of_o spain_n in_o the_o most_o swift_a river_n tagus_n in_o which_o the_o gold_n be_v say_v to_o be_v find_v run_v through_o the_o course_n of_o the_o sun_n none_o otherwise_o then_o danubus_fw-la and_o three_o other_o in_o the_o world_n make_v their_o course_n from_o the_o west_n to_o the_o east_n which_o strange_a fight_n twelve_o thousand_o person_n see_v in_o the_o presence_n of_o charles_n the_o emperor_n the_o five_o of_o that_o name_n of_o such_o strange_a experiment_n i_o shall_v not_o need_v here_o to_o speak_v much_o other_o there_o be_v that_o dare_v affirm_v that_o a_o certain_a ship_n be_v in_o such_o sort_n drive_v with_o violent_a wind_n and_o furious_a sea_n with_o such_o a_o swift_a course_n that_o the_o pilot_n stand_v in_o the_o keel_n of_o the_o ship_n near_o unto_o the_o mast_n shoot_v a_o arrow_n out_o of_o a_o cross-bow_n the_o arrow_n fall_v down_o before_o his_o foot_n and_o come_v not_o so_o far_o as_o the_o forepart_n or_o forecastle_n of_o the_o ship_n i_o 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of_o the_o river_n and_o therefore_o in_o savour_n of_o the_o commonwealth_n i_o have_v invent_v these_o kind_n of_o ship_n that_o i_o may_v hereby_o as_o by_o my_o seal_n confirm_v the_o good_a will_v i_o bear_v to_o our_o posterity_n now_o therefore_o it_o may_v suffice_v to_o have_v say_v thus_o much_o of_o this_o swift_a motion_n which_o i_o have_v prove_v with_o my_o own_o strength_n of_o reason_n and_o sufficient_o declare_v the_o frame_n and_o use_v thereof_o whereunto_o it_o may_v be_v easy_a for_o expert_a man_n to_o add_v more_o according_a to_o the_o excellency_n of_o their_o wit_n and_o cunning._n for_o in_o all_o science_n it_o be_v easy_a to_o add_v to_o invention_n then_o to_o invent._n let_v we_o now_o not_o only_o consider_v what_o commodity_n this_o may_v bring_v to_o ourselves_o but_o also_o to_o the_o brabantine_n sail_v from_o antuerp_n to_o brussels_n in_o the_o new_a river_n for_o that_o which_o they_o attempt_v dangerous_o with_o great_a vexation_n and_o shog_a in_o wagon_n by_o foul_a and_o tedious_a journey_n often_o wet_a to_o the_o skin_n for_o the_o space_n of_o a_o whole_a day_n may_v by_o water_n be_v do_v more_o convenient_o in_o the_o space_n of_o four_o or_o five_o hour_n even_o against_o the_o river_n and_o wind._n and_o lest_o the_o reader_n shall_v seem_v to_o refute_v our_o say_n while_o he_o think_v that_o those_o thing_n which_o he_o esteem_v for_o miracle_n to_o exceed_v the_o limit_n of_o nature_n i_o will_v show_v manifest_o by_o one_o demonstration_n of_o the_o forementioned_a enterpriser_n the_o manner_n how_o he_o descend_v to_o the_o bottom_n of_o the_o river_n his_o body_n remain_v dry_a as_o before_o i_o have_v affirm_v but_o here_o first_o let_v we_o consider_v that_o natural_o the_o water_n or_o sea_n as_o other_o element_n intend_v to_o a_o sperical_a form_n and_o with_o its_o globositie_n or_o rise_n overpass_v most_o high_a mountain_n but_o hear_v again_o will_v arise_v another_o doubt_n to_o the_o inexpert_a that_o be_v if_o the_o sea_n be_v high_a than_o the_o land_n how_o be_v it_o then_o that_o it_o do_v not_o drown_v and_o cover_v the_o earth_n whereunto_o i_o answer_v that_o the_o dryness_n of_o the_o earth_n may_v so_o long_o resist_v the_o moistness_n of_o the_o water_n until_o it_o receive_v or_o imbibe_n too_o much_o moistness_n which_o may_v thus_o be_v natural_o prove_v fill_v a_o cup_n a_o glass_n or_o other_o vessel_n with_o water_n or_o wine_n to_o the_o brim_n so_o that_o the_o fullness_n thereof_o may_v seem_v to_o swell_v as_o if_o it_o will_v overflow_v the_o brim_n of_o the_o cup._n then_o may_v you_o yet_o put_v therein_o many_o piece_n of_o gold_n without_o shed_v one_o drop_n of_o water_n but_o if_o the_o extremity_n of_o the_o brim_n be_v once_o wet_a immediate_o the_o water_n overflow_v because_o the_o dryness_n of_o the_o vessel_n do_v participate_v of_o the_o moistness_n
join_v b_o c_o by_o a_o line_n then_o by_o 4._o of_o the_o first_o the_o triangle_n b_o h_o c_o shall_v be_v equal_a to_o the_o triangle_n f_o s_o g_o and_o shall_v be_v equal_a to_o the_o portion_n f_o n_o g_o by_o the_o 17._o of_o archimedes_n de_fw-fr quadratura_fw-la parabolae_fw-la by_o the_o help_n of_o the_o first_o conception_n of_o euclid_n i_o do_v the_o like_a of_o the_o portion_n of_o f_o g_o x_o to_o who_o by_o a_o equal_a triangle_n o_o p_o k_n than_o i_o draw_v p_o qui_fw-fr equal_o distant_a o_o k_o and_o r_n v_n equal_o distant_a o_o p_o by_o 31_o of_o the_o first_o of_o euclid_n then_o by_o 41._o of_o the_o same_o o_fw-fr p_o r_o shall_v be_v half_a of_o the_o superficies_n o_o v._n now_o then_o i_o somewhat_o portrait_n c_o h_n then_z upon_z b_o h_z i_o constitute_v a_o superficial_a of_o equidistant_a side_n have_v a_o angle_n of_o b_o h_o a_o by_o 44._o of_o the_o first_o of_o euclid_n twice_o assumpt_v to_o the_o diameter_n of_o the_o first_o superficies_n a_o p_o b_o then_o by_o 41._o of_o the_o same_o by_o the_o first_o conception_n of_o the_o trigon_n a_o b_o c_o shall_v be_v equal_a of_o the_o superficies_n f_o g_o n_o x._o grant_v which_o be_v the_o intent_n aristotle_n to_o say_v the_o truth_n be_v a_o excellent_a searcher_n of_o thing_n yet_o i_o will_v not_o say_v as_o some_o say_v which_o have_v never_o read_v the_o the_o work_n of_o aristotle_n or_o understand_v they_o not_o that_o every_o word_n of_o aristotle_n be_v almost_o a_o sentence_n and_o that_o aristotle_n be_v the_o god_n of_o philosopher_n and_o that_o he_o never_o err_v in_o one_o word_n but_o be_v divine_a in_o all_o thing_n such_o miserable_a man_n if_o they_o know_v what_o it_o be_v to_o speak_v with_o demonstration_n and_o what_o by_o experience_n to_o the_o sense_n will_v never_o have_v say_v such_o thing_n for_o sense_n simple_o in_o those_o thing_n which_o be_v not_o proper_o sensible_a we_o be_v oftentimes_o deceive_v and_o whereas_o we_o can_v perceive_v the_o 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the_o horizon_n r_o a_o t_o the_o earth_n e_o a_o m._n who_o centre_n be_v a_o and_o the_o sight_n g_o the_o vapour_n o_o e_z then_o whereas_o the_o radical_a line_n pass_v from_o any_o rare_a thin_a or_o transparent_a in_o any_o transparent_a of_o more_o thickness_n make_v a_o perpendicular_a by_o the_o 45._o of_o the_o second_o of_o vitellio_n it_o be_v manifest_a therefore_o that_o the_o star_n i_o to_o be_v see_v by_o the_o line_n i_o d_o e_o which_o line_n shall_v be_v crooked_a because_o that_o simple_a air_n be_v thin_a than_o vapour_n and_o fire_n thin_a than_o air._n also_o the_o matter_n or_o substance_n of_o heaven_n be_v thin_a than_o fire_n by_o the_o 50._o of_o the_o 10_o of_o vitellio_n furthermore_o the_o high_a part_n of_o the_o air_n be_v thin_a than_o the_o low_a part_n the_o same_o i_o say_v also_o of_o water_n and_o fire_n if_o we_o may_v call_v fire_n the_o high_a part_n of_o the_o body_n and_o near_o unto_o the_o concavity_n of_o the_o moon_n and_o of_o every_o superior_a part_n of_o element_n and_o so_o the_o star_n by_o the_o line_n d_o e_o seem_v to_o be_v above_o the_o horizon_n in_o the_o point_n v._o but_o vitellio_n also_o in_o his_o 10_o book_n in_o the_o proposition_n 49._o teach_v perspective_o and_o how_o it_o may_v be_v instrumental_o prove_v how_o the_o star_n may_v be_v see_v in_o the_o horizon_n without_o their_o proper_a place_n by_o reason_n of_o incurnation_n or_o crooking_a of_o the_o beam_n whereof_o it_o follow_v that_o they_o do_v not_o mathematical_o define_v the_o horizon_n which_o say_v it_o be_v the_o terminer_n or_o ender_n of_o the_o sight_n and_o of_o the_o great_a circle_n of_o the_o sphere_n whereas_o by_o the_o demonstration_n before_o the_o circle_n end_v of_o the_o sight_n be_v cut_v the_o sphere_n in_o two_o unequal_a portion_n and_o that_o the_o high_a portion_n be_v great_a than_o the_o low_a for_o if_o the_o horizon_n be_v the_o end_a of_o the_o sight_n and_o one_o of_o the_o great_a circle_n than_o the_o earth_n be_v not_o equal_o about_o the_o centre_n or_o middle_n of_o the_o world_n or_o else_o the_o middle_n of_o the_o world_n be_v without_o the_o earth_n but_o if_o the_o earth_n do_v equal_o compass_v about_o the_o middle_n ergo_fw-la the_o end_a of_o the_o sight_n be_v not_o of_o the_o great_a circle_n in_o the_o sphere_n or_o contrarity_n therefore_o if_o we_o shall_v see_v any_o star_n above_o the_o end_a of_o the_o sight_n we_o shall_v not_o therefore_o think_v it_o to_o be_v in_o the_o twelve_o station_n of_o heaven_n this_o be_v to_o be_v understand_v by_o reasonable_a manner_n for_o the_o virtue_n of_o the_o star_n appear_v chief_o in_o the_o great_a circle_n who_o pole_n be_v zenith_n pass_v by_o the_o 90_o degree_n of_o the_o equinoctial_a from_o the_o intersection_n or_o divide_v of_o the_o same_o with_o the_o meridian_n towards_o the_o east_n furthermore_o the_o difference_n between_o the_o end_a of_o the_o sight_n and_o the_o great_a circle_n be_v not_o only_o one_o diameter_n of_o the_o star_n but_o of_o degree_n which_o if_o it_o be_v not_o we_o can_v by_o no_o mean_n use_v the_o proposition_n 49_o of_o vitellio_n and_o therefore_o it_o be_v no_o small_a error_n of_o they_o that_o say_v that_o the_o horizon_n be_v the_o end_a of_o the_o fight_n and_o one_o of_o the_o great_a circle_n in_o the_o sphere_n and_o that_o ever_o the_o middle_n of_o heaven_n appear_v unto_o we_o for_o evermore_o then_o half_o appear_v unto_o we_o for_o the_o incurvation_n or_o crooking_a of_o the_o beam_n but_o he_o that_o will_v see_v more_o example_n of_o these_o thing_n let_v he_o read_v the_o four_o book_n of_o vitellio_n and_o the_o ten_o and_o in_o some_o part_v the_o second_o and_o 5_o of_o the_o same_o in_o all_o of_o which_o he_o shall_v see_v somewhat_o how_o easy_o we_o may_v be_v deceive_v by_o this_o sense_n but_o the_o like_a of_o other_o sense_n be_v not_o to_o be_v doubt_v therefore_o not_o without_o weak_a and_o slender_a judgement_n they_o call_v 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this_o conclusion_n i_o leave_v to_o the_o experiment_n of_o such_o as_o please_v to_o make_v trial_n of_o it_o but_o to_o pursue_v our_o present_a design_n there_o be_v not_o any_o one_o error_n that_o breed_v a_o great_a confusion_n in_o magnetical_a knowledge_n than_o the_o mistake_n of_o the_o right_a understanding_n oâ—_n the_o true_a north_n and_o south_n end_n as_o well_o in_o magnet_n themselves_o as_o also_o in_o magnetical_a body_n whosoever_o therefore_o will_v take_v a_o little_a pain_n to_o understand_v this_o well_o shall_v free_v himself_o from_o many_o intricate_a difficulty_n in_o thâ—_n argument_n which_o otherwise_o must_v needs_o befall_v he_o wherein_o some_o have_v lime_v themselves_o have_v falleâ—_n into_o many_o error_n every_o one_o still_o beget_v another_o worse_a than_o himself_o all_o those_o which_o write_v beforâ—_n doctor_n gilbert_n do_v name_v that_o end_n of_o a_o magnet_n whicâ—_n be_v place_v in_o a_o wooden_a dish_n and_o set_v to_o swiâ—_n in_o water_n will_v turn_v and_o settle_v itself_o as_o we_o have_v say_v towards_o the_o north_n the_o north_n end_n of_o the_o magnet_n and_o the_o other_o the_o south_n end_n and_o even_o so_o do_v they_o oâ—_n all_o dyal_n needle_n compass_n and_o magnetical_a body_n but_o doctor_n gilbert_n not_o for_o any_o new_a fangle_a innovation_n or_o self_n conceit_n but_o upon_o good_a reason_n and_o firm_a demonstration_n avouch_v and_o prove_v the_o contrary_a and_o clear_o show_v that_o the_o former_a vulgar_a assertion_n serious_o defend_v tend_v to_o the_o overthrow_n of_o all_o magnetical_a philosophy_n by_o undermine_v of_o as_o it_o be_v the_o whole_a frame_n thereof_o and_o yet_o in_o common_a speech_n the_o old_a rule_n may_v hold_v loquendum_fw-la cum_fw-la vulgo_fw-la sentiendum_fw-la cuâ—_n sapientibâ—â—_n for_o it_o will_v seem_v a_o strange_a speech_n to_o a_o mariner_n to_o tell_v he_o that_o his_o flower_n de_fw-fr luce_n be_v become_v the_o south_n point_n of_o the_o compass_n 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south_n of_o the_o one_o â—o_o the_o north_n of_o the_o other_o but_o the_o end_n of_o the_o one_o in_o the_o other_o will_v always_o fly_v from_o those_o of_o the_o like_a denomination_n as_o the_o north_n end_n of_o the_o one_o from_o the_o north_n end_n of_o the_o other_o and_o the_o south_n end_n of_o the_o one_o from_o the_o south_n end_n of_o the_o other_o for_o as_o much_o then_o as_o all_o magnet_n themselves_o and_o all_o magnetical_a body_n be_v so_o place_v as_o that_o they_o have_v their_o free_a motion_n compose_v themselves_o magnetical_o towards_o the_o pole_n of_o the_o earth_n it_o must_v needs_o be_v that_o it_o be_v the_o true_a natural_a south_n end_n of_o the_o magnet_n or_o magnetical_a needle_n that_o point_v towards_o the_o north_n of_o the_o earth_n and_o it_o be_v the_o true_a natural_a north_n end_n of_o the_o magnet_n or_o magnetical_a needle_n that_o pont_v towards_o the_o south_n of_o the_o earth_n because_o the_o contrary_a end_n do_v affect_v one_o another_o and_o each_o of_o they_o do_v natural_o fly_v the_o one_o end_n of_o the_o one_o from_o the_o end_n of_o the_o other_o which_o be_v of_o like_a denomination_n unto_o itself_o for_o example_n in_o this_o follow_a diagram_n of_o the_o whole_a magnet_n e_o a._n be_v suppose_v to_o note_v the_o true_a natural_a north_n end_n thereof_o and_o b._n the_o south_n end_n this_o magnet_n be_v place_v in_o a_o wooden_a dish_n swim_v in_o water_n free_o must_v and_o will_v of_o magnetical_a necessity_n with_o his_o true_a north_n end_n a._n settle_v himself_o so_o that_o a._n must_v point_v towards_o the_o south_n of_o the_o earth_n and_o the_o south_n end_n b._n towards_o the_o north_n of_o the_o earth_n because_o all_o magnet_n and_o magnetical_a body_n do_v natural_o affect_v the_o one_o the_o contrary_a end_n of_o the_o other_o and_o do_v avoid_v and_o fly_v from_o their_o end_n of_o
shall_v be_v move_v the_o golden_a body_n equal_a to_o that_o of_o silver_n with_o silver_n body_n with_o the_o golden_a uneqal_n as_o shall_v be_v declare_v hereafter_o furthermore_o 6_o physic_n cap._n 1._o in_o the_o end_n and_o in_o a_o manner_n through_o all_o the_o chapter_n of_o the_o same_o book_n he_o confirm_v the_o same_o but_o in_o the_o four_o he_o say_v thus_o whereas_o every_o thing_n that_o move_v move_v in_o some_o other_o and_o in_o some_o time_n and_o that_o movable_a be_v motion_n of_o the_o whole_a the_o same_z or_o all_o one_o shall_v be_v the_o division_n of_o the_o time_n and_o the_o move_a and_o of_o to_o be_v move_v and_o of_o that_o which_o be_v move_v as_o also_o of_o that_o in_o the_o which_o be_v move_v afterward_o he_o give_v demonstration_n after_o his_o manner_n but_o cap_n 7._o he_o will_v the_o same_o where_o he_o intend_v that_o infinite_a time_n nothing_o may_v pass_v into_o infinite_a greatness_n etc._n etc._n furthermore_o aristotle_n in_o his_o first_o book_n de_fw-fr calo_n confirm_v the_o same_o say_v simple_o that_o the_o reason_n or_o consideration_n of_o time_n be_v contrary_a to_o the_o reason_n of_o weight_n as_o if_o half_a a_o weight_n be_v move_v in_o this_o time_n the_o double_a be_v move_v in_o the_o half_a of_o this_o etc._n etc._n and_o this_o cap._n 6._o furthermore_o cap._n 8._o of_o the_o same_o book_n he_o say_v the_o fire_n in_o as_o much_o as_o it_o be_v great_a than_o the_o earth_n so_o much_o the_o soon_o and_o swiftly_o it_o come_v to_o its_o rest_a place_n etc._n etc._n also_o in_o his_o second_o book_n de_fw-fr calo_n cap._n 8._o he_o say_v thus_o as_o in_o other_o thing_n the_o great_a body_n be_v the_o more_o swift_o move_v by_o his_o proper_a course_n or_o motion_n even_o so_o also_o in_o the_o heavenly_a circle_n and_o again_o cap._n 13._o he_o affirm_v the_o same_o in_o two_o place_n say_v that_o the_o great_a earth_n be_v swiftly_o move_v item_n lib._n de_fw-fr carlo_n cap._n 2._o he_o say_v thus_o if_o according_a to_o the_o proportion_n which_o have_v the_o space_n of_o c_o d._n the_o body_n of_o b_o shall_v be_v divide_v all_o b_o in_o the_o same_o time_n shalâ—_n be_v move_v by_o c_o e_z in_o the_o which_o time_n part_n of_o b_o by_z c_z d_o of_o necessity_n wherefore_o it_o follow_v that_o b_o be_v move_v by_o swift_a motion_n than_o part_n of_o b._n afterward_o he_o make_v a_o like_a demonstration_n say_v thus_o the_o swiftness_n of_o the_o less_o to_o the_o swiftness_n of_o the_o great_a have_v such_o proportion_n as_o the_o great_a body_n to_o the_o less_o etc._n etc._n again_o in_o his_o 3d._a book_n de_fw-fr carlo_n cap._n 5._o in_o the_o end_n of_o it_o he_o say_v likewise_o that_o so_o much_o the_o more_o every_o thing_n be_v move_v as_o it_o be_v the_o great_a as_o also_o the_o fire_n the_o great_a it_o be_v be_v so_o much_o of_o swift_a motion_n etc._n etc._n he_o confirm_v the_o same_o cap._n 2._o &_o four_o of_o the_o same_o book_n where_o yet_o speak_v more_o clear_o he_o faith_n that_o the_o great_a fire_n rise_v swiftlyeâ—_n upward_o than_o a_o less_o and_o a_o great_a piece_n of_o gold_n or_o lead_n do_v swiftly_o move_v downward_o and_o the_o like_a of_o heavyer_n body_n and_o more_o clear_o can_v no_o man_n gather_v the_o meaning_n of_o aristotle_n vitelio_n in_o his_o second_o book_n of_o perspective_n in_o the_o second_o proposition_n have_v fall_v into_o the_o same_o error_n i_o pretermit_v his_o ignorance_n in_o that_o proposition_n where_o he_o think_v that_o there_o be_v no_o quantity_n insensible_a but_o let_v this_o pass_v with_o other_o error_n the_o which_o at_o another_o time_n shall_v be_v show_v in_o their_o place_n he_o that_o will_v read_v other_o philosopher_n shall_v see_v that_o they_o all_o accord_n with_o the_o mind_n and_o sentence_n of_o aristotle_n who_o also_o in_o divers_a other_o place_n confirm_v the_o same_o but_o to_o have_v rehearse_v these_o principal_a place_n may_v suffice_v and_o therefore_o we_o shall_v now_o come_v to_o the_o demonstration_n this_o propound_a demonstration_n i_o will_v show_v apparent_o that_o it_o may_v the_o better_o be_v understand_v and_o forasmuch_o as_o aristotle_n in_o his_o work_n de_fw-fr insidentibus_fw-la aquae_fw-la have_v speak_v nothing_o of_o the_o proportion_n of_o motion_n of_o element_n it_o be_v manifest_a that_o he_o have_v not_o yet_o search_v this_o proposition_n for_o there_o be_v the_o proper_a place_n of_o this_o matter_n but_o it_o be_v not_o grant_v to_o any_o one_o man_n to_o know_v all_o thing_n and_o therefore_o it_o be_v very_o difficult_a to_o many_o to_o imagine_v the_o supposition_n whereas_o archimedes_n make_v none_o other_o demonstration_n but_o that_o natural_a motion_n be_v not_o cause_v of_o any_o other_o then_o of_o the_o excess_n or_o proceed_n of_o a_o body_n in_o a_o element_n above_o or_o upon_o the_o say_a element_n the_o demonstration_n let_v it_o be_v thus_o understand_v let_v we_o imagine_v for_o example_n two_o body_n of_o water_n of_o which_o the_o one_o shall_v be_v equal_a to_o the_o body_n o_o and_o the_o other_o to_o the_o body_n g_o or_o to_o one_o of_o the_o body_n n_o l_o k_n h_n which_o shall_v be_v all_o one_o then_o sixteen_o of_o the_o five_o the_o proportion_n of_o o_o to_o g_z or_o one_o of_o the_o aforesaid_a body_n be_v the_o same_o which_o be_v of_o the_o watery_a equal_a o_o to_o the_o watery_a equal_a g_o by_o the_o proposition_n declare_v before_o the_o proportion_n of_o the_o watery_a body_n equal_a o_o the_o heaviness_n of_o the_o watery_a body_n equal_a g_o be_v the_o same_o which_o be_v between_o the_o quantity_n of_o the_o self_n same_o body_n but_o we_o must_v understand_v they_o to_o be_v sustain_v or_o weigh_v in_o a_o rare_a or_o thin_a element_n the_o proportion_n thereof_o shall_v be_v the_o same_o which_o shall_v be_v between_o the_o proportion_n of_o body_n d_o and_z g_z by_o the_o eleven_o of_o the_o five_o the_o aforesaid_a proportion_n be_v thereto_o furthermore_o let_v we_o imagine_v the_o heaviness_n of_o body_n o_o and_o g_o so_o the_o other_o gravity_n and_o heaviness_n shall_v be_v those_o which_o shall_v be_v move_v without_o impepiment_n as_o appear_v by_o the_o 7_o of_o archimedes_n de_fw-fr insidentibus_fw-la aquae_fw-la and_o whereas_o by_o the_o fifteen_o of_o the_o five_o of_o euclid_n the_o proportion_n of_o these_o heaume_n body_n be_v the_o â—aâ—e_n which_o be_v beetween_n d_o and_z g_z by_o the_o nineteenth_o of_o the_o five_o aforesaid_a the_o resistance_n of_o the_o mean_a or_o middle_a to_o d_o shall_v be_v quadruple_a to_o the_o resistance_n of_o g._n the_o same_o also_o do_v i_o say_v to_o every_o one_o of_o the_o body_n n_o l_o k_n h._n it_o appear_v by_o common_a science_n that_o resistance_n of_o the_o mean_a to_o the_o body_n n_o l_o k_n h_n be_v equal_a to_o that_o which_o be_v to_o the_o body_n d_o but_o be_v the_o same_o to_o which_o g_z by_o the_o first_o conception_n of_o euclid_n furthermore_o if_o there_o be_v two_o body_n all_o of_o one_o figure_n but_o of_o divers_a homogeneite_n or_o substance_n and_o of_o unequal_a corporality_n and_o for_o example_n either_o of_o they_o heavy_a than_o the_o mean_a or_o the_o middle_n in_o the_o which_o they_o be_v move_v and_o that_o also_o the_o lesser_a of_o they_o be_v heavy_a than_o the_o big_a yet_o that_o the_o great_a weigh_n more_o than_o the_o less_o than_o i_o say_v that_o the_o less_o shall_v be_v swift_a in_o motion_n and_o the_o same_o shall_v be_v the_o proportion_n of_o time_n to_o the_o less_o which_o be_v to_o the_o great_a which_o be_v also_o the_o great_a kind_n of_o heaviness_n to_o the_o kind_n of_o the_o less_o take_v away_o so_o much_o heaviness_n from_o both_o as_o be_v the_o half_a of_o every_o of_o they_o let_v it_o be_v for_o example_n two_o body_n m_n and_o n_o of_o the_o same_o form_n and_o divers_a homogeneite_n or_o substance_n and_o the_o same_o also_o to_o be_v unequal_a for_o of_o equal_n there_o be_v no_o doubt_n of_o the_o which_o the_o great_a shall_v be_v m_n but_o of_o the_o kind_n of_o the_o body_n n_n to_o be_v heavy_a than_o the_o kind_n of_o the_o body_n m_o put_v the_o case_n also_o that_o the_o body_n m_o be_v heavy_a than_o the_o body_n n_n and_o each_o of_o they_o all_o heavy_a than_o the_o mean_a or_o middle_a body_n by_o which_o they_o move_v then_o will_v i_o show_v the_o proportion_n understand_v first_o a_o five_o j._n to_o be_v equal_a and_o like_a figure_n to_o the_o body_n m_o but_o of_o the_o kind_n of_o the_o body_n n._n let_v we_o imagine_v also_o that_o the_o body_n m_o in_o heaviness_n to_o exceed_v the_o middle_n or_o mean_a in_o double_a proportion_n a_o v._o
i_o or_o in_o the_o eight_o proportion_n so_o than_o the_o move_n of_o the_o body_n a_o v._o i_o shall_v in_o the_o seve_v proportion_n be_v swift_a than_o the_o body_n m_o because_o the_o resistance_n of_o the_o body_n m_o be_v subdupla_fw-la and_o to_o the_o body_n a_o v._o i_o be_v suboctupla_fw-la by_o the_o seven_o of_o archimedes_n de_fw-fr insidentibus_fw-la aquae_fw-la but_o by_o the_o aforesaid_a demonstration_n the_o body_n m_o shall_v be_v move_v in_o the_o same_o time_n which_o the_o body_n a_o five_o i._n wherefore_o by_o the_o the_o first_o conception_n of_o the_o mind_n add_v upon_o euclid_n by_o companus_fw-la the_o proposition_n be_v dear_a the_o like_a reason_n be_v also_o of_o violent_a motion_n take_v the_o proportion_n of_o the_o move_a strength_n and_o take_v away_o the_o proportion_n of_o the_o half_a or_o middle_n also_o whereas_o be_v two_o equal_a angle_n about_o the_o horizon_n or_o under_o but_o in_o contrary_a motion_n of_o nature_n because_o violent_a motion_n be_v swift_a in_o the_o begin_n than_o in_o the_o end_n and_o the_o contrary_n chance_v in_o the_o motion_n of_o nature_n for_o with_o violent_a motion_n the_o motion_n of_o nature_n be_v ever_o somewhat_o mix_v if_o horizontical_o or_o anguler_o it_o shall_v be_v above_o or_o beneath_o the_o horizon_n and_o nature_n work_v so_o much_o until_o it_o bring_v violent_a motion_n to_o some_o end_n but_o if_o the_o perpendicular_o violence_n shall_v be_v make_v about_o the_o horizon_n and_o towards_o the_o place_n which_o that_o body_n natural_o move_v unto_o than_o nature_n can_v strive_v against_o or_o withstand_v but_o that_o violence_n do_v ever_o go_v with_o it_o in_o respect_n of_o the_o end_n from_o whence_o furthermore_o by_o the_o aforesaid_a it_o be_v manifest_a that_o to_o be_v false_a which_o aristotle_n say_v 7_o phisic_n in_o the_o last_o chapter_n where_o he_o say_v if_o a_o be_v that_o which_o move_v b_o and_z b_o that_o which_o be_v move_v and_o c_o the_o longitude_n whereby_o and_o d_o in_o which_o the_o motion_n be_v that_o be_v to_o say_v in_o equal_a time_n and_o power_n equal_a a_o the_o half_a of_o b_o shall_v move_v by_o the_o double_a of_o c_o and_o c_o in_o the_o half_a of_o d_o for_o so_o shall_v be_v the_o similitude_n of_o the_o reason_n etc._n etc._n that_o it_o be_v false_a i_o will_v thus_o demonstrate_v let_v we_o first_o imagine_v two_o body_n as_o before_o in_o any_o mean_a or_o middle_a homogenie_n etc._n etc._n and_o let_v n_n for_o example_n m_n and_o n_o and_o that_o m_o be_v double_a in_o quantity_n to_o the_o body_n n_n and_o that_o the_o weigt_n of_o n_n be_v with_o one_o of_o the_o weight_n of_o m_n and_o also_o that_o the_o body_n a_o v._o i_o be_v equal_a to_o the_o body_n m_o in_o quantity_n and_o in_o likeness_n or_o kind_n of_o the_o body_n n_o then_o by_o common_a science_n the_o body_n of_o a_o v._o i_o shall_v be_v double_a in_o heaviness_n to_o the_o body_n m._n and_o grant_v that_o the_o body_n m_o by_o double_a in_o heaviness_n above_o the_o half_a then_o shall_v the_o body_n a_o v._o i_o be_v quadruple_a in_o heaviness_n above_o the_o say_v half_a wherefore_o the_o resistance_n take_v away_o let_v be_v leave_v the_o time_n in_o which_o the_o body_n a_o v._o i_o be_v quadruple_a in_o heaviness_n above_o the_o say_v half_a wherefore_o the_o resistance_n take_v away_o let_v be_v leave_v the_o time_n in_o which_o the_o body_n a_o v._o i_o in_o the_o same_o time_n shall_v be_v move_v the_o body_n n_n by_o the_o aforesaid_a or_o if_o in_o the_o same_o time_n the_o body_n n_n shall_v be_v move_v with_o the_o body_n m_o yet_o the_o space_n by_o which_o n_n shall_v be_v triple_a to_o that_o by_o which_o m._n for_o the_o reason_n be_v all_o one_o of_o violent_a motion_n the_o same_o shall_v precise_o come_v to_o pass_v if_o instead_o of_o the_o excess_n of_o weight_n above_o the_o half_a we_o shall_v take_v the_o virtue_n or_o power_n of_o move_v etc._n etc._n as_o before_o arristotle_n likewise_o err_v in_o his_o 4_o physic_n chap._n 8._o where_o he_o discourse_v the_o vacue_n say_v that_o the_o same_o or_o else_o all_o one_o shall_v be_v the_o proportion_n of_o motion_n of_o any_o body_n by_o divers_a element_n as_o if_o the_o air_n be_v in_o subtlety_n double_a to_o the_o water_n in_o double_a time_n b._n the_o mean_n shall_v pass_v to_o that_o time_n in_o which_o by_o the_o mean_a d_o and_o c_o the_o it_z i_o shall_v be_v double_a of_o the_o time_n e_o and_z c._n now_o to_o show_v the_o error_n of_o aristotle_n let_v we_o first_o understand_v a_o body_n to_o pass_v through_o water_n by_o natural_a motion_n as_o for_o example_n by_o a_o grant_v space_n let_v we_o also_o imagine_v that_o body_n in_o double_a to_o exceed_v the_o water_n in_o the_o weight_n and_o that_o the_o water_n in_o heaviness_n exceed_v the_o air_n in_o double_a proportion_n than_o the_o grant_v body_n shall_v be_v quadruple_a to_o the_o air._n wherefore_o in_o the_o haviness_n the_o resistance_n of_o time_n take_v away_o in_o the_o which_o the_o motion_n of_o that_o body_n in_o the_o air_n by_o equal_a space_n to_o that_o by_o the_o which_o in_o water_n to_o the_o time_n wherein_o by_o water_n in_o the_o grant_v space_n be_v move_v the_o proportion_n shall_v be_v subtriple_a and_o not_o subduple_n as_o aristotle_n affirm_v aristotle_n also_o err_v in_o the_o same_o chapter_n suppose_v that_o if_o motion_n shall_v be_v grant_v in_o void_a the_o same_o or_o all_o one_o shall_v be_v the_o reason_n of_o time_n to_o time_n as_o be_v between_o move_a body_n which_o be_v impossible_a by_o the_o aforesaid_a for_o those_o body_n shall_v be_v move_v be_v equal_a time_n although_o they_o shall_v be_v of_o divers_a kind_n form_n and_o bigness_n by_o which_o place_n also_o be_v easy_a to_o gather_v that_o the_o mind_n of_o aristotle_n be_v that_o the_o proportion_n of_o motion_n to_o motion_n be_v the_o same_o thing_n which_o greatness_n have_v between_o they_o according_a to_o the_o heaviness_n and_o lightness_n simple_o but_o that_o this_o also_o may_v the_o more_o clear_o be_v understand_v imagine_v the_o body_n m_o and_z n_z in_o void_a and_o that_o the_o body_n n_o be_v of_o the_o same_o weight_n which_o a_o v._o i_o but_o of_o divers_a kind_n and_o consequent_o of_o divers_a bigness_n then_o whereas_o those_o body_n have_v no_o resistance_n there_o be_v no_o doubt_n but_o that_o they_o shall_v be_v move_v by_o equal_a time_n by_o equal_a space_n i_o will_v take_v therefore_o the_o body_n a_o v._o i_o of_o the_o kind_n of_o the_o body_n n_n but_o of_o quantity_n of_o the_o body_n m._n now_o then_o by_o the_o mean_a of_o the_o true_a method_n of_o the_o demonstration_n before_o show_v a_o v._o i_o and_o n_n shall_v be_v move_v in_o equal_a time_n with_o the_o body_n n_z by_o equal_a space_n wherefore_o by_o the_o first_o conception_n in_o the_o same_o in_o the_o m_n wherefore_o it_o follow_v etc._n etc._n furthermore_o also_o where_o aristotle_n 7._o phific_n speak_v of_o the_o comparison_n of_o motion_n say_v that_o a_o right_a line_n be_v not_o comparable_a to_o a_o crooked_a line_n because_o there_o shall_v be_v find_v some_o right_a line_n equal_a of_o circular_a line_n either_o great_a or_o less_o for_o whereas_o by_o reason_n of_o the_o definition_n give_v by_o he_o in_o the_o 6_o phisic_n to_o the_o swiftness_n and_o slowness_n of_o motion_n it_o seem_v to_o he_o that_o it_o can_v be_v that_o circular_a motion_n shall_v be_v comparable_a to_o right_a motion_n in_o the_o which_o he_o be_v manifest_o deceive_v and_o chief_o think_v that_o a_o right_a line_n can_v be_v find_v equal_a great_a or_o lesser_a to_o the_o circular_a line_n whereas_o archimedes_n in_o his_o first_o proposition_n in_o geometry_n show_v the_o contrary_a and_o that_o by_o mathematical_a demonstration_n and_o not_o by_o the_o opinion_n of_o aristotle_n for_o archimedes_n show_v there_o by_o what_o mean_v we_o may_v find_v a_o right_a line_n great_a or_o less_o than_o any_o circular_a line_n constitute_v figure_n of_o right_a line_n without_o or_o within_o the_o circle_n etc._n etc._n but_o some_o man_n may_v say_v that_o though_o a_o right_a line_n may_v be_v grant_v great_a or_o less_o than_o any_o circular_a line_n yet_o that_o the_o same_o can_v be_v find_v equal_a whereas_o in_o the_o fifteen_o of_o euclid_n the_o three_o be_v show_v that_o a_o great_a angle_n may_v be_v find_v then_o be_v the_o angle_n of_o a_o contingence_n and_o that_o by_o the_o motion_n of_o the_o right_a line_n of_o the_o great_a angle_n passage_n be_v make_v to_o the_o right_a line_n contingent_a or_o touch_v the_o circle_n yet_o that_o it_o can_v be_v that_o with_o the_o contigent_a line_n it_o