Selected quad for the lemma: end_n

Word A Word B Word C Word D Occurrence Frequency Band MI MI Band Prominent
end_n line_n point_n require_v 1,303 5 9.1027 5 false
View all documents for the selected quad

Text snippets containing the quad

ID Title Author Corrected Date of Publication (TCP Date of Publication) STC Words Pages
A97051 Due correction for Mr Hobbes· Or Schoole discipline, for not saying his lessons right. In answer to his Six lessons, directed to the professors of mathematicks. / By the professor of geometry. Wallis, John, 1616-1703. 1656 (1656) Wing W576; Thomason E1577_1; ESTC R204165 114,934 142

There are 3 snippets containing the selected quad. | View original text

of_o it_o it_o may_v be_v so_o and_o it_o be_v all_o one_o to_o i_o whether_o you_o believe_v it_o to_o be_v true_a or_o no._n you_o may_v think_v if_o you_o please_v that_o the_o corollary_n be_v true_a still_o it_o will_v not_o hurt_v i_o yet_o if_o you_o consider_v what_o have_v be_v say_v before_o you_o shall_v have_v see_v the_o reason_n viz._n because_o the_o aggregate_v of_o the_o impetus_fw-la do_v not_o constitute_v a_o semiparabole_fw-la but_o the_o compliment_n of_o a_o semiparabola_fw-la which_o be_v not_o ⅔_n but_o ⅓_n of_o the_o parallelogram_n the_o five_o article_n have_v the_o same_o fault_n with_o the_o four_o and_o run_v all_o upon_o the_o same_o mistake_n the_o main_a foundation_n of_o all_o these_o continue_a error_n be_v i_o tell_v you_o the_o ignorance_n of_o what_o be_v proportion_n duplicate_v triplicate_v subduplicate_v subtriplicate_v etc._n etc._n of_o three_o number_n in_o continual_a proportion_n if_o the_o first_o be_v the_o jest_n the_o proportion_n of_o the_o first_o to_o the_o second_o be_v duplicate_v of_o what_o it_o have_v to_o the_o three_o not_o subduplicate_v that_o be_v your_o opinion_n cap._n 13._o §_o 16._o of_o the_o latin_a in_o the_o english_a you_o have_v retract_v that_o error_n in_o part_n yet_o retain_v all_o the_o ill_a consequence_n that_o follow_v from_o it_o next_o you_o suppose_v the_o aggregate_n of_o the_o impetus_fw-la increase_v in_o the_o duplicate_v triplicate_v etc._n etc._n proportion_n of_o the_o time_n to_o be_v design_v by_o the_o parabola_fw-la and_o parabolaster_n as_o if_o their_o ordinates_n do_v increase_v in_o the_o duplicate_v triplicate_v etc._n etc._n proportion_n of_o their_o diameter_n cujus_fw-la contrarium_fw-la verum_fw-la est_fw-la whereas_o you_o shall_v have_v design_v they_o by_o the_o compliment_n of_o those_o figure_n but_o you_o ask_v i_o what_o line_n that_o compliment_n be_v no_o line_n good_a sir_n but_o a_o figure_n which_o with_o the_o figure_n of_o the_o semiparabola_fw-la etc._n etc._n do_v compleare_v the_o parallelogram_n you_o ought_v therefore_o as_o i_o then_o tell_v you_o but_o you_o understand_v it_o not_o to_o have_v describe_v your_o parabola_fw-la the_o other_o way_n that_o the_o convex_v not_o the_o concave_n of_o the_o parabolicall_a line_n shall_v have_v be_v towards_o the_o line_n of_o time_n ab_fw-la so_o shall_v the_o point_n k_o have_v fall_v between_o n_o and_o f_o and_o the_o convex_a of_o the_o parabola_fw-la with_o at_o the_o tangent_fw-la and_o by_o a_o parallel_n of_o the_o diameter_n have_v contain_v the_o compliment_n of_o that_o parabola_fw-la who_o diameter_n therefore_o must_v have_v be_v ac_fw-la and_o its_o ordinate_a ci._n next_o in_o pursuance_n of_o this_o error_n you_o make_v the_o whole_a velocity_n in_o these_o acceleration_n in_o duplicate_v triplicate_v etc._n etc._n proportion_n of_o the_o time_n to_o be_v ⅔_n ¾_n etc._n etc._n of_o the_o velocity_n of_o a_o uniform_a motion_n with_o the_o great_a acquire_v impetus_fw-la because_o the_o parabola_fw-la and_o parabolaster_n have_v such_o proportion_n to_o their_o para_n ●lelograms_n whereas_o they_o be_v indeed_o but_o ⅓_n ¼_n etc._n etc._n thereof_o for_o such_o be_v the_o proportion_n of_o the_o compliment_n of_o those_o figure_n to_o their_o parallellogram_n now_o upon_o these_o false_a principle_n with_o many_o more_o consonant_a hereunto_o you_o ground_n not_o only_o the_o doctrine_n of_o the_o four_o and_o five_o article_n but_o also_o most_o of_o those_o that_o follow_v especial_o the_o thirteen_o and_o thenceforth_o to_o the_o end_n of_o the_o chapter_n which_o be_v all_o therefore_o of_o as_o little_a worth_n as_o these_o but_o enough_o of_o this_o the_o first_o five_o article_n therefore_o be_v find_v to_o be_v unsound_a and_o many_o way_n faulty_a the_o six_o seven_o and_o eight_o article_n i_o do_v let_v pass_v for_o sound_n and_o you_o quarrel_n with_o i_o for_o so_o do_v but_o i_o say_v withal_o you_o may_v have_v deliver_v as_o much_o to_o better_a purpose_n in_o three_o line_n as_o there_o you_o do_v in_o five_o page_n beside_o such_o petty_a error_n all_o along_o as_o it_o be_v endless_a every_o where_o to_o take_v notice_n of_o which_o give_v you_o a_o new_a occasion_n to_o rail_v at_o symbol_n after_o these_o three_o there_o be_v not_o one_o sound_a article_n to_o the_o end_n of_o the_o chapter_n and_o what_o those_o be_v before_o we_o have_v hear_v already_o the_o nine_o article_n be_v this_o if_o a_o thing_n be_v move_v by_o two_o movent_n at_o once_o concur_v in_o what_o angle_n soever_o of_o which_o the_o one_o be_v move_v uniform_o the_o other_o with_o motion_n uniform_o acceleeat_v from_o rest_n till_o it_o acqu●e_v a_o impetus_fw-la equal_a to_o that_o of_o the_o uniform_a motion_n the_o line_n in_o which_o the_o thing_n move_v be_v carry_v will_v be_v the_o crooked_a line_n of_o a_o semiparabola_fw-la very_o good_a but_o of_o what_o semiparabola_fw-la for_o hitherto_o we_o have_v nothing_o but_o a_o proporsion_n of_o galilaeo_n transcribe_v you_o tell_v we_o ●t_z shall_v be_v that_o semiparabola_fw-la who_o busis_n be_v the_o impetus_fw-la last_v acquire_v and_o this_o be_v the_o whole_a designation_n of_o your_o parabola_fw-la to_o this_o designation_n i_o object_v many_o thing_n first_o that_o the_o basis_n of_o a_o semiparabala_n be_v not_o a_o impetus_fw-la but_o a_o line_n and_o therefore_o it_o be_v absurd_a to_o talk_v of_o a_o semiparabola_fw-la who_o basis_n be_v a_o impetus_fw-la second_o if_o it_o be_v say_v that_o a_o impetus_fw-la may_v be_v design_v by_o a_o line_n i_o grant_v it_o a_o line_n may_v be_v the_o symbol_n of_o a_o impetus_fw-la as_o well_o as_o a_o letter_n but_o this_o line_n be_v what_o line_n you_o please_v for_o any_o impetus_fw-la may_v be_v design_v by_o any_o line_n at_o pleasure_n &_o so_o to_o say_v that_o it_o be_v a_o semiparabola_fw-la who_o basis_n be_v that_o line_n which_o design_v the_o impetus_fw-la be_v all_o one_o as_o to_o say_v it_o be_v a_o semiparabola_fw-la who_o basis_n be_v what_o line_n you_o please_v so_o that_o we_o have_v not_o so_o much_o as_o the_o basis_n of_o this_o semiparabola_fw-la determine_v three_o suppose_v that_o the_o base_a have_v be_v determine_v as_o it_o be_v not_o yet_o it_o be_v a_o simple_a thing_n to_o think_v that_o determine_v the_o basis_n do_v determine_v the_o parabola_fw-la for_o there_o may_v be_v infinite_a parabola_n describe_v upon_o the_o same_o base_a you_o do_v not_o tell_v we_o what_o altitude_n what_o diameter_n nor_o what_o inclination_n this_o parabola_fw-la be_v to_o have_v now_o to_o this_o you_o keep_v a_o bawl_n but_o say_v nothing_o to_o the_o business_n you_o tell_v we_o that_o you_o have_v say_v what_o angle_n soever_o that_o be_v you_o suppose_v your_o mevent_v to_o concur_v in_o what_o angle_n ●soever_o but_o you_o say_v nothing_o of_o what_o be_v to_o be_v the_o angle_n of_o inclination_n in_o the_o parabola_fw-la you_o may_v have_v say_v indeed_o it_o be_v to_o be_v the_o same_o with_o that_o of_o the_o movent_n but_o you_o do_v not_o and_o therefore_o i_o blame_v you_o for_o omit_v it_o then_o as_o to_o the_o diameter_n you_o may_v have_v say_v but_o you_o do_v not_o that_o the_o line_n of_o the_o acccelerate_v motion_n will_v be_v the_o diameter_n it_o be_v another_o fault_n therefore_o not_o to_o say_v so_o for_o that_o have_v be_v requisite_a to_o the_o determine_n of_o the_o parabola_fw-la but_o when_o you_o have_v so_o say_v this_o have_v but_o determine_v the_o position_n of_o the_o diameter_n not_o its_o magnitude_n it_o may_v be_v long_o or_o short_a at_o pleasure_n notwithstanding_o this_o then_o as_o to_o the_o altitude_n of_o it_o this_o remain_v as_o much_o undetermined_a as_o the_o rest_n you_o tell_v we_o neither_o where_o the_o vertex_fw-la be_v nor_o how_o far_o it_o be_v suppose_v to_o be_v distant_a from_o the_o base_a you_o may_v have_v say_v but_o you_o do_v not_o that_o the_o point_n of_o rest_n where_o the_o two_o motion_n begin_v be_v the_o vertex_fw-la and_o it_o be_v your_o fault_n you_o do_v not_o say_v so_o in_o the_o latin_a as_o you_o have_v now_o do_v in_o the_o english_a but_o have_v you_o so_o say_v you_o have_v not_o thereby_o determine_v either_o the_o altitude_n or_o the_o diameter_n length_n you_o say_v the_o vertex_fw-la and_o base_a be_v give_v i_o have_v not_o the_o wit_n to_o see_v that_o the_o altitude_n of_o the_o parabola_fw-la be_v determine_v no_o true_o nor_o have_v i_o yet_o but_o it_o seem_v you_o have_v so_o little_a wit_n as_o to_o think_v it_o be_v have_v the_o vertex_fw-la and_o base_a be_v positione_n data_fw-la i_o confess_v it_o have_v be_v determine_v for_o then_o i_o have_v be_v tell_v how_o far_o off_o from_o the_o base_a the_o vertex_fw-la have_v be_v but_o when_o the_o base_a be_v only_o magnitudine_fw-la data_fw-la there_o be_v no_o
three_o of_o 1_o to_o 8._o this_o be_v that_o you_o will_v have_v have_v i_o learn_v but_o good_a sir_n you_o have_v forget_v that_o since_o that_o time_n you_o have_v unlearned_a it_o yourself_o for_o your_o 16._o artic_a of_o chap._n 13._o as_o it_o now_o stand_v correct_v in_o the_o english_a teach_v we_o another_o doctrine_n viz._n that_o if_o 1_o 2_o 4_o 8_o be_v continual_o proportional_a 1_o to_o 8_o shall_v be_v as_o well_o triplicate_v though_o not_o big_a of_o 1_o to_o 2_o not_o this_o triplicate_v of_o that_o as_o 8_o to_o 1_o be_v of_o 2_o to_o 1._o the_o case_n be_v now_o alter_v from_o what_o it_o be_v in_o the_o latin_a and_o therefore_o you_o be_v quite_o in_o a_o wrong_a box_n when_o in_o your_o english_a you_o cite_v chapt._n 13._o art_n 16_o to_o patronize_v this_o absurdity_n for_o in_o so_o do_v you_o do_v but_o cut_v your_o own_o throat_n you_o must_v now_o learn_v to_o sing_v another_o song_n called_z palinodia_fw-la well_o this_o be_v one_o of_o the_o fault_n of_o this_o article_n they_o that_o have_v a_o mind_n to_o see_v the_o rest_n of_o they_o may_v consult_v what_o i_o say_v before_o where_o i_o have_v note_v a_o parcel_n of_o two_o dozen_o in_o the_o 11._o article_n you_o do_v but_o undertake_v to_o demonstrate_v a_o proposition_n of_o archimedes_n your_o demonstration_n beside_o that_o it_o depend_v upon_o the_o second_o article_n which_o be_v yet_o undemonstrate_v be_v otherwise_o also_o faulty_a as_o i_o then_o tell_v you_o and_o therefore_o to_o say_v that_o i_o allow_v this_o to_o be_v demonstrate_v if_o your_o second_o bid_v be_v demonstrate_v be_v a_o untruth_n for_o i_o tell_v you_o then_o that_o your_o manner_n of_o infer_v this_o from_o that_o be_v very_o absurd_a the_o 12_o article_n like_o all_o the_o rest_n since_o the_o second_o beside_o their_o other_o fault_n depend_v upon_o the_o second_o and_o therefore_o till_o that_o be_v demonstrate_v this_o must_v fall_v with_o it_o in_o the_o 13._o art_n you_o undertake_v to_o demonstrate_v this_o proposition_n of_o archimedes_n that_o the_o superficies_n of_o any_o portion_n of_o a_o sphere_n be_v equal_a to_o that_o circle_n who_o radius_fw-la be_v a_o straight_a line_n draw_v from_o the_o pole_n of_o the_o portion_n to_o the_o circumference_n of_o its_o base_a your_o demonstration_n i_o say_v be_v of_o no_o force_n but_o may_v as_o well_o be_v apply_v to_o a_o portion_n of_o any_o conoeid_n parabolicall_a hyperbolical_a ellipticall_a or_o any_o other_o as_o to_o the_o portion_n of_o a_o sphere_n by_o the_o truth_n of_o this_o say_v you_o let_v any_o man_n judge_v of_o your_o and_o my_o geometry_n content_a it_o be_v but_o transcribe_v your_o demonstration_n &_o insert_v the_o word_n conoeid_v vertex_fw-la section_n by_o the_o axis_n etc._n etc._n where_o you_o have_v sphere_n pole_n great_a circle_n etc._n etc._n which_o term_n in_o the_o conoeid_n answer_v to_o those_o in_o the_o sphere_n and_o the_o work_n be_v do_v let_v bac_n in_o the_o seven_o figure_n be_v a_o portion_n of_o a_o sphere_n or_o conoeid_n parabolicall_a hyperbolical_a ellipticall_a etc._n etc._n who_o axis_n be_v ae_n and_o who_o basis_n be_v bc_n and_o let_v ab_fw-la be_v the_o straight_a line_n draw_v from_o the_o pole_n or_o vertex_fw-la a_o to_o the_o base_a in_o b_o and_o let_v ad_fw-la equal_a to_o ab_fw-la touch_v the_o great_a circle_n or_o section_n make_v by_o a_o plain_a pass_v through_o the_o axis_n of_o the_o conoeid_n bac_n in_o the_o pole_n or_o vertex_fw-la a._n it_o be_v to_o be_v prove_v that_o a_o circle_n make_v by_o the_o radius_fw-la ad_fw-la be_v equal_a to_o the_o superficies_n of_o the_o portion_n bac_n let_v the_o plain_a aebd_a be_v understand_v to_o make_v a_o revolution_n about_o the_o axis_n ae_n and_o it_o be_v manifest_a that_o by_o the_o straight_a line_n ad_fw-la a_o circle_n will_v be_v describe_v and_o by_o the_o arch_n or_o section_n ab_fw-la the_o superficies_n of_o a_o sphere_n or_o conoeid_v mention_v and_o last_o by_o the_o subtense_n ab_fw-la the_o superficies_n of_o a_o right_a cone_n now_o see_v both_o the_o straight_a line_n ab_fw-la and_o the_o arch_n or_o section_n ab_fw-la make_v one_o and_o the_o same_o revolution_n and_o both_o of_o they_o have_v the_o same_o extreme_a point_n a_o &_o b_o the_o cause_n why_o the_o spherical_a or_o conoeidicall_a superficies_n which_o be_v make_v by_o the_o arch_n or_o section_n be_v great_a than_o the_o conicall_a superficies_n which_o be_v make_v by_o the_o subtense_n be_v that_o ab_fw-la the_o arch_n or_o section_n be_v great_a than_o ab_fw-la the_o subtense_n and_o the_o cause_n why_o it_o be_v great_a consist_v in_o this_o that_o although_o they_o be_v both_o draw_v from_o a_o to_o b_o yet_o the_o subtense_n be_v draw_v straight_o but_o the_o arch_n or_o section_n angular_o namely_o according_a to_o that_o angle_n which_o the_o arch_n or_o section_n make_v with_o the_o subtense_n which_o angle_n be_v equal_a to_o the_o angle_n dab_n for_o the_o angle_n of_o contact_n whether_o of_o circle_n or_o other_o crooked_a line_n add_v nothing_o to_o the_o angle_n at_o the_o segment_n as_o have_v be_v show_v as_o to_o circle_n in_o the_o 14_o chapter_n of_o the_o 16_o article_n and_o as_o to_o all_o other_o crooked_a line_n lesson_n 3._o pag._n 28._o lin_v ult_n wherefore_o the_o magnitude_n of_o the_o angle_n dab_n be_v the_o cause_n why_o the_o superficies_n of_o the_o portion_n describe_v by_o the_o arch_n or_o section_n ab_fw-la be_v great_a than_o the_o superficies_n of_o the_o right_a cone_n describe_v by_o the_o subtense_n ab_fw-la again_o the_o cause_n why_o the_o circle_n describe_v by_o the_o tangent_fw-la ad_fw-la be_v great_a than_o the_o superficies_n of_o the_o right_a cone_n describe_v by_o the_o subtense_n ab_fw-la notwithstanding_o that_o the_o tangent_fw-la and_o subtense_n be_v equal_a and_o both_o move_v round_o in_o the_o same_o time_n be_v this_o that_o ad_fw-la stand_v at_o right_a angle_n to_o the_o axis_fw-la but_o ab_fw-la oblique_o which_o obliquity_n consist_v in_o the_o same_o angle_n dab_n see_v therefore_o that_o the_o quantity_n of_o the_o angle_n dab_n be_v that_o which_o make_v the_o excess_n both_o of_o the_o superficies_n of_o the_o portion_n and_o of_o the_o circle_n make_v by_o the_o radius_fw-la ad_fw-la above_o the_o superficies_n of_o the_o right_a cone_n describe_v by_o the_o subtense_n ab_fw-la it_o follow_v that_o both_o the_o superficies_n of_o the_o portion_n and_o that_o of_o the_o circle_n do_v equal_o exceed_v the_o superficies_n of_o the_o cone_n wherefore_o the_o circle_n make_v by_o ad_fw-la or_o ab_fw-la and_o the_o spherical_a or_o conoeidicall_a superficies_n make_v by_o the_o arch_n or_o section_n ab_fw-la be_v equal_a to_o one_o another_o which_o be_v to_o be_v prove_v show_v i_o now_o if_o you_o can_v for_o you_o have_v pawn_v all_o your_o geometry_n upon_o this_o one_o issue_n where_o the_o demonstration_n halt_v more_o on_o my_o part_n then_o it_o do_v on_o you_o or_o where_o be_v it_o that_o it_o do_v not_o as_o strong_o proceed_v in_o the_o case_n of_o any_o conoeid_n as_o of_o a_o sphere_n all_o that_o you_o can_v think_v of_o by_o way_n of_o exception_n and_o you_o have_v have_v time_n to_o think_v on_o it_o ever_o since_o i_o write_v last_o amount_v to_o no_o more_o but_o this_o which_o yet_o be_v nothing_o to_o the_o purpose_n you_o ask_v in_o case_n the_o crooked_a line_n ab_fw-la be_v not_o the_o arch_n of_o a_o circle_n whether_o do_v i_o think_v that_o the_o angle_n which_o it_o make_v with_o the_o subtense_n ab_fw-la at_o the_o point_v a_o &_o b_o must_v needs_o be_v equal_a i_o say_v that_o its_o possible_a that_o in_o some_o case_n it_o may_v be_v so_o and_o i_o can_v for_o a_o need_n show_v you_o where_o and_o therefore_o at_o least_o as_o to_o those_o case_n you_o be_v clear_o go_v for_o you_o have_v nothing_o else_o to_o say_v for_o yourself_o but_o this_o be_v nothing_o at_o all_o to_o the_o purpose_n whether_o they_o be_v or_o no_o for_o the_o angle_n at_o b_o what_o ever_o it_o be_v come_v not_o into_o consideration_n at_o all_o nor_o be_v so_o much_o as_o once_o name_v in_o all_o the_o demonstration_n so_o that_o its_o equality_n or_o inequality_n with_o that_o at_o a_o make_v nothing_o at_o all_o to_o the_o business_n and_o therefore_o your_o exception_n be_v not_o worth_a a_o straw_n think_v of_o a_o better_a against_o the_o next_o time_n or_o else_o all_o your_o geometry_n be_v forfeit_v and_o they_o be_v like_a to_o have_v a_o great_a purchase_n that_o get_v it_o be_v they_o not_o at_o the_o 14._o article_n have_v before_o art_n 4._o undertake_v to_o teach_v the_o way_n of_o draw_v and_o continue_v those_o curve_v line_n by_o point_n and_o direct_v we_o for_o the_o word_n
require_v do_v not_o please_v you_o for_o that_o end_n to_o take_v mean_a proportional_o you_o now_o tell_v we_o how_o that_o may_v be_v do_v viz._n by_o these_o curve_v line_n first_o draw_v i_o ask_v whether_o this_o be_v not_o to_o commit_v a_o circle_n you_o tell_v i_o no._n but_o mean_v while_o take_v no_o notice_n of_o that_o which_o be_v the_o main_a objection_n viz._n that_o this_o construction_n of_o you_o be_v but_o go_v about_o the_o bush_n for_o upon_o supposition_n that_o we_o have_v those_o line_n already_o draw_v the_o find_n of_o mean_a proportional_o by_o they_o may_v be_v perform_v with_o much_o more_o ease_n than_o the_o way_n you_o take_v and_o i_o show_v you_o how_n but_o that_o which_o stick_v most_o in_o your_o stomach_n be_v a_o clause_n in_o the_o close_a of_o this_o chap._n i_o tell_v you_o that_o some_o considerable_a proposition_n of_o this_o chapter_n and_o i_o can_v have_v tell_v you_o which_o be_v true_a though_o you_o have_v miss_v in_o your_o demonstration_n however_o you_o come_v by_o they_o but_o that_o i_o be_v confident_a they_o be_v none_o of_o your_o own_o and_o you_o know_v i_o guess_v right_o and_o lest_o you_o shall_v think_v i_o deal_v unworthy_o to_o intimate_v that_o you_o have_v they_o elsewhere_o unless_o i_o can_v show_v you_o where_o i_o tell_v you_o that_o i_o do_v no_o worse_o than_o those_o that_o a_o while_n before_o have_v hang_v a_o man_n for_o steal_v a_o horse_n from_o a_o unknown_a person_n there_o be_v evidence_n enough_o that_o the_o horse_n be_v steal_v though_o they_o do_v not_o know_v from_o who_o so_o though_o i_o know_v not_o whence_o you_o have_v take_v they_o yet_o i_o have_v ground_n enough_o to_o judge_v they_o be_v not_o your_o own_o and_o since_o that_o time_n and_o before_o that_o book_n be_v full_o print_v i_o find_v whence_o you_o have_v they_o namely_o out_o of_o mersennus_n as_o i_o tell_v you_o then_o pag._n 132_o 133_o 134._o and_o to_o take_v they_o out_o of_o mersennus_n be_v all_o one_o as_o to_o rob_v a_o carrier_n for_o there_o be_v at_o least_o three_o man_n have_v right_a to_o the_o good_n and_o some_o of_o they_o if_o they_o have_v be_v ask_v will_v scarce_o have_v give_v way_n that_o you_o shall_v publish_v their_o invention_n in_o your_o own_o name_n des_fw-mi chartes_n fermat_n and_o robervall_n and_o perhaps_o a_o four_o have_v as_o much_o right_n as_o any_o one_o of_o these_o and_o that_o be_v cavallerio_n who_o though_o i_o then_o do_v not_o know_v it_o have_v contrary_a to_o what_o you_o affirm_v that_o they_o be_v never_o demonstrate_v by_o any_o but_o you_o self_n and_o that_o as_o wise_o as_o one_o can_v wish_v demonstrate_v those_o proposition_n in_o a_o tractate_n of_o his_o de_fw-fr usu_fw-la indivisibilium_fw-la in_o potestatibus_fw-la cossicis_fw-la but_o though_o the_o thing_n be_v true_a enough_o and_o you_o can_v deny_v it_o yet_o you_o do_v not_o like_o the_o comparison_n and_o will_v have_v i_o consider_v who_o it_o be_v be_v hang_v upon_o hamans_n gallow_n and_o true_o i_o can_v tell_v you_o that_o too_o for_o a_o need_n the_o first_o letter_n of_o his_o name_n be_v h._n but_o enough_o of_o this_o sect_n xii_o concern_v his_o 18_o 19_o 20._o chapter_n well_o we_o have_v make_v pretty_a quick_a work_n with_o the_o 17_o chapter_n with_o the_o 18_o we_o shall_v be_v yet_o quick_a the_o charge_n against_o this_o chapter_n be_v that_o it_o be_v all_o false_a and_o you_o confess_v it_o not_o one_o true_a article_n in_o the_o whole_a but_o you_o tell_v we_o in_o the_o english_a it_o be_v all_o well_o it_o be_v now_o so_o correct_v in_o the_o english_a as_o that_o i_o shall_v not_o be_v able_a if_o i_o can_v sufficient_o imagine_v motion_n that_o be_v if_o i_o can_v be_v giddy_a enough_o to_o reprehend_v very_o well_o it_o be_v a_o good_a hear_n when_o man_n grow_v better_a they_o that_o have_v a_o mind_n to_o believe_v it_o may_v i_o be_o not_o bind_v to_o undeceive_v they_o we_o have_v have_v experience_n all_o along_o that_o you_o have_v a_o special_a knack_n at_o mend_v as_o sour_a ale_n do_v in_o summer_n you_o grant_v that_o i_o have_v true_o demonstrate_v what_o be_v before_o to_o be_v all_o false_a you_o will_v have_v i_o do_v so_o again_o will_v you_o very_o good_a when_o i_o have_v nothing_o else_o to_o do_v i_o will_v consider_v of_o it_o they_o that_o think_v it_o worth_a the_o while_n may_v take_v the_o pain_n to_o examine_v it_o a_o second_o time_n for_o my_o part_n i_o think_v i_o have_v bestow_v as_o much_o pain_n upon_o it_o already_o as_o it_o deserve_v and_o somewhat_o more_o and_o all_o the_o amendment_n that_o i_o find_v be_v this_o that_o whereas_o before_o we_o have_v three_o false_a article_n now_o we_o have_v but_o two_o and_o the_o number_n of_o true_a one_o just_a as_o many_o as_o we_o have_v before_o viz._n never_o a_o one_o in_o the_o 19_o chapter_n there_o be_v fault_n enough_o in_o conscience_n for_o a_o matter_n of_o no_o great_a difficulty_n than_o that_o be_v i_o note_v some_o of_o they_o and_o leave_v the_o reader_n to_o pick_v up_o the_o rest_n two_o or_o three_o of_o the_o light_a touch_n about_o method_n you_o take_v notice_n of_o and_o make_v a_o business_n to_o justify_v or_o excuse_v they_o and_o the_o main_a exception_n as_o you_o use_v to_o do_v you_o pass_v over_o with_o a_o light_a touch_n and_o a_o way_n i_o tell_v you_o in_o the_o begin_n of_o it_o that_o your_o chapter_n hang_v together_o like_o a_o rope_n of_o sand_n and_o it_o be_v true_a enough_o for_o they_o have_v no_o connexion_n at_o all_o there_o be_v so_o few_o hook_a atom_n that_o a_o man_n can_v tell_v how_o to_o tack_n they_o together_o next_o that_o have_v in_o your_o 24_o chapter_n undertake_v to_o show_v we_o what_o be_v the_o angle_n of_o incidence_n and_o what_o the_o angle_n of_o reflection_n and_o that_o the_o angle_n of_o incidence_n and_o of_o reflection_n be_v equal_a you_o do_v in_o pursuance_n of_o that_o assertion_n in_o this_o 19_o chapter_n show_v we_o the_o consequence_n thereof_o upon_o this_o i_o ask_v why_o not_o either_o this_o after_o that_o or_o that_o before_o this_o you_o tell_v i_o that_o think_v i_o what_o i_o will_v you_o think_v that_o method_n still_o the_o best_a to_o set_v the_o cart_n before_o the_o horse_n then_o you_o tell_v we_o that_o i_o say_v you_o define_v not_o here_o nay_o that_o be_v false_a i_o do_v not_o say_v so_o and_o it_o be_v not_o the_o first_o time_n that_o i_o have_v take_v you_o trip_v in_o this_o kind_n but_o many_o chapter_n after_o that_o i_o say_v i_o do_v confess_v and_o you_o know_v it_o be_v true_a what_o a_o angle_n of_o incidence_n and_o what_o a_o angle_n of_o reflection_n be_v and_o then_o talk_v against_o haste_n and_o oversight_n but_o if_o yourself_o have_v not_o be_v over_o hasty_a or_o rather_o wilful_o pervert_v my_o word_n you_o may_v have_v see_v and_o you_o know_v it_o well_o enough_o that_o i_o blame_v you_o here_o and_o two_o or_o three_o time_n before_o not_o so_o much_o for_o use_v word_n before_o you_o have_v define_v they_o for_o this_o fault_n as_o i_o remember_v i_o mention_v but_o once_o and_o there_o you_o take_v it_o patient_o but_o for_o define_v word_n so_o long_o after_o you_o have_v use_v they_o for_o when_o word_n for_o two_o or_o three_o chapter_n together_o have_v be_v suppose_v and_o frequent_o so_o use_v as_o of_o know_a signification_n whether_o they_o have_v be_v before_o define_v or_o not_o it_o be_v ridiculous_a for_o a_o mathen_n atician_n to_o come_v drop_v in_o with_o definition_n of_o they_o at_o latter_a end_n as_o your_o fashion_n be_v like_o mustard_n after_o meat_n for_o these_o definition_n shall_v either_o have_v come_v in_o due_a time_n or_o else_o not_o at_o all_o the_o two_o first_o article_n be_v very_o trivial_a and_o yet_o as_o if_o it_o be_v impossible_a for_o you_o be_v the_o way_n never_o so_o plain_a not_o to_o stumble_v there_o want_v at_o least_o in_o the_o english_a a_o determination_n in_o the_o second_o corollary_n and_o yet_o as_o if_o that_o be_v to_o make_v amends_o for_o other_o there_o be_v one_o too_o much_o if_o upon_o any_o point_n say_v you_o between_z b_o and_o d_o fig._n 2._o yes_o or_o any_o where_o else_o upon_o the_o same_o straight_a line_n produce_v either_o way_n though_o not_o between_o those_o point_n there_o fall_v from_o the_o point_n a_o you_o shall_v have_v say_v a_o straight_a line_n as_o ac_fw-la who_o reflect_a line_n be_v ch_z this_o also_o produce_v beyond_o c_o will_n fall_n upon_o f._n here_o i_o say_v that_o limitation_n between_o b_o and_o d_o be_v redundant_fw-la and_o that_o from_o the_o point_n a_o be_v