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to_o be_v equal_a be_v say_v to_o be_v so_o from_o the_o equality_n of_o body_n as_o two_o line_n be_v say_v to_o be_v equal_a when_o they_o be_v coincident_a with_o the_o length_n of_o one_o and_o the_o same_o body_n and_o equal_a time_n which_o be_v measure_v by_o equal_a length_n of_o body_n by_o the_o same_o motion_n and_o the_o reason_n be_v because_o there_o be_v no_o subject_a of_o quantity_n or_o of_o equality_n or_o of_o any_o other_o accident_n but_o body_n all_o which_o i_o think_v certain_o be_v evident_a enough_o to_o any_o uncorrupted_a judgement_n and_o therefore_o that_o i_o need_v first_o to_o define_v equality_n in_o the_o subject_a thereof_o which_o be_v body_n and_o then_o to_o declare_v in_o what_o sense_n it_o be_v attribute_v to_o time_n motion_n and_o other_o thing_n that_o be_v not_o body_n the_o nine_o objection_n be_v a_o egregious_a cavil_n have_v set_v down_o the_o definition_n of_o equal_a body_n i_o consider_v that_o some_o man_n may_v not_o allow_v the_o 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this_o be_v i_o leave_v to_o be_v judge_v by_o any_o reader_n that_o have_v have_v the_o fortune_n to_o see_v the_o world_n and_o converse_v with_o honest_a man_n against_o the_o fourteen_o article_n where_o i_o prove_v that_o the_o same_o body_n have_v always_o the_o same_o magnitude_n you_o object_v nothing_o but_o this_o that_o though_o it_o be_v grant_v that_o the_o same_o boâ—y_n have_v the_o same_o magnitude_n while_o it_o rest_v yet_o i_o bring_v nothing_o to_o prove_v that_o when_o it_o change_v place_n it_o may_v not_o also_o change_v its_o magnitude_n by_o be_v enlarge_v or_o contract_v there_o be_v no_o doubt_n but_o to_o a_o body_n whether_o at_o rest_n or_o in_o motion_n â—oâ—e_v body_n may_v be_v add_v or_o part_n of_o it_o take_v away_o but_o than_o it_o be_v not_o the_o same_o body_n unless_o the_o whole_a and_o the_o part_n be_v all_o one_o it_o the_o school_n have_v not_o set_v your_o wit_n awry_o you_o can_v never_o have_v be_v so_o stupid_a as_o not_o to_o see_v 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quantity_n have_v to_o another_o he_o ask_v how_o great_a or_o how_o little_a the_o one_o be_v comparative_o to_o or_o in_o respect_n of_o the_o other_o when_o a_o geometrician_n prefix_v before_o his_o demonstration_n a_o dâ—â—inition_n he_o do_v it_o not_o as_o a_o part_n of_o his_o geometry_n but_o of_o natural_a evidence_n not_o to_o be_v demonstrate_v by_o argument_n but_o to_o be_v understand_v in_o understand_v the_o language_n wherein_o it_o be_v set_v down_o though_o the_o matter_n may_v nevertheless_o if_o beside_o geometry_n he_o have_v wit_n be_v of_o some_o help_n to_o his_o disciple_n to_o make_v he_o understand_v it_o the_o soon_o but_o when_o there_o be_v no_o significant_a definition_n prefix_v as_o in_o this_o case_n where_o euclides_n definition_n of_o proportion_n that_o it_o be_v a_o whatsâ—iâ—aâ—t_a habituâ—e_n of_o two_o quantity_n etc._n etc._n be_v in_o significant_a and_o you_o allege_v no_o other_o every_o one_o that_o will_v learn_v geometry_n must_v 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simple_o proportion_n have_v consider_v this_o i_o define_v proportion_n chap._n 11._o arti._n 3._o in_o this_o manner_n ratio_fw-la est_fw-la relatio_fw-la antecedentis_fw-la ad_fw-la consequens_fw-la secundum_fw-la magnitudinem_fw-la proportion_n be_v the_o relation_n of_o the_o antecedent_n to_o the_o consequent_a in_o magnitude_n have_v immediate_o before_o define_v relative_n antecedent_n and_o consequent_a in_o the_o same_o article_n and_o by_o way_n of_o explication_n add_v that_o such_o relation_n be_v nothing_o else_o but_o that_o one_o of_o the_o quantity_n be_v equal_a to_o the_o other_o or_o exceed_v it_o by_o some_o quantity_n or_o be_v by_o some_o quantity_n exceed_v by_o it_o and_o for_o exemplification_n of_o the_o same_o i_o add_v further_o that_o the_o proportion_n of_o three_o to_o two_o be_v that_o three_o exceed_v two_o by_o a_o unity_n but_o say_v not_o that_o the_o unity_n or_o
argument_n but_o fall_v into_o a_o loud_a oncethmus_n the_o special_a figure_n wherewith_o you_o grace_v you_o oratory_n offend_v with_o my_o unexpected_a cross_v of_o the_o doctrine_n you_o teach_v that_o proportion_n consist_v it_o a_o quotient_a for_o that_o be_v deny_v you_o your_o come_v to_o nothing_o that_o be_v to_o just_a as_o much_o as_o it_o be_v worth_a but_o be_v not_o you_o very_o simple_a man_n to_o say_v that_o all_o mathematician_n speak_v so_o when_o it_o be_v not_o speak_v when_o do_v you_o see_v any_o man_n but_o yourselves_o publish_v his_o demonstration_n by_o sign_n not_o general_o receive_v except_o it_o be_v not_o with_o intention_n to_o demonstrate_v but_o to_o tâ—â—ch_v the_o use_n of_o sign_n have_v pappus_n no_o analytiques_n or_o want_v he_o the_o wit_n to_o â—…ten_v his_o reckon_n by_o sign_n or_o have_v he_o not_o proceed_v analytical_o in_o a_o hundred_o problem_n especial_o in_o his_o seven_o book_n and_o never_o use_v symbol_n symbol_n be_v poor_a unhandsome_a though_o necessary_a scaffold_n of_o demonstration_n and_o ought_v no_o more_o to_o appear_v in_o public_a than_o the_o most_o dâ—â—â—rmed_a necessary_a business_n which_o you_o do_v in_o your_o chamber_n but_o why_o say_v you_o be_v this_o â—…tion_n to_o the_o proportion_n of_o the_o great_a to_o the_o less_o i_o will_v tell_v you_o because_o iterate_v of_o the_o proportion_n of_o the_o less_o to_o the_o great_a be_v a_o make_n of_o the_o proportion_n less_o and_o the_o defect_n great_a and_o it_o be_v absurd_a to_o say_v that_o the_o take_n of_o the_o same_o quantity_n twice_o shall_v make_v it_o less_o and_o thence_o it_o be_v that_o in_o quantity_n which_o begin_v with_o the_o less_o as_o one_o two_o four_o the_o proportion_n of_o one_o to_o two_o be_v great_a than_o that_o of_o one_o to_o four_o as_o be_v demonstrate_v by_o euclid_n elem._n 5._o prop._n 8._o and_o by_o consequent_a the_o proportion_n of_o one_o to_o four_o be_v a_o proportion_n of_o great_a littleness_n then_o that_o of_o one_o to_o two_o and_o who_o be_v there_o that_o when_o he_o know_v that_o the_o respective_a greatness_n of_o four_o to_o one_o be_v double_a to_o that_o of_o the_o respective_a greatness_n of_o four_o to_o two_o or_o of_o two_o to_o one_o will_v not_o present_o acknowledge_v that_o the_o respective_a greatness_n of_o one_o to_o two_o or_o two_o to_o four_o be_v double_a to_o the_o respective_a greatness_n of_o one_o to_o four_o but_o this_o be_v too_o deep_a for_o such_o man_n as_o take_v their_o opinion_n not_o from_o weigh_v but_o from_o read_v last_o you_o object_n against_o the_o corollary_n of_o art_n 28._o which_o you_o make_v absurd_a enough_o by_o rehearse_v it_o thus_o si_fw-la quantitas_fw-la aliqua_fw-la divisa_fw-la supponatur_fw-la in_o part_n aliquot_fw-la aequales_fw-la numero_fw-la infinitas_fw-la etc._n etc._n do_v you_o think_v that_o of_o part_n aliquot_fw-la or_o of_o part_n aliquotae_n it_o can_v be_v say_v without_o absurdity_n that_o they_o be_v numero_fw-la infinitae_fw-la and_o then_o you_o say_v i_o seem_v to_o mean_v that_o if_o of_o the_o quantity_n ab_fw-la there_o be_v suppose_v a_o part_n cb_n infinite_o little_a and_o that_o between_o ac_fw-la and_o ab_fw-la be_v take_v two_o mean_n one_o arithmetical_a ae_n the_o other_o geometrical_a ad_fw-la the_o difference_n between_o ad_fw-la and_o ae_n will_v be_v infinite_o little_a my_o meaningis_fw-la and_o be_v sufficient_o express_v that_o the_o say_v mean_n take_v every_o where_o not_o in_o one_o place_n only_o will_v be_v the_o same_o throughout_o and_o you_o that_o say_v there_o need_v not_o so_o much_o pain_n to_o prove_v it_o and_o think_v you_o do_v it_o short_a prove_v it_o not_o at_o all_o for_o why_o may_v not_o i_o pretend_v against_o your_o demonstration_n that_o be_v the_o arithmetical_a difference_n be_v great_a than_o bd_o the_o geometrical_a difference_n you_o bring_v nothing_o to_o prove_v it_o and_o if_o you_o suppose_v it_o you_o suppose_v the_o thing_n you_o be_v to_o prove_v hitherto_o you_o have_v proceed_v in_o such_o manner_n with_o your_o elenchus_n as_o that_o so_o many_o objection_n as_o you_o have_v make_v so_o many_o false_a proposition_n you_o have_v advance_v which_o be_v a_o peculiar_a excellence_n of_o you_o that_o for_o so_o great_a a_o stipend_n as_o you_o receive_v you_o will_v give_v place_n to_o no_o man_n live_v for_o the_o number_n and_o grossness_n of_o error_n you_o teach_v your_o scholar_n at_o the_o fourteen_o chapter_n your_o first_o exception_n be_v to_o the_o second_o article_n where_o i_o define_v a_o plain_a in_o this_o manner_n a_o plain_a superficies_n be_v that_o which_o be_v describe_v by_o a_o straight_a line_n so_o move_v as_o that_o every_o point_n thereof_o describe_v a_o several_a straight_a lâ—…_n in_o which_o you_o require_v first_o that_o instead_o of_o describe_v i_o shall_v have_v say_v can_v describe_v why_o do_v you_o not_o require_v of_o euclid_n in_o the_o definition_n of_o a_o cone_n instead_o of_o continetur_fw-la be_v contain_v he_o say_v contineri_fw-la potest_fw-la can_v be_v contain_v it_o i_o tell_v you_o how_o one_o plain_a be_v generate_v can_v you_o apply_v the_o same_o generation_n to_o any_o other_o plain_a but_o you_o object_n that_o the_o plain_a of_o a_o circle_n may_v be_v generate_v by_o the_o motion_n of_o the_o radius_fw-la who_o every_o point_n describe_v not_o a_o straight_o but_o a_o crooked_a line_n wherein_o you_o be_v deceive_v for_o you_o can_v draw_v a_o circle_n though_o you_o can_v draw_v the_o perimeter_n of_o a_o circle_n but_o in_o a_o plain_a already_o generate_v for_o the_o motion_n of_o a_o straight_a line_n who_o one_o point_n rest_v describe_v with_o the_o other_o point_v several_a perimeter_n of_o circle_n may_v as_o well_o describe_v a_o conique_a superficies_n as_o a_o plain_n the_o question_n therefore_o be_v how_o you_o will_v in_o your_o definition_n take_v in_o the_o plain_n which_o must_v be_v generate_v before_o you_o begin_v to_o describe_v your_o circle_n and_o before_o you_o know_v what_o point_n to_o make_v your_o centre_n this_o objection_n therefore_o be_v to_o no_o purpose_n and_o beside_o that_o it_o reflect_v upon_o the_o perfect_a definition_n of_o euclid_n before_o the_o eleven_o element_n it_o can_v make_v good_a his_o definition_n which_o be_v nothing_o worth_a of_o a_o plain_a superficies_n before_o his_o first_o element_n in_o the_o next_o place_n you_o reprehend_v brief_o this_o corollary_n that_o two_o plain_n can_v enclose_v a_o solid_a i_o shall_v indeed_o have_v add_v with_o the_o base_a on_o who_o extreme_n they_o insist_v but_o this_o be_v not_o a_o fault_n to_o be_v ashamed_a of_o for_o any_o man_n by_o his_o own_o understanding_n may_v have_v mend_v my_o expression_n without_o depart_v from_o my_o meaning_n but_o from_o your_o doctrine_n that_o a_o superficies_n have_v no_o thickness_n it_o be_v impossible_a to_o include_v a_o solid_a with_o any_o number_n of_o plain_n whatsoever_o unless_o you_o say_v that_o solid_a be_v include_v which_o nothing_o at_o all_o include_v at_o the_o three_o article_n where_o i_o say_v of_o crooked_a line_n some_o be_v every_o where_o crooked_a and_o some_o have_v part_n not_o crooked_a you_o ask_v i_o what_o crooked_a line_n have_v part_v not_o crooked_a and_o i_o answer_v it_o be_v that_o line_n which_o with_o a_o straight_a line_n make_v a_o rectilineall_a triangle_n but_o this_o you_o say_v can_v stand_v with_o what_o i_o say_v before_o namely_o that_o a_o straight_a and_o crooked_a line_n can_v be_v coincident_a which_o be_v true_a nor_o be_v there_o any_o contradiction_n for_o that_o part_n of_o a_o crooked_a line_n which_o be_v straight_o may_v with_o a_o straight_a line_n be_v coincident_a to_o the_o four_o article_n where_o i_o define_v the_o centre_n of_o a_o circle_n to_o be_v that_o point_n of_o the_o radius_fw-la which_o in_o the_o description_n of_o the_o circle_n be_v unmoved_a you_o object_n as_o a_o contradiction_n that_o i_o have_v before_o define_v a_o point_n to_o be_v the_o body_n which_o be_v move_v in_o the_o description_n of_o a_o line_n foolish_o as_o i_o have_v already_o show_v at_o your_o objection_n to_o chap._n 8._o art_n 12._o but_o at_o the_o six_o article_n where_o i_o say_v that_o crooked_a and_o incongruous_a line_n touch_v one_o another_o but_o in_o one_o point_n you_o make_v a_o cavil_n from_o this_o that_o a_o circle_n may_v touch_v a_o parabola_fw-la in_o two_o point_n tell_v i_o true_o do_v you_o read_v and_o understand_v these_o word_n that_o follow_v a_o crooked_a line_n can_v be_v congruent_a with_o a_o straight_a line_n because_o if_o it_o can_v one_o and_o the_o same_o line_n shall_v be_v both_o straight_a and_o crooked_a if_o you_o do_v you_o can_v not_o but_o understand_v the_o sense_n of_o my_o word_n to_o be_v this_o when_o two_o crooked_a line_n which_o
to_o the_o idea_n which_o they_o signify_v beside_o if_o you_o but_o consider_v how_o none_o of_o the_o ancient_n ever_o use_v any_o of_o they_o in_o their_o publish_a demonstration_n of_o geometry_n nor_o in_o their_o book_n of_o arithmetic_n more_o than_o for_o the_o root_n and_o potestates_fw-la themselves_z and_o how_o bad_a success_n you_o have_v have_v yourself_o in_o the_o unskilful_a use_v of_o they_o you_o will_v not_o i_o think_v for_o the_o future_a be_v so_o much_o in_o love_n with_o they_o as_o to_o demonstrate_v by_o they_o that_o first_o part_n you_o promise_v of_o your_o opera_fw-la matheâ—atica_fw-la in_o which_o if_o you_o make_v not_o amends_o for_o that_o which_o you_o have_v already_o publish_v you_o will_v much_o disgrace_v those_o mathematician_n you_o address_v your_o epistle_n to_o or_o otherwise_o have_v commend_v as_o also_o the_o university_n as_o to_o this_o kind_n of_o learning_n in_o the_o sight_n of_o learned_a man_n beyond_o sea_n and_o thus_o have_v 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that_o your_o objection_n against_o it_o be_v but_o so_o many_o error_n of_o your_o own_o proceed_v from_o misunderstanding_n of_o the_o porposition_n you_o have_v read_v in_o euclid_n and_o other_o master_n of_o geometry_n i_o leave_v it_o to_o your_o consideration_n to_o who_o belong_v according_a to_o your_o own_o sentence_n the_o unhandsome_a attribute_n you_o so_o often_o give_v i_o upon_o supposition_n that_o you_o yourselves_o be_v in_o the_o right_n and_o i_o mistake_v and_o come_v now_o to_o purge_v myself_o of_o those_o great_a accusation_n which_o concern_v my_o manner_n it_o can_v be_v expect_v there_o shall_v be_v much_o science_n of_o any_o kind_n in_o a_o man_n that_o want_v judgement_n nor_o judgement_n in_o a_o man_n that_o know_v not_o the_o manner_n due_a to_o a_o public_a disputation_n in_o writing_n wherein_o the_o scope_n of_o either_o party_n ought_v to_o be_v no_o other_o than_o the_o examination_n and_o manifestation_n of_o the_o truth_n for_o whatsoever_o be_v add_v of_o contumely_n eiâ—…er_o direct_o or_o scommatical_o be_v want_n of_o charity_n and_o uncivil_a unless_o it_o be_v do_v by_o way_n of_o reddition_n from_o he_o that_o be_v first_o provoke_v to_o it_o i_o say_v unless_o it_o be_v by_o way_n of_o reddition_n for_o so_o be_v the_o judgement_n give_v by_o the_o emperor_n vespasian_n in_o a_o quarrel_n between_o a_o senato_n and_o a_o knight_n of_o rome_n which_o have_v give_v he_o ill_a language_n for_o when_o the_o knight_n have_v prove_v that_o the_o first_o ill_a language_n proceed_v from_o the_o senator_n the_o emperor_n acquit_v he_o in_o these_o word_n maledici_fw-la senctor_fw-la ibus_fw-la non_fw-la oportere_fw-la remalâ—dicere_fw-la fas_fw-la &_o ciutle_a esse_fw-la nevertheless_o now_o a_o day_n uncivil_a word_n be_v common_o and_o bitter_o use_v by_o all_o that_o write_v in_o matter_n of_o controversy_n especial_o in_o divinity_n except_v now_o and_o then_o such_o writer_n as_o have_v be_v more_o than_o ordinary_o well_o 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confess_v and_o therefore_o i_o must_v as_o well_o as_o i_o can_v seek_v out_o the_o ground_n upon_o which_o you_o build_v your_o accusation_n which_o ground_n see_v you_o be_v not_o acquaint_v with_o my_o conversation_n must_v be_v either_o in_o my_o publish_a write_n or_o report_v to_o you_o by_o honest_a man_n and_o without_o suspicion_n of_o interest_n in_o report_v it_o as_o for_o my_o self-conceit_n and_o ostentation_n you_o shall_v find_v no_o such_o matter_n in_o my_o write_n that_o which_o you_o allege_v from_o thence_o be_v first_o that_o in_o the_o epistle_n dedicatory_a i_o say_v of_o my_o book_n de_fw-fr corpore_fw-la though_o it_o be_v little_a yet_o it_o be_v full_a and_o if_o good_a may_v go_v for_o great_a great_a enough_o when_o a_o man_n present_v a_o gift_n great_a or_o small_a to_o his_o better_n adorn_v it_o the_o best_a he_o can_v to_o make_v it_o the_o more_o acceptable_a he_o that_o think_v this_o to_o be_v ostentation_n and_o self-conceit_n be_v little_o 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