they_o be_v to_o be_v use_v be_v that_o which_o we_o call_v philosophiaprima_fw-la it_o be_v not_o the_o work_n of_o a_o geometrician_n as_o a_o geometrician_n to_o define_v what_o be_v equality_n or_o proportion_n or_o any_o other_o word_n he_o use_v though_o it_o be_v the_o work_n of_o the_o same_o man_n as_o a_o man_n his_o geometrical_a part_n be_v to_o draw_v from_o they_o as_o many_o true_a and_o useful_a theorem_n as_o he_o can_v you_o object_n second_o that_o a_o pyramid_n may_v be_v equal_a to_o a_o cube_n whilst_o it_o be_v a_o pyramid_n true_o and_o so_o also_o whilst_o it_o be_v a_o pyramid_n it_o have_v a_o possibility_n by_o flexion_n and_o transposition_n of_o part_n to_o become_v a_o cube_n and_o to_o be_v put_v into_o the_o place_n where_o another_o cube_n equal_a to_o it_o be_v before_o this_o be_v to_o argue_v like_o a_o child_n that_o have_v not_o yet_o the_o perfect_a understanding_n of_o any_o language_n in_o the_o three_o and_o four_o objection_n you_o teach_v i_o to_o define_v equal_a body_n it_o i_o will_v needs_o define_v they_o by_o place_n by_o the_o equality_n of_o place_n and_o to_o say_v that_o body_n be_v equal_a that_o have_v equal_a place_n teach_v other_o if_o you_o can_v to_o measure_v their_o grain_n not_o by_o the_o same_o but_o equal_a bushel_n in_o the_o five_o objection_n you_o except_v against_o the_o word_n can_v in_o that_o i_o say_v that_o body_n be_v equal_a which_o can_v fill_v the_o same_o place_n for_o the_o great_a body_n can_v you_o say_v fill_v the_o place_n of_o the_o less_o though_o not_o reciprocal_o the_o less_o of_o the_o great_a it_o be_v true_a that_o though_o the_o place_n of_o the_o less_o can_v never_o be_v the_o place_n of_o the_o great_a r_o yet_o it_o may_v be_v fill_v by_o a_o part_n of_o the_o great_a but_o it_o be_v not_o then_o the_o great_a body_n that_o fill_v the_o place_n of_o the_o less_o but_o a_o part_n of_o it_o that_o be_v to_o say_v a_o less_o body_n howsoever_o to_o take_v away_o from_o simple_a man_n this_o straw_n they_o stumble_v at_o i_o have_v now_o put_v the_o definition_n of_o equal_a body_n into_o these_o word_n equal_a body_n be_v those_o whereof_o every_o one_o can_v fill_v the_o place_n of_o every_o other_o and_o if_o my_o definition_n displease_v you_o propound_v your_o own_o either_o of_o equal_a body_n or_o of_o equal_n simple_o but_o you_o have_v none_o take_v therefore_o this_o of_o i_o the_o six_o be_v a_o very_a admirable_a exception_n what_o say_v you_o if_o the_o same_o body_n can_v sometime_o take_v up_o a_o great_a sometime_o a_o lesser_a place_n as_o by_o rarefaction_n and_o condensation_n i_o understand_v very_o well_o that_o body_n may_v be_v sometime_o thin_a and_o sometime_o thick_a as_o they_o chance_v to_o stand_v close_o together_o or_o further_o from_o one_o another_o so_o in_o the_o mathematick-school_n when_o you_o read_v your_o learned_a lecture_n you_o have_v a_o thick_a or_o throng_a audience_n of_o disciple_n which_o in_o a_o great_a church_n will_v be_v but_o a_o very_a thin_a company_n i_o understand_v how_o thick_a and_o thin_a may_v be_v attribute_v to_o body_n in_o the_o plural_a as_o to_o a_o company_n but_o i_o understand_v not_o how_o any_o one_o of_o they_o be_v thick_a in_o the_o school_n then_o in_o the_o church_n or_o how_o any_o one_o of_o they_o take_v up_o a_o great_a room_n in_o the_o school_n when_o he_o can_v get_v in_o then_o in_o the_o street_n for_o i_o conceive_v the_o dimension_n of_o the_o body_n and_o of_o the_o place_n whether_o the_o place_n be_v fill_v with_o gold_n or_o with_o air_n to_o be_v coincident_a and_o the_o same_o and_o consequent_o both_o the_o quantity_n of_o the_o air_n and_o the_o quantity_n of_o the_o gold_n to_o be_v several_o equal_a to_o the_o quantity_n of_o the_o place_n and_o therefore_o also_o by_o the_o first_o axiom_n of_o euclid_n equal_a to_o one_o another_o insomuch_o as_o if_o the_o same_o air_n shall_v be_v by_o condensation_n contain_v in_o a_o part_n of_o the_o place_n it_o have_v the_o dimension_n of_o it_o will_v be_v the_o same_o with_o the_o dimension_n of_o part_n of_o the_o place_n that_o be_v shall_v be_v less_o than_o they_o be_v and_o by_o consequence_n the_o quantity_n less_o and_o then_o either_o the_o same_o body_n must_v be_v less_o also_o or_o we_o must_v make_v a_o difference_n between_o great_a body_n and_o body_n of_o great_a quantity_n which_o no_o man_n do_v that_o have_v not_o lose_v his_o wit_n by_o trust_v they_o with_o absurd_a teacher_n when_o you_o receive_v salary_n if_o the_o steward_n give_v you_o for_o every_o shilling_n a_o piece_n of_o six_o penny_n and_o then_o say_v every_o shilling_n be_v condense_v into_o the_o room_n of_o a_o six_o penny_n i_o believe_v you_o will_v like_v this_o doctrine_n of_o you_o much_o the_o worse_o you_o see_v how_o by_o your_o ignorance_n you_o confound_v the_o affair_n of_o mankind_n as_o far_o forth_o as_o they_o give_v credit_n to_o your_o opinion_n though_o it_o be_v but_o little_a for_o nature_n abhor_v even_o empty_a word_n such_o as_o be_v in_o the_o meaning_n you_o assign_v they_o rarefy_v and_o condense_v and_o you_o will_v be_v as_o well_o understand_v if_o you_o shall_v say_v coin_v word_n by_o your_o own_o power_n that_o the_o same_o body_n may_v take_v up_o sometime_o a_o great_a sometime_o a_o lesser_a place_n by_o wallifaction_n and_o wardensation_n as_o by_o rarefaction_n and_o condensation_n you_o see_v how_o admirable_a this_o your_o objection_n be_v in_o the_o seven_o objection_n you_o bewray_v another_o kind_n of_o ignorance_n which_o be_v the_o ignorance_n of_o what_o be_v the_o proper_a work_n of_o the_o several_a part_n of_o philosophy_n though_o it_o be_v out_o of_o doubt_n say_v you_o that_o the_o same_o body_n can_v have_v several_a magnitude_n yet_o see_v it_o be_v matter_n of_o natural_a philosophy_n nor_o have_v any_o thing_n to_o do_v with_o the_o present_a business_n to_o what_o purpose_n be_v it_o to_o mention_v it_o in_o a_o mathematical_a definition_n it_o seem_v by_o this_o that_o all_o this_o while_o you_o think_v it_o be_v a_o piece_n of_o the_o geometry_n of_o euclid_n no_o less_o to_o make_v the_o definition_n he_o use_v then_o to_o infer_v from_o they_o the_o theorem_n he_o demonstrate_v which_o be_v not_o true_a for_o he_o that_o tell_v you_o in_o what_o sense_n you_o be_v to_o take_v the_o appelation_n of_o those_o thing_n which_o he_o name_v in_o his_o discourse_n teach_v you_o but_o his_o language_n that_o afterward_o he_o may_v teach_v you_o his_o art_n but_o teach_v of_o language_n be_v not_o mathematic_a nor_o logic_n nor_o physic_n nor_o any_o other_o science_n and_o therefore_o to_o call_v a_o definition_n as_o you_o do_v mathematical_a or_o physical_a be_v a_o mark_n of_o ignorance_n in_o a_o professor_n unexcusable_a all_o doctrine_n begin_v at_o the_o understanding_n of_o word_n and_o proceed_v by_o reason_v till_o it_o conclude_v in_o science_n he_o that_o will_v learn_v geometry_n must_v understand_v the_o term_n before_o he_o begin_v which_o that_o he_o may_v do_v the_o master_n demonstrate_v nothing_o but_o use_v his_o natural_a prudence_n only_o as_o all_o man_n do_v when_o they_o endeavour_v to_o make_v their_o meaning_n clear_o know_v for_o word_n understand_v be_v but_o the_o seed_n and_o no_o part_n of_o the_o harvest_n of_o philosophy_n and_o this_o seed_n be_v it_o which_o aristotle_n go_v about_o to_o sow_v in_o his_o twelve_o book_n of_o metaphysic_n and_o in_o his_o eight_o book_n concern_v the_o hear_n of_o natural_a philosophy_n and_o in_o these_o book_n he_o define_v time_n place_n substance_n or_o essence_n quantity_n relation_n etc._n etc._n that_o from_o thence_o may_v be_v take_v the_o definition_n of_o the_o most_o general_a word_n for_o principle_n in_o the_o several_a part_n of_o science_n so_o that_o all_o definition_n proceed_v from_o common_a understanding_n of_o which_o it_o any_o man_n right_o write_v he_o may_v proper_o call_v his_o writing_n philosophia_fw-la prima_fw-la that_o be_v the_o seed_n or_o the_o ground_n of_o philosophy_n and_o this_o be_v the_o method_n i_o have_v use_v define_v place_n magnitude_n and_o the_o other_o the_o most_o general_a appellation_n in_o that_o part_n which_o i_o entitle_v philosophia_fw-la prima_fw-la but_o you_o now_o not_o understand_v this_o talk_v of_o mathematical_a definition_n you_o will_v say_v perhaps_o that_o other_o do_v the_o same_o as_o well_o as_o you_o it_o may_v be_v so_o but_o the_o appeach_v of_o other_o do_v not_o make_v your_o ignorance_n the_o less_o in_o the_o eight_o place_n you_o object_n not_o but_o ask_v i_o why_o i_o define_v equal_a body_n apart_o i_o will_v tell_v you_o because_o all_o other_o thing_n which_o be_v say_v
touch_v by_o a_o straight_a line_n the_o angle_n of_o contingence_n will_v neither_o add_v any_o thing_n to_o nor_o take_v any_o thing_n from_o a_o rectilineall_a right_a angle_n but_o that_o it_o be_v because_o the_o angle_n of_o contact_n be_v no_o angle_n or_o no_o quantity_n be_v not_o true_a for_o it_o be_v therefore_o a_o angle_n because_o a_o angle_n of_o contact_n and_o therefore_o quantity_n because_o one_o angle_n of_o contact_n may_v be_v great_a than_o another_o and_o therefore_o heterogeneal_a because_o the_o measure_n of_o a_o angle_n of_o contact_n can_v congruere_fw-la be_v apply_v to_o the_o measure_n of_o a_o rectilineall_a angle_n as_o they_o think_v it_o may_v who_o affirm_v with_o you_o that_o the_o nature_n of_o a_o angle_n consist_v in_o that_o which_o be_v contain_v between_o the_o line_n that_o comprehend_v it_o viz._n in_o a_o plain_a superficies_n and_o thus_o you_o see_v in_o how_o few_o line_n and_o without_o bâ—achygraphie_n your_o treatise_n of_o the_o angle_n of_o contingence_n be_v discover_v for_o the_o great_a part_n to_o be_v false_a and_o for_o the_o rest_n nothing_o but_o a_o detection_n of_o some_o error_n of_o clavius_n ground_v on_o the_o same_o false_a principle_n with_o your_o own_o to_o return_v now_o from_o your_o treatise_n of_o the_o angle_n of_o contact_n back_o again_o to_o your_o elenchus_n the_o fault_n you_o find_v at_o art_n 18._o be_v that_o i_o understand_v not_o that_o euclid_n make_v a_o plain_a angle_n to_o be_v that_o which_o be_v contain_v between_o the_o two_o line_n that_o form_n it_o it_o be_v true_a that_o i_o do_v not_o understand_v that_o euclid_n be_v so_o absurd_a as_o to_o think_v the_o nature_n of_o a_o angle_n to_o consist_v in_o superficies_n but_o i_o understand_v that_o you_o have_v not_o have_v the_o wit_n to_o understand_v euclid_n the_o nineteen_o article_n of_o i_o in_o this_o fourteen_o chapter_n be_v this_o all_o respect_n or_o variety_n of_o position_n of_o two_o line_n seem_v to_o be_v comprehend_v in_o four_o kind_n for_o they_o be_v either_o parallel_n or_o be_v if_o need_v be_v produce_v make_v a_o angle_n or_o if_o draw_v out_o fair_a enough_o touch_v or_o last_o they_o be_v asymptotes_n in_o which_o you_o be_v first_o offend_v with_o the_o word_n it_o seem_v but_o i_o allow_v you_o that_o never_o err_v to_o be_v more_o peremptory_a than_o i_o be_o for_o to_o i_o it_o seem_v i_o say_v again_o seem_v that_o such_o a_o phrase_n in_o case_n i_o shall_v leave_v out_o something_o in_o the_o enumeration_n of_o the_o several_a kind_n of_o position_n will_v save_v i_o from_o be_v censure_v for_o untruth_n and_o yet_o your_o instance_n of_o two_o straight_a line_n in_o divers_a plain_n do_v not_o make_v my_o enumeration_n insufficient_a for_o those_o line_n though_o not_o parallel_n nor_o cut_v both_o the_o plain_n yet_o be_v move_v parallel_o from_o one_o plain_a to_o another_o will_v fall_v into_o one_o or_o other_o of_o the_o kind_n of_o position_n by_o i_o enumerate_v and_o consequent_o be_v as_o much_o that_o position_n as_o two_o straight_a line_n in_o the_o same_o plain_a not_o parallel_n make_v the_o same_o angle_n though_o not_o produce_v till_o they_o meet_v which_o they_o will_v make_v if_o they_o be_v so_o produce_v for_o you_o have_v no_o where_o prove_v nor_o can_v prove_v that_o two_o such_o line_n do_v not_o make_v a_o angle_n it_o be_v not_o the_o actual_a concurrence_n of_o the_o line_n but_o the_o arch_n of_o a_o circle_n draw_v upon_o that_o point_n for_o centre_n in_o which_o they_o will_v meet_v if_o they_o be_v produce_v and_o intercept_v between_o they_o that_o constitute_v the_o angle_n also_o your_o objection_n concern_v asymptotes_n in_o general_a be_v absurd_a you_o will_v have_v i_o add_v that_o their_o distance_n shall_v at_o last_o be_v 〈◊〉_d then_o any_o distance_n that_o can_v be_v assign_v and_o so_o make_v the_o definition_n of_o the_o genus_fw-la the_o same_o with_o that_o of_o the_o species_n but_o because_o you_o be_v not_o professor_n of_o logic_n it_o be_v not_o necessary_a for_o i_o to_o follow_v your_o council_n in_o like_a manner_n if_o we_o understand_v one_o line_n to_o be_v move_v towards_o another_o always_o paralle_o to_o its_o self_n which_o be_v though_o not_o actual_o yet_o potential_o the_o same_o position_n all_o the_o rest_n of_o your_o instance_n will_v come_v to_o nothing_o at_o the_o two_o and_o twenty_o article_n you_o object_n to_o i_o the_o use_n of_o the_o word_n figure_n before_o i_o have_v define_v it_o wherein_o also_o you_o do_v absurd_o for_o i_o have_v no_o where_o before_o make_v such_o use_n of_o the_o word_n figure_n as_o to_o argue_v any_o thing_n from_o it_o and_o therefore_o your_o objection_n be_v just_a as_o wise_a as_o if_o you_o have_v round_a fault_n with_o put_v the_o word_n figure_n in_o the_o title_n of_o the_o chapter_n place_v before_o the_o book_n if_o you_o have_v know_v the_o nature_n of_o demonstration_n you_o have_v not_o object_v this_o you_o add_v further_o that_o by_o my_o definition_n of_o figure_n a_o solid_a sphere_n and_o a_o sphere_n make_v hollow_a within_o be_v the_o same_o figure_n but_o you_o say_v not_o why_o nor_o can_v you_o â—â—â—iver_v any_o such_o thing_n from_o my_o definition_n that_o which_o deceive_v your_o shallowness_n be_v that_o you_o take_v those_o point_n that_o be_v in_o the_o concave_a superficies_n of_o a_o hollow_a sphere_n not_o to_o be_v contiguous_a to_o any_o thing_n without_o it_o because_o that_o whole_a concave_a superficies_n be_v within_o the_o whole_a sphere_n last_o for_o the_o fault_n you_o find_v with_o the_o definition_n of_o like_a figure_n in_o like_a position_n i_o confess_v there_o want_v the_o same_o word_n which_o be_v want_v in_o the_o definition_n of_o parallel_n namely_o ad_fw-la easdem_fw-la part_n the_o same_o way_n which_o shall_v have_v be_v add_v in_o the_o end_n of_o the_o definition_n of_o like_a figure_n etc._n etc._n and_o may_v easy_o be_v supply_v by_o any_o student_n of_o geometry_n that_o be_v not_o otherwise_o a_o fool_n at_o the_o fifteen_o chapter_n art_n 1._o numb_a 6._o you_o object_n as_o a_o contradiction_n that_o i_o make_v motion_n to_o be_v the_o measure_n of_o time_n and_o yet_o in_o other_o place_n do_v usual_o measure_v motion_n and_o the_o affection_n thereof_o by_o time_n if_o your_o thought_n be_v your_o own_o and_o not_o take_v rash_o out_o of_o book_n you_o can_v not_o but_o with_o all_o man_n else_o that_o see_v time_n measure_v by_o clock_n dial_n hour-glass_n and_o the_o like_a have_v conceive_v sufficient_o that_o there_o can_v be_v of_o time_n any_o other_o measure_n beside_o motion_n and_o that_o the_o most_o universal_a measure_n of_o motion_n be_v a_o line_n describe_v by_o some_o other_o motion_n which_o line_n be_v once_o expose_v to_o sense_n and_o the_o motion_n whereby_o it_o be_v describe_v sufficient_o explicate_v will_v serve_v to_o measure_v all_o other_o motion_n and_o their_o time_n for_o time_n and_o motion_n time_n be_v but_o the_o mental_a image_n or_o remembrance_n of_o the_o motion_n have_v but_o one_o and_o the_o same_o dimension_n which_o be_v a_o line_n but_o you_o that_o will_v have_v i_o measure_v swiftness_n and_o slowness_n by_o long_a and_o short_a motion_n what_o do_v you_o mean_v by_o long_a and_o short_a motion_n be_v long_o and_o short_a in_o the_o motion_n or_o in_o the_o duration_n of_o the_o motion_n which_o be_v time_n or_o be_v the_o motion_n or_o the_o duration_n of_o the_o motion_n that_o which_o be_v expose_v or_o design_v by_o a_o line_n geometrician_n say_v often_o let_v the_o line_n a_o b_o be_v the_o time_n but_o never_o say_v let_v the_o line_n a_o b_o be_v the_o motion_n there_o be_v no_o unlearned_a man_n that_o understand_v not_o what_o be_v time_n and_o motion_n and_o measure_n and_o yet_o you_o that_o undertake_v to_o teach_v it_o most_o egregious_a professor_n understand_v it_o not_o at_o the_o second_o article_n you_o bring_v another_o argument_n which_o it_o seem_v in_o its_o proper_a place_n you_o have_v forget_v to_o prove_v that_o a_o point_n be_v not_o quantity_n not_o consider_v but_o absolute_o nothing_o which_o be_v this_o that_o if_o a_o point_n be_v not_o nothing_o than_o the_o whole_a be_v great_a than_o its_o two_o half_n how_o do_v that_o follow_v be_v it_o impossible_a when_o a_o line_n be_v divide_v into_o two_o half_n that_o the_o middle_a point_n shall_v be_v divide_v into_o two_o half_n also_o be_v quantity_n at_o the_o seven_o article_n i_o have_v sufficient_o demonstrate_v that_o all_o motion_n be_v infinite_o propagate_v as_o far_o as_o space_n be_v fill_v with_o body_n you_o allege_v no_o fault_n in_o the_o demonstration_n but_o object_n from_o sense_n that_o the_o skip_n of_o a_o flea_n be_v not_o
n_o and_o let_v the_o inteâ—â—â—ction_n of_o the_o two_o line_n a_o c_o and_o d_o o_fw-fr be_v in_o r_o which_o be_v do_v the_o triangle_n m_o n_o t_o r_o c_o t_o will_v be_v like_a and_o equal_a therefore_o m_z n_o and_o r_o c_o be_v equal_a and_o â—…sequently_o the_o strait_a line_n i_o m_o t_o u_o shall_v pass_v through_o c._n divide_v therefore_o a_o c_o in_o the_o midst_n at_o it_o and_o s_o n_o in_o the_o midst_n at_o l_o and_o join_v to_o n_o l_o l_o the_o line_n l_o l_o t_o n_o and_o c_o t_o produce_v with_o all_o meet_a i_o 〈◊〉_d one_o and_o the_o same_o point_n of_o b_o s_o produce_v suppose_v at_o q._n therefore_o the_o point_n q_o be_v give_v by_o the_o two_o know_a point_n t_o and_o i_o the_o line_n draw_v from_o q_o through_o equal_a part_n of_o the_o sine_fw-la of_o the_o arch_n b_o i_o for_o example_n through_o the_o point_n p_o q_o r_o of_o the_o sine_fw-la m_o i_o shall_v cut_v off_o equal_a arch_n as_o b_o l_o l_o n_o n_o o_o o_o i._n and_o this_o be_v enough_o to_o make_v good_a that_o problem_n as_o to_o your_o objection_n the_o straight_a line_n therefore_o b_o u_o for_o any_o thing_n you_o have_v say_v be_v prove_v equal_a to_o the_o arch_n b_o i_o and_o the_o division_n of_o any_o angle_n give_v into_o any_o proportion_n give_v the_o quadrature_n of_o any_o sector_n and_o the_o construction_n of_o any_o equilateral_a pâ—lygon_n be_v also_o give_v and_o though_o in_o this_o also_o i_o shall_v have_v err_v yet_o it_o can_v be_v deny_v but_o that_o i_o have_v use_v a_o more_o natural_a a_o more_o geometrical_a and_o a_o more_o perspicuous_a method_n in_o thes_n search_n of_o this_o so_o difficult_a a_o problem_n than_o you_o have_v do_v in_o your_o arithmetica_fw-la infinitorum_fw-la for_o though_o it_o be_v true_a that_o the_o aggregate_v of_o all_o the_o mean_a proportional_n between_o the_o radius_fw-la together_o with_o a_o infinite_o little_a part_n of_o the_o same_o and_o the_o radius_fw-la want_v a_o infinite_o little_a part_n of_o the_o same_o and_o again_o between_o the_o radius_fw-la together_o with_o two_o infinite_o little_a part_n and_o the_o radius_fw-la want_v two_o infinite_o little_a part_n and_o so_o on_o eternal_o will_v be_v equal_a to_o the_o quadrant_n a_o thing_n which_o every_o mean_a geometrician_n know_v before_o yet_o it_o be_v absurd_a to_o think_v those_o mean_n can_v be_v calculate_v in_o number_n by_o interpol_v of_o a_o symbol_n especial_o when_o you_o make_v that_o symbol_n to_o stand_v for_o a_o numbet_n neither_o true_a nor_o surd_a as_o if_o there_o be_v a_o number_n that_o can_v neither_o be_v utter_v in_o word_n nor_o not_o be_v utter_v in_o word_n for_o what_o else_o be_v surd_a but_o that_o which_o can_v be_v speak_v to_o the_o five_o article_n though_o your_o discourse_n be_v long_o you_o object_v but_o two_o thing_n one_o be_v that_o whereas_o the_o spirall_n of_o a_o chiâ—edes_n be_v make_v of_o two_o motion_n one_o straight_o the_o other_o circular_a both_o uniform_a i_o take_v the_o motion_n compound_v of_o they_o both_o for_o one_o of_o those_o that_o be_v compound_v conclude_v false_o that_o the_o generation_n of_o the_o spirall_n be_v like_a to_o the_o generation_n of_o the_o parabola_fw-la what_o heed_n you_o use_v to_o take_v in_o your_o reprehension_n appear_v most_o manifest_o in_o this_o objection_n for_o i_o say_v in_o that_o demonstration_n of_o i_o that_o the_o velocity_n of_o the_o point_n a_o in_o describe_v the_o spirall_n increase_v continual_o in_o proportion_n to_o the_o time_n for_o see_v it_o go_v on_o uniform_o in_o the_o semidiameter_n it_o be_v impossible_a it_o shall_v not_o pass_v into_o great_a and_o great_a circle_n proportional_o to_o the_o time_n and_o consequent_o it_o must_v have_v a_o swift_a and_o swift_a motion_n circular_a to_o be_v compound_v with_o the_o uniform_a motion_n in_o every_o point_n of_o the_o radius_fw-la as_o it_o turn_v about_o this_o objection_n therefore_o be_v nothing_o but_o a_o effect_n of_o a_o will_v without_o cause_n to_o contradict_v the_o other_o objection_n be_v that_o grant_v all_o to_o be_v true_a hitherto_o yet_o because_o it_o depend_v upon_o the_o find_n of_o a_o straight_a line_n equal_a to_o a_o parabolicâ—ll_a line_n in_o the_o 18_o chapter_n where_o i_o be_v deceive_v i_o be_o also_o deceive_v here_o true_a but_o because_o in_o the_o 18_o chapter_n of_o this_o english_a eâ—ition_n i_o have_v find_v a_o straight_a line_n equal_a to_o a_o parabolicall_a line_n i_o have_v also_o find_v a_o straight_a line_n equal_a to_o the_o spirall_n line_n of_o archimeâ—â—s_n i_o must_v here_o pâ—t_v you_o in_o mind_n that_o by_o these_o word_n in_o your_o objection_n to_o the_o five_o article_n at_o your_o number_n 2_o quatenus_fw-la verum_fw-la â—st_fw-la etc._n etc._n we_o have_v demonstrate_v prop._n 10_o 11_o 13._o arithmet_n infinite_a you_o make_v it_o appear_v that_o you_o think_v your_o spirall_n make_v of_o arche_n or_o circle_n be_v the_o true_a spirall_n of_o archimedes_n which_o be_v full_o â—s_v absurd_a as_o the_o quadrature_n of_o joseph_n scaliger_n who_o geometry_n you_o so_o much_o dâ—spise_v to_o the_o six_o article_n which_o be_v a_o digression_n concern_v the_o analytiques_n of_o geometrician_n you_o deny_v that_o the_o efficient_a cause_n of_o the_o construction_n ought_v to_o be_v contain_v in_o the_o demonstration_n as_o if_o any_o problem_n can_v be_v know_v to_o be_v true_o do_v otherwise_o then_o by_o know_v first_o how_o that_o be_v to_o say_v by_o what_o efficient_a cause_n and_o in_o what_o manner_n it_o be_v to_o be_v do_v whatsoever_o be_v do_v without_o that_o knowledge_n can_v be_v demonstrate_v to_o be_v do_v as_o you_o see_v in_o your_o computation_n of_o the_o parabola_fw-la and_o parabolocides_n in_o your_o arithmetica_fw-la infinitorum_fw-la and_o whereas_o i_o say_v that_o the_o end_n of_o all_o straight_a line_n draw_v from_o a_o straight_a line_n and_o pass_v through_o one_o and_o the_o same_o point_n if_o their_o part_n be_v proportional_a shall_v be_v in_o aâ—…aight_a line_n be_v true_a and_o accurate_a as_o also_o if_o they_o begin_v in_o the_o circumference_n of_o a_o circle_v they_o 〈◊〉_d also_o be_v in_o the_o circumference_n of_o another_o circle_n and_o so_o be_v this_o if_o the_o proportion_n be_v duplicate_v they_o shall_v be_v in_o a_o parabola_fw-la all_o this_o i_o say_v be_v true_a and_o accurate_o speak_v but_o this_o be_v no_o place_n for_o the_o demonstration_n of_o it_o other_o have_v do_v it_o and_o i_o perceive_v by_o that_o you_o put_v in_o by_o parenthesis_n intelligiâ—_n credo_fw-la inter_fw-la â—duâ—s_fw-la peripheriâ—â—_n concentrics_n that_o you_o understand_v not_o what_o i_o mean_v hitherto_o reach_v your_o objection_n to_o my_o geometry_n for_o the_o rest_n of_o your_o book_n it_o contain_v nothing_o but_o a_o collection_n of_o lie_n wherewith_o you_o do_v what_o you_o can_v to_o extenuate_v as_o vulgar_a and_o disgrace_n as_o false_a that_o which_o follow_v and_o to_o which_o you_o have_v make_v no_o special_a objection_n i_o shall_v therefore_o only_o add_v in_o this_o place_n concern_v your_o analytica_fw-la per_fw-la potestates_fw-la that_o it_o be_v no_o art_n for_o the_o rule_n both_o in_o mr._n ougthred_n and_o in_o des_n cartes_n be_v this_o when_o a_o problem_n or_o question_n be_v propound_v suppose_v the_o thing_n require_v do_v and_o then_o use_v a_o fit_a ratiocination_n put_v a_o or_o some_o other_o vowel_n for_o the_o magnitude_n seek_v how_o be_v a_o man_n the_o better_a for_o this_o rule_n without_o another_o rule_n how_o to_o know_v when_o the_o ratiocinatión_n be_v fit_a there_o may_v therefore_o be_v in_o this_o kind_n of_o analysis_n more_o or_o less_o natural_a prudence_n according_a as_o the_o analyst_n be_v more_o or_o less_o wisâ—_n or_o as_o one_o man_n in_o choose_v of_o the_o unknown_a quantity_n with_o which_o he_o will_v begin_v or_o in_o choose_v the_o way_n of_o the_o consequence_n which_o he_o will_v draw_v from_o the_o hypothesis_n may_v have_v better_a luck_n than_o another_o but_o this_o be_v nothing_o to_o art_n a_o man_n may_v sometime_o spend_v a_o whole_a day_n in_o derive_v of_o consequence_n in_o vain_a and_o perhaps_o another_o time_n solve_v the_o same_o problem_n in_o a_o few_o minute_n i_o shall_v also_o add_v that_o symbol_n though_o they_o shorten_v the_o writing_n yet_o they_o do_v not_o make_v the_o reader_n understand_v it_o sooner_o than_o if_o it_o be_v write_v in_o word_n for_o the_o conception_n of_o the_o line_n and_o figure_n without_o which_o a_o man_n learn_v nothing_o must_v proceed_v from_o word_n either_o speak_v or_o think_v upon_o so_o that_o there_o be_v a_o double_a labour_n of_o the_o mind_n one_o to_o reduce_v your_o symbol_n to_o word_n which_o be_v also_o symbol_n another_o to_o attend_v
your_o book_n of_o geometry_n the_o expectation_n of_o that_o which_o shall_v be_v write_v by_o i_o be_v raise_v partly_o by_o the_o cogitata_fw-la physico-mathematica_a of_o mersennus_n wherein_o i_o be_o often_o name_v with_o honour_n and_o partly_o by_o other_o with_o who_o i_o then_o converse_v in_o paris_n without_o any_o ostentation_n that_o no_o man_n have_v a_o great_a expectation_n of_o any_o thing_n that_o shall_v proceed_v from_o either_o of_o you_o two_o i_o be_o content_a to_o let_v it_o be_v your_o praise_n another_o argument_n of_o my_o self-conceit_n you_o take_v from_o my_o contempt_n of_o the_o writer_n of_o metaphysic_n and_o school-divinity_n if_o that_o be_v a_o sign_n of_o self-conceit_n i_o must_v confess_v i_o be_o guilty_a and_o if_o your_o geometry_n have_v then_o be_v publish_v i_o have_v contemn_v that_o as_o much_o but_o yet_o i_o can_v see_v the_o consequence_n unless_o you_o lend_v i_o your_o better_a logic_n from_o despise_v insignificant_a and_o absurd_a language_n to_o self-conceit_n and_o again_o in_o your_o vindiciae_fw-la academiarum_fw-la you_o put_v for_o boast_v that_o in_o my_o leviathan_n pag._n 180._o i_o will_v have_v that_o book_n by_o entire_a sovereignty_n impose_v upon_o the_o university_n and_o in_o my_o review_n pag._n 395._o that_o i_o say_v of_o my_o leviathan_n i_o think_v it_o mâ—y_v be_v profitable_o print_v and_o more_o profitable_o teach_v in_o the_o university_n the_o cause_n of_o my_o writing_n that_o book_n be_v the_o consideration_n of_o what_o the_o minister_n before_o and_o in_o the_o begin_n of_o the_o civil_a war_n by_o their_o preach_n and_o write_v do_v contribute_v thereunto_o which_o i_o see_v not_o only_o to_o â—end_n to_o the_o abatement_n of_o the_o then_o civil_a power_n but_o also_o to_o the_o gain_n of_o as_o much_o thereof_o as_o they_o can_v as_o do_v afterwards_o more_o plain_o appear_v unto_o themselves_o i_o see_v also_o that_o those_o minister_n and_o many_o other_o gentleman_n who_o be_v of_o their_o opinion_n bring_v their_o doctrine_n against_o the_o civil_a power_n from_o their_o study_n in_o the_o university_n see_v therefore_o that_o so_o much_o as_o can_v be_v contribute_v to_o the_o peace_n of_o our_o country_n and_o the_o settlement_n of_o sovereign_a power_n without_o any_o army_n must_v proceed_v from_o teach_v i_o have_v reason_n to_o wish_v that_o civil_a doctrine_n be_v true_o teach_v in_o the_o university_n and_o if_o i_o have_v not_o think_v that_o i_o be_v such_o i_o have_v never_o write_v it_o and_o have_v write_v it_o if_o i_o have_v not_o recommend_v it_o to_o such_o as_o have_v the_o power_n to_o cause_v it_o to_o be_v teach_v i_o have_v write_v it_o to_o no_o purpose_n to_o i_o therefore_o that_o never_o do_v write_v any_o thing_n in_o philosophy_n to_o show_v my_o wit_n but_o as_o i_o think_v at_o least_o to_o benefit_v some_o part_n or_o other_o of_o mankind_n it_o be_v very_o necessary_a to_o commend_v my_o doctrine_n to_o such_o man_n as_o shall_v have_v the_o power_n and_o right_o to_o regulate_v the_o university_n i_o say_v my_o doctrine_n i_o say_v not_o my_o leviathan_n for_o wise_a man_n may_v so_o digest_v the_o same_o doctrine_n as_o to_o fit_v it_o better_o for_o a_o public_a teach_n but_o as_o it_o be_v i_o believe_v it_o have_v frame_v the_o mine_n of_o a_o thousand_o gentleman_n to_o a_o conscientious_a obedience_n to_o present_a government_n which_o otherwise_o will_v have_v waver_v in_o that_o point_n this_o therefore_o be_v no_o vaunt_a but_o a_o necessary_a part_n of_o the_o business_n i_o take_v in_o hand_n you_o ought_v also_o to_o have_v consider_v that_o this_o be_v say_v in_o the_o close_a of_o that_o part_n of_o my_o book_n which_o concern_v policy_n mere_o civil_a which_o part_n if_o you_o the_o astronomer_n that_o noâ—_n think_v the_o doctrine_n unworthy_a to_o be_v teach_v be_v please_v once_o to_o honour_n with_o praise_n print_v before_o it_o you_o be_v not_o very_o constant_a noâ—_n ingenuous_a but_o whether_o you_o do_v so_o or_o not_o i_o be_o not_o curtain_n though_o it_o be_v â—old_a i_o for_o certain_a if_o it_o be_v not_o you_o it_o be_v some_o body_n else_o who_o judgement_n have_v as_o much_o weight_n at_o least_o as_o you_o and_o for_o any_o thing_n you_o have_v to_o say_v from_o your_o own_o knowledge_n i_o remember_v not_o that_o ever_o i_o see_v either_o of_o your_o face_n yet_o you_o the_o professor_n of_o geometry_n go_v about_o oblique_o to_o make_v i_o believe_v that_o vindex_n have_v discourse_v with_o i_o once_o at_o least_o though_o i_o remember_v it_o not_o i_o suppose_v it_o therefore_o true_a but_o this_o i_o be_o sure_a be_v false_a that_o either_o he_o or_o any_o man_n live_v do_v ever_o hear_v i_o brag_v of_o my_o science_n or_o praise_v myself_o but_o when_o my_o defence_n require_v it_o perhaps_o some_o of_o our_o philosopher_n that_o be_v at_o paris_n at_o the_o same_o time_n and_o acquaint_v with_o the_o same_o learned_a man_n that_o i_o be_v acquaint_v with_o may_v take_v for_o brag_v the_o maintain_n of_o my_o opinion_n and_o the_o not_o yield_v to_o the_o â—_z alieadge_v against_o they_o if_o that_o be_v ostentation_n they_o tell_v you_o the_o truth_n but_o you_o that_o be_v so_o wise_a shall_v have_v consider_v that_o even_o such_o man_n as_o profess_v philosophy_n be_v carry_v away_o with_o the_o passion_n of_o emulation_n and_o envy_n the_o sole_a ground_n of_o this_o your_o accusation_n as_o well_o as_o other_o man_n and_o instance_a in_o yourselves_o and_o this_o be_v sufficient_a to_o shake_v off_o your_o aspersion_n â—f_a ostentation_n and_o self-conceit_n for_o if_o i_o add_v that_o my_o acquaintance_n know_v that_o i_o aâ—_n natural_o of_o modest_a rather_o then_o of_o boast_a speech_n you_o will_v not_o believe_v it_o because_o you_o distinguish_v not_o between_o that_o which_o be_v say_v upon_o provocation_n and_o that_o which_o be_v say_v without_o 〈◊〉_d from_o vain_a glory_n the_o next_o accusation_n be_v that_o i_o will_v be_v very_o angry_a with_o all_o man_n that_o do_v not_o present_o submit_v to_o my_o dictate_v and_o that_o for_o advance_v the_o reputation_n of_o my_o own_o skill_n i_o care_v not_o what_o unwoâ—…y_a 〈◊〉_d â—ast_v on_o other_o this_o be_v in_o the_o epistle_n place_v before_o the_o vindiciae_fw-la academiarum_fw-la subscribe_v by_o n_o s_o as_o the_o plain_a song_n for_o h_n d_o in_o the_o rest_n of_o the_o book_n to_o dâ—scant_v upon_o i_o know_v well_o enough_o the_o author_n name_n and_o be_o sorry_a that_o n_o saint_n have_v lend_v his_o name_n to_o be_v abuse_v to_o so_o ill_a a_o pâ—â—posâ—_n but_o how_o do_v this_o appear_v what_o argument_n what_o witness_n be_v tâ—ere_o of_o it_o you_o offer_v noâ—e_o or_o aâ—…_n i_o conscious_a of_o any_o i_o begin_v to_o suspect_v since_o you_o the_o professor_n of_o geometry_n have_v in_o your_o objection_n to_o the_o 20_o chapter_n these_o word_n concern_v vindex_n oâ—ularis_fw-la ille_fw-la testis_fw-la de_fw-la quo_fw-la hâ—c_fw-la agitur_fw-la erat_fw-la ni_fw-fr fallor_fw-la ille_fw-la ipse_fw-la that_o vindex_n himself_o in_o other_o company_n have_v 〈◊〉_d a_o visit_n on_o i_o see_v you_o will_v have_v i_o believe_v it_o let_v it_o be_v so_o and_o as_o it_o be_v likely_a not_o long_o after_o my_o return_n into_o england_n at_o which_o time_n for_o the_o â—â—putation_n it_o seem_v i_o have_v get_v by_o my_o boast_n divers_a person_n that_o profess_v to_o love_v philosophy_n and_o mathematics_n come_v to_o sâ—e_v i_o and_o some_o of_o 〈◊〉_d to_o let_v i_o see_v they_o and_o hear_v and_o applaud_v what_o they_o applaud_v in_o themselves_o i_o see_v now_o it_o have_v happen_v to_o i_o with_o vinâ—ex_n as_o it_o happen_v to_o dr._n harvey_n with_o morâ—…s_n mâ—ranus_n 〈◊〉_d jesuit_n come_v out_o of_o flanders_n hither_o especial_o as_o he_o say_v to_o see_v what_o learned_a man_n in_o divinity_n eâ—â—iâ—ues_n physic_n and_o geometry_n be_v here_o yet_o alive_a to_o the_o end_n 〈◊〉_d by_o discourse_v with_o thâ—m_n in_o these_o science_n he_o may_v correct_v either_o his_o own_o or_o their_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d be_v bâ—ought_v 〈◊〉_d saya_v to_o that_o most_o civil_a and_o renown_a old_a man_n dr._n haâ—vey_n 〈◊〉_d very_a well_o and_o in_o good_a earnest_n if_o he_o have_v make_v good_a use_n of_o the_o time_n which_o be_v uâ—â—y_a 〈◊〉_d afford_v he_o he_o may_v have_v learn_v of_o he_o or_o of_o no_o man_n live_v very_a 〈◊〉_d knowledge_n concern_v the_o circulation_n of_o the_o blood_n the_o generation_n of_o live_a creature_n aâ—d_v mâ—ny_v other_o difficult_a point_n of_o natural_a philosophy_n and_o if_o he_o have_v have_v any_o thing_n in_o he_o but_o common_a and_o childish_a learning_n he_o can_v have_v show_v it_o no_o where_o more_o to_o his_o advantage_n then_o before_o he_o that_o be_v so_o great_a