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into_o the_o river_n searchio_n viii_o his_o second_o letter_n in_o answer_n to_o certain_a objection_n propose_v and_o difficulty_n observe_v
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to_o he_o in_o this_o manner_n 9_o questo_fw-la lo_o comunico_fw-la a_o v._o s._n per_fw-la lettera_fw-la prima_fw-la che_fw-it ad_fw-la alcun_fw-fr altro_fw-it con_fw-mi attenderne_a principalment_fw-it il_fw-it parer_fw-la svo_fw-la e_fw-it doppo_fw-it quello_fw-it do_v nostri_fw-la amici_n discosti_fw-la conpensiero_n d'_fw-fr inviaâ—ne_fw-fr poi_fw-fr altre_n copy_n ad_fw-la altri_fw-la amici_n d'italia_fw-la e_fw-it di_fw-it francia_n quando_fw-la io_fw-it ne_fw-la venga_fw-mi da_fw-mi lei_fw-it consigliato_fw-it e_fw-la qui_fw-la pregandola_n a_fw-fr 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_v 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
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 â—or_a 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 tap_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 fromthâ—e_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 the_o first_o as_o the_o velocity_n of_o the_o cord_n by_o the_o first_o hole_n have_v reciprocal_o to_o the_o velocity_n of_o the_o codâ—s_n by_o the_o second_o hole_n and_o thus_o its_o clear_a that_o when_o there_o be_v draw_v through_o two_o hole_n equal_a quantity_n of_o cord_n in_o equal_a time_n but_o with_o unequal_a velocity_n it_o will_v be_v necessary_a that_o the_o thickness_n of_o all_o the_o four_o cord_n shall_v have_v the_o same_o reciprocal_a proportion_n to_o the_o thickness_n of_o the_o swift_a cord_n that_o the_o velocity_n of_o the_o swift_a cord_n have_v to_o the_o velocity_n of_o the_o slow_a the_o which_o be_v verify_v likewise_o in_o the_o fluid_a element_n of_o water_n and_o to_o the_o end_n that_o this_o principal_a fundamental_a be_v well_o understand_v i_o will_v also_o note_v a_o certain_a observation_n make_v my_o i_n in_o the_o art_n of_o 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
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 iâ—_n 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 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 1st_a the_o height_n of_o the_o river_n diminish_v only_o 1_o 10_o