metaphysical_a empusa_n not_o by_o skirmish_n but_o by_o let_v in_o the_o light_n upon_o she_o for_o i_o be_o confident_a if_o any_o confidence_n of_o a_o write_n can_v proceed_v from_o the_o writer_n fear_v circumspection_n &_o diffidence_n that_o in_o the_o three_o former_a part_n of_o this_o book_n all_o that_o i_o have_v say_v be_v sufficient_o demonstrate_v from_o definition_n &_o all_o in_o the_o four_o part_n from_o supposition_n not_o absurd_a but_o if_o there_o appear_v to_o your_o lordship_n any_o thing_n less_o full_o demonstrate_v then_o to_o satisfy_v every_o reader_n the_o cause_n be_v this_o that_o i_o profess_v to_o write_v not_o all_o to_o all_o but_o some_o thing_n to_o geometrician_n only_o but_o that_o your_o lordship_n will_v be_v satisfy_v i_o can_v doubt_v there_o remain_v the_o second_o section_n which_o be_v concern_v man._n that_o part_n thereof_o where_o i_o handle_v the_o optic_n contain_v six_o chapter_n together_o with_o the_o table_n of_o the_o figure_n belong_v to_o they_o i_o have_v already_o write_v &_o engravenly_v by_o i_o above_o these_o six_o year_n the_o rest_n shall_v as_o soon_o as_o i_o can_v be_v add_v to_o it_o though_o by_o the_o contumely_n &_o petty_a injury_n of_o some_o unskilful_a man_n i_o know_v already_o by_o experience_n how_o much_o great_a thanks_o will_v be_v due_a then_o pay_v i_o for_o tell_v man_n the_o truth_n of_o what_o man_n be_v but_o the_o burden_n i_o have_v take_v on_o i_o i_o mean_v to_o carry_v through_o not_o strive_v to_o appease_v but_o rather_o to_o revenge_v myself_o of_o envy_n by_o increase_a it_o for_o it_o content_v i_o that_o i_o have_v your_o lordship_n favour_n which_o be_v all_o you_o require_v i_o acknowledge_v and_o for_o which_o with_o my_o prayer_n to_o almighty_a god_n for_o your_o lordship_n safety_n i_o shall_v to_o my_o power_n be_v always_o thankful_a london_n april_n 23_o 1655._o your_o lordship_n most_o humble_a servant_n thomas_n hobbes_n the_o author_n epistle_n to_o the_o reader_n think_v not_o courteous_a reader_n that_o the_o philosophy_n the_o element_n whereof_o i_o be_o go_v to_o set_v in_o order_n be_v that_o which_o make_v philosopher_n stone_n nor_o that_o which_o be_v find_v in_o the_o metaphsique_n code_o but_o that_o it_o be_v the_o natural_a reason_n of_o man_n busy_o fly_v up_o and_o down_o among_o the_o creature_n &_o bring_v back_o a_o true_a report_n of_o their_o order_n cause_n &_o effect_n philosophy_n therefore_o the_o child_n of_o the_o world_n and_o your_o own_o mind_n be_v within_o yourself_o perhaps_o not_o fashion_v yet_o but_o like_o the_o world_n its_o father_n as_o it_o be_v in_o the_o beginning_n a_o thing_n confuse_v do_v therefore_o as_o the_o statuary_n do_v who_o by_o hew_v off_o that_o which_o be_v superfluous_a do_v not_o make_v but_o find_v the_o image_n or_o imitate_v the_o creation_n if_o you_o will_v be_v a_o philosopher_n in_o good_a earnest_n let_v your_o reason_n move_v upon_o the_o deep_a of_o your_o own_o cogitation_n and_o experience_n those_o thing_n that_o lie_v in_o confusion_n must_v be_v set_v asunder_o distinguish_v and_o every_o one_o stamp_v with_o its_o own_o name_n set_v in_o order_n that_o be_v to_o say_v your_o method_n must_v resemble_v that_o of_o the_o creation_n the_o order_n of_o the_o creation_n be_v light_n distinction_n of_o day_n and_o night_n the_o firmament_n the_o luminary_n sensible_a creature_n man_n and_o after_o the_o creation_n the_o commandment_n therefore_o the_o order_n of_o contemplation_n will_v be_v reason_n definition_n space_n the_o star_n sensible_a quality_n man_n and_o after_o man_n be_v grow_v up_o subjection_n to_o command_n in_o the_o first_o part_n of_o this_o section_n which_o be_v entitle_v logic_n i_o set_v up_o the_o light_n of_o reason_n in_o the_o second_o which_o have_v for_o title_n the_o ground_n of_o philosophy_n i_o distinguish_v the_o most_o common_a notion_n by_o accurate_a definition_n for_o the_o avoid_n of_o confusion_n and_o obscurity_n the_o three_o part_n concern_v the_o expansion_n of_o space_n that_o be_v geometry_n the_o four_o contain_v the_o motion_n of_o the_o star_n together_o with_o the_o doctrine_n of_o sensible_a quality_n in_o the_o second_o section_n if_o it_o please_v god_n shall_v be_v handle_v man._n in_o the_o three_o section_n the_o doctrine_n of_o subjection_n be_v handle_v already_o this_o be_v the_o method_n i_o follow_v and_o if_o it_o like_v you_o you_o may_v use_v the_o same_o for_o i_o do_v but_o propound_v not_o commend_v to_o you_o any_o thing_n of_o i_o but_o whatsoever_o shall_v be_v the_o method_n you_o will_v like_v i_o will_v very_o fain_o commend_v philosophy_n to_o you_o that_o be_v to_o say_v the_o study_n of_o wisdom_n for_o want_v of_o which_o we_o have_v all_o suffer_v much_o damage_n late_o for_o even_o they_o that_o study_v wealth_n do_v it_o out_o of_o love_n to_o wisdom_n for_o their_o treasure_n serve_v they_o but_o for_o a_o looking-glass_n wherein_o to_o behold_v and_o contemplate_v their_o own_o wisdom_n nor_o do_v they_o that_o love_v to_o be_v employ_v in_o public_a business_n aim_v at_o any_o thing_n but_o place_n wherein_o to_o show_v their_o wisdom_n neither_o do_v voluptuous_a man_n neglect_v philosophy_n but_o only_o because_o they_o know_v not_o how_o great_a a_o pleasure_n it_o be_v to_o the_o mind_n of_o man_n to_o be_v ravish_v in_o the_o vigorous_a and_o perpetual_a embrace_n of_o the_o most_o beauteous_a world_n last_o though_o for_o nothing_o else_o yet_o because_o the_o mind_n of_o man_n be_v no_o less_o impatient_a of_o empty_a time_n than_o nature_n be_v of_o empty_a place_n to_o the_o end_n you_o be_v not_o force_v for_o want_v of_o what_o to_o do_v to_o be_v troublesome_a to_o man_n that_o have_v business_n or_o take_v hurt_v by_o fall_v into_o idle_a company_n but_o have_v somewhat_o of_o your_o own_o wherewith_o to_o fill_v up_o your_o time_n i_o recommend_v unto_o you_o the_o study_n of_o philosophy_n farewell_n t._n h._n the_o title_n of_o the_o chapter_n the_o first_o part_n or_o logic_n chap._n 1_o of_o philosophy_n chap._n 2_o of_o name_n chap._n 3_o of_o proportion_n chap._n 4_o of_o syllogism_n chap._n 5_o of_o err_v falsity_n and_o caption_n chap._n 6_o of_o method_n the_o second_o part_n or_o the_o first_o ground_n of_o philosophy_n chap._n 7_o of_o place_n and_o time_n chap._n 8_o of_o body_n and_o accident_n chap._n 9_o of_o cause_n and_o effect_n chap._n 10_o of_o power_n and_o act._n chap._n 11_o of_o identity_n and_o difference_n chap._n 12_o of_o quantity_n chap._n 13_o of_o analogisme_n or_o the_o same_o proportion_n chap._n 14_o of_o straight_a and_o crock_v angle_n and_o figure_n the_o three_o part_n of_o the_o proportion_n of_o motion_n and_o magnitude_n chap._n 15_o of_o the_o nature_n property_n and_o divers_a consideration_n of_o motion_n and_o endeavour_n chap._n 16_o of_o motion_n accelerate_a and_o uniform_a and_o of_o motion_n by_o concourse_n chap._n 17_o of_o figure_n deficient_a chap._n 18_o of_o the_o equation_n of_o straight_a line_n which_o the_o crooked_a line_n of_o parabolas_fw-la and_o other_o figure_n make_v in_o imitation_n of_o parabolas_fw-la chap._n 19_o of_o angle_n of_o incidence_n and_o reflection_n equal_a by_o supposition_n chap._n 20_o of_o the_o dimension_n of_o a_o circle_n and_o the_o division_n of_o arch_n or_o angle_n chap._n 21_o of_o circular_a motion_n chap._n 22_o of_o other_o variety_n of_o motion_n chap._n 23_o of_o the_o centre_n of_o equiponderation_n of_o body_n press_v downward_o in_o straight_o parallel_a line_n chap._n 24_o of_o refraction_n and_o reflection_n the_o four_o part_n of_o physic_n or_o the_o phaenomena_n of_o nature_n chap._n 25_o of_o sense_n and_o animal_n motion_n chap._n 26_o of_o the_o world_n and_o of_o the_o star_n chap._n 27_o of_o light_n heatt_z and_o of_o colour_n chap._n 28_o of_o cold_a wind_n hard_a ice_n restitution_n of_o body_n bend_v diaphanous_a lightning_n and_o thunder_n and_o of_o the_o head_n of_o river_n chap._n 29_o of_o sound_n odour_n savour_n and_o touch._n chap._n 30_o of_o gravity_n computation_n or_o logic_n chap._n i._o of_o philosophy_n 1_o the_o introduction_n 2_o the_o definition_n of_o philosophy_n explain_v 3_o ratiocination_n of_o the_o mind_n 4_o property_n what_o they_o be_v 5_o how_o property_n be_v know_v by_o generation_n &_o contrary_o 6_o the_o scope_n of_o philosophy_n 7_o the_o utility_n of_o it_o 8_o the_o subject_a 9_o the_o part_n of_o it_o 10_o the_o epilogue_n philosophy_n seem_v to_o i_o to_o be_v among_o man_n now_o in_o the_o same_o manner_n as_o corn_n and_o wine_n be_v say_v to_o have_v be_v in_o the_o world_n in_o ancient_a time_n for_o from_o the_o begin_n there_o be_v vine_n and_o ear_n of_o corn_n grow_v here_o and_o there_o in_o the_o field_n but_o no_o care_n be_v take_v for_o the_o
the_o name_n of_o the_o part_n of_o any_o speech_n be_v explicate_v be_v it_o not_o necessary_a that_o the_o definition_n shall_v be_v a_o name_n compound_v of_o they_o for_o example_n when_o these_o name_n aequilaterall_a quadrilaterall_a right-angled_n be_v sufficient_o understand_v it_o be_v not_o necessary_a in_o geometry_n that_o there_o shall_v be_v at_o all_o such_o a_o name_n as_o square_n for_o define_v name_n be_v receive_v in_o philosophy_n for_o brevity_n sake_n only_o five_o that_o compound_v name_n which_o be_v define_v one_o way_n in_o some_o one_o part_n of_o philosophy_n may_v in_o another_o part_n of_o the_o same_o be_v otherwise_o define_v as_o a_o parabola_fw-la and_o a_o hyperbole_n have_v one_o definition_n in_o geometry_n and_o another_o in_o rhetoric_n for_o definition_n be_v institute_v and_o serve_v for_o the_o understanding_n of_o the_o doctrine_n which_o be_v treat_v of_o and_o therefore_o as_o in_o one_o part_n of_o philosophy_n a_o definition_n may_v have_v in_o it_o some_o one_o fit_a name_n for_o the_o more_o brief_a explanation_n of_o some_o proposition_n in_o geometry_n so_o it_o may_v have_v the_o same_o liberty_n in_o other_o part_n of_o philosophy_n for_o the_o use_n of_o name_n be_v particular_a even_o where_o many_o agree_v to_o the_o settle_n of_o they_o and_o arbitrary_a six_o that_o no_o name_n can_v be_v define_v by_o any_o one_o word_n because_o no_o one_o word_n be_v sufficient_a for_o the_o resolve_v of_o one_o or_o more_o word_n seven_o that_o a_o define_v name_n ought_v not_o to_o be_v repeat_v in_o the_o definition_n for_o a_o define_v name_n be_v the_o whole_a compound_v and_o a_o definition_n be_v the_o resolution_n of_o that_o compound_v into_o part_n but_o no_o totall_n can_v be_v part_n of_o itself_o 16_o any_o two_o definition_n that_o may_v be_v compound_v into_o a_o syllogism_n produce_v a_o conclusion_n which_o because_o it_o be_v derive_v from_o principle_n that_o be_v from_o definition_n be_v say_v to_o be_v demonstrate_v and_o the_o derivation_n or_o composition_n itself_o be_v call_v a_o demonstration_n in_o like_a manner_n if_o a_o syllogism_n be_v make_v of_o two_o proposition_n whereof_o one_o be_v a_o definition_n the_o other_o a_o demonstrate_v conclusion_n or_o neither_o of_o they_o be_v a_o definition_n but_o both_o former_o demonstrate_v that_o syllogism_n be_v also_o call_v a_o demonstration_n and_o so_o successive_o the_o definition_n therefore_o of_o a_o demonstration_n be_v this_o a_o demonstration_n be_v a_o syllogism_n or_o series_n of_o syllogism_n derive_v and_o continue_v from_o the_o definition_n of_o name_n to_o the_o last_o conclusion_n and_o from_o hence_o it_o may_v be_v understand_v that_o all_o true_a ratiocination_n which_o take_v its_o beginning_n from_o true_a principle_n produce_v science_n and_o be_v true_a demonstration_n for_o as_o for_o the_o original_a of_o the_o name_n although_o that_o which_o the_o greek_n call_v 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d and_o the_o latin_n demonstratio_fw-la be_v understand_v by_o they_o for_o that_o sort_n only_o of_o ratiocination_n in_o which_o by_o the_o describe_v of_o certain_a line_n and_o figure_n they_o place_v the_o thing_n they_o be_v to_o prove_v as_o it_o be_v before_o man_n eye_n which_o be_v proper_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d or_o to_o show_v by_o the_o figure_n yet_o they_o seem_v to_o have_v do_v it_o for_o this_o reason_n that_o unless_o it_o be_v in_o geometry_n in_o which_o only_o there_o be_v place_n for_o such_o figure_n there_o be_v no_o ratiocination_n certain_a and_o end_v in_o science_n their_o doctrine_n concern_v all_o other_o thing_n be_v nothing_o but_o controversy_n and_o clamour_n which_o nevertheless_o happen_v not_o because_o the_o truth_n to_o which_o they_o pretend_v can_v not_o be_v make_v evident_a without_o figure_n but_o because_o they_o want_v true_a principle_n from_o which_o they_o may_v derive_v their_o ratiocination_n and_o therefore_o there_o be_v no_o reason_n but_o that_o if_o true_a definition_n be_v praemise_v in_o all_o sort_n of_o doctrine_n the_o demonstration_n also_o will_v be_v true_a 17_o it_o be_v proper_a to_o methodical_a demonstration_n first_o that_o there_o be_v a_o true_a succession_n of_o one_o reason_n to_o another_o according_a to_o the_o rule_n of_o syllogize_v deliver_v above_o second_o that_o the_o praemiss_n of_o all_o syllogism_n be_v demonstrate_v from_o the_o first_o definition_n three_o that_o after_o definition_n he_o that_o teach_v or_o demonstrate_v any_o thing_n proceed_v in_o the_o same_o method_n by_o which_o he_o find_v it_o out_o namely_o that_o in_o the_o first_o place_n those_o thing_n be_v demonstrate_v which_o immediate_o succeed_v to_o universal_a definition_n in_o which_o be_v contain_v that_o part_n of_o philosophy_n which_o be_v call_v philosophia_fw-la prima_fw-la next_o those_o thing_n which_o may_v be_v demonstrate_v by_o simple_a motion_n in_o which_o geometry_n consist_v after_o geome_v try_v such_o thing_n as_o may_v be_v teach_v or_o show_v by_o manifest_a action_n that_o be_v by_o thrust_v from_o or_o pulling_z towards_z and_o after_o these_o the_o motion_n or_o mutation_n of_o the_o invisible_a part_n of_o thing_n and_o the_o doctrine_n of_o sense_n &_o imagination_n &_o of_o the_o internal_a passion_n especial_o those_o of_o man_n in_o which_o be_v comprehend_v the_o ground_n of_o civil_a duty_n or_o civil_a philosophy_n which_o take_v up_o the_o last_o place_n and_o that_o this_o method_n ought_v to_o be_v keep_v in_o all_o sort_n of_o philosophy_n be_v evident_a from_o hence_o that_o such_o thing_n as_o i_o have_v say_v be_v to_o be_v teach_v last_o can_v be_v demonstrate_v till_o such_o as_o be_v propound_v to_o be_v first_o treat_v of_o be_v full_o understand_v of_o which_o method_n no_o other_o example_n can_v be_v give_v but_o that_o treatise_n of_o the_o element_n of_o philosophy_n which_o i_o shall_v begin_v in_o the_o next_o chapter_n and_o continue_v to_o the_o end_n of_o the_o work_n 18_o beside_o those_o paralogisme_n who_o fault_n lie_v either_o in_o the_o falsity_n of_o the_o praemiss_n or_o the_o want_n of_o true_a composition_n of_o which_o i_o have_v speak_v in_o the_o praecedent_a chapter_n there_o be_v two_o more_o which_o be_v frequent_a in_o demonstration_n one_o whereof_o be_v common_o call_v petitio_fw-la principii_fw-la the_o other_o be_v the_o suppose_n of_o a_o false_a cause_n and_o these_o do_v not_o only_o deceive_v unskilful_a learner_n but_o sometime_o master_n themselves_o by_o make_v they_o take_v that_o for_o well_o demonstrate_v which_o be_v not_o demonstrate_v at_o all_o petitio_fw-la principii_fw-la be_v when_o the_o conclusion_n to_o be_v prove_v be_v disguise_v in_o other_o word_n and_o put_v for_o the_o definition_n or_o principle_n from_o whence_o it_o be_v to_o be_v demonstrate_v and_o thus_o by_o put_v for_o the_o cause_n of_o the_o thing_n seek_v either_o the_o thing_n itself_o or_o some_o effect_n of_o it_o they_o make_v a_o circle_n in_o their_o demonstration_n as_o for_o example_n he_o that_o will_v demonstrate_v that_o the_o earth_n stand_v still_o in_o the_o centre_n of_o the_o world_n and_o shall_v suppose_v the_o earth_n gravity_n to_o be_v the_o cause_n thereof_o and_o define_v gravity_n to_o be_v a_o quality_n by_o which_o every_o heavy_a body_n tend_v towards_o the_o centre_n of_o the_o world_n will_v lose_v his_o labour_n for_o the_o question_n be_v what_o be_v the_o cause_n of_o that_o quality_n in_o the_o earth_n and_o therefore_o he_o that_o suppose_v gravity_n to_o be_v the_o cause_n put_v the_o thing_n itself_o for_o its_o own_o cause_n of_o a_o false_a cause_n i_o find_v this_o example_n in_o a_o certain_a treatise_n where_o the_o thing_n to_o be_v demonstrate_v be_v the_o motion_n of_o the_o earth_n he_o begin_v therefore_o with_o this_o that_o see_v the_o earth_n and_o the_o sun_n be_v not_o always_o in_o the_o same_o situation_n it_o must_v needs_o be_v that_o one_o of_o they_o be_v local_o move_v which_o be_v true_a next_o he_o affirm_v that_o the_o vapour_n which_o the_o sun_n raise_v from_o the_o earth_n and_o sea_n be_v by_o reason_n of_o this_o motion_n necessary_o move_v which_o also_o be_v true_a from_o whence_o he_o infer_v the_o wind_n be_v make_v and_o this_o may_v pass_v for_o grant_v and_o by_o these_o wind_n he_o say_v the_o water_n of_o the_o sea_n be_v move_v and_o by_o their_o motion_n the_o bottom_n of_o the_o sea_n as_o if_o it_o be_v beat_v forward_o move_v round_o and_o let_v this_o also_o be_v grant_v wherefore_o he_o conclude_v the_o earth_n be_v move_v which_o be_v nevertheless_o be_v a_o paralogism_n for_o if_o that_o wind_n be_v the_o cause_n why_o the_o earth_n be_v from_o the_o beginning_n move_v round_o and_o the_o motion_n either_o of_o the_o sun_n or_o the_o earth_n be_v the_o cause_n of_o that_o wind_n than_o the_o motion_n of_o the_o sun_n or_o
fhg_n and_o the_o straight_a line_n da_fw-la db_fw-la and_o dc_o proportional_a to_o the_o straight_a line_n he_o hf_n and_o hg_n i_o say_v the_o three_o point_n a_o b_o and_o c_o have_v like_a situation_n with_o the_o three_o point_n e_o f_o &_o g_o or_o be_v place_v alike_o for_o if_o he_o be_v understand_v to_o be_v lay_v upon_o da_fw-la so_o that_o the_o point_n h_n be_v in_o d_o the_o point_n f_o will_v be_v in_o the_o straight_a line_n db_n by_o reason_n of_o the_o equality_n of_o the_o angel_n adb_n and_o ehf_n and_o the_o point_n g_o will_v be_v in_o the_o straight_a line_n dc_o by_o reason_n of_o the_o equality_n of_o the_o angel_n bdc_n and_o fhg_a and_o the_o strright_a line_n ab_fw-la and_o of_o as_o also_o bc_n and_o fg_n will_v be_v parallel_n because_o ad._n ed_z bh_n fh_o cd_o gh_o be_v proportional_n by_o construction_n and_o therefore_o the_o distance_n between_o the_o point_v a_o and_o b_o and_o the_o points_z b_o and_o c_o will_v be_v proportional_a to_o the_o 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therefore_o explain_v these_o in_o the_o three_o last_o chapter_n i_o think_v â—it_a to_o add_v they_o to_o this_o part_n and_o so_o pass_v to_o the_o next_o of_o the_o proportion_n of_o motion_n and_o magnitude_n chap._n xv._n of_o the_o nature_n property_n and_o diverse_a consideration_n of_o motion_n and_o endeavour_n 1_o repetition_n of_o some_o principle_n of_o the_o doctrine_n of_o motion_n former_o set_v down_o 2_o other_o principle_n add_v to_o they_o 3_o certain_a theorem_n concern_v the_o nature_n of_o motion_n 4_o diverse_a consideration_n of_o motion_n 5_o the_o way_n by_o which_o the_o first_o endeavour_n of_o body_n move_v â—endoth_a 6_o in_o motion_n which_o be_v make_v by_o concourse_n one_o of_o the_o movent_n cease_v the_o endeavour_n be_v make_v by_o the_o way_n by_o which_o the_o rest_n tend_v 7_o the_o endeavour_n of_o any_o move_v body_n which_o have_v its_o motion_n in_o the_o circumference_n of_o a_o circle_n part_n from_o the_o same_o proceed_v afterward_o in_o a_o straight_a line_n which_o touch_v the_o circle_n 8_o how_o much_o great_a the_o velocity_n or_o magnitude_n be_v of_o a_o movent_fw-la so_o much_o great_a be_v the_o efficacy_n thereof_o upon_o any_o other_o body_n in_o its_o way_n 1_o the_o next_o thing_n in_o order_n to_o be_v treat_v of_o be_v motion_n and_o magnitude_n which_o be_v the_o most_o common_a accident_n of_o all_o body_n this_o place_n therefore_o most_o proper_o belong_v to_o the_o element_n of_o geometry_n but_o because_o this_o part_n of_o philosophy_n have_v be_v improve_v by_o the_o best_a wit_n of_o all_o age_n have_v afford_v great_a plenty_n of_o matter_n than_o can_v well_o be_v thrust_v together_o within_o the_o narrow_a limit_n of_o this_o discourse_n i_o think_v fit_a to_o admonish_v the_o reader_n that_o before_o he_o proceed_v further_o he_o take_v into_o his_o hand_n the_o work_v of_o euclid_n archimedes_n apollonius_n and_o other_o as_o well_o ancient_a as_o modern_a writer_n for_o to_o what_o end_n be_v it_o to_o do_v over_o again_o that_o which_o be_v already_o do_v the_o little_a therefore_o that_o i_o shall_v say_v concern_v geometry_n in_o some_o of_o the_o follow_a chapter_n shall_v be_v such_o only_a as_o be_v new_a and_o conduce_v to_o natural_a philosophy_n i_o have_v already_o deliver_v some_o of_o the_o principle_n of_o this_o doctrine_n in_o the_o 8_o &_o 9_o chapter_n which_o i_o shall_v brief_o put_v together_o here_o that_o the_o reader_n in_o go_v on_o may_v have_v their_o light_n near_o at_o hand_n first_o therefore_o in_o the_o 8_o chap._n and_o 10_o article_n motion_n be_v define_v to_o be_v the_o continual_a privation_n of_o one_o place_n and_o acquisition_n of_o another_o second_o it_o be_v there_o show_v that_o whatsoever_o be_v move_v be_v move_v in_o time_n three_o in_o the_o same_o chap._n 11._o article_n i_o have_v define_v rest_n to_o be_v when_o a_o body_n remain_v for_o some_o time_n in_o one_o place_n four_o it_o be_v there_o show_v that_o whatsoever_o be_v move_v be_v not_o in_o any_o determine_a place_n as_o also_o that_o the_o same_o have_v be_v move_v be_v still_o move_v and_o will_v yet_o be_v move_v so_o that_o in_o every_o part_n of_o that_o space_n in_o which_o motion_n be_v make_v we_o may_v consider_v three_o time_n namely_o the_o past_a the_o present_a and_o the_o future_a time_n five_o in_o the_o 15_o article_n of_o the_o same_o chapter_n i_o have_v define_v velocity_n or_o swiftness_n to_o be_v motion_n consider_v as_o power_n namely_o that_o power_n by_o which_o a_o body_n moved_n may_v in_o a_o certain_a time_n transmit_v a_o certain_a length_n which_o also_o may_v more_o brief_o be_v enunciate_v thus_o velocity_n be_v the_o quantity_n of_o motion_n determine_v by_o time_n and_o line_n six_o in_o the_o same_o chap._n 16._o article_n i_o have_v show_v that_o motion_n be_v the_o measure_n of_o time_n seven_o in_o the_o same_o chap._n 17_o art_n i_o have_v define_v motion_n to_o be_v equal_o swift_a when_o in_o equal_a time_n equal_a length_n be_v transmit_v by_o they_o eight_o in_o the_o 18_o article_n of_o the_o same_o chapter_n motion_n be_v define_v to_o be_v equal_a when_o the_o swiftness_n of_o one_o move_v body_n compute_v in_o every_o part_n of_o its_o magnitude_n be_v equal_a to_o the_o swiftness_n of_o another_o compute_v also_o in_o every_o part_n of_o its_o magnitude_n from_o whence_o it_o be_v to_o be_v note_v that_o motion_n equal_a to_o one_o another_o and_o motion_n equal_o swift_a do_v not_o signify_v the_o same_o thing_n for_o when_o two_o horse_n draw_v abr_a the_o motion_n of_o both_o be_v great_a than_o the_o motion_n of_o either_o of_o they_o single_o but_o the_o swiftness_n of_o both_o together_o be_v but_o equal_a to_o that_o of_o either_o nine_o in_o the_o 19_o article_n of_o the_o
draw_v from_o the_o proposition_n which_o prove_v the_o same_o but_o the_o cause_n of_o his_o construction_n be_v in_o the_o thing_n themselves_o and_o consist_v in_o motion_n or_o in_o the_o concourse_n of_o motion_n wherefore_o those_o proposition_n in_o which_o analysis_n end_v be_v definition_n but_o such_o as_o signify_v in_o what_o manner_n the_o construction_n or_o generation_n of_o the_o thing_n proceed_v for_o otherwise_o when_o he_o go_v back_o by_o synthesis_n to_o the_o proof_n of_o his_o problem_n he_o will_v come_v to_o no_o demonstration_n at_o all_o there_o be_v no_o true_a demonstration_n but_o such_o as_o be_v scientifical_a and_o no_o demonstration_n be_v scientifical_a but_o that_o which_o proceed_v from_o the_o knowledge_n of_o the_o cause_n from_o which_o the_o construction_n of_o the_o problem_n be_v draw_v to_o collect_v therefore_o what_o have_v be_v say_v into_o few_o word_n analysis_n be_v ratiocination_n from_o the_o suppose_a construction_n or_o 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time_n as_o well_o as_o from_o congruence_n and_o there_o be_v motion_n by_o which_o two_o quantity_n whether_o line_n or_o superficies_n though_o one_o of_o they_o be_v crooked_a the_o other_o straight_o may_v be_v make_v congruous_a or_o coincident_a and_o this_o method_n archimedes_n make_v use_v of_o in_o his_o book_n de_fw-fr spiralibus_fw-la also_o the_o equality_n or_o inequality_n of_o two_o quantity_n may_v be_v find_v out_o and_o demonstrate_v from_o the_o consideration_n of_o weight_n as_o the_o same_o archimedes_n do_v in_o his_o quadrature_n of_o the_o parabola_fw-la beside_o equality_n and_o equality_n be_v find_v out_o often_o by_o the_o division_n of_o the_o two_o quantity_n into_o part_n which_o be_v consider_v as_o undivisible_a as_o cavallerius_n bonaventura_n have_v do_v in_o our_o time_n and_o archimedes_n often_o last_o the_o same_o be_v perform_v by_o the_o consideration_n of_o the_o power_n of_o line_n or_o the_o root_n of_o those_o power_n and_o by_o the_o 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to_o which_o they_o be_v apply_v be_v to_o one_o another_o in_o proportion_n duplicate_v to_o that_o of_o the_o contiguous_a apply_v line_n they_o will_v all_o terminate_v in_o a_o conical_a section_n which_o section_n be_v the_o place_n of_o their_o termination_n be_v call_v a_o solid_a place_n because_o it_o serve_v for_o the_o find_v out_o of_o the_o quantity_n of_o any_o equation_n which_o consist_v of_o three_o dimension_n there_o be_v therefore_o three_o way_n of_o find_v out_o the_o cause_n of_o equality_n or_o inequality_n between_o two_o give_v quantity_n namely_o first_o by_o the_o computation_n of_o motion_n for_o by_o equal_a motion_n &_o equal_a time_n equal_a space_n be_v describe_v and_o ponderation_n be_v motion_n second_o by_o indivisibles_n because_o all_o the_o part_n together_o take_v be_v equal_a to_o the_o whole_a and_o three_o by_o the_o power_n for_o when_o they_o be_v equal_a their_o root_n also_o be_v equal_a and_o contrary_o the_o power_n be_v equal_a when_o 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geometrician_n without_o vieta_n though_o vieta_n be_v a_o most_o admirable_a geometrician_n but_o he_o that_o have_v vieta_n for_o his_o master_n not_o so_o without_o euclid_n and_o as_o for_o that_o part_n of_o analysis_n which_o work_v by_o the_o power_n though_o it_o be_v esteem_v by_o some_o geometrician_n not_o the_o chief_a to_o be_v the_o best_a way_n of_o solve_v all_o problem_n yet_o it_o be_v a_o thing_n of_o no_o great_a extent_n it_o be_v all_o contain_v in_o the_o doctrine_n of_o rectangle_v and_o rectangle_v solid_n so_o that_o although_o they_o come_v to_o a_o equation_n which_o determine_v the_o quantity_n seek_v yet_o they_o can_v sometime_o by_o art_n exhibit_v that_o quantity_n in_o a_o plain_a but_o in_o some_o conique_a section_n that_o be_v as_o geometrician_n say_v not_o geometrical_o but_o mechanical_o now_o such_o problem_n as_o these_o they_o call_v solid_a and_o when_o they_o can_v exhibit_v the_o quantity_n seek_v for_o with_o the_o help_n of_o a_o 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the_o ancient_a geometrician_n