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understanding_n must_v be_v make_v my_o fault_n my_o demonstration_n be_v this_o in_o the_o parallelogram_n a_o b_o c_o d_o fig._n 11._o let_v the_o side_n a_o b_o be_v conceive_v to_o be_v move_v uniform_o till_o it_o lie_v in_o c_o d_o and_o let_v the_o time_n of_o that_o motion_n be_v a_o c_o or_o b_o d._n and_o in_o the_o same_o time_n let_v it_o be_v conceive_v that_o a_o c_o be_v move_v with_o uniform_a acceleration_n till_o it_o lie_v in_o b_o d._n to_o which_o you_o object_n that_o then_o the_o acceleration_n last_o acquire_v must_v be_v far_o great_a than_o that_o wherewith_o a_o b_o be_v move_v uniform_o else_o it_o shall_v never_o come_v to_o the_o place_n you_o will_v have_v it_o in_o the_o same_o time_n what_o proof_n bring_v you_o for_o this_o none_o here_o where_o then_o no_o where_o that_o i_o remember_v on_o the_o contrary_n i_o have_v prove_v art_n 9_o of_o this_o chapter_n that_o the_o line_n describe_v by_o the_o concourse_n of_o those_o two_o motion_n namely_o uniform_a from_o a_o b_o to_z c_z d_o and_o uniform_o accelerate_a from_o a_o c_o to_z b_o d_o be_v the_o crooked_a line_n of_o the_o sâ—miparabola_fw-la a_o h_o d._n and_o though_o i_o have_v not_o yet_o it_o be_v well_o know_v that_o the_o same_o be_v demonstrate_v by_o galileo_n and_o see_v it_o be_v manifest_a that_o in_o what_o proportion_n the_o motion_n be_v accelerate_a in_o the_o line_n a_o b_o in_o the_o same_o proportion_n the_o impetus_fw-la beginning_n from_o rest_n in_o a_o be_v increase_v in_o the_o same_o time_n which_o impetus_fw-la be_v design_v all_o the_o way_n by_o the_o ordinate_a line_n of_o the_o semi-parabola_a the_o great_a impetus_fw-la acquire_v must_v needs_o be_v the_o base_a of_o the_o semiparabola_fw-la namely_o b_o d_o equal_a to_o a_o c_o which_o design_v the_o whole_a time_n i_o can_v therefore_o imagine_v what_o shall_v make_v you_o say_v without_o proof_n that_o the_o great_a acquire_v impetus_fw-la be_v great_a than_o that_o which_o be_v design_v 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manner_n but_o to_o come_v again_o to_o your_o objection_n you_o say_v i_o make_v a_o great_a space_n run_v over_o in_o the_o same_o time_n by_o the_o slow_a motion_n then_o by_o the_o swift_a how_o do_v that_o appear_v because_o there_o be_v no_o doubt_n but_o the_o swiftness_n be_v great_a where_o the_o great_a impetus_fw-la be_v always_o maintain_v then_o where_o it_o be_v attain_v to_o in_o the_o same_o time_n from_o rest._n true_a but_o that_o be_v when_o they_o be_v consider_v asunder_o without_o concourse_n but_o not_o then_o when_o by_o the_o concourse_n they_o debilitate_v one_o another_o and_o describe_v a_o three_o line_n different_a from_o both_o the_o line_n which_o they_o will_v describe_v single_o in_o this_o place_n i_o compare_v their_o effect_n as_o contribute_v to_o the_o the_o description_n of_o the_o parabolicall_a line_n a_o h_n d._n what_o the_o effect_n of_o their_o several_a motion_n be_v when_o they_o be_v consider_v asunder_o be_v sufficient_o show_v bâ—fore_o in_o the_o first_o article_n you_o shall_v first_o have_v get_v into_o your_o mind_n the_o perfect_a and_o distinct_a ideá_n of_o all_o the_o motion_n mention_v in_o this_o chapter_n and_o then_o have_v venture_v upon_o the_o censure_n of_o they_o but_o not_o before_o and_o then_o you_o will_v have_v see_v that_o the_o body_n move_v from_o a_o describe_v not_o the_o line_n a_o c_o nor_o the_o line_n a_o b_o but_o a_o three_o namely_o the_o semiparabolicall_a line_n a_o h_n d._n again_o where_o i_o say_v wherefore_o if_o the_o whole_a a_o b_o be_v uniform_o move_v to_o c_o d_o in_o the_o same_o time_n wherein_o a_o c_z be_v move_v uniform_o to_o f_o g_z you_o ask_v i_o whether_o with_o the_o same_o impetus_fw-la or_o not_o how_o be_v it_o possible_a that_o in_o the_o same_o time_n two_o unequal_a length_n shall_v be_v pass_v over_o with_o the_o same_o impetus_fw-la but_o why_o say_v you_o do_v you_o not_o tell_v we_o with_o what_o impetus_fw-la a_o c_o comes_z to_z f_o g_o what_o need_n be_v there_o of_o that_o when_o all_o man_n know_v that_o in_o uniform_a motion_n and_o the_o same_o time_n impetus_fw-la be_v to_o impetus_fw-la as_o length_n to_o length_n which_o to_o have_v express_v have_v not_o â—een_n pertinent_a to_o the_o demonstration_n that_o which_o follow_v in_o the_o demonstration_n rursus_fw-la suppono_fw-la quod_fw-la latus_fw-la a_o c_o etc._n etc._n to_o these_o word_n ut_fw-la ostensum_fw-la est_fw-la art_n 12_o you_o confute_v with_o say_v you_o have_v prove_v that_o article_n to_o be_v false_a but_o you_o may_v see_v now_o if_o you_o please_v at_o the_o same_o place_n that_o i_o have_v prove_v your_o objection_n to_o be_v frivolous_a after_o this_o you_o run_v on_o without_o any_o argument_n against_o the_o rest_n of_o the_o demonstration_n show_v nothing_o all_o the_o way_n but_o that_o the_o variety_n and_o concourse_n of_o motion_n the_o speculation_n whereof_o you_o have_v not_o be_v use_v to_o have_v make_v you_o giddy_a to_o the_o nineteen_o article_n you_o apply_v the_o same_o objection_n which_o you_o make_v to_o the_o eighteen_o which_o have_v be_v answer_v it_o appear_v that_o from_o the_o very_a beginning_n of_o your_o elenchus_n to_o this_o place_n all_o your_o objection_n except_o such_o as_o be_v make_v to_o three_o or_o four_o mistake_n of_o small_a importance_n in_o set_v down_o my_o mind_n be_v mere_a paralogism_n and_o such_o as_o be_v less_o pardonable_a than_o any_o paralogism_n in_o orontius_n both_o because_o the_o subject_a as_o less_o difficult_a be_v more_o easy_o master_v and_o because_o the_o same_o fault_n be_v more_o shameful_o commit_v by_o a_o reprehender_n then_o by_o any_o other_o man_n i_o have_v once_o add_v to_o these_o nineteen_o article_n a_o twenty_o which_o be_v this_o if_o from_o a_o point_n in_o the_o circumference_n there_o be_v draw_v a_o chord_n and_o a_o tangent_fw-la equal_a to_o it_o the_o angle_n which_o they_o make_v shall_v be_v double_a to_o the_o aggregate_v 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chapter_n of_o his_o clavis_fw-la mathematicae_fw-la where_o he_o say_v that_o 43_o 7_o be_v the_o proportion_n of_o 31_o to_o 7_o for_o his_o meaning_n be_v that_o the_o proportion_n of_o 43_o 7_o to_o one_o be_v the_o proportion_n of_o 31_o to_o 7_o whereas_o if_o he_o mean_v as_o you_o do_v than_o 86_o 7_o shall_v be_v double_a the_o proportion_n of_o 31_o to_o 7._o partly_o also_o because_o you_o think_v as_o in_o the_o end_n of_o the_o twenty_o proposition_n that_o if_o the_o proportion_n of_o the_o numerator_n of_o these_o fraction_n to_o their_o denominator_n decrease_v eternal_o they_o shall_v so_o vanish_v at_o last_o as_o to_o leave_v the_o proportion_n of_o the_o sum_n of_o all_o the_o square_n to_o the_o sum_n of_o the_o great_a so_o often_o take_v that_o be_v a_o infinite_a number_n of_o time_n as_o one_o to_o three_o or_o the_o sum_n of_o the_o great_a to_o the_o sum_n of_o the_o increase_a square_n as_o three_o to_o one_o for_o which_o there_o be_v no_o more_o reason_n 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