10_o d_o 5_o define_v duplicate_v and_o triplicate_v proportion_n etc._n etc._n in_o this_o manner_n if_o three_o magnitude_n be_v in_o continual_a proportion_n the_o first_o to_o the_o last_o have_v duplicate_v proportion_n of_o what_o it_o have_v to_o the_o second_o if_o four_o triplicate_v etc._n etc._n and_o that_o indifferent_o whether_o the_o first_o or_o last_o be_v the_o big_a now_o you_o that_o you_o may_v show_v yourself_o wise_a than_o euclid_n and_o be_v the_o first_o that_o ever_o make_v the_o ground_n of_o geometry_n firm_a and_o coherent_a think_v it_o be_v to_o be_v limit_v to_o this_o case_n only_o when_o the_o first_o quantity_n be_v the_o great_a and_o therefore_o thus_o define_v the_o proportion_n of_o a_o great_a quantity_n to_o a_o less_o very_o wary_o be_v say_v to_o be_v multiply_v by_o a_o number_n when_o other_o proportion_n equal_a to_o it_o be_v add_v and_o therefore_o if_o the_o quantity_n continue_v in_o the_o same_o proportion_n be_v three_o the_o 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but_o also_o the_o double_a or_o twice_o as_o great_a and_o again_o that_o the_o proportion_n of_o 4_o to_o 6_o be_v double_a to_o the_o proportion_n of_o 4_o to_o 9_o etc._n etc._n which_o will_v have_v deserve_v whip_v at_o another_o time_n but_o because_o he_o say_v the_o rest_n so_o well_o i_o will_v spare_v he_o for_o this_o once_o he_o do_v it_o seem_v believe_v there_o be_v a_o difference_n between_o double_a and_o duplicate_v though_o he_o do_v not_o yet_o know_v what_o it_o be_v he_o will_v learn_v against_o next_o time_n and_o to_o the_o like_a
good_a inference_n we_o be_v teach_v less_o 5._o §_o 43._o as_o stand_v on_o the_o same_o ground_n with_o the_o demonstration_n of_o all_o such_o geometrician_n ancient_a and_o modern_a as_o have_v infer_v any_o thing_n in_o the_o manner_n follow_v viz._n if_o it_o be_v not_o great_a nor_o less_o than_o it_o be_v equal_a but_o it_o be_v neither_o great_a nor_o less_o therefore_o etc._n etc._n if_o it_o be_v great_a say_v by_o how_o much_o by_o so_o much_o it_o be_v not_o great_a by_o so_o much_o therefore_o it_o be_v not_o great_a if_o it_o be_v less_o say_v by_o now_o much_o &c._n &c._n which_o be_v good_a demonstration_n be_v together_o with_o this_o overthrow_v if_o this_o inference_n be_v not_o good_a that_o be_v if_o thing_n which_o differ_v less_o than_o any_o assignable_a quantity_n may_v not_o be_v repute_v equal_a but_o now_o to_o say_v thus_o that_o the_o distance_n of_o a_o hyperbole_n from_o a_o straight_a line_n draw_v beyond_o its_o asymptote_n and_o the_o parallel_n thereunto_o do_v continual_o decrease_v so_o as_o if_o it_o be_v suppose_v infinite_o produce_v it_o must_v be_v suppose_v to_o be_v at_o length_n the_o same_o with_o that_o of_o the_o asymptote_n from_o the_o say_a parallel_n because_o neither_o great_a nor_o less_o by_o any_o assignable_a quantity_n which_o be_v but_o the_o result_n of_o his_o own_o assertion_n be_v all_o one_o as_o to_o say_v that_o a_o quantity_n may_v grow_v less_o and_o less_o eternal_o so_o as_o at_o last_o to_o be_v equal_a to_o another_o quantity_n or_o which_o be_v all_o one_o say_v he_o that_o there_o be_v a_o last_o in_o eternity_n which_o be_v his_o four_o charge_n and_o what_o absurdity_n be_v in_o it_o fall_v upon_o himself_o just_o as_o when_o have_v tell_v we_o cap._n 16._o §_o 20._o punctum_fw-la inter_fw-la quantitates_fw-la nihil_fw-la est_fw-la ut_fw-la inter_fw-la numeros_fw-la cyphra_fw-la and_o cap._n 14._o §_o 16._o punctum_fw-la ad_fw-la lineam_fw-la neque_fw-la rationem_fw-la habet_fw-la neque_fw-la quantitatem_fw-la ullam_fw-la he_o rail_v upon_o i_o twenty_o time_n over_o as_o if_o i_o have_v somewhere_o say_v a_o point_n be_v nothing_o only_o because_o i_o say_v with_o euclid_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d five_o it_o be_v his_o usual_a language_n in_o design_v a_o angle_n to_o say_v it_o be_v contain_v or_o comprehend_v by_o or_o between_o the_o two_o side_n as_o for_o example_n cap._n 14._o §_o 9_o three_o time_n in_o two_o line_n idem_fw-la angulus_fw-la est_fw-la qui_fw-la comprehenditur_fw-la inter_fw-la ab_fw-la &_o ac_fw-la cum_fw-la eo_fw-la qui_fw-la comprehenditur_fw-la inter_fw-la ae_n &_o of_o vel_fw-la inter_fw-la ab_fw-la &_o of_o and_o §_o 15._o cor_fw-la 1._o angulâ—s_fw-la comprehensos_fw-la a_o duabus_fw-la rectis_fw-la and_o §_o 16._o angulus_fw-la qui_fw-la continetur_fw-la inter_fw-la ab_fw-la &_o eandem_fw-la ab_fw-la etc._n etc._n and_o it_o be_v well_o enough_o so_o to_o speak_v but_o now_o forget_v that_o it_o be_v himself_o that_o say_v so_o he_o deliver_v it_o as_o a_o principle_n of_o we_o that_o the_o nature_n of_o a_o angle_n consist_v in_o that_o which_o lie_v between_o the_o line_n which_o comprehend_v it_o that_o be_v say_v he_o a_o angle_n be_v a_o superficies_n six_o when_o he_o have_v say_v absurd_o enough_o cap._n 11._o §_o 5._o consistit_fw-la ratio_fw-la antecedentis_fw-la ad_fw-la consequens_fw-la in_fw-la differentia_fw-la hoc_fw-la est_fw-la in_fw-la ea_fw-la parte_fw-la majoris_fw-la qua_fw-la minus_fw-la ab_fw-la eo_fw-la superatur_fw-la sive_fw-la in_o majoris_fw-la dempto_fw-la minore_fw-la residuo_fw-la &c_n &c_n and_o again_o ratio_fw-la binarii_fw-la ad_fw-la quinarium_fw-la est_fw-la ternarius_fw-la etc._n etc._n and_o cap._n 12._o §_o 8._o ratio_fw-la inaequalium_fw-la linearum_fw-la of_o ig_n consistit_fw-la in_o differentia_fw-la gf_n and_o the_o like_a elsewhere_o which_o be_v all_o one_o as_o to_o say_v that_o the_o nature_n of_o proportion_n consist_v in_o a_o number_n a_o line_n a_o 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