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or_o any_o
though_o indeed_o they_o have_v a_o influence_n upon_o the_o element_n it_o be_v requisite_a if_o you_o will_v prove_v generation_n and_o corruption_n in_o celestial_a body_n that_o you_o show_v that_o there_o reside_v contrariety_n between_o they_o sagr._fw-la see_v how_o i_o will_v find_v those_o contrariety_n between_o they_o the_o first_o fountain_n from_o whence_o you_o derive_v the_o contrariety_n of_o the_o element_n be_v the_o contrariety_n of_o their_o motion_n upward_o and_o downward_o it_o therefore_o be_v necessary_a that_o those_o principle_n be_v in_o like_a manner_n contrary_n to_o each_o other_o quality_n upon_o which_o those_o motion_n depend_v and_o because_o that_o be_v movable_a upward_o by_o lightness_n and_o this_o downward_o by_o gravity_n it_o be_v necessary_a that_o lightness_n and_o gravity_n be_v contrary_a to_o each_o other_o no_o less_o be_v we_o to_o believe_v those_o other_o principle_n to_o be_v contrary_n which_o be_v the_o cause_n that_o this_o be_v heavy_a and_o that_o light_a but_o by_o your_o own_o confession_n levity_n and_o gravity_n follow_v as_o consequent_n of_o rarity_n and_o density_n therefore_o rarity_n and_o density_n shall_v be_v contrary_n density_n the_o which_o condition_n or_o affection_n be_v so_o ample_o find_v in_o celestial_a body_n that_o you_o esteem_v the_o star_n to_o be_v only_o more_o dense_a part_n of_o their_o heaven_n and_o if_o this_o be_v so_o it_o follow_v that_o the_o density_n of_o the_o star_n exceed_v that_o of_o the_o rest_n of_o heaven_n by_o almost_o infinite_a degree_n which_o be_v manifest_a in_o that_o heaven_n be_v infinite_o transparent_a and_o the_o star_n extreme_o opacous_a and_o for_o that_o there_o be_v there_o above_o no_o other_o quality_n but_o more_o and_o less_o density_n and_o rarity_n which_o may_v be_v cause_n of_o the_o great_a or_o less_o transparency_n there_o be_v then_o such_o contrariety_n between_o the_o celestial_a body_n it_o be_v necessary_a that_o they_o also_o be_v generable_a and_o corruptible_a in_o the_o same_o manner_n as_o the_o elementary_a body_n be_v or_o else_o that_o contrariety_n be_v not_o the_o cause_n of_o corruptibility_n element_n etc._n etc._n simpl._n there_o be_v no_o necessity_n either_o of_o one_o or_o the_o other_o for_o that_o density_n and_o rarity_n in_o celestial_a body_n be_v not_o contrary_n to_o each_o other_o as_o in_o elementary_a body_n for_o that_o they_o depend_v not_o on_o the_o primary_n quality_n cold_a and_o heat_n which_o be_v contrary_n but_o on_o the_o more_o or_o less_o matter_n in_o proportion_n to_o quantity_n now_o much_o and_o little_a speak_v only_o a_o relative_a opposition_n that_o be_v the_o least_o of_o opposition_n and_o which_o have_v nothing_o to_o do_v with_o generation_n and_o corruption_n sagr._fw-la therefore_o affirm_v that_o density_n and_o rarity_n which_o among_o the_o element_n shall_v be_v the_o cause_n of_o gravity_n and_o levity_n which_o may_v be_v the_o cause_n of_o contrary_a motion_n sursum_fw-la and_o deorsâ—â—m_fw-la on_o which_o again_o depend_v the_o contrariety_n for_o generation_n and_o corruption_n it_o suffice_v not_o that_o they_o be_v those_o densness_n and_o rareness_n which_o under_o the_o same_o quantity_n or_o if_o you_o will_v mass_n contain_v much_o or_o little_a matter_n but_o it_o be_v necessary_a that_o they_o be_v densness_n and_o rareness_n cause_v by_o the_o primary_n quality_n hot_a and_o cold_a otherwise_o they_o will_v operate_v nothing_o at_o all_o but_o if_o this_o be_v so_o corruptible_a aristotle_n have_v deceive_v we_o for_o that_o he_o shall_v have_v tell_v it_o we_o at_o first_o and_o so_o have_v leave_v write_v that_o those_o simple_a body_n be_v generable_a and_o corruptible_a that_o be_v movable_a with_o simple_a motion_n upward_o and_o downward_o dependent_a on_o levity_n and_o gravity_n cause_v by_o rarity_n and_o density_n make_v by_o much_o or_o little_a matter_n by_o reason_n of_o heat_n and_o cold_a and_o not_o to_o have_v stay_v at_o the_o simple_a motion_n sursum_fw-la and_o deorsùm_fw-la for_o i_o assure_v you_o that_o to_o the_o make_n of_o body_n heavy_a or_o light_a whereby_o they_o come_v to_o be_v move_v with_o contrary_a motion_n any_o kind_n of_o density_n and_o rarity_n suffice_v whether_o it_o proceed_v from_o heat_n and_o cold_a or_o what_o else_o you_o please_v for_o heat_n and_o cold_a have_v nothing_o to_o do_v in_o this_o affair_n and_o you_o shall_v upon_o experiment_n find_v that_o a_o red_a iron_n which_o you_o must_v grant_v to_o have_v heat_n weigh_v as_o much_o and_o move_v in_o the_o same_o manner_n as_o when_o it_o be_v cold_a but_o to_o overpass_v this_o also_o how_o know_v you_o but_o that_o celestial_a rarity_n and_o density_n depend_v on_o heat_n and_o cold_a simpl._n i_o know_v it_o because_o those_o quality_n be_v not_o among_o celestial_a body_n which_o be_v neither_o hot_a nor_o cold_a salv_n i_o see_v we_o be_v again_o go_v about_o to_o engulph_n ourselves_o in_o a_o bottomless_a ocean_n where_o there_o be_v no_o get_n to_o shore_n for_o this_o be_v a_o navigation_n without_o compass_n star_n or_o rudder_n so_o that_o it_o will_v follow_v either_o that_o we_o be_v force_v to_o pass_v from_o shelf_n to_o shelf_n or_o run_v on_o ground_n or_o to_o sail_v continual_o in_o danger_n of_o be_v lose_v therefore_o if_o according_a to_o your_o advice_n we_o shall_v proceed_v in_o our_o main_a design_n we_o must_v of_o necessity_n for_o the_o present_a overpass_v this_o general_a consideration_n whether_o direct_a motion_n be_v necessary_a in_o nature_n and_o agree_v with_o some_o body_n and_o come_v to_o the_o particular_a demonstration_n observation_n and_o experiment_n propound_v in_o the_o first_o place_n all_o those_o that_o have_v be_v hitherto_o allege_v by_o aristotle_n ptolomey_n and_o other_o to_o prove_v the_o stability_n of_o the_o earth_n endeavour_v in_o the_o next_o place_n to_o answer_v they_o and_o produce_v in_o the_o last_o place_n those_z by_o which_o other_o may_v be_v persuade_v that_o the_o earth_n be_v no_o less_o than_o the_o moon_n or_o any_o other_o planet_n to_o be_v number_v among_o natural_a body_n that_o move_v circular_o sagr._fw-la i_o shall_v the_o more_o willing_o incline_v to_o this_o in_o that_o i_o be_o better_a satisfy_v with_o your_o architectonical_a and_o general_a discourse_n than_o with_o that_o of_o aristotle_n for_o you_o convince_v i_o without_o the_o least_o scruple_n and_o the_o other_o at_o every_o step_n cross_v my_o way_n with_o some_o block_n and_o i_o see_v no_o reason_n why_o simplicius_n shall_v not_o be_v present_o satisfy_v with_o the_o argument_n you_o allege_v to_o prove_v that_o there_o can_v be_v no_o such_o thing_n in_o nature_n as_o a_o motion_n by_o a_o right_a line_n if_o we_o do_v but_o presuppose_v that_o the_o part_n of_o the_o universe_n be_v dispose_v in_o a_o excellent_a constitution_n and_o perfect_a order_n salv_n stay_v a_o little_a good_a sagredus_fw-la for_o just_a now_o a_o way_n come_v into_o my_o mind_n how_o i_o may_v give_v simplicius_n satisfaction_n provide_v that_o he_o will_v not_o be_v so_o strict_o wed_v to_o every_o expression_n of_o aristotle_n as_o to_o hold_v it_o heresy_n to_o recede_v in_o any_o thing_n from_o he_o nor_o be_v there_o any_o question_n to_o be_v make_v but_o that_o if_o we_o grant_v the_o excellent_a disposition_n and_o perfect_a order_n of_o the_o part_n of_o the_o universe_n as_o to_o local_a situation_n that_o then_o there_o be_v no_o other_o but_o the_o circular_a motion_n and_o rest_n for_o as_o to_o the_o motion_n by_o a_o right_a line_n i_o see_v not_o how_o it_o can_v be_v of_o use_n for_o any_o thing_n but_o to_o reduce_v to_o their_o natural_a constitution_n some_o integral_a body_n that_o by_o some_o accident_n be_v remove_v and_o separate_v from_o their_o whole_a as_o we_o say_v above_o let_v we_o now_o consider_v the_o whole_a terrestrial_a globe_n and_o inquire_v the_o best_a we_o can_v whether_o it_o and_o the_o other_o mundane_a body_n be_v to_o conserve_v themselves_o in_o their_o perfect_a and_o natural_a disposition_n it_o be_v necessary_a to_o say_v 〈◊〉_d that_o it_o rest_v and_o keep_v perpetual_o immovable_a in_o its_o place_n or_o else_o that_o continue_v always_o in_o its_o place_n it_o revolve_v in_o its_o self_n or_o that_o it_o turn_v about_o a_o centre_n move_v by_o the_o circumference_n of_o a_o circle_n immovable_a of_o which_o accident_n both_o aristotle_n and_o ptolomey_n and_o all_o their_o follower_n say_v that_o it_o have_v ever_o observe_v and_o shall_v continual_o keep_v the_o first_o that_o be_v a_o perpetual_a rest_n in_o the_o same_o place_n downward_o now_o why_o i_o pray_v you_o ought_v they_o not_o to_o have_v say_v that_o its_o natural_a affection_n be_v to_o rest_v immovable_a rather_o than_o to_o make_v natural_a unto_o it_o the_o motion_n sense_n downward_o with_o which_o motion_n it_o never_o do_v or_o shall_v
sit_fw-la ratio_fw-la totius_fw-la &_o partium_fw-la those_o country_n be_v a_o part_n of_o the_o earth_n as_o well_o as_o we_o they_o must_v of_o necessity_n be_v alterable_a as_o these_o be_v salv_n and_o why_o have_v you_o not_o without_o be_v put_v to_o believe_v other_o man_n relation_n examine_v and_o observe_v those_o alteration_n with_o your_o own_o eye_n simpl._n because_o those_o place_n beside_o that_o they_o be_v not_o expose_v to_o our_o eye_n be_v so_o remote_a that_o our_o sight_n can_v reach_v to_o comprehend_v therein_o such_o like_a mutation_n salv_n see_v now_o how_o you_o have_v unaware_o discover_v the_o fallacy_n of_o your_o argument_n for_o if_o you_o say_v that_o the_o alteration_n that_o be_v see_v on_o the_o earth_n near_o at_o hand_n can_v by_o reason_n of_o the_o too_o great_a distance_n be_v see_v in_o america_n much_o less_o can_v you_o see_v they_o in_o the_o moon_n which_o be_v so_o many_o hundred_o time_n more_o remote_a and_o if_o you_o believe_v the_o 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therefore_o we_o have_v no_o cause_n to_o say_v that_o any_o of_o the_o celestial_a body_n be_v alterable_a etc._n etc._n salv_n that_o so_o great_a alteration_n have_v happen_v in_o the_o moon_n i_o dare_v not_o say_v but_o for_o all_o that_o i_o be_o not_o yet_o certain_a but_o that_o such_o change_n may_v occur_v and_o because_o such_o a_o mutation_n can_v only_o represent_v unto_o we_o some_o kind_n of_o variation_n between_o the_o more_o clear_a and_o more_o obscure_a part_n of_o the_o moon_n i_o know_v not_o whether_o we_o have_v have_v on_o earth_n observant_a selenographer_n who_o have_v for_o any_o considerable_a number_n of_o year_n instruct_v we_o with_o so_o exact_a selenography_n as_o that_o we_o shall_v confident_o conclude_v that_o there_o have_v no_o such_o change_n happen_v in_o the_o face_n of_o the_o moon_n of_o the_o figuration_n of_o which_o i_o find_v no_o more_o particular_a description_n than_o the_o say_n of_o some_o that_o it_o represent_v a_o humane_a face_n of_o other_o that_o it_o be_v like_o the_o muzzle_n of_o a_o lion_n and_o of_o other_o that_o it_o be_v cain_n with_o a_o bundle_n of_o thorn_n on_o his_o back_n therefore_o to_o say_v heaven_n be_v unalterable_a because_o that_o in_o the_o moon_n or_o other_o celestial_a body_n no_o such_o alteration_n be_v see_v as_o discover_v themselves_o on_o earth_n be_v a_o bad_a illation_n and_o conclude_v nothing_o sagr._fw-la and_o there_o be_v another_o odd_a kind_n of_o scruple_n in_o this_o argument_n of_o simplicius_n run_v in_o my_o mind_n which_o i_o will_v glad_o have_v answer_v therefore_o i_o demand_v of_o he_o whether_o the_o earth_n before_o the_o mediterranean_a inundation_n be_v generable_a and_o corruptible_a or_o else_o begin_v then_o so_o to_o be_v simpl._n it_o be_v doubtless_o generable_a and_o corruptible_a also_o before_o that_o time_n but_o that_o be_v so_o vast_a a_o mutation_n that_o it_o may_v have_v be_v observe_v as_o far_o as_o the_o moon_n sagr._fw-la go_v to_o 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notion_n more_o absurd_a than_o the_o former_a and_o what_o a_o folly_n it_o be_v to_o say_v the_o celestial_a part_n be_v unalterable_a because_o no_o star_n do_v generate_v or_o corrupt_v therein_o what_o then_o have_v any_o one_o see_v a_o terrestrial_a globe_n corrupt_v and_o another_o regenerate_v in_o its_o place_n and_o yet_o be_v it_o not_o on_o all_o hand_n grant_v by_o philosopher_n that_o there_o be_v very_o few_o star_n in_o heaven_n less_o than_o the_o earth_n globe_n but_o very_o many_o that_o be_v much_o big_a so_o that_o for_o a_o star_n in_o heaven_n to_o corrupt_v will_v be_v no_o less_o than_o if_o the_o whole_a terrestrial_a globe_n shall_v be_v destroy_v therefore_o if_o for_o the_o true_a proof_n of_o generation_n and_o corruption_n in_o the_o universe_n it_o be_v necessary_a that_o so_o vast_a body_n as_o a_o star_n must_v corrupt_v and_o regenerate_v you_o may_v satisfy_v yourself_o and_o cease_v your_o opinion_n for_o i_o assure_v you_o that_o you_o shall_v 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when_o he_o shall_v see_v any_o such_o accident_n he_o will_v hold_v the_o contrary_n and_o 〈◊〉_d as_o indeed_o it_o be_v meet_v sensible_a experiment_n to_o natural_a reason_n for_o have_v he_o not_o make_v any_o reckon_n of_o the_o sense_n he_o will_v not_o then_o from_o the_o not_o see_v of_o any_o sensible_a mutation_n have_v argue_v immutability_n simpl._n aristotle_n deduce_v his_o principal_a argument_n à _fw-la priori_fw-la show_v the_o necessity_n of_o the_o inalterability_n of_o heaven_n by_o natural_a manifest_a and_o clear_a principle_n and_o then_o stablish_v the_o same_o à _fw-fr posteriori_fw-la by_o sense_n and_o the_o tradition_n of_o the_o ancients_n salv_n this_o you_o speak_v of_o be_v the_o method_n he_o have_v observe_v in_o deliver_v his_o doctrine_n but_o i_o do_v not_o bethink_v it_o yet_o to_o be_v that_o wherewith_o he_o
whereupon_o the_o reflex_n ray_n issue_n united_o towards_o one_o and_o the_o same_o place_n but_o the_o rest_n of_o the_o pavement_n which_o be_v dry_a have_v its_o protuberance_n that_o be_v a_o innumerable_a variety_n of_o inclination_n in_o its_o small_a particle_n whereupon_o the_o reflection_n of_o the_o light_n scatter_v towards_o all_o part_n but_o more_o weak_o than_o if_o they_o have_v go_v all_o unite_a together_o and_o therefore_o the_o same_o show_v almost_o all_o alike_o behold_v several_a way_n but_o far_o less_o clear_a than_o the_o moisten_a brick_n i_o conclude_v therefore_o that_o the_o surface_n of_o the_o sea_n behold_v from_o the_o moon_n in_o like_a manner_n as_o it_o will_v appear_v most_o equal_a the_o island_n and_o rock_n deduct_v so_o it_o will_v show_v less_o clear_a than_o that_o of_o the_o earth_n which_o be_v montanous_a and_o uneven_a and_o but_o that_o i_o will_v not_o seem_v as_o the_o say_n be_v to_o harp_n too_o much_o on_o one_o string_n i_o can_v 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not_o of_o therefore_o i_o dare_v not_o affirm_v the_o moon_n to_o consist_v of_o one_o thing_n more_o than_o another_o it_o have_v be_v see_v already_o that_o a_o silver_n plate_n boil_v be_v touch_v with_o the_o burnisher_n become_v of_o white_a obscure_a that_o the_o moist_a part_n of_o the_o earth_n show_v more_o obscure_a than_o the_o dry_a that_o in_o the_o top_n of_o hill_n the_o woody_a part_n appear_v more_o gloomy_a than_o the_o naked_a and_o barren_a which_o happen_v because_o there_o fall_v very_o much_o shadow_n among_o the_o tree_n but_o the_o open_a place_n be_v illuminate_v all_o over_o by_o the_o sun_n and_o this_o mixtion_n of_o shadow_n have_v such_o operation_n that_o in_o tuft_a velvet_n the_o silk_n which_o be_v cut_v be_v of_o a_o far_o dark_a colour_n than_o that_o which_o be_v not_o cut_v by_o mean_n of_o the_o shadow_n diffuse_v betwixt_o thread_n and_o thread_n and_o a_o plain_a velvet_n show_v much_o black_a than_o a_o taffeta_n make_v of_o the_o same_o 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against_o themselves_o observation_n experience_n and_o reason_n of_o far_o great_a force_n than_o those_o allege_v by_o aristotle_n ptolemy_n and_o other_o opposer_n of_o the_o same_o conclusion_n and_o by_o this_o mean_v you_o shall_v come_v to_o ascertain_v yourself_o that_o they_o be_v not_o induce_v through_o want_n of_o knowledge_n or_o expetience_n to_o follow_v that_o opinion_n sagr._fw-la it_o be_v requisite_a that_o upon_o this_o occasion_n i_o relate_v unto_o you_o some_o accident_n that_o befall_v i_o so_o soon_o as_o i_o first_o begin_v to_o hear_v speak_v of_o this_o new_a doctrine_n be_v very_o young_a and_o have_v scarce_o finish_v my_o course_n of_o philosophy_n which_o i_o leave_v off_o as_o be_v set_v upon_o other_o employment_n there_o chance_v to_o come_v into_o these_o part_n a_o certain_a foreigner_n of_o rostock_n who_o name_n as_o i_o remember_v be_v christianus_n vurstitius_n thereupon_o a_o follower_n of_o copernicus_n who_o in_o a_o academy_n make_v two_o 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a_o manifest_a example_n in_o myself_o that_o the_o far_o i_o go_v the_o more_o i_o be_o confound_v sagr._fw-la this_o be_v a_o sign_n that_o those_o reason_n that_o hitherto_o seem_v conclude_v unto_o you_o and_o assure_v you_o in_o the_o truth_n of_o your_o opinion_n begin_v to_o change_v countenance_n in_o your_o mind_n and_o to_o let_v you_o by_o degree_n if_o not_o embrace_v at_o least_o look_v towards_o the_o contrary_a tenant_n but_o i_o that_o have_v be_v hitherto_o indifferent_a do_v great_o hope_v to_o acquire_v rest_n and_o satisfaction_n by_o our_o future_a discourse_n and_o you_o will_v not_o deny_v but_o i_o may_v if_o you_o please_v but_o to_o hear_v what_o persuade_v i_o to_o this_o expectation_n simpl._n i_o will_v glad_o hearken_v to_o the_o same_o and_o shall_v be_v no_o less_o glad_a that_o the_o like_a effect_n may_v be_v wrought_v in_o i_o sagr._fw-la favour_v i_o therefore_o with_o answer_v to_o what_o i_o shall_v ask_v you_o and_o first_o tell_v i_o simplicius_n 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always_o at_o the_o same_o rate_n as_o v_o g._n ah_o being_n divide_v in_o two_o equal_a part_n in_o f_o the_o parallel_n he_o shall_v be_v double_a to_o fg_v and_o sub-dividing_a favorina_n in_o two_o equal_a part_n the_o parallel_n produce_v from_o the_o point_n of_o the_o division_n shall_v be_v the_o half_a of_o fg_v and_o continue_v the_o sub-division_n in_o infinitum_fw-la the_o subsequent_a parallel_n shall_v be_v always_o half_a of_o the_o next_o precede_v but_o it_o do_v not_o so_o fall_v out_o in_o the_o line_n intercept_v between_o the_o tangent_fw-la and_o the_o circumference_n of_o the_o circle_n for_o if_o the_o same_o sub-division_n be_v make_v in_o favorina_n and_o suppose_v for_o example_n that_o the_o parallel_n which_o come_v from_o the_o point_n h_n be_v double_a unto_o that_o which_o come_v from_o f_o this_o shall_v be_v more_o than_o double_a to_o the_o next_o follow_v and_o continual_o the_o near_o we_o come_v towards_o the_o contact_n a_o we_o shall_v fiâ—â—_n the_o precedent_a line_n contain_v the_o next_o follow_v three_o four_o ten_o a_o hundred_o a_o thousand_o a_o hundred_o thousand_o a_o hundred_o million_o of_o time_n and_o more_o in_o infinitum_fw-la the_o brevity_n therefore_o of_o such_o line_n be_v so_o reduce_v that_o it_o far_o exceed_v what_o be_v requisite_a to_o make_v the_o project_n though_o never_o so_o light_a return_n nay_o more_o continue_v unremovable_a upon_o the_o circumference_n sagr._fw-la i_o very_o well_o comprehend_v the_o whole_a discourse_n and_o upon_o what_o it_o lay_v all_o its_o stress_n yet_o nevertheless_o methinks_v that_o he_o that_o will_v take_v pain_n to_o pursue_v it_o may_v yet_o start_v some_o further_a question_n by_o say_v that_o of_o those_o two_o cause_n which_o render_v the_o descent_n of_o the_o movable_a slow_o and_o slow_a in_o infinitum_fw-la it_o be_v manifest_a that_o that_o which_o depend_v on_o the_o vicinity_n to_o the_o first_o term_n of_o the_o descent_n increase_v always_o in_o the_o same_o proportion_n like_v as_o the_o parallel_n always_o retain_v the_o same_o proportion_n to_o each_o other_o etc._n etc._n but_o that_o the_o diminution_n of_o the_o same_o velocity_n dependent_a on_o the_o diminution_n of_o the_o gravity_n of_o the_o movable_a which_o be_v the_o second_o cause_n do_v also_o observe_v the_o same_o proportion_n do_v not_o so_o plain_o appear_v and_o who_o shall_v assure_v we_o that_o it_o do_v not_o proceed_v according_a to_o the_o proportion_n of_o the_o line_n intercept_v between_o the_o secant_fw-la and_o the_o circumference_n or_o whether_o with_o a_o great_a proportion_n salv_n i_o have_v assume_v for_o a_o truth_n that_o the_o velocity_n of_o moveable_n descend_v natural_o will_v follow_v the_o proportion_n of_o their_o gravity_n with_o the_o favour_n of_o simplicius_n and_o of_o aristotle_n who_o do_v in_o many_o place_n affirm_v the_o same_o as_o a_o proposition_n manifest_a you_o in_o favour_n of_o my_o adversary_n bring_v the_o same_o into_o question_n
and_o say_v that_o its_o possible_a that_o the_o velocity_n increase_v with_o great_a proportion_n yea_o and_o great_a in_o infinitum_fw-la than_o that_o of_o the_o gravity_n so_o that_o all_o that_o have_v be_v say_v fall_v to_o the_o ground_n for_o maintain_v whereof_o i_o say_v that_o the_o proportion_n of_o the_o velocity_n be_v much_o less_o than_o that_o of_o the_o gravity_n and_o thereby_o i_o do_v not_o only_o support_v but_o confirm_v the_o premise_n and_o for_o proof_n of_o this_o i_o appeal_v unto_o experience_n which_o will_v show_v we_o that_o a_o grave_a body_n howbeit_o thirty_o or_o forty_o time_n big_a than_o another_o as_o for_o example_n a_o ball_n of_o lead_n and_o another_o of_o sugar_n will_v not_o move_v much_o more_o than_o twice_o as_o fast_o now_o if_o the_o projection_n will_v not_o be_v make_v albeit_o the_o velocity_n of_o the_o cadent_a body_n shall_v diminish_v according_a to_o the_o proportion_n of_o the_o gravity_n much_o less_o will_v it_o be_v make_v so_o long_o as_o the_o velocity_n be_v but_o little_o diminish_v by_o abate_v much_o from_o the_o gravity_n but_o yet_o suppose_v that_o the_o velocity_n diminish_v with_o a_o proportion_n much_o great_a than_o that_o wherewith_o the_o gravity_n decrease_v nay_o though_o it_o be_v the_o selfsame_a wherewith_o those_o parallel_n contain_v between_o the_o tangent_fw-la and_o circumference_n do_v decrease_v yet_o can_v i_o see_v any_o necessity_n why_o i_o shall_v grant_v the_o projection_n of_o matter_n of_o never_o so_o great_a levity_n yea_o i_o far_o aver_v that_o there_o can_v no_o such_o projection_n follow_v mean_v always_o of_o matter_n not_o proper_o and_o absolute_o light_a that_o be_v void_a of_o all_o gravity_n and_o that_o of_o their_o own_o nature_n move_v upward_o but_o that_o descend_v very_o slow_o and_o have_v very_o small_a gravity_n and_o that_o which_o move_v i_o so_o to_o think_v be_v that_o the_o diminution_n of_o gravity_n make_v according_a to_o the_o proportion_n of_o the_o parallel_n between_o the_o tangent_fw-la and_o the_o circumference_n have_v for_o its_o ultimate_a and_o high_a term_n the_o nullity_n of_o weight_n as_o those_o parallel_n have_v for_o their_o last_o term_n of_o their_o diminution_n the_o contact_n itself_o which_o be_v a_o indivisible_a point_n now_o gravity_n never_o diminish_v so_o far_o as_o to_o its_o last_o term_n for_o then_o the_o movable_n will_v cease_v to_o be_v grave_a but_o yet_o the_o space_n of_o the_o reversion_n of_o the_o project_n to_o the_o circumference_n be_v reduce_v to_o the_o ultimate_a minuity_n which_o be_v when_o the_o movable_a rest_v upon_o the_o circumference_n in_o the_o very_a point_n of_o contact_n so_o as_o that_o to_o return_v thither_o it_o have_v no_o need_n of_o space_n and_o therefore_o let_v the_o propension_n to_o the_o motion_n of_o descent_n be_v never_o so_o small_a yet_o be_v it_o always_o more_o than_o sufficient_a to_o reconduct_n the_o movable_a to_o the_o circumference_n from_o which_o it_o be_v distant_a but_o its_o least_o space_n that_o be_v nothing_o at_o all_o sagr._fw-la your_o discourse_n i_o must_v confess_v be_v very_o accurate_a and_o yet_o no_o less_o conclude_v than_o it_o be_v ingenuous_a and_o it_o must_v be_v grant_v that_o to_o go_v about_o to_o handle_v natural_a question_n without_o geometry_n be_v to_o attempt_v a_o impossibility_n salv_n but_o simplicius_n will_v not_o say_v so_o and_o yet_o i_o do_v not_o think_v that_o he_o be_v one_o of_o those_o peripatetic_n that_o dissuade_v their_o disciple_n from_o study_v the_o mathematics_n as_o science_n that_o vitiate_v the_o reason_n and_o render_v it_o less_o apt_a for_o contemplation_n simp_n i_o will_v not_o do_v so_o much_o wrong_n to_o plato_n but_o yet_o i_o may_v true_o say_v with_o aristotle_n that_o he_o too_o much_o lose_v himself_o in_o and_o too_o much_o dote_v upon_o that_o his_o geometry_n for_o that_o in_o conclusion_n these_o mathematical_a subtlety_n salviatus_n be_v true_a in_o abstract_n but_o apply_v to_o sensible_a and_o physical_a matter_n they_o hold_v not_o good_a for_o the_o mathematician_n will_v very_o well_o demonstrate_v for_o example_n that_o sphaera_fw-la tangit_fw-la planum_fw-la in_o puncto_fw-la a_o position_n like_a to_o that_o in_o dispute_n but_o when_o one_o come_v to_o the_o matter_n thing_n succeed_v quite_o another_o way_n and_o so_o i_o may_v say_v of_o these_o angle_n of_o contact_n and_o these_o proportion_n which_o all_o evaporate_v into_o air_n when_o they_o be_v apply_v to_o thing_n material_a and_o sensible_a salv_n you_o do_v not_o think_v then_o that_o the_o tangent_fw-la touch_v the_o superficies_n of_o the_o terrestrial_a globe_n in_o one_o point_n only_o simp_n no_o not_o in_o one_o sole_a point_n but_o i_o believe_v that_o a_o right_a line_n go_v many_o ten_o and_o hundred_o of_o yard_n touch_v the_o surface_n not_o only_o of_o the_o earth_n but_o of_o the_o water_n before_o it_o separate_v from_o the_o same_o salv_n but_o if_o i_o grant_v you_o this_o do_v not_o you_o perceive_v that_o it_o make_v so_o much_o the_o more_o against_o your_o cause_n for_o if_o it_o be_v suppose_v that_o the_o tangent_fw-la be_v separate_v from_o the_o terrestrial_a superficies_n yet_o it_o have_v be_v however_o demonstrate_v that_o by_o reason_n of_o the_o great_a acuity_n of_o the_o angle_n of_o contingence_n if_o happy_o it_o may_v be_v call_v a_o angle_n the_o project_n will_v not_o separate_v from_o the_o same_o how_o much_o less_o cause_n of_o separation_n will_v it_o have_v if_o that_o angle_n shall_v be_v whole_o close_v contradiction_n and_o the_o superficies_n and_o the_o tangent_fw-la become_v all_o one_o perceive_v you_o not_o that_o the_o projection_n will_v do_v the_o same_o thing_n upon_o the_o surface_n of_o the_o earth_n which_o be_v asmuch_o as_o to_o say_v it_o will_v do_v just_o nothing_o at_o all_o you_o see_v then_o the_o power_n of_o truth_n which_o while_o you_o strive_v to_o oppose_v it_o your_o own_o assault_n themselves_o uphold_v and_o defend_v it_o but_o in_o regard_n that_o you_o have_v retract_v this_o error_n i_o will_v be_v loath_a to_o leave_v you_o in_o that_o other_o which_o you_o hold_v namely_o that_o a_o material_a sphere_n do_v not_o touch_v a_o plain_a in_o one_o sole_a point_n and_o i_o can_v wish_v some_o few_o hour_n conversation_n with_o some_o person_n conversant_a in_o geometry_n may_v make_v you_o a_o little_a more_o intelligent_a among_o those_o who_o know_v nothing_o thereof_o now_o to_o show_v you_o how_o great_a their_o error_n be_v who_o say_v that_o a_o sphere_n v_o g._n of_o brass_n do_v not_o touch_v a_o plain_a v_o g._n of_o steel_n in_o one_o sole_a point_n tell_v i_o what_o conceit_n you_o will_v entertain_v of_o one_o that_o shall_v constant_o aver_v that_o the_o sphere_n be_v not_o true_o a_o sphere_n simp_n i_o will_v esteem_v he_o whole_o devoid_a of_o reason_n salv_n he_o be_v in_o the_o same_o case_n who_o say_v that_o the_o material_a sphere_n do_v not_o touch_v a_o plain_a only_o also_o material_a in_o one_o only_a point_n for_o to_o say_v this_o be_v the_o same_o as_o to_o affirm_v that_o the_o sphere_n be_v not_o a_o sphere_n and_o that_o this_o be_v true_a tell_v i_o in_o what_o it_o be_v that_o you_o constitute_v the_o sphere_n to_o consist_v that_o be_v what_o it_o be_v that_o make_v the_o sphere_n differ_v from_o all_o other_o solid_a body_n simp_n i_o believe_v that_o the_o essence_n of_o a_o sphere_n consist_v in_o have_v all_o the_o right_a line_n produce_v from_o its_o centre_n to_o the_o circumference_n sphere_n equal_a salv_n so_o that_o if_o those_o line_n shall_v not_o be_v equal_a that_o same_o solidity_n will_v be_v no_o long_o a_o sphere_n simp_n true_a salv_n go_v to_o tell_v i_o whether_o you_o believe_v that_o among_o the_o many_o line_n that_o may_v be_v draw_v between_o two_o point_n there_o may_v be_v more_o than_o one_o right_a line_n only_o simp_n there_o can_v be_v but_o one_o 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worth_a than_o the_o wool_n of_o a_o goat_n and_o whereas_o our_o argumentation_n shall_v continual_o be_v conversant_a about_o serious_a and_o weighty_a point_n we_o consume_v our_o time_n in_o frivolous_a and_o impertinent_a wrangling_n problem_n let_v we_o call_v to_o mind_n i_o pray_v you_o that_o the_o search_n of_o the_o world_n constitution_n be_v one_o of_o the_o great_a and_o noble_a problem_n that_o be_v in_o nature_n and_o so_o much_o the_o great_a inasmuch_o as_o it_o be_v direct_v to_o the_o resolve_v of_o that_o other_o to_o wit_n of_o the_o cause_n of_o the_o sea_n ebb_v and_o flow_v inquire_v into_o by_o all_o the_o famous_a man_n that_o have_v hitherto_o be_v in_o the_o world_n and_o possible_o find_v out_o by_o none_o of_o they_o therefore_o if_o we_o have_v nothing_o more_o remain_v for_o the_o full_a confutation_n of_o the_o argument_n take_v from_o the_o earth_n vertigo_n which_o be_v the_o last_o allege_v to_o prove_v its_o immobility_n upon_o its_o own_o centre_n let_v we_o pass_v to_o the_o examination_n of_o those_o thing_n that_o be_v allege_v for_o and_o against_o the_o annual_a motion_n sagr._fw-la i_o will_v not_o have_v you_o salviatus_fw-la measure_v our_o wit_n by_o the_o scale_n of_o you_o you_o who_o use_v to_o be_v continual_o busy_v about_o the_o sublimest_n contemplation_n esteem_v those_o notion_n frivolous_a and_o below_o you_o which_o we_o think_v matter_n worthy_a of_o our_o profound_a thought_n yet_o sometime_o for_o our_o satisfaction_n do_v not_o disdain_v to_o stoop_v so_o low_a as_o to_o give_v way_n a_o little_a to_o our_o curiosity_n as_o to_o the_o refutation_n of_o the_o last_o argument_n take_v from_o the_o extrusion_n of_o the_o diurnal_a vertigo_n far_o less_o than_o what_o have_v be_v say_v will_v have_v give_v i_o satisfaction_n and_o yet_o the_o thing_n superfluous_o speak_v seem_v to_o i_o so_o ingenious_a that_o they_o have_v be_v so_o far_o from_o weary_v my_o fancy_n as_o that_o they_o have_v by_o reason_n of_o their_o novelty_n entertain_v i_o all_o along_o with_o so_o great_a delight_n that_o i_o know_v not_o how_o to_o desire_v great_a therefore_o if_o you_o have_v any_o other_o speculation_n to_o add_v produce_v it_o for_o i_o as_o to_o my_o own_o particular_a shall_v glad_o hearken_v to_o it_o salv_n i_o have_v always_o take_v great_a delight_n in_o those_o thing_n which_o i_o have_v have_v the_o fortune_n to_o discover_v and_o next_o to_o that_o which_o be_v my_o chief_a content_n i_o find_v great_a pleasure_n in_o impart_v they_o to_o some_o friend_n that_o apprehend_v and_o seem_v to_o like_v they_o now_o in_o regard_n you_o be_v one_o of_o these_o slack_v a_o little_a the_o reins_o of_o my_o ambition_n which_o be_v much_o please_v when_o i_o show_v myself_o more_o perspicacious_a than_o some_o other_o that_o have_v the_o reputation_n of_o a_o sharp_a sight_n i_o will_v for_o a_o full_a and_o true_a measure_n of_o the_o past_a dispute_n produce_v another_o fallacy_n of_o the_o sectator_n of_o ptolomey_n and_o aristotle_n which_o i_o take_v from_o the_o argument_n allege_v sagr._fw-la see_v how_o greedy_o i_o wait_v to_o hear_v it_o salv_n we_o have_v hitherto_o over-passed_n and_o grant_v to_o ptolomey_n as_o a_o effect_n indubitable_a that_o the_o extrusion_n of_o the_o stone_n proceed_v from_o the_o velocity_n of_o the_o wheel_n turn_v round_o upon_o its_o centre_n the_o cause_n of_o the_o say_a extrusion_n increase_v in_o proportion_n as_o the_o velocity_n of_o the_o vertigo_n or_o whirl_v be_v augment_v from_o whence_o it_o be_v infer_v that_o the_o velocity_n of_o the_o earth_n vertigo_n be_v very_o much_o great_a than_o that_o of_o any_o machine_n whatsoever_o that_o we_o can_v make_v to_o turn_v round_o artificial_o the_o extrusion_n of_o stone_n of_o animal_n etc._n etc._n will_v consequent_o be_v far_o more_o violent_a now_o i_o observe_v that_o there_o be_v a_o great_a fallacy_n in_o this_o discourse_n in_o that_o we_o do_v compare_v these_o velocity_n indifferent_o and_o absolute_o to_o one_o another_o it_o be_v true_a that_o if_o i_o compare_v the_o velocity_n of_o the_o same_o wheel_n or_o of_o two_o wheel_n equal_a to_o each_o other_o that_o which_o shall_v be_v more_o swift_o turn_v round_o shall_v extrude_v the_o stone_n with_o great_a violence_n and_o the_o velocity_n increase_a the_o cause_n of_o the_o projection_n shall_v likewise_o increase_v but_o when_o the_o velocity_n be_v augment_v not_o by_o increase_a the_o velocity_n in_o the_o same_o wheel_n which_o will_v be_v by_o cause_v it_o to_o make_v a_o great_a number_n of_o revolution_n in_o equal_a time_n but_o by_o increase_a the_o diameter_n and_o make_v the_o wheel_n great_a so_o as_o that_o the_o conversion_n take_v up_o the_o same_o time_n in_o the_o lesser_a wheel_n as_o in_o the_o great_a big_a the_o velocity_n be_v great_a only_o in_o the_o big_a wheel_n for_o that_o its_o circumference_n be_v big_a there_o be_v no_o man_n that_o think_v that_o the_o 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authority_n 461_o the_o copernican_n system_v more_o plain_o assert_v in_o scripture_n than_o the_o ptolomaick_a 469_o copernican_n copernican_n be_v
earth_n answer_v by_o example_n of_o the_o like_a motion_n in_o other_o celestial_a body_n 236_o a_o four_o argument_n of_o claramontius_n against_o the_o copernican_n hypothesis_n of_o the_o earth_n mobility_n 239_o from_o the_o earth_n obscurity_n and_o the_o splendour_n of_o the_o fix_a star_n it_o be_v argue_v that_o it_o be_v movable_a and_o they_o immovable_a 239_o a_o five_o argument_n of_o claramontius_n against_o the_o copernican_n hypothesis_n of_o the_o earth_n mobility_n 240_o another_o difference_n between_o the_o earth_n and_o celestial_a body_n take_v from_o purity_n and_o impurity_n 240_o it_o seem_v a_o solecism_n to_o affirm_v that_o the_o earth_n be_v not_o in_o heaven_n 241_o grant_v to_o the_o earth_n the_o annual_a it_o must_v of_o necessity_n also_o have_v the_o diurnal_a motion_n assign_v to_o it_o 300_o discourse_n more_o than_o childish_a that_o serve_v to_o keep_v fool_n in_o the_o opinion_n of_o the_o earth_n stability_n 301_o the_o difficulty_n remove_v that_o arise_v from_o the_o earth_n move_v about_o the_o sun_n not_o solitary_o but_o in_o consort_n with_o the_o moon_n 307_o the_o axis_n of_o the_o earth_n continue_v always_o parallel_v to_o itself_o and_o describe_v a_o cylindraical_a superficies_n incline_v to_o the_o orb._n 344_o the_o orb_n of_o the_o earth_n never_o incline_v but_o be_v immutable_o the_o same_o 345_o the_o earth_n approach_v or_o recede_v from_o the_o fix_a star_n of_o the_o ecliptic_a the_o quantity_n of_o the_o grand_a orb._n 349_o if_o in_o the_o fix_a star_n one_o shall_v discover_v any_o mutation_n the_o motion_n of_o the_o earth_n will_v be_v undeniable_a 351_o necessary_a proposition_n for_o the_o better_a conceive_n of_o the_o consequence_n of_o the_o earth_n motion_n 354_o a_o admirable_a accident_n depend_v on_o the_o not-inclining_a of_o the_o earth_n axis_n 358_o four_o several_a motion_n assign_v to_o the_o earth_n 362_o the_o three_o motion_n ascribe_v to_o the_o earth_n be_v rather_o a_o rest_a 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immovable_a 386_o the_o most_o potent_a and_o primary_n cause_v of_o the_o ebb_a and_o flow_v 390_o sundry_a accident_n that_o happen_v in_o the_o ebb_n and_o flow_n 391_o reason_n renew_v of_o the_o particular_a accident_n observe_v in_o the_o ebb_n and_o flow_n 393_o second_o cause_n why_o in_o several_a sea_n and_o lake_n there_o be_v no_o ebb_n and_o flow_n 394_o the_o reason_n why_o the_o ebb_n and_o flow_n for_o the_o most_o part_n be_v every_o six_o hour_n 395_o the_o cause_n why_o some_o sea_n though_o very_o long_o suffer_v no_o ebb_a and_o flow_v 395_o ebb_n and_o flow_n why_o great_a in_o the_o extremity_n of_o gulf_n and_o least_o in_o the_o middle_a part_n 396_o a_o discussion_n of_o some_o more_o abstruse_a accident_n observe_v in_o the_o ebb_a and_o flow_v 396_o the_o ebb_a and_o flow_v may_v depend_v on_o the_o diurnal_a motion_n of_o heaven_n 404_o the_o ebb_a and_o flow_v can_v depend_v on_o the_o motion_n of_o heaven_n 405_o the_o cause_n of_o the_o period_n of_o 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all_o other_o whatsoever_o not_o only_o those_o that_o be_v contrary_a to_o but_o even_o all_o that_o ever_o so_o little_o disagree_v with_o or_o vary_v from_o they_o as_o harsh_a to_o the_o ear_n discolour_v to_o the_o eye_n unpleasant_a to_o the_o smell_n nauseous_a to_o the_o taste_n rough_a to_o the_o touch._n and_o no_o wonder_n for_o physical_a truth_n be_v ordinary_o judge_v and_o consider_v by_o man_n not_o according_a to_o their_o essence_n but_o according_a to_o the_o prescript_n of_o some_o one_o who_o description_n or_o definition_n of_o they_o gain_v he_o authority_n among_o the_o vulgar_a which_o authority_n nevertheless_o since_o it_o be_v no_o more_o than_o humane_a ought_v not_o to_o be_v so_o esteem_v as_o that_o that_o which_o do_v manifest_o appear_v to_o the_o contrary_a whether_o from_o better_a reason_n late_o find_v out_o or_o from_o sense_n itself_o shall_v for_o its_o sake_n be_v contemn_v and_o slight_v nor_o be_v posterity_n so_o to_o be_v confine_v but_o that_o it_o may_v and_o dare_v not_o only_o proceed_v far_a but_o also_o bring_v to_o light_v better_a and_o true_a experiment_n than_o those_o which_o have_v be_v deliver_v to_o we_o by_o the_o ancient_n for_o the_o genius_n of_o the_o ancient_n as_o in_o invention_n they_o do_v not_o much_o surpass_v the_o wit_n of_o our_o time_n so_o for_o the_o perfect_a of_o invention_n this_o age_n of_o we_o seem_v not_o only_o to_o equal_v but_o far_o to_o excel_v former_a age_n knowledge_n whether_o in_o the_o liberal_a or_o mechanical_a art_n daily_o grow_v to_o a_o great_a height_n which_o assertion_n may_v be_v easy_o prove_v be_v it_o not_o that_o in_o so_o clear_a a_o case_n there_o will_v be_v more_o danger_n of_o obscure_v than_o hope_n of_o illustrate_v it_o with_o any_o far_a light_n but_o that_o i_o may_v not_o whole_o be_v silent_a in_o this_o point_n have_v not_o the_o several_a experiment_n of_o modern_n in_o many_o thing_n stop_v the_o mouth_n
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
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
with_o industry_n true_o heroical_a and_o admirable_a by_o monsignor_n maffei_n barherino_n then_o perfect_a for_o the_o way_n and_o now_o pope_n and_o be_v necessitate_v that_o i_o may_v be_v able_a to_o walk_v in_o the_o cave_n and_o for_o other_o cause_n i_o let_v down_o the_o sluice_n of_o the_o say_a cave_n at_o the_o mouth_n of_o the_o lake_n no_o soon_o be_v they_o stop_v but_o a_o great_a many_o of_o the_o people_n of_o the_o town_n and_o village_n coast_v upon_o the_o lake_n flock_v thither_o begin_v to_o make_v grievous_a complaint_n that_o if_o those_o sluice_n be_v keep_v shut_v not_o only_o the_o lake_n will_v want_v its_o due_a vent_n but_o also_o the_o part_n adjacent_a to_o the_o lake_n will_v be_v over_o fly_v to_o their_o very_a great_a detriment_n and_o because_o at_o first_o appearance_n their_o motion_n seem_v very_o reasonable_a i_o find_v myself_o hard_o put_v to_o it_o see_v no_o way_n to_o persuade_v such_o a_o multitude_n that_o the_o prejudice_n which_o they_o pretend_v i_o shall_v do_v they_o by_o keep_v the_o sluice_n shut_v for_o two_o day_n be_v absolute_o insensible_a and_o that_o by_o keep_v they_o open_a the_o lake_n do_v not_o ebb_v in_o the_o same_o time_n so_o much_o as_o the_o thickness_n of_o a_o sheet_n of_o paper_n and_o therefore_o i_o be_v necessitate_v to_o make_v use_n of_o the_o authority_n i_o have_v and_o so_o follow_v my_o business_n as_o cause_v require_v without_o any_o regard_n to_o that_o rabble_n tumultuous_o assemble_v now_o when_o i_o be_o not_o work_v with_o mattock_n or_o spade_n but_o with_o the_o pen_n and_o discourse_n i_o intend_v to_o demonstrate_v clear_o to_o those_o that_o be_v capable_a of_o reason_n and_o that_o have_v well_o understand_v the_o ground_n of_o this_o my_o treatise_n that_o the_o fear_n be_v altogether_o vain_a which_o those_o people_n conceit_v and_o therefore_o i_o say_v that_o the_o emissary_n or_o sluice_n of_o the_o lake_n of_o perugia_n stand_v in_o the_o same_o manner_n as_o at_o present_a and_o the_o water_n pass_v through_o it_o with_o the_o same_o velocity_n as_o now_o to_o examine_v how_o much_o the_o lake_n may_v abate_v in_o two_o day_n space_n we_o ought_v to_o consider_v what_o proportion_n the_o superficies_n of_o the_o whole_a lake_n have_v to_o the_o measure_n of_o the_o section_n of_o the_o emissary_n and_o afterward_o to_o infer_v that_o the_o velocity_n of_o the_o water_n by_o the_o emissary_n or_o sluice_n shall_v have_v the_o same_o proportion_n to_o the_o abatement_n of_o the_o lake_n and_o to_o prove_v thorough_o and_o clear_o this_o discourse_n i_o intend_v to_o demonstrate_v the_o follow_a proposition_n that_o which_o have_v be_v demonstrate_v in_o the_o vessel_n fall_v out_o exact_o also_o in_o our_o lake_n of_o perugia_n and_o its_o emissary_n and_o because_o the_o immensity_n of_o the_o superficies_n of_o the_o lake_n be_v in_o proportion_n to_o the_o superficies_n of_o the_o emissary_n or_o sluice_n as_o many_o million_o to_o one_o as_o may_v be_v easy_o calculate_v it_o be_v manifest_a that_o such_o abatement_n shall_v be_v imperceptible_a and_o almost_o nothing_o in_o two_o day_n space_n nay_o in_o four_o or_o six_o and_o all_o this_o will_v be_v true_a when_o we_o suppose_v that_o for_o that_o time_n there_o enter_v no_o other_o water_n into_o the_o lake_n from_o ditch_n or_o rivulet_n which_o fall_v into_o the_o lake_n will_v render_v such_o abatement_n yet_o less_o now_o we_o see_v that_o it_o be_v necessary_a to_o examine_v such_o abatement_n and_o rise_n with_o excellent_a reason_n or_o at_o least_o with_o accurate_a experiment_n before_o we_o resolve_v and_o conclude_v any_o thing_n and_o how_o far_o the_o vulgar_a be_v distant_a from_o a_o right_a judgement_n in_o such_o matter_n appendix_n xiii_o for_o great_a confirmation_n of_o all_o this_o which_o i_o have_v say_v i_o will_v instance_n in_o another_o like_a case_n which_o also_o i_o meet_v with_o heretofore_o wherein_o for_o that_o the_o business_n be_v not_o right_o understand_v many_o disorder_n vast_a expense_n and_o considerable_a mischief_n have_v follow_v there_o be_v heretofore_o a_o emissary_n or_o sluice_n make_v to_o drain_v the_o water_n which_o from_o rain_n spring_n and_o rivulet_n fall_v into_o a_o lake_n to_o the_o end_n the_o shore_n adjoin_v on_o the_o lake_n shall_v be_v free_a from_o the_o overflow_n of_o the_o water_n but_o because_o perhaps_o the_o enterprise_n be_v not_o well_o manage_v and_o carry_v on_o it_o fall_v out_o that_o the_o field_n adjacent_a to_o the_o say_a channel_n can_v not_o drain_v but_o continue_v under_o water_n to_o which_o disorder_v a_o present_a remedy_n have_v be_v use_v namely_o in_o a_o time_n convenient_a to_o stop_v up_o the_o sluice_n by_o mean_n of_o certain_a floodgate_n keep_v on_o purpose_n for_o that_o end_n and_o thus_o abate_v the_o level_n of_o the_o water_n in_o the_o emissary_n in_o the_o space_n of_o three_o or_o four_o day_n the_o field_n have_v be_v haply_o drain_v but_o on_o the_o other_o part_n the_o proprietor_n border_v on_o the_o lake_n oppose_v this_o grievous_o complain_v that_o whilst_o the_o floodgate_n be_v shut_v and_o the_o course_n of_o the_o water_n of_o the_o sluice_n hinder_v the_o lake_n overflow_v the_o land_n adjacent_a by_o mean_n of_o the_o river_n that_o fall_v into_o it_o to_o their_o very_a great_a damage_n and_o so_o continue_v their_o suit_n they_o get_v more_o of_o vexation_n than_o satisfaction_n now_o be_v ask_v my_o opinion_n herein_o i_o judge_v it_o requisite_a since_o the_o point_n in_o controversy_n be_v about_o the_o rise_n and_o fall_v of_o the_o lake_n that_o the_o say_a abatement_n when_o the_o floodgate_n be_v open_a and_o increase_v when_o they_o be_v shut_v shall_v be_v exact_o measure_v and_o tell_v they_o that_o it_o may_v be_v easy_o do_v at_o a_o time_n when_o no_o extraordinary_a water_n fall_v into_o the_o lake_n neither_o of_o rain_n or_o otherwise_o and_o the_o lake_n be_v undisturbed_a by_o wind_n that_o may_v drive_v the_o water_n to_o any_o side_n by_o plant_v near_o to_o a_o islet_n which_o be_v about_o the_o middle_n of_o the_o lake_n a_o thick_a post_n on_o which_o shall_v be_v make_v the_o mark_n of_o the_o lake_n rise_v and_o fall_v for_o two_o or_o three_o day_n i_o will_v not_o at_o that_o time_n pawn_n or_o resolute_o declare_v my_o judgement_n in_o regard_n i_o may_v be_v by_o divers_a accident_n mislead_v but_o this_o i_o tell_v they_o that_o by_o what_o i_o have_v demonstrate_v and_o particular_o that_o which_o i_o have_v say_v above_o touch_v the_o lake_n of_o perugia_n i_o incline_v great_o to_o think_v that_o these_o rise_n and_o fall_n will_v prove_v imperceptible_a and_o inconsiderable_a and_o therefore_o that_o in_o case_n experience_n shall_v make_v good_a my_o reason_n it_o will_v be_v to_o no_o purpose_n for_o they_o to_o continue_v dispute_v and_o wrangle_v which_o cause_v according_a to_o the_o proverb_n a_o great_a deal_n of_o 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for_o then_o the_o overflowing_n become_v hurtful_a it_o be_v to_o be_v desire_v also_o that_o if_o any_o proposition_n be_v produce_v touch_v these_o affair_n it_o may_v be_v propound_v the_o most_o distinct_o that_o may_v be_v possible_a and_o not_o consist_v in_o general_n especial_o when_o the_o dispute_n be_v of_o the_o rise_n of_o velocity_n of_o tardity_n of_o much_o and_o little_a water_n thing_n that_o be_v all_o to_o be_v specify_v by_o measure_n 6._o your_o letter_n say_v in_o the_o next_o place_n that_o signore_v bartolotti_n confess_v that_o if_o the_o mouth_n of_o the_o fiume_n morto_fw-it may_v always_o be_v keep_v open_a it_o will_v be_v better_a to_o let_v it_o continue_v as_o it_o be_v the_o which_o that_o i_o may_v not_o yield_v to_o he_o in_o courtesy_n i_o confess_v for_o the_o keep_n it_o stop_v on_o all_o side_n will_v be_v a_o thing_n most_o pernicious_a but_o admit_v of_o his_o confession_n i_o again_o reply_n that_o fiume_n morto_fw-it ought_v not_o to_o be_v 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servant_n d._n benedetto_n castelli_n upon_o this_o occasion_n i_o will_v here_o insert_v a_o discourse_n that_o i_o make_v upon_o the_o draining_n and_o improvement_n of_o the_o pontine_n fen_n for_o that_o i_o think_v that_o whatsoever_o may_v be_v do_v well_o and_o to_o purpose_n in_o this_o matter_n have_v absolute_a dependence_n on_o the_o perfect_a knowledge_n of_o that_o so_o important_a proposition_n by_o i_o demonstrate_v and_o explain_v in_o my_o treatise_n of_o the_o mensuration_n of_o run_v water_n namely_o that_o the_o same_o water_n of_o a_o river_n do_v continual_o change_v measure_n according_a as_o it_o alter_v and_o change_v the_o velocity_n of_o its_o course_n so_o that_o the_o measure_n of_o the_o thickness_n of_o a_o river_n in_o one_o site_n to_o the_o measure_n of_o the_o same_o river_n in_o another_o site_n have_v the_o same_o proportion_n reciprocal_o that_o the_o velocity_n in_o this_o site_n have_v to_o the_o velocity_n in_o the_o first_o site_n and_o this_o 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which_o do_v not_o keep_v within_o its_o bank_n when_o they_o be_v abundant_a but_o increase_a above_o its_o channel_n they_o unite_v with_o those_o of_o the_o evacuator_fw-la and_o disperse_v through_o the_o fen_n be_v raise_v with_o great_a prejudice_n and_o much_o great_a than_o be_v conceive_v according_a to_o what_o have_v be_v demonstrate_v in_o the_o second_o consideration_n upon_o the_o lake_n of_o venice_n nor_o be_v it_o to_o any_o purpose_n to_o say_v that_o if_o we_o shall_v measure_v all_o the_o water_n that_o disimbogue_v from_o fiume_n sisto_n and_o gather_v they_o into_o one_o sum_n we_o shall_v not_o find_v they_o to_o be_v such_o as_o that_o they_o shall_v be_v able_a to_o make_v the_o water_n of_o the_o fen_n to_o increase_v by_o reason_n of_o the_o great_a expansion_n of_o they_o over_o which_o that_o body_n of_o water_n be_v to_o
to_o carry_v it_o into_o main-po_n at_o stellata_fw-la for_o the_o reason_n that_o cardinal_n capponi_n most_o ingenious_o enumerate_v in_o a_o short_a but_o wellgrounded_n tract_n of_o his_o not_o because_o that_o indeed_o it_o will_v not_o both_o by_o purl_n and_o by_o breach_n occasion_n some_o inconvenience_n especial_o in_o the_o beginning_n but_o because_o i_o hold_v this_o for_o the_o incomodity_n of_o it_o to_o be_v a_o far_o less_o evil_a than_o any_o of_o the_o rest_n and_o because_o that_o by_o this_o mean_n there_o be_v no_o occasion_n give_v to_o they_o of_o ferrara_n to_o explain_v that_o they_o be_v deprive_v of_o the_o hope_n of_o ever_o see_v the_o po_n again_o under_o the_o wall_n of_o their_o city_n to_o who_o where_o it_o may_v be_v do_v it_o be_v but_o reason_n that_o satisfaction_n shall_v be_v give_v it_o be_v certain_a that_o po_n be_v place_v by_o nature_n in_o the_o midst_n of_o this_o great_a valley_n make_v by_o the_o apennine_n hill_n and_o by_o the_o 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the_o church_n of_o gambarone_fw-la or_o a_o little_a high_o or_o low_o as_o shall_v be_v judge_v least_o prejudicial_a when_o it_o come_v to_o the_o execution_n and_o this_o for_o two_o principal_a reason_n the_o one_o because_o that_o then_o it_o will_v run_v along_o by_o the_o confine_n of_o the_o church_n patrimony_n without_o separate_a ferrara_n from_o the_o rest_n of_o it_o the_o other_o be_v because_o the_o line_n be_v short_a and_o consequent_o the_o fall_n great_a for_o that_o in_o a_o space_n of_o ten_o mile_n and_o one_o three_o it_o fall_v twenty_o six_o foot_n more_o by_o much_o than_o be_v require_v by_o artist_n and_o will_v go_v by_o place_n where_o it_o can_v do_v but_o little_a hurt_n notwithstanding_o that_o the_o person_n interress_v study_n to_o amplify_v it_o incredible_o on_o the_o contrary_a there_o be_v but_o only_o two_o objection_n that_o be_v worthy_a to_o be_v examine_v one_o that_o the_o drain_v and_o ditch_n of_o s._n bianca_n of_o the_o channel_n of_o cento_n and_o of_o burana_n and_o all_o those_o other_o that_o enter_v into_o po_n do_v hinder_v this_o diversion_n of_o reno_n by_o the_o increase_n of_o the_o water_n in_o the_o po._n the_o other_o be_v that_o po_n rise_v about_o the_o transom_n of_o the_o pilaster-sluice_n very_o near_o 20_o foot_n the_o reno_n will_v have_v no_o fall_n into_o the_o same_o whereupon_o it_o will_v rise_v to_o a_o terrible_a height_n at_o which_o it_o will_v not_o be_v possible_a to_o make_v or_o keep_v the_o bank_n make_v so_o that_o it_o will_v break_v out_o and_o drown_v the_o meadow_n and_o cause_n mischief_n and_o damage_n unspeakable_a and_o irreparable_a as_o be_v evident_a by_o the_o experiment_n make_v upon_o panaro_n which_o be_v confine_v between_o bank_n that_o it_o may_v go_v into_o po_n this_o not_o be_v neither_o in_o its_o great_a excrescense_n it_o break_v out_o into_o the_o territory_n of_o final_a and_o of_o ferrara_n and_o though_o that_o may_v be_v do_v it_o will_v thereupon_o ensue_v that_o there_o be_v let_v into_o the_o channel_n of_o po_n 2800._o square_a foot_n of_o water_n for_o so_o much_o we_o account_v those_o of_o reno_n and_o panaro_n take_v together_o in_o their_o great_a height_n the_o superficies_n of_o it_o will_v rise_v at_o least_o four_o foot_n insomuch_o that_o either_o it_o will_v be_v requisite_a to_o raise_v its_o bank_n all_o the_o way_n unto_o the_o sea_n to_o the_o same_o height_n which_o the_o treasure_n of_o the_o indies_n will_v not_o suffice_v to_o effect_v or_o else_o there_o will_v be_v a_o necessity_n of_o endure_v excessive_a breach_n to_o these_o two_o head_n be_v the_o argument_n reduce_v which_o be_v large_o amplify_v against_o our_o opinion_n and_o i_o shall_v answer_v first_o to_o the_o last_o as_o most_o material_a i_o say_v therefore_o that_o there_o be_v three_o case_n to_o be_v consider_v first_o po_n high_a and_o reno_n low_a second_o reno_n high_a and_o po_n low_a three_o reno_n and_o po_n both_o high_a together_o 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judgement_n be_v approve_v in_o these_o affair_n i_o return_v now_o from_o where_o i_o digress_v and_o affirm_v it_o as_o indubitable_a that_o reno_n neither_o can_v nor_o aught_o to_o continue_v long_o where_o it_o at_o this_o day_n be_v and_o that_o it_o can_v go_v into_o any_o other_o place_n but_o that_o whither_o cardinal_n capponi_n design_v to_o carry_v it_o and_o which_o at_o present_a please_v i_o better_o than_o any_o other_o or_o into_o volana_n whence_o it_o be_v take_v away_o the_o vigilance_n of_o man_n be_v able_a to_o obviate_v part_n of_o those_o mischief_n which_o it_o may_v do_v there_o but_o from_o its_o removal_n beside_o the_o alleviation_n of_o the_o harm_n which_o by_o itself_o be_v cause_v there_o will_v also_o result_v the_o diminution_n of_o that_o which_o be_v occasion_v by_o the_o other_o brook_n to_o the_o right_a hand_n of_o the_o po_n of_o argenta_n forasmuch_o as_o the_o say_v po_n want_v all_o the_o water_n of_o reno_n it_o will_v of_o necessity_n 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water_n right_o honourable_a and_o most_o noble_a sir_n have_v not_o a_o great_a prerogative_n than_o its_o have_v be_v the_o production_n of_o the_o command_n of_o pope_n vrban_n viii_o when_o his_o holiness_n be_v please_v to_o enjoin_v i_o to_o go_v with_o monsignore_n corsini_n in_o the_o visitation_n that_o be_v impose_v upon_o he_o in_o the_o year_n 1625._o of_o the_o water_n of_o ferrara_n bologna_n romagna_n and_o romagnola_n for_o that_o on_o that_o occasion_n apply_v my_o whole_a study_n to_o my_o service_n and_o duty_n i_o publish_v in_o that_o treatise_n some_o particular_n till_o than_o not_o right_o understand_v and_o consider_v that_o i_o know_v by_o any_o one_o although_o they_o be_v in_o themselves_o most_o important_a and_o of_o extraordinary_a consequence_n yet_o i_o must_v render_v thanks_o to_o your_o lordship_n for_o the_o honour_n you_o have_v do_v to_o that_o my_o tract_n but_o wish_v withal_o that_o your_o esteem_n of_o it_o may_v not_o prejudice_v the_o universal_a esteem_n that_o the_o world_n have_v of_o your_o honour_n most_o refine_a judgement_n as_o to_o that_o point_n which_o i_o touch_v upon_o in_o the_o conclusion_n namely_o that_o the_o consideration_n of_o the_o velocity_n of_o run_v water_n supply_v the_o consideration_n of_o the_o misprint_v length_n omit_v in_o the_o common_a way_n of_o measure_v run_v water_n your_o lordship_n have_v command_v i_o that_o in_o favour_n of_o practice_n and_o for_o the_o perfect_a discovery_n of_o the_o disorder_n that_o common_o happen_v now_o adays_o in_o the_o distribution_n of_o the_o water_n of_o fountain_n i_o shall_v demonstrate_v that_o the_o knowledge_n of_o the_o velocity_n serve_v for_o the_o find_n of_o the_o length_n i_o have_v think_v fit_a to_o satisfy_v your_o command_n by_o relate_v a_o fable_n which_o if_o i_o do_v not_o deceive_v myself_o will_v make_v out_o to_o we_o the_o truth_n thereof_o insomuch_o that_o the_o rest_n of_o my_o treatise_n shall_v thereby_o also_o become_v more_o manifest_a and_o intelligible_a even_o to_o those_o who_o find_v therein_o some_o kind_n of_o obscurity_n in_o the_o day_n of_o yore_o before_o that_o the_o admirable_a art_n of_o weave_v be_v in_o use_n there_o be_v find_v in_o persia_n a_o vast_a and_o unvaluable_a treasure_n which_o consist_v in_o a_o huge_a multitude_n of_o piece_n of_o ermesin_n or_o damask_n i_o know_v not_o whether_o which_o as_o i_o take_v it_o amount_v to_o near_o two_o thousand_o piece_n which_o be_v of_o such_o a_o nature_n that_o though_o their_o breadth_n and_o thickness_n be_v finite_a and_o determinate_a as_o they_o use_v to_o be_v at_o this_o day_n yet_o nevertheless_o their_o length_n be_v in_o a_o certain_a sense_n infinite_a for_o that_o those_o two_o thousand_o piece_n day_n and_o night_n without_o cease_v issue_v out_o with_o their_o end_n at_o such_o a_o rate_n that_o of_o each_o piece_n there_o issue_v 100_o ell_n a_o day_n from_o a_o deep_a and_o dark_a cave_n consecrate_v by_o the_o superstition_n of_o those_o people_n to_o the_o fabulous_a arachne_n in_o those_o innocent_a and_o early_a time_n i_o take_v it_o to_o have_v be_v in_o that_o so_o much_o applaud_v and_o desire_v golden_a age_n it_o be_v leave_v to_o the_o liberty_n of_o any_o one_o to_o cut_v off_o of_o those_o piece_n what_o quantity_n they_o please_v without_o any_o difficulty_n but_o that_o felicity_n decay_v and_o degenerate_v which_o be_v altogether_o ignorant_a of_o meum_fw-la and_o tuum_fw-la term_n certain_o most_o pernicious_a the_o original_a of_o all_o evil_n and_o cause_n of_o all_o discord_n there_o be_v by_o those_o people_n strong_a and_o vigilant_a guard_n place_v upon_o the_o cave_n who_o resolve_v to_o make_v merchandise_n of_o the_o stuff_v and_o in_o this_o manner_n they_o begin_v to_o set_v a_o price_n upon_o that_o inestimable_a treasure_n sell_v the_o propriety_n in_o those_o piece_n to_o divers_a merchant_n to_o some_o they_o sell_v a_o right_a in_o one_o to_o some_o in_o two_o and_o to_o some_o in_o more_o but_o that_o which_o be_v the_o worst_a of_o all_o there_o be_v find_v out_o by_o the_o insatiable_a avarice_n of_o these_o man_n crafty_a invention_n to_o deceive_v the_o merchant_n also_o who_o come_v to_o buy_v the_o aforesaid_a commodity_n and_o to_o make_v themselves_o master_n some_o of_o one_o some_o of_o two_o and_o some_o of_o more_o end_n of_o those_o piece_n of_o stuff_n and_o in_o particular_a there_o be_v certain_a ingenuous_a machine_n place_v in_o the_o more_o secret_a place_n of_o the_o cave_n with_o which_o at_o the_o pleasure_n of_o the_o guard_n they_o do_v retard_v the_o velocity_n of_o those_o stuff_n in_o their_o issue_v out_o of_o the_o cave_n insomuch_o that_o he_o who_o ought_v to_o have_v have_v 100_o ell_n of_o stuff_n in_o a_o day_n have_v not_o above_o 50_o and_o he_o who_o shall_v hauâ—_n have_v 400_o enjoy_v the_o benefit_n of_o 50._o only_a and_o so_o all_o the_o rest_n be_v defraud_v of_o their_o right_n the_o surplusage_n be_v sell_v appropriate_v and_o share_v at_o the_o will_n of_o the_o corrupt_a officer_n so_o that_o the_o business_n be_v without_o all_o order_n or_o justice_n insomuch_o that_o the_o goddess_n arachne_n be_v displease_v at_o those_o people_n deprive_v every_o one_o of_o their_o benefit_n and_o with_o a_o dreadful_a earthquake_n for_o ever_o close_v the_o mouth_n of_o the_o cave_n in_o punishment_n of_o so_o much_o impiety_n and_o malice_n nor_o do_v it_o avail_v they_o to_o excuse_v themselves_o by_o say_v that_o they_o allow_v the_o buyer_n the_o breadth_n and_o thickness_n bargain_v for_o and_o that_o of_o the_o length_n which_o be_v infinite_a there_o can_v no_o account_n be_v keep_v for_o the_o wise_a and_o prudent_a priest_n of_o the_o sacred_a grotto_n answer_v that_o the_o deceit_n lie_v in_o the_o length_n which_o they_o be_v defraud_v of_o
against_o the_o law_n of_o god_n since_o that_o thereby_o the_o same_o measure_n be_v make_v sometime_o great_a and_o sometime_o lesser_a a_o disorder_n so_o enormous_a and_o execrable_a that_o i_o shall_v take_v the_o boldness_n to_o say_v that_o for_o this_o sole_a respect_n it_o ought_v to_o be_v condemn_v and_o prohibit_v likewise_o by_o human_a law_n which_o shall_v enact_v that_o in_o this_o business_n there_o shall_v be_v employ_v either_o this_o our_o rule_n or_o some_o other_o that_o be_v more_o exquisite_a and_o practicable_a whereby_o the_o measure_n may_v keep_v one_o constant_a and_o determinate_a tenor_n as_o we_o make_v it_o and_o not_o as_o it_o be_v now_o to_o make_v pondus_fw-la &_o pondus_fw-la mensura_fw-la &_o mensura_fw-la and_o this_o be_v all_o that_o i_o have_v to_o offer_v to_o your_o most_o illustrious_a lordship_n in_o obedience_n to_o your_o command_n reserve_v to_o myself_o the_o give_v of_o a_o more_o exact_a account_n of_o this_o my_o invention_n when_o the_o occasion_n shall_v offer_v of_o reduce_v to_o practice_n so_o holy_a just_a and_o necessary_a a_o reformation_n of_o the_o measure_n of_o run_v water_n and_o of_o aqueduct_n in_o particular_a which_o rule_n may_v also_o be_v of_o great_a benefit_n in_o the_o division_n of_o the_o great_a water_n to_o overflow_n ground_n and_o for_o other_o use_n i_o humble_o bow_v your_o most_o devote_a and_o most_o oblige_a servant_n d._n benedetto_n castelli_n abb._n casin_n finis_fw-la a_o table_n of_o the_o most_o observable_a matter_n in_o this_o treatise_n of_o the_o mensuration_n of_o run_v water_n a_o 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
litigious_a lawyer_n that_o be_v extertain_v in_o a_o ill_a cause_n keep_v close_o to_o sâ—me_v exâ—ression_n fall_v from_o the_o adverse_a party_n at_o unaware_o unaware_o or_o progression_n the_o apparent_a diversity_n of_o motion_n in_o the_o planet_n be_v insensible_a in_o the_o fix_a star_n suppose_v that_o a_o fix_a star_n of_o the_o six_o magnitude_n be_v no_o big_a than_o the_o sun_n the_o diversity_n which_o be_v so_o great_a in_o the_o planet_n in_o the_o fix_a star_n be_v almost_o insensible_a the_o distance_n of_o the_o sun_n contain_v 1208_o semid_n of_o the_o earth_n earth_n the_o diameter_n of_o the_o sun_n half_o a_o degree_n the_o diameter_n of_o a_o fix_a star_n of_o the_o first_o magnitude_n and_o of_o one_o of_o the_o six_o the_o apparent_a diameter_n of_o the_o sun_n how_o much_o it_o be_v big_a than_o that_o of_o a_o fix_a star_n the_o distance_n of_o a_o fix_a star_n of_o the_o six_o magnitude_n how_o much_o it_o be_v the_o star_n be_v suppose_v to_o be_v equal_a to_o the_o sun_n in_o the_o fix_a star_n the_o diversity_n of_o aspect_n cause_v by_o the_o grand_a orb_n be_v little_o more_o than_o that_o cause_v by_o the_o earth_n in_o the_o sun_n a_o star_n of_o the_o six_o magnitude_n suppose_v by_o tycho_n and_o the_o author_n of_o the_o book_n of_o conclusion_n a_o hundred_o and_o six_o million_o of_o time_n big_a than_o needs_o the_o computation_n of_o the_o magnitude_n of_o the_o fix_a star_n in_o respect_n to_o the_o grand_a orb._n a_o common_a error_n of_o all_o the_o astronomer_n touch_v the_o magnitude_n of_o the_o star_n venus_n render_v the_o error_n of_o astronomer_n in_o determine_v the_o magnitude_n of_o star_n inexcusable_a a_o way_n to_o measure_v the_o apparent_a diameter_n of_o a_o star_n star_n render_v in_o latin_a corum_n that_o be_v to_o say_v northwest_n northwest_n i_o e._n be_v subtend_v by_o the_o diameter_n of_o a_o fix_a star_n of_o the_o first_o magnitude_n not_o more_o than_o five_o sec._n min._n the_o circle_n of_o the_o pupil_n of_o the_o eye_n enlarge_v and_o contract_v contract_v panicum_fw-la a_o small_a grain_n like_o to_o mill_n i_o take_v it_o to_o be_v the_o same_o with_o that_o call_v bird_n seed_n seed_n strisce_n how_o to_o find_v the_o distance_n of_o the_o ray_n concourse_n from_o the_o pupil_n all_o astronomer_n agree_v that_o the_o great_a magnitude_n of_o the_o orb_n be_v the_o cause_n of_o the_o tardity_n of_o the_o conversion_n by_o another_o supposition_n take_v from_o astronomer_n the_o distance_n of_o the_o fix_a star_n be_v calculate_v to_o be_v 10800_o semidiameter_n of_o the_o grand_a orb._n by_o the_o proportion_n of_o jupiter_n and_o of_o mars_n the_o starry_a sphere_n be_v find_v to_o be_v yet_o more_o remoâ—e_a immeâ—se_a magnitude_n and_o number_n be_v incomprehensible_a by_o our_o understanding_n god_n &_o nature_n do_v employ_v themselves_o in_o care_v for_o man_n as_o if_o they_o mind_v nothing_o else_o a_o example_n of_o god_n care_n of_o mankind_n take_v from_o the_o sun_n it_o be_v great_a rashness_n to_o censure_v that_o to_o be_v superfluous_a in_o hâ—ll_a verse_n which_o we_o do_v not_o perceive_v to_o be_v make_v for_o we_o by_o deprive_v heaven_n of_o some_o star_n one_o may_v come_v to_o know_v what_o influence_n it_o have_v upon_o we_o many_o thing_n may_v be_v in_o heaven_n that_o be_v invisible_a to_o we_o great_a small_a immense_a etc._n etc._n be_v relative_a term_n vanity_n of_o those_o man_n discourse_n who_o judge_v the_o starry_a sphere_n too_o vast_a in_o the_o copernican_n hypothesis_n hypothesis_n spelloncola_n which_o be_v here_o put_v for_o the_o lest_o of_o fish_n the_o space_n assign_v to_o a_o fix_a star_n be_v much_o less_o than_o that_o of_o a_o planet_n a_o star_n be_v call_v in_o respect_n of_o the_o space_n that_o environ_n it_o the_o whole_a starry_a sphere_n behold_v from_o a_o great_a distance_n may_v appear_v as_o small_a as_o one_o single_a star_n instance_n of_o the_o author_n of_o the_o conclusion_n by_o 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