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book_n call_v part_n time_n 1,761 5 3.1267 3 false
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ID Title Author Corrected Date of Publication (TCP Date of Publication) STC Words Pages
A44014 Six lessons to the professors of the mathematiques one of geometry the other of astronomy, in the chaires set up by the noble and learned Sir Henry Savile in the University of Oxford. Hobbes, Thomas, 1588-1679. 1656 (1656) Wing H2260; ESTC R22309 102,047 75

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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 b●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 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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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