a river_n shall_v have_v eternal_o reciprocal_a and_o like_a proportion_n with_o their_o measure_n this_o principle_n and_o fundamental_a well_o establish_v that_o the_o same_o current_n of_o water_n change_v measure_n according_a to_o its_o vary_v of_o velocity_n that_o be_v lessen_v the_o measure_n when_o the_o velocity_n increase_v and_o increase_a the_o measure_n when_o the_o velocity_n decrease_v i_o pass_v to_o the_o consideration_n of_o many_o particular_a accident_n in_o this_o admirable_a matter_n and_o all_o depend_v on_o this_o sole_a proposition_n the_o sense_n of_o which_o i_o have_v oft_o repeat_v that_o it_o may_v be_v well_o understand_v corollary_n i._n and_o first_o we_o hence_o conclude_v that_o the_o same_o stream_n of_o a_o torrent_n namely_o those_o stream_n which_o carry_v equal_a quantity_n of_o water_n in_o equal_a time_n make_v not_o the_o same_o depth_n or_o measure_n in_o the_o river_n in_o which_o they_o enter_v unless_o when_o in_o the_o entrance_n into_o the_o river_n they_o acquire_v or_o to_o say_v better_o keep_v the_o same_o velocity_n because_o if_o the_o velocicity_n acquire_v in_o the_o river_n shall_v be_v different_a also_o the_o measure_n shall_v be_v diverse_a and_o consequent_o the_o depth_n as_o be_v demonstrate_v corollary_n ii_o and_o because_o successive_o as_o the_o river_n be_v more_o and_o more_o full_a it_o be_v constitute_v ordinary_o in_o great_a &_o great_a velocity_n hence_o it_o be_v that_o the_o same_o stream_n of_o the_o torrent_n that_o enter_v into_o the_o river_n make_v less_o and_o less_o depth_n as_o the_o river_n grow_v more_o and_o more_o full_a since_o that_o also_o the_o water_n of_o the_o torrent_n be_v enter_v into_o the_o river_n go_v acquire_v great_a and_o great_a velocity_n and_o therefore_o diminish_v in_o measure_n and_o height_n corollary_n iii_o we_o observe_v also_o that_o while_o the_o main_a river_n be_v shallow_a if_o there_o fall_v but_o a_o gentle_a rain_n it_o sudden_o much_o increase_v and_o rise_v but_o when_o the_o river_n be_v already_o swell_v though_o there_o fall_v again_o another_o new_a violent_a shower_n yet_o it_o increase_v not_o at_o the_o same_o rate_n as_o before_o proportionable_o to_o the_o rain_n which_o fall_v which_o thing_n we_o may_v affirm_v particular_o to_o depend_v on_o this_o that_o in_o the_o first_o case_n while_o the_o river_n be_v low_a it_o be_v find_v also_o very_o slow_a and_o therefore_o the_o little_a water_n which_o enter_v into_o it_o pass_v and_o run_v with_o little_a velocity_n and_o consequent_o occupy_v a_o great_a measure_n but_o when_o the_o river_n be_v once_o augment_v by_o new_a water_n be_v also_o make_v more_o swift_a it_o cause_v the_o great_a flood_n of_o water_n which_o fall_v to_o bear_v a_o less_o measure_n and_o not_o to_o make_v such_o a_o depth_n corollary_n iu._n from_o the_o thing_n demonstrate_v be_v manifest_a also_o that_o whilst_o a_o torrent_n enter_v into_o a_o river_n at_o the_o time_n of_o ebb_n than_o the_o torrent_n move_v with_o such_o a_o certain_a velocity_n what_o ever_o it_o be_v pass_v by_o its_o extreme_a part_n wherewith_o it_o communicate_v with_o the_o river_n in_o which_o part_n the_o torrent_n be_v measure_v shall_v have_v such_o a_o certain_a measure_n but_o the_o river_n swell_v and_o rise_v also_o those_o part_n of_o the_o torrent_n augment_v in_o greatness_n and_o measure_n though_o the_o torrent_n in_o that_o instant_n disimbogue_a no_o more_o water_n than_o it_o do_v before_o so_o that_o the_o river_n be_v swell_v we_o be_v to_o consider_v two_o mouth_n of_o the_o same_o torrent_n one_o less_o before_o the_o rise_n the_o other_o great_a after_o the_o rise_n which_o mouth_n discharge_v equal_a quantity_n of_o water_n in_o equal_a time_n therefore_o the_o velocity_n by_o the_o lesser_a mouth_n shall_v be_v great_a than_o the_o velocity_n by_o the_o great_a mouth_n and_o thus_o the_o torrent_n shall_v be_v retard_v from_o its_o ordinary_a course_n corollary_n v._n from_o which_o operation_n of_o nature_n proceed_v another_o effect_n worthy_a of_o consideration_n and_o it_o
through_o those_o water_n to_o sandolo_n and_o these_o fishing-wears_a be_v such_o impediment_n that_o some_o one_o of_o they_o make_v the_o water_n of_o the_o river_n in_o the_o upper_a part_n to_o rise_v half_o a_o palm_n and_o sometime_o a_o whole_a palm_n and_o more_o so_o that_o when_o they_o be_v all_o gather_v together_o these_o impediment_n amount_v to_o more_o than_o seven_o or_o possible_o than_o eight_o palm_n there_o concur_v for_o a_o three_o most_o potent_a cause_n of_o the_o water_n continue_v high_a in_o the_o evacuate_n or_o draining_n channel_n and_o consequent_o on_o the_o plain_n the_o great_a abundance_n of_o water_n that_o issue_v from_o fiume_n sisto_n the_o water_n of_o which_o do_v not_o keep_v within_o its_o bank_n when_o they_o be_v abundant_a but_o increase_a above_o its_o channel_n they_o unite_v with_o those_o of_o the_o evacuator_fw-la and_o disperse_v through_o the_o fen_n be_v raise_v with_o great_a prejudice_n and_o much_o great_a than_o be_v conceive_v according_a to_o what_o have_v be_v demonstrate_v in_o the_o second_o consideration_n upon_o the_o lake_n of_o venice_n nor_o be_v it_o to_o any_o purpose_n to_o say_v that_o if_o we_o shall_v measure_v all_o the_o water_n that_o disimbogue_v from_o fiume_n sisto_n and_o gather_v they_o into_o one_o sum_n we_o shall_v not_o find_v they_o to_o be_v such_o as_o that_o they_o shall_v be_v able_a to_o make_v the_o water_n of_o the_o fen_n to_o increase_v by_o reason_n of_o the_o great_a expansion_n of_o they_o over_o which_o that_o body_n of_o water_n be_v to_o distend_v for_o to_o this_o instance_n we_o answer_v with_o that_o which_o we_o have_v give_v notice_n of_o in_o the_o first_o consideration_n touch_v the_o lake_n of_o venice_n treat_v of_o the_o abatement_n that_o be_v cause_v by_o the_o brent_n let_v into_o the_o lake_n and_o moreover_o if_o i_o shall_v add_v thereto_o that_o which_o i_o write_v in_o the_o second_o consideration_n it_o will_v be_v very_o apparent_a how_o great_o harmful_a and_o prejudicial_a these_o excursion_n of_o water_n from_o fiume_n sisto_n may_v be_v which_o be_v not_o keep_v under_o and_o confine_v within_o the_o river_n therefore_o proceed_v to_o the_o provision_n and_o operation_n that_o be_v to_o be_v account_v principal_a i_o reduce_v they_o to_o three_o head_n in_o the_o first_o place_n it_o be_v necessary_a to_o throw_v down_o those_o wear_v and_o to_o take_v the_o pisciaries_n quite_o away_o observe_v a_o maxim_n in_o my_o judgement_n infallible_a that_o fish_v and_o sow_v be_v two_o thing_n that_o can_v never_o consist_v together_o fish_v being_n on_o the_o water_n and_o sow_v on_o land_n second_o it_o will_v be_v necessary_a to_o cut_v under_o water_n in_o the_o bottom_n of_o the_o river_n those_o weed_n and_o plant_n that_o grow_v and_o increase_v in_o the_o river_n and_o leave_v they_o to_o be_v carry_v into_o the_o sea_n by_o the_o stream_n for_o by_o this_o mean_v these_o reed_n shall_v not_o spring_v up_o and_o distend_v along_o the_o bottom_n of_o the_o river_n by_o mean_n of_o the_o beast_n tread_v upon_o they_o and_o the_o same_o aught_o to_o be_v do_v often_o and_o with_o care_n and_o must_v not_o be_v delay_v till_o the_o mischief_n increase_v and_o the_o champain_n ground_n be_v drown_v but_o one_o ought_v to_o order_v matter_n so_o as_o that_o they_o may_v not_o drown_v and_o i_o will_v affirm_v that_o otherwise_o this_o principal_a point_n will_v become_v a_o most_o considerable_a inconvenience_n three_o it_o be_v necessary_a to_o make_v good_a the_o bank_n of_o fiume_n sisto_n on_o the_o left_a hand_n and_o to_o procure_v that_o those_o water_n may_v run_v in_o the_o channel_n and_o not_o break_v forth_o and_o it_o be_v to_o be_v note_v that_o it_o be_v not_o enough_o to_o do_v one_o or_o two_o of_o those_o thing_n but_o we_o be_v to_o put_v they_o all_o in_o execution_n for_o omit_v any_o thing_n the_o whole_a machine_n will_v be_v out_o of_o tune_n and_o spoil_v but_o proceed_v with_o due_a care_n you_o shall_v not_o only_a drain_n the_o pontine_n fen_n but_o by_o mean_n of_o this_o last_o particular_a the_o current_n of_o fiume_n sisto_n shall_v scour_v its_o own_o channel_n of_o its_o self_n even_o to_o the_o carry_v part_n of_o it_o away_o and_o haply_o with_o this_o abundance_n of_o water_n that_o it_o shall_v bear_v the_o mouth_n della_fw-it torre_n may_v be_v open_v and_o keep_v open_a into_o the_o sea_n and_o it_o will_v last_o of_o all_o be_v of_o admirable_a benefit_n to_o cleanse_v fiume_n sisto_n from_o many_o tree_n and_o bush_n wherewith_o it_o be_v overgrow_v and_o with_o this_o i_o conclude_v that_o the_o improvement_n or_o drain_n possible_a to_o be_v make_v consist_v in_o these_o three_o particular_n first_o in_o take_v away_o the_o fish_n wear_v leave_v the_o course_n of_o the_o water_n free_a second_o in_o keep_v the_o principal_a river_n clear_a from_o weed_n and_o plant_n three_o in_o keep_v the_o water_n of_o fiume_n sisto_n in_o its_o own_o channel_n all_o which_o be_v thing_n that_o may_v be_v do_v with_o very_o little_a charge_n and_o to_o the_o manifest_a benefit_n of_o the_o whole_a country_n and_o to_o the_o render_v the_o air_n wholesome_o in_o all_o those_o place_n adjoin_v to_o the_o pontine_n fen_n a_o consideration_n upon_o the_o draining_n of_o the_o territory_n of_o bologna_n ferrara_n and_o romagna_fw-la by_o d._n benedetto_n castelli_n abbot_n of_o s._n benedetto_n aloisio_n mathematician_n to_o p._n vrban_n viii_o and_o professor_n in_o the_o university_n of_o rome_n the_o weghty_a business_n of_o the_o draining_n of_o the_o territory_n of_o bologna_n ferrara_n and_o romagna_n have_v be_v punctual_o handle_v and_o declare_v in_o write_v from_o the_o excellent_a memory_n of_o the_o right_n honourable_a and_o noble_a monsignore_n corsini_n who_o be_v heretofore_o depute_a commissary_n general_n and_o visitor_n of_o those_o water_n i_o be_o not_o able_a to_o make_v such_o another_o discourse_n upon_o the_o same_o subject_a but_o will_v only_o say_v somewhat_o for_o far_a confirmation_n of_o that_o which_o i_o have_v say_v in_o this_o book_n upon_o the_o lake_n of_o venice_n upon_o the_o pontine_n fen_n and_o upon_o the_o draining_n of_o those_o plain_n of_o pisa_n lie_v between_o the_o river_n arno_n and_o serchio_n whereby_o it_o be_v manifest_a that_o in_o all_o the_o aforementioned_a case_n and_o in_o the_o present_a one_o that_o we_o be_v in_o hand_n with_o there_o have_v in_o time_n past_a very_o gross_a error_n be_v commit_v through_o the_o not_o have_v ever_o well_o understand_v the_o true_a measure_n of_o run_v water_n and_o here_o it_o be_v to_o be_v note_v that_o the_o business_n be_v that_o in_o venice_n the_o diversion_n of_o the_o water_n of_o the_o lake_n by_o divert_v the_o brent_n be_v debate_v and_o in_o part_n execute_v without_o consideration_n have_v how_o great_a abatement_n of_o water_n may_v follow_v in_o the_o lake_n if_o the_o brent_n be_v divert_v as_o i_o have_v show_v in_o the_o first_o consideration_n upon_o this_o particular_a from_o which_o act_n there_o have_v ensue_v very_o bad_a consequence_n not_o only_o the_o difficulty_n of_o navigation_n but_o it_o have_v infect_v the_o wholsomnesse_n of_o the_o air_n and_o cause_v the_o stoppage_n of_o the_o port_n of_o venice_n and_o on_o the_o contrary_a the_o same_o inadvertency_n of_o not_o consider_v what_o rise_v of_o the_o water_n the_o reno_n and_o other_o river_n be_v open_v into_o the_o valley_n of_o bologna_n and_o ferrara_n may_v cause_v in_o the_o say_a valley_n be_v the_o certain_a cause_n that_o so_o many_o rich_a and_o fertile_a field_n be_v drown_v under_o water_n convert_v the_o happy_a habitation_n and_o dwelling_n of_o man_n into_o miserable_a receptacle_n for_o fish_n thing_n which_o doubtless_o will_v never_o have_v happen_v if_o those_o river_n have_v be_v keep_v at_o their_o height_n and_o reno_n have_v be_v turn_v into_o main-po_n and_o the_o other_o river_n into_o that_o of_o argenta_n and_o of_o volano_n now_o there_o have_v sufficient_a be_v speak_v by_o the_o abovenamed_a monsig_n corsini_n in_o his_o relation_n i_o will_v only_o add_v one_o conceit_n of_o my_o own_o which_o after_o the_o river_n shall_v be_v regulate_v as_o have_v be_v say_v i_o very_o believe_v will_v be_v of_o extraordinary_a profit_n i_o much_o doubt_v indeed_o that_o i_o shall_v find_v it_o a_o hard_a matter_n to_o persuade_v man_n to_o be_v of_o my_o mind_n but_o yet_o nevertheless_o i_o will_v not_o question_v but_o that_o those_o at_o least_o who_o shall_v have_v understand_v what_o i_o have_v say_v and_o demonstrate_v concern_v the_o manner_n and_o proportion_n according_a to_o which_o the_o abatement_n and_o rise_n of_o running_n water_n proceed_v that_o be_v make_v by_o the_o diversion_n and_o introduction_n of_o water_n will_v apprehend_v
farci_fw-la parte_fw-la d'_fw-fr alcuna_fw-la dell_fw-it sue_v peregrine_fw-la speculationi_fw-la con_fw-mi sincerissimo_fw-la affetto_fw-it etc._n etc._n and_o the_o most_o acute_a mathematician_n signore_n evangelista_n terricelli_n late_a professor_n to_o the_o grand_a duke_n in_o immediate_a succession_n after_o galileo_n make_v this_o honourable_a and_o grateful_a mention_n of_o he_o and_o his_o book_n 191._o omitto_fw-la magnum_fw-la illum_fw-la nutantis_fw-la maris_fw-la motum_fw-la praetereo_fw-la etiam_fw-la omnem_fw-la fluminum_fw-la aquarumque_fw-la currentium_fw-la tum_fw-la mensurum_fw-la tum_fw-la usum_fw-la quarum_fw-la omnis_fw-la doctrina_fw-la reperta_fw-la primum_fw-la fuit_fw-la ab_fw-la abbate_n benedicto_n castellio_n preceptore_fw-la meo_fw-la scripsit_fw-la ille_fw-la scientiam_fw-la svam_fw-la &_o illam_fw-la non_fw-la solum_fw-la demonstratione_fw-la verum_fw-la etiam_fw-la opere_fw-la confirmavit_fw-la maxima_fw-la cum_fw-la principum_fw-la &_o populorum_fw-la utilitate_fw-la majore_fw-la cum_fw-la admiratione_n phylosophorum_fw-la extat_fw-la illius_fw-la libre_fw-la veer_fw-la aureus_fw-la §_o i_o have_v only_o two_o particular_n more_o to_o offer_v the_o english_a reader_n the_o one_o concern_v the_o book_n and_o it_o be_v this_o that_o after_o the_o general_a aprobation_n it_o have_v have_v in_o italy_n i_o can_v but_o think_v it_o deserve_v the_o same_o civil_a entertainment_n with_o we_o in_o regard_n that_o it_o come_v with_o no_o less_o novelty_n facility_n verity_n and_o utility_n to_o we_o than_o to_o those_o who_o the_o author_n favour_v with_o the_o original_a our_o river_n and_o sewer_n through_o public_a distraction_n and_o private_a encroachment_n be_v in_o great_a disorder_n as_o those_o channel_n for_o instance_n which_o former_o be_v navigable_a unto_o the_o very_a wall_n of_o york_n and_o salisbury_n &c_n &c_n our_o port_n be_v choke_v and_o obstruct_v by_o shelf_n and_o setlement_n our_o fen_n do_v in_o a_o great_a part_n lie_v waste_n and_o unimproved_a now_o all_o these_o may_v be_v and_o as_o i_o find_v by_o the_o confession_n of_o some_o who_o practice_n upon_o the_o copy_n of_o the_o first_o book_n only_o of_o our_o author_n have_v get_v they_o both_o money_n and_o reputation_n in_o part_n have_v be_v remedy_v by_o the_o way_n and_o mean_n he_o here_o set_v down_o the_o truth_n be_v the_o argument_n have_v be_v pass_v over_o with_o a_o universal_a silence_n so_o that_o to_o this_o day_n i_o have_v not_o see_v any_o thing_n that_o have_v be_v write_v demonstrative_o and_o with_o mathematical_a certainty_n concern_v the_o same_o save_v only_o what_o this_o learned_a prelate_n have_v deliver_v of_o his_o own_o invention_n in_o these_o treatise_n who_o yet_o have_v so_o full_o and_o plain_o handle_v the_o whole_a doctrine_n that_o i_o may_v affirm_v his_o work_n to_o be_v every_o way_n absolute_a it_o must_v be_v confess_v the_o demonstration_n of_o the_o second_o proposition_n of_o the_o second_o book_n do_v not_o well_o please_v the_o author_n and_o have_v he_o live_v he_o will_v have_v supply_v that_o defect_n but_o be_v prevent_v by_o death_n the_o reader_n must_v content_v himself_o with_o the_o mechanical_a proof_n that_o he_o give_v you_o of_o the_o truth_n of_o so_o excellent_a a_o conclusion_n §_o the_o other_o particular_a that_o i_o be_o to_o offer_v be_v that_o out_o of_o my_o desire_n to_o contribute_v what_o lie_v in_o i_o to_o the_o complete_n of_o this_o piece_n for_o english_a practice_n i_o have_v exee_v my_o promise_n not_o only_o in_o give_v you_o the_o second_o and_o follow_a book_n which_o be_v not_o extant_a at_o the_o time_n of_o tender_v my_o overture_n but_o also_o in_o that_o i_o have_v add_v a_o map_n or_o plat_v of_o all_o the_o river_n lake_n fen_n etc._n etc._n mention_v throughout_o the_o work_n and_o if_o i_o have_v not_o keep_v touch_n in_o point_n of_o time_n let_v it_o be_v consider_v that_o i_o be_o the_o translator_n and_o not_o the_o printer_n to_o conclude_v according_a to_o your_o acceptance_n of_o these_o my_o endeavour_n you_o may_v expect_v some_o other_o tract_n of_o no_o less_o profit_n and_o delight_n farewell_n t._n s._n errata_fw-la of_o the_o second_o part_n of_o the_o first_o tome_n in_o preface_n read_v ferdinando_n ii_o ibid._n l'aqua_fw-la page_n 2._o line_n 26_o for_o must_v read_v much_o p._n 3._o l._n 22_o r._n and_o let_v l._n 25._o r._n water_n 〈…〉_z 41._o r._n tappe_n as_o every_o where_o else_o page_n 4._o l._n 18._o r._n cord_n page_n 6._o l._n 9_o r._n acquire_v or_o page_n 9_o l._n 1._o r._n irreperable_a p._n 10._o l._n 13._o r._n dissimboguement_fw-fr for_o page_n 17._o r._n p._n 15._o p._n 15._o l._n 27_o r._n in_o l._n 36_o r._n be_v as_o l._n 38_o r._n 〈◊〉_d p._n 17._o l._n 12_o giuliâ—_n l._n â—7_n r._n measurer_n l._n 25_o r._n measure_v it_o r._n necessary_o p._n 23._o l._n 19_o r._n for_o help_n for_o page_n 31._o r._n p._n 32._o p._n 24_o l._n 14_o r._n to_o l._n 17_o r._n nam_o of_o the._n l._n 23_o r._n easy_a p._n 25._o l._n 38._o r._n cock_n p._n 29._o l._n 7._o r._n last_v p._n 31._o l._n 32._o r._n so_o p._n 41._o l._n 20._o r._n to_o the_o line_n p._n 48._o l._n 19_o r._n us_o the_o *_o id_fw-la figure_n false_a p._n 52._o l._n 30_o and_o 31._o for_o theorem_fw-la r._n proposition_n p._n 53._o l._n 29._o r._n again_o p._n 57_o l._n 19_o r._n same_o if_o l._n 44._o r._n bodily_a p._n 58._o l._n 9_o r._n gather_v l._n 40._o omit_v p._n 60._o l._n 2._o omit_v if_o p._n 65._o l._n 1._o r._n tidâ—_n deal_n p._n 66._o l._n 35._o r._n stoppage_n of_o p._n 68_o l._n 12_o for_o lord_n the_o r._n lord_n l._n ult_n for_o they_o r._n it_n p._n 69._o l._n 14._o r._n to_o one_o id_fw-la carry_v deal_n to_o p._n 71._o l._n 20_o r._n and_o that_o l._n 25_o r._n brace_n it_o l._n 29._o r._n brace_n l._n 44_o r._n the_o brent_n p._n 72._o l._n 23._o r._n serene_a highness_n p._n 73._o l._n 24_o r._n deliberation_n l._n 26_o for_o sum_n r._n moddel_n l._n 40._o r._n month_n p._n 79._o l._n 18._o r._n that_o into_o p._n 82._o l._n 22._o deal_n p_o 85._o l._n 9_o 10._o deal_n a_o free_a drame_n p._n 88_o l._n 5._o r._n palm_n p._n 89._o l._n 8._o r._n prince_n p._n 92._o l._n 3._o r._n discourse_n p._n 93._o l._n 31._o r._n tautology_n p._n 94._o l._n 9_o r._n miracle_n p._n 97._o l._n 13._o r._n weighty_a p._n 101._o l._n 21._o r._n marrara_n p._n 107._o l._n 28_o r._n patrimony_n l._n 40._o r._n above_o p._n 111._o l._n 16._o r._n say_v for_o p._n 432._o r._n p._n 114._o p._n 114._o l._n 35._o r._n of_o 200._o l._n 41._o r._n close_v p._n 115._o l._n 29._o r._n constant_a of_o the_o mensuration_n of_o run_v water_n lib_fw-la i._o what_o and_o of_o how_o great_a moment_n the_o consideration_n of_o motion_n be_v in_o natural_a thing_n be_v so_o manifest_a that_o the_o prince_n of_o peripatetic_n pronounce_v that_o in_o his_o school_n now_o much_o use_v sentence_n ignorato_fw-la motu_fw-la ignoratur_fw-la natura_fw-la thence_o it_o be_v that_o true_a philosopher_n have_v so_o travail_v in_o the_o contemplation_n of_o the_o celestial_a motion_n and_o in_o the_o speculation_n of_o the_o motion_n of_o animal_n that_o they_o have_v arrive_v to_o a_o wonderful_a height_n and_o sublimity_n of_o understanding_n under_o the_o same_o science_n of_o motion_n be_v comprehend_v all_o that_o which_o be_v write_v by_o mechanitian_n concern_v engine_n move_v of_o themselves_o machines_n move_a by_o the_o force_n of_o air_n and_o those_o which_o serve_v to_o move_v weight_n and_o immense_a magnitude_n with_o small_a force_n there_o appertain_v to_o the_o science_n of_o motion_n all_o that_o which_o have_v be_v write_v of_o the_o alteration_n not_o only_o of_o body_n but_o of_o our_o mind_n also_o and_o in_o sum_n this_o ample_a matter_n of_o motion_n be_v so_o extend_v and_o dilate_a that_o there_o be_v few_o thing_n which_o fall_v under_o man_n notice_n which_o be_v not_o conjoin_v with_o motion_n or_o at_o least_o depend_v thereupon_o or_o to_o the_o knowledge_n thereof_o direct_v and_o of_o almost_o every_o of_o they_o there_o have_v be_v write_v and_o compose_v by_o sublime_a wit_n learned_a treatise_n and_o instruction_n and_o because_o that_o in_o the_o year_n pass_v i_o have_v occasion_n by_o order_n of_o our_o lord_n pope_n vrban_n 8._o to_o apply_v my_o thought_n to_o the_o motion_n of_o the_o water_n of_o river_n a_o matter_n difficult_a most_o important_a and_o little_o handle_v by_o other_o have_v concern_v the_o same_o observe_v some_o particular_n not_o well_o observe_v or_o consider_v till_o now_o but_o of_o great_a moment_n both_o in_o public_a and_o private_a affair_n i_o have_v think_v good_a to_o publish_v they_o to_o the_o end_n that_o ingenious_a spirit_n may_v have_v occasion_n to_o discuss_v more_o exact_o than_o hitherto_o have_v be_v do_v so_o necessary_a and_o
profitable_a a_o matter_n and_o to_o supply_v also_o my_o defect_n in_o this_o short_a and_o difficult_a tractate_n difficult_a i_o say_v for_o the_o truth_n be_v these_o knowledge_n though_o of_o thing_n next_o our_o sense_n be_v sometime_o more_o abstruse_a and_o hide_a than_o the_o knowledge_n of_o thing_n more_o remote_a and_o much_o better_a and_o with_o great_a exquisitness_n be_v know_v the_o motion_n of_o the_o planet_n and_o period_n of_o the_o star_n than_o those_o of_o river_n and_o sea_n as_o that_o singular_a light_n of_o philosophy_n of_o our_o time_n and_o my_o master_n signore_n galileo_n galilei_n wise_o observe_v in_o his_o book_n concern_v the_o solar_a spot_n and_o to_o proceed_v with_o a_o due_a order_n in_o science_n i_o will_v take_v some_o supposition_n and_o cognition_n sufficient_o clear_a from_o which_o i_o will_v afterward_o proceed_v to_o the_o deduce_v of_o the_o principal_a conclusion_n but_o to_o the_o end_n that_o what_o i_o have_v write_v at_o the_o end_n of_o this_o discourse_n in_o a_o demonstrative_a and_o geometrical_a method_n may_v also_o be_v understand_v of_o those_o which_o never_o have_v apply_v their_o thought_n to_o the_o study_n of_o geometry_n i_o have_v endeavour_v to_o explain_v my_o conceit_n by_o a_o example_n and_o with_o the_o consideration_n of_o the_o natural_a thing_n themselves_o must_v after_o the_o same_o order_n in_o which_o i_o begin_v to_o doubt_v in_o this_o matter_n and_o have_v place_v this_o particular_a treatise_n here_o in_o the_o beginning_n advert_v nevertheless_o that_o he_o who_o desire_v more_o full_a and_o absolute_a solidity_n of_o reason_n may_v overpass_v this_o prefatory_a discourse_n and_o only_o consider_v what_o be_v treat_v of_o in_o the_o demonstration_n place_v towards_o the_o end_n and_o return_v afterward_o to_o the_o consideration_n of_o the_o thing_n collect_v in_o the_o corollary_n and_o appendix_n which_o demonstration_n notwithstanding_o may_v be_v pretermit_v by_o he_o that_o have_v not_o see_v at_o least_o the_o first_o six_o book_n of_o the_o element_n of_o euclid_n so_o that_o he_o diligent_o observe_v that_o which_o follow_v i_o say_v therefore_o that_o have_v in_o time_n past_a on_o divers_a occasion_n hear_v speak_v of_o the_o measure_n of_o the_o water_n of_o river_n and_o fountain_n say_v such_o a_o river_n be_v two_o or_o three_o thousand_o foot_n of_o water_n such_o a_o spring-water_n be_v twenty_o thirty_o or_o forty_o inch_n etc._n etc._n although_o in_o such_o manner_n i_o have_v find_v all_o to_o treat_v thereof_o in_o word_n and_o writing_n without_o variety_n and_o as_o we_o be_v wont_n to_o say_v constanti_fw-la sermone_fw-la yea_o even_a artist_n and_o ingeneer_n as_o if_o it_o be_v a_o thing_n that_o admit_v not_o of_o any_o doubt_n yet_o howsoever_o i_o remain_v still_o enfold_v in_o such_o a_o obscurity_n that_o i_o well_o know_v i_o understand_v nothing_o at_o all_o of_o that_o which_o other_o pretend_v full_a and_o clear_o to_o understand_v and_o my_o doubt_n arise_v from_o my_o frequent_a observation_n of_o many_o trench_n and_o channel_n which_o carry_v water_n to_o turn_v mill_n in_o which_o trench_n and_o channel_n the_o water_n be_v measure_v be_v find_v pretty_a deep_a but_o if_o afterward_o the_o same_o water_n be_v measure_v in_o the_o fall_n it_o make_v to_o turn_v the_o wheel_n of_o the_o mill_n it_o be_v much_o less_o not_o amount_v often_o to_o the_o ten_o part_n nor_o sometime_o to_o the_o twenty_o insomuch_o that_o the_o same_o run_a water_n come_v to_o be_v one_o while_n more_o another_o while_n less_o in_o measure_n in_o divers_a part_n of_o its_o channel_n and_o for_o that_o reason_n this_o vulgar_a manner_n of_o measure_v run_a water_n as_o indeterminate_v and_o uncertain_a be_v by_o i_o just_o suspect_v the_o measure_n be_v to_o be_v determinate_a and_o the_o same_o and_o here_o i_o free_o confess_v that_o i_o have_v singular_a help_n to_o resolve_v this_o difficulty_n from_o the_o excellent_a &_o accurate_a way_n of_o discourse_v as_o in_o allother_n matter_n so_o also_o in_o this_o of_o the_o right_n honourable_a and_o true_o noble_a signior_n ciampoli_n secretary_n of_o the_o pope_n secret_a affair_n who_o moreover_o not_o spare_v for_o the_o cost_n of_o the_o same_o generous_o give_v i_o occasion_n a_o few_o year_n past_a to_o try_v by_o exact_a experiment_n that_o which_o past_o concern_v this_o particular_a and_o to_o explain_v all_o more_o clear_o with_o a_o example_n we_o suppose_v a_o vessel_n fill_v with_o water_n as_o for_o instance_n a_o butt_n which_o be_v keep_v full_a though_o still_o water_n run_v out_o and_o the_o water_n run_v out_o by_o two_o tap_n equal_a of_o bigness_n one_o put_v in_o the_o bottom_n of_o the_o vessel_n and_o the_o other_o in_o the_o upper_a part_n it_o be_v manifest_a that_o in_o the_o time_n wherein_o from_o the_o upper_a part_n shall_v issue_v a_o determinate_a measure_n of_o water_n from_o the_o inferior_a part_n there_o shall_v issue_v four_o five_o and_o many_o more_o of_o the_o same_o measure_n according_a to_o the_o difference_n of_o the_o height_n of_o the_o tap_n and_o the_o distance_n of_o the_o upper_a tap_n from_o the_o superficies_n and_o level_n of_o the_o water_n of_o the_o vessel_n and_o all_o this_o will_v always_o follow_v though_o as_o have_v be_v say_v the_o tap_n be_v equal_a and_o the_o water_n in_o discharge_v keep_v the_o say_a tap_n always_o full_a where_o first_o we_o note_v that_o although_o the_o measure_n of_o the_o tap_n be_v equal_a nevertheless_o there_o issue_v from_o they_o in_o equal_a time_n unequal_a quantity_n of_o water_n and_o if_o we_o shall_v more_o attentive_o consider_v this_o business_n we_o shall_v find_v that_o the_o water_n by_o the_o low_a tap_n run_v and_o pass_v with_o much_o great_a velocity_n than_o it_o do_v by_o the_o upper_a whatever_o be_v the_o reason_n if_o therefore_o we_o will_v have_v such_o a_o quantity_n of_o water_n discharge_v from_o the_o upper_a tap_n as_o will_v discharge_v from_o the_o nether_a in_o the_o same_o time_n it_o be_v plain_a that_o either_o the_o upper_a tapâ—_n must_v be_v multiply_v in_o such_o sort_n that_o so_o many_o more_o tap_n in_o number_n be_v place_v above_o than_o below_o as_o the_o nether_a tap_n shall_v be_v more_o swift_a than_o the_o upper_a or_o the_o upper_a tap_n make_v so_o much_o big_a than_o the_o nether_a by_o how_o much_o that_o beneath_o shall_v be_v more_o swift_a than_o that_o above_o and_o so_o then_o in_o equal_a time_n the_o same_o quantity_n of_o water_n shall_v discharge_v from_o the_o upper_a as_o do_v from_o the_o nether_a part_n i_o will_v declare_v myself_o by_o another_o example_n if_o we_o shall_v imagine_v that_o two_o cord_n or_o line_n of_o equal_a thickness_n be_v draw_v through_o two_o hole_n of_o equal_a bore_n but_o so_o that_o the_o first_o pass_v with_o quadruple_a velocity_n to_o the_o second_o it_o be_v manifest_a that_o if_o in_o a_o determinate_a time_n we_o shall_v by_o the_o first_o bear_v have_v draw_v four_o ell_n of_o the_o line_n in_o the_o same_o time_n by_o the_o second_o hole_n we_o shall_v have_v draw_v but_o one_o ell_n of_o cord_n only_o and_o if_o by_o the_o first_o there_o pass_v twelve_o ell_n then_o through_o the_o second_o there_o shall_v pass_v only_o three_o ell_n and_o in_o short_a the_o quantity_n of_o cord_n shall_v have_v the_o same_o proportion_n to_o the_o cord_n that_o the_o volocity_n have_v to_o the_o velocity_n and_o therefore_o we_o desire_v to_o compensate_a the_o tardity_n of_o the_o second_o cord_n and_o maintain_v the_o same_o tardity_n to_o draw_v through_o the_o second_o hole_n as_o much_o cord_n as_o through_o the_o first_o it_o will_v be_v necessary_a to_o draw_v through_o the_o second_o bear_v four_o end_n of_o cord_n so_o that_o the_o thickness_n of_o all_o the_o cord_n by_o the_o second_o hole_n have_v the_o same_o proportion_n to_o the_o thickness_n of_o the_o cord_n which_o pass_v only_o by_o 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be_v that_o the_o course_n of_o the_o water_n retard_v as_o have_v be_v say_v in_o those_o ultimate_a part_n of_o the_o torrent_n if_o it_o shall_v happen_v that_o the_o torrent_n grow_v torbid_v and_o muddy_a and_o its_o stream_n be_v retard_v in_o such_o a_o degree_n that_o it_o be_v not_o able_a to_o carry_v away_o those_o minute_n grain_n of_o earth_n which_o compose_v the_o muddinesse_n in_o this_o case_n the_o torrent_n shall_v clear_v away_o the_o mud_n and_o carry_v away_o the_o sand_n at_o the_o bottom_n of_o its_o own_o channel_n in_o the_o extreme_a part_n of_o its_o mouth_n which_o raise_v and_o void_v sand_n shall_v again_o afterward_o be_v carry_v away_o when_o the_o river_n abate_v the_o torrent_n shall_v return_v to_o move_v with_o its_o primitive_a velocity_n corollary_n vi._n whilst_o it_o be_v demonstrate_v that_o the_o same_o water_n have_v different_a measure_n in_o its_o channel_n or_o course_n according_a as_o it_o vary_v in_o velocity_n so_o that_o the_o 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and_o blow_v against_o the_o current_n retard_v its_o course_n and_o ordinary_a velocity_n shall_v necessary_o amplify_v the_o measure_n of_o the_o same_o river_n and_o consequent_o shall_v be_v in_o great_a part_n cause_n or_o we_o may_v say_v potent_a concause_n of_o make_v the_o extraordinary_a inundation_n which_o river_n use_v to_o make_v and_o it_o be_v most_o certain_a that_o as_o often_o as_o a_o strong_a and_o continual_a wind_n shall_v blow_v against_o the_o current_n of_o a_o river_n and_o shall_v reduce_v the_o water_n of_o the_o river_n to_o such_o tardity_n of_o motion_n that_o in_o the_o time_n wherein_o before_o it_o run_v five_o mile_n it_o now_o move_v but_o one_o such_o a_o river_n will_v increase_v to_o five_o time_n the_o measure_n though_o there_o shall_v not_o be_v add_v any_o other_o quantity_n of_o water_n which_o thing_n indeed_o have_v in_o it_o something_o of_o strange_a but_o it_o be_v most_o certain_a for_o that_o look_v what_o proportion_n the_o water_n 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water_n dependent_a on_o the_o boisterous_a and_o constant_a wind_n that_o blow_v in_o those_o time_n as_o be_v note_v in_o the_o memorial_n corollary_n ix_o it_o be_v most_o manifest_a that_o by_o the_o great_a abundance_n of_o water_n the_o torrent_n may_v increase_v and_o of_o themselves_o alone_o exorbitant_o swell_v the_o river_n and_o have_v demonstrate_v that_o also_o without_o new_a water_n but_o only_o by_o the_o notable_a retardment_n the_o river_n rise_v and_o increase_v in_o measure_n in_o proportion_n as_o the_o velocity_n decrease_v hence_o it_o be_v apparent_a that_o each_o of_o these_o cause_n be_v able_a of_o itself_o and_o separate_v from_o the_o other_o to_o swell_v the_o river_n when_o it_o shall_v happen_v that_o both_o these_o two_o cause_n conspire_v the_o augmentation_n of_o the_o river_n in_o such_o a_o case_n there_o must_v follow_v very_o great_a and_o irrepable_a inundation_n corollary_n x._o from_o what_o have_v be_v demonstrate_v we_o may_v with_o facility_n resolve_v the_o doubt_n which_o have_v trouble_v and_o still_o pose_v the_o most_o diligent_a but_o incautelous_a observer_n of_o river_n who_o measure_v the_o stream_n and_o torrent_n which_o fall_v into_o another_o river_n as_o those_o for_o instance_n which_o enter_v into_o the_o po_n or_o those_o which_o fall_v into_o tiber_n and_o have_v sum_v the_o total_a of_o these_o measure_n and_o confer_v the_o measure_n of_o the_o river_n and_o brook_n which_o fall_v into_o tiber_n with_o the_o measure_n of_o tiber_n and_o the_o measure_n of_o those_o which_o disimbogue_v into_o po_n with_o the_o measure_n of_o po_n they_o find_v they_o not_o equal_a as_o it_o seem_v to_o they_o they_o ought_v to_o be_v and_o this_o be_v because_o they_o have_v not_o well_o note_v the_o most_o important_a point_n of_o the_o variation_n of_o velocity_n and_o how_o that_o it_o be_v the_o most_o potent_a cause_n of_o wonderful_o alter_v the_o measure_n of_o run_a water_n but_o we_o most_o facil_o resolve_v the_o doubt_n may_v say_v that_o these_o water_n diminish_v the_o measure_n be_v once_o enter_v the_o principal_a channel_n because_o they_o increase_v in_o velocity_n corollary_n xi_o through_o the_o ignorance_n of_o the_o force_n of_o the_o velocity_n of_o the_o water_n in_o alter_v its_o measure_n &_o augment_v it_o when_o the_o velocity_n diminish_v and_o diminish_v it_o when_o the_o velocity_n augment_v the_o architect_n giovanni_n fontana_n endeavour_v to_o measure_n and_o and_o to_o cause_n to_o be_v measure_v by_o his_o nephew_n all_o the_o brook_n and_o river_n which_o discharge_v their_o water_n into_o tiber_n at_o the_o time_n of_o the_o innundation_n which_o happen_v at_o rome_n in_o the_o year_n 1598._o and_o publish_v a_o small_a treatise_n thereof_o wherein_o he_o sum_v up_o the_o measure_n of_o the_o extraordinary_a water_n which_o fall_v into_o tiber_n and_o make_v account_n that_o it_o be_v about_o five_o hundred_o ell_n more_o than_o ordinary_a and_o in_o the_o end_n of_o that_o treatise_n conclude_v that_o to_o remove_v the_o innundation_n whole_o from_o rome_n it_o will_v be_v necessary_a to_o make_v two_o other_o channel_n equal_a to_o that_o at_o present_a and_o that_o less_o will_v not_o suffice_v and_o find_v afterward_o that_o the_o whole_a stream_n pass_v under_o the_o bridge_n quattro-capi_a the_o arch_n whereof_o be_v of_o a_o far_o less_o measure_n than_o five_o hundred_o ell_n conclude_v that_o under_o the_o say_a bridge_n past_o a_o hundred_o fifty_o one_o ell_n of_o water_n compress_v i_o have_v set_v down_o the_o precise_a term_n of_o compress_a water_n write_v by_o fontana_n wherein_o i_o find_v many_o error_n the_o first_o of_o which_o be_v to_o think_v that_o the_o measure_n of_o these_o water_n compress_v in_o the_o channel_n of_o those_o brook_n and_o river_n shall_v maintain_v themselves_o the_o same_o in_o tiber_n which_o by_o his_o leave_n be_v most_o false_a when_o ever_o those_o water_n reduce_v into_o tiber_n 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the_o time_n of_o innundation_n four_o ten_o and_o twenty_o time_n less_o water_n than_o another_o mouth_n equal_a to_o the_o first_o in_o greatness_n as_o will_v occur_v when_o the_o first_o mouth_n be_v four_o ten_o or_o twenty_o time_n less_o swift_a than_o the_o second_o whereupon_o whilst_o fontana_n sum_v up_o the_o ell_n and_o foot_n of_o the_o measure_n of_o those_o brook_n and_o river_n into_o a_o total_a aggregate_v he_o commit_v the_o same_o error_n with_o he_o which_o will_v add_v into_o one_o sum_n diverse_a money_n of_o diverse_a value_n and_o diverse_a place_n but_o that_o have_v the_o same_o name_n as_o if_o one_o shall_v say_v ten_o crown_n of_o roman_a money_n four_o crown_n of_o gold_n thirteen_o crown_n of_o florence_n five_o crown_n of_o venice_n and_o eight_o crown_n of_o mantua_n shall_v make_v the_o same_o sum_n with_o forty_o crown_n of_o gold_n or_o forty_o crown_n of_o mantua_n three_o it_o may_v happen_v that_o some_o river_n or_o current_n in_o the_o part_n near_o rome_n in_o the_o time_n of_o its_o flow_n do_v not_o send_v forth_o more_o water_n than_o ordinary_a and_o however_o it_o be_v a_o thing_n very_o clear_a that_o whilst_o the_o stream_n come_v from_o the_o superior_a part_n that_o same_o brook_n or_o river_n will_v be_v augment_v in_o measure_n as_o have_v be_v note_v in_o the_o four_o corollary_n in_o such_o sort_n that_o fontana_n may_v have_v inculcate_v and_o note_v that_o same_o river_n or_o current_n as_o concur_v to_o the_o innundation_n although_o it_o be_v therein_o altogether_o unconcern_v moreover_o in_o the_o four_o place_n we_o must_v note_v that_o it_o may_v so_o fall_v out_o that_o such_o a_o river_n not_o only_o be_v uninteress_v in_o the_o innundation_n though_o augment_v in_o measure_n but_o it_o may_v i_o say_v happen_v that_o it_o be_v instrumental_a to_o the_o asswage_a the_o innundation_n by_o augment_v in_o the_o measure_n of_o its_o own_o channel_n which_o matter_n be_v sufficient_o evident_a for_o if_o 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water_n compress_v for_o that_o i_o do_v not_o understand_v that_o water_n be_v like_o cotton_n or_o wool_n which_o matter_n may_v be_v press_v and_o tread_v as_o it_o happen_v also_o to_o the_o air_n which_o receive_v compression_n in_o such_o sort_n that_o after_o that_o in_o some_o certain_a place_n a_o quantity_n of_o air_n shall_v be_v reduce_v to_o its_o natural_a constitution_n and_o have_v take_v up_o all_o the_o say_a place_n yet_o nevertheless_o compress_v the_o first_o air_n with_o force_n and_o violence_n it_o be_v reduce_v into_o far_o less_o room_n and_o will_v admit_v four_o or_o six_o time_n as_o much_o air_n as_o before_z as_o be_v experimental_o engine_n see_v in_o the_o wind-gun_n invent_v in_o our_o day_n by_o m._n vincenzo_n vincenti_fw-la of_o urbin_n which_o property_n of_o the_o air_n of_o admit_v condensation_n be_v also_o see_v in_o the_o portable_a fountain_n of_o the_o same_o m._n vincenzo_n which_o fountain_n spurt_v the_o water_n on_o high_a by_o force_n 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the_o water_n put_v therein_o will_v be_v more_o press_v and_o crowd_v and_o therefore_o in_o our_o case_n according_a to_o our_o principle_n we_o will_v say_v that_o the_o water_n of_o that_o stream_n pass_v all_o under_o the_o say_a bridge_n quattro-capi_a for_o that_o be_v there_o most_o swift_a it_o ought_v of_o consequence_n to_o be_v less_o in_o measure_n and_o here_o one_o may_v see_v into_o how_o many_o error_n a_o man_n may_v run_v through_o ignorance_n of_o a_o true_a and_o real_a principle_n which_o once_o know_v and_o well_o understand_v take_v away_o all_o mist_n of_o doubt_v and_o easy_o resolve_v all_o difficulty_n corollary_n xii_o through_o the_o same_o inadvertency_n of_o not_o regard_v the_o variation_n of_o velocity_n in_o the_o same_o current_n there_o be_v commit_v by_o ingineer_n and_o learned_a man_n error_n of_o very_a great_a moment_n and_o i_o can_v thereof_o produce_v example_n but_o for_o good_a reason_n i_o pass_v they_o over_o in_o silence_n when_o they_o think_v and_o propose_v by_o derive_v new_a channel_n from_o great_a river_n to_o diminish_v the_o measure_n of_o the_o water_n in_o the_o river_n and_o to_o diminish_v it_o proportional_o according_a to_o the_o measure_n of_o the_o water_n which_o they_o make_v to_o pass_v through_o the_o channel_n as_o make_v u.g._n a_o channel_n fifty_o foot_n broad_a in_o which_o the_o derive_v water_n be_v to_o run_v waste_n ten_o foot_n deep_a they_o think_v they_o have_v diminish_v the_o measure_n of_o the_o water_n in_o the_o river_n five_o hundred_o foot_n which_o thing_n do_v not_o indeed_o so_o fall_v out_o and_o the_o reason_n be_v plain_a for_o that_o the_o channel_n be_v derive_v the_o rest_n of_o the_o main_a river_n diminish_v in_o velocity_n and_o therefore_o retain_v a_o great_a measure_n than_o it_o have_v at_o first_o before_o the_o derivation_n of_o the_o channel_n and_o moreover_o if_o the_o channel_n be_v derive_v it_o shall_v not_o conserve_v the_o same_o velocity_n which_o it_o have_v at_o first_o in_o the_o main_a river_n but_o shall_v diminish_v it_o it_o will_v be_v necessary_a that_o it_o have_v a_o great_a measure_n than_o it_o have_v before_o in_o the_o river_n and_o therefore_o to_o account_v aright_o there_o shall_v not_o be_v so_o much_o water_n derive_v into_o the_o channel_n as_o shall_v diminish_v the_o river_n according_a to_o the_o quantity_n of_o the_o water_n in_o the_o channel_n as_o be_v pretend_v corollary_n xiii_o this_o same_o consideration_n give_v i_o occasion_n to_o discover_v a_o most_o ordinary_a error_n observe_v by_o i_o in_o the_o business_n of_o the_o water_n of_o ferara_n when_o i_o be_v in_o those_o part_n in_o service_n of_o the_o most_o reverend_a and_o illustrious_a monsignor_n corsini_n the_o sublime_a wit_n of_o who_o have_v be_v a_o very_a great_a help_n to_o
i_o in_o these_o contemplation_n it_o be_v very_o true_a i_o have_v be_v much_o perplex_v whether_o i_o shall_v commit_v this_o particular_a to_o paper_n or_o pass_v it_o over_o in_o silence_n for_o that_o i_o have_v ever_o doubt_v that_o the_o opinion_n so_o common_a and_o moreover_o confirm_v with_o a_o most_o manifest_a experiment_n may_v not_o only_o make_v this_o my_o conjecture_n to_o be_v esteem_v far_o from_o true_a but_o also_o to_o discredit_v with_o the_o world_n the_o rest_n of_o this_o my_o treatise_n nevertheless_o i_o have_v at_o last_o resolve_v not_o to_o be_v want_v to_o myself_o and_o to_o truth_n in_o a_o matter_n of_o itself_o and_o for_o other_o consequence_n most_o important_a nor_o do_v it_o seem_v to_o i_o requisite_a in_o difficult_a matter_n such_o as_o these_o we_o have_v in_o hand_n to_o resign_v ourselves_o to_o the_o common_a opinion_n since_o it_o will_v be_v very_o strange_a if_o the_o multitude_n in_o such_o matter_n shall_v hit_v on_o the_o truth_n nor_o aught_o that_o to_o be_v hold_v difficult_a in_o which_o even_o the_o vulgar_a do_v know_v the_o truth_n and_o right_n beside_o that_o i_o hope_v moreover_o to_o prove_v all_o in_o such_o sort_n that_o person_n of_o solid_a judgement_n shall_v rest_v full_o persuade_v so_o that_o they_o but_o keep_v in_o mind_n the_o principal_a ground_n and_o foundation_n of_o all_o this_o treatise_n and_o though_o that_o which_o i_o will_v propose_v be_v a_o particular_a as_o i_o have_v say_v pertain_v only_o to_o the_o interest_n of_o ferara_n yet_o nevertheless_o from_o this_o particular_a doctrine_n well_o understand_v good_a judgement_n may_v be_v make_v of_o other_o the_o like_a case_n in_o general_n i_o say_v then_o for_o great_a perspecuity_n and_o better_a understanding_n of_o the_o whole_a that_o about_o thirteen_o mile_n above_o ferara_n near_o to_o stellata_fw-la the_o main_a of_o po_n branch_a itself_o into_o two_o part_n with_o one_o of_o its_o arm_n it_o come_v close_o to_o ferara_n retain_v the_o name_n of_o the_o po_n of_o ferara_n and_o here_o again_o it_o divide_v itself_o into_o two_o other_o branch_n and_o that_o which_o continue_v on_o the_o right_a hand_n be_v call_v the_o po_n of_o argenta_n and_o of_o primaro_n and_o that_o on_o the_o leave_v the_o po_n of_o volana_n but_o for_o that_o the_o bed_n of_o the_o po_n of_o ferara_n be_v heretofore_o augment_v and_o raise_v it_o follow_v that_o it_o rest_v whole_o deprive_v of_o the_o water_n of_o the_o great_a po_n except_o in_o the_o time_n of_o its_o great_a swell_n for_o in_o that_o case_n this_o po_n of_o ferara_n be_v restrain_v with_o a_o bank_n near_o to_o bondeno_n will_v come_v also_o in_o the_o overflowing_n of_o the_o main_a po_n to_o be_v free_a from_o its_o water_n but_o the_o lord_n of_o ferara_n be_v wont_n at_o such_o time_n as_o the_o po_n threaten_v to_o break_v out_o to_o cut_v the_o bank_n by_o which_o cut_v there_o disgorge_v such_o a_o torrent_n of_o water_n that_o it_o be_v observe_v that_o the_o main_a po_n in_o the_o space_n of_o some_o few_o hour_n abate_v near_o a_o foot_n and_o all_o person_n that_o i_o have_v speak_v with_o hitherto_o move_v by_o this_o experiment_n think_v that_o it_o be_v of_o great_a profit_n and_o benefit_n to_o keep_v ready_a this_o vent_n and_o to_o make_v use_n of_o it_o in_o the_o time_n of_o its_o fullness_n and_o indeed_o the_o thing_n consider_v simple_o and_o at_o the_o first_o appearance_n it_o seem_v that_o none_o can_v think_v otherwise_o the_o rather_o for_o that_o many_o examine_v the_o matter_n narrow_o measure_v that_o body_n of_o water_n which_o run_v by_o the_o channel_n or_o bed_n of_o the_o po_n of_o ferara_n and_o make_v account_n that_o the_o body_n of_o the_o water_n of_o the_o great_a po_n be_v diminish_v the_o quantity_n of_o the_o body_n of_o the_o water_n which_o run_v by_o the_o po_n of_o ferara_n but_o if_o we_o well_o remember_v what_o have_v be_v say_v in_o the_o begin_n of_o the_o treatise_n and_o how_o much_o the_o variety_n of_o the_o velocity_n of_o the_o say_a water_n import_v and_o the_o knowledge_n of_o they_o be_v necessary_a to_o conclude_v the_o true_a quantity_n of_o the_o run_a water_n we_o shall_v find_v it_o manifest_v that_o the_o benefit_n of_o this_o vent_n be_v far_o less_o than_o it_o be_v general_o think_v and_o mereover_o we_o shall_v find_v if_o i_o deceive_v not_o myself_o that_o there_o follow_v from_o thence_o so_o many_o mischief_n that_o i_o can_v great_o incline_v to_o believe_v that_o it_o be_v more_o to_o the_o purpose_n whole_o to_o stop_v it_o up_o than_o to_o maintain_v it_o open_a yet_o i_o be_o not_o so_o wed_v to_o my_o opinion_n but_o that_o i_o be_o ready_a to_o change_v my_o judgement_n upon_o strength_n of_o better_a reason_n especial_o of_o one_o that_o shall_v have_v first_o well_o understand_v the_o beginning_n of_o this_o my_o discourse_n which_o i_o frequent_o inculcate_v because_o it_o be_v absolute_o impossible_a without_o this_o advertisement_n to_o treat_v of_o these_o matter_n and_o not_o commit_v very_o great_a error_n i_o propose_v therefore_o to_o consideration_n that_o although_o it_o be_v true_a that_o whilst_o the_o water_n of_o the_o main_a po_n be_v at_o its_o great_a height_n the_o bank_n and_o dam_n then_o cut_v of_o the_o po_n of_o ferara_n and_o the_o superior_a water_n have_v a_o very_a great_a fall_n into_o the_o channel_n of_o ferara_n they_o precipitate_v into_o the_o same_o with_o great_a violence_n and_o velocity_n and_o with_o the_o same_o in_o the_o beginning_n or_o little_o less_o they_o run_v towards_o the_o po_n of_o volana_n and_o of_o argenta_n on_o the_o sea_n coast_n yet_o after_o the_o space_n of_o some_o few_o hour_n the_o po_n of_o ferara_n be_v full_a and_o the_o superior_a water_n not_o find_v so_o great_a a_o diclivity_n there_o as_o they_o have_v at_o the_o begin_n of_o the_o cut_n they_o fall_v not_o into_o the_o same_o with_o the_o former_a velocity_n but_o with_o far_o less_o and_o thereby_o a_o great_a deal_n less_o water_n begin_v to_o issue_v from_o the_o great_a po_n and_o if_o we_o diligent_o compare_v the_o velocity_n at_o the_o first_o cut_v with_o the_o velocity_n of_o the_o water_n after_o the_o cut_v make_v and_o when_o the_o po_n of_o ferara_n shall_v be_v full_a of_o water_n we_o shall_v find_v perhaps_o that_o to_o be_v fifteen_o or_o twenty_o time_n great_a than_o this_o and_o consequent_o the_o water_n which_o issue_v from_o the_o great_a po_n that_o first_o impetuosity_n be_v past_a shall_v be_v only_o the_o fifteen_o or_o twenty_o part_n of_o that_o which_o issue_v at_o the_o beginning_n and_o therefore_o the_o water_n of_o the_o main_a po_n will_v return_v in_o a_o small_a time_n almost_o to_o the_o first_o height_n and_o here_o i_o will_v pray_v those_o who_o rest_v not_o whole_o satisfy_v with_o what_o have_v be_v say_v that_o for_o the_o love_n of_o truth_n and_o the_o common_a good_a they_o will_v please_v to_o make_v diligent_a observation_n whether_o in_o the_o time_n of_o great_a flood_n the_o say_a bank_n or_o dam_n at_o bondeno_n be_v cut_v and_o that_o in_o few_o hour_n the_o main_a po_n diminish_v as_o have_v be_v say_v about_o a_o foot_n in_o its_o height_n that_o they_o will_v observe_v i_o say_v whether_o a_o day_n or_o two_o be_v past_a the_o water_n of_o the_o main_a po_n return_v almost_o to_o their_o first_o height_n for_o if_o this_o shall_v follow_v it_o will_v be_v very_o clear_a that_o the_o benefit_n which_o result_v from_o this_o diversion_n or_o vent_n be_v not_o so_o great_a as_o be_v universal_o presume_v i_o say_v it_o be_v not_o so_o great_a as_o be_v presume_v because_o though_o it_o be_v grant_v for_o true_a that_o the_o water_n of_o the_o main_a po_n abate_v at_o the_o begin_n of_o the_o vent_n yet_o this_o benefit_n happen_v to_o be_v but_o temporary_a and_o for_o a_o few_o hour_n if_o the_o rise_n of_o po_n and_o the_o danger_n of_o break_v forth_o be_v of_o short_a duration_n as_o it_o ordinary_o befall_v in_o the_o overflowing_n of_o torrent_n in_o such_o a_o case_n the_o profit_n of_o the_o vent_n will_v be_v of_o some_o esteem_n but_o because_o the_o swell_n of_o po_n continue_v for_o thirty_o or_o sometime_o for_o forty_o day_n therefore_o the_o gain_n which_o result_v from_o the_o vent_n prove_v to_o be_v inconsiderable_a it_o remain_v now_o to_o consider_v the_o notable_a harm_n which_o follow_v the_o say_a sluice_n or_o vent_n that_o so_o reflection_n be_v make_v and_o the_o profit_n and_o the_o detriment_n compare_v one_o may_v right_o judge_v and_o choose_v that_o which_o shall_v be_v most_o convenient_a the_o first_o prejudice_n therefore_o which_o arise_v from_o this_o vent_n or_o sluice_n be_v that_o the_o
channel_n of_o ferara_n primaro_n and_o volana_n fill_v with_o water_n all_o those_o part_n from_o bondeno_n to_o the_o sea_n side_n be_v alarm_v and_o endanger_v thereby_o second_o the_o water_n of_o the_o po_n of_o primaro_n have_v free_a ingress_n into_o the_o upper_a valley_n they_o fill_v they_o to_o the_o great_a damage_n of_o the_o field_n adjacent_a and_o obstruct_v the_o course_n of_o the_o ordinary_a trench_n in_o the_o same_o valley_n insomuch_o that_o all_o the_o care_n cost_n and_o labour_n about_o the_o drain_n and_o free_v the_o upper_a valley_n from_o water_n will_v also_o become_v vain_a and_o ineffectual_a three_o i_o consider_v that_o these_o water_n of_o the_o po_n of_o ferara_n be_v pass_v downward_o towards_o the_o sea_n at_o the_o time_n that_o the_o main_a po_n be_v in_o its_o great_a excrescence_n and_o height_n it_o be_v manifest_a by_o experience_n that_o when_o the_o great_a po_n diminish_v than_o these_o water_n pass_v by_o the_o po_n of_o ferara_n begin_v to_o retard_v in_o their_o course_n and_o final_o come_v to_o turn_v the_o current_n upward_o towards_o stellata_fw-la rest_v first_o in_o the_o intermediate_v time_n almost_o fix_v and_o stand_v and_o therefore_o depose_v the_o muddinesse_n they_o fill_v up_o the_o channel_n of_o the_o river_n or_o current_n of_o ferara_n four_o and_o last_o there_o follow_v from_o this_o same_o diversion_n another_o notable_a damage_n and_o it_o be_v like_a to_o that_o which_o follow_v the_o breach_n make_v by_o river_n near_o to_o which_o breach_n in_o the_o low_a part_n namely_o below_o the_o breach_n there_o be_v beget_v in_o the_o channel_n of_o the_o river_n a_o certain_a ridge_n or_o shelf_n that_o be_v the_o bottom_n of_o the_o river_n be_v raise_v as_o be_v sufficient_o manifest_a by_o experience_n and_o thus_o just_a in_o the_o same_o manner_n cut_v the_o bank_n at_o bondeno_n there_o be_v at_o it_o be_v a_o breach_n make_v from_o which_o follow_v the_o rise_n in_o the_o low_a part_n of_o the_o main_a po_n be_v past_o the_o mouth_n of_o pamaro_n which_o thing_n how_o pernicious_a it_o be_v let_v any_o one_o judge_n that_o understand_v these_o matter_n and_o therefore_o both_o for_o the_o small_a benefit_n and_o so_o many_o harm_n that_o ensue_v from_o maintain_v this_o diversion_n i_o shall_v think_v it_o be_v more_o sound_a advice_n to_o keep_v that_o bank_n always_o whole_a at_o bondeno_n or_o in_o any_o other_o convenient_a place_n and_o not_o to_o permit_v that_o the_o water_n of_o the_o grand_a po_n shall_v ever_o come_v near_o to_o ferara_n corollary_n fourteen_o in_o the_o grand_a river_n which_o fall_v into_o the_o sea_n as_o here_o in_o italy_n po_n adige_n artesia_n and_o arno_n which_o be_v arm_v with_o bank_n against_o their_o excrescency_n it_o be_v observe_v that_o far_o from_o the_o sea_n they_o need_v bank_n of_o a_o notable_a height_n which_o height_n go_v afterward_o by_o degree_n diminish_v the_o more_o it_o approach_v to_o the_o seacoast_n in_o such_o sort_n that_o the_o po_n distant_a from_o the_o sea_n about_o fifty_o or_o sixty_o mile_n at_o ferara_n shall_v have_v bank_n that_o be_v above_o twenty_o foot_n high_o than_o the_o ordinary_a water-mark_n but_o ten_o or_o twelve_o mile_n from_o the_o sea_n the_o bank_n be_v not_o twelve_o foot_n high_o than_o the_o say_v ordinary_a water-mark_n though_o the_o breadth_n of_o the_o river_n be_v the_o same_o so_o that_o the_o excrescence_n of_o the_o same_o innundation_n happen_v to_o be_v far_o great_a in_o measure_n remote_a from_o the_o sea_n then_o near_o and_o yet_o it_o shall_v seem_v that_o the_o same_o quantity_n of_o water_n pass_v by_o every_o place_n the_o river_n shall_v need_v to_o have_v the_o same_o altitude_n of_o bank_n in_o all_o place_n but_o we_o by_o our_o principle_n and_o fundamental_o may_v be_v able_a to_o render_v the_o reason_n of_o that_o effect_n and_o say_v that_o that_o excess_n of_o quantity_n of_o water_n above_o the_o ordinary_a water_n go_v always_o acquire_v great_a velocity_n the_o near_a it_o approach_v the_o sea_n and_o therefore_o decrease_v in_o measure_n and_o consequen_o in_o height_n and_o this_o perhaps_o may_v have_v be_v the_o cause_n in_o great_a part_n why_o the_o tiber_n in_o the_o innundation_n anno_fw-la 1578._o issue_v not_o forth_o of_o its_o channel_n below_o rome_n towards_o the_o sea_n corollary_n xv._n from_o the_o same_o doctrine_n may_v be_v render_v a_o most_o manifest_a reason_n why_o the_o fall_a water_n go_v lessen_v in_o their_o descent_n so_o that_o the_o same_o fall_a water_n measure_v at_o the_o begin_n of_o its_o fall_n be_v great_a and_o big_a and_o afterward_o by_o degree_n lessen_v in_o measure_n the_o more_o it_o be_v remote_a from_o the_o begin_n of_o the_o fall_n which_o depend_v on_o no_o other_o than_o on_o the_o acquisition_n which_o it_o successive_o make_v of_o great_a velocity_n it_o be_v a_o most_o familiar_a conclusion_n among_o philosopher_n that_o grave_a body_n fall_v the_o more_o they_o remove_v from_o the_o begin_n of_o their_o motion_n the_o more_o they_o acquire_v of_o swiftness_n and_o therefore_o the_o water_n as_o a_o grave_a body_n falling_z gradual_o velocitates_fw-la and_o therefore_o decrease_v in_o measure_n and_o lessen_v corollary_n xvi_o and_o on_o the_o contrary_a the_o spirting_n of_o a_o fountain_n of_o water_n which_o spring_n on_o high_a work_v a_o contrary_a effect_n namely_o in_o the_o beginning_n they_o be_v small_a and_o afterward_o become_v great_a and_o big_a and_o the_o reason_n be_v most_o manifest_a because_o in_o the_o beginning_n they_o be_v very_o swift_a and_o afterward_o gradual_o relent_v their_o impetuosity_n and_o motion_n so_o that_o in_o the_o begin_n of_o the_o excursion_n that_o they_o make_v they_o ought_v to_o be_v small_a and_o afterward_o to_o grow_v big_a as_o in_o the_o effect_n be_v see_v appendix_n i._n into_o the_o error_n of_o not_o consider_v how_o much_o the_o different_a velocity_n of_o the_o same_o run_a water_n in_o several_a place_n of_o its_o current_n be_v able_a to_o change_v the_o measure_n of_o the_o same_o water_n and_o to_o make_v it_o great_a or_o less_o i_o think_v if_o i_o be_v not_o deceive_v that_o giulio_n frontino_n a_o noble_a ancient_a writer_n may_v have_v fall_v in_o the_o second_o book_n which_o he_o write_v of_o the_o aqueduct_n of_o the_o city_n of_o rome_n whilst_o find_v the_o measure_n of_o the_o water_n water_n commentariis_fw-la less_o than_o it_o be_v in_o erogatione_fw-la 1263._o quinary_n he_o think_v that_o so_o much_o difference_n may_v proceed_v from_o the_o negligence_n of_o the_o measure_n and_o when_o afterward_o with_o his_o own_o industry_n he_o measure_v the_o same_o water_n at_o the_o beginning_n of_o the_o aqueduct_n find_v it_o near_o 10000_o quinary_n big_a than_o it_o be_v in_o commentariis_fw-la he_o judge_v that_o the_o overplus_n be_v imbezile_v by_o minister_n and_o partaker_n which_o in_o part_n may_v be_v so_o for_o it_o be_v but_o too_o true_a that_o the_o public_a be_v almost_o always_o defraud_v yet_o nevertheless_o i_o very_o believe_v withal_o that_o beside_o the_o fraud_n of_o these_o officer_n the_o velocity_n of_o the_o water_n in_o the_o place_n wherein_o frontino_n measure_v it_o may_v be_v different_a from_o those_o velocity_n which_o be_v find_v in_o other_o place_n before_o measure_v by_o other_o and_o therefore_o the_o measure_n of_o the_o water_n may_v yea_o ought_v necessary_o to_o be_v different_a it_o have_v be_v by_o we_o demonstrate_v that_o the_o measure_n of_o the_o same_o run_a water_n have_v reciprocal_a proportion_n to_o their_o velocity_n which_o frontino_n not_o well_o consider_v and_o find_v the_o water_n in_o commentariis_fw-la 12755._o quinary_n in_o erogatione_fw-la 14018_o and_o in_o his_o own_o measure_n ad_fw-la capita_fw-la ductuum_fw-la at_o the_o head_n of_o the_o fountain_n 22755._o quinary_n or_o thereabouts_o he_o think_v that_o in_o all_o these_o place_n there_o past_a different_a quantity_n of_o water_n namely_o great_a at_o the_o fountain_n head_n than_o that_o which_o be_v in_o erogatione_fw-la and_o this_o he_o judge_v great_a than_o that_o which_o be_v in_o commentariis_fw-la appendix_n ii_o a_o like_a mistake_n chance_v late_o in_o the_o aqueduct_v of_o acqua-paola_n which_o water_n shall_v be_v 2000_o inch_n and_o so_o many_o effective_o aught_o to_o be_v allow_v and_o it_o have_v be_v give_v in_o so_o to_o be_v by_o the_o signor_n of_o bracciano_n to_o the_o apostolic-chamber_n and_o there_o be_v a_o measure_n thereof_o make_v at_o the_o begin_n of_o the_o aqueduct_v which_o measure_n prove_v afterward_o much_o less_o and_o short_a consider_v and_o take_v in_o rome_n and_o thence_o follow_v discontent_n and_o great_a disorder_n and_o all_o because_o this_o property_n of_o running-water_n of_o increase_v in_o measure_n where_o the_o velocity_n decrease_v and_o of_o
diminish_v in_o measure_n where_o the_o velocity_n augment_v be_v not_o look_v into_o appendix_n iii_o a_o like_a error_n in_o my_o judgement_n have_v be_v commit_v by_o all_o those_o learned_a man_n which_o to_o prevent_v the_o diversion_n of_o the_o reno_n of_o bologna_n into_o po_n by_o the_o channel_n through_o which_o it_o at_o present_a run_v judge_v that_o the_o reno_n be_v in_o its_o great_a excrescence_n about_o 2000_o foot_n and_o the_o po_n be_v near_o 1000_o foot_n broad_a they_o judge_v i_o say_v that_o let_v the_o reno_n into_o po_n it_o will_v have_v raise_v the_o water_n of_o po_n two_o foot_n from_o which_o rise_n they_o conclude_v afterward_o most_o exorbitant_a disorder_n either_o of_o extraordinary_a inundation_n or_o else_o of_o immense_a and_o intolerable_a expense_n to_o the_o people_n in_o raise_v the_o bank_n of_o po_n and_o reno_n and_o with_o such_o like_a weakness_n often_o vain_o disturb_v the_o mind_n of_o the_o person_n concern_v but_o now_o from_o the_o thing_n demonstrate_v it_o be_v manifest_a that_o the_o measure_n of_o the_o reno_n in_o reno_n will_v be_v different_a from_o the_o measure_n of_o reno_n in_o po_n in_o case_n that_o the_o velocity_n of_o the_o reno_n in_o po_n shall_v differ_v from_o the_o velocity_n of_o reno_n in_o reno_n as_o be_v more_o exact_o determine_v in_o the_o four_o proposition_n appendix_n iu._n no_o less_o likewise_o be_v those_o ingeneer_n and_o artist_n deceive_v that_o have_v affirm_v that_o let_v the_o reno_n into_o po_n there_o will_v be_v no_o rise_n at_o all_o in_o the_o water_n of_o po_n for_o the_o truth_n be_v that_o let_v reno_n into_o po_n there_o will_v always_o be_v a_o rise_n but_o sometime_o great_a sometime_o less_o as_o the_o po_n shall_v have_v a_o swift_a or_o slow_a current_n so_o that_o if_o the_o po_n shall_v be_v constitute_v in_o a_o great_a velocity_n the_o rise_n will_v be_v very_o small_a and_o if_o the_o say_v po_n shall_v be_v slow_a in_o its_o course_n than_o the_o rise_n will_v be_v notable_a appendix_n v._n and_o here_o it_o will_v not_o be_v beside_o the_o purpose_n to_o advertise_v that_o the_o measure_n partment_n and_o distribution_n of_o the_o water_n of_o fountain_n can_v be_v make_v exact_o unless_o there_o be_v consider_v beside_o the_o measure_n the_o velocity_n also_o of_o the_o water_n which_o particular_a not_o be_v thorough_o observe_v be_v the_o cause_n of_o continual_a miscarriage_n in_o such_o like_a affair_n appendix_n vi._n like_a consideration_n ought_v to_o be_v have_v with_o the_o great_a diligence_n for_o that_o a_o error_n therein_o be_v more_o prejudicial_a i_o say_v aught_o to_o be_v have_v by_o those_o which_o part_n and_o divide_v water_n for_o the_o water_v of_o field_n as_o be_v do_v in_o the_o territory_n of_o brescia_n bergama_n crema_fw-la pavia_n lodigiano_n cremona_n and_o other_o place_n for_o if_o they_o have_v not_o regard_v to_o the_o most_o important_a point_n of_o the_o variation_n of_o the_o velocity_n of_o the_o water_n but_o only_o to_o the_o bare_a vulgar_a measure_n there_o will_v always_o very_o great_a disorder_n and_o prejudices_fw-la ensue_v to_o the_o person_n concern_v appendix_n vii_o it_o seem_v that_o one_o may_v observe_v that_o whilst_o the_o water_n run_v along_o a_o channel_n current_n or_o conduit_n its_o velocity_n be_v retard_v withhold_v and_o impede_v by_o its_o touch_v the_o bank_n of_o side_n of_o the_o say_a channel_n or_o current_n which_o as_o immovable_a not_o follow_v the_o motion_n of_o the_o water_n interrupt_v its_o velocity_n from_o which_o particular_a be_v true_a as_o i_o believe_v it_o to_o be_v most_o true_a and_o from_o our_o consideration_n we_o have_v a_o occasion_n of_o discover_v a_o very_a nice_a mistake_n into_o which_o those_o common_o fall_v who_o divide_v the_o water_n of_o fountain_n which_o division_n be_v wont_a to_o be_v by_o what_o i_o have_v see_v here_o in_o rome_n perform_v two_o way_n the_o first_o of_o which_o be_v with_o the_o measure_n of_o like_a figure_n as_o circle_n or_o square_n have_v cut_v through_o a_o plate_n of_o metal_n several_a circle_n or_o square_n one_o of_o half_a 〈◊〉_d inch_n another_o of_o one_o inch_n another_o of_o two_o of_o three_o of_o four_o etc._n etc._n with_o which_o they_o afterward_o adjust_a the_o cock_n to_o dispense_v the_o water_n the_o other_o manner_n of_o divide_v the_o water_n of_o fountain_n be_v with_o rectangle_n paralellogram_n of_o the_o same_o height_n but_o of_o different_a base_n in_o such_o sort_n likewise_o that_o one_o paralellogram_n be_v of_o half_a a_o inch_n another_o of_o one_o two_o three_o etc._n etc._n in_o which_o manner_n of_o measure_v and_o divide_v the_o water_n it_o shall_v seem_v that_o the_o cock_n be_v place_v in_o one_o and_o the_o same_o plain_a equidistant_a from_o the_o level_n or_o superior_a superficies_n of_o the_o water_n of_o the_o well_o and_o the_o say_a measure_n be_v most_o exact_o make_v the_o water_n ought_v consequent_o also_o to_o be_v equal_o divide_v and_o part_v according_a to_o the_o proportion_n of_o the_o measure_n but_o if_o we_o well_o consider_v every_o particular_a we_o shall_v find_v that_o the_o cock_n as_o they_o successive_o be_v great_a discharge_v always_o more_o water_n than_o the_o just_a quantity_n in_o comparison_n of_o the_o lesser_a that_o be_v to_o speak_v more_o proper_o the_o water_n which_o pass_v through_o the_o great_a cock_n have_v always_o a_o great_a proportion_n to_o that_o which_o pass_v through_o the_o lesser_a than_o the_o great_a cock_n have_v to_o the_o lesser_a all_o which_o i_o will_v declare_v by_o a_o example_n the_o like_a error_n occur_v also_o in_o the_o other_o manner_n of_o measure_v the_o water_n of_o a_o fountain_n as_o may_v easy_o be_v collect_v from_o what_o have_v be_v say_v and_o observe_v above_o appendix_n viii_o the_o same_o contemplation_n discover_v the_o error_n of_o those_o architect_n who_o be_v to_o erect_v a_o bridge_n of_o sundry_a arch_n over_o a_o river_n consider_v the_o ordinary_a breadth_n of_o the_o river_n which_o be_v v_o g._n forty_o fathom_n and_o the_o bridge_n be_v to_o consist_v of_o four_o arch_n it_o suffice_v they_o that_o the_o breadth_n of_o all_o the_o four_o arch_n take_v together_o be_v forty_o fathom_n not_o consider_v that_o in_o the_o ordinary_a channel_n of_o the_o river_n the_o water_n have_v only_o two_o impediment_n which_o retard_v its_o velocity_n namely_o the_o touch_v and_o glide_v along_o the_o two_o side_n or_o shore_n of_o the_o river_n but_o the_o same_o water_n in_o pass_v under_o the_o bridge_n in_o our_o case_n meet_v with_o eight_o of_o the_o same_o impediment_n bear_v and_o thrust_v upon_o two_o side_n of_o each_o arch_n to_o omit_v the_o impediment_n of_o the_o bottom_n for_o that_o it_o be_v the_o same_o in_o the_o river_n and_o under_o the_o bridge_n from_o which_o inadvertency_n sometime_o follow_v very_o great_a disorder_n as_o quotidian_a practice_n show_v we_o appendix_n ix_o it_o be_v also_o worthy_a to_o consider_v the_o great_a and_o admirable_a benefit_n that_o those_o field_n receive_v which_o be_v wont_a to_o drink_v up_o the_o rain-water_n with_o difficulty_n through_o the_o height_n of_o the_o water_n in_o the_o principal_a ditch_n in_o which_o case_n the_o careful_a husbandman_n cut_v away_o the_o reed_n and_o rush_n in_o the_o ditch_n through_o which_o the_o water_n pass_v whereupon_o may_v be_v present_o see_v so_o soon_o as_o the_o reed_n and_o rush_n be_v cut_v a_o notable_a ebb_n in_o the_o level_n of_o the_o water_n in_o the_o ditch_n insomuch_o that_o sometime_o it_o be_v observe_v that_o the_o water_n be_v abate_v after_o the_o say_v cut_v a_o three_o and_o more_o of_o what_o it_o be_v before_o the_o cut_n the_o which_o effect_v seem_o might_n depend_v on_o this_o that_o before_o those_o weed_n take_v up_o room_n in_o the_o ditch_n and_o for_o that_o cause_n the_o water_n keep_v a_o high_a level_n and_o the_o say_a plant_n be_v afterward_o cut_v and_o remove_v the_o water_n come_v to_o abate_v possess_v the_o place_n that_o before_o be_v occupy_v by_o the_o weed_n which_o opinion_n though_o probable_a and_o at_o first_o sight_n satisfactory_a be_v nevertheless_o insufficient_a to_o give_v the_o total_a reason_n of_o that_o notable_a abatement_n which_o have_v be_v speak_v of_o but_o it_o be_v necessary_a to_o have_v recourse_n to_o our_o consideration_n of_o the_o velocity_n in_o the_o course_n of_o the_o water_n the_o chief_a and_o true_a cause_n of_o the_o variation_n of_o the_o measure_n of_o the_o same_o running-water_n for_o that_o multitude_n of_o reed_n weed_n and_o plant_v disperse_v through_o the_o current_n of_o the_o ditch_n do_v chance_n notable_o to_o retard_v the_o course_n of_o the_o water_n and_o therefore_o the_o measure_n of_o the_o water_n increase_v and_o those_o
impediment_n remove_v the_o same_o water_n gain_v velocity_n and_o therefore_o decrease_v in_o measure_n and_o consequent_o in_o height_n and_o perhaps_o this_o point_n well_o understand_v may_v be_v of_o great_a profit_n to_o the_o field_n adjacent_a to_o the_o pontine_n fen_n and_o i_o doubt_v not_o but_o if_o the_o river_n ninfa_n and_o the_o other_o principal_a brook_n of_o those_o territory_n be_v keep_v well_o cleanse_v from_o weed_n their_o water_n will_v be_v at_o a_o low_a level_n and_o consequent_o the_o drain_v of_o the_o field_n will_v run_v into_o they_o more_o ready_o it_o be_v always_o to_o be_v hold_v for_o undoubted_a that_o the_o measure_n of_o the_o water_n before_o the_o cleanse_n have_v the_o same_o proportion_n to_o the_o measure_n after_o cleanse_v that_o the_o velocity_n after_o the_o cleanse_n have_v to_o the_o velocity_n before_o the_o cleanse_n and_o because_o those_o weed_n be_v cleanse_v away_o the_o course_n of_o the_o water_n notable_o increase_v it_o be_v therefore_o necessary_a that_o the_o say_a water_n abate_v in_o measure_n and_o become_v low_o appendix_n x._o we_o have_v above_o observe_v some_o error_n that_o be_v commit_v in_o distribute_v the_o water_n of_o fountain_n and_o those_o that_o serve_v to_o water_n field_n it_o seem_v now_o fit_a by_o way_n of_o a_o close_a to_o this_o discourse_n to_o advertise_v by_o what_o mean_v these_o division_n may_v be_v make_v just_o and_o without_o error_n i_o therefore_o think_v that_o one_o might_n two_o several_a way_n exquisite_o divide_v the_o water_n of_o fountain_n the_o first_o will_v be_v by_o diligent_o examine_v first_o how_o much_o water_n the_o whole_a fountain_n discharge_v in_o a_o determinate_a time_n as_o for_o instance_n how_o many_o barrel_n or_o tun_n it_o carry_v in_o a_o set_a time_n and_o in_o case_n you_o be_v afterward_o to_o distribute_v the_o water_n distribute_v it_o at_o the_o rate_n of_o somany_a barrel_n or_o tun_n in_o that_o same_o time_n and_o in_o this_o case_n the_o participant_n will_v have_v their_o punctual_a share_n nor_o can_v it_o ever_o happen_v to_o send_v out_o more_o water_n than_o be_v reckon_v to_o be_v in_o the_o principal_a fountain_n as_o befall_v giulio_n frontino_n and_o as_o also_o it_o frequent_o happen_v in_o the_o modern_a aqueduct_n to_o the_o public_a and_o private_a detriment_n the_o other_o way_n of_o divide_v the_o same_o water_n of_o a_o fountain_n be_v also_o sufficient_o exact_a and_o easy_a and_o may_v be_v by_o have_v one_o only_a size_n for_o the_o cock_n or_o pipe_n as_o suppose_v of_o a_o inch_n or_o of_o half_a a_o inch_n and_o when_o the_o case_n require_v to_o dispense_v two_o three_o and_o more_o inch_n take_v so_o many_o cock_n of_o the_o say_a measure_n as_o do_v evacuate_v the_o water_n which_o be_v to_o be_v emit_v and_o if_o we_o be_v to_o make_v use_n only_o of_o one_o great_a cock_n we_o be_v to_o place_v one_o to_o discharge_v for_o example_n four_o inch_n and_o have_v the_o former_a sole_a measure_n of_o a_o inch_n we_o must_v make_v a_o cock_n that_o be_v big_a its_o true_a than_o the_o cock_n of_o one_o inch_n but_o not_o simple_o in_o a_o quadruple_a proportion_n for_o that_o it_o will_v discharge_v more_o than_o just_a so_o much_o water_n as_o have_v be_v say_v above_o but_o we_o ought_v to_o examine_v diligent_o how_o much_o water_n the_o little_a cock_n emit_v in_o a_o hour_n and_o then_o enlarge_v and_o contract_v the_o great_a cock_n so_o that_o it_o may_v discharge_v four_o time_n as_o much_o water_n as_o the_o lesser_a in_o the_o same_o time_n and_o by_o this_o mean_v we_o shall_v avoid_v the_o disorder_n hint_v in_o the_o seven_o appendix_n it_o will_v be_v necessary_a nevertheless_o to_o accommodate_v the_o cock_n of_o the_o cistern_n so_o that_o the_o level_n of_o the_o water_n in_o the_o cistern_n may_v always_o rest_v at_o one_o determinate_a mark_n above_o the_o cock_n otherwise_o the_o cock_n will_v emit_v sometime_o great_a and_o sometime_o less_o abundance_n of_o water_n and_o because_o it_o may_v be_v that_o the_o same_o water_n of_o the_o fountain_n may_v be_v some_o time_n more_o abundant_a sometime_o less_o in_o such_o case_n it_o will_v be_v necessary_a to_o adjust_a the_o cistern_n so_o that_o the_o excess_n above_o the_o ordinary_a water_n discharge_v into_o the_o public_a fountain_n that_o so_o the_o particular_a participant_n may_v have_v always_o the_o same_o abundance_n of_o water_n appendix_n xi_o much_o more_o difficult_a be_v the_o division_n of_o the_o water_n which_o serve_v to_o water_v the_o field_n it_o not_o be_v possible_a to_o observe_v so_o commodious_o what_o quantity_n of_o water_n the_o whole_a ditch_n send_v forth_o in_o one_o determinate_a time_n as_o may_v be_v do_v in_o fountain_n yet_o nevertheless_o if_o the_o second_o proposition_n by_o we_o a_o little_a below_o demonstrate_v be_v well_o understand_v there_o may_v be_v thence_o take_v a_o very_a safe_a and_o just_a way_n to_o distribute_v such_o water_n the_o proposition_n therefore_o by_o we_o demonstrate_v be_v this_o if_o there_o be_v two_o section_n namely_o two_o mouth_n of_o river_n the_o quantity_n of_o the_o water_n which_o pass_v by_o the_o first_o have_v a_o proportion_n to_o that_o which_o pass_v by_o the_o second_o compound_v of_o the_o proportion_n of_o the_o first_o section_n to_o the_o second_o and_o of_o the_o velocity_n through_o the_o first_o to_o the_o velocity_n through_o the_o second_o as_o i_o will_v declare_v for_o example_n by_o help_n of_o practice_n that_o i_o may_v be_v understand_v by_o all_o in_o a_o matter_n so_o important_a let_v the_o two_o mouth_n of_o the_o river_n be_v a_o and_o b_o and_o let_v the_o mouth_n a_o be_v in_o measure_n and_o content_v thirty_o two_o foot_n and_o the_o mouth_n b_o eight_o foot_n here_o you_o must_v take_v notice_n that_o it_o be_v not_o always_o true_a that_o the_o water_n which_o pass_v by_o a_o have_v the_o same_o proportion_n to_o that_o which_o pass_v by_o b_o that_o the_o mouth_n a_o have_v to_o the_o mouth_n b_o but_o only_o when_o the_o velocitye_n by_o each_o of_o those_o passage_n be_v equal_a but_o if_o the_o velocitye_n shall_v be_v unequal_a it_o may_v be_v that_o the_o say_v mouth_n may_v emit_v equal_a quantity_n of_o water_n in_o equal_a time_n though_o their_o measure_n be_v unequal_a and_o it_o may_v be_v also_o that_o the_o big_a do_v discharge_v a_o great_a quantity_n of_o water_n and_o last_o it_o may_v be_v that_o the_o less_o mouth_n discharge_v more_o water_n than_o the_o great_a and_o all_o this_o be_v manifest_a by_o the_o thing_n note_v in_o the_o begin_n of_o this_o discourse_n and_o by_o the_o say_v second_o proposition_n now_o to_o examine_v the_o proportion_n of_o the_o water_n that_o pass_v by_o one_o ditch_n to_o that_o which_o pass_v by_o another_o that_o this_o be_v know_v the_o same_o water_n and_o mouth_n of_o ditch_n may_v be_v then_o adjust_v we_o be_v to_o keep_v account_v not_o only_o of_o the_o greatness_n of_o the_o mouth_n or_o passage_n of_o the_o water_n but_o of_o the_o velocity_n also_o which_o we_o will_v do_v by_o first_o find_v two_o number_n that_o have_v the_o same_o proportion_n between_o themselves_o as_o have_v the_o mouth_n which_o be_v the_o number_n 32_o and_o 8_o in_o our_o example_n then_o this_o be_v do_v let_v the_o velocity_n of_o the_o water_n by_o the_o passage_n a_o and_o b_o be_v examine_v which_o may_v be_v do_v keep_v account_n what_o space_n a_o piece_n of_o wood_n or_o other_o body_n that_o swim_v be_v carry_v by_o the_o stream_n in_o one_o determinate_a time_n as_o for_o instance_n in_o 50_o pulse_n and_o then_o work_v by_o the_o golden_a rule_n as_o the_o velocity_n by_o a_o be_v to_o the_o velocity_n by_o b_o so_o be_v the_o number_n 8_o to_o another_o number_n which_o be_v 4._o it_o be_v clear_a by_o what_o be_v demonstrate_v in_o the_o say_v second_o proposition_n that_o the_o quantity_n of_o water_n which_o pass_v by_o the_o mouth_n a_o shall_v have_v the_o same_o proportion_n of_o that_o which_o pass_v by_o the_o mouth_n b_o that_o 8_o have_v to_o 1._o such_o proportion_n be_v compose_v of_o the_o proportion_n of_o 32_o to_o 8_o and_o of_o 8_o to_z 4_o namely_o to_o the_o greatness_n of_o the_o mouth_n a_o to_o the_o greatness_n of_o the_o mouth_n b_o and_o of_o the_o velocity_n in_o a_o to_o the_o velocity_n in_o b._n this_o be_v do_v we_o must_v then_o contract_v the_o mouth_n which_o discharge_v more_o than_o its_o just_a quantity_n of_o water_n or_o enlarge_v the_o other_o which_o discharge_v less_o as_o shall_v be_v most_o commodious_a in_o practice_n which_o to_o he_o that_o have_v understand_v this_o little_a that_o have_v be_v deliver_v will_v be_v very_o easy_a appendix_n xii_o these_o
operation_n about_o water_n as_o i_o have_v hitherto_o on_o sundry_a occasion_n observe_v be_v involve_v in_o so_o many_o difficulty_n and_o such_o a_o multiplicity_n of_o most_o extravagant_a accident_n that_o it_o be_v no_o marvel_n if_o continual_o many_o and_o very_o important_a error_n be_v therein_o commit_v by_o many_o and_o even_o by_o ingeneer_n themselves_o and_o learned-man_n and_o because_o many_o time_n they_o concern_v not_o only_o the_o public_a but_o private_a interest_n hence_o it_o be_v that_o it_o not_o only_o belong_v to_o artist_n to_o treat_v thereof_o but_o very_o oft_o even_o the_o vulgar_a themselves_o pretend_v to_o give_v their_o judgement_n therein_o and_o i_o have_v be_v trouble_v many_o time_n with_o a_o necessity_n of_o treat_v not_o only_o with_o those_o which_o either_o by_o practice_n or_o particular_a study_n understand_v somewhat_o in_o these_o matter_n but_o also_o with_o people_n whole_o void_a of_o those_o notion_n which_o be_v necessary_a for_o one_o that_o will_v on_o good_a ground_n discourse_v about_o this_o particular_a and_o thus_o many_o time_n have_v meet_v with_o more_o difficulty_n in_o the_o thick_a skull_n of_o man_n than_o in_o precipitous_a torrent_n and_o vast_a fen_n and_o in_o particular_a i_o have_v occasion_n some_o year_n past_a to_o go_v see_v the_o cave_n or_o emissary_n of_o the_o lake_n of_o perugia_n make_v many_o year_n ago_o by_o braccio_n fortobraccio_n but_o for_o that_o it_o be_v with_o great_a ruin_n by_o time_n decay_v and_o render_v unuseful_a it_o be_v repair_v with_o industry_n true_o heroical_a and_o admirable_a by_o monsignor_n maffei_n barberino_n then_o perfect_a for_o the_o way_n and_o now_o pope_n and_o be_v necessitate_v that_o i_o may_v be_v able_a to_o walk_v in_o the_o cave_n and_o for_o other_o cause_n i_o let_v down_o the_o sluice_n of_o the_o say_a cave_n at_o the_o mouth_n of_o the_o lake_n no_o soon_o be_v they_o stop_v but_o a_o great_a many_o of_o the_o people_n of_o the_o town_n and_o village_n coast_v upon_o the_o lake_n flock_v thither_o begin_v to_o make_v grievous_a complaint_n that_o if_o those_o sluice_n be_v keep_v shut_v not_o only_o the_o lake_n will_v want_v its_o due_a vent_n but_o also_o the_o part_n adjacent_a to_o the_o lake_n will_v be_v over_o fly_v to_o their_o very_a great_a detriment_n and_o because_o at_o first_o appearance_n their_o motion_n seem_v very_o reasonable_a i_o find_v myself_o hard_o put_v to_o it_o see_v no_o way_n to_o persuade_v such_o a_o multitude_n that_o the_o prejudice_n which_o they_o pretend_v i_o shall_v do_v they_o by_o keep_v the_o sluice_n shut_v for_o two_o day_n be_v absolute_o insensible_a and_o that_o by_o keep_v they_o open_a the_o lake_n do_v not_o ebb_v in_o the_o same_o time_n so_o much_o as_o the_o thickness_n of_o a_o sheet_n of_o paper_n and_o therefore_o i_o be_v necessitate_v to_o make_v use_n of_o the_o authority_n i_o have_v and_o so_o follow_v my_o business_n as_o cause_v require_v without_o any_o regard_n to_o that_o rabble_n tumultuous_o assemble_v now_o when_o i_o be_o not_o work_v with_o mattock_n or_o spade_n but_o with_o the_o pen_n and_o discourse_n i_o intend_v to_o demonstrate_v clear_o to_o those_o that_o be_v capable_a of_o reason_n and_o that_o have_v well_o understand_v the_o ground_n of_o this_o my_o treatise_n that_o the_o fear_n be_v altogether_o vain_a which_o those_o people_n conceit_v and_o therefore_o i_o say_v that_o the_o emissary_n or_o sluice_n of_o the_o lake_n of_o perugia_n stand_v in_o the_o same_o manner_n as_o at_o present_a and_o the_o water_n pass_v through_o it_o with_o the_o same_o velocity_n as_o now_o to_o examine_v how_o much_o the_o lake_n may_v abate_v in_o two_o day_n space_n we_o ought_v to_o consider_v what_o proportion_n the_o superficies_n of_o the_o whole_a lake_n have_v to_o the_o measure_n of_o the_o section_n of_o the_o emissary_n and_o afterward_o to_o infer_v that_o the_o velocity_n of_o the_o water_n by_o the_o emissary_n or_o sluice_n shall_v have_v the_o same_o proportion_n to_o the_o abatement_n of_o the_o lake_n and_o to_o prove_v thorough_o and_o clear_o this_o discourse_n i_o intend_v to_o demonstrate_v the_o follow_a proposition_n that_o which_o have_v be_v demonstrate_v in_o the_o vessel_n fall_v out_o exact_o also_o in_o our_o lake_n of_o perugia_n and_o its_o emissary_n and_o because_o the_o immensity_n of_o the_o superficies_n of_o the_o lake_n be_v in_o proportion_n to_o the_o superficies_n of_o the_o emissary_n or_o sluice_n as_o many_o million_o to_o one_o as_o may_v be_v easy_o calculate_v it_o be_v manifest_a that_o such_o abatement_n shall_v be_v imperceptible_a and_o almost_o nothing_o in_o two_o day_n space_n nay_o in_o four_o or_o six_o and_o all_o this_o will_v be_v true_a when_o we_o suppose_v that_o for_o that_o time_n there_o enter_v no_o other_o water_n into_o the_o lake_n from_o ditch_n or_o rivulet_n which_o fall_v into_o the_o lake_n will_v render_v such_o abatement_n yet_o less_o now_o we_o see_v that_o it_o be_v necessary_a to_o examine_v such_o abatement_n and_o rise_n with_o excellent_a reason_n or_o at_o least_o with_o accurate_a experiment_n before_o we_o resolve_v and_o conclude_v any_o thing_n and_o how_o far_o the_o vulgar_a be_v distant_a from_o a_o right_a judgement_n in_o such_o matter_n appendix_n xiii_o for_o great_a confirmation_n of_o all_o this_o which_o i_o have_v say_v i_o will_v instance_n in_o another_o like_a case_n which_o also_o i_o meet_v with_o heretofore_o wherein_o for_o that_o the_o business_n be_v not_o right_o understand_v many_o disorder_n vast_a expense_n and_o considerable_a mischief_n have_v follow_v there_o be_v heretofore_o a_o emissary_n or_o sluice_n make_v to_o drain_v the_o water_n which_o from_o rain_n spring_n and_o rivulet_n fall_v into_o a_o lake_n to_o the_o end_n the_o shore_n adjoin_v on_o the_o lake_n shall_v be_v free_a from_o the_o overflow_n of_o the_o water_n but_o because_o perhaps_o the_o enterprise_n be_v not_o well_o manage_v and_o carry_v on_o it_o fall_v out_o that_o the_o field_n adjacent_a to_o the_o say_a channel_n can_v not_o drain_v but_o continue_v under_o water_n to_o which_o disorder_v a_o present_a remedy_n have_v be_v use_v namely_o in_o a_o time_n convenient_a to_o stop_v up_o the_o sluice_n by_o mean_n of_o certain_a floodgate_n keep_v on_o purpose_n for_o that_o end_n and_o thus_o abate_v the_o level_n of_o the_o water_n in_o the_o emissary_n in_o the_o space_n of_o three_o or_o four_o day_n the_o field_n have_v be_v haply_o drain_v but_o on_o the_o other_o part_n the_o proprietor_n border_v on_o the_o lake_n oppose_v this_o grievous_o complain_v that_o whilst_o the_o floodgate_n be_v shut_v and_o the_o course_n of_o the_o water_n of_o the_o sluice_n hinder_v the_o lake_n overflow_v the_o land_n adjacent_a by_o mean_n of_o the_o river_n that_o fall_v into_o it_o to_o their_o very_a great_a damage_n and_o so_o continue_v their_o suit_n they_o get_v more_o of_o vexation_n than_o satisfaction_n now_o be_v ask_v my_o opinion_n herein_o i_o judge_v it_o requisite_a since_o the_o point_n in_o controversy_n be_v about_o the_o rise_n and_o fall_v of_o the_o lake_n that_o the_o say_a abatement_n when_o the_o floodgate_n be_v open_a and_o increase_v when_o they_o be_v shut_v shall_v be_v exact_o measure_v and_o tell_v they_o that_o it_o may_v be_v easy_o do_v at_o a_o time_n when_o no_o extraordinary_a water_n fall_v into_o the_o lake_n neither_o of_o rain_n or_o otherwise_o and_o the_o lake_n be_v undisturbed_a by_o wind_n that_o may_v drive_v the_o water_n to_o any_o side_n by_o plant_v near_o to_o a_o islet_n which_o be_v about_o the_o middle_n of_o the_o lake_n a_o thick_a post_n on_o which_o shall_v be_v make_v the_o mark_n of_o the_o lake_n rise_v and_o fall_v for_o two_o or_o three_o day_n i_o will_v not_o at_o that_o time_n pawn_n or_o resolute_o declare_v my_o judgement_n in_o regard_n i_o may_v be_v by_o divers_a accident_n miss_v but_o this_o i_o tell_v they_o that_o by_o what_o i_o have_v demonstrate_v and_o particular_o that_o which_o i_o have_v say_v above_o touch_v the_o lake_n of_o perugia_n i_o incline_v great_o to_o think_v that_o these_o rise_n and_o fall_n will_v prove_v imperceptible_a and_o inconsiderable_a and_o therefore_o that_o in_o case_n experience_n shall_v make_v good_a my_o reason_n it_o will_v be_v to_o no_o purpose_n for_o they_o to_o continue_v dispute_v and_o wrangle_v which_o cause_v according_a to_o the_o proverb_n a_o great_a deal_n of_o cry_n but_o produce_v not_o much_o wool_n last_o it_o import_v very_o much_o to_o know_v what_o a_o rain_n continue_v for_o many_o day_n can_v do_v in_o raise_v these_o lake_n i_o will_v here_o insert_v the_o copy_n of_o a_o letter_n which_o i_o write_v former_o to_o signior_n galileo_n galilaei_n chief_a philosopher_n to_o
the_o grand_a duke_n of_o tuscany_n wherein_o i_o have_v deliver_v one_o of_o my_o conceit_n in_o this_o business_n and_o it_o may_v be_v by_o this_o letter_n i_o may_v more_o strong_o confirm_v what_o i_o have_v say_v above_o the_o copy_n of_o a_o letter_n to_o signore_n galileo_n galilaei_n chief_a philosopher_n to_o the_o most_o serene_a great_a duke_n of_o tuscany_n worthy_a and_o most_o excellent_a sir_n in_o satisfaction_n of_o my_o promise_n in_o my_o former_a letter_n of_o represent_v unto_o you_o some_o of_o my_o consideration_n make_v upon_o the_o lake_n thrasimeno_n i_o say_v that_o in_o time_n past_a be_v in_o perugia_n where_o we_o hold_v our_o general_n convention_n have_v understand_v that_o the_o lake_n thrasimeno_n by_o the_o great_a drought_n of_o many_o month_n be_v much_o abate_v it_o come_v into_o my_o head_n to_o go_v private_o and_o see_v this_o novelty_n both_o for_o my_o particular_a satisfaction_n as_o also_o that_o i_o may_v be_v able_a to_o relate_v the_o whole_a to_o my_o patron_n upon_o the_o certitude_n of_o my_o own_o sight_n of_o the_o place_n and_o so_o be_v come_v to_o the_o emissary_n of_o the_o lake_n i_o find_v that_o the_o level_n of_o the_o lake_n surface_n be_v ebb_v about_o five_o roman_a palm_n of_o its_o wont_a watermark_n insomuch_o that_o it_o be_v low_a than_o the_o transome_n of_o the_o mouth_n of_o the_o emissary_n by_o the_o length_n of_o this_o describe_v line_n and_o therefore_o no_o water_n issue_v out_o of_o the_o lake_n to_o the_o great_a prejudice_n of_o all_o the_o place_n and_o village_n circumjacent_a in_o regard_n that_o the_o water_n which_o use_v to_o run_v from_o the_o say_a lake_n turn_v 22_o mill_n which_o not_o go_v necessitate_v the_o inhabitant_n of_o those_o part_n to_o go_v a_o day_n journey_n and_o more_o to_o grind_v upon_o the_o tiber._n be_v return_v to_o perugia_n there_o follow_v a_o rain_n not_o very_o great_a but_o constant_a and_o even_o which_o last_v for_o the_o space_n of_o eight_o hour_n or_o thereabouts_o and_o it_o come_v into_o my_o thought_n to_o examine_v be_v in_o perugia_n how_o much_o the_o lake_n be_v increase_v and_o raise_v by_o this_o rain_n suppose_v as_o it_o be_v probable_a enough_o that_o the_o rain_n have_v be_v universal_a over_o all_o the_o lake_n and_o like_a to_o that_o which_o fall_v in_o perugia_n and_o to_o this_o purpose_n i_o take_v a_o glass_n form_v like_o a_o cylinder_n about_o a_o palm_n high_a and_o half_a a_o palm_n broad_a and_o have_v put_v in_o water_n sufficient_a to_o cover_v the_o bottom_n of_o the_o glass_n i_o note_v diligent_o the_o mark_n of_o the_o height_n of_o the_o water_n in_o the_o glass_n and_o afterward_o expose_v it_o to_o the_o open_a weather_n to_o receive_v the_o rainwater_n which_o fall_v into_o it_o and_o i_o let_v it_o stand_v for_o the_o space_n of_o a_o hour_n and_o have_v observe_v that_o in_o that_o time_n the_o water_n be_v rise_v in_o the_o vessel_n the_o height_n of_o the_o follow_a line_n i_o consider_v that_o if_o i_o have_v expose_v to_o the_o same_o rain_n such_o other_o vessel_n equal_a to_o that_o the_o water_n will_v have_v rise_v in_o they_o all_o according_a to_o that_o measure_n and_o thereupon_o conclude_v that_o also_o in_o all_o the_o whole_a extent_n of_o the_o lake_n it_o be_v necessary_a the_o water_n shall_v be_v raise_v in_o the_o space_n of_o a_o hour_n the_o same_o measure_n yet_o here_o i_o consider_v two_o difficulty_n that_o may_v disturb_v and_o alter_v such_o a_o effect_n or_o at_o least_o render_v it_o inobserveable_a which_o afterward_o well_o weigh_v and_o resolve_v leave_v i_o as_o i_o will_v tell_v you_o anon_o in_o the_o conclusion_n the_o more_o confirm_v that_o the_o lake_n ought_v to_o be_v increase_v in_o the_o space_n of_o eight_o hour_n that_o the_o rain_n last_v eight_o time_n that_o measure_n and_o whilst_o i_o again_o expose_v the_o glass_n to_o repeat_v the_o experiment_n there_o come_v unto_o i_o a_o engineer_n to_o talk_v with_o i_o touch_v certain_a affair_n of_o our_o monastary_n of_o perugia_n and_o discourse_v with_o he_o i_o show_v he_o the_o glass_n out_o at_o my_o chamber_n window_n expose_v in_o a_o court-yard_n and_o communicate_v to_o he_o my_o fancy_n relate_v unto_o he_o all_o that_o i_o have_v do_v but_o i_o soon_o perceive_v that_o this_o brave_a fellow_n conceit_v i_o to_o be_v but_o of_o a_o dull_a brain_n for_o he_o smile_v say_v unto_o i_o sir_n you_o deceive_v yourself_o i_o be_o of_o opinion_n that_o the_o lake_n will_v not_o be_v increase_v by_o this_o rain_n so_o much_o as_o the_o thickness_n of_o a_o penny_n julio_n hear_v he_o pronounce_v this_o his_o opinion_n with_o freeness_n and_o confidence_n i_o urge_v he_o to_o give_v i_o some_o reason_n for_o what_o he_o say_v assure_v he_o that_o i_o will_v change_v my_o judgement_n when_o i_o see_v the_o strength_n of_o his_o argument_n to_o which_o he_o answer_v that_o he_o have_v be_v very_o conversant_a about_o the_o lake_n and_o be_v every_o 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to_o the_o mouth_n of_o the_o emissary_n of_o the_o lake_n with_o order_n to_o bring_v i_o a_o exact_a account_n how_o he_o find_v the_o water_n of_o the_o lake_n in_o respect_n of_o the_o transome_n of_o the_o sluice_n now_o here_o signore_n galileo_n i_o will_v not_o have_v you_o think_v that_o i_o have_v bring_v the_o matter_n in_o hand_n to_o concern_v i_o in_o my_o honour_n but_o believe_v i_o and_o there_o be_v witness_n of_o the_o same_o still_o live_a that_o my_o messenger_n return_v in_o the_o evening_n to_o perugia_n he_o bring_v i_o word_n that_o the_o water_n of_o the_o lake_n begin_v to_o run_v through_o the_o cave_n and_o that_o it_o be_v rise_v almost_o a_o finger_n breadth_n above_o the_o transome_n insomuch_o that_o add_v this_o measure_n to_o that_o of_o the_o lowness_n of_o the_o surface_n of_o the_o lake_n beneath_o the_o transome_n before_o the_o rain_n it_o be_v manifest_a that_o the_o rise_n of_o the_o lake_n cause_v by_o the_o rain_n be_v to_o a_o hair_n those_o four_o finger_n breadth_n that_o i_o have_v judge_v it_o to_o be_v two_o day_n after_o i_o have_v another_o bout_n with_o the_o engineer_n and_o relate_v to_o he_o the_o whole_a business_n to_o which_o he_o know_v not_o what_o to_o answer_v now_o the_o two_o difficulty_n which_o i_o think_v of_o able_a to_o impede_fw-la my_o conclusion_n be_v these_o follow_v first_o i_o consider_v that_o it_o may_v be_v that_o the_o wind_n blow_v from_o the_o side_n where_o the_o sluice_n stand_v to_o the_o lake-ward_n the_o mole_n and_o mass_n of_o the_o water_n of_o the_o lake_n may_v be_v drive_v to_o the_o contrary_a shore_n on_o which_o the_o water_n rise_v it_o may_v be_v fall_v at_o the_o mouth_n of_o the_o emissary_n and_o so_o the_o observation_n may_v be_v much_o obscure_v but_o this_o difficulty_n whole_o vanish_v by_o reason_n of_o the_o air_n great_a tranquillity_n which_o it_o keep_v at_o that_o time_n for_o no_o wind_n be_v stir_v on_o any_o side_n neither_o whilst_o it_o rain_v nor_o afterward_o the_o second_o difficulty_n which_o put_v the_o rise_n in_o doubt_n be_v that_o have_v observe_v in_o florence_n and_o elsewhere_o those_o pond_n into_o which_o the_o rain-water_n fall_v from_o the_o house_n be_v convey_v through_o the_o common-shore_n and_o that_o they_o be_v not_o thereby_o ever_o fill_v but_o that_o they_o swallow_v all_o that_o abundance_n of_o water_n that_o run_v into_o they_o by_o those_o conveyance_n which_o serve_v they_o with_o water_n insomuch_o that_o those_o conveyance_n which_o in_o time_n of_o drought_n maintain_v the_o pond_n when_o there_o come_v new_a abundance_n of_o water_n into_o the_o pond_n they_o drink_v it_o up_o and_o swallow_v it_o a_o like_a effect_n may_v
also_o fall_v out_o in_o the_o lake_n in_o which_o there_o be_v many_o vein_n as_o it_o be_v very_o likely_a that_o maintain_v and_o feed_v the_o lake_n these_o vein_n may_v imbibe_n the_o new_a addition_n of_o the_o rain-water_n and_o so_o by_o that_o mean_n annul_v the_o rise_n or_o else_o diminish_v it_o in_o such_o sort_n as_o to_o render_v it_o inobservable_a but_o this_o difficulty_n be_v easy_o resolve_v by_o consider_v my_o treatise_n of_o the_o measure_n of_o running-water_n forasmuch_o as_o have_v demonstrate_v that_o the_o abatement_n of_o a_o lake_n bear_v the_o reciprocal_a proportion_n to_o the_o velocity_n of_o the_o emissary_n which_o the_o measure_n of_o the_o section_n of_o the_o emissary_n of_o the_o lake_n have_v to_o the_o measure_n of_o the_o surface_n of_o the_o lake_n make_v the_o calculation_n and_o account_n though_o in_o gross_a by_o suppose_v that_o its_o vein_n be_v sufficient_o large_a and_o that_o the_o velocity_n in_o they_o be_v notable_a in_o drink_v up_o the_o water_n of_o the_o lake_n yet_o i_o find_v nevertheless_o that_o many_o week_n and_o month_n will_v be_v spend_v in_o drink_v up_o the_o newcome_a abundance_n of_o water_n by_o the_o rain_n so_o that_o i_o rest_v sure_a that_o the_o rise_a will_v ensue_v as_o in_o effect_v it_o do_v and_o because_o many_o of_o accurate_a judgement_n have_v again_o cause_v i_o to_o question_v this_o rise_n set_v before_o i_o that_o the_o earth_n be_v parch_v by_o the_o great_a drought_n that_o have_v so_o long_o continue_v it_o may_v be_v that_o that_o bank_n of_o earth_n which_o environ_v the_o brink_n of_o the_o lake_n be_v dry_a and_o imbibe_v great_a abundance_n of_o water_n from_o the_o increase_a lake_n will_v not_o suffer_v it_o to_o increase_v in_o height_n i_o say_v therefore_o that_o if_o we_o will_v right_o consider_v this_o doubt_n here_o propose_v we_o shall_v in_o the_o very_a consideration_n of_o it_o see_v it_o resolve_v for_o it_o be_v suppose_v that_o that_o list_v or_o 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thousand_o quart_n of_o water_n and_o suppose_v that_o the_o lake_n be_v sixty_o square_a mile_n three_o thousand_o brace_n long_o we_o shall_v find_v that_o to_o dispense_v the_o water_n possess_v by_o the_o bank_n about_o the_o lake_n above_o the_o total_a surface_n of_o the_o lake_n it_o ought_v to_o be_v spread_v so_o thin_a that_o one_o sole_a quart_n of_o water_n may_v overspread_v ten_o thousand_o square_a brace_n of_o surface_n such_o a_o thinness_n as_o must_v much_o exceed_v that_o of_o a_o leaf_n of_o beat_a gold_n and_o also_o less_o than_o that_o skin_n of_o water_n which_o cover_v the_o bubble_n of_o it_o and_o such_o will_v that_o be_v which_o those_o man_n will_v have_v substract_v from_o the_o rise_n of_o the_o lake_n but_o again_o in_o the_o space_n of_o a_o quarter_n of_o a_o hour_n at_o the_o begin_n of_o the_o rain_n all_o that_o bank_n be_v soak_v by_o the_o say_a rain_n so_o that_o we_o need_v not_o for_o the_o moisten_a of_o it_o employ_v a_o drop_n of_o that_o water_n which_o fall_v into_o the_o lake_n beside_o we_o have_v not_o bring_v to_o account_v that_o abundance_n of_o water_n which_o run_v in_o time_n of_o rain_n into_o the_o lake_n from_o the_o steepness_n of_o the_o adjacent_a hill_n and_o mountain_n which_o will_v be_v enough_o to_o supply_v all_o our_o occasion_n so_o that_o neither_o ought_v we_o for_o this_o reason_n to_o question_v our_o pretend_a rise_v and_o this_o be_v what_o have_v fall_v in_o my_o way_n touch_v the_o consideration_n of_o the_o thrasimcnian_a lake_n after_o which_o perhaps_o somewhat_o rash_o wander_v beyond_o my_o bound_n i_o proceed_v to_o another_o contemplation_n which_o i_o will_v relate_v to_o you_o hope_v that_o you_o will_v receive_v it_o as_o collect_v with_o these_o caution_n requisite_a in_o such_o like_a affair_n wherein_o we_o ought_v not_o too_o positive_o to_o affirm_v any_o thing_n of_o our_o own_o head_n for_o certain_a but_o aught_o to_o submit_v all_o to_o the_o sound_n and_o secure_a deliberation_n of_o the_o holy_a mother-church_n as_o i_o do_v this_o of_o i_o and_o all_o other_o most_o ready_a to_o change_v my_o judgement_n and_o conform_v myself_o always_o to_o the_o deliberation_n of_o my_o superior_n continue_v therefore_o my_o abovesaid_a conceit_n about_o the_o rise_n of_o the_o water_n in_o the_o glass_n try_v before_o it_o come_v into_o my_o mind_n that_o the_o forementioned_a rain_n have_v be_v very_o gentle_a it_o may_v well_o be_v that_o if_o there_o shall_v have_v fall_v a_o rain_n fifty_o a_o hundred_o or_o a_o thousand_o time_n great_a than_o this_o and_o much_o more_o intense_a which_o will_v ensue_v as_o oft_o as_o those_o fall_a drop_n be_v four_o five_o or_o ten_o time_n big_a than_o those_o of_o the_o abovementioned_a rain_n keep_v the_o same_o number_n in_o such_o a_o case_n its_o manifest_a that_o in_o the_o space_n of_o a_o hour_n the_o water_n will_v rise_v in_o our_o glass_n two_o three_o and_o perhaps_o more_o yard_n or_o brace_n and_o 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never_o cease_v to_o move_v away_o and_o as_o infinite_a be_v judge_v incomprehensible_a and_o such_o as_o that_o there_o be_v no_o exact_a knowledge_n to_o be_v have_v thereof_o &_o so_o there_o come_v to_o be_v no_o account_n make_v thereof_o but_o if_o we_o shall_v make_v strict_a reflection_n upon_o our_o consideration_n of_o the_o velocity_n of_o water_n we_o shall_v find_v that_o keep_v account_n of_o the_o same_o there_o be_v a_o reckon_n also_o make_v of_o the_o length_n forasmuch_o as_o whilst_o we_o say_v the_o water_n of_o such_o a_o spring_n run_v with_o the_o velocity_n of_o pass_v a_o thousand_o or_o two_o thousand_o pace_n a_o hour_n this_o in_o substance_n be_v no_o other_o than_o if_o we_o have_v say_v such_o a_o fountain_n discharge_v in_o a_o hour_n a_o water_n of_o a_o thousand_o or_o two_o thousand_o pace_n long_o so_o that_o albeit_o the_o total_a length_n of_o run_v water_n be_v incomprehensible_a as_o be_v infinite_a yet_o nevertheless_o it_o be_v render_v 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of_o which_o we_o speak_v be_v at_o right_a angle_n with_o the_o bank_n supposition_n iii_o it_o be_v to_o be_v suppose_v that_o we_o speak_v of_o river_n when_o they_o be_v at_o ebb_n in_o that_o state_n of_o shallowness_n or_o at_o flow_v in_o that_o state_n of_o deepness_n and_o not_o in_o their_o transition_n from_o the_o ebb_n to_o the_o flow_a or_o from_o the_o flow_n to_o the_o ebb_n declaration_n of_o term_n first_o if_o a_o river_n shall_v be_v cut_v by_o a_o plane_n at_o right_a angle_n to_o the_o surface_n of_o the_o water_n of_o the_o river_n and_o to_o the_o bank_n of_o the_o river_n that_o same_o divide_v plane_n we_o call_v the_o section_n of_o the_o river_n and_o this_o section_n by_o the_o supposition_n above_o shall_v be_v a_o right_a angle_a parallelogram_n second_o we_o call_v those_o section_n equal_o swift_a by_o which_o the_o water_n run_v with_o equal_a velocity_n and_o more_o swift_a and_o less_o swift_a that_o section_n of_o another_o by_o which_o the_o water_n run_v with_o great_a or_o less_o velocity_n axiom_n i._n section_n equal_a and_o equal_o swift_a discharge_v equal_a quantity_n of_o water_n in_o equal_a time_n axiom_n ii_o section_n equal_o swift_a and_o that_o discharge_v equal_a quantity_n of_o water_n in_o equal_a time_n shall_v be_v equal_a axiom_n iii_o section_n equal_a and_o that_o discharge_v equal_a quantity_n of_o water_n in_o equal_a time_n shall_v be_v equal_o swift_a axiom_n iu._n when_o section_n be_v unequal_a but_o equal_o swift_a the_o quantity_n of_o the_o water_n that_o pass_v through_o the_o first_o section_n shall_v have_v the_o same_o proportion_n to_o the_o quantity_n that_o pass_v through_o the_o second_o that_o the_o first_o section_n have_v to_o the_o second_o section_n which_o be_v manifest_a because_o the_o velocity_n be_v the_o same_o the_o difference_n of_o the_o water_n that_o pass_v shall_v be_v according_a to_o the_o difference_n of_o the_o section_n axiom_n v._n if_o the_o section_n shall_v be_v equal_a and_o of_o unequal_a velocity_n the_o quantity_n of_o the_o water_n that_o pass_v through_o the_o first_o shall_v have_v the_o same_o proportion_n to_o that_o which_o pass_v through_o the_o second_o that_o the_o velocity_n of_o the_o first_o section_n shall_v have_v to_o the_o velocity_n of_o the_o second_o section_n which_o also_o be_v manifest_a because_o the_o section_n be_v equal_a the_o difference_n of_o the_o water_n which_o pass_v depend_v on_o the_o velocity_n petition_n a_o section_n of_o a_o river_n be_v give_v we_o may_v suppose_v another_o equal_a to_o the_o give_v of_o different_a breadth_n height_n and_o velocity_n proposition_n i._n the_o section_n of_o the_o same_o river_n discharge_v equal_a quantity_n of_o water_n in_o equal_a time_n although_o the_o section_n themselves_o he_o unequal_a let_v the_o two_o section_n be_v a_o and_o b_o in_o the_o river_n c_o run_v from_o a_o towards_z b_o i_o say_v that_o they_o discharge_v equal_a quantity_n of_o water_n in_o equal_a time_n for_o if_o great_a quantity_n of_o water_n shall_v pass_v through_o a_o than_o pass_v through_o b_o it_o will_v follow_v that_o the_o water_n in_o the_o intermediate_v space_n of_o the_o river_n c_o will_v increase_v continual_o which_o be_v manifest_o false_a but_o if_o more_o water_n shall_v issue_v through_o the_o section_n b_o than_o enter_v at_o the_o section_n a_o the_o water_n in_o the_o intermediate_v space_n c_o will_v grow_v continual_o less_o and_o always_o ebb_v which_o be_v likewise_o false_a therefore_o the_o quantity_n of_o water_n that_o pass_v through_o the_o section_n b_o be_v equal_a to_o the_o quantity_n of_o water_n which_o pass_v through_o the_o section_n a_o and_o therefore_o the_o section_n of_o the_o same_o river_n discharge_v etc._n etc._n which_o be_v to_o be_v demonstrate_v proposition_n ii_o in_o two_o section_n of_o river_n the_o quantity_n of_o the_o water_n which_o pass_v by_o one_o section_n be_v to_o that_o which_o pass_v by_o the_o second_o in_o a_o proportion_n compound_v of_o the_o proportion_n of_o the_o first_o section_n to_o the_o second_o and_o of_o the_o velocity_n through_o the_o first_o to_o the_o velocity_n of_o the_o second_o let_v a_o and_o b_o be_v two_o section_n of_o a_o river_n i_o say_v that_o the_o quantity_n of_o water_n which_o pass_v through_o a_o be_v to_o that_o which_o pass_v through_o b_o in_o a_o proportion_n compound_v of_o the_o proportion_n of_o the_o first_o section_n a_o to_o the_o section_n b_o and_o of_o the_o velocity_n through_o a_o to_o the_o velocity_n through_o b_o let_v a_o section_n be_v suppose_v equal_a to_o the_o section_n a_o in_o magnitude_n but_o of_o velocity_n equal_a to_o the_o section_n b_o and_o let_v it_o be_v g_z and_o as_o the_o section_n a_o be_v to_o the_o section_n b_o so_fw-mi let_v the_o line_n f_o be_v to_o the_o line_n d_o and_o as_o the_o velocity_n a_o be_v to_o the_o velocity_n by_o b_o so_o let_v the_o line_n d_o be_v to_o the_o line_n r_o therefore_o the_o water_n which_o pass_v through_o a_o shall_v be_v to_o that_o which_o pass_v through_o g_z in_o regard_v the_o section_n a_o and_o g_o be_v of_o equal_a bigness_n but_o of_o 〈◊〉_d equal_a velocity_n as_o the_o velocity_n through_o a_o to_o the_o velocity_n through_o g_z but_o as_o the_o velocity_n through_o a_o be_v to_o the_o velocity_n through_o g_o so_o be_v the_o velocity_n through_o a_o to_o the_o velocity_n through_o b_o namely_o as_o the_o line_n d_o to_o the_o line_n r_o therefore_o the_o quantity_n of_o the_o water_n which_o pass_v the_o through_o a_o shall_v be_v to_o the_o quantity_n which_o pass_v through_o g_o as_o the_o line_n d_o be_v to_o the_o line_n r_o but_o the_o quantity_n which_o pass_v through_o g_o be_v to_o that_o which_o pass_v through_o b_o in_o regard_n the_o section_n g_o and_o b_o be_v equal_o swift_a as_o the_o section_n g_o to_o the_o section_n b_o that_o be_v as_o the_o section_n a_o to_o the_o section_n b_o that_o be_v as_o the_o line_n f_o to_o the_o line_n d_o therefore_o by_o the_o equal_a and_o perturb_a proportionality_n the_o quantity_n of_o the_o water_n which_o pass_v through_o a_o have_v the_o same_o proportion_n to_o that_o which_o pass_v through_o b_o that_o the_o line_n f_o have_v to_o the_o line_n r_o but_o f_o to_o r_o have_v a_o proportion_n compound_v of_o the_o proportion_n of_o f_o to_o d_o and_o of_o d_o to_z r_z that_o be_v of_o the_o section_n a_o to_o the_o section_n b_o and_o of_o the_o velocity_n through_o a_o to_o the_o velocity_n through_o b_o therefore_o also_o the_o quantity_n of_o water_n which_o pass_v through_o the_o section_n a_o shall_v have_v a_o proportion_n to_o that_o which_o pass_v through_o the_o section_n b_o compound_v of_o the_o proportion_n of_o the_o section_n a_o to_o the_o section_n b_o and_o of_o the_o
velocity_n through_o a_o to_o the_o velocity_n through_o b_o and_o therefore_o in_o two_o section_n of_o river_n the_o quantity_n of_o water_n which_o pass_v by_o the_o first_o etc._n etc._n which_o be_v to_o be_v demonstrate_v corollary_n the_o same_o follow_v though_o the_o quantity_n of_o the_o water_n which_o pass_v through_o the_o section_n a_o be_v equal_a to_o the_o quantity_n of_o water_n which_o pass_v through_o the_o section_n b_o as_o be_v manifest_a by_o the_o same_o demonstration_n proposition_n iii_o in_o two_o section_n unequal_a through_o which_o pass_v equal_a quantity_n of_o water_n in_o equal_a time_n the_o section_n have_v to_o one_o another_o reciprocal_a proportion_n to_o their_o velocity_n let_v the_o two_o unequal_a section_n by_o which_o pass_v equal_a quantity_n of_o water_n in_o equal_a time_n be_v a_o the_o great_a and_o b_o the_o lesser_a i_o say_v that_o the_o section_n a_o shall_v have_v the_o same_o proportion_n to_o the_o section_n b_o that_o reciprocal_o the_o velocity_n through_o b_o have_v to_o the_o velocity_n through_o a_o for_o suppose_v that_o as_o the_o water_n that_o pass_v through_o a_o be_v to_o that_o which_o pass_v through_o b_o so_o be_v the_o line_n e_o to_o the_o line_n f_o therefore_o the_o quantity_n of_o water_n which_o pass_v through_o a_o be_v equal_a to_o that_o which_o pass_v through_o b_o the_o line_n e_o shall_v also_o be_v equal_a to_o the_o line_n f_o suppose_v moreover_o that_o as_o the_o section_n a_o be_v to_o the_o section_n b_o so_o be_v the_o line_n f_o to_o the_o line_n g_o and_o because_o the_o quantity_n of_o water_n which_o pass_v through_o the_o section_n a_o be_v to_o that_o which_o pass_v through_o the_o section_n b_o in_o a_o proportion_n compose_v of_o the_o proportion_n of_o the_o section_n a_o to_o the_o section_n b_o and_o of_o the_o velocity_n through_o a_o to_o the_o velocity_n through_o b_o therefore_o the_o line_n e_o shall_v be_v the_o line_n to_o f_o in_o a_o proportion_n compound_v of_o the_o same_o proportion_n namely_o of_o the_o proportion_n of_o the_o section_n a_o to_o the_o section_n b_o and_o of_o the_o velocity_n through_o a_o to_o the_o velocity_n through_o b_o but_o the_o line_n e_o have_v to_o the_o line_n g_o the_o proportion_n of_o the_o section_n a_o to_o the_o section_n b_o therefore_o the_o proportion_n remain_v of_o the_o line_n g_o to_o the_o line_n f_o shall_v be_v the_o proportion_n of_o the_o velocity_n through_o a_o to_o the_o velocity_n through_o b_o therefore_o also_o the_o line_n g_o shall_v be_v to_o the_o line_n e_o as_o the_o velocity_n by_o a_o to_o the_o velocity_n by_o b_o and_o convers_o the_o velocity_n through_o b_o shall_v be_v to_o the_o velocity_n through_o a_o as_o the_o line_n e_o to_o the_o line_n g_o that_o be_v to_o say_v as_o the_o section_n a_o to_o the_o section_n b_o and_o therefore_o in_o two_o section_n etc._n etc._n which_o be_v to_o be_v demonstrate_v corollary_n hence_o it_o be_v manifest_a that_o section_n of_o the_o same_o river_n which_o be_v no_o other_o than_o the_o vulgar_a measure_n of_o the_o river_n have_v betwixt_o themselves_o reciprocal_a proportion_n to_o their_o velocity_n for_o in_o the_o first_o proposition_n we_o have_v demonstrate_v that_o the_o section_n of_o the_o same_o river_n discharge_v equal_a quantity_n of_o water_n in_o equal_a time_n therefore_o by_o what_o have_v now_o be_v demonstrate_v the_o section_n of_o the_o same_o river_n shall_v have_v reciprocal_a proportion_n to_o their_o velocity_n and_o therefore_o the_o same_o run_a water_n change_v measure_n when_o it_o change_v velocity_n namely_o increase_v the_o measure_n when_o it_o decrease_v the_o velocity_n and_o decrease_v the_o measure_n when_o it_o increase_v the_o velocity_n on_o which_o principal_o depend_v all_o that_o which_o have_v be_v say_v above_o in_o the_o discourse_n and_o observe_v in_o the_o corollary_n and_o appendix_n and_o therefore_o be_v worthy_a to_o be_v well_o understand_v and_o heed_v proposition_n iu._n if_o a_o river_n fall_v into_o another_o river_n the_o height_n of_o the_o first_o in_o its_o own_o channel_n shall_v be_v to_o the_o height_n that_o it_o shall_v make_v in_o the_o second_o channel_n in_o a_o proportion_n compound_v of_o the_o proportion_n of_o the_o breadth_n of_o the_o channel_n of_o the_o second_o to_o the_o breadth_n of_o the_o channel_n of_o the_o first_o and_o of_o the_o velocity_n acquire_v in_o the_o channel_n of_o the_o second_o to_o that_o which_o it_o have_v in_o its_o proper_a and_o first_o channel_n let_v the_o river_n ab_fw-la who_o height_n be_v ac_fw-la and_o breadth_n cb_n that_o be_v who_o section_n be_v acb_n let_v it_o enter_v i_o say_v into_o another_o river_n as_o broad_a as_o the_o line_n of_o and_o let_v it_o therein_o make_v the_o rise_n or_o height_n de_fw-fr that_o be_v to_o say_v let_v it_o have_v its_o section_n in_o the_o river_n whereinto_o it_o fall_v def_n i_o say_v that_o the_o height_n ac_fw-la have_v to_o the_o height_n de_fw-fr the_o proportion_n compound_v of_o the_o proportion_n of_o the_o breadth_n of_o to_o the_o breadth_n cb_n and_o of_o the_o velocity_n through_o df_n to_o the_o velocity_n through_o ab_fw-la let_v we_o suppose_v the_o section_n g_o equal_a in_o velocity_n to_o the_o section_n ab_fw-la and_o in_o breadth_n equal_a to_o of_o which_o carry_v a_o quantity_n of_o water_n equal_a to_o that_o which_o the_o section_n ab_fw-la carry_v in_o equal_a time_n and_o consequent_o equal_a to_o that_o which_o df_n carry_v moreover_o as_o the_o breadth_n of_o be_v to_o the_o breadth_n cb_n so_o let_v the_o line_n h_n be_v to_o the_o line_n i_o and_o as_o the_o velocity_n of_o df_n be_v to_o the_o velocity_n of_o ab_fw-la so_o let_v the_o line_n i_o be_v to_o the_o line_n l_o because_o therefore_o the_o two_o section_n ab_fw-la and_o g_o be_v equal_o swift_a and_o discharge_v equal_a quantity_n of_o water_n in_o equal_a time_n they_o shall_v be_v equal_a section_n and_o therefore_o the_o height_n of_o ab_fw-la to_o the_o height_n of_o g_o shall_v be_v as_o the_o breadth_n of_o g_o to_o the_o breadth_n of_o ab_fw-la that_o be_v as_o of_o to_o cb_n that_o be_v as_o the_o line_n h_n to_o the_o line_n i_o but_o because_o the_o water_n which_o pass_v through_o g_o be_v equal_a to_o that_o which_o pass_v through_o def_n therefore_o the_o section_n g_o to_o the_o section_n def_n shall_v have_v the_o reciprocal_a proportion_n of_o the_o velocity_n through_o def_n to_o the_o velocity_n through_o g_z but_o also_o the_o height_n of_o g_o be_v to_o the_o height_n de_fw-fr as_o the_o section_n g_o to_o the_o section_n def_n therefore_o the_o height_n of_o g_o be_v to_o the_o height_n de_fw-fr as_o the_o velocity_n through_o def_n be_v to_o the_o velocity_n through_o g_z that_o be_v as_o the_o velocity_n through_o def_n be_v to_o the_o velocity_n through_o ab_fw-la that_o be_v final_o as_o the_o line_n i_o to_o the_o line_n l_o therefore_o by_o equal_a proportion_n the_o height_n of_o ab_fw-la that_o be_v ac_fw-la shall_v be_v to_o the_o height_n de_fw-fr as_o h_n to_o l_o that_o be_v compound_v of_o the_o proportion_n of_o the_o breadth_n of_o to_o the_o breadth_n cb_n and_o of_o the_o velocity_n through_o df_n to_o the_o velocity_n through_o a_o b_o so_o that_o if_o a_o river_n fall_v into_o another_o river_n etc._n etc._n which_o be_v to_o be_v demonstrate_v proposition_n v._n if_o a_o river_n discharge_v a_o certain_a quantity_n of_o water_n in_o a_o certain_a time_n and_o after_o that_o there_o come_v into_o it_o a_o flood_n the_o quantity_n of_o water_n which_o be_v discharge_v in_o as_o much_o time_n at_o the_o flood_n be_v to_o that_o which_o be_v discharge_v before_o whilst_o the_o river_n be_v low_a in_o a_o proportion_n compound_v of_o the_o proportion_n of_o the_o velocity_n of_o the_o flood_n to_o the_o velocity_n of_o the_o first_o water_n and_o of_o the_o height_n of_o the_o flood_n to_o the_o height_n of_o the_o first_o water_n suppose_v a_o river_n which_o whilst_o it_o be_v low_a run_v by_o the_o section_n of_o and_o after_o a_o flood_n come_v into_o the_o same_o and_o run_v through_o the_o section_n df_n i_o say_v that_o the_o quantity_n of_o the_o water_n which_o be_v discharge_v through_o df_n be_v to_o that_o which_o be_v discharge_v through_o of_o in_o a_o proportion_n compound_v of_o the_o proportion_n of_o the_o velocity_n through_o df_n to_o the_o velocity_n through_o of_o and_o of_o the_o height_n db_n to_o the_o height_n ab_fw-la as_o the_o velocity_n through_o df_n be_v to_o the_o velocity_n through_o of_o so_o let_v the_o line_n r_o to_o the_o line_n s_o and_o as_o the_o height_n db_n be_v to_o the_o height_n ab_fw-la so_o let_v the_o line_n s_o to_o the_o line_n t_o and_o let_v we_o
suppose_v a_o section_n lmn_n equal_a to_o df_n in_o height_n and_o breadth_n that_o be_v lm_o equal_a to_o db_v and_o mn_v equal_a to_o bf_n but_o let_v it_o be_v in_o velocity_n equal_a to_o the_o section_n of_o therefore_o the_o quantity_n of_o water_n which_o run_v through_o df_n shall_v be_v to_o that_o which_o run_v through_o ln_o as_o the_o velocity_n through_o df_n be_v to_o the_o velocity_n through_o ln_o that_o be_v to_o the_o velocity_n through_o of_o and_o the_o line_n r_o be_v to_o the_o line_n s_o as_o the_o velocity_n through_o df_n to_o the_o velocity_n through_o of_o therefore_o the_o quantity_n which_o run_v through_o df_n to_o that_o which_o run_v through_o ln_o shall_v have_v the_o proportion_n of_o r_o to_o saint_n but_o the_o quantity_n which_o run_v through_o ln_o to_o that_o which_o run_v through_o of_o the_o section_n be_v equal_o swift_a shall_v be_v in_o proportion_n as_o the_o section_n ln_o to_o the_o section_n of_o that_o be_v as_o db_v to_o ab_fw-la that_o be_v as_o the_o line_n s_o to_o the_o line_n t_o therefore_o by_o equal_a proportion_n the_o quantity_n of_o the_o water_n which_o run_v through_o df_n shall_v be_v in_o proportion_n to_o that_o which_o run_v through_o of_o as_o r_o be_v to_o t_o that_o be_v compound_v of_o the_o proportion_n of_o the_o height_n db_n to_o the_o height_n ab_fw-la and_o of_o the_o velocity_n through_o df_n to_o the_o velocity_n through_o of_o and_o therefore_o if_o a_o river_n discharge_v a_o certain_a quantity_n etc._n etc._n which_o be_v to_o be_v demonstrate_v annotation_n the_o same_o may_v have_v be_v demonstrate_v by_o the_o second_o proposition_n above_o demonstrate_v as_o be_v manifest_a proposition_n vi._n if_o two_o equal_a stream_n of_o the_o same_o torrent_n fall_v into_o a_o river_n at_o divers_a time_n the_o height_n make_v in_o the_o river_n by_o the_o torrent_n shall_v have_v between_o themselves_o the_o reciprocal_a proportion_n of_o the_o velocity_n acquire_v in_o the_o river_n let_v a_o and_o b_o be_v two_o equal_a stream_n of_o the_o same_o torrent_n which_o fall_v into_o a_o river_n at_o divers_a time_n make_v the_o height_n cd_o and_o fg_v that_o be_v the_o stream_n a_o make_v the_o height_n cd_o and_o the_o stream_n b_o make_v the_o height_n fg_v that_o be_v let_v their_o section_n in_o the_o river_n into_o which_o they_o be_v fall_v be_v ce_fw-fr and_o fh_n i_o say_v that_o the_o height_n cd_o shall_v be_v to_o the_o height_n fg_v in_o reciprocal_a proportion_n as_o the_o velocity_n through_o fh_n to_o the_o velocity_n through_o ce_fw-fr for_o the_o quantity_n of_o water_n which_o pass_v through_o a_o be_v equal_a to_o the_o quantity_n which_o pass_v through_o b_o in_o equal_a time_n also_o the_o quantity_n which_o pass_v through_o ce_fw-fr shall_v be_v equal_a to_o that_o which_o pass_v through_o f_o h_n and_o therefore_o the_o proportion_n that_o the_o section_n ce_fw-fr have_v to_o the_o section_n fh_v shall_v be_v the_o same_o that_o the_o 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business_n certain_o most_o important_a as_o be_v the_o concernment_n of_o that_o most_o noble_a and_o most_o admirable_a city_n and_o indeed_o of_o all_o italy_n yea_o of_o all_o europe_n asia_n &_o africa_n &_o one_o may_v true_o say_v of_o all_o the_o whole_a world_n and_o be_v to_o proceed_v according_a to_o the_o method_n necessary_a in_o science_n i_o will_v propose_v in_o the_o first_o place_n certain_a definition_n of_o those_o term_n whereof_o we_o be_v to_o make_v use_n in_o our_o discourse_n and_o then_o lay_v down_o certain_a principle_n we_o will_v demonstrate_v some_o problem_n and_o theorem_n necessary_a for_o the_o understanding_n of_o those_o thing_n which_o we_o be_v to_o deliver_v and_o moreover_o recount_v sundry_a case_n that_o have_v happen_v we_o will_v prove_v by_o practice_n of_o what_o utility_n this_o contemplation_n of_o the_o measure_n of_o run_v water_n be_v in_o the_o more_o important_a affair_n both_o public_a and_o private_a definition_n i._n two_o 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its_o measure_n as_o have_v be_v demonstrate_v in_o the_o first_o book_n supposition_n i._n it_o be_v suppose_v that_o the_o river_n equal_a in_o breadth_n and_o quick_a height_n that_o have_v the_o same_o inclination_n of_o bed_n or_o bottom_n ought_v also_o to_o have_v equal_a velocity_n the_o accidental_a impediment_n be_v remove_v that_o be_v disperse_v throughout_o the_o course_n of_o the_o water_n and_o abstract_v also_o from_o the_o external_a wind_n which_o may_v velocitate_fw-la and_o retard_v the_o course_n of_o the_o water_n of_o the_o river_n supposition_n ii_o let_v we_o suppose_v also_o that_o if_o there_o be_v two_o river_n that_o be_v in_o their_o bed_n of_o equal_a length_n and_o of_o the_o same_o inclination_n but_o of_o quick_a height_n unequal_a they_o ought_v to_o move_v with_o like_a velocity_n according_a to_o the_o
sense_n explain_v in_o the_o second_o definition_n supposition_n iii_o because_o it_o will_v often_o be_v requisite_a to_o measure_v the_o time_n exact_o in_o the_o follow_a problem_n we_o take_v that_o to_o be_v a_o excellent_a way_n to_o measure_v the_o time_n which_o be_v show_v i_o many_o year_n since_o by_o signore_n galileo_n galilaei_n which_o be_v as_o follow_v a_o string_n be_v to_o be_v take_v three_o roman_a foot_n long_o to_o the_o end_n of_o which_o a_o bullet_n of_o lead_n be_v to_o be_v hang_v of_o about_o two_o or_o three_o ounce_n and_o hold_v it_o by_o the_o other_o end_n the_o plummet_n be_v to_o be_v remove_v from_o its_o perpendicularity_n a_o palm_n more_o or_o less_o and_o then_o let_v go_v which_o will_v make_v many_o swing_v to_o and_o again_o pass_v and_o repass_v the_o perpendicular_a before_o that_o it_o stay_v in_o the_o same_o now_o it_o be_v require_v to_o measure_v the_o time_n that_o be_v spend_v in_o any_o whatsoever_o operation_n those_o vibration_n be_v to_o be_v number_v that_o be_v make_v whilst_o the_o work_n last_v and_o they_o shall_v be_v so_o many_o second_o minute_n of_o a_o hour_n if_o so_o be_v that_o the_o string_n be_v three_o roman_a foot_n long_o but_o in_o short_a string_n the_o vibration_n be_v more_o frequent_a and_o in_o long_a less_o frequent_a and_o all_o this_o still_o follow_v whether_o the_o plummet_n be_v little_a or_o much_o remove_v from_o its_o perpendicularity_n or_o whether_o the_o weight_n of_o the_o lead_v be_v great_a or_o lesser_a these_o thing_n be_v pre-supposed_n we_o will_v lay_v down_o some_o familiar_a problem_n from_o which_o we_o shall_v pass_v to_o the_o notion_n and_o question_n more_o subtle_a and_o curious_a which_o will_v also_o prove_v profitable_a and_o not_o to_o be_v slight_v in_o this_o business_n of_o water_n proposition_n i._o problem_n 1._o a_o channel_n of_o running-water_n be_v give_v the_o breadth_n of_o which_o pass_v through_o a_o regulator_n be_v three_o palm_n and_o 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and_o that_o we_o may_v be_v able_a afterward_o to_o divide_v and_o share_v they_o to_o particular_a person_n just_o which_o will_v prevent_v infinite_a suit_n and_o controversy_n that_o every_o day_n happen_v in_o these_o matter_n proposition_n ii_o theorem_fw-la i._n if_o a_o river_n move_v with_o such_o a_o certain_a velocity_n through_o its_o regulator_n shall_v have_v a_o give_v quick_a height_n and_o afterward_o by_o new_a water_n shall_v increase_v to_o be_v double_a it_o shall_v also_o increase_v double_a in_o velocity_n let_v the_o quick_a height_n of_o a_o river_n in_o the_o regulator_n abcd_n be_v the_o perpendicular_a fb_n and_o afterward_o by_o new_a water_n that_o be_v add_v to_o the_o river_n let_v the_o water_n be_v suppose_v to_o be_v raise_v to_o g_o so_o that_o gb_n may_v be_v double_a to_o ebb_v i_o say_v that_o all_o the_o water_n gc_n shall_v be_v double_a in_o velocity_n to_o that_o of_o aec_fw-la for_o the_o water_n gf_n have_v for_o its_o bed_n the_o bottom_n 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down_o in_o the_o second_o corollary_n of_o the_o four_o theorem_fw-la of_o this_o with_o its_o table_n and_o the_o use_n thereof_o annex_v corollary_n hence_o it_o follow_v that_o when_o a_o river_n increase_v in_o quick_a height_n by_o the_o addition_n of_o new_a water_n it_o also_o increase_v in_o velocity_n so_o that_o the_o velocity_n have_v the_o same_o proportion_n to_o the_o velocity_n that_o the_o quick_a height_n have_v to_o the_o quick_a height_n as_o may_v be_v demonstrate_v in_o the_o same_o manner_n propos_fw-fr iii_o problem_n ii_o a_o channel_n of_o water_n be_v give_v who_o breadth_n exceed_v not_o twenty_o palm_n or_o thereabouts_o and_o who_o quick_a height_n be_v less_o than_o five_o palm_n to_o measure_v the_o quantity_n of_o the_o water_n that_o run_v through_o the_o channel_n in_o a_o time_n give_v place_v in_o the_o channel_n a_o regulator_n and_o observe_v the_o quick_a height_n in_o the_o say_a regulator_n then_o let_v the_o water_n be_v turn_v away_o from_o the_o channel_n by_o a_o chanellet_n of_o three_o or_o four_o palm_n in_o breadth_n or_o thereabouts_o and_o that_o be_v do_v measure_v the_o quantity_n of_o the_o water_n which_o pass_v through_o the_o say_a chanellet_n as_o have_v be_v teach_v in_o the_o second_o proposition_n and_o at_o the_o same_o time_n observe_v exact_o how_o much_o the_o quick_a height_n shall_v be_v abate_v in_o the_o great_a channel_n by_o mean_n of_o the_o diversion_n of_o the_o chanellet_n and_o all_o these_o particular_n be_v perform_v multiply_v the_o quick_a height_n of_o the_o great_a channel_n into_o itself_o and_o likewise_o multiply_v into_o itself_o the_o lesser_a height_n of_o the_o say_v big_a channel_n and_o the_o lesser_a square_a be_v take_v from_o the_o great_a the_o remainder_n shall_v have_v the_o same_o proportion_n to_o
the_o whole_a great_a square_n as_o the_o water_n of_o the_o chanellet_n divert_v have_v to_o the_o water_n of_o the_o big_a channel_n and_o because_o the_o water_n of_o the_o chanellet_n be_v know_v by_o the_o method_n lay_v down_o in_o the_o first_o theorem_n and_o the_o term_n of_o the_o theorem_fw-la be_v also_o know_v the_o quantity_n of_o the_o water_n which_o run_v through_o the_o big_a channel_n shall_v be_v also_o know_v by_o the_o golden_a rule_n which_o be_v that_o that_o be_v desire_v to_o be_v know_v we_o will_v explain_v the_o whole_a business_n by_o a_o example_n let_v a_o channel_n be_v for_o example_n 15_o palm_n broad_a its_o quick_a height_n before_o its_o diversion_n by_o the_o chanellet_n shall_v be_v suppose_v to_o be_v 24_o inch_n but_o after_o the_o diversion_n let_v the_o quick_a height_n of_o the_o channel_n be_v only_o 22_o inch_n therefore_o the_o great_a height_n to_o the_o lesser_a be_v as_o the_o number_n 11._o to_o 12._o but_o the_o square_n of_o 11._o be_v 121_o and_o the_o square_a of_o 12._o be_v 144_o the_o difference_n between_o the_o say_v lesser_a square_a and_o the_o great_a be_v 23._o therefore_o the_o divert_a water_n be_v to_o the_o whole_a water_n as_o 23._o to_o 144_o which_o be_v well_o near_o as_o 1_o to_z 6_o 6_o 23_o and_o that_o be_v the_o proportion_n that_o the_o quantity_n of_o the_o water_n which_o run_v through_o the_o chanellet_n shall_v have_v to_o all_o the_o water_n that_o run_v through_o the_o great_a channel_n now_o if_o we_o shall_v find_v by_o the_o rule_n mention_v above_o in_o the_o first_o proposition_n that_o the_o quantity_n of_o the_o water_n that_o run_v through_o the_o chanellet_n be_v v_o g._n a_o hundred_o barrel_n in_o the_o space_n of_o 15_o second_o minute_n of_o a_o hour_n it_o be_v manifest_a that_o the_o water_n which_o run_v through_o the_o great_a channel_n in_o the_o say_a time_n of_o 35_o min._n sec_fw-la shall_v be_v about_o 600_o barrel_n the_o same_o operation_n perform_v another_o way_n and_o because_o very_o often_o in_o apply_v the_o theory_n to_o practise_v it_o happen_v that_o all_o the_o necessary_a particular_n in_o the_o theory_n can_v so_o easy_o be_v put_v in_o execution_n therefore_o we_o will_v here_o add_v another_o way_n of_o perform_v the_o same_o problem_n if_o it_o shall_v chance_v to_o happen_v that_o the_o chanellet_n can_v not_o commodious_o be_v divert_v from_o the_o great_a channel_n but_o that_o it_o be_v easy_a for_o the_o water_n of_o another_o small_a channel_n to_o be_v bring_v into_o the_o great_a channel_n which_o water_n of_o the_o small_a channel_n may_v be_v easy_o measure_v as_o have_v be_v show_v in_o the_o first_o problem_n or_o in_o case_n that_o there_o do_v fall_v into_o a_o great_a channel_n a_o lesser_a channel_n that_o may_v be_v divert_v and_o measure_v therefore_o i_o say_v in_o the_o first_o case_n if_o we_o will_v measure_v the_o quantity_n of_o the_o water_n that_o run_v in_o a_o certain_a time_n through_o the_o great_a channel_n into_o which_o another_o lesser_a channel_n that_o be_v measurable_a may_v be_v bring_v we_o must_v first_o exact_o measure_v the_o chanellet_n and_o then_o observe_v the_o quick_a height_n of_o the_o great_a channel_n before_o the_o introduction_n of_o the_o lesser_a and_o have_v bring_v in_o the_o say_a chanellet_n we_o must_v agnin_n find_v the_o proportion_n that_o the_o water_n of_o the_o chanellet_n have_v to_o all_o the_o water_n of_o the_o great_a channel_n for_o these_o term_n of_o the_o proportion_n be_v know_v as_o also_o the_o quantity_n of_o the_o water_n of_o the_o chanellet_n we_o shall_v also_o come_v to_o know_v the_o quantity_n of_o the_o water_n that_o run_v through_o the_o great_a channel_n it_o be_v likewise_o manifest_a that_o we_o shall_v obtain_v our_o intent_n if_o the_o case_n be_v that_o there_o enter_v into_o the_o great_a channel_n another_o lesser_a channel_n that_o be_v measurable_a and_o that_o may_v be_v divert_v consideration_n it_o will_v be_v necessary_a to_o make_v use_n of_o this_o doctrine_n in_o the_o distribution_n of_o the_o water_n that_o be_v employ_v to_o overflow_v the_o field_n as_o be_v use_v in_o the_o brescian_a cremonese_n bergamase_v lodigian_a milanese_n territory_n and_o many_o other_o place_n where_o very_o great_a suit_n and_o difference_n arise_v which_o not_o be_v to_o be_v determine_v with_o intelligible_a reason_n come_v oftentimes_o to_o be_v decide_v by_o force_n of_o arm_n and_o instead_o of_o flow_v their_o ground_n with_o water_n they_o cruel_o flow_v they_o with_o the_o shed_n of_o humane_a blood_n impious_o invert_v the_o course_n of_o peace_n and_o justice_n sow_v such_o disorder_n and_o feud_n as_o that_o they_o be_v sometime_o accompany_v with_o the_o ruin_n of_o whole_a city_n or_o else_o unprofitable_o charge_v they_o with_o vain_a and_o sometime_o prejudicial_a expense_n propos_fw-fr iv._o theor._n ii_o if_o a_o river_n increase_v in_o quick_a height_n the_o quantity_n of_o water_n which_o the_o river_n discharge_v after_o the_o increase_n have_v the_o proportion_n compound_v of_o the_o proportion_n of_o the_o quick_a height_n to_o the_o quick_a height_n and_o of_o the_o velocity_n to_o the_o velocity_n let_v there_o be_v a_o river_n which_o whilst_o it_o be_v low_a run_v through_o the_o regulator_n df_n with_o the_o quick_a height_n ab_fw-la and_o afterward_o let_v a_o flood_n come_v and_o then_o let_v it_o run_v with_o the_o height_n db_n i_o say_v that_o the_o quantity_n of_o the_o water_n that_o be_v discharge_v through_o df_n to_o that_o which_o discharge_v through_o of_o have_v the_o proportion_n compound_v of_o the_o proportion_n of_o the_o velocity_n through_o df_n to_o the_o velocity_n through_o of_o and_o of_o the_o height_n db_n to_o the_o height_n ab_fw-la as_o the_o velocity_n through_o df_n be_v to_o the_o velocity_n through_o of_o so_o let_v the_o line_n r_o be_v to_o the_o line_n s_o and_o as_o the_o height_n db_n be_v to_o the_o height_n ab_fw-la so_o let_v the_o line_n s_o be_v to_o the_o line_n t._n and_o let_v a_o section_n be_v suppose_v lmn_n equal_a to_o the_o section_n df_n in_o height_n and_o length_n but_o let_v it_o be_v in_o velocity_n equal_a to_o the_o section_n af._n therefore_o the_o quantity_n of_o the_o water_n that_o run_v through_o df_n to_o that_o which_o run_v through_o ln_o shall_v be_v as_o the_o velocity_n through_o df_n to_o the_o velocity_n of_o ln_o that_o be_v to_o the_o velocity_n through_o ln_o that_o be_v to_o the_o velocity_n through_o af._n therefore_o the_o quantity_n of_o water_n which_o run_v through_o df_n to_o that_o which_o pass_v through_o ln_o shall_v have_v the_o proportion_n that_o r_o have_v to_o saint_n but_o the_o quantity_n of_o the_o water_n that_o run_v through_o ln_o to_o that_o which_o run_v through_o of_o the_o section_n be_v equal_o swift_a shall_v have_v the_o proportion_n that_o the_o section_n ln_o have_v to_o the_o section_n of_o that_o be_v that_o the_o height_n bd_o have_v to_o the_o height_n basilius_n that_o be_v that_o saint_n have_v to_o t._n therefore_o by_o equal_a proportion_n the_o quantity_n of_o the_o water_n which_o run_v by_o df_n to_o that_o which_o run_v by_o of_o shall_v have_v the_o proportion_n of_o r_o to_o t_n that_o be_v shall_v be_v compound_v of_o the_o proportion_n of_o the_o height_n db_n to_o the_o height_n ab_fw-la and_o of_o the_o velocity_n through_o df_n to_o the_o velocity_n through_o af._n and_o therefore_o if_o a_o river_n increase_v in_o quick_a height_n the_o quantity_n of_o the_o water_n that_o run_v after_o the_o increase_n to_o that_o which_o run_v before_o the_o increase_n have_v the_o proportion_n compound_v etc._n etc._n which_o be_v to_o be_v demonstrate_v corollary_n i._n hence_o it_o follow_v that_o we_o have_v show_v that_o the_o quantity_n of_o the_o water_n which_o run_v whilst_o the_o river_n be_v high_a to_o that_o which_o run_v whilst_o it_o be_v low_a have_v the_o proportion_n compound_v of_o the_o velocity_n to_o the_o velocity_n and_o of_o the_o height_n to_o the_o height_n and_o it_o have_v be_v demonstrate_v that_o the_o velocity_n to_o the_o velocity_n be_v as_o the_o height_n to_o the_o height_n it_o follow_v i_o say_v that_o the_o quantity_n of_o the_o water_n that_o run_v whilst_o the_o river_n be_v high_a to_o that_o which_o run_v whilst_o it_o be_v low_a have_v duplicate_v proportion_n of_o the_o height_n to_o the_o height_n that_o be_v the_o proportion_n that_o the_o square_n of_o the_o height_n have_v corollary_n ii_o upon_o which_o thing_n depend_v the_o reason_n of_o that_o which_o i_o have_v say_v in_o my_o second_o consideration_n that_o if_o by_o the_o diversion_n of_o 5_o 9_o of_o the_o water_n that_o enter_v by_o the_o river_n into_o the_o moor_n or_o fen_n the_o water_n
from_o the_o syphon_n the_o say_a channel_n remain_v quite_o dry_a and_o this_o do_v i_o measure_v the_o quick_a height_n of_o the_o channel_n with_o care_n and_o afterward_o divide_v it_o exact_o into_o 10_o equal_a part_n and_o cause_v 19_o of_o those_o syphon_n to_o be_v take_v away_o so_o that_o the_o channel_n do_v not_o run_v water_n save_v only_o with_o 81_o of_o those_o syphon_n i_o again_o observe_v the_o quick_a height_n of_o the_o water_n in_o the_o same_o site_n observe_v before_o and_o find_v that_o its_o height_n be_v diminish_v precise_o the_o ten_o part_n of_o all_o its_o first_o height_n and_o thus_o continue_v to_o take_v away_o 17._o other_o syphon_n the_o height_n be_v likewise_o diminish_v 1_o 10_o of_o all_o its_o first_o quick_a height_n and_o try_v to_o take_v away_o 15._o syphon_n than_o 13_o then_z 11_o then_z 9_o then_z 7_o then_z 5_o and_o then_o 3._o always_o in_o these_o diversion_n make_v in_o order_n as_o have_v be_v say_v there_o ensue_v still_o a_o abatement_n of_o 1_o 10_o of_o the_o whole_a height_n and_o here_o be_v one_o thing_n worthy_a of_o observation_n that_o the_o water_n increase_a in_o or_o through_o the_o channel_n its_o quick_a height_n be_v different_a in_o different_a cite_v of_o the_o channel_n that_o be_v still_o lesser_a the_o more_o one_o approach_v to_o the_o outlet_a notwithstanding_o which_o the_o abatement_n follow_v in_o all_o place_n proportionable_o that_o be_v in_o all_o its_o cite_v the_o first_o part_n of_o the_o height_n of_o that_o site_n diminish_v and_o moreover_o the_o water_n issue_v from_o the_o channel_n and_o dilate_a into_o a_o broad_a course_n from_o which_o likewise_o have_v divers_a outlet_n and_o mouth_n yet_o nevertheless_o in_o that_o breadth_n also_o the_o quick_a height_n successive_o vary_v and_o alter_v in_o the_o same_o proportion_n nor_o do_v i_o here_o desist_v my_o observation_n but_o the_o water_n be_v diminish_v that_o issue_v from_o the_o syphon_n and_o there_o be_v but_o one_o of_o they_o leave_v that_o discharge_v water_n i_o observe_v the_o quick_a height_n that_o it_o make_v in_o the_o abovesaid_a cite_v the_o which_o be_v likewise_o 1_o 10_o of_o all_o the_o first_o height_n there_o be_v add_v to_o the_o water_n of_o that_o syphon_n the_o water_n of_o three_o other_o syphon_n so_o that_o all_o the_o water_n be_v of_o 4_o syphon_n and_o consequent_o quadruple_a to_o the_o first_o syphon_n but_o the_o quick_a height_n be_v only_o double_a and_o add_v five_o siphons_n the_o quick_a height_n become_v triple_a and_o with_o add_v seven_o syphon_n the_o height_n increase_v quadruple_a and_o so_o by_o add_v of_o 9_o it_o increase_v quintuple_a and_o by_o add_v of_o 11._o it_o increase_v sextuple_a and_o by_o add_v of_o 13._o it_o increase_v septuple_a and_o by_o add_v of_o 15._o octuple_a and_o by_o add_v of_o 17._o nonuple_n and_o last_o by_o add_v 19_o syphon_n so_o that_o all_o the_o water_n be_v centuple_a to_o the_o water_n of_o one_o syphon_n yet_o nevertheless_o the_o quick_a height_n of_o all_o this_o water_n be_v only_a decuple_n to_o the_o first_o height_n conjoin_v by_o the_o water_n that_o issue_v from_o one_o only_a syphon_n for_o the_o more_o clear_a understanding_n of_o all_o which_o i_o have_v make_v the_o follow_a figure_n in_o which_o we_o have_v the_o mouth_n a_o that_o maintain_v the_o water_n of_o the_o vessel_n bc_n in_o the_o same_o level_n though_o it_o continual_o run_v to_o the_o brim_n of_o the_o vessel_n be_v put_v 25._o syphon_n and_o there_o may_v be_v many_o more_o divide_v into_o 5_o class_n defgh_a and_o the_o first_o d_o be_v of_o one_o only_a syphon_n the_o second_o e_z of_o three_o syphon_n the_o three_o f_o of_o five_o the_o fourth_z g_z of_o 7_o the_o five_o h_n of_o 9_o and_o one_o may_v suppose_v the_o six_o of_o 11_o the_o seven_o of_o 13_o syphon_n and_o so_o of_o the_o other_o class_n all_o contain_v in_o consequent_a odd_a number_n successive_o we_o be_v content_a to_o represent_v in_o the_o figure_n no_o more_o but_o the_o five_o forename_a class_n to_o avoid_v confusion_n the_o gather_a water_n defgh_o which_o run_v through_o the_o channel_n ikl_n and_o fall_v into_o the_o outlet_a mnop_n and_o so_o much_o suffice_v for_o the_o explanation_n of_o this_o experiment_n propos_fw-fr v._o prob._n iii_o any_o river_n of_o any_o bigness_n if_o be_v give_v to_o examine_v the_o quantity_n of_o the_o water_n that_o run_v through_o the_o river_n in_o a_o time_n assign_v by_o what_o we_o have_v say_v already_o in_o the_o two_o precede_a problem_n we_o may_v also_o resolve_v this_o that_o we_o have_v now_o before_o we_o and_o it_o be_v do_v by_o divert_v in_o the_o first_o place_n from_o the_o great_a river_n a_o good_a big_a measurable_a channel_n as_o be_v teach_v in_o the_o second_o problem_n and_o observe_v the_o abatement_n of_o the_o river_n cause_v by_o the_o diversion_n of_o the_o channel_n and_o find_v the_o proportion_n that_o the_o water_n of_o the_o channel_n have_v to_o that_o of_o the_o river_n then_o let_v the_o water_n of_o the_o channel_n be_v measure_v by_o the_o second_o problem_n and_o work_v as_o above_o and_o you_o shall_v have_v your_o desire_n consideration_n i._o and_o although_o it_o seem_v as_o if_o it_o may_v prove_v difficult_a and_o almost_o impossible_a to_o make_v use_n of_o the_o regulator_n number_n if_o one_o be_v about_o to_o measure_v the_o water_n of_o some_o great_a river_n and_o consequent_o will_v be_v impossible_a or_o at_o least_o very_a difficult_a to_o reduce_v the_o theory_n of_o the_o first_o problem_n into_o practice_n yet_o nevertheless_o i_o can_v say_v that_o such_o great_a conceit_n of_o measure_v the_o water_n of_o a_o great_a river_n be_v not_o to_o come_v into_o the_o mind_n of_o any_o but_o great_a personage_n and_o potent_a prince_n of_o who_o it_o be_v expect_v for_o their_o extraordinary_a concern_v that_o they_o will_v make_v these_o kind_n of_o inquiry_n as_o if_o here_o in_o italy_n it_o shall_v be_v of_o the_o river_n tiber_n velino_n chiana_n arno_n serchio_n adice_n in_o which_o it_o seem_v real_o difficult_a to_o apply_v the_o regulator_n to_o find_v exact_o the_o quick_a height_n of_o the_o river_n but_o because_o in_o such_o like_a case_n sometime_o it_o will_v turn_v to_o account_v to_o be_v at_o some_o charge_n to_o come_v to_o the_o exact_a and_o true_a knowledge_n of_o the_o quantity_n of_o water_n which_o that_o river_n carry_v by_o knowledge_n whereof_o other_o great_a disbursment_n may_v afterward_o be_v avoid_v that_o will_v oft_o time_n be_v make_v in_o vain_a and_o prevent_v the_o disgust_n which_o sometime_o happen_v among_o prince_n upon_o this_o ground_n i_o think_v it_o will_v be_v well_o to_o show_v also_o the_o way_n how_o to_o make_v use_n of_o the_o regulator_n in_o these_o great_a river_n in_o which_o if_o we_o will_v but_o open_v our_o eye_n we_o shall_v meet_v with_o good_a one_o and_o those_o make_v without_o great_a cost_n or_o labour_n which_o will_v serve_v our_o turn_n for_o upon_o such_o like_a river_n there_o be_v wear_v or_o lock_n make_v to_o cause_v the_o water_n to_o rise_v and_o to_o turn_v they_o for_o the_o service_n of_o mill_n or_o the_o like_a now_o in_o these_o case_n it_o be_v sufficient_a that_o one_o erect_v upon_o the_o two_o extreme_n of_o the_o wear_v two_o pilaster_n either_o of_o wood_n or_o brick_n which_o with_o the_o bottom_n of_o the_o wear_n do_v compose_v our_o regulator_n wherewith_o we_o may_v make_v our_o desire_a operation_n yea_o the_o channel_n itself_o divert_v shall_v serve_v without_o make_v any_o other_o diversion_n or_o union_n and_o in_o brief_a if_o the_o business_n be_v but_o manage_v by_o a_o judicious_a person_n there_o may_v way_n and_o help_n be_v make_v use_n of_o according_a to_o occasion_n of_o which_o it_o will_v be_v too_o tedious_a to_o speak_v and_o therefore_o this_o little_a that_o have_v be_v hint_v shall_v suffice_v consideration_n ii_o from_o what_o have_v be_v declare_v if_o it_o shall_v be_v well_o understand_v may_v be_v deduce_v many_o benefit_n and_o convenience_n not_o only_o in_o divide_v of_o run_v water_n for_o infinite_a use_n that_o they_o be_v put_v to_o in_o turn_v of_o corne-mill_n paper-mill_n gin_n powder-mill_n rice-mill_n iron-mill_n oil-mill_n sawing-mill_n mirtle-mill_n felling-mill_n fulling-mill_n silk-mill_n and_o such_o other_o machine_n but_o also_o in_o order_v navigable_a channel_n divert_v river_n and_o channel_n of_o water_n or_o terminate_n and_o limit_v the_o size_n of_o pipe_n for_o fountain_n in_o all_o which_o affair_n there_o be_v great_a error_n comâ—â—â—ed_v to_o the_o loss_n of_o much_o expense_n the_o channel_n and_o pipe_n that_o be_v make_v sometime_o not_o be_v sufficient_a to_o carry_v the_o design_v water_n and_o sometime_o they_o
be_v make_v big_a than_o be_v necessary_a which_o disorder_n shall_v be_v avoid_v if_o the_o engineer_n be_v advise_v of_o the_o thing_n abovesaid_a and_o in_o case_n that_o to_o these_o notion_n there_o be_v add_v the_o knowledge_n of_o philosophy_n and_o mathematics_n agreeable_a to_o the_o sublime_a discovery_n of_o signore_n galileo_n and_o the_o further_a improvement_n thereof_o by_o signore_n evangelista_n torricelli_n mathematician_n to_o the_o grand_a duke_n of_o tuscany_n who_o have_v subtle_o and_o admirable_o handle_v this_o whole_a business_n of_o motion_n one_o shall_v then_o come_v to_o the_o knowledge_n of_o particular_a notion_n of_o great_a curiosity_n in_o the_o theorick_n and_o of_o extraordinary_a benefit_n in_o the_o practic_n that_o daily_a occur_v in_o these_o business_n and_o to_o show_v in_o effect_n of_o what_o utility_n these_o notion_n be_v i_o have_v think_v fit_a to_o insert_v in_o this_o place_n the_o consideration_n by_o i_o make_v upon_o the_o lake_n of_o venice_n and_o to_o represent_v at_o large_a by_o the_o experience_n of_o the_o last_o year_n 1641._o the_o most_o serene_a erizzo_n than_o duke_n of_o the_o say_a republic_n be_v therefore_o at_o venice_n in_o the_o year_n aforesaid_a i_o be_v request_v by_o the_o most_o illustrious_a and_o most_o excellent_a signore_n giovanni_n basadonna_n a_o senator_n of_o great_a worth_n and_o merit_n that_o i_o will_v ingenous_o deliver_v my_o opinion_n touch_v the_o state_n of_o the_o lake_n of_o venice_n and_o after_o i_o have_v discourse_v with_o his_o honour_n several_a time_n in_o the_o end_n i_o have_v order_n to_o set_v down_o the_o whole_a business_n in_o writing_n who_o have_v afterward_o read_v it_o private_o the_o say_a signore_n impart_v the_o same_o with_o like_a privacy_n to_o the_o most_o serene_a prince_n and_o i_o receive_v order_n to_o represent_v the_o same_o to_o the_o full_a college_n as_o according_o i_o do_v in_o the_o month_n of_o may_n the_o same_o year_n and_o it_o be_v as_o follow_v consideration_n concern_v the_o lake_n of_o venice_n by_o d._n benedetto_n castelli_n abbot_n of_o s._n benedetto_n aloysio_n mathematician_n to_o pope_n vrban_n viii_o and_o professor_n in_o rome_n consideration_n i._n though_o the_o principal_a cause_n be_v but_o one_o only_a that_o in_o my_o judgement_n threaten_v irreparable_a ruin_n to_o the_o lake_n of_o venice_n in_o the_o present_a state_n in_o which_o it_o now_o stand_v yet_o nevertheless_o i_o think_v that_o two_o head_n may_v be_v consider_v and_o this_o consideration_n may_v peradventure_o serve_v we_o for_o to_o facilitate_v and_o explain_v the_o opportune_a remedy_n though_o not_o to_o render_v the_o state_n of_o thing_n absolute_o unchangeable_a and_o eternal_a a_o enterprise_n impossible_a and_o especial_o in_o that_o which_o have_v have_v some_o beginning_n ought_v likewise_o necessary_o to_o have_v its_o end_n or_o at_o least_o to_o prevent_v the_o danger_n for_o many_o hundred_o of_o year_n and_o possible_o it_o may_v in_o the_o mean_a time_n by_o the_o mutation_n itself_o be_v bring_v into_o a_o better_a condition_n i_o say_v therefore_o that_o the_o present_a disorder_n may_v be_v consider_v under_o two_o head_n one_o be_v the_o very_a notable_a discovery_n of_o land_n that_o be_v observe_v at_o the_o time_n of_o low_a water_n the_o which_o beside_o the_o obstruct_n of_o navigation_n in_o the_o lake_n and_o also_o in_o the_o channel_n do_v likewise_o threaten_v another_o mischief_n and_o disorder_n worthy_a of_o very_o particular_a consideration_n which_o be_v that_o the_o sun_n dry_v up_o that_o mud_n especial_o in_o the_o time_n of_o hot_a summer_n do_v raise_v thence_o the_o putrify_a and_o pernicious_a vapour_n fog_n and_o exhalation_n that_o infect_v the_o air_n and_o may_v render_v the_o city_n unhabitable_a the_o second_o head_n be_v the_o great_a stoppage_n that_o daily_o be_v grow_v in_o the_o port_n especial_o of_o venice_n at_o malamoco_n concern_v which_o matter_n i_o will_v hint_n certain_a general_a point_n and_o then_o will_v proceed_v to_o the_o more_o particular_a and_o important_a affair_n and_o first_o i_o say_v that_o i_o hold_v it_o altogether_o impossible_a to_o effect_v any_o thing_n though_o never_o so_o profitable_a which_o do_v not_o bring_v with_o it_o some_o mischief_n and_o therefore_o the_o good_a and_o the_o hurt_n ought_v to_o be_v very_o well_o weigh_v and_o then_o the_o less_o harmful_a part_n to_o be_v embrace_v second_o i_o propose_v to_o consideration_n that_o the_o so_o notable_a discovery_n of_o earth_n &_o mud_n have_v not_o be_v long_o observe_v as_o i_o understand_v from_o old_a person_n that_o can_v remember_v passage_n for_o fifty_o year_n past_a which_o thing_n be_v true_a as_o to_o i_o it_o seem_v most_o true_a it_o shall_v appear_v that_o it_o can_v not_o but_o be_v good_a to_o reduce_v matter_n to_o that_o pass_n that_o they_o be_v at_o former_o lay_v aside_o all_o affection_n or_o passion_n that_o self-flattering_a mind_n have_v entertain_v for_o their_o own_o conceit_n or_o at_o least_o it_o shall_v be_v necessary_a speedy_o to_o consult_v the_o whole_a three_o i_o hold_v that_o it_o be_v necessary_a to_o weigh_v whether_o from_o the_o foresay_a discovery_n of_o land_n it_o follow_v that_o only_o the_o earth_n rise_v as_o it_o be_v common_o think_v by_o all_o without_o dispute_n or_o whether_o the_o water_n be_v abate_v and_o fall_v away_o or_o else_o whether_o it_o proceed_v from_o both_o the_o one_o and_o other_o cause_n and_o here_o it_o will_v be_v seasonable_a to_o inquire_v what_o share_v the_o say_a cause_n may_v have_v each_o consider_v apart_o in_o the_o foresay_a effect_n for_o in_o the_o first_o case_n if_o the_o earth_n have_v be_v raise_v it_o will_v be_v necessary_a to_o consider_v of_o take_v it_o down_o and_o remove_v it_o but_o if_o the_o water_n have_v fail_v or_o abate_v i_o believe_v that_o it_o will_v be_v extreme_o necessary_a to_o restore_v and_o raise_v they_o and_o if_o both_o these_o reason_n have_v conspire_v in_o this_o effect_n it_o will_v be_v necessary_a to_o remedy_v they_o each_o apart_o and_o i_o do_v for_o my_o part_n think_v that_o the_o so_o notable_a appearance_n of_o shelf_n at_o the_o time_n of_o low_a water_n proceed_v principal_o from_o the_o decrease_n and_o abatement_n of_o the_o water_n which_o may_v confident_o be_v affirm_v to_o need_v no_o other_o proof_n in_o regard_n that_o the_o brent_n have_v be_v actual_o divert_v which_o do_v former_o discharge_v its_o water_n into_o the_o lake_n as_o to_o the_o other_o point_n of_o the_o great_a stoppage_n of_o port_n i_o hold_v that_o all_o proceed_v from_o the_o violence_n of_o the_o sea_n which_o be_v sometime_o disturb_v by_o wind_n especial_o at_o the_o time_n of_o the_o water_n flow_v do_v continual_o raise_v from_o its_o bottom_n immense_a heap_n of_o sand_n carry_v they_o by_o the_o tide_n and_o force_n of_o the_o wave_n into_o the_o lake_n it_o not_o have_v on_o its_o part_n any_o sttength_n of_o current_n that_o may_v raise_v and_o carry_v they_o away_o they_o sink_v to_o the_o bottom_n and_o so_o they_o choke_v up_o the_o port_n and_o that_o this_o effect_n happen_v in_o this_o manner_n we_o have_v most_o frequent_a experience_n thereof_o along_o the_o seacoast_n and_o i_o have_v observe_v in_o tuscany_n on_o the_o roman-shore_n and_o in_o the_o kingdom_n of_o of_o naples_n that_o when_o a_o river_n fall_v into_o the_o sea_n there_o be_v always_o see_v in_o the_o sea_n itself_o at_o the_o place_n of_o the_o river_n outlet_a the_o resemblance_n as_o it_o be_v of_o a_o halfmoon_n or_o a_o great_a shelf_n of_o settle_a sand_n under_o water_n much_o high_a than_o the_o rest_n of_o the_o shore_n and_o it_o be_v call_v in_o tuscany_n il_fw-fr cavallo_n and_o here_o in_o venice_n lo_o sâ—anto_n the_o which_o come_v to_o be_v cut_v by_o the_o current_n of_o the_o river_n one_o while_o on_o the_o right_a side_n another_o while_n on_o the_o left_a and_o sometime_o in_o the_o midst_n according_a as_o the_o wind_n sit_v and_o a_o like_a effect_n i_o have_v observe_v in_o certain_a little_a rillet_n of_o water_n along_o the_o lake_n of_o bolsena_n with_o no_o other_o difference_n save_v that_o of_o small_a and_o great_a now_o whoso_o well_o consider_v this_o effect_n plain_o see_v that_o it_o proceed_v from_o no_o other_o than_o from_o the_o contrariety_n of_o the_o stream_n of_o the_o river_n to_o the_o impetus_fw-la of_o the_o sea-wave_n see_v that_o great_a abundance_n of_o sand_n which_o the_o sea_n continual_o throw_v upon_o the_o shore_n come_v to_o be_v drive_v into_o the_o sea_n by_o the_o stream_n of_o the_o river_n and_o in_o that_o place_n where_o those_o two_o impediment_n meet_v with_o equal_a force_n the_o sand_n settle_v under_o water_n and_o thereupon_o be_v make_v that_o same_o shelf_n for_o cavallo_n the_o which_o if_o the_o
river_n carry_v water_n and_o that_o any_o considerable_a store_n it_o shall_v be_v thereby_o cut_v and_o break_v one_o while_o in_o one_o place_n and_o another_o while_n in_o another_o as_o have_v be_v say_v according_a as_o the_o wind_n blow_v and_o through_o that_o channel_n it_o be_v that_o vessel_n fall_v down_o into_o the_o sea_n and_o again_o make_v to_o the_o river_n as_o into_o a_o port._n but_o if_o the_o water_n of_o the_o river_n shall_v not_o be_v continual_a or_o shall_v be_v weak_a in_o that_o case_n the_o force_n of_o the_o sea-wind_n shall_v drive_v such_o a_o quantity_n of_o sand_n into_o the_o mouth_n of_o the_o port_n and_o of_o the_o river_n as_o shall_v whole_o choke_v it_o up_o and_o hereupon_o there_o be_v see_v along_o the_o seaside_n very_o many_o lake_n and_o meers_n which_o at_o certain_a time_n of_o the_o year_n abound_v with_o water_n and_o the_o lake_n bear_v down_o that_o enclosure_n and_o run_v into_o the_o sea_n now_o it_o be_v necessary_a to_o make_v the_o like_a reflection_n on_o our_o port_n of_o venice_n malamocco_n bondolo_n and_o chiozza_n which_o in_o a_o certain_a sense_n be_v no_o other_o than_o creek_n mouth_n and_o open_n of_o the_o shore_n that_o part_v the_o lake_n from_o the_o main_a sea_n and_o therefore_o i_o hold_v that_o if_o the_o water_n in_o the_o lake_n be_v plentiful_a they_o will_v have_v strength_n to_o scour_v the_o mouth_n of_o the_o port_n thorough_o &_o with_o great_a force_n but_o the_o water_n in_o the_o lake_n fail_v the_o sea_n will_v without_o any_o opposal_n bring_v such_o a_o drift_n of_o sand_n into_o the_o port_n that_o if_o it_o do_v not_o whole_o choke_v they_o up_o it_o shall_v render_v they_o at_o least_o unprofitable_a and_o impossible_a for_o bark_n and_o great_a vessel_n many_o other_o consideration_n may_v be_v propound_v concern_v these_o two_o head_n of_o the_o stoppage_n of_o the_o port_n and_o of_o the_o appearance_n of_o the_o ouze_n and_o mud_n in_o the_o lake_n but_o so_o much_o shall_v suffice_v we_o to_o have_v hint_v to_o make_v way_n for_o discourse_v of_o the_o operation_n about_o the_o oportune_a remedy_n yet_o before_o that_o i_o propound_v my_o opinion_n i_o say_v that_o i_o know_v very_o well_o that_o my_o proposal_n at_o first_o sight_n will_v seem_v absurd_a and_o inconvenient_a and_o therefore_o as_o such_o will_v perhaps_o be_v reject_v by_o the_o most_o and_o so_o much_o the_o rather_o for_o that_o it_o will_v prove_v direct_o contrary_a to_o what_o have_v hitherto_o be_v and_o as_o i_o hear_v be_v intend_v to_o be_v do_v and_o i_o be_o not_o so_o wed_v to_o my_o opinion_n but_o that_o i_o do_v consider_v what_o other_o may_v judge_v thereof_o but_o be_v it_o as_o it_o will_v i_o be_o oblige_v to_o speak_v my_o thought_n free_o and_o that_o be_v do_v i_o will_v leave_v it_o to_o wise_a man_n than_o myself_o when_o they_o shall_v have_v well_o consider_v my_o reason_n to_o judge_v and_o deliberate_v of_o the_o quid_fw-la agendum_fw-la and_o if_o the_o sentence_n shall_v go_v against_o i_o i_o appeal_v to_o the_o most_o equitable_a and_o inexorable_a tribunal_n of_o nature_n who_o not_o care_v in_o the_o least_o to_o please_v either_o one_o party_n or_o another_o will_v be_v always_o a_o punctual_a and_o inviolable_a executrix_fw-la of_o her_o eternal_a decree_n against_o which_o neither_o humane_a deliberation_n nor_o our_o vain_a desire_n shall_v ever_o have_v power_n to_o rebel_v i_o add_v by_o word_n of_o mouth_n that_o which_o follow_v though_o your_o highness_n interest_n yourself_o in_o this_o noble_a college_n and_o cause_v it_o to_o be_v confirm_v in_o the_o authority_n senate_n by_o universal_a vote_n that_o the_o wind_n do_v not_o blow_v that_o the_o sea_n do_v not_o fluctuate_v that_o the_o river_n do_v not_o run_v yet_o shall_v the_o wind_n be_v always_o deaf_a the_o sea_n shall_v be_v constant_a in_o its_o inconstancy_n and_o the_o river_n most_o obstinate_a and_o these_o shall_v be_v my_o judge_n and_o to_o their_o determination_n i_o refer_v myself_o by_o what_o have_v be_v say_v in_o my_o opinion_n that_o be_v make_v very_o clear_a and_o manifest_a which_o in_o the_o begin_n of_o this_o discourse_n i_o glance_v at_o namely_o that_o the_o whole_a disorder_n although_o it_o be_v divide_v into_o two_o head_n into_o the_o discovery_n of_o the_o mud_n and_o of_o the_o stoppage_n port_n yet_o nevertheless_o by_o the_o application_n of_o one_o only_a remedy_n and_o that_o in_o my_o esteem_n very_o easy_a the_o whole_a shall_v be_v remove_v and_o this_o it_o be_v that_o there_o be_v restore_v into_o the_o lake_n as_o much_o water_n as_o can_v be_v possible_a and_o in_o particular_a from_o the_o upper_a part_n of_o venice_n take_v care_n that_o the_o water_n be_v as_o free_a from_o mud_n as_o be_v possible_a and_o that_o this_o be_v the_o true_a and_o real_a remedy_n of_o the_o precedent_a disorder_n be_v manifest_a for_o in_o the_o passage_n that_o this_o water_n shall_v make_v through_o the_o lake_n it_o shall_v of_o itself_o by_o degree_n clear_v the_o channel_n in_o sundry_a part_n of_o they_o according_a to_o the_o current_n that_o it_o shall_v successive_o acquire_v and_o in_o this_o manner_n be_v disperse_v through_o the_o lake_n it_o shall_v maintain_v the_o water_n in_o the_o same_o and_o in_o the_o channel_n much_o high_o as_o i_o shall_v prove_v hereafter_o a_o thing_n that_o will_v make_v navigation_n commodious_a and_o that_o which_o moreover_o be_v of_o great_a moment_n in_o our_o business_n those_o shelf_n of_o mud_n which_o now_o discover_v themselves_o at_o the_o time_n of_o low-water_n shall_v be_v always_o cover_v so_o that_o the_o putrefaction_n of_o the_o air_n shall_v also_o be_v remedy_v and_o last_o this_o abundance_n of_o water_n be_v always_o of_o discharge_v itself_o into_o the_o sea_n by_o the_o port_n i_o do_v not_o doubt_v but_o that_o their_o bottom_n will_v be_v scour_v and_o that_o these_o effect_n must_v follow_v nature_n herself_o seem_v to_o persuade_v there_o remain_v only_o one_o great_a doubt_n whether_o that_o abundance_n of_o water_n that_o shall_v be_v bring_v into_o the_o lake_n may_v be_v real_o sufficient_a to_o make_v the_o water_n rise_v so_o much_o as_o to_o keep_v the_o shelf_n cover_v and_o to_o facilitate_v navigation_n which_o ought_v to_o be_v at_o least_o half_a a_o yard_n brace_n or_o thereabouts_o and_o indeed_o it_o seem_v at_o first_o sight_n to_o be_v impossible_a that_o the_o sole_a water_n of_o the_o name_n brent_n let_v into_o the_o lake_n and_o disperse_v over_o the_o same_o can_v occasion_v so_o notable_a a_o height_n of_o water_n and_o the_o more_o to_o confirm_v the_o difficulty_n one_o may_v say_v reduce_v the_o reason_n to_o calculation_n that_o in_o case_n the_o brent_n be_v 40._o brace_n broad_a and_o two_o and_o a_o half_a high_a and_o the_o breadth_n of_o the_o lake_n be_v 20000._o brace_n it_o will_v seem_v necessary_a that_o the_o height_n of_o the_o water_n of_o the_o brent_n dilate_v and_o distend_v through_o the_o lake_n will_v be_v but_o only_o 1_o 200_o of_o a_o brace_n in_o height_n which_o be_v imperceptible_a and_o will_v be_v of_o no_o avail_n to_o our_o purpose_n nay_o more_o it_o be_v very_o certain_a that_o the_o burn_v run_v very_o muddy_a and_o foul_a this_o will_v occasion_v very_o great_a mischief_n fill_v and_o contract_v the_o lake_n and_o for_o that_o reason_n this_o remedy_n ought_v as_o pernicious_a to_o be_v total_o exclude_v and_o condemn_v i_o here_o confess_v that_o i_o be_o surprise_v at_o the_o form_n of_o the_o argument_n as_o if_o i_o be_v in_o a_o certain_a manner_n convince_v that_o i_o dare_v not_o adventure_v to_o say_v more_o or_o open_v my_o mouth_n in_o this_o matter_n but_o the_o strength_n itself_o of_o the_o argument_n as_o be_v found_v upon_o the_o mean_n of_o gemoetrical_a and_o arithmetical_a calculation_n have_v open_v i_o the_o way_n to_o discover_v a_o very_a crafty_a fraud_n that_o be_v couch_v in_o the_o same_o argument_n which_o fraud_n i_o will_v make_v out_o to_o any_o one_o that_o have_v but_o any_o insight_n in_o geometry_n and_o arithmetic_n and_o as_o it_o be_v impossible_a that_o such_o a_o argument_n shall_v be_v produce_v by_o any_o but_o such_o as_o have_v taste_v of_o these_o in_o such_o affair_n most_o profitable_a and_o most_o necessary_a science_n so_o do_v not_o i_o pretend_v to_o make_v myself_o understand_v save_v only_o by_o such_o to_o who_o i_o will_v evince_v so_o clear_o as_o that_o more_o it_o can_v be_v desire_v the_o error_n and_o fraud_n wherein_o those_o ancient_n and_o modern_n have_v be_v and_o always_o be_v entangle_v that_o have_v in_o any_o way_n yet_o handle_v this_o matter_n of_o consider_v the_o measure_n and_o quantity_n of_o the_o water_n that_o move_v
and_o so_o great_a be_v the_o esteem_n that_o i_o have_v for_o that_o which_o i_o be_o now_o about_o to_o say_v touch_v this_o particular_a that_o i_o be_o content_a that_o all_o the_o rest_n of_o my_o discourse_n be_v reject_v provide_v that_o that_o be_v perfect_o understand_v which_o i_o be_o hereafter_o to_o propose_v i_o hold_v and_o know_v it_o to_o be_v a_o main_a principle_n upon_o which_o all_o that_o be_v found_v that_o can_v be_v say_v either_o well_o or_o handsome_o on_o this_o particular_a the_o other_o discourse_n may_v have_v a_o appearance_n of_o be_v probable_a but_o this_o hit_v the_o mark_n as_o full_a as_o can_v be_v desire_v arrive_v at_o the_o high_a degree_n of_o certainty_n i_o have_v seventeen_o year_n since_o as_o i_o represent_v to_o the_o most_o serene_a prince_n and_o to_o the_o right_n honourable_a the_o precedent_n of_o the_o lord_n the_o commissioner_n of_o the_o affair_n sewer_n write_v a_o treatise_n of_o the_o measure_n of_o the_o water_n that_o move_v in_o which_o i_o geometrical_o demonstrate_v and_o declare_v this_o business_n and_o they_o who_o shall_v have_v well_o understand_v the_o ground_n of_o my_o discourse_n will_v rest_v full_o satisfy_v with_o that_o which_o i_o be_o now_o about_o to_o propose_v but_o that_o all_o may_v become_v rhe_n more_o easy_a i_o will_v more_o brief_o explicate_v and_o declare_v so_o much_o thereof_o as_o i_o have_v demonstrate_v in_o the_o discourse_n which_o will_v suffice_v for_o our_o purpose_n and_o if_o that_o shall_v not_o be_v enough_o we_o have_v always_o the_o experiment_n of_o a_o very_a easy_a and_o cheap_a way_n to_o clear_v up_o the_o whole_a business_n and_o moreover_o i_o will_v take_v the_o boldness_n to_o affirm_v that_o in_o case_n there_o shall_v not_o for_o the_o present_a any_o deliberation_n be_v make_v concern_v this_o affair_n according_a to_o my_o opinion_n yet_o nevertheless_o it_o will_v be_v at_o some_o time_n or_o other_o or_o if_o it_o be_v not_o thing_n will_v grow_v worse_o and_o worse_o for_o more_o clear_a understanding_n therefore_o it_o ought_v to_o be_v know_v that_o it_o be_v require_v as_o it_o be_v general_o use_v to_o measure_v the_o water_n of_o a_o river_n its_o breadth_n and_o its_o depth_n be_v take_v and_o these_o two_o dimension_n be_v multiply_v together_o the_o product_n be_v affirm_v to_o be_v the_o quantity_n of_o that_o river_n as_o for_o example_n if_o a_o river_n shall_v be_v 100_o foot_n broad_a and_o 20._o foot_n high_a it_o will_v be_v say_v that_o that_o river_n be_v 2000_o foot_n of_o water_n and_o so_o if_o a_o ditch_n shall_v be_v 15._o foot_n broad_a and_o 5._o foot_n high_a this_o same_o ditch_n will_v be_v affirm_v to_o be_v 75._o foot_n of_o water_n and_o this_o manner_n of_o measure_v run_v water_n have_v be_v use_v by_o the_o ancient_n and_o by_o modern_n with_o no_o other_o difference_n save_v only_o that_o some_o have_v make_v use_n of_o the_o foot_n other_o of_o the_o palm_n other_o of_o the_o brace_n and_o other_o of_o other_o measure_n now_o because_o that_o in_o observe_v these_o water_n that_o move_v i_o frequent_o find_v that_o the_o same_o water_n of_o the_o same_o river_n be_v in_o some_o cite_v of_o its_o channel_n pretty_a big_a and_o in_o other_o much_o less_o not_o arrive_v in_o some_o place_n to_o the_o twenty_o nor_o to_o the_o hundred_o part_n of_o that_o which_o it_o be_v see_v to_o be_v in_o other_o place_n therefore_o this_o vulgar_a way_n of_o measure_v the_o water_n that_o move_v for_o that_o they_o do_v not_o give_v i_o a_o certain_a and_o stable_a measure_n and_o quantity_n of_o water_n begin_v deserve_o to_o be_v suspect_v by_o i_o as_o difficult_a and_o defective_a be_v always_o various_a and_o the_o measure_n on_o the_o contrary_a be_v to_o be_v always_o determinate_a and_o the_o same_o it_o be_v therefore_o write_v that_o pondus_fw-la &_o pondus_fw-la mensura_fw-la &_o mensura_fw-la utrumque_fw-la abominabile_fw-la est_fw-la apud_fw-la deum_fw-la exod._n i_o consider_v that_o in_o the_o territory_n of_o brescia_n my_o native_a country_n and_o in_o other_o place_n where_o water_n be_v divide_v to_o overflow_v the_o ground_n by_o the_o like_a way_n of_o measure_v they_o there_o be_v commit_v grievous_a and_o most_o important_a error_n to_o the_o great_a prejudice_n of_o the_o public_a and_o of_o private_a person_n neither_o they_o that_o sell_v nor_o they_o that_o buy_v understand_v the_o true_a quantity_n of_o that_o which_o be_v sell_v and_o buy_v in_o regard_n that_o the_o same_o square_a measure_n as_o be_v accustom_v in_o those_o part_n assign_v one_o particular_a person_n carry_v to_o sometime_o above_o twice_o or_o thrice_o as_o much_o water_n as_o do_v the_o same_o square_a measure_n assign_v to_o another_o which_o thing_n prove_v to_o be_v the_o same_o inconvenience_n as_o if_o the_o measure_n wherewith_o wine_n and_o oil_n be_v buy_v and_o sell_v shall_v hold_v twice_o or_o thrice_o as_o much_o wine_n or_o oil_n at_o one_o time_n as_o at_o another_o now_o this_o consideration_n invite_v my_o mind_n and_o curiosity_n to_o the_o find_v out_o of_o the_o true_a measure_n of_o run_v water_n and_o in_o the_o end_n by_o occasion_n of_o a_o most_o important_a business_n that_o i_o be_v employ_v in_o some_o year_n since_o with_o great_a intensenesse_n of_o mind_n and_o with_o the_o sure_a direction_n of_o geometry_n i_o have_v discover_v the_o mistake_n which_o be_v that_o we_o be_v upon_o the_o business_n of_o take_v the_o measure_n of_o the_o water_n that_o move_v do_v make_v use_n of_o two_o dimension_n only_o namely_o breadth_n and_o depth_n keep_v no_o account_n of_o the_o length_n and_o yet_o the_o water_n be_v though_o run_v a_o body_n it_o be_v necessary_a in_o form_v a_o conceit_n of_o its_o quantity_n in_o relation_n to_o another_o to_o keep_v account_n of_o all_o the_o three_o dimension_n that_o be_v of_o length_n breadth_n and_o depth_n here_o a_o objection_n have_v be_v put_v to_o i_o in_o behalf_n of_o the_o ordinary_a way_n of_o measure_v run_v water_n in_o opposition_n to_o what_o i_o have_v above_o consider_v and_o propose_v and_o i_o be_v tell_v it_o be_v true_a that_o in_o measure_v a_o body_n that_o stand_v still_o one_o ought_v to_o take_v all_o the_o three_o dimension_n but_o in_o measure_v a_o body_n that_o continual_o move_v as_o the_o water_n the_o case_n be_v not_o the_o same_o for_o the_o length_n be_v not_o to_o be_v have_v the_o length_n of_o the_o water_n that_o move_v be_v infinite_a as_o never_o finish_v its_o run_n and_o consequent_o be_v incomprehensible_a by_o humane_a understanding_n and_o therefore_o with_o reason_n nay_o upon_o necessity_n it_o come_v to_o be_v omit_v in_o answer_n to_o this_o i_o say_v that_o in_o the_o abovesaid_a discourse_n two_o thing_n be_v to_o be_v consider_v distinct_o first_o whether_o it_o be_v possible_a to_o frame_v any_o conceit_n of_o the_o quantity_n of_o the_o body_n of_o the_o water_n with_o two_o dimension_n only_o and_o 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carry_v in_o a_o determinate_a time_n of_o a_o hour_n of_o a_o day_n or_o of_o a_o month_n etc._n etc._n i_o say_v that_o it_o be_v a_o very_a possible_a and_o profitable_a enquiry_n by_o reason_n of_o the_o innumerable_a benefit_n that_o may_v be_v derive_v thence_o it_o much_o import_v to_o know_v how_o much_o water_n a_o channel_n carry_v in_o a_o time_n give_v and_o i_o have_v demonstrate_v the_o same_o above_o in_o the_o begin_n of_o this_o book_n and_o of_o this_o we_o stand_v in_o need_n in_o the_o business_n of_o the_o lake_n that_o so_o we_o may_v be_v able_a to_o determine_v how_o much_o shall_v be_v the_o height_n of_o the_o brent_n when_o it_o be_v spread_v all_o over_o the_o lake_n for_o the_o three_o dimension_n of_o a_o body_n be_v give_v the_o
body_n be_v know_v and_o the_o quantity_n of_o a_o body_n be_v give_v if_o you_o have_v but_o two_o dimension_n the_o three_o shall_v be_v know_v and_o thus_o dive_v far_o and_o far_o into_o this_o consideration_n i_o find_v that_o the_o velocity_n of_o the_o course_n of_o the_o water_n may_v be_v a_o hundred_o time_n great_a or_o lesser_a in_o one_o part_n of_o its_o channel_n than_o in_o another_o and_o therefore_o although_o there_o shall_v be_v two_o mouth_n of_o water_n equal_a in_o bigness_n yet_o nevertheless_o it_o may_v come_v to_o pass_v that_o one_o may_v discharge_v a_o hundred_o or_o a_o thousand-time_n more_o water_n than_o another_o and_o this_o will_v be_v if_o the_o water_n in_o one_o of_o the_o mouth_n shall_v run_v with_o a_o hundred_o or_o a_o thousand_o time_n great_a velocity_n than_o the_o other_o for_o that_o it_o will_v be_v the_o same_o as_o to_o say_v that_o the_o swift_a be_v a_o hundred_o or_o a_o thousand_o time_n long_o than_o the_o slow_a and_o in_o this_o manner_n i_o discover_v that_o to_o keep_v account_n of_o the_o velocity_n be_v the_o keep_a account_n of_o the_o length_n and_o therefore_o it_o be_v manifest_a that_o when_o two_o mouth_n discharge_v the_o same_o quantity_n of_o water_n in_o a_o equal_a velocity_n it_o be_v necessary_a that_o the_o less_o swift_a mouth_n be_v so_o much_o big_a than_o the_o more_o swift_a as_o the_o more_o swift_a exceed_v in_o velocity_n the_o less_o swift_a as_o for_o example_n in_o case_n two_o river_n shall_v carry_v equal_a quantity_n of_o water_n in_o equal_a time_n but_o that_o one_o of_o they_o shall_v be_v four_o time_n more_o swift_a than_o the_o other_o the_o more_o slow_a shall_v of_o necessity_n be_v four_o time_n more_o large_a and_o because_o the_o same_o river_n in_o any_o part_n thereof_o always_o discharge_v the_o same_o quantity_n of_o water_n in_o equal_a time_n as_o be_v demonstrate_v in_o the_o first_o proposition_n of_o the_o first_o book_n book_n of_o the_o measure_n 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time_n of_o low-water_n so_o many_o shelf_n and_o such_o heap_n of_o mud_n as_o do_v now_o appear_v 4._o the_o air_n will_v become_v more_o wholesome_a for_o that_o it_o shall_v not_o be_v so_o infect_v by_o putrid_a vapour_n exhale_v by_o the_o sun_n so_o long_o as_o the_o miry_a ouze_n shall_v be_v cover_v by_o the_o water_n 5._o last_o in_o the_o current_n of_o these_o advantageous_a water_n which_o must_v issue_v out_o of_o the_o lake_n into_o the_o sea_n beside_o those_o of_o the_o tide_n the_o port_n will_v be_v keep_v scour_v and_o clear_a and_o this_o be_v as_o much_o as_o i_o shall_v offer_v for_o the_o present_a touch_v this_o weighty_a business_n always_o submit_v myself_o to_o sound_a judgement_n of_o the_o abovesaid_a write_n i_o present_v a_o copy_n at_o venice_n at_o a_o full_a college_n in_o which_o i_o read_v it_o all_o and_o it_o be_v hearken_v to_o with_o very_o great_a attention_n and_o at_o last_o i_o present_v it_o to_o the_o duke_n and_o leave_v some_o copy_n 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basadonna_n who_o after_o he_o have_v well_o consider_v my_o paper_n carry_v it_o to_o the_o council_n and_o after_o that_o those_o lord_n have_v for_o many_o month_n mature_o consider_v thereon_o they_o in_o the_o end_n resolve_v to_o suspend_v the_o execution_n of_o the_o diversion_n which_o they_o have_v before_o consult_v to_o make_v of_o the_o river_n sile_z and_o of_o four_o other_o river_n which_o also_o fall_v into_o the_o lake_n a_o thing_n by_o i_o blame_v in_o this_o second_o paper_n as_o most_o prejudicial_a and_o harmful_a the_o writing_n speak_v as_o follow_v consideration_n concern_v the_o lake_n of_o venice_n part_n ii_o if_o the_o discourse_v well_o about_o the_o truth_n of_o thing_n most_o serene_a prince_n be_v as_o the_o carry_n of_o burden_n
in_o which_o we_o see_v that_o a_o hundred_o horse_n carry_v a_o great_a weight_n than_o one_o horse_n only_o it_o will_v seem_v that_o one_o may_v make_v more_o account_n of_o the_o opinion_n of_o many_o man_n than_o of_o one_o alone_a but_o because_o that_o discourse_v more_o resemble_v run_v than_o carry_v burden_n in_o which_o we_o see_v that_o one_o barb_n alone_o run_v fast_a than_o a_o hundred_o heavy-heeled_a jade_n therefore_o i_o have_v ever_o more_o esteem_v one_o conclusion_n well_o manage_v and_o well_o consider_v by_o one_o understanding_n man_n although_o alone_o than_o the_o common_a and_o vulgar_a opinion_n especial_o when_o they_o concern_v abstruse_a and_o arduous_a point_n nay_o in_o such_o case_n the_o opinion_n mould_v and_o frame_v by_o the_o most_o ignorant_a and_o stupid_a vulgar_a have_v be_v ever_o suspect_v by_o i_o as_o false_a for_o that_o it_o will_v be_v a_o great_a wonder_n if_o in_o difficult_a matter_n a_o common_a capacity_n shall_v hit_v upon_o that_o which_o be_v handsome_a good_a and_o true_a hence_o i_o have_v and_o do_v hold_v in_o very_o great_a veneration_n the_o sum_n of_o the_o government_n of_o the_o most_o serene_a and_o eternal_a republic_n of_o venice_n which_o although_o as_o be_v in_o nature_n a_o commonwealth_n it_o ought_v to_o be_v govern_v by_o the_o great_a part_n yet_o nevertheless_o in_o arduous_a affair_n it_o be_v always_o direct_v by_o the_o grave_a judgement_n of_o few_o and_o not_o judge_v blind_o by_o the_o plebeian_n rout._n it_o be_v true_a that_o he_o that_o propound_v proposition_n far_o above_o the_o reach_n of_o common_a capacity_n run_v a_o great_a hazard_n of_o be_v very_o often_o condemn_v without_o further_a process_n or_o knowledge_n of_o the_o cause_n but_o yet_o for_o all_o that_o the_o truth_n be_v not_o to_o be_v desert_v in_o most_o weighty_a affair_n but_o ought_v rather_o to_o be_v explain_v in_o due_a place_n and_o time_n with_o all_o possible_a perspicuity_n that_o so_o be_v 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reward_n of_o the_o readiness_n that_o i_o have_v express_v to_o obey_v and_o serve_v they_o but_o i_o be_v above_o measure_n encourage_v and_o please_v to_o see_v that_o those_o few_o who_o vouchsafe_v to_o hear_v i_o be_v all_o either_o thorough_o persuade_v that_o my_o opinion_n be_v well_o ground_v or_o at_o least_o suspend_v their_o prudent_a verdict_n to_o more_o mature_a deliberation_n and_o though_o at_o the_o first_o bout_n i_o chance_v to_o propose_v a_o thing_n that_o be_v total_o contrary_a to_o the_o most_o receive_v and_o antiquate_a opinion_n and_o to_o the_o resolution_n and_o consultation_n take_v above_o a_o hundred_o year_n ago_o move_v by_o these_o thing_n and_o to_o satisfy_v also_o to_o the_o promise_n that_o i_o have_v make_v of_o tender_v unto_o they_o what_o shall_v far_o offer_v itself_o unto_o i_o touch_v the_o same_o business_n i_o have_v resolve_v to_o present_a to_o the_o throne_n of_o your_o highness_n another_o consideration_n of_o no_o less_o importance_n which_o perhaps_o at_o first_o sight_n will_v appear_v a_o strange_a paradox_n but_o yet_o bring_v to_o the_o test_n and_o touchstone_n of_o experience_n it_o shall_v prove_v most_o clear_a and_o evident_a if_o it_o shall_v be_v account_v of_o so_o that_o it_o succee_v to_o the_o benefit_n of_o your_o highness_n i_o shall_v have_v obtain_v my_o desire_n and_o intent_n and_o if_o not_o i_o shall_v have_v satisfy_v myself_o and_o shall_v not_o have_v be_v want_v to_o the_o obligation_n of_o your_o most_o faithful_a servant_n and_o native_a subject_n that_o which_o i_o propound_v in_o the_o mouth_n pass_v touch_v the_o most_o important_a business_n of_o the_o lake_n though_o it_o do_v only_o express_o concern_v the_o point_n of_o the_o diversion_n of_o the_o mouth_n of_o the_o lake_n already_o make_v and_o put_v in_o execution_n yet_o it_o may_v be_v understand_v and_o apply_v also_o to_o the_o diversion_n under_o debate_n to_o be_v make_v of_o the_o other_o five_o river_n and_o of_o the_o sile_z in_o particular_a now_o touch_v this_o i_o have_v the_o fortune_n to_o offer_v a_o admirable_a accident_n that_o we_o meet_v with_o when_o we_o come_v to_o the_o effect_n which_o i_o very_o believe_v will_v be_v a_o utter_a ruin_n to_o the_o lake_n of_o venice_n i_o say_v therefore_o that_o by_o divert_v these_o five_o river_n that_o remain_v although_o their_o water_n that_o they_o discharge_v for_o the_o present_a into_o the_o lake_n be_v not_o all_o take_v together_o 4_o 5_o part_n of_o what_o the_o brent_n alone_o do_v carry_v yet_o nevertheless_o the_o abatement_n of_o the_o water_n of_o the_o lake_n which_o shall_v ensue_v upon_o this_o last_o diversion_n of_o four_o part_n which_o be_v the_o whole_a water_n shall_v prove_v double_a to_o that_o which_o have_v happen_v by_o the_o diversion_n of_o brent_n only_o although_o that_o the_o brent_n alone_o carry_v five_o part_n of_o that_o water_n of_o which_o the_o river_n that_o be_v to_o be_v divert_v carry_v four_o a_o wonder_n real_o great_a and_o altogether_o unlikely_a for_o the_o reduce_v all_o this_o proposition_n to_o be_v understand_v be_v as_o if_o we_o shall_v say_v that_o there_o be_v give_v we_o three_o river_n of_o which_o the_o first_o discharge_v five_o part_n the_o second_o three_o and_o the_o three_o one_o and_o that_o from_o the_o diversion_n of_o the_o first_o there_o do_v follow_v such_o a_o certain_a abatement_n or_o fall_n from_o the_o take_n away_o of_o the_o second_o there_o ought_v to_o follow_v also_o so_o much_o more_o abatement_n and_o last_o from_o the_o withdraw_n of_o the_o three_o the_o water_n ought_v to_o fall_v so_o much_o more_o which_o be_v whole_o impossible_a and_o yet_o it_o be_v most_o certain_a and_o beside_o the_o demonstration_n that_o persuade_v i_o to_o it_o which_o i_o shall_v explain_v in_o due_a time_n i_o can_v set_v before_o your_o eye_n such_o a_o experiment_n as_o be_v not_o to_o be_v deny_v by_o any_o one_o although_o obstinate_a and_o i_o will_v make_v it_o plain_o see_v and_o feel_v that_o by_o take_v away_o only_o four_o part_n of_o the_o five_o which_o shall_v have_v be_v take_v away_o the_o abatement_n prove_v double_a to_o the_o abatement_n ensue_v upon_o the_o divert_v first_o of_o the_o five_o only_o which_o thing_n be_v true_a as_o most_o certain_o it_o be_v it_o will_v give_v we_o to_o understand_v how_o pernicious_a this_o diversion_n of_o five_o river_n be_v like_a to_o prove_v if_o it_o shall_v be_v put_v in_o execution_n by_o this_o little_a that_o i_o have_v hint_v and_o the_o much_o that_o i_o can_v say_v let_v your_o highness_n gather_v with_o what_o circumspection_n this_o business_n ought_v to_o be_v manage_v and_o with_o how_o great_a skill_n he_o ought_v to_o be_v furnish_v who_o will_v behave_v himself_o well_o in_o these_o difficult_a affair_n i_o have_v not_o at_o this_o time_n explain_v the_o demonstration_n nor_o have_v i_o so_o much_o as_o propound_v the_o way_n to_o make_v the_o experiment_n that_o i_o be_o able_a to_o make_v in_o confirmation_n of_o what_o i_o have_v say_v that_o so_o by_o some_o one_o or_o other_o misapprehending_a the_o demonstration_n and_o maim_v the_o experiment_n the_o truth_n may_v not_o happen_v to_o shine_v with_o less_o clarity_n than_o it_o do_v when_o all_o mist_n of_o difficulty_n be_v remove_v and_o if_o so_o be_v no_o account_n shall_v be_v make_v of_o the_o reason_n by_o i_o allege_v and_o that_o man_n shall_v shut_v their_o eye_n against_o the_o experiment_n that_o without_o cost_n or_o charge_n may_v be_v make_v i_o do_v declare_v and_o protest_v that_o there_o shall_v follow_v very_o great_a damage_n to_o the_o field_n of_o the_o main_a land_n and_o extraordinary_a sum_n shall_v be_v expend_v to_o no_o purpose_n the_o lake_n undoubted_o will_v become_v almost_o dry_a and_o will_v
prove_v impassable_a for_o navigation_n with_o a_o manifest_a danger_n of_o corrupt_v the_o air_n and_o in_o the_o last_o place_n there_o will_v unavoidable_o ensue_v the_o choke_n and_o stoppage_n of_o the_o port_n of_o venice_n upon_o the_o 20_o of_o december_n 1641._o i_o impart_v this_o my_o second_o consideration_n to_o the_o most_o excellent_a signore_n basadonna_n present_v he_o with_o a_o copy_n thereof_o among_o other_o write_n which_o i_o have_v think_v good_a to_o insert_v although_o they_o seem_v not_o to_o belong_v direct_o to_o our_o business_n of_o the_o lake_n the_o way_n to_o examine_v the_o mud_n and_o sand_n that_o enter_v and_o remain_v in_o the_o lake_n of_o venice_n to_o the_o most_o excellent_a signore_n gio._n basadonna_n two_o very_o considerable_a objection_n have_v be_v make_v against_o my_o opinion_n concern_v the_o lake_n of_o venice_n one_o be_v that_o of_o which_o i_o have_v speak_v at_o large_a in_o my_o first_o consideration_n namely_o that_o the_o brent_n have_v be_v take_v out_o of_o the_o lake_n can_v have_v be_v the_o occasion_n of_o the_o notable_a fall_n of_o the_o water_n in_o the_o lake_n as_o i_o pretend_v and_o consequent_o that_o the_o turn_a brent_n into_o the_o lake_n will_v be_v no_o considerable_a remedy_n in_o regard_n that_o the_o water_n of_o brent_n and_o the_o great_a expansion_n of_o the_o lake_n over_o which_o the_o water_n of_o brent_n be_v to_o diffuse_v and_o spread_v be_v consider_v it_o be_v find_v that_o the_o rise_n prove_v insensible_a the_o second_o objection_n be_v that_o the_o brent_n be_v very_o muddy_a and_o therefore_o if_o it_o shall_v fall_v muddy_a into_o the_o lake_n the_o sand_n will_v sink_v and_o fill_v up_o the_o same_o touch_v the_o first_o query_n enough_o have_v be_v say_v in_o my_o first_o consideration_n where_o i_o have_v plain_o discover_v the_o deceit_n of_o the_o argument_n and_o show_v its_o fallacy_n it_o remain_v now_o to_o examine_v the_o second_o to_o which_o in_o the_o first_o place_n i_o say_v that_o one_o of_o the_o first_o thing_n that_o i_o propose_v in_o this_o affair_n be_v that_o i_o hold_v it_o impossible_a to_o do_v any_o act_n though_o never_o so_o beneficial_a that_o be_v not_o also_o accompany_v by_o some_o inconvenience_n and_o mischief_n and_o therefore_o we_o be_v to_o consider_v well_o the_o profit_n and_o the_o loss_n and_o prejudice_n and_o they_o both_o be_v weigh_v we_o shall_v be_v able_a to_o choose_v the_o lesser_a evil_a second_o i_o admit_v it_o to_o be_v most_o true_a that_o brent_n be_v at_o some_o time_n muddy_a but_o it_o be_v also_o true_a that_o for_o the_o great_a part_n of_o the_o year_n it_o be_v not_o muddy_a three_o i_o do_v not_o see_v nor_o understand_v what_o strength_n this_o objection_n have_v be_v take_v so_o at_o large_a and_o in_o general_a and_o methinks_v that_o it_o be_v not_o enough_o to_o say_v that_o the_o brent_n run_v muddy_a and_o to_o assert_v that_o it_o depose_v its_o muddinesse_n in_o the_o lake_n but_o we_o ought_v moreover_o to_o proceed_v to_o particular_n and_o show_v how_o much_o this_o mud_n be_v and_o in_o what_o time_n this_o choke_n up_o of_o the_o port_n may_v be_v effect_v for_o the_o reason_n be_v but_o too_o apparent_a and_o particular_a that_o conclude_v the_o ruin_n of_o the_o lake_n and_o that_o in_o a_o very_a short_a time_n for_o mention_n be_v make_v of_o day_n the_o water_n diversion_n be_v make_v and_o moreover_o we_o have_v the_o circumstance_n of_o a_o experiment_n the_o state_n of_o thing_n be_v observe_v to_o have_v grow_v worse_o since_o the_o say_a diversion_n and_o i_o have_v demonstrate_v that_o in_o case_n the_o diversion_n of_o the_o sile_z and_o the_o other_o river_n shall_v be_v put_v in_o execution_n the_o lake_n will_v in_o a_o few_o day_n become_v almost_o dry_a and_o the_o port_n will_v be_v lose_v with_o other_o mischievous_a consequence_n but_o on_o the_o other_o side_n although_o that_o we_o do_v grant_v the_o choke_n of_o they_o 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little_a water_n in_o it_o that_o it_o shall_v cease_v to_o be_v navigable_a and_o the_o port_n shall_v most_o infallible_o be_v choke_v up_o i_o will_v therefore_o say_v upon_o experience_n in_o answer_n to_o this_o objection_n that_o it_o be_v very_o necessary_a first_o well_n to_o discourse_n and_o rational_o to_o particularize_v and_o ascertain_v the_o best_a that_o may_v be_v this_o point_n of_o the_o quantity_n of_o this_o sink_a mud_n or_o sand._n now_o i_o fear_v i_o shall_v make_v myself_o ridiculous_a to_o those_o who_o measure_v the_o thing_n of_o nature_n with_o the_o shallowness_n of_o their_o brain_n do_v think_v that_o it_o be_v absolute_o impossible_a to_o make_v this_o enquiry_n and_o will_v say_v unto_o i_o quis_fw-la mensus_fw-la est_fw-la pugillo_fw-la aquas_fw-la &_o terram_fw-la palmo_fw-la ponderavit_fw-la yet_o nevertheless_o i_o will_v propound_v a_o way_n whereby_o at_o least_o in_o gross_a one_o may_v find_v out_o the_o same_o take_v a_o vessel_n of_o cylindrical_a figure_n hold_v two_o barrel_n of_o water_n or_o thereabouts_o and_o then_o fill_v it_o with_o the_o water_n of_o brent_n at_o its_o mouth_n or_o fall_n into_o the_o lake_n but_o in_o the_o lake_n at_o the_o time_n that_o the_o brent_n run_v muddy_a and_o after_o it_o have_v begin_v to_o run_v muddy_a for_o eight_o or_o ten_o hour_n to_o give_v the_o mud_n time_n to_o go_v as_o far_o as_o s._n nicolo_n to_o issue_v into_o the_o sea_n and_o at_o the_o same_o time_n take_v another_o vessel_n like_a and_o equal_a to_o the_o first_o and_o fill_v it_o with_o the_o water_n of_o the_o lake_n towards_o s._n nicolo_n but_o take_v notice_n that_o this_o operation_n ought_v to_o be_v make_v at_o the_o time_n when_o the_o water_n go_v out_o and_o when_o the_o sea_n be_v calm_a and_o then_o when_o the_o water_n shall_v have_v settle_v in_o the_o aforesaid_a vessel_n take_v out_o the_o clear_a water_n and_o consider_v the_o quantity_n of_o sand_n that_o remain_v behind_o and_o let_v it_o be_v set_v down_o or_o keep_v in_o mind_n and_o i_o be_o easy_o induce_v to_o think_v that_o that_o shall_v be_v a_o great_a quantity_n of_o sand_n which_o shall_v be_v leave_v in_o the_o first_o vessel_n than_o that_o leave_v in_o the_o second_o vessel_n afterward_o when_o the_o brent_n shall_v come_v to_o be_v clear_a let_v both_o the_o operation_n be_v repeat_v and_o observe_v the_o quantity_n of_o sand_n in_o the_o aforesaid_a vessel_n for_o if_o the_o sand_n in_o the_o first_o vessel_n shall_v be_v most_o it_o will_v be_v a_o sign_n that_o in_o the_o revolution_n of_o a_o year_n the_o brent_n will_v depose_v sand_n in_o the_o lake_n and_o in_o this_o manner_n one_o may_v calculate_v to_o a_o small_a matter_n what_o proportion_n the_o sand_n that_o enter_v into_o the_o lake_n have_v to_o that_o which_o remain_v and_o by_o that_o proportion_n one_o may_v judge_v how_o expedient_a it_o shall_v be_v for_o public_a benefit_n and_o if_o at_o several_a time_n of_o the_o year_n you_o careful_o repeat_v the_o same_o operation_n or_o rather_o observation_n you_o will_v come_v to_o a_o more_o exact_a knowledge_n in_o this_o business_n and_o it_o will_v be_v good_a to_o make_v the_o say_a operation_n at_o those_o time_n when_o the_o lake_n be_v disturb_v by_o strong_a high_a wind_n and_o make_v muddy_a by_o its_o own_o mud_n raise_v by_o the_o commotion_n of_o the_o water_n this_o notion_n will_v give_v we_o great_a light_n if_o the_o same_o observation_n shall_v be_v make_v towards_o the_o mouth_n of_o lio_o at_o such_o time_n as_o the_o water_n flow_v and_o ebb_n in_o calm_a season_n for_o so_o one_o shall_v come_v to_o know_v whether_o the_o water_n of_o the_o lake_n be_v more_o thick_a at_o the_o go_v out_o than_o at_o the_o entrance_n i_o have_v propound_v the_o
forego_n way_n of_o measure_v sand_n and_o mud_n to_o show_v that_o we_o be_v not_o so_o general_o and_o inconsiderate_o to_o pronounce_v any_o sentence_n but_o proceed_v to_o strict_a inquiry_n and_o then_o deliberate_v what_o shall_v be_v most_o expedient_a to_o be_v do_v other_o may_v propose_v more_o equisite_a examination_n but_o this_o shall_v serve_v i_o for_o the_o present_a i_o will_v add_v only_o that_o if_o any_o one_o have_v great_a curiosity_n it_o will_v be_v profitable_a to_o have_v it_o in_o investigate_a more_o exact_o the_o quantity_n of_o the_o water_n that_o enter_v into_o the_o lake_n by_o the_o mean_n that_o i_o have_v show_v in_o the_o begin_n of_o this_o book_n when_o he_o shall_v have_v find_v the_o proportion_n of_o the_o quantity_n of_o water_n to_o the_o quantity_n of_o sand_n or_o mud_n he_o shall_v come_v to_o know_v how_o much_o sand_n the_o brent_n shall_v leave_v in_o the_o lake_n in_o the_o space_n of_o a_o year_n but_o to_o perform_v these_o thing_n there_o be_v require_v person_n of_o discretion_n and_o fidelity_n and_o that_o be_v employ_v by_o public_a order_n for_o there_o will_v thence_o result_v eminent_a benefit_n and_o profit_n here_o be_v want_v letter_n from_o several_a person_n to_o the_o reverend_a father_n francisco_n di_fw-mi s._n giuseppe_n in_o execution_n of_o the_o command_n that_o you_o lay_v upon_o i_o in_o your_o former_a letter_n by_o order_n from_o the_o most_o serene_a my_o lord_n prince_n leopold_n that_o i_o shall_v speak_v my_o judgement_n concern_v the_o disimboguement_fw-fr of_o the_o river_n call_v fiume_n morto_fw-la whether_o it_o ought_v to_o be_v let_v into_o the_o sea_n or_o into_o serchio_n i_o say_v that_o i_o chance_v 18._o year_n since_o to_o be_v present_a when_o the_o say_a mouth_n be_v open_v into_o the_o sea_n and_o that_o of_o serchio_n stop_v which_o work_n be_v do_v to_o remedy_v the_o great_a innundation_n that_o be_v make_v in_o all_o that_o country_n and_o plain_a of_o pisa_n that_o lie_v between_o the_o river_n arno_n and_o the_o mountain_n of_o s._n giuliano_n and_o the_o river_n serchio_n which_o plain_o continue_v long_o under_o water_n insomuch_o that_o not_o only_o in_o the_o winter_n but_o also_o for_o a_o great_a part_n of_o the_o summer_n those_o field_n be_v overflow_v and_o when_o that_o the_o mouth_n of_o fiume_n morto_fw-la be_v effectual_o open_v into_o the_o sea_n the_o place_n be_v present_o free_v from_o the_o water_n and_o drain_v to_o the_o great_a satisfaction_n of_o the_o owner_n of_o those_o ground_n and_o here_o i_o judge_v it_o worth_a your_o notice_n that_o for_o the_o generality_n of_o those_o that_o possess_v estate_n in_o those_o part_n they_o desire_v that_o the_o mouth_n of_o fiume_n morto_fw-it may_v stand_v open_a to_o the_o sea_n and_o those_o who_o will_v have_v it_o open_a into_o serchio_n be_v person_n that_o have_v no_o other_o concernment_n there_o save_o the_o hope_n of_o gain_v by_o have_v the_o dispose_n of_o commission_n and_o the_o like_a &c_n &c_n but_o for_o the_o more_o plain_a understanding_n of_o that_o which_o be_v to_o be_v say_v it_o must_v be_v know_v that_o the_o resolution_n of_o open_v the_o say_a mouth_n into_o serchio_n be_v take_v in_o the_o time_n of_o the_o great_a duke_n ferdinando_n the_o first_o upon_o the_o same_o motive_n that_o be_v at_o this_o time_n again_o propose_v as_o your_o letter_n tell_v i_o since_o that_o it_o manifest_o appear_v that_o fiume_n morto_fw-la have_v and_o have_v its_o mouth_n open_a to_o the_o sea_n the_o plain_n have_v be_v keep_v dry_a and_o it_o be_v also_o true_a that_o the_o fury_n of_o the_o south_n and_o south-west-wind_n carry_v such_o abundance_n of_o sand_n into_o the_o mouth_n or_o outlet_a of_o fiume_n morto_fw-la that_o it_o whole_o stop_v it_o up_o especial_o when_o the_o water_n on_o pisa_n side_n be_v low_a and_o shallow_a and_o they_o think_v that_o turn_v the_o lake_n of_o fiume_n morto_fw-la into_o serchio_n and_o the_o serchio_n maintain_v continual_o its_o own_o mouth_n with_o the_o force_n of_o its_o water_n open_a to_o the_o sea_n and_o consequent_o also_o fiume_n morto_fw-la they_o will_v have_v have_v the_o outlet_a clear_a and_o open_a and_o in_o this_o manner_n they_o think_v that_o the_o plain_a of_o pisa_n will_v have_v be_v free_v from_o the_o water_n the_o business_n pass_v for_o current_n at_o first_o sight_n but_o experience_n prove_v the_o contrary_a and_o reason_n confirm_v the_o same_o for_o the_o height_n of_o the_o water_n of_o those_o plain_n be_v regulate_v by_o the_o height_n of_o the_o water_n in_o the_o mouth_n of_o fiume_n morto_fw-la that_o be_v the_o water_n at_o the_o mouth_n be_v high_a the_o water_n also_o do_v rise_v in_o the_o field_n and_o when_o the_o water_n at_o the_o mouth_n be_v low_a the_o water_n of_o the_o field_n do_v likewise_o abate_v nor_o be_v it_o enough_o to_o say_v that_o the_o outlet_a or_o vent_v of_o fiume_n morto_fw-la be_v continual_a but_o it_o must_v be_v very_o low_a now_o if_o fiume_n morto_fw-la do_v determine_v in_o serchio_n it_o be_v manifest_a that_o it_o will_v determine_v high_a for_o serchio_n terminate_a in_o the_o sea_n when_o ever_o it_o more_o and_o more_o abound_v with_o water_n and_o riseth_z it_o be_v necessary_a that_o also_o fiume_n morto_fw-la have_v its_o level_n high_a and_o consequent_o shall_v keep_v the_o water_n in_o the_o plain_n high_o nay_o it_o have_v happen_v sometime_o and_o i_o speak_v it_o upon_o my_o own_o sight_n that_o fiume_n morto_fw-la have_v reverse_v its_o course_n upward_o towards_o pisa_n which_o case_n will_v ever_o happen_v whensoever_o the_o pisan_a water_n chance_v to_o be_v low_a than_o the_o level_n of_o those_o of_o serchio_n for_o in_o that_o case_n the_o water_n of_o serchio_n return_v back_o upon_o the_o plain_n through_o fiume_n morto_fw-la in_o such_o sort_n that_o the_o muddiness_n and_o the_o serchio_n have_v be_v observe_v to_o be_v carry_v by_o this_o return_n as_o far_o as_o the_o wall_n of_o pisa_n and_o then_o before_o such_o time_n as_o so_o great_a water_n can_v be_v assuage_v which_o come_v in_o with_o great_a fury_n and_o go_v out_o by_o little_a and_o little_a there_o do_v pass_v very_o many_o day_n and_o month_n nay_o sometime_o one_o being_n never_o able_a to_o find_v the_o water_n of_o serchio_n when_o at_o the_o shallow_a so_o low_a as_o the_o sea_n in_o level_n which_o be_v the_o low_a place_n of_o the_o water_n it_o thence_o do_v follow_v that_o the_o water_n of_o fiume_n morto_fw-it shall_v never_o at_o any_o time_n of_o the_o year_n so_o long_o as_o they_o determine_v in_o serchio_n be_v so_o low_a as_o they_o come_v to_o be_v when_o the_o same_o fiume_n morto_fw-la determine_v in_o the_o sea_n it_o be_v true_a indeed_o that_o the_o mouth_n of_o fiume_n morto_fw-la open_v into_o the_o sea_n be_v subject_a to_o the_o inconvenience_n of_o be_v stop_v up_o by_o the_o force_n of_o wind_n but_o in_o this_o case_n it_o be_v necessary_a to_o take_v some_o pain_n in_o open_v it_o which_o may_v easy_o be_v do_v by_o cut_v that_o sand_n a_o little_a which_o stay_v in_o the_o mouth_n after_o that_o the_o wind_n be_v lay_v and_o it_o be_v enough_o if_o you_o make_v a_o trench_n little_o more_o than_o two_o palm_n in_o breadth_n for_o the_o water_n once_o beginning_n to_o run_v into_o it_o it_o will_v in_o a_o few_o hour_n carry_v that_o sand_n away_o with_o it_o and_o there_o will_v ensue_v a_o deep_a and_o broad_a trench_n that_o will_v drain_v away_o all_o the_o water_n of_o the_o plain_n in_o very_o little_a time_n and_o i_o have_v find_v by_o practice_n that_o there_o have_v be_v a_o great_a quantity_n of_o sand_n drive_v back_o by_o the_o fury_n of_o the_o south-west-wind_n into_o the_o mouth_n of_o fiume_n morto_fw-la i_o have_v cause_v the_o little_a gutter_n to_o be_v make_v in_o the_o morning_n somewhat_o before_o noon_n a_o mouth_n have_v be_v open_v of_o 40._o brace_n wide_a and_o notable_o deep_a insomuch_o that_o the_o water_n which_o before_o have_v incommode_v all_o the_o champion_n run_v away_o in_o less_o than_o three_o day_n and_o leave_v the_o country_n free_a and_o dry_a to_o the_o admiration_n of_o all_o man_n there_o be_v present_a upon_o the_o place_n at_o this_o business_n on_o the_o same_o day_n that_o i_o open_v the_o mouth_n the_o most_o serene_a great_a duke_n the_o most_o serene_a arch-dutchess_n mother_n all_o the_o commissioner_n of_o sewer_n with_o many_o other_o person_n and_o peasant_n of_o those_o part_n and_o they_o all_o see_v very_o well_o that_o it_o be_v never_o possible_a that_o a_o little_a bark_n of_o eight_o oar_n which_o be_v come_v from_o legorn_a to_o wait_v upon_o the_o great_a duke_n shall_v ever_o be_v able_a to_o master_v the_o current_n
and_o to_o make_v up_o into_o fiume_n morto_fw-la and_o his_o highness_n who_o come_v with_o a_o intent_n to_o cause_v the_o say_a mouth_n towards_o the_o sea_n to_o be_v stop_v and_o that_o into_o serchio_n to_o be_v open_v change_v his_o judgement_n give_v order_n that_o it_o shall_v be_v leave_v open_a towards_o the_o sea_n as_o it_o be_v do_v and_o if_o at_o this_o day_n it_o shall_v return_v into_o serchio_n i_o be_o very_o certain_a that_o it_o will_v be_v necessary_a to_o open_v it_o again_o into_o the_o sea_n and_o there_o be_v also_o charge_n and_o order_n give_v to_o a_o person_n appoint_v for_o the_o purpose_n that_o he_o shall_v take_v care_n to_o open_v the_o say_a mouth_n as_o have_v be_v say_v upon_o occasion_n and_o thus_o thing_n have_v succeed_v very_o well_o unto_o this_o very_a time_n but_o from_o the_o middle_n of_o october_n until_o this_o first_o of_o february_n there_o have_v continue_v high_a south_n and_o south-west-wind_n with_o frequent_a and_o abundant_a rain_n it_o be_v no_o wonder_n that_o some_o innundation_n have_v happen_v but_o yet_o i_o will_v affirm_v that_o great_a mischief_n will_v have_v follow_v if_o the_o mouth_n have_v be_v open_v into_o serchio_n this_o which_o i_o have_v hitherto_o say_v be_v very_o clear_a and_o intelligible_a to_o all_o such_o as_o have_v but_o competent_a insight_n and_o indifferent_a skill_n in_o these_o affair_n but_o that_o which_o i_o be_o now_o about_o to_o propose_v far_o will_n i_o be_o very_o certain_a be_v understand_v by_o yourself_o but_o it_o will_v seem_v strange_a and_o unlikely_a to_o many_o other_o the_o point_n be_v that_o i_o say_v that_o by_o raise_v the_o level_n of_o fiume_n morto_fw-la one_o half_a brace_n only_o at_o its_o mouth_n it_o will_v penipenitrate_v into_o serchio_n far_a than_o it_o will_v into_o the_o sea_n it_o shall_v cause_v the_o water_n to_o rise_v three_o or_o perhaps_o more_o brace_n upon_o the_o field_n towards_o pisa_n and_o still_o more_o by_o degree_n as_o they_o shall_v recede_v far_o from_o the_o seaside_n and_o thus_o there_o will_v follow_v very_o great_a inundation_n and_o considerable_a mischief_n and_o to_o know_v that_o this_o be_v true_a you_o be_v to_o take_v notice_n of_o a_o accident_n which_o i_o give_v warning_n of_o in_o my_o discourse_n of_o the_o measure_n of_o run_v water_n where_o also_o i_o give_v the_o reason_n thereof_o 1._o coral_n 14._o the_o accident_n be_v this_o that_o there_o come_v a_o land-flood_n for_o example_n into_o arno_n which_o make_v it_o to_o rise_v above_o its_o ordinary_a mouth_n wthin_n pisa_n or_o a_o little_a above_o or_o below_o the_o city_n six_o or_o seven_o brace_n this_o same_o height_n become_v always_o lesser_a and_o lesser_a the_o more_o we_o approach_v towards_o the_o seaside_n insomuch_o that_o near_o to_o the_o sea_n the_o say_a river_n shall_v be_v raise_v hardly_o half_a a_o brace_n whence_o it_o follow_v of_o necessary_a consequence_n that_o shall_v i_o again_o be_v at_o the_o seaside_n and_o know_v nothing_o of_o what_o happen_v shall_v see_v the_o river_n arno_n raise_v by_o the_o accession_n of_o a_o land-flood_n one_o three_o of_o a_o brace_n i_o can_v certain_o infer_v that_o the_o same_o river_n be_v raise_v in_o pisa_n those_o same_o six_o or_o seven_o brace_n and_o that_o which_o i_o say_v of_o arno_n be_v true_a of_o all_o river_n that_o fall_v into_o the_o sea_n which_o thing_n be_v true_a it_o be_v necessary_a to_o make_v great_a account_n of_o every_o small_a rise_n that_o fiume_n morto_fw-la make_v towards_o the_o seaside_n by_o fall_v into_o serchio_n for_o although_o the_o rise_n of_o fiume_n morto_fw-la by_o be_v to_o disgorge_v its_o water_n into_o serchio_n towards_o the_o sea_n be_v only_o a_o quarter_n of_o a_o brace_n we_o may_v very_o well_o be_v sure_a that_o far_o from_o the_o sea_n about_o pisa_n and_o upon_o those_o field_n the_o rise_n shall_v be_v much_o great_a and_o shall_v become_v two_o or_o three_o brace_n and_o because_o the_o country_n lie_v low_a that_o same_o â—ise_v will_v cause_v a_o continual_a innundation_n of_o the_o plain_n like_a as_o it_o do_v before_o i_o cause_v the_o mouth_n to_o be_v open_v into_o the_o sea_n and_o therefore_o i_o conclude_v that_o the_o mouth_n of_o fiume_n morto_fw-la aught_o by_o no_o mean_n to_o be_v open_v into_o serchio_n but_o aught_o to_o be_v continue_v into_o the_o sea_n use_v all_o diligence_n to_o keep_v it_o open_v after_o the_o manner_n aforesaid_a so_o soon_o as_o ever_o the_o wind_n shall_v be_v lay_v and_o if_o they_o shall_v do_v otherwise_o i_o confident_o affirm_v that_o there_o will_v daily_o follow_v great_a damage_n not_o only_o in_o the_o plain_n but_o also_o in_o the_o wholesomeness_n of_o the_o air_n as_o have_v be_v see_v in_o time_n past_a and_o again_o it_o ough_v with_o all_o care_n to_o be_v procure_v that_o no_o water_n do_v by_o any_o mean_v run_v or_o fall_v from_o the_o trench_n of_o libra_n into_o the_o plain_a of_o pisa_n for_o 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the_o field_n and_o this_o be_v as_o much_o as_o i_o find_v to_o be_v true_a in_o the_o assertion_n of_o signore_n bartolotti_n without_o his_o confirm_v it_o by_o any_o other_o proof_n as_o indeed_o it_o need_v none_o that_o the_o level_n of_o fiume_n morto_fw-la rise_v in_o e_o and_o many_o mile_n far_a upward_o it_o rise_v much_o nor_o do_v i_o ever_o affirm_v the_o contrary_n 3._o concern_v the_o difficulty_n of_o open_v the_o mouth_n of_o fiume_n morto_fw-la into_o the_o sea_n that_o which_o ill_n castellano_n say_v be_v most_o certain_a namely_o that_o at_o the_o entrance_n upon_o the_o open_n of_o the_o mouth_n it_o be_v necessary_a to_o make_v a_o deep_a trench_n but_o i_o say_v that_o at_o that_o time_n it_o be_v difficult_a to_o open_v it_o
unless_o upon_o great_a occasion_n for_o that_o the_o difficulty_n proceed_v from_o the_o water_n of_o fiume_n morto_fw-la be_v low_o and_o the_o field_n drain_v 4._o as_o to_o the_o particular_a of_o the_o cause_n that_o you_o tell_v i_o man_n press_v so_o much_o unto_o the_o most_o serene_a grand_a duke_n and_o to_o the_o prince_n i_o have_v not_o much_o to_o say_v because_o it_o be_v not_o my_o profession_n nor_o have_v i_o consider_v of_o the_o same_o yet_o i_o believe_v that_o when_o the_o prince_n and_o his_o highness_n see_v the_o benefit_n of_o his_o people_n and_o subject_n in_o one_o scale_n of_o the_o balance_n and_o the_o accommodation_n of_o huntsman_n in_o the_o other_o his_o highness_n will_v incline_v to_o the_o profit_n of_o his_o subject_n such_o have_v i_o always_o find_v his_o clemency_n and_o nobleness_n of_o mind_n but_o if_o i_o be_v to_o put_v in_o my_o vote_n upon_o this_o business_n i_o will_v say_v that_o the_o point_n of_o spear_n and_o the_o mouth_n of_o gun_n the_o yelp_a of_o dog_n the_o wilynesse_n of_o huntsman_n who_o run_v thorough_a and_o narrow_o search_v all_o those_o wood_n thicket_n and_o heathe_n be_v the_o true_a destroyer_n of_o buck_n and_o boar_n and_o not_o a_o little_a salt-water_n which_o settle_v at_o last_o in_o some_o low_a place_n and_o spread_v not_o very_o far_o yet_o nevertheless_o i_o will_v not_o enter_v upon_o any_o such_o point_n but_o confine_v myself_o sole_o to_o the_o business_n before_o i_o 5._o that_o experiment_n of_o join_v together_o the_o water_n of_o fiume_n morto_fw-la and_o that_o of_o serchio_n by_o a_o little_a trench_n to_o see_v what_o advantage_n the_o level_n e_o hath_z upon_o the_o level_n i_o do_v not_o give_v i_o full_a satisfaction_n take_v so_o particular_o for_o it_o may_v come_v to_o pass_v that_o sometime_o e_z may_v be_v high_o and_o sometime_o a_o low_a and_o i_o do_v not_o question_v but_o that_o when_o serchio_n be_v low_a and_o fiume_n morto_fw-la full_a of_o water_n the_o level_n of_o fiume_n morto_fw-it will_v be_v high_a than_o that_o of_o serchio_n but_o serchio_n be_v full_a and_o fiume_n morto_fw-la scant_a of_o water_n the_o contrary_n will_v follow_v if_o the_o mouth_n shall_v be_v open_v to_o the_o sea_n and_o here_o it_o shall_v seem_v to_o i_o that_o it_o ought_v to_o be_v consider_v that_o there_o be_v as_o much_o advantage_n from_o e_o to_o the_o sea_n through_o the_o little_a trench_n open_v anew_o into_o serchio_n as_o from_o e_o to_o the_o sea_n by_o the_o mouth_n of_o fiume_n morto_fw-la but_o the_o difficulty_n which_o be_v that_o we_o be_v to_o regard_v in_o our_o case_n be_v that_o the_o course_n of_o the_o water_n through_o the_o trench_n be_v three_o time_n long_o than_o the_o course_n of_o the_o mouth_n of_o fiume_n morto_fw-la as_o appear_v by_o the_o draught_n or_o plat_v which_o you_o send_v i_o which_o i_o know_v to_o be_v very_o exact_o draw_v for_o that_o the_o situation_n of_o those_o place_n be_v fresh_a in_o my_o memory_n here_o i_o must_v give_v notice_n that_o the_o water_n of_o fiume_n morto_fw-la determine_v through_o the_o trench_n in_o serchio_n the_o water_n of_o which_o fiume_n morto_fw-la be_v for_o certain_a never_o so_o low_a as_o the_o sea_n their_o pendency_n or_o declivity_n shall_v for_o two_o cause_n be_v less_o than_o the_o pendency_n of_o those_o water_n through_o the_o mouth_n towards_o the_o sea_n that_o be_v because_o of_o the_o length_n of_o the_o line_n through_o the_o trench_n and_o because_o of_o the_o height_n of_o their_o entrance_n into_o serchio_n a_o thing_n which_o be_v of_o very_o great_a import_n in_o discharge_v the_o water_n which_o come_v sudden_o as_o he_o shall_v plain_o see_v who_o shall_v have_v understand_v my_o book_n of_o the_o measure_n of_o run_v water_n and_o this_o be_v the_o reason_n why_o all_o the_o country_n do_v grow_v dry_a upon_o the_o open_n of_o the_o mouth_n into_o the_o sea_n and_o here_o i_o propose_v to_o consideration_n that_o which_o the_o peasant_n about_o pisa_n relate_v namely_o that_o the_o water_n in_o the_o field_n do_v no_o considerable_a harm_n by_o continue_v there_o five_o or_o six_o yea_o or_o eight_o day_n and_o therefore_o the_o work_n of_o the_o country_n be_v to_o open_v the_o mouth_n of_o fiume_n morto_fw-la in_o such_o manner_n that_o the_o water_n be_v come_v they_o may_v have_v the_o trench_n free_a and_o ready_a when_o that_o the_o water_n come_v it_o may_v have_v a_o free_a drain_v and_o may_v not_o stay_v there_o above_o eight_o or_o nine_o day_n for_o then_o the_o overflowing_n become_v hurtful_a it_o be_v to_o be_v desire_v also_o that_o if_o any_o proposition_n be_v produce_v touch_v these_o affair_n it_o may_v be_v propound_v the_o most_o distinct_o that_o may_v be_v possible_a and_o not_o consist_v in_o general_n especial_o when_o the_o dispute_n be_v of_o the_o rise_n of_o velocity_n of_o tardity_n of_o much_o and_o little_a water_n thing_n that_o be_v all_o to_o be_v specify_v by_o measure_n 6._o your_o letter_n say_v in_o the_o next_o place_n that_o signore_n bartolotti_n confess_v that_o if_o the_o mouth_n of_o the_o fiume_n morto_fw-it may_v always_o be_v keep_v open_a it_o will_v be_v better_a to_o let_v it_o continue_v as_o it_o be_v the_o which_o that_o i_o may_v not_o yield_v to_o he_o in_o courtesy_n i_o confess_v for_o the_o keep_n it_o stop_v on_o all_o side_n will_v be_v a_o thing_n most_o pernicious_a but_o admit_v of_o his_o confession_n i_o again_o reply_n that_o fiume_n morto_fw-it ought_v not_o to_o be_v let_v into_o serchio_n but_o immediate_o into_o the_o sea_n because_o although_o sometime_o the_o mouth_n to_o sea-ward_n be_v stop_v up_o yet_o for_o all_o that_o the_o raise_n of_o the_o bank_n above_o the_o plain_n which_o be_v all_o the_o business_n of_o importance_n shall_v be_v ever_o lesser_a if_o we_o make_v use_v of_o the_o mouth_n lead_v to_o the_o sea_n than_o use_v that_o of_o serchio_n 7._o i_o will_v not_o omit_v to_o mention_v a_o kind_n of_o scruple_n that_o i_o have_v concern_v the_o position_n of_o sign_n bartolotti_n that_o be_v where_o he_o say_v that_o the_o two_o mouth_n a_o and_o d_o be_v equal_a to_o the_o like_a mouth_n into_o the_o sea_n now_o it_o seem_v to_o i_o that_o the_o mouth_n a_o of_o fiume_n morto_fw-la into_o serchio_n be_v absolute_o within_o serchio_n nor_o can_v it_o be_v make_v low_a and_o be_v regulate_v by_o the_o height_n of_o serchio_n but_o the_o mouth_n of_o fiume_n morto_fw-la terminate_v and_o aught_o to_o be_v understand_v to_o terminate_v in_o the_o sea_n itself_o the_o low_a place_n and_o this_o i_o believe_v be_v very_o well_o perceive_v by_o sig._n bartolotti_n but_o i_o can_v tell_v why_o he_o pass_v it_o over_o without_o declare_v it_o and_o we_o see_v not_o that_o the_o mouth_n d_o fall_v far_a from_o the_o sea_n which_o mouth_n ought_v to_o be_v let_v into_o the_o sea_n itself_o and_o so_o the_o advantage_n of_o the_o mouth_n into_o the_o sea_n more_o clear_o appear_v 8._o that_o which_o sig._n bartolotti_n add_v that_o when_o it_o be_v high_a water_n at_o such_o time_n as_o the_o water_n be_v out_o and_o when_o wind_n choke_v up_o fiume_n morto_fw-la they_o not_o only_o retard_v it_o but_o return_v the_o course_n of_o the_o water_n upward_o very_o leisurely_o persuade_v i_o more_o ready_o to_o believe_v that_o sig._n bartolotti_n know_v very_o well_o that_o the_o mouth_n of_o fiume_n morto_fw-la let_v into_o serchio_n be_v hurtful_a for_o by_o this_o he_o acknowledge_v that_o the_o mouth_n towards_o the_o sea_n do_v in_o such_o sort_n drain_v the_o country_n of_o the_o water_n as_o that_o they_o become_v very_o low_a and_o therefore_o upon_o every_o little_a impetus_fw-la the_o water_n turn_v their_o course_n and_o from_o the_o motion_n be_v exceed_v slow_a be_v infer_v that_o the_o abundance_n of_o sea-water_n that_o come_v into_o fiume_n morto_fw-la be_v so_o much_o as_o be_v believe_v and_o as_o sig._n bartolotti_n affirm_v 9_o after_o that_o sig._n bartolotti_n have_v say_v what_o he_o promise_v above_o namely_o that_o when_o the_o wind_n blow_v strong_o do_v stop_v up_o fiume_n morto_fw-la and_o not_o only_o retard_v but_o turn_v the_o course_n upward_o the_o time_n be_v rainy_n and_o the_o mouth_n of_o fiume_n morto_fw-la shut_v up_o the_o wave_n of_o the_o sea_n pass_v over_o the_o bank_n of_o fiume_n morto_fw-la at_o that_o time_n say_v signore_n bartolotti_n the_o champain_n shall_v know_v the_o benefit_n of_o fiume_n morto_fw-la discharge_v into_o serchio_n and_o the_o mouth_n a_o shall_v stand_v always_o open_a and_o fiume_n morto_fw-it may_v always_o constant_o run_v out_o as_o also_o the_o rain_n and_o rain-water_n although_o the_o hurtful_a tempest_n shall_v last_v many_o day_n etc._n etc._n
and_o i_o reply_v that_o all_o the_o art_n consist_v in_o this_o for_o the_o benefit_n of_o those_o field_n do_v not_o depend_v on_o or_o consist_v in_o say_v that_o fiume_n morto_fw-la be_v always_o open_a and_o fiume_n morto_fw-la drain_v continual_o but_o all_o the_o business_n of_o profit_n lie_v and_o consist_v in_o maintain_v the_o water_n low_a in_o those_o plain_n and_o those_o ditch_n which_o shall_v never_o be_v effect_v whilst_o the_o world_n stand_v if_o you_o let_v fiume_n morto_fw-la into_o serchio_n but_o yet_o it_o may_v by_o open_v the_o mouth_n into_o the_o sea_n and_o so_o much_o reason_n and_o nature_n prove_v and_o which_o import_v experience_n confirm_v 10._o in_o the_o ten_o place_n i_o come_v to_o consider_v the_o answer_n that_o be_v make_v to_o another_o proposition_n in_o the_o letter_n which_o i_o write_v to_o father_n francisco_n which_o prudent_o of_o itself_o alone_a may_v serve_v to_o clear_v this_o whole_a business_n i_o say_v in_o my_o letter_n that_o great_a account_n be_v to_o be_v make_v of_o every_o small_a rise_n and_o ebb_v of_o the_o water_n near_o to_o the_o sea_n in_o fiume_n morto_fw-la for_o that_o these_o rise_n and_o fall_n although_o that_o they_o be_v small_a near_o to_o the_o seaside_n yet_o nevertheless_o they_o operate_v and_o be_v accompany_v by_o notable_a rise_n and_o fall_n within_o land_n and_o far_o from_o the_o seaside_n and_o i_o have_v declare_v by_o a_o example_n of_o arno_n in_o which_o a_o land-flood_n fall_v that_o make_v it_o increase_v above_o its_o ordinary_a height_n within_o pisa_n six_o or_o seven_o brace_n that_o this_o height_n of_o the_o same_o flood_n become_v still_o lesser_a the_o near_o we_o approach_v to_o the_o seacoast_n nor_o shall_v the_o say_a river_n be_v raise_v hardly_o half_a a_o brace_n whereupon_o it_o necessry_o follow_v that_o if_o i_o shall_v return_v to_o the_o seaside_n and_o not_o know_v any_o think_v of_o that_o which_o happen_v at_o pisa_n and_o see_v the_o river_n arno_n raise_v by_o a_o land-flood_n half_a a_o brace_n i_o may_v confident_o affirm_v the_o say_a river_n to_o be_v raise_v in_o pisa_n those_o six_o or_o seven_o brace_n etc._n etc._n from_o such_o like_a accident_n i_o conclude_v in_o the_o same_o letter_n that_o it_o be_v necessary_a to_o make_v great_a account_n of_o every_o little_a rise_n that_o fiume_n morto_fw-it shall_v make_v towards_o the_o sea_n now_o come_v bartolotti_n and_o perhaps_o because_o i_o know_v not_o how_o to_o express_v myself_o better_a understand_v not_o my_o proposition_n and_o speak_v that_o which_o indeed_o be_v true_a but_o yet_o beside_o our_o case_n nor_o have_v i_o ever_o say_v the_o contrary_a and_o withal_o do_v not_o apply_v it_o to_o his_o purpose_n nay_o i_o say_v that_o if_o he_o have_v well_o apply_v it_o this_o alone_o have_v be_v able_a to_o have_v make_v he_o change_v his_o opinion_n and_o because_o he_o say_v that_o i_o say_v that_o it_o be_v true_a when_o the_o abatement_n proceed_v from_o some_o cause_n above_o as_o namely_o by_o rain_n or_o open_v of_o lake_n but_o when_o the_o cause_n be_v from_o below_o that_o be_v by_o some_o stop_n as_o for_o instance_n some_o fisher_n wear_v or_o lock_n or_o some_o impediment_n remote_a from_o the_o sea_n although_o at_o the_o level_n it_o shall_v rise_v some_o brace_n where_o the_o impediment_n be_v yet_o that_o rise_n shall_v go_v upward_o and_o here_o he_o finish_v his_o discourse_n and_o conclude_v not_o any_o thing_n more_o to_o which_o i_o say_v first_o that_o i_o have_v also_o say_v the_o same_o in_o the_o proposition_n namely_o that_o a_o flood_n come_v which_o make_v arno_n to_o rise_v in_o pisa_n six_o or_o seven_o brace_n which_o i_o take_v to_o be_v a_o superior_a cause_n whether_o it_o be_v rain_n or_o the_o open_n of_o lake_n as_o best_o please_v bartolotti_n in_o such_o a_o case_n i_o say_v and_o in_o no_o other_o for_o towards_o the_o seacoast_n it_o shall_v not_o cause_v a_o rise_n of_o full_a half_a a_o brace_n and_o therefore_o see_v arno_n at_o the_o seaside_n to_o be_v raise_v by_o a_o flood_n whether_o of_o rain_n or_o of_o open_v of_o lake_n half_a a_o brace_n it_o may_v be_v infer_v that_o at_o pisa_n it_o shall_v be_v raise_v those_o six_o or_o seven_o brace_n which_o variety_n well_o consider_v explain_v all_o this_o affair_n in_o favour_n of_o my_o opinion_n for_o the_o rise_n that_o be_v make_v by_o the_o impediment_n place_v below_o of_o fish_v wear_v and_o lock_n operate_v at_o the_o beginning_n raise_v the_o water_n that_o be_v near_o to_o the_o impediment_n and_o afterward_o less_o and_o less_o as_o we_o retire_v upward_o from_o the_o impediment_n provide_v yet_o that_o we_o speak_v not_o of_o a_o flood_n that_o come_v by_o accession_n but_o only_o of_o the_o ordinary_a water_n impede_v but_o there_o be_v a_o new_a accession_n as_o in_o our_o case_n than_o the_o water_n of_o the_o flood_n i_o say_v shall_v make_v a_o great_a rise_n in_o the_o part_n superior_a far_o from_o the_o impediment_n and_o these_o impediment_n shall_v come_v to_o be_v those_o that_o shall_v overflow_v the_o plain_n as_o happen_v eighteen_o or_o nineteen_o year_n ago_o before_o the_o open_n of_o fiume_n morto_fw-la into_o the_o sea_n the_o same_o will_v certain_o follow_v if_o fiume_n morto_fw-la be_v let_v into_o serchio_n here_o i_o can_v allege_v a_o very_a pretty_a case_n that_o befall_v i_o in_o la_fw-fr 〈◊〉_d campagna_n di_fw-it roma_fw-it near_o to_o the_o seaside_n where_o i_o drain_v a_o bog_n or_o fen_n of_o the_o nature_n of_o the_o water_n of_o pisa_n and_o i_o succeed_v in_o the_o enterprise_n the_o water_n in_o their_o site_n towards_o the_o sea_n abate_v only_o three_o palm_n and_o yet_o in_o the_o fen_n they_o fall_v more_o than_o fifteen_o palm_n but_o the_o business_n will_v be_v long_o and_o not_o so_o easy_o to_o be_v declare_v and_o i_o be_o certain_a that_o sig._n bartolotti_n have_v consider_v this_o will_v alter_v his_o judgement_n and_o withal_o will_v know_v that_o remit_v that_o impediment_n anew_o which_o i_o have_v leave_v for_o less_o than_o three_o i_o alm_n towards_o the_o sea_n the_o water_n in_o the_o fen_n will_v return_v with_o the_o first_o flood_n and_o rain_n to_o the_o same_o height_n as_o before_o as_o likewise_o fiume_n morto_fw-la will_n do_v if_o it_o shall_v be_v let_v again_o into_o serchio_n here_o i_o entreat_v your_o honour_n to_o do_v i_o the_o favour_n to_o importune_v p._n francisco_n in_o my_o behalf_n that_o he_o will_v be_v please_v to_o declare_v my_o meaning_n in_o the_o aforesaid_a letter_n to_o sig._n bartolotti_n for_o i_o hope_v that_o if_o he_o will_v understand_v this_o point_n he_o will_v be_v no_o long_o so_o tenacious_a in_o his_o opinion_n next_o that_o these_o lord_n in_o the_o commission_n of_o sewer_n with_o the_o right_n honourable_a the_o marquesse_n of_o s._n angelo_n and_o your_o honour_n do_v approve_v of_o my_o judgement_n do_v very_o much_o rejoice_v i_o but_o because_o that_o i_o know_v that_o they_o do_v it_o not_o in_o design_n to_o compliment_v i_o but_o only_o to_o serve_v his_o highness_n our_o grand_a duke_n i_o free_o profess_v that_o i_o will_v pretend_v no_o far_o obligation_n from_o they_o therein_o than_o i_o account_v myself_o to_o owe_v to_o those_o who_o opinion_n be_v contrary_a to_o i_o for_o that_o i_o know_v that_o they_o have_v the_o same_o end_n the_o definitive_a sentence_n of_o this_o whole_a business_n be_v that_o they_o give_v these_o plain_n these_o drain_v and_o these_o water_n far_o fetch_v appellation_n 11._o as_o to_o the_o quantity_n of_o the_o water_n that_o fiume_n morto_fw-la discharge_v into_o the_o sea_n there_o be_v very_o great_a dispute_n about_o it_o and_o i_o have_v be_v present_a at_o some_o of_o they_o but_o let_v your_o honour_n believe_v i_o that_o as_o this_o be_v not_o continual_a but_o only_o during_o a_o few_o day_n so_o it_o will_v never_o be_v of_o any_o great_a prejudice_n to_o these_o field_n and_o if_o your_o lordship_n will_v be_v ascertain_v thereof_o you_o may_v please_v to_o go_v to_o fiume_n morto_fw-la at_o about_o a_o mile_n distance_n from_o the_o sea_n in_o the_o time_n of_o these_o strong_a wind_n and_o observe_v the_o current_n from_o thence_o upward_o for_o you_o shall_v find_v it_o extreme_a slow_a and_o consequent_o will_v know_v that_o the_o quantity_n of_o the_o water_n that_o be_v repulse_v be_v very_o small_a and_o this_o seem_v to_o be_v contradict_v by_o the_o rule_n of_o rise_n proceed_v from_o cause_n below_o which_o occasion_n no_o considerable_a alteration_n far_o from_o the_o sea_n i_o be_o necessitate_v to_o go_v to_o morrow_n out_o of_o rome_n with_o his_o eminence_n cardinal_n gaetano_n about_o certain_a affair_n touch_v water_n therefore_o
that_o my_o conjecture_n be_v ground_v upon_o reason_n and_o although_o i_o descend_v not_o to_o the_o exactness_n of_o particular_n i_o will_v open_v the_o way_n to_o other_o who_o have_v observe_v the_o requisite_a rule_n of_o consider_v the_o quantity_n of_o the_o water_n that_o be_v introduce_v or_o that_o happen_v to_o be_v divert_v shall_v be_v able_a with_o punctuality_n to_o examine_v the_o whole_a business_n and_o then_o resolve_v on_o that_o which_o shall_v be_v expedient_a to_o be_v do_v reflect_v therefore_o upon_o the_o first_o proposition_n that_o the_o rise_n of_o a_o run_v water_n make_v by_o the_o accession_n of_o new_a water_n into_o the_o river_n be_v to_o one_o another_o as_o the_o square-root_n of_o the_o quantity_n of_o the_o water_n that_o run_v and_o consequent_o that_o the_o same_o come_v to_o pass_v in_o the_o diversion_n insomuch_o that_o a_o river_n run_v in_o height_n one_o such_o a_o certain_a measure_n to_o make_v it_o increase_v double_a in_o height_n the_o water_n be_v to_o be_v increase_v to_o three_o time_n as_o much_o as_o it_o run_v before_o so_o that_o when_o the_o water_n shall_v be_v quadruple_a the_o height_n shall_v be_v double_a and_o if_o the_o water_n be_v centuple_a the_o height_n will_v be_v decuple_n only_o and_o so_o from_o one_o quantity_n to_o another_o and_o on_o the_o contrary_a in_o the_o diversion_n if_o of_o the_o 100_o part_n of_o water_n that_o run_v through_o a_o river_n there_o shall_v be_v divert_v 19_o 100_o the_o height_n of_o the_o river_n diminish_v only_o 1_o 10_o and_o continue_v to_o divert_v 17_o 100_o the_o height_n of_o the_o river_n abate_v likewise_o 1_o 10_o and_o so_o proceed_v to_o divert_v 15_o 100_o and_o then_o 13_o 100_o and_o then_o 11_o 100_o and_o then_o 9_o 100_o and_o then_o 7_o 100_o and_o then_o 5_o 100_o and_o then_o 3_o 100_o always_o by_o each_o of_o these_o diversion_n the_o height_n of_o the_o run_v water_n diminish_v the_o ten_o part_n although_o that_o the_o diversion_n be_v so_o unequal_a reflect_v i_o say_v upon_o this_o infallible_a truth_n i_o have_v have_v a_o conceit_n that_o though_o the_o reno_n and_o other_o river_n be_v divert_v from_o the_o valley_n and_o there_o be_v only_o leave_v the_o channel_n of_o navigation_n which_o be_v only_o the_o 1_o 20_o part_n of_o the_o whole_a water_n that_o fall_v into_o the_o valley_n yet_o nevertheless_o the_o water_n in_o those_o same_o valley_n will_v retain_v a_o ten_o part_n of_o that_o height_n that_o become_v conjoin_v by_o the_o concourse_n of_o all_o the_o river_n and_o therefore_o i_o shall_v think_v that_o it_o be_v the_o best_a resolution_n to_o maintain_v the_o channel_n of_o navigation_n if_o it_o be_v possible_a continuate_a unto_o the_o po_n of_o ferrara_n and_o from_o thence_o to_o carry_v it_o into_o the_o po_n of_o volano_n for_o beside_o that_o it_o will_v be_v of_o very_o great_a ease_n in_o the_o navigation_n of_o bologna_n and_o ferrara_n the_o say_a water_n will_v render_v the_o po_n of_o volano_n navigable_a as_o far_o as_o to_o the_o very_a wall_n of_o ferrara_n and_o consequent_o the_o navigation_n will_v be_v continuate_a from_o bologna_n to_o the_o seaside_n but_o to_o manage_v this_o enterprise_n well_o it_o be_v necessary_a to_o measure_v the_o quantity_n of_o the_o water_n that_o the_o river_n discharge_v into_o the_o valley_n and_o that_o which_o the_o channel_n of_o navigation_n carry_v in_o manner_n as_o i_o have_v demonstrate_v at_o the_o begin_n of_o this_o book_n for_o this_o once_o know_v we_o shall_v also_o come_v to_o know_v how_o profitable_a this_o diversion_n of_o the_o channel_n of_o navigation_n from_o the_o valley_n be_v like_a to_o prove_v which_o yet_o will_v still_o be_v unprofitable_a if_o so_o be_v that_o all_o the_o river_n that_o discharge_v their_o water_n into_o the_o valley_n shall_v not_o first_o be_v drain_v according_a to_o what_o have_v be_v above_o advertise_v abbot_n castelli_n in_o the_o present_a consideration_n refer_v himself_o to_o the_o relation_n of_o monsig_n corsini_n ground_v upon_o the_o observation_n and_o precept_n of_o the_o say_a abbot_n as_o be_v see_v in_o the_o present_a discourse_n i_o think_v it_o convenient_a for_o the_o complete_n of_o the_o work_n of_o our_o author_n upon_o these_o subject_n to_o insert_v it_o in_o this_o place_n a_o relation_n of_o the_o water_n in_o the_o territory_n of_o bologna_n and_o ferrara_n by_o the_o right_n honourable_a and_o illustrious_a monsignore_n corsini_n a_o native_a of_o tuscany_n superintendent_n of_o the_o general_n drain_v and_o precedent_n of_o romagna_n the_o rheno_n and_o other_o brook_n of_o romagna_n be_v by_o the_o advice_n of_o p._n agostino_n spernazzati_n the_o jesuit_n towards_o the_o latter_a end_n of_o the_o time_n of_o pope_n clement_n viii_o notwithstanding_o the_o opposition_n of_o the_o bolognesi_n and_o other_o concern_v therein_o divert_v from_o their_o channel_n for_o the_o more_o commodious_a cleanse_n of_o the_o po_n of_o ferrara_n and_o of_o its_o two_o branch_n of_o primaro_n and_o volano_n in_o order_n to_o the_o introduce_v the_o water_n of_o the_o main-po_n into_o they_o to_o the_o end_n that_o their_o wont_a torrent_n be_v restore_v they_o may_v carry_v the_o muddy-water_n thence_o into_o the_o sea_n and_o restore_v to_o the_o city_n the_o navigation_n which_o be_v last_o as_o be_v manifest_a by_o the_o brief_a of_o the_o say_a pope_n clement_n direct_v to_o the_o cardinal_n san_n clemence_n bear_v date_n the_o 22._o of_o august_n 1604._o the_o work_n of_o the_o say_v cleanse_v and_o introduce_v of_o the_o say_v po_n either_o as_o be_v such_o in_o itself_o or_o by_o the_o contention_n of_o the_o cardinal_n legate_n then_o in_o these_o part_n and_o the_o jarring_n that_o happen_v betwixt_o they_o prove_v so_o difficult_a that_o after_o the_o expense_n of_o vast_a sum_n in_o the_o space_n of_o 21._o year_n there_o have_v be_v nothing_o do_v save_o the_o render_n of_o it_o the_o more_o difficult_a to_o be_v effect_v interim_n the_o torrent_n with_o their_o water_n both_o muddy_a and_o clear_a have_v damage_v the_o ground_n lie_v on_o the_o right_a hand_n of_o the_o po_n of_o argenta_n and_o the_o rheno_n those_o on_o its_o bank_n of_o which_o i_o will_v speak_v in_o the_o first_o place_n as_o of_o that_o which_o be_v of_o great_a importance_n and_o from_o which_o the_o principal_a cause_n of_o the_o mischief_n that_o result_v from_o the_o rest_n do_v proceed_v this_o rheno_n have_v overflow_v the_o lordship_n tennency_n of_o sanmartina_n in_o circumference_n about_o fourteen_o mile_n give_v it_o before_o and_o part_n of_o that_o of_o cominale_n give_v it_o afterward_o as_o it_o be_v for_o a_o receptacle_n from_o whence_o have_v depose_v the_o matter_n of_o its_o muddiness_n it_o issue_v clear_a by_o the_o mouth_n of_o masi_fw-la and_o of_o lievaloro_n into_o the_o po_n of_o primaro_n and_o of_o volano_n do_v break_v down_o the_o encompass_v bank_n or_o dam_n towards_o s._n martino_n and_o that_o of_o its_o new_a channel_n on_o the_o right_a hand_n near_o to_o torre_n del_fw-it fondo_n by_o the_o breach_n on_o this_o side_n it_o stream_v out_o in_o great_a abundance_n from_o the_o upper_a part_n of_o cominale_n and_o in_o the_o part_n about_o raveda_n pioggio_n caprara_n ghiare_fw-it di_fw-it reno_n saint_n '_o agostino_n san_n prospero_n san_n vincenzo_n and_o other_o and_o make_v they_o to_o become_v incultivable_a it_o make_v also_o those_o place_n above_o but_o little_a fruitful_a by_o reason_n of_o the_o impediment_n that_o their_o drain_v receive_v find_v the_o conveyance_n call_v riolo_n and_o scorsuro_fw-la not_o only_o fill_v by_o la_fw-fr motta_n and_o la_fw-fr belletta_n but_o that_o they_o turn_v backward_o of_o themselves_o but_o by_o the_o mouth_n in_o the_o enclose_v bank_n or_o dam_n at_o borgo_n di_fw-mi s._n martino_n issue_v with_o violence_n it_o first_o give_v obstruction_n to_o the_o ancient_a navigation_n of_o la_fw-fr torre_n de_fw-fr la_fw-fr fossa_n and_o afterward_o to_o the_o modern_a of_o the_o mouth_n of_o masi_fw-la so_o that_o at_o present_a the_o commerce_n between_o bologna_n and_o ferrara_n be_v lose_v nor_o can_v it_o ever_o be_v in_o any_o durable_a way_n renew_v whilst_o that_o this_o exceed_v its_o due_a bound_n and_o what_o ever_o money_n shall_v be_v employ_v about_o the_o same_o shall_v be_v without_o any_o equivalent_a benefit_n and_o to_o the_o manifest_a and_o notable_a prejudice_n of_o the_o exchequer_n apostolic_a chamber_n thence_o pass_v into_o the_o valley_n of_o marzara_n it_o swell_v high_a not_o only_o by_o the_o rise_n of_o the_o water_n but_o by_o the_o raise_n of_o the_o bottom_n by_o reason_n of_o the_o matter_n sink_v thither_o after_o land-flood_n and_o dilate_v so_o that_o it_o cover_v all_o the_o meadow_n thereabouts_o nor_o do_v it_o receive_v with_o the_o wont_a
facility_n the_o drain_v of_o the_o upper_a ground_n of_o which_o the_o next_o unto_o it_o lie_v under_o the_o water_n that_o return_v upward_o by_o the_o conveyance_n and_o the_o more_o remote_a not_o find_v a_o passage_n for_o rain-water_n that_o settle_v become_v either_o altogether_o unprofitable_a or_o little_a better_a from_o this_o valley_n by_o the_o trench_n or_o ditch_n of_o marzara_n or_o of_o la_fw-fr duca_n by_o la_fw-fr buova_n or_o mouth_n of_o castaldo_n de_fw-fr rossi_n and_o by_o the_o new_a passage_n it_o fall_v into_o the_o po_n of_o argenta_n which_o be_v to_o receive_v it_o clear_a that_o so_o it_o may_v sink_v far_o therein_o and_o receive_v it_o muddy_a because_o it_o have_v acquire_v a_o quick_a course_n there_o will_v arise_v a_o very_a contrary_a effect_n here_o therefore_o the_o superficies_n of_o the_o water_n keep_v high_a until_o it_o come_v to_o the_o sea_n hinder_v the_o valley_n of_o ravenna_n where_o the_o river_n senio_fw-la those_o of_o san_n bernardino_n where_fw-mi santerno_fw-la be_v turn_v those_o of_o buon_n '_o acquisto_fw-la and_o those_o of_o marmorto_n where_o the_o idice_n quaderna_n sellero_n fall_v in_o from_o swallow_v and_o take_v in_o their_o water_n by_o their_o usual_a inlets_a yet_o many_o time_n as_o i_o myself_o have_v see_v in_o the_o visitation_n they_o drink_v they_o up_o plentiful_o whereupon_o be_v conjoin_v with_o the_o muddinesse_n of_o those_o river_n that_o fall_v into_o the_o same_o they_o swell_v and_o dilate_v and_o overflow_v some_o ground_n and_o deprive_v other_o of_o their_o drain_v in_o like_a manner_n as_o have_v be_v say_v of_o that_o of_o marrara_n insomuch_o that_o from_o the_o point_n of_o s._n giorgio_n as_o far_o as_o s._n alberto_n all_o those_o that_o be_v between_o the_o valley_n and_o po_n be_v spoil_v of_o those_o that_o be_v between_o valley_n and_o valley_n many_o be_v in_o a_o very_a bad_a condition_n and_o those_o that_o be_v some_o considerable_a space_n above_o not_o 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thence_o redound_v to_o this_o city_n and_o that_o go_v by_o torre_n deal_v fondo_n through_o sanmartina_n to_o the_o mouth_n de_fw-fr masi_fw-la by_o the_o chapel_n of_o vigarano_n unto_o the_o sea_n it_o be_v by_o this_o way_n 70._o mile_n nor_o be_v the_o fall_v great_a than_o 26._o 5._o 6._o foot_n so_o that_o it_o will_v come_v to_o fall_v but_o 4._o inch_n &_o a_o half_a or_o thereabouts_o in_o a_o mile_n whereas_o the_o common_a opinion_n of_o the_o skilful_a to_o the_o end_n that_o the_o torrent_n may_v not_o depose_v their_o sand_n that_o they_o bring_v with_o they_o in_o land-flood_n require_v the_o twenty_o four_o part_n of_o the_o hundred_o part_n of_o their_o whole_a length_n which_o in_o our_o case_n account_v according_a to_o the_o measure_n of_o these_o place_n be_v 16._o inch_n a_o we_o mile_n whereupon_o the_o sink_n of_o the_o mud_n and_o sand_n will_v most_o certain_o follow_v and_o so_o a_o immense_a heighten_v of_o the_o line_n of_o the_o bottom_n and_o 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who_o at_o present_a receive_v damage_n by_o it_o can_v endure_v to_o hear_v thereof_o the_o reason_n that_o induce_v these_o last_o name_v to_o be_v so_o averse_a thereto_o be_v either_o because_o that_o this_o undertake_n will_v render_v the_o introduction_n of_o the_o water_n of_o main-po_n more_o difficult_a or_o because_o they_o fear_v the_o danger_n thereof_o the_o other_o decline_v the_o project_n either_o for_o that_o they_o know_v that_o reno_n can_v long_o continue_v in_o that_o course_n or_o because_o they_o fear_v that_o it_o be_v too_o much_o expose_v to_o those_o man_n revengeful_a cutting_n of_o it_o who_o do_v not_o desire_v it_o shall_v and_o if_o a_o man_n have_v any_o other_o way_n he_o ought_v in_o my_o opinion_n to_o forbear_v that_o
which_o to_o such_o as_o stand_v in_o need_n of_o its_o removal_n be_v less_o satisfactory_a and_o to_o such_o as_o oppose_v it_o more_o prejudicial_a to_o conclude_v i_o exceed_o honour_v the_o judgement_n of_o cardinal_n capponi_n who_o have_v to_o his_o natural_a ability_n and_o prudence_n add_v a_o particular_a study_n observation_n and_o experience_n of_o these_o water_n for_o the_o space_n of_o three_o year_n together_o do_v not_o think_v that_o reno_n can_v go_v by_o volana_n to_o which_o agree_v the_o opinion_n of_o cardinal_n s._n marcello_n legate_n of_o this_o city_n of_o who_o for_o his_o exquisite_a understanding_n we_o ought_v to_o make_v great_a account_n but_o if_o ever_o this_o shall_v be_v resolve_v on_o it_o will_v be_v material_o necessary_a to_o unite_v the_o quick_a and_o run_v water_n of_o the_o little_a channel_n of_o cento_n of_o the_o channel_n navilio_n of_o guazzaloca_n and_o at_o its_o very_a beginning_n those_o of_o dardagna_n which_o at_o present_a be_v one_o of_o the_o spring_n or_o head_n of_o panaro_n that_o so_o they_o may_v assist_v it_o in_o carry_v its_o sand_n and_o the_o matter_n of_o its_o muddiness_n into_o the_o sea_n and_o then_o there_o will_v not_o fail_v to_o be_v a_o great_a evacuation_n and_o scour_a but_o withal_o the_o proprietor_n in_o the_o islet_n of_o san_n giorgio_n and_o of_o ferrara_n must_v prepare_v themselves_o to_o endure_v the_o inconvenience_n of_o purl_n or_o sewing_n of_o the_o water_n from_o the_o river_n through_o the_o boggy_a ground_n thereabouts_o i_o shall_v more_o easy_o incline_v therefore_o to_o carry_v it_o into_o main-po_n at_o stellata_fw-la for_o the_o reason_n that_o cardinal_n capponi_n most_o ingenious_o enumerate_v in_o a_o short_a but_o well-grounded_n tract_n of_o his_o not_o because_o that_o indeed_o it_o will_v not_o both_o by_o purl_n and_o by_o breach_n occasion_n some_o inconvenience_n especial_o in_o the_o beginning_n but_o because_o i_o hold_v this_o for_o the_o incomodity_n of_o it_o to_o be_v a_o far_o less_o evil_a than_o any_o of_o the_o rest_n and_o because_o that_o by_o this_o mean_n there_o be_v no_o occasion_n give_v to_o they_o of_o ferrara_n to_o explain_v that_o they_o be_v deprive_v of_o the_o hope_n of_o ever_o see_v the_o po_n again_o under_o the_o wall_n of_o their_o city_n to_o who_o where_o it_o may_v be_v do_v it_o be_v but_o reason_n that_o satisfaction_n shall_v be_v give_v it_o be_v certain_a that_o po_n be_v place_v by_o nature_n in_o the_o midst_n of_o this_o great_a valley_n make_v by_o the_o apennine_n hill_n and_o by_o the_o alps_o to_o carry_v as_o the_o master-drain_n to_o the_o sea_n that_o be_v the_o grand_a receptacle_n of_o all_o water_n those_o particular_a stream_n which_o descend_v from_o they_o that_o the_o reno_n by_o all_o geographer_n strabo_n pliny_n solima_n mella_n and_o other_o be_v enumerate_v among_o the_o river_n that_o fall_v into_o the_o say_v po._n that_o although_o po_n shall_v of_o itself_o change_v its_o course_n yet_o will_v reno_n go_v to_o look_v it_o out_o if_o the_o work_v erect_v by_o humane_a industry_n do_v not_o obstruct_v its_o passage_n so_o that_o it_o neither_o be_v nor_o aught_o to_o seem_v strange_a if_o one_o for_o the_o great_a common_n good_a shall_v turn_v it_o into_o the_o same_o now_o at_o stellata_fw-la it_o may_v go_v several_a way_n into_o po_n as_o appear_v by_o the_o level_v that_o be_v take_v by_o my_o order_n of_o all_o which_o i_o shall_v best_o like_v the_o turn_n of_o it_o to_o la_fw-fr botta_n do_v ghislieri_n carry_v it_o above_o bondeno_n to_o the_o church_n of_o gambarone_fw-la or_o a_o little_a high_o or_o low_o as_o shall_v be_v judge_v least_o prejudicial_a when_o it_o come_v to_o the_o execution_n and_o this_o for_o two_o principal_a reason_n the_o one_o because_o that_o then_o it_o will_v run_v along_o by_o the_o confine_n of_o the_o church_n p_o trimony_n without_o separate_a ferrara_n from_o the_o rest_n of_o it_o the_o other_o be_v because_o the_o line_n be_v short_a and_o consequent_o the_o fall_n great_a for_o that_o in_o a_o space_n of_o ten_o mile_n and_o one_o three_o it_o fall_v twenty_o six_o foot_n more_o by_o much_o than_o be_v require_v by_o artist_n and_o will_v go_v by_o place_n where_o it_o can_v do_v but_o little_a hurt_n notwithstanding_o that_o the_o person_n interress_v study_n to_o amplify_v it_o incredible_o on_o the_o contrary_a there_o be_v but_o only_o two_o objection_n that_o be_v worthy_a to_o be_v examine_v one_o that_o the_o drain_v and_o ditch_n of_o s._n bianca_n of_o the_o channel_n of_o cento_n and_o of_o burana_n and_o all_o those_o other_o that_o enter_v into_o po_n do_v hinder_v this_o diversion_n of_o reno_n by_o the_o increase_n of_o the_o water_n in_o the_o po._n the_o other_o be_v that_o po_n rise_v about_o the_o transom_n of_o the_o pilaster-sluice_n very_o near_o 20_o foot_n the_o reno_n will_v have_v no_o fall_n into_o the_o same_o whereupon_o it_o will_v rise_v to_o a_o terrible_a height_n at_o which_o it_o will_v not_o be_v possible_a to_o make_v or_o keep_v the_o bank_n make_v so_o that_o it_o will_v break_v out_o and_o drown_v the_o meadow_n and_o cause_n mischief_n and_o damage_n unspeakable_a and_o irreparable_a as_o be_v evident_a by_o the_o experiment_n make_v upon_o panaro_n which_o be_v confine_v between_o bank_n that_o it_o may_v go_v into_o po_n this_o not_o be_v neither_o in_o its_o great_a excrescense_n it_o break_v out_o into_o the_o territory_n of_o final_a and_o of_o ferrara_n and_o though_o that_o may_v be_v do_v it_o will_v thereupon_o ensue_v that_o there_o be_v let_v into_o the_o channel_n of_o po_n 2800._o square_a foot_n of_o water_n for_o so_o much_o we_o account_v those_o of_o reno_n and_o panaro_n take_v together_o in_o their_o great_a height_n the_o superficies_n of_o it_o will_v rise_v at_o least_o four_o foot_n insomuch_o that_o either_o it_o will_v be_v requisite_a to_o raise_v its_o bank_n all_o the_o way_n unto_o the_o sea_n to_o the_o same_o height_n which_o the_o treasure_n of_o the_o indies_n will_v not_o suffice_v to_o effect_v or_o else_o there_o will_v be_v a_o necessity_n of_o endure_v excessive_a breach_n to_o these_o two_o head_n be_v the_o argument_n reduce_v which_o be_v large_o amplify_v against_o our_o opinion_n and_o i_o shall_v answer_v first_o to_o the_o last_o as_o most_o material_a i_o say_v therefore_o that_o there_o be_v three_o case_n to_o be_v consider_v first_o po_n high_a and_o reno_n low_a second_o reno_n high_a and_o po_n low_a three_o reno_n and_o po_n both_o high_a together_o as_o to_o the_o first_o and_o second_o there_o be_v no_o difficulty_n in_o they_o for_o if_o po_n shall_v not_o be_v at_o its_o great_a height_n reno_n shall_v ever_o have_v a_o fall_n into_o it_o and_o there_o shall_v need_v no_o humane_a artifice_n about_o the_o bank_n and_o if_o reno_n shall_v be_v low_a po_n shall_v regurgitate_v and_o flow_v up_o into_o the_o channel_n of_o it_o and_o also_o from_o thence_o no_o inconvenience_n shall_v follow_v the_o three_o remain_v from_o which_o there_o be_v expect_v many_o mischief_n but_o it_o be_v a_o most_o undoubted_a truth_n that_o the_o excrescency_n of_o reno_n as_o come_v from_o the_o adjacent_a appennines_n and_o rains_n be_v to_o continue_v but_o seven_o or_o eight_o hour_n at_o most_o and_o so_o will_v never_o or_o very_o rare_o happen_v to_o be_v at_o the_o same_o time_n with_o those_o of_o po_n cause_v by_o the_o melt_a of_o the_o snow_n of_o the_o alps_o at_o least_o 400._o mile_n distance_n from_o thence_o but_o because_o it_o sometime_o may_v happen_v i_o reply_v that_o when_o it_o come_v to_o pass_v reno_n shall_v not_o go_v into_o po_n but_o it_o shall_v have_v allow_v it_o one_o or_o two_o vent_v namely_o into_o the_o channel_n of_o ferrara_n as_o it_o have_v ever_o have_v and_o into_o sanmartina_n where_o it_o run_v at_o present_a and_o wherewith_o there_o be_v no_o doubt_n but_o that_o the_o person_n concern_v will_v be_v well_o please_v it_o be_v a_o great_a benefit_n to_o they_o to_o have_v the_o water_n overflow_v their_o ground_n once_o every_o four_o or_o five_o year_n instead_o of_o see_v it_o annoy_v they_o continual_o yea_o the_o vent_n may_v be_v regulate_v reserve_v for_o it_o the_o channel_n in_o which_o reno_n at_o present_a run_v and_o instead_o of_o turn_v it_o by_o a_o dam_n at_o la_fw-fr betta_n de_fw-fr ghislieri_n perhaps_o to_o turn_v it_o by_o help_n of_o strong_a sluice_n that_o may_v upon_o all_o occasion_n be_v open_v and_o shut_v and_o for_o my_o part_n i_o do_v not_o question_v but_o that_o the_o proprietor_n themselves_o in_o sanmartina_n will_v make_v a_o channel_n for_o it_o which_o receive_v and_o confine_v it_o in_o the_o time_n of_o the_o vent_v may_v carry_v the_o
sand_n into_o the_o po_n of_o primaro_n nor_o need_v there_o thence_o be_v fear_v any_o stoppage_n by_o mud_n and_o sand_n since_o that_o it_o be_v suppose_v that_o there_o will_v but_o very_o seldom_o be_v any_o necessity_n of_o use_v it_o so_o that_o time_n will_v be_v allow_v upon_o occasion_n to_o scour_v and_o cleanse_v it_o and_o in_o this_o manner_n all_o those_o prodigy_n vanish_v that_o be_v raise_v with_o so_o much_o fear_n from_o the_o entrance_n of_o the_o water_n of_o reno_n swell_v into_o po_n when_o it_o be_v high_a to_o which_o there_o need_v no_o other_o answer_n yet_o nevertheless_o we_o do_v not_o take_v that_o quantity_n of_o water_n that_o be_v carry_v by_o reno_n and_o by_o panaro_n to_o be_v so_o great_a as_o be_v affirm_v for_o that_o p._n d._n benedetto_n castelli_n have_v no_o less_o accute_o than_o accurate_o observe_v the_o measure_n of_o this_o kind_n note_v that_o the_o breadth_n and_o depth_n of_o a_o river_n be_v not_o enough_o to_o resolve_v the_o question_n true_o but_o that_o there_o be_v respect_n to_o be_v have_v to_o the_o velocity_n of_o the_o water_n and_o the_o term_n of_o time_n thing_n hitherto_o not_o consider_v by_o the_o skilful_a in_o these_o affair_n and_o therefore_o they_o be_v not_o able_a to_o say_v what_o quantity_n of_o water_n the_o say_v river_n carry_v nor_o to_o conclude_v of_o the_o rise_n that_o will_v follow_v thereupon_o nay_o it_o be_v most_o certain_a that_o if_o all_o the_o river_n that_o fall_v into_o po_n which_o be_v above_o thirty_o shall_v rise_v at_o the_o rate_n that_o these_o compute_v reno_n to_o do_v a_o hundred_o foot_n of_o bank_n will_v not_o suffice_v and_o yet_o they_o have_v far_o few_o so_o that_o this_o confirm_v the_o rule_n of_o r._n p._n d._n benedetto_n namely_o that_o the_o proportion_n of_o the_o height_n of_o the_o water_n of_o reno_n in_o reno_n to_o the_o height_n of_o the_o water_n of_o reno_n in_o po_n be_v compound_v of_o the_o proportion_n of_o the_o breadth_n of_o the_o channel_n of_o po_n to_o that_o of_o reno_n and_o of_o the_o velocity_n of_o the_o water_n of_o reno_n in_o po_n to_o the_o velccity_n of_o the_o water_n of_o reno_n in_o reno_n a_o manifest_a argument_n that_o there_o can_v in_o it_o by_o this_o new_a augmentation_n of_o water_n follow_v any_o alteration_n that_o necessitate_v the_o raise_n of_o its_o bank_n as_o appear_v by_o the_o example_n of_o panaro_n which_o have_v be_v so_o far_o from_o swell_a po_n that_o it_o have_v rather_o assuage_v it_o for_o it_o have_v carry_v away_o many_o shelf_n and_o many_o islet_n that_o have_v grow_v in_o its_o bed_n for_o want_v of_o water_n sufficient_a to_o bear_v away_o the_o matter_n of_o land-flood_n in_o so_o broad_a a_o channel_n and_o as_o be_v learn_v by_o the_o trial_n make_v by_o we_o in_o panaro_n with_o the_o water_n of_o burana_n for_o erect_v in_o the_o river_n stand_v mark_n and_o shut_v the_o say_a sluice_n we_o can_v see_v no_o sensible_a abatement_n nor_o much_o less_o after_o we_o have_v open_v it_o sensible_a increasment_n by_o which_o we_o judge_v that_o the_o same_o be_v to_o succeed_v to_o po_n by_o let_v in_o of_o reno_n burana_n have_v great_a proportion_n to_o panaro_n than_o reno_n to_o po_n consider_v the_o state_n of_o those_o river_n in_o which_o the_o observation_n be_v make_v so_o that_o there_o be_v no_o long_o any_o occasion_n for_o those_o great_a raising_n of_o bank_n and_o the_o danger_n of_o the_o rupture_n as_o well_o of_o reno_n as_o of_o po_n do_v vanish_v as_o also_o the_o fear_n lest_o that_o the_o sluice_n which_o empty_a into_o po_n shall_v receive_v obstruction_n which_o if_o they_o shall_v yet_o it_o will_v be_v over_o in_o a_o few_o hour_n and_o as_o to_o the_o breach_n of_o panaro_n which_o happen_v in_o 1623._o i_o know_v not_o why_o see_v that_o it_o be_v confess_v that_o the_o po_n be_v not_o at_o that_o time_n at_o its_o height_n one_o shall_v rather_o charge_v it_o with_o the_o crime_n than_o quit_v it_o thereof_o the_o truth_n be_v that_o the_o bank_n be_v not_o make_v of_o proof_n since_o that_o the_o same_o now_o continue_v whole_a and_o good_a and_o panaro_n do_v not_o break_v out_o nay_o there_o be_v when_o it_o break_v more_o than_o a_o foot_n and_o half_a of_o its_o bank_n above_o the_o water_n and_o to_o spare_v but_o it_o break_v thorough_a by_o a_o mole_n work_v or_o by_o the_o hole_n of_o a_o water-rat_n or_o some_o such_o vermin_n and_o by_o occasion_n of_o the_o badness_n of_o the_o say_a bank_n as_o i_o find_v by_o the_o testimony_n of_o some_o witness_n examine_v by_o my_o command_n that_o i_o may_v know_v the_o truth_n thereof_o nor_o can_v i_o here_o forbear_v to_o say_v that_o it_o will_v be_v better_o if_o in_o such_o matter_n man_n be_v more_o candid_a and_o sincere_a but_o to_o secure_v ourselves_o nevertheless_o to_o the_o utmost_a of_o our_o power_n from_o such_o like_a breach_n which_o may_v happen_v at_o the_o first_o by_o reason_n of_o the_o newness_n of_o the_o bank_n i_o presuppose_v that_o from_o po_n unto_o the_o place_n whence_o reno_n be_v cut_v there_o ought_v to_o be_v a_o high_a and_o thick_a fence_n make_v with_o its_o bank_n so_o that_o there_o will_v be_v no_o cause_n to_o fear_v any_o whatsoever_o accession_n of_o water_n although_o that_o concurrence_n of_o three_o river_n which_o be_v by_o some_o more_o ingenious_o aggravate_v than_o faithful_o state_v by_o that_o which_o be_v say_v above_o be_v true_a to_o who_o i_o think_v not_o myself_o bind_v to_o make_v any_o far_a reply_n neither_o to_o those_o who_o say_v that_o po_n will_v ascend_v upward_o into_o reno_n since_o that_o these_o be_v the_o same_o person_n who_o will_v introduce_v a_o small_a branch_n of_o the_o say_v po_n into_o the_o channel_n of_o ferrara_n that_o so_o it_o may_v convey_v to_o the_o sea_n not_o reno_n only_o but_o also_o all_o the_o other_o brook_n of_o which_o we_o complain_v and_o because_o that_o withal_o it_o be_v impossible_a that_o a_o river_n so_o capacious_a as_o po_n shall_v be_v incommode_v by_o a_o torrent_n that_o as_o i_o may_v say_v have_v no_o proportion_n to_o it_o i_o come_v now_o to_o the_o business_n of_o the_o ditch_n and_o drain_v and_o as_o to_o the_o conveyance_n of_o burana_n it_o have_v heretofore_o be_v debate_v to_o turn_v it_o into_o main-po_n so_o that_o in_o this_o case_n it_o will_v receive_v no_o harm_n and_o though_o it_o be_v not_o remove_v yet_o will_v it_o by_o a_o trench_n under_o ground_n pursue_v the_o course_n that_o it_o now_o hold_v and_o also_o will_v be_v able_a to_o disimbogue_a again_o into_o the_o say_a new_a channel_n of_o reno_n which_o conform_v to_o the_o superficies_n of_o the_o water_n of_o po_n will_v continue_v at_o a_o low_a level_n than_o that_o which_o panara_n have_v when_o it_o come_v to_o ferrara_n into_o which_o burana_n do_v nevertheless_o empty_a itself_o for_o some_o time_n the_o conveyance_n or_o drain_n of_o santa_n bianca_n and_o the_o little_a channel_n of_o cento_n 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that_o occasion_n apply_v my_o whole_a study_n to_o my_o service_n and_o duty_n i_o publish_v in_o that_o treatise_n some_o particular_n till_o than_o not_o right_o understand_v and_o consider_v that_o i_o know_v by_o any_o one_o although_o they_o be_v in_o themselves_o most_o important_a and_o of_o extraordinary_a consequence_n yet_o i_o must_v render_v thanks_o to_o your_o lordship_n for_o the_o honour_n you_o have_v do_v to_o that_o my_o tract_n but_o wish_v withal_o that_o your_o esteem_n of_o it_o may_v not_o prejudice_v the_o universal_a esteem_n that_o the_o world_n have_v of_o your_o honour_n most_o refine_a judgement_n as_o to_o that_o point_n which_o i_o touch_v upon_o in_o the_o conclusion_n namely_o that_o the_o consideration_n of_o the_o velocity_n of_o run_v water_n supply_v the_o consideration_n of_o the_o misprint_v length_n omit_v in_o the_o common_a way_n of_o measure_v run_v water_n your_o lordship_n have_v command_v i_o that_o in_o favour_n of_o practice_n and_o 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themselves_o master_n some_o of_o one_o some_o of_o two_o and_o some_o of_o more_o end_n of_o those_o piece_n of_o stuff_n and_o in_o particular_a there_o be_v cetain_v ingenuous_a machine_n place_v in_o the_o more_o secret_a place_n of_o the_o cave_n with_o which_o at_o the_o pleasure_n of_o the_o guard_n they_o do_v retard_v the_o velocity_n of_o those_o stuff_n in_o their_o issue_v out_o of_o the_o cave_n insomuch_o that_o he_o who_o ought_v to_o have_v have_v 100_o ell_n of_o stuff_n in_o a_o day_n have_v not_o above_o 50_o and_o he_o who_o shall_v have_v have_v 400_o enjoy_v the_o benefit_n of_o 50._o only_a and_o so_o all_o the_o rest_n be_v defraud_v of_o their_o right_n the_o surplusage_n be_v sell_v appropriate_v and_o share_v at_o the_o will_n of_o the_o corrupt_a officer_n so_o that_o the_o business_n be_v without_o all_o order_n or_o justice_n insomuch_o that_o the_o goddess_n arachne_n be_v displease_v at_o those_o people_n deprive_v every_o one_o of_o their_o benefit_n 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purpose_n and_o occasion_n so_o that_o we_o shall_v thereby_o be_v able_a to_o know_v how_o many_o quart_n of_o water_n a_o aqueduct_v will_v discharge_v in_o a_o give_v time_n of_o hour_n month_n or_o year_n and_o in_o this_o manner_n we_o may_v constitute_v a_o cock_n that_o shall_v discharge_v a_o certain_a and_o determinate_a quantity_n of_o water_n in_o a_o time_n give_v and_o because_o daily_a experience_n show_v we_o that_o the_o spring_n of_o aqueduct_n do_v not_o maintain_v they_o always_o equal_o high_a and_o full_a of_o water_n but_o that_o sometime_o they_o increase_v and_o sometime_o decrease_v which_o accident_n may_v possible_o procure_v some_o difficulty_n in_o our_o distribution_n therefore_o to_o the_o end_n that_o all_o manner_n of_o scruple_n may_v be_v remove_v i_o conceive_v that_o it_o will_v be_v convenient_a to_o provide_v a_o cistern_n according_a to_o the_o occasion_n into_o which_o there_o may_v always_o fall_v one_o certain_a quantity_n of_o water_n which_o shall_v not_o be_v great_a than_o that_o which_o the_o principal_a pipe_n discharge_v in_o time_n of_o drought_n when_o the_o spring_n be_v bare_a of_o water_n that_o so_o in_o this_o cistern_n the_o water_n may_v always_o keep_v at_o one_o constant_a height_n then_o to_o the_o cistern_n so_o prepare_v we_o be_v to_o fasten_v the_o cock_n of_o particular_a person_n to_o who_o the_o water_n be_v sell_v by_o the_o reverend_a apostolic_a chamber_n according_a to_o what_o have_v be_v observe_v before_o and_o that_o quantity_n of_o water_n which_o remain_v over_o and_o above_o be_v to_o be_v discharge_v into_o another_o cistern_n in_o which_o the_o cock_n of_o the_o water_n for_o public_a service_n and_o of_o those_o which_o people_n buy_v upon_o particular_a occasion_n be_v to_o be_v place_v and_o when_o the_o business_n shall_v have_v be_v bring_v to_o this_o pass_n there_o will_v likewise_o a_o remedy_n be_v find_v to_o the_o so_o many_o disorder_n that_o continual_o happen_v of_o which_o for_o brevity_n sake_n i_o will_v instance_n in_o but_o four_o only_a which_o concern_v both_o public_a and_o private_a benefit_n as_o be_v in_o my_o judgement_n the_o most_o enormous_a and_o intolerable_a the_o first_o inconvenience_n it_o that_o in_o the_o common_a way_n of_o measure_v dispense_n and_o sell_v the_o water_n of_o aqueduct_n it_o be_v not_o understand_v neither_o by_o the_o buyer_n nor_o seller_n what_o the_o quantity_n true_o be_v that_o be_v buy_v and_o sell_v nor_o can_v i_o ever_o meet_v with_o any_o either_o engineer_n or_o architect_n or_o artist_n or_o other_o that_o be_v able_a to_o decipher_v to_o i_o what_o one_o or_o two_o or_o ten_o inch_n of_o water_n be_v but_o by_o our_o above_o declare_a rule_n for_o dispense_n the_o water_n of_o aqueduct_n we_o may_v very_o easy_o know_v the_o true_a quantity_n of_o water_n that_o be_v buy_v or_o sell_v as_o that_o it_o be_v so_o many_o tun_n a_o hour_n so_o many_o a_o day_n so_o many_o in_o a_o year_n etc._n etc._n the_o second_o disorder_n that_o happen_v at_o present_a in_o the_o distribution_n of_o aqueduct_n be_v that_o as_o the_o business_n be_v now_o govern_v it_o lie_v in_o the_o power_n of_o a_o sordid_a mason_n to_o take_v unjust_o from_o one_o and_o give_v undeserved_o to_o another_o more_o or_o less_o water_n than_o belong_v to_o they_o of_o right_a and_o i_o have_v see_v it_o do_v of_o my_o own_o experience_n but_o in_o our_o way_n of_o measure_v and_o distribute_v water_n there_o can_v no_o fraud_n be_v commit_v and_o put_v the_o case_n that_o they_o shall_v be_v commit_v it_o be_v a_o easy_a matter_n to_o know_v it_o and_o amend_v it_o by_o repair_v to_o the_o tribunal_n appoint_v three_o it_o happen_v very_o often_o and_o we_o have_v example_n thereof_o both_o ancient_a and_o modern_a
that_o in_o dispense_n the_o water_n after_o the_o common_a and_o vulgar_a way_n there_o be_v sometime_o more_o water_n dispend_v than_o there_o be_v in_o the_o register_n in_o which_o there_o will_v be_v register_v as_o they_o say_v two_o hundred_o inch_n for_o example_n and_o there_o will_v be_v dispense_v two_o hundred_o and_o fifty_o inch_n or_o more_o which_o passage_n happen_v in_o the_o time_n of_o nerva_n the_o emperor_n as_o giulio_n frontino_n write_v in_o his_o 2._o book_n de_fw-fr aquaductibus_fw-la vrbis_fw-la romae_fw-la where_o he_o observe_v that_o they_o have_v in_o commentariis_fw-la 12755._o quinary_n of_o water_n and_o find_v that_o they_o dispense_v 14018._o quinary_n and_o the_o like_a error_n have_v continue_v and_o be_v in_o use_n also_o modern_o until_o our_o time_n but_o if_o our_o rule_n shall_v be_v observe_v we_o shall_v incur_v no_o such_o disorder_n nay_o there_o will_v always_o be_v give_v to_o every_o one_o his_o share_n according_a to_o the_o holy_a end_n of_o exact_a justice_n which_o that_o unicuique_fw-la quod_fw-la suum_fw-la est_fw-la as_o on_o the_o contrary_a it_o be_v manifest_a that_o his_o divine_a majesty_n hate_v and_o abominate_v pondus_fw-la &_o pondus_fw-la mensura_fw-la &_o mensura_fw-la as_o the_o holy_a ghost_n speak_v by_o the_o mouth_n of_o solomon_n in_o the_o proverb_n chap._n 20._o pondus_fw-la &_o pondus_fw-la mensura_fw-la &_o mensura_fw-la utrumque_fw-la abominabile_fw-la est_fw-la apud_fw-la deum_fw-la and_o therefore_o who_o be_v it_o that_o see_v not_o that_o the_o way_n of_o divide_v and_o measure_v of_o water_n common_o use_v be_v express_o against_o the_o law_n of_o god_n since_o that_o thereby_o the_o same_o measure_n be_v make_v sometime_o great_a and_o sometime_o lesser_a a_o disorder_n so_o enormous_a and_o execrable_a that_o i_o shall_v take_v the_o boldness_n to_o say_v that_o for_o this_o sole_a respect_n it_o ought_v to_o be_v condemn_v and_o prohibit_v likewise_o by_o human_a law_n which_o shall_v enact_v that_o in_o this_o business_n there_o shall_v be_v employ_v either_o this_o our_o rule_n or_o some_o other_o that_o be_v more_o exquisite_a and_o practicable_a whereby_o the_o measure_n may_v keep_v one_o constant_a and_o determinate_a tenor_n as_o we_o make_v it_o and_o not_o as_o it_o be_v now_o to_o make_v pondus_fw-la &_o pondus_fw-la mensura_fw-la &_o mensura_fw-la and_o this_o be_v all_o that_o i_o have_v to_o offer_v to_o your_o most_o illustrious_a lordship_n in_o obedience_n to_o your_o command_n reserve_v to_o myself_o the_o give_v of_o a_o more_o exact_a account_n of_o this_o my_o invention_n when_o the_o occasion_n shall_v offer_v of_o reduce_v to_o practice_n so_o holy_a just_a and_o necessary_a a_o reformation_n of_o the_o measure_n of_o run_v water_n and_o of_o aqueduct_n in_o particular_a which_o rule_n may_v also_o be_v of_o great_a benefit_n in_o the_o division_n of_o the_o great_a water_n to_o overflow_n ground_n and_o for_o other_o use_n i_o humble_o bow_v your_o most_o devote_a and_o most_o oblige_a servant_n d._n benedetto_n castelli_n abb._n casin_n finis_fw-la a_o table_n of_o the_o most_o observable_a matter_n in_o this_o treatise_n of_o the_o mensuration_n of_o run_v water_n a_o a_o batement_n of_o a_o river_n in_o different_a and_o unequal_a diversion_n be_v always_o equal_a which_o be_v prove_v with_o 100_o syphon_n page_n 75_o arno_n river_n when_o it_o rise_v upon_o a_o land-flood_n near_o the_o sea_n one_o three_o of_o a_o brace_n it_o rise_v about_o pisa_n 6._o or_o 7._o brace_n 82_o b_o banks_n near_o to_o the_o sea_n low_o than_o far_o from_o thence_o corollary_n fourteen_o 16_o brent_n river_n divert_v from_o the_o lake_n of_o venice_n and_o its_o effect_n 64_o brent_n suppose_v insufficient_a to_o remedy_v the_o inconvenience_n of_o the_o lake_n and_o the_o falsity_n of_o that_o supposition_n 67_o brent_n and_o its_o benefit_n in_o the_o lake_n 70_o its_o deposition_n of_o sand_n in_o the_o lake_n how_o great_a it_o be_v 78_o 79_o bridge_n over_o river_n and_o how_o they_o be_v to_o be_v make_v appendix_n viii_o 20_o burana_n river_n its_o rise_n and_o fall_v in_o panaro_n 110_o c_o castelli_n apply_v himself_o to_o this_o study_n by_o order_n of_o urban_n viii_o 2_o channel_n of_o navigation_n in_o the_o valley_n of_o bologna_n and_o its_o inconvenience_n 99_o carry_v into_o the_o po_n of_o ferrara_n and_o its_o benefit_n ibid._n ciampoli_n a_o lover_n of_o those_o observation_n of_o water_n 3_o d_o difficulty_n of_o this_o business_n of_o measure_v water_n 2_o disorder_n that_o happen_v in_o the_o distribution_n of_o the_o water_n of_o aqueduct_n and_o their_o remedy_n 113_o distribution_n of_o the_o water_n of_o fountain_n and_o aqueduct_n appendix_n x._o 22_o distribution_n of_o water_n to_o overflow_n ground_n appendix_n xi_o 23_o 69_o 70_o diversion_n of_o reno_n and_o other_o brook_n of_o romagna_n advise_v by_o p._n spernazzati_n to_o what_o end_n it_o be_v 100_o drain_v and_o ditch_n the_o benefit_n they_o receive_v by_o cut_v away_o the_o weed_n and_o reed_n appendix_n ix_o 21_o drain_v and_o sewer_n obstruct_v in_o the_o diversion_n of_o reno_n into_o main_a po_n and_o a_o remedy_n for_o the_o same_o 110_o e_z engineer_n unversed_a in_o the_o matter_n of_o water_n 2_o erour_n find_v in_o the_o common_a way_n of_o measure_v run_v water_n 68_o 69_o error_n in_o derive_v the_o water_n of_o acqua_fw-la paola_n appendix_n ii_o 17_o 18_o error_n of_o bartolotti_n 86_o 87_o error_n of_o engineer_n in_o the_o derivation_n of_o channel_n corollary_n xii_o 12_o error_n of_o engineer_n in_o measure_v of_o reno_n in_o po._n appendix_n iii_o ibid._n error_n of_o other_o engineer_n contrary_a to_o the_o precedent_n appendix_n iu._n ibid._n error_n of_o giovanni_n fontana_n in_o measure_v water_n corollary_n xi_o 9_o error_n of_o giulio_n frontino_n in_o measure_v the_o water_n of_o aqueduct_n appendix_n i._n 17_o error_n commit_v in_o cut_v the_o bank_n at_o bondeno_n in_o the_o swell_n of_o po_n corollary_n xiii_o 81_o f_o fen_n pontine_n drain_v by_o pope_n sixtus_n quintus_fw-la with_o vast_a expense_n 92_o the_o ruin_n and_o miscarriage_n thereof_o 93_o tardity_n of_o the_o principal_a channel_n that_o drain_v they_o cause_n of_o the_o drown_v ibid._n they_o be_v obstruct_v by_o the_o fishing-wears_a which_o swell_v the_o river_n 94_o water_n of_o fiume_n sisto_n which_o flow_v in_o great_a abundance_n into_o the_o evacuator_fw-la of_o the_o say_a fen_n 94_o 95_o remedy_n to_o the_o disorder_n of_o those_o fen_n 95_o 96_o fontana_n giovanni_n his_o error_n in_o measure_v water_n corollary_n xi_o 9_o fiume_n morto_fw-la whether_o it_o ought_v to_o fall_v into_o the_o sea_n or_o into_o serchio_n 79_o let_v into_o serchio_n and_o its_o inconvenience_n 79_o 80_o the_o dangerous_a rise_n of_o its_o water_n when_o to_o be_v expect_v 81_o its_o inconvenience_n when_o it_o be_v high_a in_o level_a than_o serchio_n and_o why_o it_o rise_v most_o on_o the_o seacoast_n at_o such_o time_n as_o the_o wind_n make_v the_o sea_n to_o swell_v 83_o g_o galileo_n galilaei_n honourable_o mention_v page_z 2_o 28_o his_o rule_n for_o measure_v the_o time_n 49_o h_n height_n vide_fw-la quick_a height_n different_a make_v by_o the_o same_o stream_n of_o a_o brook_n or_o torrent_n according_a to_o the_o divers_a velocity_n in_o the_o entrance_n of_o the_o river_n corollary_n i._n 6_o height_n different_a make_v by_o the_o torrent_n in_o the_o river_n according_a to_o the_o different_a height_n of_o the_o river_n corollary_n ii_o ibid._n k_o knowledge_n of_o motion_n how_o much_o iâ—_n import_v 1_o l_o lake_n of_o perugia_n and_o be_v observation_n make_v on_o it_o appendix_n xii_o 42_o lake_n of_o thrasimenus_n and_o consideration_n upon_o it_o a_o letter_n write_v to_o sig._n galileo_n galilaei_n 28_o lake_n of_o venice_n and_o consideration_n upon_o it_o 63_o 73_o low_a water_n which_o let_v the_o bottom_n of_o it_o be_v discover_v 64_o the_o stoppage_n and_o choke_n of_o the_o port_n a_o main_a cause_n of_o the_o disorder_n of_o the_o lake_n and_o the_o grand_a remedy_n to_o those_o disorder_n what_o it_o be_v 66_o lake_n and_o meers_n along_o the_o seacoast_n and_o the_o cause_n thereof_o 65_o length_n of_o water_n how_o it_o be_v to_o be_v measure_v 70_o m_o measure_n and_o distribution_n of_o water_n appendix_n v._n 18_o measure_n of_o river_n that_o fall_v into_o other_o difficult_a coral_n x_o 9_o measure_n of_o the_o run_v water_n of_o a_o channel_n of_o a_o height_n know_v by_o a_o regulator_n of_o a_o measure_n give_v in_o a_o time_n assign_v proposition_n i._o problem_n i_o 50_o measure_n of_o the_o water_n of_o any_o river_n of_o any_o greatness_n in_o a_o time_n give_v proposition_n v._o problem_n iii_o 60_o measure_n that_o show_v how_o much_o water_n a_o river_n discharge_v in_o a_o time_n give_v 48_o mole-hole_n motion_n the_o principal_a
subject_n of_o philosophy_n 1_o mud._n vide_fw-la sand._n n_o navigation_n from_o bologna_n to_o ferrara_n be_v become_v impossible_a till_o such_o time_n as_o reno_n be_v divert_v 101_o navigation_n in_o the_o lake_n of_o venice_n endanger_v and_o how_o restore_v 65_o 70_o p_o perpendicularity_n of_o the_o bank_n of_o the_o river_n to_o the_o upper_a superficies_n of_o it_o 37_o perpendicularity_n of_o the_o bank_n to_o the_o bottom_n 37_o perugia_n vide_fw-la lake_n pontine_n vide_fw-la fen_n port_n of_o venice_n malamocco_n bondolo_n and_o chiozza_n choke_v up_o for_o want_n of_o water_n in_o the_o lake_n 65_o proportion_n of_o unequal_a section_n of_o equal_a velocity_n and_o of_o equal_a section_n of_o unequal_a velocity_n axiom_n iu._n and_o v._o 38_o proportion_n of_o equal_a and_o unequal_a quantity_n of_o water_n which_o pass_v by_o the_o section_n of_o different_a river_n proposition_n ii_o 39_o proportion_n of_o unequal_a section_n that_o in_o equal_a time_n discharge_v equal_a quantity_n of_o water_n proposition_n iii_o 41_o proportion_n wherewith_o one_o river_n fall_v into_o another_o vary_v in_o height_n proposition_n iu_o 44_o proportion_n of_o the_o water_n discharge_v by_o a_o river_n in_o the_o time_n of_o flood_n to_o the_o water_n discharge_v in_o a_o equal_a time_n by_o the_o say_a river_n before_o or_o after_o the_o flood_n proposition_n v._n 44_o proportion_n of_o the_o height_n make_v by_o two_o equal_a brook_n or_o stream_n fall_v into_o the_o same_o river_n proposition_n vi_o 45_o proportion_n of_o the_o water_n which_o a_o river_n discharge_v increase_a in_o quick-height_n by_o the_o addition_n of_o new_a water_n to_o that_o which_o it_o discharge_v after_o the_o increase_n be_v make_v proposition_n iu._n theor._n ii_o 54_o proportion_n of_o a_o river_n when_o high_a to_o itself_o when_o low_o coral_n i._o 55_o q_o quantity_n of_o run_v water_n be_v never_o certain_a if_o with_o the_o vulgar_a way_n of_o measure_v they_o their_o velocity_n be_v not_o consider_v 32_o quantity_n of_o water_n which_o be_v discharge_v by_o a_o river_n answer_v in_o equality_n to_o the_o velocity_n and_o time_n in_o which_o they_o be_v discharge_v axiom_n i_o two_o iii_o 38_o quick-height_n of_o a_o river_n what_o it_o be_v definition_n v._n 48_o r_o reason_n of_o the_o proverb_n take_v heed_n of_o the_o still_a water_n coral_n vi_o 7_o reason_n of_o monsignore_n corsini_n against_o the_o diversion_n of_o reno_n into_o the_o po_n of_o volano_n 105_o reason_n of_o cardinal_n capponi_n and_o monsig_n corsini_n for_o the_o turn_n of_o reno_n into_o main_n po._n 106_o two_o objection_n on_o the_o contrary_a and_o answer_n to_o they_o 104_o &_o 105_o what_o ought_v to_o be_v the_o proportion_n of_o the_o height_n of_o reno_n be_v reno_n and_o of_o reno_n in_o po._n 110_o regulator_n what_o it_o be_v definition_n iu_o 48_o relation_n of_o the_o water_n of_o bologna_n and_o ferrara_n by_o monsignore_n corsini_n 100_o reno_n in_o the_o valley_n and_o its_o bad_a effect_n 100_o 101_o two_o way_n to_o divert_v it_o 103_o the_o facility_n and_o utility_n of_o those_o way_n ibid._n the_o difficulty_n object_v 104_o reply_n to_o bartolotti_n touch_v the_o danger_n of_o turn_v fiume_n morto_n into_o serchio_n 83_o retardment_n of_o the_o course_n of_o a_o river_n cause_v by_o its_o bank_n appendix_n vii_o 19_o rise_n make_v by_o floodgate_n but_o small_a appendix_n xiii_o 26_o river_n that_o be_v shallow_a swell_v much_o upon_o small_a shower_n such_o as_o be_v deep_o rise_v but_o little_a upon_o great_a flood_n corollary_n iii_o 6_o river_n the_o high_o they_o be_v the_o swift_a ibid._n rivers_z the_o high_o they_o be_v thelesse_o they_o increase_v upon_o flood_n 49_o river_n when_o they_o be_v to_o have_v equal_a and_o when_o like_a velocity_n ibid._n river_n in_o fall_v into_o the_o sea_n form_n a_o shelf_n of_o sand_n call_v cavallo_n 65_o five_o river_n to_o be_v divert_v from_o the_o lake_n of_o venice_n and_o the_o inconvenience_n that_o will_v ensue_v thereupon_o 74_o 75_o a_o river_n of_o quick-height_n and_o velocity_n in_o its_o regulator_n be_v give_v if_o the_o height_n be_v redouble_v by_o new_a water_n it_o redouble_v also_o in_o velocity_n proposition_n ii_o theorem_fw-la i_o 51_o keep_v the_o proportion_n of_o the_o height_n to_o the_o velocity_n corollary_n 52_o saint_n sand_n and_o mud_n that_o enter_v into_o the_o lake_n of_o venice_n and_o the_o way_n to_o examine_v it_o 76_o sea_n agitate_a and_o drive_v by_o the_o wind_n stop_v up_o the_o port_n 64_o 65_o section_n of_o a_o river_n what_o they_o be_v definition_n i._n 37_o section_n equal_o swift_a what_o they_o be_v definition_n ii_o ibid._n section_n of_o river_n be_v give_v to_o conceive_v other_o equal_v to_o they_o of_o different_a breadth_n height_n and_o velocity_n petition_n 38_o section_n of_o the_o same_o river_n and_o their_o proportion_n to_o their_o velocity_n coral_n i._o 42_o section_n of_o a_o river_n discharge_v in_o any_o whatsoever_o place_n of_o the_o say_a river_n equal_a quantity_n of_o water_n in_o equal_a time_n proposition_n i._n 39_o sile_z river_n what_o mischief_n it_o threaten_v divert_v from_o the_o lake_n 74_o spirting_n of_o water_n grow_v big_a the_o high_o they_o go_v coral_n xvi_o 16_o stream_n of_o river_n how_o they_o increase_v and_o vary_v coral_n i._o 6_o stream_n retard_v and_o the_o effect_n thereof_o coral_n ix_o 8_o t_o table_n of_o the_o height_n addition_n and_o quantity_n of_o water_n and_o its_o use_n 56_o thrasimenus_n vide_fw-la lake_n time_n how_o it_o be_v measure_v in_o these_o operation_n of_o the_o water_n 49_o torrent_n increase_v at_o the_o increase_n of_o a_o river_n though_o they_o carry_v no_o more_o water_n than_o before_o coral_n iv._o 6_o torrent_n when_o they_o depose_v and_o carry_v away_o the_o sand._n coral_n v._o 7_o torrent_n and_o their_o effect_n in_o a_o river_n 6_o 7_o torrent_n that_o fall_v into_o the_o valley_n or_o into_o po_n of_o 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