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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
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 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 cod_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
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
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 velocity_n through_o fh_n have_v to_o the_o velocity_n through_o ce_fw-fr but_o the_o section_n ce_fw-fr be_v to_o the_o section_n fh_v as_o cd_o to_o fg_v by_o reason_n they_o be_v of_o the_o same_o breadth_n therefore_o cd_o shall_v be_v to_o fg_v in_o reciprocal_a proportion_n as_o the_o velocity_n through_o fh_n be_v to_o the_o velocity_n through_o ce_fw-fr and_o therefore_o if_o two_o equal_a stream_n of_o the_o same_o torrent_n etc._n etc._n which_o be_v to_o be_v demonstrate_v of_o the_o mensuration_n of_o run_v water_n lib._n ii_o have_v in_o the_o close_a of_o my_o treatise_n of_o the_o mensuration_n of_o run_v water_n promise_v to_o declare_v upon_o another_o occasion_n other_o particular_n more_o obscure_a and_o of_o very_o great_a concern_v upon_o the_o same_o argumement_n i_o now_o do_v perform_v my_o promise_n on_o the_o occasion_n that_o i_o have_v the_o past_a year_n 1641._o to_o propound_v my_o thought_n touch_v the_o state_n of_o the_o lake_n of_o venice_n a_o 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 river_n be_v say_v to_o move_v with_o equal_a velocity_n when_o in_o equal_a time_n they_o pass_v space_n of_o equal_a length_n definition_n ii_o river_n be_v say_v to_o move_v with_o like_a velocity_n when_o their_o proportional_a part_n do_v move_v alike_o that_o be_v the_o upper_a part_n alike_o to_o the_o upper_a and_o the_o low_a to_o the_o low_a so_o that_o if_o the_o upper_a part_n of_o one_o river_n shall_v be_v more_o swift_a than_o the_o upper_a part_n of_o another_o then_o also_o the_o low_a part_n of_o the_o former_a shall_v be_v more_o swift_a than_o the_o part_n correspondent_a to_o it_o in_o the_o second_o proportional_o definition_n iii_o to_o measure_v a_o river_n or_o run_v water_n be_v in_o our_o sense_n to_o find_v out_o how_o many_o determinate_a measure_n or_o weight_n of_o water_n in_o a_o give_v time_n pass_v through_o the_o river_n or_o channel_n of_o the_o water_n that_o be_v to_o be_v measure_v definition_n iu._n if_o a_o machine_n be_v make_v either_o of_o brick_n or_o of_o stone_n or_o of_o wood_n so_o compose_v that_o two_o side_n of_o the_o say_a machine_n be_v place_v at_o right_a angel_n upon_o the_o end_n of_o a_o three_o side_n that_o be_v suppose_v to_o be_v place_v in_o the_o bottom_n of_o a_o river_n parallel_n to_o the_o horizon_n in_o such_o a_o manner_n that_o all_o the_o water_n which_o run_v through_o the_o say_a river_n pass_v through_o the_o say_a machine_n and_o if_o all_o the_o water_n come_v to_o be_v divert_v that_o run_v through_o the_o say_a river_n the_o upper_a superficies_n of_o that_o three_o side_n place_v in_o the_o bottom_n do_v remain_v uncover_v and_o dry_a and_o that_o the_o dead_a water_n be_v not_o above_o it_o this_o same_o machine_n shall_v be_v call_v by_o we_o sluice_n regulator_n and_o that_o three_o side_n of_o the_o machine_n which_o stand_v horizontal_o be_v call_v the_o bottom_n of_o the_o regulator_n and_o the_o other_o two_o side_n be_v call_v the_o bank_n of_o the_o regulator_n as_o be_v see_v in_o this_o first_o figure_n abcd_n shall_v be_v the_o regulator_n bc_n the_o bottom_n and_o the_o other_o two_o side_n ab_fw-la and_o cd_o be_v its_o bank_n definition_n v._n by_o the_o quick_a height_n we_o mean_v the_o perpendicular_a from_o the_o upper_a superficies_n of_o the_o river_n unto_o the_o upper_a superficies_n of_o the_o bottom_n of_o the_o regulator_n as_o in_o the_o forego_n figure_n the_o line_n gh_o definition_n vi._n if_o the_o water_n of_o a_o river_n be_v suppose_v to_o be_v mark_v by_o three_o side_n of_o a_o regulator_n that_o rightangle_v parallelogram_n comprehend_v between_o the_o bank_n of_o the_o regulator_n and_o the_o bottom_n and_o the_o superficies_n of_o the_o water_n be_v call_v a_o section_n of_o the_o river_n annotation_n here_o it_o be_v to_o be_v note_v that_o the_o river_n itself_o may_v have_v sundry_a and_o divers_a height_n in_o several_a part_n of_o its_o channel_n by_o reason_n of_o the_o various_a velocity_n of_o the_o water_n and_o 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