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_a 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 unequal_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 c_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 ab_fw-la 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
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._n 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 of59._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 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 49_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
he_o who_o desire_v more_o full_a and_o absolute_a solidity_n of_o reason_n may_v overpass_v this_o prefatory_a discourse_n and_o only_o consider_v what_o be_v treat_v of_o in_o the_o demonstration_n place_v towards_o the_o end_n and_o return_v afterward_o to_o the_o consideration_n of_o the_o thing_n collect_v in_o the_o corollary_n and_o appendix_n which_o demonstration_n notwithstanding_o may_v be_v pretermit_v by_o he_o that_o have_v not_o see_v at_o least_o the_o first_o six_o book_n of_o the_o element_n of_o euclid_n so_o that_o he_o diligent_o observe_v that_o which_o follow_v i_o say_v therefore_o that_o have_v in_o time_n past_a on_o divers_a occasion_n hear_v speak_v of_o the_o measure_n of_o the_o water_n of_o river_n and_o fountain_n say_v such_o a_o river_n be_v two_o or_o three_o thousand_o foot_n of_o water_n such_o a_o spring-water_n be_v twenty_o thirty_o or_o forty_o inch_n etc._n etc._n although_o in_o such_o manner_n i_o have_v find_v all_o to_o treat_v thereof_o in_o word_n and_o writing_n without_o variety_n and_o as_o we_o be_v wont_n to_o say_v constanti_fw-la sermone_fw-la yea_o even_a artist_n and_o ingeneer_n as_o if_o it_o be_v a_o thing_n that_o admit_v not_o of_o any_o doubt_n yet_o howsoever_o i_o remain_v still_o enfold_v in_o such_o a_o obscurity_n that_o i_o well_o know_v i_o understand_v nothing_o at_o all_o of_o that_o which_o other_o pretend_v full_a and_o clear_o to_o understand_v and_o my_o doubt_n arise_v from_o my_o frequent_a observation_n of_o many_o trench_n and_o channel_n which_o carry_v water_n to_o turn_v mill_n in_o which_o trench_n and_o channel_n the_o water_n be_v measure_v be_v find_v pretty_a deep_a but_o if_o afterward_o the_o same_o water_n be_v measure_v in_o the_o fall_n it_o make_v to_o turn_v the_o wheel_n of_o the_o mill_n it_o be_v much_o less_o not_o amount_v often_o to_o the_o ten_o part_n nor_o sometime_o to_o the_o twenty_o insomuch_o that_o the_o same_o run_a water_n come_v to_o be_v one_o while_n more_o another_o while_n less_o in_o measure_n in_o divers_a part_n of_o its_o channel_n and_o for_o that_o reason_n this_o vulgar_a manner_n of_o measure_v run_a water_n as_o indeterminate_v and_o uncertain_a be_v by_o i_o just_o suspect_v the_o measure_n be_v to_o be_v determinate_a and_o the_o same_o and_o here_o i_o free_o confess_v that_o i_o have_v singular_a help_n to_o resolve_v this_o difficulty_n from_o the_o excellent_a &_o accurate_a way_n of_o discourse_v as_o in_o allother_n matter_n so_o also_o in_o this_o of_o the_o right_n honourable_a and_o true_o noble_a signior_n ciampoli_n secretary_n of_o the_o pope_n secret_a affair_n who_o moreover_o not_o spare_v â—or_a the_o cost_n of_o the_o same_o generous_o give_v i_o occasion_n a_o few_o year_n past_a to_o try_v by_o exact_a experiment_n that_o which_o past_o concern_v this_o particular_a and_o to_o explain_v all_o more_o clear_o with_o a_o example_n we_o suppose_v a_o vessel_n fill_v with_o water_n as_o for_o instance_n a_o butt_n which_o be_v keep_v full_a though_o still_o water_n run_v out_o and_o the_o water_n run_v out_o by_o two_o tap_n equal_a of_o bigness_n one_o put_v in_o the_o bottom_n of_o the_o vessel_n and_o the_o other_o in_o the_o upper_a part_n it_o be_v manifest_a that_o in_o the_o time_n wherein_o from_o the_o upper_a part_n shall_v issue_v a_o determinate_a measure_n of_o water_n from_o the_o inferior_a part_n there_o shall_v issue_v four_o five_o and_o many_o more_o of_o the_o same_o measure_n according_a to_o the_o difference_n of_o the_o height_n of_o the_o tap_n and_o the_o distance_n of_o the_o upper_a tap_n from_o the_o superficies_n and_o level_n of_o the_o water_n of_o the_o vessel_n and_o all_o this_o will_v always_o follow_v though_o as_o have_v be_v say_v the_o tap_n be_v equal_a and_o the_o water_n in_o discharge_v keep_v the_o say_a tap_n always_o full_a where_o first_o we_o note_v that_o although_o the_o measure_n of_o the_o tap_n be_v equal_a nevertheless_o there_o issue_v from_o they_o in_o equal_a time_n unequal_a quantity_n of_o water_n and_o if_o we_o shall_v more_o attentive_o consider_v this_o business_n we_o shall_v find_v that_o the_o water_n by_o the_o low_a tap_n run_v and_o pass_v with_o much_o great_a velocity_n than_o it_o do_v by_o the_o upper_a whatever_o be_v the_o reason_n if_o therefore_o we_o will_v have_v such_o a_o quantity_n of_o water_n discharge_v from_o the_o upper_a tap_n as_o will_v discharge_v from_o the_o nether_a in_o the_o same_o time_n it_o be_v plain_a that_o either_o the_o upper_a tap_n must_v be_v multiply_v in_o such_o sort_n that_o so_o many_o more_o tap_n in_o number_n be_v place_v above_o than_o below_o as_o the_o nether_a tap_n shall_v be_v more_o swift_a than_o the_o upper_a or_o the_o upper_a tap_n make_v so_o much_o big_a than_o the_o nether_a by_o how_o much_o that_o beneath_o shall_v be_v more_o swift_a than_o that_o above_o and_o so_o then_o in_o equal_a time_n the_o same_o quantity_n of_o water_n shall_v discharge_v from_o the_o upper_a as_o do_v fromthâ—e_o nether_a part_n i_o will_v declare_v myself_o by_o another_o example_n if_o we_o shall_v imagine_v that_o two_o cord_n or_o line_n of_o equal_a thickness_n be_v draw_v through_o two_o hole_n of_o equal_a bore_n but_o so_o that_o the_o first_o pass_v with_o quadruple_a velocity_n to_o the_o second_o it_o be_v manifest_a that_o if_o in_o a_o determinate_a time_n we_o shall_v by_o the_o first_o bear_v have_v draw_v four_o ell_n of_o the_o line_n in_o the_o same_o time_n by_o the_o second_o hole_n we_o shall_v have_v draw_v but_o one_o ell_n of_o cord_n only_o and_o if_o by_o the_o first_o there_o pass_v twelve_o ell_n then_o through_o the_o second_o there_o shall_v pass_v only_o three_o ell_n and_o in_o short_a the_o quantity_n of_o cord_n shall_v have_v the_o same_o proportion_n to_o the_o cord_n that_o the_o volocity_n have_v to_o the_o velocity_n and_o therefore_o we_o desire_v to_o compensate_a the_o tardity_n of_o the_o second_o cord_n and_o maintain_v the_o same_o tardity_n to_o draw_v through_o the_o second_o hole_n as_o much_o cord_n as_o through_o the_o first_o it_o will_v be_v necessary_a to_o draw_v through_o the_o second_o bear_v four_o end_n of_o cord_n so_o that_o the_o thickness_n of_o all_o the_o cord_n by_o the_o second_o hole_n have_v the_o same_o proportion_n to_o the_o thickness_n of_o the_o cord_n which_o pass_v only_o by_o the_o first_o as_o the_o velocity_n of_o the_o cord_n by_o the_o first_o hole_n have_v reciprocal_o to_o the_o velocity_n of_o the_o codâ—s_n by_o the_o second_o hole_n and_o thus_o its_o clear_a that_o when_o there_o be_v draw_v through_o two_o hole_n equal_a quantity_n of_o cord_n in_o equal_a time_n but_o with_o unequal_a velocity_n it_o will_v be_v necessary_a that_o the_o thickness_n of_o all_o the_o four_o cord_n shall_v have_v the_o same_o reciprocal_a proportion_n to_o the_o thickness_n of_o the_o swift_a cord_n that_o the_o velocity_n of_o the_o swift_a cord_n have_v to_o the_o velocity_n of_o the_o slow_a the_o which_o be_v verify_v likewise_o in_o the_o fluid_a element_n of_o water_n and_o to_o the_o end_n that_o this_o principal_a fundamental_a be_v well_o understand_v i_o will_v also_o note_v a_o certain_a observation_n make_v my_o i_n in_o the_o art_n of_o wyer-drawing_a or_o spin_v gold_n silver_n brass_n and_o iron_n and_o it_o be_v this_o that_o such_o artificer_n desire_v more_o and_o more_o to_o disgrosse_v and_o subtillize_v the_o say_a metal_n have_v wound_n about_o a_o rocket_n or_o barrel_n the_o thread_n of_o the_o metal_n they_o place_v the_o rocket_n in_o a_o frame_n upon_o a_o steadfast_a axis_n in_o such_o sort_n that_o the_o rocket_n may_v turn_v about_o in_o itself_o then_o make_v one_o end_n of_o the_o thread_n to_o pass_v by_o force_n through_o a_o plate_n of_o steel_n pierce_v with_o divers_a hole_n great_a and_o lesser_a as_o need_n require_v fasten_v the_o same_o end_n of_o the_o thread_n to_o another_o rocket_n they_o wind_v up_o the_o thread_n which_o pass_v through_o a_o bear_v less_o than_o the_o thickness_n of_o the_o thread_n be_v of_o force_n constrain_v to_o disgrosse_v and_o subtillize_v now_o that_o which_o be_v intense_o to_o be_v observe_v in_o this_o business_n be_v this_o that_o the_o part_n of_o the_o thread_n before_o the_o hole_n be_v of_o such_o a_o thickness_n but_o the_o part_n of_o the_o same_o thread_n after_o it_o be_v pass_v the_o hole_n be_v of_o a_o lesser_a thickness_n and_o yet_o nevertheless_o the_o mass_n and_o weight_n of_o the_o thread_n which_o be_v draw_v forth_o be_v ever_o equal_a to_o the_o mass_n and_o weight_n of_o the_o thread_n which_o be_v wind_v up_o but_o if_o we_o shall_v well_o consider_v the_o matter_n we_o shall_v find_v that_o the_o thick_a the_o thread_n before_o the_o hole_n
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 verbi_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 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 sueh_a 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 excrescence_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 windgun_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 v._n g._n a_o channel_n fifty_o foot_n broad_a in_o which_o the_o derive_v water_n be_v to_o run_v waste_n ten_o foot_n deep_a they_o think_v they_o have_v diminish_v the_o measure_n of_o the_o water_n in_o the_o river_n five_o hundred_o foot_n which_o thing_n do_v not_o indeed_o so_o fall_v out_o and_o the_o reason_n be_v plain_a for_o that_o the_o channel_n be_v derive_v the_o rest_n of_o the_o main_a river_n diminish_v in_o velocity_n and_o therefore_o retain_v a_o great_a measure_n than_o it_o have_v at_o first_o before_o the_o derivation_n of_o the_o channel_n and_o moreover_o if_o the_o channel_n be_v derive_v it_o shall_v not_o conserve_v the_o same_o velocity_n which_o it_o have_v at_o first_o in_o the_o main_a river_n but_o shall_v diminish_v it_o it_o will_v be_v necessary_a that_o it_o have_v a_o great_a measure_n than_o it_o have_v before_o in_o the_o river_n and_o therefore_o to_o account_v aright_o there_o shall_v not_o be_v so_o much_o water_n derive_v into_o the_o channel_n as_o shall_v diminish_v the_o river_n according_a to_o the_o quantity_n of_o the_o water_n in_o the_o channel_n as_o be_v pretend_v corollary_n xiii_o this_o same_o consideration_n give_v i_o occasion_n to_o discover_v a_o most_o ordinary_a error_n observe_v by_o i_o in_o the_o business_n of_o the_o water_n of_o ferara_n when_o i_o be_v in_o those_o part_n in_o service_n of_o the_o most_o reverend_a and_o illustrious_a monsignor_n corsini_n the_o sublime_a wit_n of_o who_o have_v be_v a_o very_a great_a help_n to_o i_o in_o these_o contemplation_n it_o be_v very_o true_a i_o have_v be_v much_o perplex_v whether_o i_o shall_v commit_v this_o particular_a to_o paper_n or_o pass_v it_o over_o in_o silence_n for_o that_o i_o have_v ever_o doubt_v that_o the_o opinion_n so_o common_a and_o moreover_o confirm_v with_o a_o most_o manifest_a experiment_n may_v not_o only_o make_v this_o my_o conjecture_n to_o be_v esteem_v far_o from_o true_a but_o also_o to_o discredit_v with_o the_o world_n the_o rest_n of_o this_o my_o treatise_n nevertheless_o i_o have_v at_o last_o resolve_v not_o to_o be_v want_v to_o myself_o and_o to_o truth_n in_o a_o matter_n of_o itself_o and_o for_o other_o consequence_n most_o important_a nor_o do_v it_o seem_v to_o i_o requisite_a in_o difficult_a matter_n such_o as_o these_o we_o have_v in_o hand_n to_o resign_v ourselves_o to_o the_o common_a opinion_n since_o it_o will_v be_v very_o strange_a if_o the_o multitude_n in_o such_o matter_n shall_v hit_v on_o the_o truth_n nor_o aught_o that_o to_o be_v hold_v difficult_a in_o which_o even_o the_o vulgar_a do_v know_v the_o truth_n and_o right_n beside_o that_o i_o hope_v morever_o to_o prove_v all_o in_o such_o sort_n that_o person_n of_o solid_a judgement_n shall_v rest_v full_o persuade_v so_o that_o they_o but_o keep_v in_o mind_n the_o principal_a ground_n and_o foundation_n of_o all_o this_o treatise_n and_o though_o that_o which_o i_o will_v propose_v be_v a_o particular_a as_o i_o have_v say_v pertain_v only_o to_o the_o interest_n of_o
of_o a_o very_a easy_a and_o cheap_a way_n to_o clear_v up_o the_o whole_a business_n and_o moreover_o i_o will_v take_v the_o boldness_n to_o affirm_v that_o in_o case_n there_o shall_v not_o for_o the_o present_a any_o deliberation_n be_v make_v concern_v this_o affair_n according_a to_o my_o opinion_n yet_o nevertheless_o it_o will_v be_v at_o some_o time_n or_o other_o or_o if_o it_o be_v not_o thing_n will_v grow_v worse_o and_o worse_o for_o more_o clear_a understanding_n therefore_o it_o ought_v to_o be_v know_v that_o it_o be_v require_v as_o it_o be_v general_o use_v to_o measure_v the_o water_n of_o a_o river_n its_o breadth_n and_o its_o depth_n be_v take_v and_o these_o two_o dimension_n be_v multiply_v together_o the_o product_n be_v affirm_v to_o be_v the_o quantity_n of_o that_o river_n as_o for_o example_n if_o a_o river_n shall_v be_v 100_o foot_n broad_a and_o 20._o foot_n high_a it_o will_v be_v say_v that_o that_o river_n be_v 2000_o foot_n of_o water_n and_o so_o if_o a_o ditch_n shall_v be_v 15._o foot_n broad_a and_o 5._o foot_n high_a this_o same_o ditch_n will_v be_v affirm_v to_o be_v 75._o foot_n of_o water_n and_o this_o manner_n of_o measure_v run_v water_n have_v be_v use_v by_o the_o ancient_n and_o by_o modern_n with_o no_o other_o difference_n save_v only_o that_o some_o have_v make_v use_n of_o the_o foot_n other_o of_o the_o palm_n other_o of_o the_o brace_n and_o other_o of_o other_o measure_n now_o because_o that_o in_o observe_v these_o water_n that_o move_v i_o frequent_o find_v that_o the_o same_o water_n of_o the_o same_o river_n be_v in_o some_o cite_v of_o its_o channel_n pretty_a big_a and_o in_o other_o much_o less_o not_o arrive_v in_o some_o place_n to_o the_o twenty_o nor_o to_o the_o hundred_o part_n of_o that_o which_o it_o be_v see_v to_o be_v in_o other_o place_n therefore_o this_o vulgar_a way_n of_o measure_v the_o water_n that_o move_v for_o that_o they_o do_v not_o give_v i_o a_o certain_a and_o stable_a measure_n and_o quantity_n of_o water_n begin_v deserve_o to_o be_v suspect_v by_o i_o as_o difficult_a and_o defective_a be_v always_o various_a and_o the_o measure_n on_o the_o contrary_a be_v to_o be_v always_o determinate_a and_o the_o same_o it_o be_v therefore_o write_v that_o pondus_fw-la &_o pondus_fw-la mensura_fw-la &_o mensura_fw-la utrumque_fw-la abominabile_fw-la est_fw-la apud_fw-la deum_fw-la exod._n i_o consider_v that_o in_o the_o territory_n of_o brescia_n my_o native_a country_n and_o in_o other_o place_n where_o water_n be_v divide_v to_o overflow_v the_o ground_n by_o the_o like_a way_n of_o measure_v they_o there_o be_v commit_v grievous_a and_o most_o important_a error_n to_o the_o great_a prejudice_n of_o the_o public_a and_o of_o private_a person_n neither_o they_o that_o sell_v nor_o they_o that_o buy_v understand_v the_o true_a quantity_n of_o that_o which_o be_v sell_v and_o buy_v in_o regard_n that_o the_o same_o square_a measure_n as_o be_v accustom_v in_o those_o part_n assign_v one_o particular_a person_n carry_v to_o sometime_o above_o twice_o or_o thrice_o as_o much_o water_n as_o do_v the_o same_o square_a measure_n assign_v to_o another_o which_o thing_n prove_v to_o be_v the_o same_o inconvenience_n as_o if_o the_o measure_n wherewith_o wine_n and_o oil_n be_v buy_v and_o sell_v shall_v hold_v twice_o or_o thrice_o as_o much_o wine_n or_o oil_n at_o one_o time_n as_o at_o another_o now_o this_o consideration_n invite_v my_o mind_n and_o curiosity_n to_o the_o find_v out_o of_o the_o true_a measure_n of_o run_v water_n and_o in_o the_o end_n by_o occasion_n of_o a_o most_o important_a business_n that_o i_o be_v employ_v in_o some_o year_n since_o with_o great_a intensenesse_n of_o mind_n and_o with_o the_o sure_a direction_n of_o geometry_n i_o have_v discover_v the_o mistake_n which_o be_v that_o we_o be_v upon_o the_o business_n of_o take_v the_o measure_n of_o the_o water_n that_o move_v do_v make_v use_n of_o two_o dimension_n only_o namely_o breadth_n and_o depth_n keep_v no_o account_n of_o the_o length_n and_o yet_o the_o water_n be_v though_o run_v a_o body_n it_o be_v necessary_a in_o form_v a_o conceit_n of_o its_o quantity_n in_o relation_n to_o another_o to_o keep_v account_n of_o all_o the_o three_o dimension_n that_o be_v of_o length_n breadth_n and_o depth_n here_o a_o objection_n have_v be_v put_v to_o i_o in_o behalf_n of_o the_o ordinary_a way_n of_o measure_v run_v water_n in_o opposition_n to_o what_o i_o have_v above_o consider_v and_o propose_v and_o i_o be_v tell_v it_o be_v true_a that_o in_o measure_v a_o body_n that_o stand_v still_o one_o ought_v to_o take_v all_o the_o three_o dimension_n but_o in_o measure_v a_o body_n that_o continual_o move_v as_o the_o water_n the_o case_n be_v not_o the_o same_o for_o the_o length_n be_v not_o to_o be_v have_v the_o length_n of_o the_o water_n that_o move_v be_v infinite_a as_o never_o finish_v its_o run_n and_o consequent_o be_v incomprehensible_a by_o humane_a understanding_n and_o therefore_o with_o reason_n nay_o upon_o necessity_n it_o come_v to_o be_v omit_v in_o answer_n to_o this_o i_o say_v that_o in_o the_o abovesaid_a discourse_n two_o thing_n be_v to_o be_v consider_v distinct_o first_o whether_o it_o be_v possible_a to_o frame_v any_o conceit_n of_o the_o quantity_n of_o the_o body_n of_o the_o water_n with_o two_o dimension_n only_o and_o second_o whether_o this_o length_n be_v to_o be_v find_v as_o to_o the_o first_o i_o be_o very_o certain_a that_o no_o man_n let_v he_o be_v never_o so_o great_a a_o wit_n can_v never_o promise_v to_o frame_v a_o conceit_n of_o the_o quantity_n of_o the_o body_n of_o water_n without_o the_o three_o dimension_n of_o length_n and_o hereupon_o i_o return_v to_o affirm_v that_o the_o vulgar_a rule_n of_o measure_v run_v water_n be_v vain_a and_o erroneous_a this_o point_n be_v agree_v on_o i_o come_v to_o the_o second_o which_o be_v whether_o the_o three_o dimension_n of_o length_n may_v be_v measure_v and_o i_o say_v that_o if_o one_o will_v know_v the_o whole_a length_n of_o the_o water_n of_o a_o fountain_n or_o river_n thereby_o to_o come_v to_o know_v the_o quantity_n of_o all_o the_o water_n it_o will_v prove_v a_o impossible_a enterprise_n nay_o the_o know_n of_o it_o will_v not_o be_v useful_a but_o if_o one_o will_v know_v how_o much_o water_n a_o fountain_n or_o a_o river_n carry_v in_o a_o determinate_a time_n of_o a_o hour_n of_o a_o day_n or_o of_o a_o month_n etc._n etc._n i_o say_v that_o it_o be_v a_o very_a possible_a and_o profitable_a enquiry_n by_o reason_n of_o the_o innumerable_a benefit_n that_o may_v be_v derive_v thence_o it_o much_o import_v to_o know_v how_o much_o water_n a_o channel_n carry_v in_o a_o time_n give_v and_o i_o have_v demonstrate_v the_o same_o above_o in_o the_o begin_n of_o this_o book_n and_o of_o this_o we_o stand_v in_o need_n in_o the_o business_n of_o the_o lake_n that_o so_o we_o may_v be_v able_a to_o determine_v how_o much_o shall_v be_v the_o height_n of_o the_o brent_n when_o it_o be_v spread_v all_o over_o the_o lake_n for_o the_o three_o dimension_n of_o a_o body_n be_v give_v the_o body_n be_v know_v and_o the_o quantity_n of_o a_o body_n be_v give_v if_o you_o have_v but_o two_o dimension_n the_o three_o shall_v be_v know_v and_o thus_o dive_v far_o and_o far_o into_o this_o consideration_n i_o find_v that_o the_o velocity_n of_o the_o course_n of_o the_o water_n may_v be_v a_o hundred_o time_n great_a or_o lesser_a in_o one_o part_n of_o its_o channel_n than_o in_o another_o and_o therefore_o although_o there_o shall_v be_v two_o mouth_n of_o water_n equal_a in_o bigness_n yet_o nevertheless_o it_o may_v come_v to_o pass_v that_o one_o may_v discharge_v a_o hundred_o or_o a_o thousand_o 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 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 tardity_n 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 40._o brace_n broad_a and_o 2_o 1_o 2_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 1st_a 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 buisiness_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_v 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 consideration_n ii_o if_o the_o discourse_v well_o about_o the_o truth_n of_o thing_n most_o serene_a prince_n be_v as_o the_o carry_n of_o burden_n in_o which_o we_o see_v that_o a_o hundred_o horse_n carry_v a_o great_a weight_n than_o one_o horse_n only_o it_o will_v seem_v that_o one_o may_v make_v more_o account_n of_o the_o opinion_n of_o many_o man_n than_o of_o one_o alone_a but_o because_o that_o discourse_v more_o resemble_v run_v than_o carry_v burden_n in_o which_o we_o see_v that_o one_o barb_n alone_o run_v fast_a than_o a_o hundred_o heavy-heeled_a jade_n therefore_o i_o have_v ever_o more_o esteem_v one_o conclusion_n well_o manage_v and_o well_o consider_v by_o one_o understanding_n man_n although_o alone_o than_o the_o common_a and_o vulgar_a opinion_n especial_o when_o they_o concern_v abstruse_a and_o arduous_a point_n nay_o in_o such_o case_n the_o opinion_n mould_v and_o frame_v by_o the_o most_o ignorant_a and_o stupid_a vulgar_a have_v be_v ever_o suspect_v by_o i_o as_o false_a for_o that_o it_o will_v be_v a_o great_a wonder_n if_o in_o difficult_a matter_n a_o common_a capacity_n shall_v hit_v upon_o that_o which_o be_v handsome_a good_a and_o true_a hence_o i_o have_v and_o do_v hold_v in_o very_o great_a veneration_n the_o sum_n of_o the_o government_n of_o the_o most_o serene_a and_o eternal_a republic_n of_o venice_n which_o although_o as_o be_v in_o nature_n a_o commonwealth_n it_o ought_v to_o be_v govern_v by_o the_o great_a part_n yet_o nevertheless_o in_o arduous_a affair_n it_o be_v always_o direct_v by_o the_o grave_a judgement_n of_o few_o and_o not_o judge_v blind_o by_o the_o plebeian_n rout._n it_o be_v true_a that_o he_o that_o propound_v
against_o the_o law_n of_o god_n since_o that_o thereby_o the_o same_o measure_n be_v make_v sometime_o great_a and_o sometime_o lesser_a a_o disorder_n so_o enormous_a and_o execrable_a that_o i_o shall_v take_v the_o boldness_n to_o say_v that_o for_o this_o sole_a respect_n it_o ought_v to_o be_v condemn_v and_o prohibit_v likewise_o by_o human_a law_n which_o shall_v enact_v that_o in_o this_o business_n there_o shall_v be_v employ_v either_o this_o our_o rule_n or_o some_o other_o that_o be_v more_o exquisite_a and_o practicable_a whereby_o the_o measure_n may_v keep_v one_o constant_a and_o determinate_a tenor_n as_o we_o make_v it_o and_o not_o as_o it_o be_v now_o to_o make_v pondus_fw-la &_o pondus_fw-la mensura_fw-la &_o mensura_fw-la and_o this_o be_v all_o that_o i_o have_v to_o offer_v to_o your_o most_o illustrious_a lordship_n in_o obedience_n to_o your_o command_n reserve_v to_o myself_o the_o give_v of_o a_o more_o exact_a account_n of_o this_o my_o invention_n when_o the_o occasion_n shall_v offer_v of_o reduce_v to_o practice_n so_o holy_a just_a and_o necessary_a a_o reformation_n of_o the_o measure_n of_o run_v water_n and_o of_o aqueduct_n in_o particular_a which_o rule_n may_v also_o be_v of_o great_a benefit_n in_o the_o division_n of_o the_o great_a water_n to_o overflow_n ground_n and_o for_o other_o use_n i_o humble_o bow_v your_o most_o devote_a and_o most_o oblige_a servant_n d._n benedetto_n castelli_n abb._n casin_n finis_fw-la a_o table_n of_o the_o most_o observable_a matter_n in_o this_o treatise_n of_o the_o mensuration_n of_o run_v water_n a_o abatement_n of_o a_o river_n in_o different_a and_o unequal_a diversion_n be_v always_o equal_a which_o be_v prove_v with_o 100_o syphon_n page_n 75_o arno_n river_n when_o it_o rise_v upon_o a_o land-flood_n near_o the_o sea_n one_o three_o of_o a_o brace_n it_o rise_v about_o pisa_n 6._o or_o 7._o brace_n 82_o b_o banks_n near_o to_o the_o sea_n low_o than_o far_o from_o thence_o corollary_n fourteen_o 16_o brent_n river_n divert_v from_o the_o lake_n of_o venice_n and_o its_o effect_n 64_o brent_n suppose_v insufficient_a to_o remedy_v the_o inconvenience_n of_o the_o lake_n and_o the_o falsity_n of_o that_o supposition_n 67_o brent_n and_o its_o benefit_n in_o the_o lake_n 70_o its_o deposition_n of_o sand_n in_o the_o lake_n how_o great_a it_o be_v 78_o 79_o bridge_n over_o river_n and_o how_o they_o be_v to_o be_v make_v appendix_n viii_o 20_o burana_n river_n its_o rise_n and_o fall_v in_o panaro_n 110_o c_o castelli_n apply_v himself_o to_o this_o study_n by_o order_n of_o urban_n viii_o 2_o channel_n of_o navigation_n in_o the_o valley_n of_o bologna_n and_o its_o inconvenience_n 99_o carry_v into_o the_o po_n of_o ferrara_n and_o its_o benefit_n ibid._n ciampoli_n a_o lover_n of_o these_o observation_n of_o water_n 3_o d_o difficulty_n of_o this_o business_n of_o measure_v water_n 2_o disorder_n that_o happen_v in_o the_o distribution_n of_o the_o water_n of_o aqueduct_n and_o their_o remedy_n 113_o distribution_n of_o the_o water_n of_o fountain_n and_o aqueduct_n appendix_n x._o 22_o distribution_n of_o water_n to_o overflow_n ground_n appendix_n xi_o 23_o 69_o 70_o diversion_n of_o reno_n and_o other_o brook_n of_o romagna_n advise_v by_o p._n spernazzati_n to_o what_o end_n it_o be_v 100_o drain_v and_o ditch_n the_o benefit_n they_o receive_v by_o cut_v away_o the_o weed_n and_o reed_n appendix_n ix_o 21_o drain_v and_o sewer_n obstruct_v in_o the_o diversion_n of_o reno_n into_o main_a po_n and_o a_o remedy_n for_o the_o same_o 110_o e_z engineer_n unversed_a in_o the_o matter_n of_o water_n 2_o erour_n find_v in_o the_o common_a way_n of_o measure_v run_v water_n 68_o 69_o error_n inderive_v the_o water_n of_o acqua_fw-la paola_n appendix_n ii_o 17_o 18_o error_n of_o bartolotti_n 86_o 87_o error_n of_o engineer_n in_o the_o derivation_n of_o chenel_n corollary_n xii_o 12_o error_n of_o engineer_n in_o measure_v of_o reno_n in_o po._n appendix_n iii_o ibid._n error_n of_o other_o engineer_n contrary_a to_o the_o precedent_n appendix_n iu._n ibid._n error_n of_o giovanni_n fontana_n in_o measure_v water_n corollary_n xi_o 9_o error_n of_o giulio_n frontino_n in_o measure_v the_o water_n of_o aqueduct_n appendix_n i._o 17_o error_n commit_v in_o cut_v the_o bank_n at_o bondeno_n in_o the_o swell_n of_o po_n corollary_n xiii_o 81_o f_o fen_n pontine_n drain_v by_o pope_n sixtus_n quintus_fw-la with_o vast_a expense_n 92_o the_o ruin_n and_o miscarriage_n thereof_o 93_o tardity_n of_o the_o principal_a channel_n that_o drain_v they_o cause_n of_o the_o drown_v ibid._n they_o be_v obstruct_v by_o the_o fishing-wears_a which_o swell_v the_o river_n 94_o water_n of_o fiume_n sisto_n which_o flow_v in_o great_a abundance_n into_o the_o evacuator_fw-la of_o the_o say_a fen_n 94_o 95_o remedy_n to_o the_o disorder_n of_o those_o fen_n 95_o 96_o fontana_n giovanni_n his_o error_n in_o measure_v water_n corollary_n xi_o 9_o fiume_n morto_fw-la whether_o it_o ought_v to_o fall_v into_o the_o sea_n or_o into_o serchio_n 79_o let_v into_o serchio_n and_o its_o inconvenience_n 79_o 80_o the_o dangerous_a rise_n of_o its_o water_n when_o to_o be_v expect_v 81_o its_o inconvenience_n when_o it_o be_v high_a in_o level_a than_o serchio_n and_o why_o it_o rise_v most_o on_o the_o seacoast_n at_o such_o time_n at_o the_o wind_n make_v the_o sea_n to_o swell_v 83_o g_o galileo_n galilaei_n honourable_o mention_v page_z 2_o 28_o his_o rule_n for_o measure_v the_o time_n 49_o h_n height_n vide_fw-la quick_a height_n different_a make_v by_o the_o same_o stream_n of_o a_o brook_n or_o torrent_n according_a to_o the_o divers_a velocity_n in_o the_o entrance_n of_o the_o river_n corollary_n i._n 6_o height_n different_a make_v by_o the_o torrent_n in_o the_o river_n according_a to_o the_o different_a height_n of_o the_o river_n corollary_n ii_o ibid._n k_o knowledge_n of_o motion_n how_o much_o it_o import_v 1_o l_o lake_n of_o perugia_n and_o he_o observation_n make_v on_o it_o appendix_n xii_o 42_o lake_n of_o thrasimenus_n and_o consideration_n upon_o it_o a_o letter_n write_v to_o sig._n galileo_n galilaei_n 28_o lake_n of_o venice_n and_o consideration_n upon_o it_o 63_o 73_o low_a water_n which_o let_v the_o bottom_n of_o it_o be_v discover_v 64_o the_o stoppage_n and_o choke_n of_o the_o port_n a_o main_a cause_n of_o the_o disorder_n of_o the_o lake_n and_o the_o grand_a remedy_n to_o those_o disorder_n what_o it_o be_v 66_o lake_n and_o meers_n along_o the_o sea-ccosts_a and_o the_o cause_n thereof_o 65_o length_n of_o water_n how_o it_o be_v to_o be_v measure_v 70_o m_o measure_n and_o distribution_n of_o water_n appendix_n v._n 18_o measure_n of_o river_n that_o fall_v into_o other_o difficult_a coral_n x._o 9_o measure_n of_o the_o run_v water_n of_o a_o channel_n of_o a_o height_n know_v by_o a_o regulator_n of_o a_o measure_n give_v in_o a_o time_n assign_v proposition_n i._o problem_n i_o 50_o measure_n of_o the_o water_n of_o any_o river_n of_o any_o greatness_n in_o a_o time_n give_v proposition_n v._o problem_n iii_o 60_o measure_n that_o show_v how_o much_o water_n a_o river_n discharge_v in_o a_o time_n give_v 48_o mole-hole_n motion_n the_o principal_a subject_n of_o philosophy_n 1_o mud._n vide_fw-la sand._n n_o navigation_n from_o bologna_n to_o ferrara_n be_v become_v impossible_a till_o such_o time_n as_o reno_n be_v divert_v 101_o navigation_n in_o the_o lake_n of_o venice_n endanger_v and_o how_o restore_v 65_o 70_o p_o perpendicularity_n of_o the_o bank_n of_o the_o river_n to_o the_o upper_a superficies_n of_o it_o 37_o perpendicularity_n of_o the_o bank_n to_o the_o bottom_n 37_o perugia_n vide_fw-la lake_n pontine_n vide_fw-la fen_n port_n of_o venice_n malamocco_n bondolo_n and_o chiozza_n choke_v up_o for_o wâ—nt_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 highâ—â—_n 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 in_o 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_a eiume_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 the_o less_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 a_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 valano_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 15_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 copernicus_n repute_v the_o earth_n a_o globe_n like_a to_o a_o planet_n celestial_a substance_n that_o be_v in_o alterable_a and_o elementary_a that_o be_v alterable_a be_v necessary_a in_o the_o opinion_n of_o aristotle_n aristotle_n make_v the_o world_n perfect_a because_o it_o have_v the_o threefold_a dimension_n aristotle_n demonstration_n to_o prove_v the_o dimension_n to_o be_v three_o and_o no_o more_o the_o number_n three_o celebrate_v among_o the_o pythagorian_n omne_fw-la totum_fw-la &_o perfectum_fw-la or_o solid_a plato_n hold_v that_o humane_a understanding_n partake_v of_o divinity_n because_o it_o understand_v number_n the_o mystery_n of_o pythagorick_a number_n fabulous_a de_fw-fr papyrio_fw-la pâ—aetextato_fw-la gellius_n 1._o 2._o 3._o a_o geometrical_a demonstration_n of_o the_o triple_a dimension_n in_o physical_a proof_n geometrical_a exactness_n be_v not_o necessary_a part_n of_o the_o world_n be_v two_o according_a to_o aristotle_n celestial_a and_o elementary_a contrary_n to_o one_o another_o local_a motion_n of_o three_o kind_n right_a circular_a &_o mix_v circular_a and_o straight_a motion_n be_v simple_a as_o proceed_v by_o simple_a line_n ad_fw-la medium_n à _fw-fr 〈◊〉_d &_o circa_fw-la medium_n the_o definition_n of_o nature_n either_o imperfect_a or_o unseasonable_a produce_v by_o aristotle_n the_o helix_fw-la about_o the_o cylinder_n may_v be_v say_v to_o be_v a_o simple_a line_n aristotle_n accommodate_v the_o rule_n of_o architecture_n to_o the_o frame_n of_o the_o world_n and_o not_o the_o frame_n to_o the_o rule_n right_o motion_n sometime_o simple_a and_o sometime_o mix_v according_a to_o arist._n the_o circular_a line_n perfect_a according_a to_o aristotle_n and_o but_o the_o right_n imperfect_a and_o why_o the_o world_n be_v suppose_v by_o the_o author_n to_o be_v perfect_o ordinate_a straight_o motion_n impossible_a in_o the_o world_n exact_o ordinate_a right_o motion_n nature_n infinite_a motion_n by_o a_o right_a line_n natural_o impossible_a nature_n attempt_v not_o thing_n impossible_a to_o be_v effect_v right_o motion_n may_v perhaps_o be_v in_o thâ—_n first_o chaos_n right_o motion_n be_v commodious_a to_o range_v in_o order_n thing_n out_o of_o order_n mundane_a body_n move_v in_o the_o begin_n in_o a_o right_a line_n and_o afterward_o circular_o according_a to_o plato_n plato_n thus_o do_v he_o covert_o and_o modest_o style_v himself_o throughout_o this_o work_n a_o movable_a be_v in_o a_o state_n of_o rest_n shall_v not_o move_v unless_o it_o have_v a_o inclination_n to_o some_o particular_a place_n the_o movable_a accelerate_v its_o motion_n go_v towards_o the_o place_n whither_o it_o have_v a_o inclination_n the_o movable_a pass_v from_o rest_n go_v through_o all_o the_o degree_n of_o tardity_n rest_v the_o infinite_a degree_n of_o tardity_n the_o movable_a do_v not_o accelerate_v save_v only_o as_o it_o approach_v near_a to_o we_o term_n nature_n to_o introduce_v in_o the_o movable_a a_o certain_a degree_n of_o velocity_n make_v it_o move_v in_o a_o right_a line_n vniform_a
the_o space_n of_o six_o hour_n in_o ancona_n in_o *_o ragusa_n in_o corfu_n where_o the_o tide_n be_v very_o small_a and_o haply_o unobservable_a who_o will_v invent_v a_o way_n to_o pour_v new_a water_n into_o a_o immovable_a vessel_n and_o to_o make_v that_o it_o rise_v only_o in_o one_o determinate_a part_n of_o it_o and_o in_o other_o place_n not_o will_v you_o say_v that_o this_o new_a water_n be_v borrow_v from_o the_o ocean_n be_v bring_v in_o by_o the_o straight_a of_o gibraltar_n this_o will_v not_o remove_v the_o doubt_n aforesaid_a but_o will_v beget_v a_o great_a and_o first_o tell_v i_o what_o ought_v to_o be_v the_o current_n of_o that_o water_n that_o enter_v at_o the_o straits_n mouth_n be_v carry_v in_o six_o hour_n to_o the_o remote_a creek_n of_o the_o mediterrane_n at_o a_o distance_n of_o two_o or_o three_o thousand_o mile_n and_o that_o return_v the_o same_o space_n again_o in_o a_o like_a time_n at_o its_o go_v back_o what_o will_v ship_n do_v that_o lie_v out_o at_o sea_n what_o will_v become_v of_o those_o that_o shall_v be_v in_o the_o straights-mough_a in_o a_o continual_a precipice_n of_o a_o vast_a accumulation_n of_o water_n that_o enter_v in_o at_o a_o channel_n but_o eight_o mile_n broad_a be_v to_o give_v admittance_n to_o so_o much_o water_n as_o in_o six_o hour_n over-floweth_a a_o tract_n of_o many_o hundred_o mile_n broad_a &_o thousand_o in_o length_n what_o tiger_n what_o falcon_n run_v or_o fly_v with_o so_o much_o swiftness_n with_o the_o swiftness_n i_o say_v of_o above_z 400_o mile_n a_o hour_n the_o current_n run_v nor_o can_v it_o be_v deny_v the_o long-waye_n of_o the_o gulf_n but_o so_o slow_o as_o that_o a_o boat_n with_o oar_n will_v out-go_v they_o though_o indeed_o not_o without_o defalk_v for_o their_o wander_n moreover_o if_o this_o water_n come_v in_o at_o the_o straight_a the_o other_o doubt_v yet_o remain_v namely_o how_o it_o come_v to_o flow_v here_o so_o high_a in_o a_o place_n so_o remote_a without_o first_o rise_v a_o like_a or_o great_a height_n in_o the_o part_n more_o adjacent_a in_o a_o word_n i_o can_v think_v that_o either_o obstinacy_n or_o sharpness_n of_o wit_n can_v ever_o find_v a_o answer_n to_o these_o objection_n nor_o consequent_o to_o maintain_v the_o stability_n of_o the_o earth_n against_o they_o keep_v within_o the_o bound_n of_o nature_n sagr._fw-la i_o have_v all_o the_o while_n perfect_o apprehend_v you_o in_o this_o and_o i_o stand_v greedy_o attend_v to_o hear_v in_o what_o manner_n these_o wonder_n may_v occur_v without_o obstruction_n from_o the_o motion_n already_o assign_v to_o the_o earth_n salv_n these_o effect_n be_v to_o ensue_v in_o consequence_n of_o the_o motion_n that_o natural_o agree_v with_o the_o earth_n it_o be_v necessary_a that_o they_o not_o only_o meet_v with_o no_o impediment_n or_o obstacle_n but_o that_o they_o do_v follow_v easy_o &_o not_o only_o that_o they_o follow_v with_o facility_n but_o with_o necessity_n so_o as_o that_o it_o be_v impossible_a that_o it_o shall_v succeed_v otherwise_o for_o such_o be_v the_o property_n &_o condition_n of_o thing_n natural_a &_o true_a have_v therefore_o show_v the_o impossibility_n of_o render_v a_o reason_n of_o the_o motion_n discern_v in_o the_o water_n difficulty_n &_o at_o the_o same_o time_n to_o maintain_v the_o immobility_n of_o the_o vessel_n that_o contain_v they_o we_o may_v proceed_v to_o inquire_v whether_o the_o mobility_n of_o the_o container_n may_v produce_v the_o require_a effect_n in_o the_o manner_n that_o it_o be_v observe_v to_o evene_v two_o kind_n of_o motion_n may_v be_v confer_v upon_o a_o vessel_n whereby_o the_o water_n therein_o contain_v fall_v may_v acquire_v a_o faculty_n of_o fluctuate_a in_o it_o one_o while_o towards_o one_o side_n and_o another_o while_n towards_o another_o and_o there_o one_o while_n to_o ebb_v and_o another_o while_n to_o flow_v the_o first_o be_v when_o first_o one_o and_o then_o another_o of_o those_o side_n be_v decline_v for_o then_o the_o water_n run_v towards_o the_o incline_a side_n will_v alternate_o be_v high_o and_o low_o sometime_o on_o one_o side_n and_o sometime_o on_o another_o but_o because_o that_o this_o rise_n and_o abate_v be_v no_o other_o than_o a_o recession_n and_o accession_n to_o the_o centre_n of_o the_o earth_n such_o a_o motion_n can_v be_v ascribe_v to_o the_o cavity_n of_o the_o say_a earth_n that_o be_v the_o vessel_n which_o contain_v the_o water_n the_o part_n of_o which_o vessel_n can_v by_o any_o whatsoever_o motion_n assign_v to_o the_o earth_n same_o be_v make_v to_o approach_v or_o recede_v from_o the_o centre_n of_o the_o same_o the_o other_o sort_n of_o motion_n be_v when_o the_o vessel_n move_v without_o incline_v in_o the_o least_o with_o a_o progressive_a motion_n not_o uniform_a but_o that_o change_v velocity_n by_o sometime_o accellerate_v and_o other_o time_n retard_v from_o which_o disparity_n it_o will_v follow_v fro_o that_o the_o water_n contain_v 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acceleration_n namely_o that_o confer_v on_o the_o bark_n a_o new_a cause_n of_o great_a velocity_n the_o prow_n and_o poop_n both_o accelerate_v in_o one_o and_o the_o same_o manner_n but_o in_o huge_a great_a vessel_n such_o as_o be_v the_o very_a long_a bottom_n of_o sea_n albeit_o they_o also_o be_v no_o other_o than_o certain_a cavity_n make_v in_o the_o solidity_n of_o the_o terrestrial_a globe_n it_o always_o admirable_o happen_v that_o their_o extreme_n do_v not_o united_o equal_a and_o at_o the_o same_o moment_n of_o time_n increase_v and_o diminish_v their_o motion_n but_o it_o happen_v that_o when_o one_o of_o its_o extreme_n have_v by_o virtue_n of_o the_o commixtion_n of_o the_o two_o motion_n diurnal_a and_o annual_a great_o retard_v its_o velocity_n the_o other_o extreme_a be_v animate_v with_o a_o extreme_a swift_a motion_n which_o for_o the_o better_a understanding_n of_o it_o we_o will_v explain_v reassume_v a_o scheme_n like_o to_o the_o former_a in_o which_o if_o we_o do_v but_o suppose_v a_o tract_n of_o sea_n to_o be_v long_o v_o g._n a_o four_o part_n as_o be_v the_o arch_n b_o c_o in_fw-la fig._n 2._o because_o the_o part_n b_o be_v as_o have_v be_v already_o declare_v very_o swift_a in_o motion_n by_o reason_n of_o the_o union_n of_o the_o two_o motion_n diurnal_a and_o annual_a towards_o one_o and_o the_o same_o way_n but_o the_o part_n c_o at_o the_o same_o time_n be_v retard_v in_o its_o motion_n as_o be_v deprive_v of_o the_o progression_n dependent_a on_o the_o diurnal_a motion_n if_o we_o suppose_v i_o say_v a_o tract_n of_o sea_n as_o long_o as_o the_o arch_n b_o c_o we_o have_v already_o see_v that_o its_o extreme_n shall_v move_v in_o the_o same_o time_n with_o great_a inequality_n and_o extreme_o different_a will_v the_o velocity_n of_o a_o tract_n of_o sea_n be_v that_o be_v in_o length_n a_o semicircle_n and_o place_v in_o the_o position_n b_o c_o d_o in_o regard_n that_o the_o extreme_a b_o will_v be_v in_o a_o most_o accelerate_v motion_n and_o the_o other_o d_o in_o a_o most_o slow_a one_o and_o the_o intermediate_v part_n towards_o c_o will_v be_v in_o a_o moderate_a motion_n and_o according_a as_o the_o say_a tract_n of_o sea_n shall_v be_v short_a they_o shall_v less_o participate_v of_o this_o extravagant_a accident_n of_o be_v in_o some_o hour_n of_o the_o day_n with_o their_o part_n diverse_o affect_v by_o velocity_n and_o tardity_n of_o motion_n so_o that_o if_o as_o in_o the_o first_o case_n we_o see_v by_o experience_n that_o the_o acceleration_n and_o retardation_n though_o equal_o impart_v to_o all_o the_o part_n of_o the_o contain_v vessel_n be_v the_o cause_n that_o the_o water_n contain_v fluctuate_v too_o and_o again_o what_o may_v we_o think_v will_v happen_v in_o a_o vessel_n so_o admirable_o dispose_v that_o retardation_n and_o acceleration_n of_o motion_n be_v very_o unequal_o contribute_v to_o its_o part_n certain_o we_o must_v needs_o grant_v that_o great_a and_o more_o wonderful_a cause_n of_o the_o commotion_n in_o the_o water_n ought_v to_o be_v look_v for_o and_o though_o it_o may_v seem_v impossible_a to_o some_o that_o in_o artificial_a machine_n and_o vessel_n we_o shall_v be_v able_a to_o experiment_n the_o effect_n of_o such_o a_o accident_n yet_o nevertheless_o it_o be_v not_o absolute_o impossible_a to_o be_v do_v and_o i_o have_v by_o i_o the_o model_n of_o a_o engine_n in_o which_o the_o effect_n of_o these_o admirable_a commixtion_n of_o motion_n may_v be_v particular_o observe_v but_o as_o to_o what_o concern_v our_o present_a purpose_n that_o which_o you_o may_v have_v hitherto_o comprehend_v with_o your_o imagination_n may_v suffice_v sagr._fw-la i_o for_o my_o own_o particular_a very_o well_o conceive_v that_o this_o admirable_a accident_n ought_v necessary_o to_o evene_v in_o the_o straits_n of_o sea_n and_o especial_o
answer_v proportionable_o as_o if_o descend_v from_o the_o same_o place_n 19_o immense_a magnitude_n and_o number_n be_v incomprehensible_a by_o our_o understand_n 332_o mars_n mars_n necessary_o include_v within_o its_o orb_n the_o earth_n and_o also_o the_o sun_n 298_o mars_n at_o its_o opposition_n to_o the_o sun_n seem_v sixty_o time_n big_a than_o towards_o the_o conjunction_n 298_o mars_n make_v a_o hot_a assault_n upon_o the_o copernican_n systeme_n 302_o marsilius_n signior_n caesar_n marsilius_n observe_v the_o meridian_n to_o be_v movable_a 422_o medicean_n the_o time_n of_o the_o medicean_n planet_n conversion_n 101_o the_o medicean_n planet_n be_v as_o it_o be_v four_o moon_n about_o jupiter_n 307_o mediterran_n mediterranean_a sea_n make_v by_o the_o separation_n of_o abila_n and_o calpen_n 35_o the_o voyage_n in_o the_o mediterran_n from_o east_n to_o west_n be_v make_v in_o short_a time_n than_o from_o west_n to_o east_n 403_o mercury_n the_o revolution_n of_o mercury_n conclude_v to_o be_v about_o the_o sun_n within_o the_o orb_n of_o venus_n 298_o mercury_n admit_v not_o of_o clear_a observation_n 307_o moon_n the_o moon_n have_v no_o generation_n of_o thing_n like_a as_o we_o have_v nor_o be_v it_o inhabit_v by_o men._n 47_o in_o the_o moon_n may_v be_v a_o generation_n of_o thing_n different_a from_o we_o 47_o there_o may_v be_v substance_n in_o the_o moon_n very_o different_a from_o we_o 48_o the_o first_o resemblance_n between_o the_o moon_n and_o earth_n which_o be_v that_o of_o figure_n be_v prove_v by_o their_o manner_n of_o be_v illuminate_v by_o the_o sun_n 48_o the_o second_o resemblance_n be_v the_o moon_n be_v opacous_a as_o the_o earth_n 48_o the_o three_o resemblance_n be_v the_o moon_n be_v dense_n and_o mountainous_a as_o the_o earth_n 49_o the_o four_o resemblance_n be_v the_o moon_n be_v distinguish_v into_o two_o different_a part_n for_o clarity_n and_o obscurity_n as_o the_o terrestrial_a globe_n into_o sea_n and_o land_n 49_o the_o five_o resemblance_n be_v mutation_n of_o figure_n in_o the_o earth_n like_o those_o of_o the_o moon_n and_o make_v with_o the_o same_o period_n 49_o all_o the_o earth_n see_v half_a only_o of_o the_o moon_n and_o half_a only_a of_o the_o moon_n see_v all_o the_o earth_n 51_o two_o spot_n in_o the_o moon_n by_o which_o it_o be_v perceive_v that_o she_o have_v respect_n to_o the_o centre_n of_o the_o earth_n in_o her_o motion_n 52_o light_n reflect_v from_o the_o earth_n into_o the_o moon_n 52_o the_o six_o resemblance_n be_v that_o the_o earth_n and_o moon_n interchangeable_o illuminate_v 53_o the_o seven_o resemblance_n be_v that_o the_o earth_n and_o moon_n interchangeable_o eclipse_v 53_o the_o secondary_a clarity_n of_o the_o moon_n esteem_v to_o be_v its_o native_a light_n 54_o the_o surface_n of_o the_o moon_n more_o sleek_a than_o any_o lookingglass_n 55_o the_o eminency_n and_o cavity_n in_o the_o moon_n be_v illusion_n of_o its_o opacous_a and_o perspicuous_a part_n 55_o the_o moon_n surface_n be_v sharp_a as_o be_v large_o prove_v 57_o the_o moon_n if_o it_o it_o be_v sleek_a like_o a_o spherical_a lookingglass_n will_v be_v invisible_a 60_o &_o 62_o the_o apparent_a vnevenness_n of_o the_o moon_n surface_n apt_o represent_v by_o mother_n of_o pearl_n 70_o the_o apparent_a vnevenness_n of_o the_o moon_n can_v be_v imitate_v by_o way_n of_o more_o and_o less_o opacity_n and_o perspicuity_n 71_o the_o various_a aspect_n of_o the_o moon_n imitable_a by_o any_o opacous_a matter_n 71_o sundry_a phaenomena_n from_o whence_o the_o moon_n montuosity_n be_v argue_v 71_o the_o moon_n appear_v bright_a by_o night_n than_o by_o day_n 72_o the_o moon_n behold_v in_o the_o day_n time_n be_v like_a to_o a_o little_a cloud_n 72_o cloud_n be_v no_o less_o apt_a than_o the_o moon_n to_o be_v illuminate_v by_o the_o sun_n 73_o a_o wall_n illuminate_v by_o the_o sun_n compare_v to_o the_o moon_n shine_v no_o less_o than_o it_o 73_o the_o three_o reflection_n of_o a_o wall_n illuminate_v more_o than_o the_o first_o of_o the_o moon_n 74_o the_o light_n of_o the_o moon_n weak_a than_o that_o of_o the_o twilight_n 74_o the_o secondary_a light_n of_o the_o moon_n cause_v by_o the_o sun_n according_a to_o some_o 76_o the_o secondary_a light_n of_o the_o moon_n appear_v in_o form_n of_o a_o ring_n i._n e._n bright_a in_o the_o extreme_a circumference_n and_o not_o in_o the_o midst_n and_o why_o 77_o the_o secondary_a light_n of_o the_o moon_n how_o it_o be_v to_o be_v observe_v 78_o the_o moon_n discus_fw-la in_o a_o solar_a eclipse_n can_v be_v see_v only_o by_o privation_n 78_o solidity_n of_o the_o moon_n globe_n argue_v from_o its_o be_v mountainous_a 81_o the_o secondary_a light_n of_o the_o moon_n clear_a before_o the_o conjunction_n than_o after_o 82_o the_o obscure_a part_n of_o the_o moon_n be_v plain_n and_o the_o more_o bright_a mountain_n 83_o long_a ledge_n of_o mountain_n about_o the_o spot_n of_o the_o moon_n 83_o there_o be_v not_o 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attribute_n which_o differ_v the_o celestial_a and_o elementary_a body_n depend_v on_o the_o motion_n assign_v they_o by_o aristotle_n 25_o peripatetic_n improper_o assign_v those_o motion_n to_o the_o element_n for_o natural_a with_o which_o they_o never_o be_v move_v and_o those_o for_o preternatural_a with_o which_o they_o always_o move_v 33_o motion_n as_o to_o the_o thing_n that_o move_v thereby_o be_v as_o if_o it_o never_o be_v and_o so_o far_o operate_v as_o it_o relate_v to_o thing_n deprâ—ved_v of_o motion_n 98_o motion_n can_v be_v make_v without_o its_o movable_a subject_n 104_o motion_n and_o rest_v principal_a accident_n in_o nature_n 112_o two_o thing_n necessary_a for_o the_o perpetuate_n of_o a_o motion_n a_o unlimited_a space_n and_o a_o incorruptible_a movable_n 117_o disparity_n in_o the_o motion_n of_o a_o stone_n fall_v from_o the_o round_a top_n of_o a_o ship_n and_o from_o the_o top_n of_o a_o tower_n 123_o the_o motion_n of_o grave_n pendula_fw-la may_v be_v perpetuate_v impediment_n be_v remove_v 203_o whence_o the_o motion_n of_o a_o cadent_a body_n be_v collect_v 224_o the_o motion_n of_o the_o eye_n argue_v the_o motion_n of_o the_o body_n look_v on_o 224_o different_a motion_n depend_v on_o the_o fluctuation_n of_o the_o ship_n 226_o our_o motion_n may_v be_v either_o intern_a or_o extern_a and_o yet_o we_o never_o perceive_v or_o feel_v it_o 229_o the_o motion_n of_o a_o boat_n insensible_a to_o those_o that_o be_v within_o it_o as_o to_o the_o sense_n of_o feel_v 229_o the_o motion_n of_o a_o boat_n sensible_a to_o sight_n join_v with_o reason_n 229_o a_o simple_a body_n as_o the_o earth_n can_v move_v with_o three_o several_a motion_n 231_o motion_n and_o rest_n be_v more_o different_a than_o right_a motion_n and_o circular_a 237_o one_o may_v more_o rational_o ascribe_v to_o the_o earth_n two_o intern_a principle_n to_o the_o right_n and_o circular_a motion_n than_o two_o to_o motion_n and_o rest._n 237_o the_o diversity_n of_o 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the_o sun_n from_o the_o summer_n solstice_n 352_o the_o sun_n pass_v one_o half_a of_o the_o zodiac_n nine_o day_n soon_o than_o the_o other_o 416_o the_o miracle_n in_o joshuah_n of_o the_o sun_n stand_v still_o answer_v not_o to_o the_o intent_n of_o lengthen_v the_o day_n but_o on_o the_o contrary_a excellent_o agree_v with_o the_o copernican_n systeme_n 456_o the_o sun_n without_o change_n of_o place_n revolve_v upon_o its_o own_o centre_n in_o the_o space_n of_o a_o month_n 457_o the_o nobility_n of_o the_o sun_n as_o be_v the_o fountain_n of_o light_n heart_n of_o the_o world_n and_o principle_n of_o motion_n 457_o the_o sun_n stand_v still_o in_o joshuah_n explain_v by_o kepler_n 462_o the_o sun_n find_v to_o be_v near_o to_o we_o than_o in_o time_n past_a by_o five_o thousand_o mile_n 469_o the_o sun_n moon_n and_o star_n be_v one_o and_o the_o same_o thing_n 485_o why_o the_o sun_n to_o our_o think_n move_v and_o not_o the_o earth_n 486_o how_o the_o sun_n be_v say_v to_o rise_v and_o set_v by_o extrinsic_a denomination_n 489_o the_o sun_n be_v the_o king_n heart_n and_o lamp_n of_o the_o world_n 497_o sympathy_n sympathy_n and_o antipathy_n term_n introduce_v by_o philosopher_n the_o more_o easy_o to_o give_v a_o reason_n of_o many_o natural_a effect_n 373_o system_fw-la of_o copernicus_n the_o copernican_n system_v once_o admit_v for_o true_a exposition_n may_v be_v find_v out_o for_o all_o those_o scripture_n than_o that_o seem_v to_o make_v against_o it_o 459_o didacus_n à _fw-la stunica_fw-la hold_v that_o the_o scripture_n may_v be_v best_a expound_v by_o the_o copernican_n system_fw-la 468_o system_fw-la of_o universe_n the_o system_fw-la of_o the_o universe_n design_v from_o the_o appearance_n 296_o the_o system_fw-la of_o the_o universe_n may_v probable_o have_v be_v intend_v to_o have_v be_v represent_v by_o the_o golden_a candlestick_n 500_o the_o system_v represent_v likewise_o by_o the_o apple_n in_o paradise_n 501_o t_o telescope_n the_o 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follower_n never_o attempt_v to_o see_v whether_o there_o be_v any_o phaenomena_n in_o the_o firmament_n for_o or_o against_o the_o annual_a motion_n 337_o tycho_n and_o other_o argue_v against_o the_o annual_a motion_n from_o the_o invariable_a elevation_n of_o the_o pole_n 338_o five_o velocity_n vniform_a velocity_n suitable_a with_o circular_a motion_n 12_o nature_n do_v not_o immediate_o confer_v a_o determinate_a degree_n of_o velocity_n although_o she_o can_v 12_o the_o velocity_n by_o the_o incline_a plane_n equal_a to_o the_o velocity_n by_o the_o perpendicular_a and_o the_o motion_n by_o the_o perpendicular_a swift_o than_o by_o the_o incline_a plane_n 14_o velocity_n be_v say_v to_o be_v equal_a when_o the_o space_n pass_v be_v proportionate_a to_o their_o time_n 15_o the_o great_a velocity_n exact_o compensate_v the_o great_a gravity_n 192_o venus_n the_o mutation_n of_o figure_n in_o venus_n argue_v its_o motion_n to_o be_v about_o the_o sun_n 295_o venus_n very_o great_a 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flow_v not_o interrupt_v by_o rest._n 251_o the_o vain_a argumentation_n of_o some_o to_o prove_v the_o element_n of_o water_n to_o be_v of_o a_o spherical_a superficies_n 377_o the_o progressive_a and_o uneven_a motion_n make_v the_o water_n in_o a_o vessel_n to_o run_v to_o and_o fro_o 387_o the_o several_a motion_n in_o the_o contain_v vessel_n may_v make_v the_o contain_v water_n to_o rise_v and_o fall_v 387_o the_o water_n raise_v in_o one_o end_n of_o the_o vessel_n return_v itself_o to_o aequilibrium_fw-la 391_o in_o the_o short_a vessel_n the_o undulation_n of_o water_n be_v more_o frequent_a 391_o the_o great_a profundity_n make_v the_o undulation_n of_o water_n the_o more_o frequent_a 391_o why_o in_o narrow_a place_n the_o course_n of_o the_o water_n be_v swift_a than_o in_o large_a 396_o the_o cause_n why_o in_o some_o narrow_a channel_n we_o see_v the_o sea_n water_n run_v always_o one_o way_n 398_o the_o water_n more_o apt_a to_o conserve_v a_o impetus_fw-la conceive_v 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world_n
in_o the_o low_a part_n namely_o below_o the_o breach_n there_o be_v beget_v in_o the_o channel_n of_o the_o river_n a_o certain_a ridge_n or_o shelf_n that_o be_v the_o bottom_n of_o the_o river_n be_v raise_v as_o be_v sufficient_o manifest_a by_o experience_n and_o thus_o just_a in_o the_o same_o manner_n cut_v the_o bank_n at_o bondeno_n there_o be_v at_o it_o be_v a_o breach_n make_v from_o which_o follow_v the_o rise_n in_o the_o low_a part_n of_o the_o main_a po_n be_v past_o the_o mouth_n of_o pamaro_n which_o thing_n how_o pernicious_a it_o be_v let_v any_o one_o judge_n that_o understand_v these_o matter_n and_o therefore_o both_o for_o the_o small_a benefit_n and_o so_o many_o harm_n that_o ensue_v from_o maintain_v this_o diversion_n i_o shall_v think_v it_o be_v more_o sound_a advice_n to_o keep_v that_o bank_n always_o whole_a at_o bondeno_n or_o in_o any_o other_o convenient_a place_n and_o not_o to_o permit_v that_o the_o water_n of_o the_o grand_a po_n shall_v ever_o come_v near_o to_o ferara_n corollary_n fourteen_o in_o the_o grand_a river_n which_o fall_v into_o the_o sea_n as_o here_o in_o italy_n po_n adige_n artesia_n and_o arno_n which_o be_v arm_v with_o bank_n against_o their_o excrescency_n it_o be_v observe_v that_o far_o from_o the_o sea_n they_o need_v bank_n of_o a_o notable_a height_n which_o height_n go_v afterward_o by_o degree_n diminish_v the_o more_o it_o approach_v to_o the_o seacoast_n in_o such_o sort_n that_o the_o po_n distant_a from_o the_o sea_n about_o fifty_o or_o sixty_o mile_n at_o ferara_n shall_v have_v bank_n that_o be_v above_o twenty_o foot_n high_o than_o the_o ordinary_a water-mark_n but_o ten_o or_o twelve_o mile_n from_o the_o sea_n the_o bank_n be_v not_o twelve_o foot_n high_o than_o the_o say_v ordinary_a water-mark_n though_o the_o breadth_n of_o the_o river_n be_v the_o same_o so_o that_o the_o excrescence_n of_o the_o same_o innundation_n happen_v to_o be_v far_o great_a in_o measure_n remote_a from_o the_o sea_n then_o near_o and_o yet_o it_o shall_v seem_v that_o the_o same_o quantity_n of_o water_n pass_v by_o every_o place_n the_o river_n shall_v need_v to_o have_v the_o same_o altitude_n of_o bank_n in_o all_o place_n but_o we_o by_o our_o principle_n and_o fundamental_o may_v be_v able_a to_o render_v the_o reason_n of_o that_o effect_n and_o say_v that_o that_o excess_n of_o quantity_n of_o water_n above_o the_o ordinary_a water_n go_v always_o acquire_v great_a velocity_n the_o near_a it_o approach_v the_o sea_n and_o therefore_o decrease_v in_o measure_n and_o consequent_o in_o height_n and_o this_o perhaps_o may_v have_v be_v the_o cause_n in_o great_a part_n why_o the_o tiber_n in_o the_o innundation_n anno_fw-la 1578._o issue_v not_o forth_o of_o its_o channel_n below_o rome_n towards_o the_o sea_n corollary_n xv._n from_o the_o same_o doctrine_n may_v be_v render_v a_o most_o manifest_a reason_n why_o the_o fall_a water_n go_v lessen_v in_o their_o descent_n so_o that_o the_o same_o fall_a water_n measure_v at_o the_o begin_n of_o its_o fall_n be_v great_a and_o big_a and_o afterward_o by_o degree_n lessen_v in_o measure_n the_o more_o it_o be_v remote_a from_o the_o begin_n of_o the_o fall_n which_o depend_v on_o no_o other_o than_o on_o the_o acquisition_n which_o it_o successive_o make_v of_o great_a velocity_n it_o be_v a_o most_o familiar_a conclusion_n among_o philosopher_n that_o grave_a body_n fall_v the_o more_o they_o remove_v from_o the_o begin_n of_o their_o motion_n the_o more_o they_o acquire_v of_o swiftness_n and_o therefore_o the_o water_n as_o a_o grave_a body_n falling_z gradual_o velocitates_fw-la and_o therefore_o decrease_v in_o measure_n and_o lessen_v corollary_n xvi_o and_o on_o the_o contrary_a the_o spirting_n of_o a_o fountain_n of_o water_n which_o spring_n on_o high_a work_v a_o contrary_a effect_n namely_o in_o the_o beginning_n they_o be_v small_a and_o afterward_o become_v great_a and_o big_a and_o the_o reason_n be_v most_o manifest_a because_o in_o the_o beginning_n they_o be_v very_o swift_a and_o afterward_o gradual_o relent_v their_o impetuosity_n and_o motion_n so_o that_o in_o the_o begin_n of_o the_o excursion_n that_o they_o make_v they_o ought_v to_o be_v small_a and_o afterward_o to_o grow_v big_a as_o in_o the_o effect_n be_v see_v appendix_n i._o into_o the_o error_n of_o not_o consider_v how_o much_o the_o different_a velocity_n of_o the_o same_o run_a water_n in_o several_a place_n of_o its_o current_n be_v able_a to_o change_v the_o measure_n of_o the_o same_o water_n and_o to_o make_v it_o great_a or_o less_o i_o think_v if_o i_o be_v not_o deceive_v that_o ginlio_n frontino_n a_o noble_a ancient_a writer_n may_v have_v fall_v in_o the_o second_o book_n which_o he_o write_v of_o the_o aqueduct_n of_o the_o city_n of_o rome_n whilst_o find_v the_o measure_n of_o the_o water_n water_n commentariis_fw-la less_o than_o it_o be_v in_o erogatione_fw-la 1263._o quinary_n he_o think_v that_o so_o much_o difference_n may_v proceed_v from_o the_o negligence_n of_o the_o measure_n and_o when_o afterward_o with_o his_o own_o industry_n he_o measure_v the_o same_o water_n at_o the_o begin_n of_o the_o aqueduct_n find_v it_o near_o 10000_o quinary_n big_a than_o it_o be_v in_o commentariis_fw-la he_o judge_v that_o the_o overplus_n be_v imbezile_v by_o minister_n and_o partaker_n which_o in_o part_n may_v be_v so_o for_o it_o be_v but_o too_o true_a that_o the_o public_a be_v almost_o always_o defraud_v yet_o nevertheless_o i_o very_o believe_v withal_o that_o beside_o the_o fraud_n of_o these_o officer_n the_o velocity_n of_o the_o water_n in_o the_o place_n wherein_o frontino_n measure_v it_o may_v be_v different_a from_o those_o velocity_n which_o be_v find_v in_o other_o place_n before_o measure_v by_o other_o and_o therefore_o the_o measure_n of_o the_o water_n may_v yea_o ought_v necessary_o to_o be_v different_a it_o have_v be_v by_o we_o demonstrate_v that_o the_o measure_n of_o the_o same_o run_a water_n have_v reciprocal_a proportion_n to_o their_o velocity_n which_o frontino_n not_o well_o consider_v and_o find_v the_o water_n in_o commentariis_fw-la 12755._o quinary_n in_o erogatione_fw-la 14018_o and_o in_o his_o own_o measure_n ad_fw-la capita_fw-la ductuum_fw-la at_o the_o head_n of_o the_o fountain_n 22755._o quinary_n or_o thereabouts_o he_o think_v that_o in_o all_o these_o place_n there_o past_a different_a quantity_n of_o water_n namely_o great_a at_o the_o fountain_n head_n than_o that_o which_o be_v in_o erogatione_fw-la and_o this_o he_o judge_v great_a than_o that_o which_o be_v in_o commentariis_fw-la appendix_n ii_o a_o like_a mistake_n chance_v late_o in_o the_o aqueduct_v of_o acqua-paola_n which_o water_n shall_v be_v 2000_o inch_n and_o so_o many_o effective_o aught_o to_o be_v allow_v and_o it_o have_v be_v give_v in_o so_o to_o be_v by_o the_o signor_n of_o bracciano_n to_o the_o apostolic-chamber_n and_o there_o be_v a_o measure_n thereof_o make_v at_o the_o begin_n of_o the_o aqueduct_v which_o measure_n prove_v afterward_o much_o less_o and_o short_a consider_v and_o take_v in_o rome_n and_o thence_o follow_v discontent_n and_o great_a disorder_n and_o all_o because_o this_o property_n of_o running-water_n of_o increase_v in_o measure_n where_o the_o velocity_n decrease_v and_o of_o diminish_v in_o measure_n where_o the_o velocity_n augment_v be_v not_o look_v into_o appendix_n iii_o a_o like_a error_n in_o my_o judgement_n have_v be_v commit_v by_o all_o those_o learned_a man_n which_o to_o prevent_v the_o diversion_n of_o the_o reno_n of_o bologna_n into_o po_n by_o the_o channel_n through_o which_o it_o at_o present_a run_v judge_v that_o the_o reno_n be_v in_o its_o great_a excrescence_n about_o 2000_o foot_n and_o the_o po_n be_v near_o 1000_o foot_n broad_a they_o judge_v i_o say_v that_o let_v the_o reno_n into_o po_n it_o will_v have_v raise_v the_o water_n of_o po_n two_o foot_n from_o which_o rise_n they_o conclude_v afterward_o most_o exorbitant_a disorder_n either_o of_o extraordinary_a inundation_n or_o else_o of_o immense_a and_o intolerable_a expense_n to_o the_o people_n in_o raise_v the_o bank_n of_o po_n and_o reno_n and_o with_o such_o like_a weakness_n often_o vain_o disturb_v the_o mind_n of_o the_o person_n concern_v but_o now_o from_o the_o thing_n demonstrare_v it_o be_v manifest_a that_o the_o measure_n of_o the_o reno_n in_o reno_n will_v be_v different_a from_o the_o measure_n of_o reno_n in_o po_n in_o case_n that_o the_o velocity_n of_o the_o reno_n in_o po_n shall_v differ_v from_o the_o velocity_n of_o reno_n in_o reno_n as_o be_v more_o exact_o determine_v in_o the_o four_o proposition_n appendix_n iu._n no_o less_o likewise_o be_v those_o ingeneer_n and_o artist_n deceive_v that_o have_v affirm_v that_o let_v the_o reno_n into_o po_n there_o will_v be_v
no_o rise_n at_o all_o in_o the_o water_n of_o po_n for_o the_o truth_n be_v that_o let_v reno_n into_o po_n there_o will_v always_o be_v a_o rise_n but_o sometime_o great_a sometime_o less_o as_o the_o po_n shall_v have_v a_o swift_a or_o slow_a current_n so_o that_o if_o the_o po_n shall_v be_v constitute_v in_o a_o great_a velocity_n the_o rise_n will_v be_v very_o small_a and_o if_o the_o say_v po_n shall_v be_v slow_a in_o its_o course_n than_o the_o rise_n will_v be_v notable_a appendix_n v._n and_o here_o it_o will_v not_o be_v beside_o the_o purpose_n to_o advertise_v that_o the_o measure_n partment_n and_o distribution_n of_o the_o water_n of_o fountain_n can_v be_v make_v exact_o unless_o there_o be_v consider_v beside_o the_o measure_n the_o velocity_n also_o of_o the_o water_n which_o particular_a not_o be_v thorough_o observe_v be_v the_o cause_n of_o continual_a miscarriage_n in_o such_o like_a affair_n appendix_n vi._n like_a consideration_n ought_v to_o be_v have_v with_o the_o great_a diligence_n for_o that_o a_o error_n therein_o be_v more_o prejudicial_a i_o say_v aught_o to_o be_v have_v by_o those_o which_o part_n and_o divide_v water_n for_o the_o water_v of_o field_n as_o be_v do_v in_o the_o territory_n of_o brescia_n bergama_n crema_fw-la pavia_n lodigiano_n cremona_n and_o other_o place_n for_o if_o they_o have_v not_o regard_v to_o the_o most_o important_a point_n of_o the_o variation_n of_o the_o velocity_n of_o the_o water_n but_o only_o to_o the_o bare_a vulgar_a measure_n there_o will_v always_o very_o great_a disorder_n and_o prejudices_fw-la ensue_v to_o the_o person_n concern_v appendix_n vii_o it_o seem_v that_o one_o may_v observe_v that_o whilst_o the_o water_n run_v along_o a_o channel_n current_n or_o conduit_n its_o velocity_n be_v retard_v withhold_v and_o impede_v by_o its_o touch_v the_o bank_n or_o side_n of_o the_o say_a channel_n or_o current_n which_o as_o immovable_a not_o follow_v the_o motion_n of_o the_o water_n interrupt_v its_o velocity_n from_o which_o particular_a be_v true_a as_o i_o believe_v it_o to_o be_v most_o true_a and_o from_o our_o consideration_n we_o have_v a_o occasion_n of_o discover_v a_o very_a nice_a mistake_n into_o which_o those_o common_o fall_v who_o divide_v the_o water_n of_o fountain_n which_o division_n be_v wont_a to_o be_v by_o what_o i_o have_v see_v here_o in_o rome_n perform_v two_o way_n the_o first_o of_o which_o be_v with_o the_o measure_n of_o like_a figure_n as_o circle_n or_o square_n have_v cut_v through_o a_o plate_n of_o metal_n several_a circle_n or_o square_n one_o of_o half_a a_o inch_n another_o of_o one_o inch_n another_o of_o two_o of_o three_o of_o four_o etc._n etc._n with_o which_o they_o afterward_o adjust_a the_o cock_n to_o dispense_v the_o water_n the_o other_o manner_n of_o divide_v the_o water_n of_o fountain_n be_v with_o rectangle_n paralellogram_n of_o the_o same_o height_n but_o of_o different_a base_n in_o such_o sort_n likewise_o that_o one_o paralellogram_n be_v of_o half_a a_o inch_n another_o of_o one_o two_o three_o etc._n etc._n in_o which_o manner_n of_o measure_v and_o divide_v the_o water_n it_o shall_v seem_v that_o the_o cock_n be_v place_v in_o one_o and_o the_o same_o plain_a equidistant_a from_o the_o level_n or_o superior_a superficies_n of_o the_o water_n of_o the_o well_o and_o the_o say_a measure_n be_v most_o exact_o make_v the_o water_n ought_v consequent_o also_o to_o be_v equal_o divide_v and_o part_v according_a to_o the_o proportion_n of_o the_o measure_n but_o if_o we_o well_o consider_v every_o particular_a we_o shall_v find_v that_o the_o cock_n as_o they_o successive_o be_v great_a discharge_v always_o more_o water_n than_o the_o just_a quantity_n in_o comparison_n of_o the_o lesser_a that_o be_v to_o speak_v more_o proper_o the_o water_n which_o pass_v through_o the_o great_a cock_n have_v always_o a_o great_a proportion_n to_o that_o which_o pass_v through_o the_o lesser_a than_o the_o great_a cock_n have_v to_o the_o lesser_a all_o which_o i_o will_v declare_v by_o a_o example_n the_o like_a error_n occur_v also_o in_o the_o other_o manner_n of_o measure_v the_o water_n of_o a_o fountain_n as_o may_v easy_o be_v collect_v from_o what_o have_v be_v say_v and_o observe_v above_o appendix_n viii_o the_o same_o contemplation_n discover_v the_o error_n of_o those_o architect_n who_o be_v to_o erect_v a_o bridge_n of_o sundry_a arch_n over_o a_o river_n consider_v the_o ordinary_a breadth_n of_o the_o river_n which_o be_v v_o g._n forty_o fathom_n and_o the_o bridge_n be_v to_o consist_v of_o four_o arch_n it_o suffice_v they_o that_o the_o breadth_n of_o all_o the_o four_o arch_n take_v together_o be_v forty_o fathom_n not_o consider_v that_o in_o the_o ordinary_a channel_n of_o the_o river_n the_o water_n have_v only_o two_o impediment_n which_o retard_v its_o velocity_n namely_o the_o touch_v and_o glide_v along_o the_o two_o side_n or_o shore_n of_o the_o river_n but_o the_o same_o water_n in_o pass_v under_o the_o bridge_n in_o our_o case_n meet_v with_o eight_o of_o the_o same_o impediment_n bear_v and_o thrust_v upon_o two_o side_n of_o each_o arch_n to_o omit_v the_o impediment_n of_o the_o bottom_n for_o that_o it_o be_v the_o same_o in_o the_o river_n and_o under_o the_o bridge_n from_o which_o inadvertency_n sometime_o follow_v very_o great_a disorder_n as_o quotidian_a practice_n show_v we_o appendix_n ix_o it_o be_v also_o worthy_a to_o consider_v the_o great_a and_o admirable_a benefit_n that_o those_o field_n receive_v which_o be_v wont_a to_o drink_v up_o the_o rain-water_n with_o difficulty_n through_o the_o height_n of_o the_o water_n in_o the_o principal_a ditch_n in_o which_o case_n the_o careful_a husbandman_n cut_v away_o the_o reed_n and_o rush_n in_o the_o ditch_n through_o which_o the_o water_n pass_v whereupon_o may_v be_v present_o see_v so_o soon_o as_o the_o reed_n and_o rush_n be_v cut_v a_o notable_a ebb_n in_o the_o level_n of_o the_o water_n in_o the_o ditch_n insomuch_o that_o sometime_o it_o be_v observe_v that_o the_o water_n be_v abate_v after_o the_o say_v cut_v a_o three_o and_o more_o of_o what_o it_o be_v before_o the_o cut_n the_o which_o effect_v seem_o might_n depend_v on_o this_o that_o before_o those_o weed_n take_v up_o room_n in_o the_o ditch_n and_o for_o that_o cause_n the_o water_n keep_v a_o high_a level_n and_o the_o say_a plant_n be_v afterward_o cut_v and_o remove_v the_o water_n come_v to_o abate_v possess_v the_o place_n that_o before_o be_v occupy_v by_o the_o weed_n which_o opinion_n though_o probable_a and_o at_o first_o sight_n satisfactory_a be_v nevertheless_o insufficient_a to_o give_v the_o total_a reason_n of_o that_o notable_a abatement_n which_o have_v be_v speak_v of_o but_o it_o be_v necessary_a to_o have_v recourse_n to_o our_o consideration_n of_o the_o velocity_n in_o the_o course_n of_o the_o water_n the_o chief_a and_o true_a cause_n of_o the_o variation_n of_o the_o measure_n of_o the_o same_o running-waterâ—_a for_o that_o multitude_n of_o reed_n weed_n and_o plant_v disperse_v through_o the_o current_n of_o the_o ditch_n do_v chance_n notable_o to_o retard_v the_o course_n of_o the_o water_n and_o therefore_o the_o measure_n of_o the_o water_n increase_v and_o those_o impediment_n remove_v the_o same_o water_n gain_v velocity_n and_o therefore_o decrease_v in_o measure_n and_o consequent_o in_o height_n and_o perhaps_o this_o point_n well_o understand_v may_v be_v of_o great_a profit_n to_o the_o field_n adjacent_a to_o the_o pontine_n fen_n and_o i_o doubt_v not_o but_o if_o the_o river_n ninfa_n and_o the_o other_o principal_a brook_n of_o those_o territory_n be_v keep_v well_o cleanse_v from_o weed_n their_o water_n will_v be_v at_o a_o low_a level_n and_o consequent_o the_o drain_v of_o the_o field_n will_v run_v into_o they_o more_o ready_o it_o be_v always_o to_o be_v hold_v for_o undoubted_a that_o the_o measure_n of_o the_o water_n before_o the_o cleanse_n have_v the_o same_o proportion_n to_o the_o measure_n after_o cleanse_v that_o the_o velocity_n after_o the_o cleanse_n have_v to_o the_o velocity_n before_o the_o cleanse_n and_o be_v cause_v 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 owe_v 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 so_o many_o 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 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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 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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 be_v 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 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the_o water_n of_o the_o river_n supposition_n ii_o let_v we_o suppose_v also_o that_o if_o there_o be_v two_o river_n that_o be_v in_o their_o bed_n of_o equal_a length_n and_o of_o the_o same_o inclination_n but_o of_o quick_a height_n unequal_a they_o ought_v to_o move_v with_o like_a velocity_n according_a to_o the_o sense_n explain_v in_o the_o second_o definition_n supposition_n iii_o because_o it_o will_v often_o be_v requisite_a to_o measure_v the_o time_n exact_o in_o the_o follow_a problem_n we_o take_v that_o to_o be_v a_o excellent_a way_n to_o measure_v the_o time_n which_o be_v show_v i_o many_o year_n since_o by_o signore_v 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 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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._o 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 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 say_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_o 6â—_n 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
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 â…•_n it_o be_v necessary_a to_o take_v 925_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 on_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 business_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 bobily_n 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
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_v signore_v 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 scanto_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 who_o so_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 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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 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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 forego_n way_n of_o measure_v sand_n and_o mud_n to_o show_v that_o we_o be_v not_o so_o general_o and_o inconsiderate_o to_o pronounce_v any_o sentence_n but_o proceed_v to_o strict_a inquiry_n and_o then_o deliberate_v what_o shall_v be_v most_o expedient_a to_o be_v do_v other_o may_v propose_v more_o exquisite_a examination_n but_o this_o shall_v serve_v i_o for_o the_o present_a i_o will_v add_v only_o that_o if_o any_o one_o have_v great_a curiosity_n it_o will_v be_v profitable_a to_o have_v it_o in_o investigate_a more_o exact_o the_o quantity_n of_o the_o water_n that_o enter_v into_o the_o lake_n by_o the_o mean_n that_o i_o have_v show_v in_o the_o begin_n of_o this_o book_n when_o he_o shall_v have_v find_v the_o proportion_n of_o the_o quantity_n of_o water_n to_o the_o quantity_n of_o sand_n or_o mud_n he_o shall_v come_v to_o know_v how_o much_o sand_n the_o brent_n shall_v leave_v in_o the_o lake_n in_o the_o space_n of_o a_o year_n but_o to_o perform_v these_o thing_n there_o be_v require_v person_n of_o discretion_n and_o fidelity_n and_o that_o be_v employ_v by_o public_a order_n for_o there_o will_v thence_o result_v eminent_a benefit_n and_o profit_n here_o be_v want_v letter_n from_o several_a person_n to_o the_o reverend_a father_n francisco_n di_fw-mi s._n giuseppe_n in_o execution_n of_o the_o command_n that_o you_o lay_v upon_o i_o in_o your_o former_a letter_n by_o order_n from_o the_o most_o serene_a my_o lord_n prince_n leopold_n that_o i_o shall_v speak_v my_o judgement_n concern_v the_o disimboguement_fw-fr of_o
of_o tycho_n make_v with_o great_a expense_n what_o instrument_n be_v apt_a for_o most_o exact_a observation_n observation_n italian_n brace_n a_o exquisite_a observation_n of_o the_o approach_n and_o departure_n of_o the_o sun_n from_o the_o summer_n solstice_n a_o place_n accommodate_v for_o the_o observation_n of_o the_o fix_a star_n as_o to_o what_o concer_n the_o annual_a motion_n of_o the_o earth_n the_o copernican_n systeme_n difficult_a to_o be_v understand_v but_o easy_a to_o be_v effect_v necessary_a preposition_n for_o the_o better_a conceive_n of_o the_o consequence_n of_o the_o earth_n motion_n a_o plain_a scheme_n represent_v the_o copernican_n hypothesis_n and_o its_o consequence_n axiom_n common_o admit_v by_o all_o philosopher_n aristotle_n tax_v plato_n for_o be_v too_o studious_a of_o geometry_n peripatetic_a philosopher_n condemn_v the_o study_n of_o geometry_n and_o why_o four_o several_a motion_n assign_v to_o the_o earth_n the_o motion_n of_o descent_n belong_v 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wit_n the_o terrestrial_a globe_n compose_v of_o sundry_a matter_n the_o intern_a part_n of_o the_o terrestrial_a globe_n must_v of_o necessity_n be_v solid_a solid_a or_o mould_n mould_n of_o which_o with_o the_o latin_a translator_n i_o must_v once_o more_o profess_v myself_o ignorant_a our_o globe_n will_v have_v be_v call_v stone_n in_o stead_n of_o earth_n of_o that_o name_n have_v be_v give_v it_o in_o the_o beginning_n the_o method_n of_o gilbert_n in_o his_o philosophy_n many_o property_n in_o the_o magnet_n 〈…〉_z the_o magnet_n arm_v take_v up_o much_o more_o iron_n than_o when_o arm_v arm_v or_o closet_n of_o rarity_n the_o first_o observer_n and_o inventor_n of_o thing_n ought_v to_o be_v admire_v the_o true_a cause_n of_o the_o multiplication_n of_o virtue_n in_o the_o magnet_n by_o mean_n of_o the_o arm_n of_o a_o new_a effect_n its_o necessary_a that_o the_o cause_n be_v likewise_o new_a it_o be_v prove_v that_o iron_n consist_v of_o part_n more_o subtle_a pure_a and_o compact_a than_o the_o magnet_n a_o sensible_a proof_n of_o the_o impurity_n of_o the_o magnet_n magnet_n the_o author_n hereby_o mean_v that_o the_o stone_n do_v not_o all_o consist_v of_o magnetic_a matter_n but_o that_o the_o white_a speck_n be_v weak_a those_o other_o part_n of_o the_o loadstone_n of_o a_o more_o dark_a &_o constant_a colour_n contain_v all_o that_o virtue_n wherewith_o body_n be_v attract_v attract_v a_o common_a sew_v needle_n sympathy_n and_o antipathy_n term_n use_v by_o philosopher_n to_o give_v a_o reason_n easy_o of_o many_o natural_a effe_v a_o pleasant_a example_n declare_v the_o invalidity_n of_o some_o phylosophical_a argumentation_n the_o several_a natural_a motion_n of_o the_o magnet_n aristole_n grant_v a_o compound_a motion_n to_o mix_a body_n the_o motion_n of_o mix_a body_n ought_v to_o be_v such_o as_o may_v result_v from_o the_o composition_n of_o the_o motion_n of_o the_o simple_a body_n compound_v with_o two_o right_a motion_n one_o can_v compose_v circular_a motion_n philosopher_n be_v force_v to_o confess_v that_o the_o magnet_n be_v compound_v of_o celestial_a substance_n and_o of_o elementary_a the_o error_n of_o those_o who_o call_v the_o magnet_n a_o mix_a body_n and_o the_o terrestrial_a globe_n a_o simble_a body_n body_n ogliopotrida_n a_o spanish_a dish_n of_o many_o ingredient_n boil_v together_o the_o discourse_n of_o peripatetic_n full_a of_o error_n and_o contradiction_n a_o improbable_a effect_n admire_v by_o gilbertus_n in_o the_o loadstone_n the_o vain_a argumentation_n of_o some_o to_o prove_v the_o element_n of_o water_n to_o be_v of_o a_o spherical_a superficies_n nature_n in_o sport_n make_v the_o ebb_a and_o flow_v of_o the_o sea_n to_o approve_v the_o earthâ—_n mobility_n the_o tide_n and_o mobility_n of_o the_o earth_n mutual_o confirm_v each_o other_o all_o terrene_a effect_n indifferent_o confirm_v the_o motion_n or_o rest_n of_o the_o earth_n except_o the_o ebb_a and_o flow_v of_o the_o sea_n the_o first_o general_a conclusion_n of_o the_o impossibility_n of_o the_o ebb_a and_o flow_v the_o immobility_n of_o the_o terrestrial_a globe_n be_v grant_v the_o knowledge_n of_o the_o effe_v contribute_v to_o the_o investigation_n of_o the_o cause_n three_o period_n of_o ebbing_n and_o flow_n diurnal_a monthly_a and_o annual_a variety_n that_o â—appen_v in_o the_o diurnal_a period_n period_n a_o strair_a so_o call_v call_v or_o ilva_n ilva_n or_o cret_o the_o cause_n of_o the_o ebb_a and_o flow_v allege_v by_o a_o certain_a modern_a philosopher_n the_o cause_n of_o the_o ebb_a and_o flow_v ascribe_v to_o the_o moon_n by_o a_o certain_a prelate_n hieronymus_n borrius_fw-la and_o other_o peripatetic_n refer_v it_o to_o the_o temperate_a heat_n of_o the_o moon_n answer_n to_o the_o vanity_n allege_v as_o cause_n of_o the_o ebb_a and_o flow_v flow_v or_o rather_o smooth_a the_o isle_n be_v token_n of_o the_o unevennesse_n of_o the_o bottom_n of_o sea_n poetic_a wit_n of_o two_o kind_n truth_n have_v not_o so_o little_a light_n as_o not_o to_o be_v discover_v amid_o the_o umbrage_n of_o falsehood_n aristotle_n hold_v those_o effect_n to_o be_v miraculous_a of_o which_o the_o cause_n be_v unknown_a it_o be_v prove_v impossible_a that_o there_o shall_v natural_o be_v any_o ebb_a and_o flow_v the_o earth_n be_v immovable_a immovable_a palm_n palm_n lio_o be_v a_o fair_a port_n in_o the_o venetian_a gulf_n lie_v n._n e._n from_o the_o city_n true_a and_o natural_a effect_n follow_v without_o difficulty_n two_o sort_n of_o motion_n of_o the_o contain_v vessel_n may_v make_v the_o contain_v water_n to_o rise_v and_o fall_v the_o cavity_n of_o the_o earth_n can_v approach_v or_o go_v far_o from_o the_o centre_n of_o the_o same_o the_o progpessive_a and_o uneven_a motion_n may_v make_v the_o water_n contain_v in_o a_o vessel_n to_o run_v to_o and_o fro_o fro_o a_o town_n lie_v s._n e._n of_o venice_n the_o part_n of_o the_o terrestrial_a globe_n accelerate_v and_o regard_v 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