and_o for_o proof_n thereof_o if_o the_o vessel_n c_o be_v as_o great_a as_o b_o it_o be_v impossible_a that_o the_o say_a vessel_n shall_v be_v fill_v with_o water_n but_o that_o the_o air_n shall_v often_o break_v forth_o and_o that_o because_o b_o be_v not_o capable_a to_o contain_v so_o much_o air_n therefore_o let_v it_o be_v hold_v that_o the_o air_n may_v be_v press_v in_o a_o close_a vessel_n to_o a_o certain_a degree_n there_o be_v another_o way_n to_o force_v the_o water_n with_o violence_n into_o the_o small_a vessel_n by_o the_o mean_n of_o a_o syringe_n as_o in_o the_o second_o figure_n prop._n 2_o the_o water_n can_v enter_v into_o a_o vessel_n but_o there_o must_v come_v forth_o as_o much_o air_n except_o the_o water_n be_v send_v in_o by_o force_n to_o demonstrate_v this_o let_v there_o be_v a_o vessel_n as_o a_o and_o let_v the_o pipe_n x_o be_v fasten_v in_o the_o cover_n thereof_o so_o that_o it_o may_v near_o touch_v the_o bottom_n of_o the_o say_a vessel_n and_o 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can_v be_v empty_v so_o that_o the_o air_n shall_v not_o enter_v therein_o as_o let_v the_o vessel_n or_o vial_n d_o be_v propose_v which_o let_v be_v full_a of_o water_n and_o let_v it_o be_v reverse_v so_o as_o the_o mouth_n or_o neck_n may_v touch_v the_o water_n which_o shall_v be_v set_v under_o it_o in_o a_o vessel_n it_o be_v certain_a that_o although_o the_o mouth_n of_o the_o say_a vial_n be_v downward_o no_o water_n shall_v run_v out_o because_o the_o air_n can_v enter_v to_o supply_v the_o place_n of_o the_o water_n that_o shall_v run_v out_o prop._n 4._o there_o can_v be_v no_o vacuity_n this_o be_v that_o which_o have_v be_v say_v in_o the_o preface_n the_o proof_n whereof_o may_v be_v gather_v from_o the_o foregoing_a corollary_n and_o divers_a other_o example_n whereof_o here_o be_v one_o if_o you_o have_v a_o copper_n pipe_n b_o whereof_o the_o end_n c_o be_v in_o the_o water_n and_o let_v the_o other_o end_n d_o be_v open_a to_o the_o end_n that_o the_o pestle_n a_o may_v be_v put_v therein_o which_o shall_v be_v like_o to_o those_o which_o be_v use_v for_o pump_n and_o forcor_n of_o water_n and_o that_o the_o say_a end_n a_o well_o environ_v with_o leather_n to_o the_o end_n that_o put_v water_n in_o e_o it_o may_v not_o run_v through_o to_o b_o then_o if_o a_o be_v raise_v to_o the_o point_n fletcher_o the_o water_n x_o which_o be_v level_n with_o the_o point_n c_o shall_v ascend_v to_o b_o to_o supply_v so_o much_o place_n as_o be_v between_o a_o and_o fletcher_o so_o the_o water_n ascend_v high_a than_o the_o level_n that_o there_o shall_v be_v no_o void_a place_n leave_v in_o b._n prop._n 5_o if_o the_o air_n be_v press_v in_o a_o vessel_n wherein_o there_o be_v water_n and_o that_o you_o give_v it_o passage_n by_o some_o pipe_n the_o say_a water_n shall_v come_v forth_o with_o violence_n if_o the_o air_n be_v press_v in_o the_o vessel_n x_o let_v it_o be_v by_o mean_n of_o a_o syringe_n or_o by_o a_o pipe_n as_o have_v be_v say_v before_o it_o be_v certain_a that_o then_o when_o the_o water_n have_v passage_n it_o come_v with_o a_o great_a deal_n more_o force_n than_o if_o it_o come_v forth_o from_o a_o open_a vessel_n as_o b._n prop._n 6._o if_o the_o water_n descend_v with_o violence_n into_o two_o equal_a vessel_n there_o shall_v enter_v more_o water_n into_o that_o vessel_n where_o the_o water_n descend_v from_o the_o high_a place_n and_o the_o air_n shall_v be_v more_o press_v therein_o and_o there_o shall_v be_v the_o same_o rate_n or_o proportion_n between_o the_o quantity_n of_o water_n contain_v in_o those_o vessel_n as_o there_o be_v between_o the_o height_n from_o whence_o the_o water_n have_v descend_v let_v there_o be_v two_o vessel_n b_o and_o c_o to_o which_o the_o water_n descend_v with_o violence_n by_o the_o pipe_n m_o and_o n_o the_o long_a of_o which_o be_v n_o from_o whence_o it_o follow_v that_o there_o enter_v more_o water_n in_o the_o vessel_n c_o then_o in_o b_o and_o there_o be_v the_o same_o rate_n of_o the_o water_n d_o to_o the_o water_n o_o as_o there_o be_v of_o the_o length_n of_o the_o pipe_n n_o to_o the_o length_n of_o the_o pipe_n m._n and_o it_o also_o follow_v from_o hence_o that_o in_o the_o vessel_n c_o where_o there_o be_v more_o water_n the_o air_n shall_v be_v more_o press_v then_o in_o b_o and_o the_o effect_n thereof_o may_v be_v see_v by_o the_o small_a pipe_n p_o and_o x_o of_o the_o which_o two_o p_o cast_v the_o water_n high_a because_o the_o air_n be_v more_o press_v in_o the_o vessel_n c_o then_o in_o the_o vessel_n b_o in_o the_o same_o manner_n as_o before_o we_o may_v proportion_v the_o air_n of_o the_o two_o vessel_n to_o the_o height_n of_o the_o water_n spring_v forth_o by_o the_o small_a pipe_n p_o and_o x_o the_o which_o ought_v to_o be_v equal_a prop._n 7._o all_o heavy_a thing_n whatsoever_o weigh_v more_o in_o the_o air_n then_o in_o the_o water_n although_o that_o every_o heavy_a body_n have_v always_o in_o its_o self_n its_o proper_a weight_n yet_o nevertheless_o they_o be_v also_o consider_v diverse_o according_a to_o the_o place_n where_o they_o be_v place_v as_o it_o be_v certain_a that_o wood_n weigh_v nothing_o in_o the_o water_n because_o it_o do_v not_o des_fw-fr end_n towards_o the_o centre_n of_o the_o earth_n which_o be_v proper_a to_o all_o heavy_a thing_n but_o if_o it_o be_v in_o the_o air_n it_o fall_v towards_o its_o centre_n with_o weight_n wherefore_o we_o may_v say_v that_o it_o weigh_v more_o in_o the_o air_n then_o in_o the_o water_n and_o so_o we_o may_v say_v of_o all_o body_n although_o they_o be_v heavy_a than_o the_o water_n for_o although_o they_o fall_v towards_o their_o centre_n of_o gravity_n in_o the_o water_n yet_o it_o be_v not_o with_o such_o swiftness_n it_o be_v not_o necessary_a to_o show_v here_o by_o what_o quantity_n the_o say_a heaviness_n be_v more_o weighty_a in_o the_o air_n then_o in_o the_o water_n send_v the_o curious_a to_o the_o book_n of_o archimedes_n concerning_o thing_n fall_v in_o the_o water_n where_o it_o be_v demonstrate_v that_o heavy_a thing_n weigh_v more_o in_o the_o air_n then_o in_o the_o water_n by_o the_o quantity_n of_o water_n which_o be_v equal_a to_o they_o a_o corollary_n it_o be_v here_o to_o be_v observe_v that_o water_n be_v of_o diverse_a weight_n and_o they_o say_v that_o on_o the_o territory_n of_o cara_fw-it in_o spain_n there_o be_v two_o fountain_n in_o the_o one_o of_o which_o divers_a thing_n be_v put_v sink_v to_o the_o bottom_n the_o which_o be_v put_v in_o the_o other_o float_v at_o top_n they_o report_v the_o same_o thing_n of_o the_o lake_n of_o sodom_n and_o of_o the_o fountain_n of_o arethus_n the_o which_o effect_n come_v to_o pass_v by_o reason_n of_o the_o weight_n of_o the_o water_n and_o from_o hence_o we_o may_v infer_v that_o one_o and_o the_o same_o thing_n weigh_v more_o in_o light_a water_n then_o in_o heavy_a water_n prop._n 8._o water_n weigh_v upon_o that_o which_o sustain_v it_o according_a to_o its_o height_n i_o have_v give_v this_o example_n because_o that_o divers_a deceive_v themselves_o upon_o this_o subject_a which_o have_v think_v to_o raise_v water_n not_o consider_v the_o weight_n when_o it_o come_v to_o be_v raise_v very_o high_a that_o which_o be_v then_o to_o be_v understand_v by_o this_o proposition_n be_v that_o the_o sucker_n c_o be_v at_o the_o end_n of_o the_o pipe_n m_o to_o sustain_v the_o water_n which_o be_v within_o the_o say_a pipe_n that_o the_o water_n weigh_v upon_o it_o according_a as_o the_o height_n thereof_o shall_v be_v in_o the_o
divers_a pinion_n and_o the_o same_o force_n move_v they_o that_o pinion_n shall_v give_v the_o most_o force_n to_o the_o wheel_n to_o raise_v any_o weight_n who_o number_n of_o tooth_n be_v the_o least_o but_o the_o say_a wheel_n shall_v turn_v slow_a as_o have_v be_v say_v and_o herein_o behold_v the_o example_n if_o the_o wheel_n a_o be_v turn_v by_o the_o pinion_n c_o of_o 10._o tooth_n and_o be_v capable_a to_o raise_v a_o weight_n of_o 200._o and_o instead_o of_o the_o pinion_n of_o 10._o tooth_n it_o be_v turn_v by_o a_o pinion_n of_o 5._o than_o it_o the_o force_n to_o raise_v 400._o but_o as_o the_o weight_n be_v double_a in_o gravity_n to_o the_o first_o so_o also_o it_o shall_v be_v as_o long_o again_o a_o raise_n up_o because_o the_o pinion_n being_n 10._o and_o the_o wheel_n 100_o the_o pinion_n ought_v not_o to_o be_v turn_v above_o 10._o time_n to_o make_v a_o whole_a turn_n or_o revolution_n of_o the_o wheel_n but_o if_o the_o pinion_n be_v 5._o it_o must_v make_v 20._o turn_n before_o the_o wheel_n make_v one_o because_o the_o number_n 5._o be_v contain_v 20_o time_n in_o 100_o and_o so_o as_o the_o pinion_n c_o be_v double_a to_o the_o pinion_n fletcher_o the_o weight_n raise_v by_o fletcher_o shall_v be_v double_a to_o the_o weight_n raise_v by_o c_o and_o the_o time_n of_o the_o raise_v it_o shall_v be_v also_o double_a prop._n 15._o if_o two_o wheel_n be_v equal_a in_o form_n and_o matter_n and_o there_o be_v unequal_a weight_n fasten_v to_o their_o axtree_n they_o can_v be_v move_v by_o the_o same_o force_n in_o the_o same_o time_n this_o proposition_n do_v in_o some_o sort_n result_n from_o the_o former_a as_o may_v be_v see_v in_o the_o demostration_n let_v there_o be_v two_o equal_a wheel_n d_o and_o f_o of_o 96._o tooth_n and_o let_v there_o be_v fasten_v to_o the_o axis_n g_o a_o weight_n of_o 300_o and_o to_o b_o one_o of_o 400_o and_o let_v it_o be_v suppose_v that_o the_o pinion_n t_o of_o eight_o tooth_n move_v the_o say_a weight_n by_o the_o mean_n of_o the_o force_n of_o one_o man_n it_o be_v certain_a that_o if_o there_o be_v put_v to_o the_o wheel_n fletcher_o a_o pinion_n equal_a to_o t_o that_o the_o same_o man_n or_o the_o same_o force_n which_o be_v only_o make_v to_o turn_v t_o will_v not_o suffice_v to_o turn_v a_o pinion_n equal_a to_o it_o in_o the_o wheel_n fletcher_o because_o of_o the_o weight_n v_o which_o be_v heavy_a than_o m_o if_o then_o you_o will_v move_v the_o weight_n v_o by_o the_o same_o force_n you_o must_v put_v to_o the_o wheel_n f_o a_o pinion_n which_o have_v such_o proportion_n to_o t_o as_o the_o weight_n m_o have_v to_o the_o weight_n v._n now_o the_o pinion_n t_o be_v of_o 8._o the_o pinion_n x_o must_v be_v of_o 6._o because_o that_o there_o be_v the_o same_o rate_n of_o 8._o to_o 6._o as_o of_o 400._o to_o 300._o and_o the_o same_o pinion_n x_o of_o 6._o tooth_n be_v move_v by_o the_o force_n aforesaid_a the_o weight_n v_o shall_v be_v raise_v but_o not_o in_o the_o same_o time_n because_o there_o be_v make_v but_o 12._o turn_v of_o t_o to_o make_v one_o turn_n of_o d_o and_o there_o must_v be_v 16._o turn_v of_o x_o to_o make_v one_o turn_n of_o f._n prop._n 16._o if_o two_o unequal_a weight_n be_v put_v to_o the_o end_n of_o the_o beam_n of_o a_o balance_n and_o if_o they_o be_v hang_v on_o a_o point_n which_o divide_v the_o beam_n into_o two_o part_n have_v the_o same_o rate_n the_o one_o to_o the_o other_o in_o length_n as_o the_o say_a weight_n have_v in_o heaviness_n those_o weight_n although_o unequal_a shall_v be_v in_o equal_a balance_n if_o the_o light_a be_v put_v to_o the_o end_n of_o the_o long_a part_n of_o the_o beam_n let_v the_o unequal_a weight_n be_v d_o and_o e_o and_o let_v d_o be_v 15._o pound_n weight_n and_o e_o 6_o i_o say_v that_o they_o be_v at_o the_o end_n of_o the_o beam_n of_o the_o balance_n ab_o if_o they_o be_v hang_v on_o a_o point_n as_o c_o so_o as_o the_o part_n ac_o may_v have_v such_o proportion_n to_o the_o part_n cb_o as_o the_o weight_n e_o to_o the_o weight_n d_o d_n be_v at_o the_o short_a distance_n from_o the_o centre_n of_o the_o beam_n shall_v not_o weigh_v more_o than_o e_o which_o be_v at_o the_o long_a end_n because_o the_o weight_n be_v heavy_a in_o proportion_n according_a to_o their_o distance_n from_o the_o point_n on_o which_o the_o beam_n of_o the_o balance_n be_v hang_v now_o if_o the_o beam_n of_o the_o balance_n be_v divide_v into_o 7_o part_n there_o shall_v be_v 5._o part_n on_o the_o one_o side_n of_o the_o centre_n and_o 2._o on_o the_o other_o which_o be_v in_o the_o same_o proportion_n as_o the_o weight_n 15._o and_o 6_o because_o 6._o be_v the_o two_o five_n of_o 15_o as_o 2._o be_v of_o 5._o and_o if_o the_o difference_n of_o the_o weight_n d_o and_o e_o be_v great_a or_o lesser_a they_o shall_v always_o be_v in_o equal_a balance_n if_o the_o beam_n be_v hang_v from_o a_o point_n which_o divide_v it_o as_o be_v before_o say_v you_o may_v see_v other_o example_n in_o the_o figure_n follow_v p_o which_o differ_v from_o this_o a_o corollary_n from_o hence_o it_o follow_v that_o two_o equal_a weight_n be_v not_o alike_o heavy_a if_o they_o be_v put_v at_o the_o end_n of_o a_o beam_n which_o be_v hang_v from_o unequal_a part_n and_o it_o must_v be_v observe_v that_o although_o the_o two_o side_n of_o the_o beam_n be_v in_o equal_a balance_n if_o they_o be_v of_o unequal_a length_n equal_a weight_n shall_v weigh_v unequal_a as_o for_o example_n if_o the_o beam_n ab_o be_v hang_v in_o c_o so_o as_o cb_o may_v be_v long_o than_o ac_o by_o a_o four_o part_n and_o yet_o ac_o and_o cb_o be_v in_o equal_a balance_n because_o the_o part_n ac_o be_v thick_a than_o the_o part_n cb_o yet_o if_o the_o equal_a weight_n d_o and_o f_o be_v put_v to_o the_o end_n of_o the_o beam_n ab_o the_o weight_n fletcher_o shall_v weigh_v a_o four_o part_n more_o which_o be_v the_o difference_n of_o bc_o and_o ac_o prop._n 17._o the_o manner_n to_o shut_v and_o open_v the_o cock_n of_o the_o phneumatique_a engine_n by_o the_o mean_n of_o water_n in_o the_o construction_n of_o the_o phneumatique_a engine_n which_o cause_v water_n to_o mount_v high_a than_o the_o spring_n there_o be_v require_v a_o vessel_n which_o ascend_v and_o descend_v by_o mean_n of_o the_o water_n to_o turn_v the_o cock_n therefore_o i_o have_v put_v here_o certain_a example_n among_o which_o you_o may_v choose_v the_o most_o convenient_a both_o for_o that_o engine_n and_o for_o the_o other_o engine_n now_o behold_v the_o effect_n of_o the_o vessel_n in_o which_o there_o be_v a_o syphon_n which_o shall_v be_v something_o low_a than_o the_o height_n of_o the_o vessel_n and_o the_o say_a syphon_n shall_v be_v large_a than_o the_o pipe_n which_o give_v water_n to_o the_o vessel_n when_o m_o be_v empty_a the_o weight_n l_o shall_v turn_v the_o cock_n towards_o it_o but_o when_o the_o pipe_n h_o have_v fill_v m_n than_o the_o say_a m_o weigh_v more_o than_o the_o weight_n l_o shall_v draw_v back_o the_o cock_n towards_o itself_o and_o then_o the_o syphon_n beginning_n to_o run_v shall_v make_v m_o light_a than_o the_o weight_n l_o and_o so_o the_o cock_n shall_v be_v turn_v back_o again_o there_o may_v be_v also_o make_v another_o vessel_n as_o fletcher_o which_o may_v be_v so_o hang_v upon_o the_o handle_n as_o it_o may_v be_v movable_a upon_o two_o pin_n and_o may_v over-turn_v and_o empty_v the_o water_n when_o it_o be_v full_a and_o to_o perform_v this_o the_o pin_n must_v not_o be_v diametrical_o opposite_a but_o more_o towards_o one_o side_n then_o towards_o the_o other_o now_o because_o the_o say_a vessel_n be_v empty_a shall_v return_v of_o itself_o the_o counter-poise_n e_o must_v be_v put_v to_o the_o light_a side_n to_o balance_v it_o equal_o this_o be_v do_v if_o there_o be_v a_o weight_n as_o have_v be_v say_v in_o the_o aforegoing_a proposition_n which_o shall_v be_v heavy_a than_o fletcher_o that_o vessel_n fletcher_o shall_v be_v at_o the_o high_a when_o it_o be_v empty_a but_o when_o it_o be_v half_a full_a being_n heavy_a than_o d_o the_o say_a vessel_n shall_v descend_v towards_o fletcher_o and_o be_v full_a it_o shall_v empty_v itself_o towards_o x_o and_o be_v empty_a it_o shall_v be_v again_o light_a than_o the_o weight_n and_o return_v to_o its_o first_o place_n where_o it_o shall_v be_v till_o it_o be_v fill_v again_o to_o descend_v the_o reason_n of_o the_o empty_n may_v be_v gather_v from_o the_o corolary_n of_o the_o 16._o proposition_n there_o may_v be_v also_o make_v
new_a and_o rare_a invention_n of_o water-work_n show_v the_o easy_a way_n to_o raise_v water_n high_o than_o the_o spring_n by_o which_o invention_n the_o perpetual_a motion_n be_v propose_v many_o hard_a labour_n perform_v and_o variety_n of_o motion_n and_o sound_n produce_v a_o work_n both_o useful_a profitable_a and_o delightful_a for_o all_o sort_n of_o people_n first_o write_v in_o french_a by_o isaak_n de_fw-fr caus_n a_o late_a famous_a engenier_n and_o now_o translate_v into_o english_a by_o john_n leak_n london_n print_v by_o joseph_n moxon_n and_o sell_v at_o his_o shop_n in_o cornhill_n at_o the_o sign_n of_o atlas_n 1659._o the_o preface_n because_o the_o raise_n of_o water_n high_o than_o the_o spring_n after_o the_o way_n principal_o intend_v in_o this_o work_n seem_v to_o be_v opposite_a to_o the_o common_a receive_a opinion_n of_o all_o time_n i_o have_v think_v it_o not_o only_o sufficient_a to_o teach_v the_o construction_n of_o the_o engine_n proper_a thereto_o but_o also_o for_o more_o ample_a satisfaction_n to_o premise_v certain_a proposition_n to_o precede_v in_o place_n of_o principle_n only_o to_o make_v you_o understand_v the_o effect_n of_o that_o motion_n by_o the_o cause_n thereof_o that_o so_o the_o way_n may_v be_v more_o accessible_a to_o the_o other_o phneumatike_a invention_n viz._n engine_n move_v by_o the_o force_n of_o air_n to_o come_v to_o which_o it_o must_v first_o be_v consider_v that_o all_o the_o element_n whether_o simple_a or_o mix_v have_v two_o principal_a motion_n viz._n natural_a and_o accidental_a the_o natural_a motion_n be_v that_o whereby_o each_o element_n search_v and_o draw_v itself_o towards_o the_o place_n assign_v thereto_o by_o the_o divine_a providence_n in_o the_o creation_n the_o accidental_a motion_n be_v that_o which_o be_v move_v by_o any_o outward_a force_n different_a from_o the_o first_o now_o although_o divers_a thing_n seem_v to_o move_v contrary_a to_o their_o order_n without_o any_o external_a agitation_n yet_o the_o reason_n be_v that_o their_o contrary_a motion_n be_v cause_v to_o hinder_v some_o other_o great_a accident_n as_o for_o example_n it_o shall_v be_v show_v that_o the_o water_n to_o shun_v vacuity_n mount_v contarry_a to_o the_o ordinary_a course_n thereof_o because_o vacuity_n be_v more_o repugnant_a to_o nature_n then_o the_o contrary_a motion_n of_o that_o element_n as_o be_v see_v by_o the_o principle_n proposition_n which_o serve_v as_o a_o foundation_n of_o this_o invention_n which_o be_v found_v upon_o this_o principle_n of_o nature_n that_o there_o can_v be_v no_o vacuity_n in_o the_o elementary_a sphere_n whereof_o the_o earth_n and_o water_n do_v supply_v the_o inferior_a part_n and_o the_o fire_n and_o air_n which_o encompass_v they_o the_o superior_a part_n and_o each_o of_o they_o be_v say_v to_o be_v heavy_a or_o light_a according_a as_o natural_o they_o be_v near_o or_o further_o from_o the_o centre_n but_o in_o these_o four_o it_o will_v be_v necessary_a to_o have_v a_o regard_n as_o well_o to_o certain_a thing_n whereof_o the_o air_n and_o water_n be_v capable_a as_o to_o those_o wherein_o they_o can_v suffer_v accident_n as_o the_o water_n which_o although_o it_o may_v be_v extend_v by_o the_o intermixture_n of_o air_n or_o atenuate_v and_o convert_v into_o air_n by_o the_o mean_n of_o heat_n which_o resolve_v it_o yet_o nevertheless_o it_o can_v be_v press_v that_o be_v to_o say_v that_o a_o certain_a quantity_n of_o water_n can_v be_v force_v by_o compression_n to_o be_v contain_v in_o less_o space_n than_o its_o natural_a extension_n and_o the_o air_n on_o the_o contrary_a may_v be_v restrain_v and_o put_v up_o be_v press_v or_o rarefy_v and_o extend_v be_v move_v beyond_o the_o other_o accident_n whereof_o it_o be_v capable_a these_o thing_n shall_v hereafter_o be_v demonstrate_v by_o proposition_n found_v upon_o experience_n which_o i_o have_v think_v to_o be_v more_o convenient_a for_o this_o purpose_n then_o to_o involve_v the_o reader_n in_o a_o labyrinth_n of_o geometrical_a proposition_n which_o although_o most_o exact_a yet_o be_v not_o altogether_o pertinent_a for_o instruction_n in_o this_o subject_a as_o for_o example_n if_o we_o shall_v build_v upon_o this_o rule_n of_o archimedes_n that_o the_o superficies_n of_o the_o water_n be_v spherical_a when_o it_o be_v not_o move_v which_o superficies_n have_v for_o its_o centre_n that_o of_o the_o whole_a earth_n there_o will_v follow_v a_o subjection_n that_o we_o must_v hold_v in_o the_o demonstration_n viz._n that_o the_o superficies_n of_o the_o water_n be_v circular_a which_o in_o the_o like_a case_n as_o be_v that_o whereof_o we_o speak_v be_v esteem_v plain_a of_o every_o one_o and_o that_o first_o because_o the_o difference_n be_v undescernable_a and_o second_o because_o it_o can_v make_v a_o defect_n in_o any_o operation_n whatsoever_o a_o liberty_n therefore_o which_o be_v not_o permit_v in_o the_o mathematics_n that_o therefore_o with_o other_o reason_n have_v move_v i_o to_o omit_v those_o demonstration_n which_o seem_v to_o i_o to_o be_v too_o punctual_a for_o this_o purpose_n note_v also_o that_o when_o i_o speak_v of_o water_n i_o mean_v water_n equal_o heavy_a without_o make_v any_o difference_n although_o in_o case_n of_o necessity_n there_o must_v be_v have_v a_o regard_n thereto_o chief_o if_o the_o difference_n be_v such_o as_o in_o the_o water_n of_o certain_a river_n whereof_o pliny_n speak_v wherein_o nothing_o will_v sink_v to_o the_o bottom_n as_o in_o the_o water_n of_o the_o lake_n alphaltite_n and_o in_o the_o water_n of_o arethuse_n which_o run_v towards_o siracuse_n and_o that_o because_o of_o their_o extreme_a weight_n which_o return_v heavy_a thing_n to_o the_o top_n as_o quick_a silver_n do_v the_o metal_n which_o sink_v not_o in_o it_o although_o it_o be_v liquid_a because_o it_o be_v more_o weighty_a and_o in_o this_o we_o must_v make_v a_o distinction_n that_o metal_n and_o heavy_a solid_n sink_v in_o water_n according_a to_o the_o figure_n they_o have_v for_o copper_n silver_n and_o gold_n sink_v not_o in_o ordinary_a water_n if_o it_o be_v beat_v out_o in_o plate_n or_o thin_a leaf_n but_o if_o it_o be_v contract_v into_o a_o more_o solid_a form_n it_o sink_v forthwith_o to_o the_o bottom_n but_o these_o and_o the_o like_a thing_n i_o shall_v treat_v of_o in_o a_o commentary_n upon_o the_o book_n of_o archimedes_n concerning_o weight_n and_o thing_n sink_v in_o water_n the_o theory_n of_o the_o conduct_n of_o water_n proposition_n 1._o the_o air_n may_v be_v press_v but_o not_o the_o water_n to_o give_v a_o example_n whereof_o let_v there_o be_v two_o vessel_n a_o and_o b_o of_o one_o form_n matter_n and_o bigness_n the_o which_o let_v be_v full_a of_o water_n it_o be_v most_o certain_a that_o in_o either_o of_o those_o vessel_n the_o water_n can_v be_v press_v so_o as_o the_o one_o of_o those_o vessel_n may_v contain_v the_o least_o part_n that_o may_v be_v more_o than_o the_o other_o but_o when_o they_o be_v only_o full_a of_o air_n i_o say_v that_o the_o say_a air_n may_v be_v press_v and_o one_o of_o those_o vessel_n may_v contain_v more_o than_o the_o other_o which_o shall_v be_v thus_o demonstrate_v let_v the_o say_a vessel_n a_o and_o b_o be_v make_v very_o close_o on_o all_o part_n and_o at_o the_o bottom_n of_o the_o vessel_n b_o let_v there_o be_v a_o small_a hole_n e_o to_o which_o the_o pipe_n ed_o be_v fasten_v the_o other_o end_n thereof_o d_o be_v fasten_v to_o the_o upper_a part_n of_o the_o vessel_n c_o the_o which_o be_v also_o make_v very_o close_a one_o every_o side_n and_o contain_v about_o a_o three_o part_n of_o the_o vessel_n b_o and_o to_o make_v the_o water_n enter_v therein_o with_o force_n it_o will_v be_v necessary_a to_o fasten_v the_o pipe_n fletcher_o near_o to_o the_o bottom_n of_o the_o vessel_n c_o the_o which_o shall_v be_v make_v as_o high_a as_o may_v be_v that_o it_o may_v give_v so_o much_o the_o more_o violence_n to_o the_o water_n the_o which_o enter_v the_o small_a vessel_n c_o shall_v make_v the_o air_n that_o be_v therein_o to_o ascend_v into_o the_o vessel_n b_o the_o which_o shall_v contain_v more_o air_n than_o a_o by_o the_o quantity_n which_o be_v in_o c_o and_o so_o the_o air_n shall_v be_v press_v in_o the_o say_a vessel_n b_o the_o which_o may_v be_v see_v if_o you_o make_v a_o small_a hole_n in_o the_o say_a vessel_n by_o the_o which_o the_o say_a air_n shall_v come_v forth_o with_o violence_n but_o if_o you_o pierce_v the_o vessel_n a_o there_o will_v not_o be_v the_o same_o effect_n because_o in_o it_o the_o air_n be_v not_o press_v but_o it_o be_v here_o to_o be_v observe_v that_o although_o the_o air_n may_v be_v press_v it_o be_v but_o only_o to_o a_o certain_a degree_n which_o be_v about_o a_o three_o part_n
another_o manner_n of_o vessel_n for_o the_o same_o use_n as_o you_o may_v see_v in_o the_o figure_n szx_fw-la prop._n 18._o of_o the_o value_n or_o suspiral_n it_o will_v be_v also_o necessary_a for_o the_o understanding_n of_o the_o follow_a engine_n to_o demonstrate_v the_o manner_n of_o the_o value_n of_o copper_n which_o open_v itself_o by_o interval_n to_o the_o intent_n that_o if_o the_o air_n may_v enter_v into_o the_o vessel_n from_o beneath_o and_o shut_v itself_o when_o the_o say_a vessel_n be_v full_a to_o the_o end_n that_o the_o water_n pass_v not_o out_o by_o it_o the_o which_o value_n shall_v be_v figure_v thus_o let_v hikl_n be_v a_o small_a box_n of_o lead_n about_o one_o inch_n and_o a_o half_a in_o diameter_n and_o 3_o inch_n long_o very_o well_o solder_v within_o the_o say_a box_n be_v the_o value_n gdce_o make_v after_o this_o manner_n gd_o be_v a_o small_a pipe_n of_o copper_n about_o ¼_o of_o a_o inch_n and_o towards_o the_o end_n d_o there_o be_v two_o small_a prop_n which_o hang_v the_o tongue_n or_o value_n of_o copper_n c_o which_o fall_v upon_o the_o hole_n d_o to_o shut_v it_o when_o there_o be_v need_n there_o be_v also_o to_o the_o box_n hikl_n a_o small_a pipe_n xm_o the_o low_a part_n of_o which_o be_v solder_v to_o the_o pipe_n oc_o then_o to_o see_v the_o effect_n of_o the_o say_a value_n let_v we_o suppose_v that_o there_o be_v two_o pipe_n to_o the_o pipe_n co_z the_o one_o to_o empty_v it_o and_o the_o other_o to_o fill_v it_o and_o let_v the_o pipe_n x_o be_v stop_v which_o be_v that_o which_o fill_v the_o say_a vessel_n and_o let_v b_o be_v open_v then_o the_o water_n that_o come_v from_o the_o vessel_n draw_v in_o the_o air_n by_o the_o small_a pipe_n dg_o and_o lift_v up_o the_o copper_n tongue_n c_o and_o b_o be_v stop_v it_o shut_v itself_o and_o when_o the_o water_n have_v fill_v the_o vessel_n co_z and_o hil_n the_o say_a water_n press_v the_o value_n against_o the_o end_n c_o there_o shall_v no_o water_n come_v forth_o prop._n 19_o of_o the_o cock_n with_o four_o vent_v this_o figure_n follow_v be_v set_v down_o to_o show_v more_o distinct_o the_o manner_n of_o the_o cock_n d_o who_o barrel_n be_v pierce_v in_o 4_o place_n to_o the_o end_n that_o the_o key_n c_o turn_v either_o one_o way_n or_o the_o other_o in_o the_o require_a time_n the_o water_n may_v sometime_o run_v out_o by_o e_o and_o sometime_o by_o fletcher_o and_o that_o fletcher_o or_o e_o may_v run_v when_o the_o hole_n of_o the_o key_n c_o shall_v agree_v with_o the_o one_o or_o the_o other_o of_o they_o it_o shall_v also_o empty_a by_o mean_n of_o the_o vessel_n m_o as_o the_o cock_n h_o shut_v when_o one_o of_o the_o pipe_n be_v open_v and_o then_o when_o the_o say_a pipe_n shut_v to_o make_v the_o other_o run_v than_o the_o cock_n shall_v open_v again_o by_o mean_n of_o the_o counterpoise_n gl_o and_o the_o pulley_n k._n as_o you_o see_v it_o in_o the_o figure_n a_o description_n of_o the_o engine_n by_o which_o part_n of_o the_o water_n be_v raise_v high_a than_o the_o spring_n to_o come_v to_o the_o construction_n of_o this_o engine_n first_o let_v there_o be_v make_v 4._o pipe_n of_o copper_n or_o of_o thick_a lead_n sufficient_a to_o bear_v the_o strength_n of_o the_o water_n and_o air_n and_o let_v they_o be_v 6._o inch_n in_o diameter_n and_o 6._o or_o 7._o foot_n long_o mark_v in_o the_o figure_n with_o the_o letter_n a_o and_o let_v the_o little_a pipe_n e_o be_v solder_v to_o the_o end_n of_o they_o at_o the_o bottom_n so_o as_o the_o water_n may_v be_v communicate_v from_o one_o to_o the_o other_o furthermore_o let_v there_o be_v solder_v four_o small_a pipe_n fletcher_o above_o the_o pipe_n a_o to_o the_o intent_n that_o the_o air_n be_v communicate_v from_o the_o one_o to_o the_o other_o also_o let_v four_o little_a pipe_n mark_v with_o the_o figure_n 3_o be_v solder_v which_o be_v those_o by_o which_o the_o water_n ascend_v and_o they_o must_v be_v solder_v a_o travers_n above_o the_o great_a pipe_n and_o the_o end_n enter_v within_o almost_o to_o the_o bottom_n moreover_o there_o must_v be_v four_o other_o great_a pipe_n make_v like_o to_o the_o first_o the_o which_o shall_v be_v put_v much_o low_a as_o you_o will_v raise_v the_o water_n high_a than_o the_o spring_n and_o let_v the_o small_a pipe_n d_o be_v solder_v in_o they_o to_o the_o end_n that_o the_o air_n may_v enter_v there_o when_o the_o water_n enter_v by_o the_o pipe_n c_o and_o therefore_o let_v they_o be_v solder_v above_o and_o let_v there_o be_v four_o pipe_n at_o i_o communicate_v all_o the_o water_n to_o the_o pipe_n gh_o and_o let_v the_o cock_n l_o be_v solder_v to_o the_o bottom_n of_o that_o pipe_n and_o above_o at_o the_o top_n let_v the_o value_n k_o be_v solder_v make_v as_o be_v before_o describe_v in_o the_o 18_o proposition_n and_o let_v the_o pipe_n d_o and_o f_o be_v make_v common_a by_o one_o pipe_n moreover_o let_v the_o small_a vessel_n s_o be_v make_v which_o may_v have_v the_o side_n about_o the_o height_n of_o one_o foot_n and_o upon_o the_o bottom_n of_o it_o by_o the_o base_a of_o the_o emboiteure_fw-fr let_v there_o be_v solder_v the_o cock_n n_o to_o which_o cock_n let_v there_o be_v the_o pipe_n o_o and_o p_o the_o which_o pipe_v i_o shall_v go_v almost_o to_o the_o bottom_n of_o one_o of_o the_o pipe_n mark_v with_o a_o and_o o_o shall_v be_v conduct_v almost_o to_o the_o bottom_n of_o the_o pipe_n c_o also_o at_o the_o top_n of_o the_o vessel_n s_o let_v there_o be_v the_o small_a pipe_n v_o to_o give_v water_n to_o the_o vessel_n y_o when_o it_o be_v require_v which_o vessel_n y_o shall_v be_v of_o copper_n have_v a_o small_a hole_n at_o the_o bottom_n concerning_o the_o motion_n whereof_o it_o have_v be_v declare_v in_o the_o foregoing_a example_n there_o must_v be_v also_o a_o counterpoise_n m_o to_o the_o intent_n that_o when_o the_o vessel_n y_o shall_v be_v empty_a it_o may_v draw_v back_o by_o its_o weight_n as_o well_o the_o vessel_n as_o the_o cock_n in_o their_o place_n behold_v here_o somuch_o as_o concern_v the_o fabric_n and_o disposition_n of_o the_o pipe_n we_o come_v now_o to_o the_o effect_n let_v t_o be_v the_o height_n of_o the_o spring_n and_o let_v the_o water_n run_v into_o the_o vessel_n s_o and_o let_v the_o pipe_n p_o be_v open_a than_o the_o vessel_n a_o shall_v be_v fill_v and_o when_o they_o be_v full_a the_o water_n shall_v begin_v to_o run_v by_o the_o small_a pipe_n v_o into_o the_o vessel_n y_o the_o which_o be_v full_a and_o then_o be_v heavy_a than_o the_o weight_n m_n shall_v descend_v towards_o r_o and_o shut_v both_o the_o cock_n l_o and_o the_o pipe_n p_o and_o then_o the_o water_n fall_v into_o s_o shall_v run_v by_o the_o pipe_n o_o into_o the_o pipe_n c_o the_o air_n of_o which_o pipe_n pass_v through_o the_o pipe_n d_o into_o the_o pipe_n fletcher_o press_v the_o water_n which_o be_v in_o a_o and_o constrain_v it_o to_o ascend_v by_o 3._o now_o when_o a_o be_v empty_a and_o c_o full_a the_o vessel_n y_o shall_v be_v also_o make_v light_n by_o mean_n of_o the_o small_a pipe_n z_o which_o empty_v the_o say_a vessel_n about_o the_o same_o time_n as_o c_o be_v fill_v then_o the_o same_o vessel_n y_o ascend_v again_o in_o its_o place_n and_o p_o open_v as_o it_o be_v before_o to_o fill_v the_o pipe_n a._o and_o so_o this_o engine_n move_v continual_o by_o which_o the_o water_n be_v raise_v high_a than_o the_o spring_n of_o the_o height_n as_o be_v between_o the_o pipe_n a_o and_o the_o pipe_n c_o behold_v here_o that_o which_o be_v to_o be_v demonstrate_v touch_v this_o engine_n which_o among_o all_o the_o phneumatique_a engine_n be_v that_o which_o with_o less_o force_n raise_v great_a quantity_n of_o water_n and_o as_o concerning_o other_o invention_n to_o conduct_n the_o water_n of_o spring_n or_o fall_a water_n or_o to_o make_v they_o navigable_a or_o to_o raise_v water_n out_o of_o river_n by_o divers_a way_n in_o great_a abundance_n for_o the_o use_n of_o town_n royal_a house_n or_o palace_n shall_v be_v demonstrate_v in_o that_o which_o follow_v it_o be_v here_o to_o be_v note_v that_o the_o frame_n of_o timber_n upon_o which_o the_o pipe_n be_v put_v and_o the_o pulley_n fasten_v in_o the_o foregoing_a figure_n be_v not_o there_o describe_v because_o they_o will_v have_v hinder_v the_o full_a sight_n of_o all_o the_o part_n of_o this_o engine_n the_o explanation_n of_o the_o plate_n and_o figure_n follow_v the_o first_o plate_n eigure_n i._n to_o raise_v water_n by_o the_o currant_n of_o a_o river_n and_o the_o
force_n of_o a_o pump_n this_o engine_n common_o call_v a_o pump_n be_v call_v by_o vitruvius_n and_o hero_n the_o stesibique_fw-la engine_n retain_v the_o name_n of_o the_o inventor_n thereof_o which_o be_v stesibius_n of_o alexandria_n i_o will_v show_v three_o way_n to_o raise_v water_n by_o this_o engine_n the_o first_o shall_v be_v by_o the_o currant_n of_o a_o river_n as_o the_o figure_n show_v where_o there_o be_v a_o water_n wheel_n and_o at_o each_o end_n of_o the_o axletree_n of_o the_o say_a wheel_n be_v a_o handle_n of_o strong_a brass_n and_o forge_v to_o sustain_v the_o force_n and_o weight_n of_o the_o say_a wheel_n and_o if_o the_o say_a wheel_n be_v ten_o foot_n broad_a and_o twelve_o foot_n in_o diameter_n the_o say_a handle_n shall_v be_v at_o least_o four_o inch_n square_a and_o shall_v be_v round_v in_o the_o middle_n at_o the_o place_n mark_v with_o a_o and_o there_o shall_v be_v also_o two_o piece_n of_o wood_n call_v lever_n mark_v with_o the_o letter_n b_o and_o c_o fit_v to_o the_o arm_n of_o the_o say_a handle_n the_o one_o of_o which_o rise_v and_o the_o other_o go_v down_o when_o the_o wheel_n turn_v and_o the_o say_a lever_n shall_v be_v also_o fit_v to_o two_o arm_n or_o branch_n mark_v with_o d_o and_o e_o the_o which_o raise_v the_o bucket_n and_o sucker_n of_o the_o pump_n alternate_o and_o so_o the_o water_n shall_v be_v raise_v to_o the_o vessel_n fletcher_o and_o from_o thence_o you_o may_v conduct_v it_o whither_o you_o please_v as_o concerning_o the_o height_n which_o it_o ought_v to_o rise_v i_o be_o of_o opinion_n that_o it_o must_v not_o be_v constrain_v to_o rise_v more_o than_o thirty_o foot_n in_o height_n with_o one_o pump_n as_o shall_v be_v teach_v in_o the_o follow_a problem_n the_o great_a pipe_n g_o be_v the_o place_n where_o the_o sucker_n lie_v which_o sustain_v the_o water_n when_o the_o bucket_n or_o sucker_n of_o the_o pump_n be_v not_o lift_v up_o the_o figure_n with_o the_o ordinary_a practice_n which_o be_v have_v of_o pump_n will_v make_v you_o easy_o understand_v this_o engine_n and_o if_o the_o currant_n of_o the_o river_n be_v strong_a and_o it_o be_v require_v to_o have_v store_n of_o water_n you_o may_v make_v the_o diameter_n within_o the_o barrel_n ten_o or_o twelve_o inch_n and_o the_o height_n eight_o or_o nine_o foot_n and_o to_o make_v it_o well_o the_o bucket_n ought_v to_o rise_v and_o fall_v four_o foot_n and_o when_o they_o be_v at_o their_o great_a height_n that_o they_o may_v have_v four_o foot_n of_o water_n above_o they_o to_o the_o intent_n that_o the_o air_n may_v not_o escape_v for_o if_o the_o water_n be_v not_o high_a enough_o between_o the_o top_n of_o the_o barrel_n and_o the_o bucket_n the_o air_n will_v pass_v through_o the_o water_n by_o bubble_n and_o make_v the_o engine_n useless_a and_o especial_o when_o the_o water_n be_v force_v to_o rise_v above_o fifteen_o or_o twenty_o foot_n therefore_o you_o must_v take_v heed_n that_o that_o accident_n do_v not_o happen_v the_o proportion_n also_o of_o the_o pipe_n mno_fw-la shall_v be_v about_o four_o inch_n in_o diameter_n if_o the_o abrrel_n be_v twelve_o if_o the_o say_a barrel_n be_v less_o the_o say_a pipe_n shall_v be_v less_o in_o proportion_n the_o explanation_n of_o the_o second_o figure_n plate_n ii_o another_o way_n to_o raise_v water_n by_o mean_n of_o a_o fall_a water_n this_o other_o manner_n of_o raise_v of_o water_n be_v do_v by_o a_o fall_a water_n raise_v so_o as_o it_o may_v fall_v upon_o the_o wheel_n a_o to_o turn_v it_o and_o in_o turn_v it_o to_o raise_v the_o water_n of_o the_o pump_n b_o to_o 24._o or_o 30._o foot_n high_a and_o the_o other_o side_n c_o take_v the_o say_a water_n in_o the_o first_o elevation_n in_o the_o trough_n d_o and_o may_v raise_v it_o from_o thence_o 24._o or_o 30._o foot_n high_a the_o aforegoing_a figure_n will_v give_v the_o manner_n and_o way_n of_o the_o raise_n of_o the_o water_n in_o the_o first_o height_n and_o the_o second_o height_n be_v do_v after_o the_o same_o manner_n as_o may_v easy_o be_v comprehend_v by_o the_o figure_n the_o which_o figure_n be_v not_o make_v high_a enough_o according_a to_o the_o proportion_n of_o the_o measure_n because_o the_o paper_n will_v not_o permit_v but_o you_o may_v easy_o imagine_v the_o say_a height_n as_o it_o ought_v to_o be_v explanation_n of_o plate_n iii_o to_o raise_v the_o water_n of_o a_o spring_n or_o river_n by_o the_o force_n of_o horse_n but_o if_o there_o be_v not_o a_o river_n strong_a enough_o nor_o a_o fall_a currant_n the_o water_n may_v be_v raise_v by_o the_o mean_n and_o force_n of_o one_o horse_n or_o more_o according_a to_o the_o quantity_n and_o the_o height_n which_o be_v desire_v this_o present_a design_n be_v make_v to_o raise_v the_o water_n 60._o foot_n high_a and_o four_o horse_n will_v raise_v about_o 60._o in_o a_o hour_n time_n which_o be_v about_o 30000._o pound_n weight_n therefore_o first_o let_v there_o be_v a_o straight_a axletree_n of_o wood_n a_o foot_n square_a and_o 60._o foot_n high_a mark_v with_o a_o the_o which_o turn_v between_o two_o pin_n and_o above_o near_o the_o end_n there_o be_v a_o wheel_n of_o 24_o tooth_n mark_v with_o b_o the_o which_o turn_v a_o lantern_n or_o pinion_n of_o 12._o staff_n mark_v with_o c_o and_o a_o wheel_n of_o eighteen_o tooth_n mark_v d._n but_o there_o be_v but_o nine_o tooth_n in_o the_o half_a of_o the_o circumference_n the_o other_o half_o be_v void_a and_o there_o be_v also_o two_o other_o wheel_n mark_v with_o e_o and_o f_o of_o equal_a bigness_n and_o also_o nine_o tooth_n on_o each_o wheel_n and_o let_v the_o tooth_a part_n of_o all_o the_o three_o wheel_n be_v put_v above_o then_o there_o must_v be_v a_o pulley_n put_v above_o mark_v with_o g_o over_o which_o a_o cord_n must_v pass_v the_o which_o must_v be_v fasten_v by_o the_o two_o end_n to_o the_o axeltree_n of_o the_o wheel_n c_o and_o f_o so_o as_o turn_v about_o one_o of_o the_o wheel_n it_o may_v unturn_v the_o other_o as_o you_o may_v see_v and_o better_o consider_v in_o the_o figure_n of_o the_o orthography_n follow_v then_o you_o must_v put_v the_o say_a wheel_n e_o and_o f_o against_o d_o so_o as_o d_o turn_v always_o the_o same_o way_n may_v make_v e_o turn_v half_o a_o turn_n and_o then_o when_o it_o shall_v be_v in_o the_o last_o tooth_n the_o first_o of_o the_o wheel_n fletcher_o shall_v represent_v itself_o against_o the_o wheel_n d_o because_o the_o wheel_n e_o shall_v make_v it_o turn_v back_o again_o by_o mean_n of_o the_o common_a cord_n and_o pully_n g_o and_o after_o the_o say_a wheel_n d_o have_v catch_v the_o first_o tooth_n of_o fletcher_o it_o shall_v continue_v to_o the_o nine_o and_o afterwards_o the_o first_o of_o the_o wheel_n e_o shall_v represent_v itself_o again_o and_o so_o the_o two_o wheel_n e_o and_o f_o shall_v turn_v forward_o and_o backward_o half_a a_o turn_n alternate_o and_o to_o the_o axletree_n h_o and_o l_o there_o shall_v be_v fasten_v two_o strong_a cord_n which_o shall_v draw_v up_o the_o two_o bucket_n which_o go_v into_o the_o barrel_n m_o and_o n_o and_o have_v about_o three_o foot_n play_v rise_v and_o fall_v and_o they_o shall_v be_v make_v of_o brass_n well_o fit_v within_o the_o barrel_n and_o that_o they_o may_v descend_v of_o themselves_o without_o be_v constrain_v and_o so_o there_o be_v no_o leather_n put_v about_o the_o bucket_n as_o be_v ordinary_o do_v in_o common_a pump_n and_o it_o be_v to_o be_v note_v that_o the_o swift_a the_o bucket_n come_v up_o so_o much_o the_o more_o water_n they_o raise_v which_o may_v be_v observe_v in_o all_o sort_n of_o pump_n it_o be_v also_o to_o be_v note_v that_o the_o two_o transverse_a piece_n op_o aught_o to_o be_v but_o one_o piece_n to_o the_o which_o the_o other_o transverse_a piece_n q_o ought_v to_o be_v join_v in_o the_o which_o the_o four_o end_n of_o the_o axeltree_n of_o the_o wheel_n bcef_a do_v turn_v the_o explanation_n of_o plate_n four_o this_o plate_n give_v a_o large_a demonstration_n of_o the_o former_a by_o mean_n of_o the_o orthography_n for_o the_o better_a understanding_n of_o the_o foregoing_a figure_n i_o have_v represent_v here_o the_o plain_a of_o the_o orthography_n to_o the_o end_n that_o by_o it_o you_o may_v understand_v the_o motion_n and_o meeting_n of_o the_o three_o wheel_n edf_o let_v then_o each_o of_o those_o wheel_n have_v nine_o tooth_n in_o the_o half_a circumference_n and_o let_v that_o part_n of_o the_o wheel_n that_o have_v the_o tooth_n in_o they_o be_v turn_v upward_o so_o as_o the_o first_o tooth_n of_o the_o one_o meet_v with_o the_o tooth_n of_o the_o wheel_n