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
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 intelligible_a by_o part_n in_o its_o velocity_n and_o so_o much_o suffice_v to_o have_v hint_v about_o this_o matter_n hope_v to_o impart_v on_o some_o other_o occasion_n other_o more_o accurate_a observation_n in_o this_o affair_n laus_fw-la deo_fw-la geometrical_a demonstration_n of_o the_o measure_n of_o run_v water_n by_o d._n benedetto_n castelli_n abbot_n of_o cassina_n and_o mathematician_n to_o p._n vrban_n viii_o dedicate_v to_o the_o most_o illustrious_a and_o most_o excellent_a prince_n don_n thaddeo_n barberini_n prince_z of_o palestrina_n and_o general_z of_o the_o holy_a church_n london_n print_v anno_fw-la domini_fw-la mdclxi_o of_o the_o mensuration_n of_o run_v water_n supposition_n i._n let_v it_o be_v suppose_v that_o the_o bank_n of_o the_o river_n of_o which_o we_o speak_v be_v erect_v perpendicular_a to_o the_o plane_n of_o the_o upper_a superficies_n of_o the_o river_n supposition_n ii_o we_o suppose_v that_o the_o plane_n of_o the_o bottom_n of_o the_o river_n 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 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
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
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 volano_n and_o their_o mischief_n prevent_v by_o the_o divert_v of_o reno_n into_o main_n po._n 100_o tiber_n and_o the_o cause_n of_o its_o inundation_n coral_n viii_o 8_o five_o valley_n of_o bologna_n and_o ferrara_n their_o inundation_n and_o disorder_n whence_o they_o proceed_v 97_o velocity_n of_o the_o water_n show_v by_o several_a example_n 3_o its_o proportion_n to_o the_o measure_n 5_o velocity_n equal_a what_o they_o be_v 47_o velocity_n like_a what_o they_o be_v 47_o 48_o velocity_n of_o water_n know_v how_o they_o help_v we_o in_o find_v the_o length_n 113_o a_o fable_n to_o explain_v the_o truth_n thereof_o ibid._n venice_n vide_fw-la lake_n use_v of_o the_o regulator_n in_o measure_v great_a river_n consideration_n i._n 60_o w_n water_n fall_v why_o they_o disgross_v coral_n xvi_o 16_o water_n how_o the_o length_n of_o they_o be_v measure_v 70_o water_n that_o be_v employ_v to_o flow_v ground_n how_o they_o be_v to_o be_v distribute_v 19_o 53_o 54_o water_n to_o be_v carry_v in_o pipe_n to_o serve_v aquaduct_n and_o conduit_n how_o they_o be_v to_o be_v measure_v 115_o 116_o way_n to_o know_v the_o rise_n of_o lake_n by_o raines_n 28_o way_n of_o the_o vulgar_a to_o measure_v the_o water_n of_o rivers_n 68_o wind_n gun_n and_o portable_a fountain_n of_o vincenzo_n vincenti_fw-la of_o urbino_n 11_o wind_n contrary_a retard_v and_o make_v river_n increase_v coral_n vii_o 8_o the_o end_n of_o the_o table_n of_o the_o second_o part_n of_o the_o first_o tome_n tome_n nella_n continuatione_fw-la dell_fw-it nuntio_fw-la â—iderio_fw-la â—iderio_fw-la lettera_fw-mi all_o p._n abbate_n d._n b._n castelli_n d'arcetro_n li._n 3._o decemb._n 16â—9_n 16â—9_n de_fw-fr motu_fw-la aquarum_fw-la lib._n 2._o prop._n 37._o p._n 191._o 191._o 191._o and_o as_o be_v at_o large_a demonstrate_v by_o that_o most_o excellent_a and_o honourable_a personage_n mr._n boil_v in_o the_o industrious_a experiment_n of_o his_o pneumatical_a engine_n engine_n engine_n artesia_n artesia_n artesia_n commentarius_fw-la bear_v many_o sense_n but_o in_o this_o place_n signify_v a_o certain_a register_n of_o the_o quantity_n of_o the_o water_n in_o the_o several_a public_a aquiduct_n of_o rome_n which_o word_n i_o find_v frequent_o use_v in_o the_o law-book_n of_o ancient_a civilian_n and_o by_o errogation_n we_o be_v to_o understand_v the_o distribution_n or_o deliver_v out_o of_o those_o store_n of_o water_n water_n water_n a_o coin_n of_o pope_n julius_n worth_n six_o penny_n penny_n penny_n or_o sluice_n sluice_n sluice_n in_o pregadi_n a_o particular_a council_n the_o senators_z of_o which_o have_v great_a authority_n authority_n authority_n a_o venice_n brace_n be_v 11_o 1â—_n of_o our_o yard_n yard_n yard_n a_o river_n of_o that_o name_n name_n name_n i._o savii_n dell_fw-it '_o acque_fw-la a_o particular_a council_n that_o take_v care_n of_o the_o lake_n and_o other_o aquatic_a affair_n affair_n affair_n he_o here_o intend_v the_o demonstration_n follow_v at_o the_o end_n of_o the_o first_o book_n book_n book_n deep_o deep_o deep_o lib._n 1._o 1._o 1._o the_o country_n or_o province_n lie_v round_o the_o city_n heretofore_o call_v lati_fw-la 〈◊〉_d 〈◊〉_d 〈◊〉_d or_o lordship_n lordship_n lordship_n the_o pope_n exchequer_n exchequer_n exchequer_n polesine_n be_v a_o plat_n of_o ground_n almost_o surround_v with_o bog_n or_o water_n like_o a_o island_n island_n island_n people_n of_o ferrara_n ferrara_n ferrara_n in_o channel_n make_v by_o hand_n hand_n hand_n the_o inch_n of_o these_o place_n be_v somewhat_o big_a than_o we_o we_o we_o of_o adriano_n adriano_n larghezza_fw-it but_o misprint_v
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
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
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 of_o run_v water_n but_o yet_o do_v not_o run_v throughout_o with_o the_o same_o velocity_n hence_o it_o be_v that_o the_o vulgar_a measure_n of_o the_o say_a river_n in_o divers_a part_n of_o its_o channel_n be_v always_o divers_a insomuch_o that_o if_o a_o river_n pass_v through_o its_o channel_n have_v such_o velocity_n that_o it_o run_v 100_o brace_n in_o the_o 1_o 60_o of_o a_o hour-and_a afterward_o the_o say_a river_n shall_v be_v reduce_v to_o so_o much_o tardi_fw-la thy_fw-mi of_o motion_n as_o that_o in_o the_o same_o time_n it_o shall_v not_o run_v more_o than_o one_o brace_n it_o will_v be_v necessary_a that_o that_o same_o river_n shall_v become_v 100_o time_n big_a in_o that_o place_n where_o it_o be_v retard_v i_o mean_v 100_o time_n big_a than_o it_o be_v in_o the_o place_n where_o it_o be_v swift_a and_o let_v it_o be_v keep_v well_o in_o mind_n that_o this_o point_n right_o understand_v will_v clear_v the_o understanding_n to_o discover_v very_o many_o accident_n worthy_a to_o be_v know_v but_o for_o this_o time_n let_v it_o suffice_v that_o we_o have_v only_o declare_v that_o which_o make_v for_o our_o purpose_n refer_v apprehensive_a and_o studious_a wit_n to_o the_o perusal_n of_o my_o aforenamed_a treatise_n for_o therein_o he_o shall_v find_v profit_n and_o delight_n both_o together_o now_o apply_v all_o to_o our_o principal_a intent_n i_o say_v that_o by_o what_o have_v be_v declare_v it_o be_v manifest_a that_o if_o the_o brent_n be_v 48._o brace_n broad_a and_o 2_o ½_o high_a in_o some_o one_o part_n of_o its_o channel_n that_o afterward_o the_o same_o water_n of_o the_o brent_n fall_v into_o the_o lake_n and_o pass_v through_o the_o same_o to_o the_o sea_n it_o shall_v lose_v so_o much_o of_o its_o velocity_n that_o it_o shall_v run_v but_o one_o brace_n in_o the_o time_n wherein_o whilst_o it_o be_v in_o its_o channel_n at_o the_o place_n aforesaid_a it_o run_v 100_o brace_n it_o will_v be_v absolute_o necessary_a that_o increase_v in_o measure_n it_o shall_v become_v a_o hundred_o time_n deep_o thick_a and_o therefore_o if_o we_o shall_v suppose_v that_o the_o lake_n be_v 20000._o brace_n the_o brent_n that_o already_o have_v be_v suppose_v in_o its_o channel_n 100_o brace_n be_v bring_v into_o the_o lake_n shall_v be_v 100_o time_n 100_o brate_v that_o be_v shall_v be_v 10000_o brace_n in_o thickness_n and_o consequent_o shall_v be_v in_o height_n half_a a_o brace_n that_o be_v 100_o 200_o of_o a_o brace_n and_o not_o 1_o 200_o of_o a_o brace_n as_o be_v conclude_v in_o the_o argument_n now_o one_o may_v see_v into_o what_o a_o gross_a error_n of_o 99_o in_o 100_o one_o may_v fall_v through_o the_o not_o well_o understand_v the_o true_a quantity_n of_o run_v water_n which_o be_v well_o understand_v do_v open_v a_o direct_a way_n to_o our_o judge_v aright_o in_o this_o most_o considerable_a affair_n and_o therefore_o admit_v that_o which_o have_v be_v demonstrate_v i_o say_v that_o i_o will_v if_o it_o do_v concern_v i_o great_o incline_v to_o consult_v upon_o the_o return_v of_o the_o brent_n again_o into_o the_o lake_n for_o it_o be_v most_o evident_a that_o the_o brent_n in_o the_o channel_n of_o its_o mouth_n be_v much_o swift_a than_o the_o brent_n be_v bring_v into_o the_o lake_n it_o will_v certain_o follow_v thereupon_o that_o the_o thickness_n of_o the_o water_n of_o brent_n in_o the_o lake_n shall_v be_v so_o much_o great_a than_o that_o of_o brent_n in_o brent_n by_o how_o much_o the_o bront_n in_o brent_n be_v swift_a than_o thh_n brent_n in_o the_o lake_n 1._o from_o which_o operation_n do_v follow_v in_o the_o first_o place_n that_o the_o lake_n be_v fill_v and_o increase_v by_o these_o water_n shall_v be_v more_o navigable_a and_o passable_a than_o at_o present_a we_o see_v it_o to_o be_v 2._o by_o the_o current_n of_o these_o water_n the_o channel_n will_v be_v scour_v and_o will_v be_v keep_v clean_o from_o time_n to_o time_n 3._o there_o will_v not_o appear_v at_o the_o 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 thereof_o with_o sundry_a senator_n and_o go_v my_o way_n promise_v with_o all_o intenseness_n to_o apply_v my_o pain_n with_o reiterated_a study_n in_o the_o public_a service_n and_o if_o any_o other_o thing_n shall_v come_v into_o my_o mind_n i_o promise_v to_o declare_v they_o sincere_o and_o so_o take_v leave_v of_o his_o serenity_n and_o that_o noble_a council_n when_o i_o be_v return_v to_o rome_n this_o business_n night_n and_o day_n continual_o run_v in_o my_o mind_n i_o happen_v to_o think_v of_o another_o admirable_a and_o most_o important_a conceit_n which_o with_o effectual_a reason_n confirm_v by_o exact_a operation_n i_o with_o the_o divine_a assistance_n make_v clear_a and_o manifest_a and_o though_o the_o thing_n at_o first_o sight_n seem_v to_o i_o a_o most_o extravagant_a paradox_n yet_o notwithstanding_o have_v satisfy_v myself_o of_o the_o whole_a business_n i_o send_v it_o in_o write_v to_o the_o most_o illustrious_a and_o most_o noble_a signore_n gio._n 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
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 measure_n of_o the_o water_n be_v always_o great_a where_o the_o velocity_n be_v lesser_a and_o on_o the_o contrary_a the_o measure_n lesser_a where_o the_o velocity_n be_v great_a from_o hence_o we_o may_v most_o elegant_o render_v the_o reason_n of_o the_o usual_a proverb_n take_v heed_n of_o the_o still_a water_n for_o that_o if_o we_o consider_v the_o self_n same_o water_n of_o a_o river_n in_o those_o part_n wherein_o it_o be_v less_o swift_a and_o thence_o call_v still_o or_o smooth_a water_n it_o shall_v be_v of_o necessity_n of_o great_a measure_n than_o in_o those_o part_n in_o which_o it_o be_v more_o swift_a and_o therefore_o ordinary_o shall_v be_v also_o more_o deep_a and_o dangerous_a for_o passenger_n whence_o it_o be_v well_o say_v take_v heed_n of_o the_o still_a water_n and_o this_o say_n have_v be_v since_o apply_v to_o thing_n moral_a corollary_n vii_o likewise_o from_o the_o thing_n demonstrate_v may_v be_v conclude_v that_o the_o wind_n which_o stop_v a_o river_n 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 velocity_n before_o the_o wind_n have_v to_o the_o velocity_n after_o the_o wind_n and_o such_o reciprocal_o be_v the_o measure_n of_o the_o same_o water_n after_o the_o wind_n to_o the_o measure_n before_o the_o wind_n and_o because_o it_o have_v be_v suppose_v in_o our_o case_n that_o the_o velocity_n be_v diminish_v to_o a_o five_o part_n therefore_o the_o measure_n shall_v be_v increase_v five_o time_n more_o than_o that_o which_o it_o be_v before_o corollary_n viii_o we_o have_v also_o probable_a the_o cause_n of_o the_o inundation_n of_o tiber_n which_o befall_v at_o rome_n in_o the_o time_n of_o alexander_n the_o six_o &_o of_o clement_n the_o seven_o which_o inundation_n come_v in_o a_o serene_a time_n and_o without_o great_a thaw_n of_o the_o snow_n which_o therefore_o much_o puzzle_v the_o wit_n of_o those_o time_n but_o we_o may_v with_o much_o probability_n affirm_v that_o the_o river_n rise_v to_o such_o a_o height_n and_o excresence_n by_o the_o retardation_n of_o the_o 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 retain_v not_o the_o same_o velocity_n which_o they_o have_v in_o the_o place_n in_o which_o fontana_n and_o his_o nephew_n measure_v they_o and_o all_o this_o be_v manifest_a from_o the_o thing_n which_o we_o have_v above_o explain_v for_o if_o the_o water_n reduce_v into_o tiber_n increase_n in_o velocity_n they_o decrease_v in_o measure_n and_o if_o they_o decrease_v in_o velocity_n they_o increase_v in_o measure_n second_o i_o consider_v that_o the_o measure_n of_o those_o brook_n and_o river_n which_o enter_v into_o tiber_n at_o the_o time_n of_o innundation_n be_v not_o between_o themselves_o real_o the_o same_o when_o their_o velocity_n be_v not_o equal_a though_o they_o have_v the_o same_o name_n of_o ell_n and_o foot_n for_o that_o its_o possible_a that_o a_o disinboguement_fw-fr of_o ten_o ell_n requadrate_v to_o speak_v in_o the_o phrase_n of_o fontana_n of_o one_o of_o those_o brook_n may_v discharge_v into_o tiber_n at_o
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 it_o be_v suppose_v that_o the_o river_n in_o the_o time_n of_o flood_n have_v not_o have_v of_o itself_o and_o from_o its_o proper_a spring_n more_o water_n than_o ordinary_a it_o be_v a_o thing_n certain_a that_o the_o water_n of_o tiber_n rise_v and_o increase_v also_o that_o river_n to_o level_v itself_o with_o the_o water_n of_o tiber_n will_v have_v retain_v some_o of_o its_o water_n in_o its_o own_o channel_n without_o discharge_v they_o into_o tiber_n or_o else_o will_v have_v ingorge_v and_o swallow_v if_o i_o may_v so_o say_v some_o of_o the_o water_n of_o tiber_n and_o in_o this_o case_n at_o the_o time_n of_o inundation_n less_o abundance_n of_o water_n will_v have_v come_v to_o rome_n and_o yet_o nevertheless_o the_o measure_n of_o that_o river_n will_v have_v be_v increase_v five_o fontana_n deceive_v himself_o when_o he_o conclude_v that_o to_o remove_v the_o inundation_n from_o rome_n it_o will_v be_v necessary_a to_o make_v two_o other_o channel_n of_o river_n that_o be_v as_o large_a as_o that_o which_o be_v the_o present_a one_o and_o that_o less_o will_v not_o suffice_v which_o i_o say_v be_v a_o fallacy_n and_o to_o convince_v he_o easy_o of_o his_o error_n it_o suffice_v to_o say_v that_o all_o the_o stream_n be_v pass_v under_o the_o bridge_n quattro-capi_a as_o he_o himself_o atte_v a_o channel_n will_v suffice_v only_o of_o the_o capacity_n of_o the_o say_a bridge_n provide_v that_o the_o water_n there_o may_v run_v with_o the_o same_o velocity_n as_o it_o do_v under_o the_o bridge_n at_o the_o time_n of_o inundation_n and_o on_o the_o contrary_a twenty_o current_n of_o capacity_n equal_a to_o the_o present_a one_o will_v not_o suffice_v if_o the_o water_n shall_v run_v with_o twenty_o time_n less_o velocity_n than_o it_o make_v at_o the_o time_n of_o the_o inundation_n six_o to_o i_o it_o seem_v a_o great_a weakness_n to_o say_v that_o there_o shall_v pass_v under_o the_o bridge_n quattro-capi_a a_o hundred_o fifty_o one_o ell_n of_o 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 of_o the_o air_n compress_v which_o whilst_o it_o seek_v to_o reduce_v its_o self_n to_o its_o natural_a constitution_n in_o the_o dilation_n cause_v that_o violence_n but_o the_o water_n can_v never_o for_o any_o thing_n i_o know_v crowd_n or_o press_v so_o as_o that_o if_o before_o the_o compression_n it_o hold_v or_o possess_v a_o place_n be_v in_o its_o natural_a constitution_n i_o believe_v not_o i_o say_v that_o it_o be_v possible_a by_o press_v and_o crowd_v to_o make_v it_o possess_v less_o room_n for_o if_o it_o be_v possible_a to_o compress_v the_o water_n and_o make_v it_o to_o occupy_v a_o less_o place_n it_o will_v thence_o follow_v that_o two_o vessel_n of_o equal_a measure_n but_o of_o unequal_a height_n shall_v be_v of_o unequal_a capacity_n and_o that_o shall_v hold_v more_o water_n which_o be_v high_a also_o a_o cylinder_n or_o other_o vessel_n more_o high_a than_o broad_a will_v contain_v more_o water_n erect_v than_o be_v lay_v along_o for_o that_o be_v erect_v 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
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 day_n upon_o it_o and_o be_v well_o assure_v that_o it_o be_v not_o at_o all_o increase_v and_o importune_v he_o further_o that_o he_o will_v give_v i_o some_o reason_n for_o his_o so_o think_v he_o propose_v to_o my_o consideration_n the_o great_a drought_n pass_v and_o that_o that_o same_o rain_n be_v nothing_o for_o the_o great_a parch_a to_o which_o i_o answer_v i_o believe_v sir_n that_o the_o surface_n of_o the_o lake_n on_o which_o the_o rain_n have_v fall_v be_v moisten_v and_o therefore_o see_v not_o how_o its_o drought_n which_o be_v nothing_o at_o all_o can_v have_v drink_v up_o any_o part_n of_o the_o rain_n for_o all_o this_o he_o persist_v in_o his_o conceit_n without_o yield_v in_o the_o least_o to_o my_o allegation_n he_o grant_v in_o the_o end_n i_o believe_v in_o civility_n to_o i_o that_o my_o reason_n be_v plausible_a and_o good_a but_o that_o in_o practice_v it_o can_v not_o hold_v at_o last_o to_o clear_v up_o all_o i_o make_v one_o be_v call_v and_o send_v he_o 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 border_n of_o bank_n which_o be_v to_o be_v occupy_v by_o the_o increase_n of_o the_o lake_n be_v a_o brace_n in_o breadth_n quite_o round_o the_o lake_n and_o that_o by_o reason_n of_o its_o dryness_n it_o suck_v in_o water_n and_o that_o by_o that_o mean_v this_o proportion_n of_o water_n co-operate_v not_o in_o raise_v of_o the_o lake_n it_o be_v absolute_o necessary_a on_o the_o other_o hand_n that_o we_o consider_v that_o the_o circuit_n of_o the_o water_n of_o the_o lake_n be_v thirty_o mile_n as_o it_o be_v common_o hold_v that_o be_v to_o say_v ninety_o thousand_o brace_n of_o florence_n in_o compass_n and_o therefore_o admit_v for_o true_a that_o each_o brace_n of_o this_o bank_n drink_v two_o quart_n of_o water_n and_o that_o for_o the_o spread_a it_o require_v three_o quart_n more_o we_o shall_v find_v that_o the_o whole_a agregate_v of_o this_o portion_n of_o water_n which_o be_v not_o employ_v in_o the_o raise_n of_o the_o lake_n will_v be_v four_o hundred_o and_o fifty_o 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 consequent_o if_o such_o a_o rain_n shall_v fall_v upon_o a_o lake_n that_o the_o say_a lake_n will_v rise_v according_a to_o the_o same_o rate_n and_o likewise_o if_o such_o a_o rain_n be_v universal_a over_o the_o whole_a terrestrial_a globe_n it_o will_v necessary_o in_o the_o space_n of_o a_o hour_n make_v a_o rise_n of_o two_o or_o three_o brace_n round_o about_o the_o say_a globe_n and_o because_o we_o have_v from_o sacred_a record_n that_o in_o the_o time_n of_o the_o deluge_n it_o rain_v forty_o day_n and_o forty_o night_n namely_o for_o the_o space_n of_o 960_o hour_n its_o clear_a that_o if_o the_o say_a rain_n have_v be_v ten_o time_n big_a than_o we_o at_o perugia_n the_o rise_n of_o the_o water_n above_o the_o terrestrial_a globe_n will_v reach_v and_o pass_v a_o mile_n high_o than_o the_o top_n of_o the_o hill_n and_o mountain_n that_o be_v upon_o the_o superficies_n of_o the_o earth_n and_o they_o also_o will_v concur_v to_o increase_v the_o rise_n and_o therefore_o i_o conclude_v that_o the_o rise_v of_o the_o water_n of_o the_o deluge_n have_v a_o rational_a congruity_n with_o natural_a discourse_n of_o which_o i_o know_v very_o well_o that_o the_o eternal_a truth_n of_o the_o divine_a leaf_n have_v no_o need_n but_o however_o i_o think_v so_o clear_a a_o agreement_n be_v worthy_a of_o our_o consideration_n which_o give_v we_o occasion_n to_o adore_v and_o admire_v the_o greatness_n of_o god_n in_o his_o mighty_a work_n in_o that_o we_o be_v sometime_o able_a in_o some_o sort_n to_o measure_v they_o by_o the_o short_a standard_n of_o our_o reason_n many_o lesson_n also_o may_v be_v deduce_v from_o the_o same_o doctrine_n which_o i_o pass_v by_o for_o that_o every_o man_n of_o himself_o may_v easy_o know_v they_o have_v once_o establish_v this_o maxim_n that_o it_o be_v not_o possible_a to_o pronounce_v any_o thing_n of_o a_o certainty_n touch_v the_o quantity_n of_o run_v water_n by_o consider_v only_o the_o single_a vulgar_a measure_n of_o the_o water_n without_o the_o velocity_n and_o so_o on_o the_o contrary_a he_o that_o compute_v only_o the_o velocity_n without_o the_o measure_n shall_v commit_v very_o great_a error_n for_o treat_v of_o the_o measure_n of_o run_v water_n it_o be_v necessary_a the_o water_n be_v a_o body_n in_o handle_v its_o quantity_n to_o consider_v in_o it_o all_o the_o three_o dimension_n of_o breadth_n depth_n and_o length_n the_o two_o first_o dimension_n be_v observe_v by_o all_o in_o the_o common_a manner_n and_o ordinary_a way_n of_o measure_v run_v water_n but_o the_o three_o dimension_n of_o length_n be_v omit_v and_o haply_o such_o a_o oversight_n be_v commit_v by_o reason_n the_o length_n of_o run_v water_n be_v repute_v in_o some_o sense_n infinite_a in_o that_o it_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 the_o height_n one_o palm_n little_o more_o or_o less_o to_o measure_v what_o water_n pass_v through_o the_o regulator_n in_o a_o time_n give_v first_o we_o be_v to_o dam_v up_o the_o channel_n so_o that_o there_o pass_v not_o any_o water_n below_o the_o dam_n then_o we_o must_v place_v in_o the_o side_n of_o the_o channel_n in_o the_o part_n above_o the_o regulator_n three_o or_o four_o or_o five_o bent-pipe_n or_o syphon_n according_a to_o the_o quantity_n of_o the_o water_n that_o run_v along_o the_o channel_n in_o such_o sort_n as_o that_o they_o may_v drink_v up_o or_o draw_v out_o of_o the_o channel_n all_o the_o water_n that_o the_o channel_n bear_v and_o then_o shall_v we_o know_v that_o the_o syphon_n drink_v up_o all_o the_o water_n when_o we_o see_v that_o the_o water_n at_o the_o dam_n do_v neither_o rise_n high_o nor_o abate_v but_o always_o keep_v in_o the_o same_o level_n these_o thing_n be_v prepare_v take_v the_o instrument_n to_o measure_v the_o time_n we_o will_v examine_v the_o quantity_n of_o the_o water_n that_o issue_v by_o one_o of_o those_o syphon_n in_o the_o space_n of_o twenty_o vibration_n and_o the_o like_a will_v we_o do_v one_o by_o one_o with_o the_o other_o syphon_n and_o then_o collect_v the_o whole_a sum_n we_o will_v say_v that_o so_o much_o be_v the_o water_n that_o pass_v and_o run_v through_o the_o regulator_n or_o channel_n the_o dam_n be_v take_v away_o in_o the_o space_n of_o twenty_o second_o minute_n of_o a_o hour_n and_o calculate_v we_o may_v easy_o reduce_v it_o to_o hour_n day_n month_n and_o year_n and_o it_o have_v fall_v to_o my_o turn_n to_o measure_v this_o way_n the_o water_n of_o mill_n and_o fountain_n and_o i_o have_v be_v well_o assure_v of_o its_o exactness_n by_o often_o repeat_v the_o same_o work_n consideration_n and_o this_o method_n must_v be_v make_v use_n of_o in_o measure_v the_o water_n that_o we_o be_v to_o bring_v into_o conduct_n and_o carry_v into_o city_n and_o castle_n for_o fountain_n 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 of_o equal_o incline_v as_o the_o bed_n bc_n and_o its_o quick_a height_n ge_n be_v equal_a to_o the_o quick_a height_n aec_fw-la and_o have_v the_o same_o breadth_n bc_n it_o shall_v have_v of_o itself_o a_o velocity_n equal_a to_o the_o velocity_n of_o the_o first_o water_n fc_n but_o because_o beside_o its_o own_o motion_n which_o be_v impart_v to_o it_o by_o the_o motion_n of_o the_o water_n aec_fw-la it_o have_v also_o over_o and_o above_o its_o own_o motion_n the_o motion_n of_o aec_fw-la and_o because_o the_o two_o water_n gc_a and_o aec_fw-la be_v alike_o in_o velocity_n by_o the_o three_o supposition_n therefore_o the_o whole_a water_n gc_n shall_v be_v double_a in_o velocity_n to_o the_o water_n aec_fw-la which_o be_v that_o which_o we_o be_v to_o demonstrate_v this_o demonstration_n be_v not_o here_o insert_v as_o perfect_a the_o author_n have_v by_o several_a letter_n to_o his_o friend_n confess_v himself_o unsatisfied_a therewith_o and_o that_o he_o intend_v not_o to_o publish_v the_o theorem_fw-la without_o a_o more_o solid_a demonstration_n which_o he_o be_v in_o hope_n to_o light_v upon_o but_o be_v overtake_v by_o death_n he_o can_v not_o give_v the_o finish_v touch_n either_o to_o this_o or_o to_o the_o rest_n of_o the_o second_o book_n in_o consideration_n of_o which_o it_o seem_v good_a to_o the_o publisher_n of_o the_o same_o rather_o to_o omit_v it_o than_o to_o do_v any_o thing_n contrary_a to_o the_o mind_n of_o the_o author_n and_o this_o he_o hint_n by_o way_n of_o advertisement_n to_o those_o that_o have_v manuscript_n copy_n of_o this_o book_n with_o the_o say_a demonstration_n for_o this_o time_n let_v the_o reader_n content_v himself_o with_o the_o knowledge_n of_o so_o ingenious_a and_o profitable_a a_o conclusion_n of_o the_o truth_n of_o which_o he_o may_v with_o small_a expense_n and_o much_o pleasure_n be_v assure_v by_o mean_n of_o the_o experiment_n to_o be_v make_v in_o the_o same_o manner_n with_o that_o which_o be_v lay_v 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
be_v abate_v such_o a_o measure_n that_o same_o shall_v be_v only_o one_o three_o of_o its_o whole_a height_n but_o moreover_o divert_v the_o 4_o 9_o it_o shall_v abate_v two_o other_o three_o a_o most_o principal_a point_n and_o such_o that_o it_o be_v not_o have_v be_v well_o understand_v have_v cause_v very_o great_a disorder_n and_o there_o will_v now_o more_o than_o ever_o follow_v extreme_a damage_n if_o one_o shall_v put_v in_o execution_n the_o diversion_n of_o the_o sile_z and_o other_o river_n and_o it_o be_v manifest_a that_o in_o the_o same_o manner_n wherewith_o it_o have_v be_v demonstrate_v that_o the_o quantity_n of_o the_o water_n increase_v quadruple_a the_o height_n will_v increase_v only_o double_a and_o the_o quantity_n increase_v nonuple_n the_o height_n increase_v triple_a so_o that_o by_o add_v to_o unit_v all_o the_o odd_a number_n according_a to_o their_o series_n the_o height_n increase_v according_a to_o the_o natural_a progression_n of_o all_o the_o number_n from_o unit_n as_o for_o example_n there_o pass_v through_o a_o regulator_n such_o a_o certain_a quantity_n of_o water_n in_o one_o time_n add_v three_o of_o those_o measure_n the_o quick_a height_n be_v two_o of_o those_o part_n which_o at_o first_o be_v one_o and_o continue_v to_o add_v five_o of_o those_o say_a measure_n the_o height_n be_v three_o of_o those_o part_n which_o at_o first_o be_v one_o and_o thus_o add_v seven_o and_o then_o nine_o and_o then_o 11._o and_o then_o 13_o etc._n etc._n the_o height_n shall_v be_v 4._o then_o 5_o than_o 6._o then_o 7_o etc._n etc._n and_o for_o the_o great_a facility_n of_o the_o work_n we_o have_v describe_v the_o follow_a table_n of_o which_o we_o will_v declare_v the_o use_n the_o table_n be_v divide_v into_o three_o series_n or_o progression_n of_o number_n the_o first_o series_n contain_v all_o the_o number_n in_o the_o natural_a progression_n begin_v at_o a_o unit_fw-la and_o be_v call_v the_o series_n of_o the_o height_n the_o second_o contain_v all_o the_o odd_a number_n begin_v at_o a_o unit_fw-la and_o be_v call_v the_o series_n of_o the_o addition_n the_o three_o contain_v all_o the_o square_a number_n begin_v at_o a_o unit_fw-la and_o be_v call_v the_o series_n of_o quantity_n height_n 1_o 2_o 3_o 4_o 5_o 6_o 7_o 8_o 9_o 10_o 11_o addition_n 1_o 3_o 5_o 7_o 9_o 11_o 13_o 15_o 17_o 19_o 21_o quantity_n 1_o 4_o 9_o 16_o 25_o 36_o 49_o 64_o 81_o 100_o 121_o the_o use_n of_o the_o aforementioned_a table_n first_o if_o we_o suppose_v the_o whole_a quick_a height_n of_o a_o river_n of_o run_v water_n to_o be_v divide_v into_o any_o number_n of_o equal_a part_n at_o pleasure_n and_o will_v abate_v the_o same_o one_o five_o by_o mean_n of_o a_o division_n let_v there_o be_v find_v in_o the_o table_n in_o the_o series_n of_o height_n the_o number_n 5._o the_o denominator_fw-la of_o the_o part_n which_o the_o river_n be_v to_o abate_v and_o take_v the_o number_n that_o be_v immediate_o under_o it_o in_o the_o row_n of_o addition_n which_o be_v 9_o which_o let_v be_v substract_v from_o the_o number_n 25._o place_v underneath_o the_o same_o in_o the_o row_n of_o quantity_n the_o remainder_n 16._o signify_v that_o of_o the_o 25._o part_n of_o water_n that_o run_v in_o the_o river_n whilst_o it_o be_v 5_o measure_n high_a there_o do_v only_o run_v 16._o part_n so_o that_o to_o make_v it_o abate_v 1_o 5_o it_o be_v necessary_a to_o take_v 9_o 25_o from_o the_o water_n that_o the_o whole_a river_n do_v carry_v so_o that_o with_o substract_v somewhat_o more_o than_o one_o three_o of_o the_o water_n of_o the_o river_n it_o be_v abate_v but_o only_o one_o five_o 2._o and_o thus_o in_o the_o second_o place_n if_o one_o the_o contrary_a one_o will_v know_v how_o much_o water_n be_v to_o be_v add_v to_o the_o say_a river_n to_o make_v it_o increase_v one_o five_o more_o in_a height_n so_o as_o that_o it_o may_v run_v in_o the_o regulator_n 6._o of_o those_o part_n high_a of_o which_o it_o run_v before_o but_o 5._o let_v 6_o be_v find_v in_o the_o row_n of_o height_n and_o let_v the_o number_n 11._o stand_v under_o the_o same_o be_v take_v and_o add_v to_o the_o number_n 25._o that_o be_v place_v under_o the_o number_n 9_o in_o the_o addition_n and_o 5._o in_o the_o height_n and_o you_o shall_v have_v 36_o which_o be_v the_o quantity_n of_o the_o water_n that_o run_v with_o the_o height_n of_o the_o river_n when_o it_o be_v high_a 6_o of_o those_o part_n whereof_o it_o be_v before_o but_o 5._o 3._o but_o if_o it_o shall_v be_v desire_v to_o know_v how_o much_o water_n it_o be_v requisite_a to_o add_v to_o make_v the_o river_n rise_v so_o as_o that_o it_o may_v run_v in_o height_n 8._o of_o those_o part_n of_o which_o before_o it_o run_v but_o 5_o one_o oughts_z to_o take_v the_o sum_n of_o the_o number_n of_o the_o series_n of_o addition_n stand_v under_o 8._o 7._o and_o 6_o which_o be_v 15._o 13._o and_o 11._o that_o be_v 39_o and_o this_o shall_v be_v the_o sum_n that_o must_v be_v add_v to_o 25_o so_o that_o to_o make_v the_o river_n to_o run_v 8._o of_o those_o part_n in_o height_n of_o which_o it_o before_o do_v run_v 5_o it_o will_v be_v necessary_a to_o add_v 39_o of_o those_o part_n of_o which_o the_o river_n before_o be_v 25._o 4._o likewise_o the_o same_o table_n give_v the_o quantity_n of_o water_n that_o run_v from_o time_n to_o time_n through_o a_o river_n that_o increase_v by_o the_o addition_n of_o new_a water_n to_o the_o same_o in_o one_o of_o its_o height_n the_o quantity_n of_o its_o water_n be_v know_v as_o for_o example_n if_o we_o know_v that_o the_o river_n in_o one_o minute_n of_o a_o hour_n discharge_v 2500._o of_o those_o measure_n of_o water_n and_o run_v in_o height_n 5._o part_n in_o the_o regulator_n and_o afterward_o shall_v see_v that_o it_o run_v 8_o palm_n high_a find_v in_o the_o row_n of_o quantity_n the_o number_n place_v under_o 8._o which_o be_v 64._o we_o will_v say_v that_o the_o river_n heighten_v carry_v of_o water_n 64._o of_o those_o part_n whereof_o it_o carry_v before_o but_o 25_o and_o because_o before_o it_o carry_v 2500._o measure_n by_o the_o golden_a rule_n we_o will_v say_v that_o the_o river_n carry_v 6400._o of_o those_o measure_n of_o which_o before_o it_o carry_v 2500._o in_o this_o progress_n of_o nature_n be_v one_o thing_n real_o curious_a and_o that_o at_o first_o sight_n seem_v to_o be_v somewhat_o paradoxal_a that_o we_o proceed_v ordinate_o in_o the_o diversion_n and_o addition_n with_o addition_n and_o diversion_n so_o unequal_a the_o abating_n do_v notwithstanding_o always_o prove_v equal_a and_o so_o do_v the_o rise_n and_o who_o will_v ever_o think_v that_o a_o river_n in_o height_n v_o g._n 10._o palm_n run_v and_o carry_v a_o hundred_o measure_n in_o a_o minute_n of_o a_o hour_n be_v to_o abate_v but_o one_o palm_n only_o by_o the_o diversion_n of_o 19_o of_o those_o measure_n and_o then_o again_o that_o the_o buisiness_n come_v to_o that_o pass_n that_o it_o abate_v likewise_o a_o palm_n by_o the_o diversion_n of_o three_o only_a of_o those_o measure_n nay_o by_o the_o diversion_n of_o but_o one_o measure_n and_o yet_o it_o be_v most_o certain_a and_o this_o truth_n meet_v with_o so_o manifest_a proof_n in_o experience_n that_o it_o be_v very_o admirable_a and_o for_o the_o full_a satisfaction_n of_o those_o who_o not_o be_v able_a to_o comprehend_v subtle_a demonstration_n desire_v to_o be_v clear_o inform_v by_o the_o matter_n of_o fact_n and_o to_o see_v with_o their_o bodily_a eye_n and_o touch_v with_o their_o hand_n what_o their_o understanding_n and_o reason_n can_v reach_v unto_o i_o will_v hear_v add_v another_o very_a easy_a way_n to_o reduce_v all_o to_o a_o experiment_n the_o which_o may_v be_v make_v in_o little_a in_o great_a or_o in_o very_o great_a of_o which_o i_o make_v use_v frequent_o to_o the_o admiration_n of_o such_o as_o see_v it_o i_o prepare_v a_o hundred_o siphons_n or_o if_o you_o will_v bow_a pipe_n all_o equal_a and_o place_v they_o at_o the_o brim_n of_o a_o vessel_n wherein_o the_o water_n be_v keep_v at_o one_o and_o the_o same_o level_n whether_o all_o the_o syphon_n work_n or_o but_o a_o certain_a number_n of_o they_o the_o mouth_n by_o which_o the_o water_n issue_v be_v all_o place_v in_o the_o same_o level_n parallel_n to_o the_o horizon_n but_o low_a in_o level_n than_o the_o water_n in_o the_o vessel_n and_o gather_v all_o the_o water_n fall_v from_o the_o syphon_n into_o another_o vessel_n stand_v low_a than_o the_o former_a i_o make_v it_o to_o run_v away_o through_o a_o channel_n in_o such_o manner_n incline_v that_o want_v 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
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 we_o may_v very_o probable_o say_v that_o it_o will_v not_o happen_v save_v only_o in_o the_o succession_n of_o many_o and_o many_o century_n of_o year_n nor_o can_v i_o think_v it_o prudent_a counsel_n to_o take_v a_o resolution_n and_o embrace_v a_o design_n now_o to_o obtain_v a_o benefit_n very_o uncertain_a and_o more_o than_o that_o which_o only_o shall_v concern_v those_o who_o be_v to_o come_v very_o many_o age_n after_o we_o and_o thereby_o bring_v a_o cetain_v inconvenience_n upon_o ourselves_o and_o upon_o our_o child_n that_o be_v now_o alive_a and_o present_a let_v it_o be_v allege_v therefore_o although_o i_o hold_v it_o false_a that_o by_o the_o diversion_n of_o the_o river_n the_o lake_n may_v be_v keep_v in_o good_a condition_n for_o several_a year_n to_o come_v but_o i_o say_v confident_o and_o hope_v to_o demonstrate_v it_o that_o the_o diversion_n will_v bring_v the_o lake_n even_o in_o our_o day_n to_o be_v almost_o dry_a and_o at_o least_o will_v leave_v so_o 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