Selected quad for the lemma: mind_n
Text snippets containing the quad
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Corrected Date of Publication (TCP Date of Publication) |
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A44014
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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.
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Hobbes, Thomas, 1588-1679.
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1656
(1656)
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Wing H2260; ESTC R22309
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102,047
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75
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body_n of_o this_o kind_n of_o magnitude_n and_o quantity_n the_o subject_n be_v body_n and_o because_o for_o the_o compute_v of_o the_o magnitude_n of_o body_n it_o be_v not_o necessary_a that_o the_o body_n themselves_o shall_v be_v present_a the_o idea_n and_o memory_n of_o they_o supply_v their_o presence_n we_o reckon_v upon_o those_o imaginary_a body_n which_o be_v the_o quantity_n themselves_o and_o say_v the_o length_n be_v so_o great_a the_o breadth_n so_o great_a etc._n etc._n which_o in_o truth_n be_v no_o better_a than_o to_o say_v the_o length_n be_v so_o long_o or_o the_o breadth_n so_o broad_a etc._n etc._n but_o in_o the_o mind_n of_o a_o inteligent_a man_n it_o breed_v no_o mistake_n beside_o the_o quantity_n of_o body_n there_o be_v a_o quantity_n of_o time_n for_o see_v man_n without_o absurdity_n do_v ask_v how_o much_o it_o be_v by_o answer_v tantum_n so_o much_o they_o make_v manifest_a there_o be_v a_o a_o quantity_n that_o belong_v unto_o time_n namely_o a_o length_n and_o because_o length_n can_v be_v a_o accident_n of_o time_n which_o be_v itself_o a_o accident_n it_o be_v the_o accident_n of_o a_o body_n and_o consequent_o the_o length_n of_o the_o time_n be_v the_o length_n of_o the_o body_n by_o which_o length_n or_o line_n we_o determine_v how_o much_o the_o time_n be_v suppose_v some_o body_n to_o be_v move_v over_o it_o also_o we_o not_o improper_o ask_v with_o how_o much_o swiftness_n a_o body_n be_v move_v and_o consequent_o there_o be_v a_o quantity_n of_o motion_n or_o swiftness_n and_o the_o measure_n of_o that_o quantity_n be_v also_o a_o line_n but_o then_o again_o we_o must_v suppose_v another_o motion_n which_o determine_v the_o time_n of_o the_o former_a also_o of_o force_n there_o be_v a_o question_n of_o how_o much_o which_o be_v to_o be_v answer_v by_o so_o much_o that_o be_v by_o quantity_n if_o the_o force_n consist_v in_o swiftness_n the_o determination_n be_v the_o same_o with_o that_o of_o swiftness_n namely_o 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at_o the_o other_o end_v circular_o and_o this_o be_v call_v surp_o a_o angle_n and_o the_o quantity_n thereof_o be_v the_o quantity_n of_o the_o arch_n which_o the_o two_o line_n intercept_v the_o other_o cause_n be_v the_o bend_n of_o a_o straight_a line_n into_o a_o circular_a or_o other_o crooked_a line_n till_o it_o touch_v the_o place_n of_o the_o same_o line_n whilst_o it_o be_v straight_o in_o one_o only_a point_n and_o this_o be_v call_v a_o angle_n of_o contingence_n and_o because_o the_o more_o it_o be_v bend_v the_o more_o it_o digress_v from_o the_o tangent_fw-la it_o may_v be_v ask_v how_o much_o more_o and_o therefore_o the_o answer_n must_v be_v make_v by_o quantity_n and_o consequent_o a_o angle_n of_o contingence_n have_v its_o quantity_n as_o well_o as_o that_o which_o be_v call_v simple_o a_o angle_n and_o in_o case_n the_o digression_n of_o two_o such_o crooked_a line_n from_o the_o tangent_fw-la be_v uniform_a as_o in_o circle_n the_o quantity_n of_o their_o digression_n may_v be_v determine_v for_o if_o a_o straight_a line_n be_v draw_v from_o the_o point_n of_o contact_n the_o digression_n of_o the_o lesser_a circle_n will_v be_v to_o the_o digression_n of_o the_o great_a circle_n as_o the_o part_n of_o the_o line_n draw_v from_o the_o point_n of_o contact_n and_o intercept_v by_o the_o circumference_n of_o the_o great_a circle_n be_v to_o the_o part_n of_o the_o same_o line_n intercept_v by_o the_o circumference_n of_o the_o lesser_a circle_n or_o which_o be_v all_o one_o as_o the_o great_a radius_fw-la be_v to_o the_o lesser_a radius_fw-la you_o may_v guess_v by_o this_o what_o will_v become_v of_o that_o part_n of_o your_o last_o book_n where_o you_o handle_v the_o question_n of_o the_o quantity_n of_o a_o angle_n of_o contingence_n also_o there_o lie_v a_o question_n of_o how_o much_o comparative_o one_o magnitude_n be_v to_o another_o magnitude_n as_o how_o much_o water_n be_v in_o a_o tun_n in_o respect_n of_o the_o ocean_n how_o much_o in_o respect_n of_o a_o piâ—_n little_a in_o the_o first_o respect_n much_o in_o the_o latter_a therefore_o the_o answer_n must_v be_v make_v by_o some_o respective_a quantity_n this_o respective_a quantity_n be_v call_v ratio_fw-la and_o proportion_n and_o be_v determine_v by_o the_o quantity_n of_o their_o difference_n and_o if_o their_o difference_n be_v compare_v also_o with_o the_o quantity_n themselves_o that_o differ_v it_o be_v call_v simple_o proportion_n or_o proportion_n geometrical_a but_o if_o the_o difference_n be_v not_o so_o compare_v than_o it_o be_v call_v proportion_n arithmetical_a and_o where_o the_o difference_n be_v none_o there_o be_v no_o quantity_n of_o the_o proportion_n which_o in_o this_o case_n be_v but_o a_o bare_a comparison_n also_o concern_v heat_n light_n and_o divers_a other_o quality_n which_o have_v degree_n there_o lie_v a_o question_n of_o how_o much_o to_o be_v answer_v by_o a_o so_o much_o and_o consequent_o they_o have_v their_o quantity_n though_o the_o same_o with_o the_o quantity_n of_o swiftness_n because_o the_o intention_n and_o remission_n of_o such_o quality_n be_v but_o the_o intention_n and_o remission_n of_o the_o swiftness_n of_o that_o motion_n by_o which_o the_o agent_n produce_v such_o a_o quality_n and_o as_o quantity_n may_v be_v consider_v in_o all_o the_o operation_n of_o nature_n so_o also_o do_v geometry_n run_v quite_o through_o the_o whole_a body_n of_o natural_a philosophy_n to_o the_o principle_n of_o geometry_n the_o definition_n appertain_v also_o of_o a_o measure_n which_o be_v this_o one_o quantity_n be_v the_o measure_n of_o another_o quantity_n when_o it_o or_o the_o multiple_n of_o it_o be_v coincident_a in_o all_o point_n with_o the_o other_o quantity_n in_o which_o definition_n in_o stead_n of_o that_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d of_o euclid_n i_o put_v coincidence_n for_o that_o superposition_n of_o quantity_n by_o which_o they_o render_v the_o word_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d can_v be_v understand_v of_o body_n but_o only_o of_o line_n and_o superficies_n nevertheless_o many_o body_n may_v be_v coincident_a successive_o with_o one_o and_o the_o same_o place_n and_o that_o place_n will_v be_v their_o measure_n as_o we_o see_v practise_v continual_o in_o the_o measure_n of_o liquid_a body_n which_o art_n of_o measure_v may_v proper_o be_v call_v 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d but_o not_o superposition_n also_o the_o definition_n of_o great_a lesle_n and_o equal_a be_v necessary_a principle_n of_o geometry_n for_o it_o can_v be_v imagine_v that_o any_o geometrician_n shall_v demonstrate_v to_o we_o the_o equality_n and_o inequality_n of_o magnitude_n except_o he_o tell_v we_o first_o what_o those_o word_n do_v signify_v and_o it_o be_v a_o wonder_n to_o i_o '_o that_o euclid_n have_v not_o any_o where_o define_v what_o be_v equal_n or_o at_o least_o what_o be_v equal_a body_n but_o serve_v his_o turn_n throughout_o with_o that_o forementioned_a 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d which_o have_v no_o place_n in_o solid_n nor_o in_o time_n nor_o in_o swiftness_n nor_o in_o circular_a or_o other_o crooked_a line_n and_o therefore_o no_o wonder_n to_o i_o why_o geometry_n have_v not_o proceed_v to_o the_o calculation_n neither_o of_o crooked_a line_n nor_o sufficient_o of_o motion_n nor_o of_o many_o other_o thing_n that_o have_v proportion_n to_o one_o another_o equal_a body_n superficies_n and_o line_n be_v those_o of_o which_o every_o one_o be_v capable_a of_o be_v co-incident_a with_o the_o place_n of_o every_o one_o of_o the_o rest_n and_o equal_a time_n wherein_o with_o one_o and_o the_o same_o motion_n equal_a line_n be_v describe_v and_o equal_o swift_a be_v those_o motion_n by_o which_o we_o run_v over_o equal_a space_n in_o any_o time_n determine_v by_o any_o other_o motion_n and_o universal_o all_o quantity_n be_v
the_o difference_n whatsoever_o it_o be_v be_v their_o proportion_n for_o unity_n and_o to_o exceed_v another_o by_o unity_n be_v not_o the_o same_o thing_n this_o be_v clear_a enough_o to_o other_o let_v we_o therefore_o see_v why_o it_o be_v not_o so_o to_o you_o you_o say_v i_o make_v proportion_n to_o consist_v in_o that_o which_o remain_v after_o the_o lesser_a quantity_n be_v substract_v out_o of_o the_o great_a and_o that_o you_o make_v it_o to_o consist_v in_o the_o quotient_a when_o one_o number_n be_v divide_v by_o the_o other_o wherein_o you_o be_v mistake_v first_o in_o that_o you_o say_v i_o make_v the_o proportion_n to_o consist_v in_o the_o remainder_n for_o i_o make_v it_o to_o consist_v in_o the_o act_n of_o exceed_v or_o of_o be_v exceed_v or_o of_o be_v equal_a whereas_o the_o remainder_n be_v always_o a_o absolute_a quantity_n and_o never_o a_o proportion_n to_o be_v more_o or_o less_o than_o another_o number_n by_o two_o be_v not_o the_o number_n two_o likewise_o to_o be_v equal_a to_o two_o where_o the_o difference_n be_v nothing_o be_v not_o that_o nothing_o again_o you_o mistake_v in_o say_v the_o proportion_n consist_v in_o the_o quotient_a for_o divide_v twenty_o by_o five_o the_o quotient_n be_v four_o be_v it_o not_o absurd_a to_o say_v that_o the_o proportion_n of_o five_o to_o twenty_o or_o of_o twenty_o to_o five_o be_v four_z you_o may_v say_v the_o proportion_n of_o five_o to_o twenty_o be_v the_o proportion_n of_o one_o to_o four_o and_o so_o say_v i._o and_o you_o may_v therefore_o also_o say_v that_o the_o proportion_n of_o one_o to_o four_o be_v a_o measure_n of_o the_o proportion_n of_o five_o to_o twenty_o as_o be_v equal_a and_o so_o say_v i._n but_o that_o be_v only_o in_o geometrical_a proportion_n and_o not_o in_o proportion_n universal_o for_o though_o the_o species_n obtain_v the_o denomination_n of_o the_o genus_fw-la yet_o it_o be_v not_o the_o genus_fw-la but_o as_o the_o quotient_n give_v we_o a_o measure_n of_o the_o proportion_n of_o the_o dividend_n to_o the_o divisor_n in_o geometrical_a proportion_n so_o also_o the_o remainder_n after_o substraction_n be_v the_o measure_n of_o proportion_n arithmetical_a you_o object_n in_o the_o next_o place_n that_o if_o the_o proportion_n of_o one_o quantity_n to_o another_o be_v nothing_o but_o the_o excess_n or_o defect_n then_o wheresoever_o the_o excess_n or_o defect_n be_v the_o same_o there_o the_o proportion_n be_v the_o same_o this_o you_o say_v follow_v in_o your_o logic_n and_o from_o thence_o that_o the_o proportion_n of_o three_o to_o two_o and_o five_o to_o four_o be_v the_o same_o but_o be_v not_o three_o to_o two_o and_o five_o to_o four_o where_o the_o excess_n be_v the_o same_o number_n the_o same_o proportion_n arithmetical_a and_o be_v not_o arithmetical_a proportion_n proportion_n you_o take_v here_o ratio_fw-la proportion_n which_o be_v the_o genus_fw-la for_o that_o species_n of_o it_o which_o be_v call_v geometrical_a because_o usual_o this_o species_n have_v the_o name_n of_o proportion_n simple_o also_o that_o the_o proportion_n of_o three_o to_o two_o be_v the_o same_o with_o that_o of_o nine_o to_o six_o be_v it_o not_o because_o the_o excess_n be_v one_o and_o three_o the_o same_o portion_n of_o three_o and_o nine_o that_o be_v to_o say_v the_o same_o excess_n comparative_o i_o wonder_v you_o ask_v i_o not_o what_o be_v the_o gâ—nus_n of_o arithmetical_a and_o geometrical_a proportion_n and_o what_o the_o difference_n the_o genus_fw-la be_v ratio_fw-la proportion_n or_o comparison_n in_o magnitude_n and_o the_o difference_n be_v that_o one_o comparison_n be_v make_v by_o the_o absolute_a quantity_n the_o other_o by_o the_o comparative_a quantity_n of_o the_o excess_n or_o defect_n if_o there_o be_v any_o can_v any_o thing_n be_v clear_a than_o this_o you_o aâ—ter_v come_v in_o with_o ignosce_fw-la hebitudini_fw-la too_o no_o purpose_n i_o be_o not_o so_o inhuman_a as_o not_o to_o pardon_v dulness_n or_o madness_n they_o be_v not_o voluntary_a fault_n but_o when_o man_n adventure_v voluntary_o to_o talk_v of_o that_o they_o understand_v not_o censorious_o and_o scornful_o i_o may_v tell_v they_o of_o it_o this_o difference_n between_o the_o excess_n or_o defect_n as_o they_o be_v simple_o or_o comparative_o reckon_v be_v thus_o explain_v all_o the_o rest_n of_o that_o you_o say_v in_o your_o objection_n to_o this_o eleven_o chapter_n save_v that_o artt._n 5._o for_o ratio_fw-la binarii_fw-la ad_fw-la quinarium_fw-la est_fw-la superarâ—_n tâ—rnario_n as_o it_o be_v in_o other_o place_n i_o have_v put_v too_o hasty_o ratio_fw-la binarii_fw-la ad_fw-la quinarium_fw-la est_fw-la ternarius_fw-la will_v be_v understand_v by_o every_o reader_n to_o be_v frivolous_a and_o to_o proceed_v from_o the_o ignorance_n of_o what_o proportion_n be_v at_o the_o twelve_o chapter_n you_o only_o note_v that_o i_o say_v that_o the_o proportion_n of_o inequality_n be_v quantity_n but_o the_o proportion_n of_o equality_n not_o quantity_n and_o refer_v that_o which_o you_o have_v to_o say_v against_o it_o to_o the_o chapter_n follow_v to_o which_o place_n i_o shall_v also_o come_v in_o the_o follow_a lesson_n of_o the_o fault_n that_o occur_v in_o demonstration_n to_o the_o same_o egregious_a professor_n of_o the_o mathematics_n in_o the_o university_n of_o oxford_n lesson_n iii_o you_o begin_v your_o reprehension_n of_o my_o thirteen_o chapter_n with_o a_o question_n whereas_o i_o divide_v proportion_n into_o arithmetical_a and_o geometrical_a you_o ask_v i_o what_o proportion_n it_o be_v i_o so_o divide_v euclid_n divide_v a_o angle_n into_o right_n obtuse_a and_o acute_a i_o may_v ask_v you_o as_o pertinent_o what_o angle_n it_o be_v he_o so_o divide_v or_o when_o you_o device_n animal_n into_o homo_fw-la and_o brâ—tum_n what_o animal_n that_o be_v which_o you_o so_o divide_v you_o see_v by_o this_o how_o absurd_a your_o question_n be_v but_o you_o say_v the_o definition_n of_o proportion_n which_o i_o make_v at_o chap._n 11._o art_n 3._o namely_o that_o proportion_n be_v the_o comparison_n of_o two_o magnitude_n one_o to_o another_o agree_v not_o neither_o with_o arithmetical_a nor_o with_o geometrical_a proportion_n i_o believe_v you_o think_v so_o then_o but_o have_v read_v what_o i_o have_v say_v in_o the_o end_n of_o the_o last_o lesson_n if_o you_o think_v so_o still_o your_o fault_n will_v be_v too_o great_a to_o be_v pardon_v easy_o but_o why_o do_v you_o think_v so_o before_o be_v it_o not_o because_o there_o be_v no_o definition_n in_o euclid_n of_o proportion_n universal_a and_o because_o he_o make_v no_o mention_n of_o proportion_n arithmetical_a and_o because_o you_o have_v not_o in_o your_o mind_n a_o sufficient_a notion_n thereof_o yourselves_o to_o supply_v that_o defect_n and_o be_v not_o this_o the_o cause_n also_o why_o you_o put_v in_o this_o parenthesis_n if_o arithmetical_a proportion_n aught_o to_o be_v call_v proportion_n which_o be_v a_o confession_n that_o you_o know_v not_o whether_o there_o be_v such_o a_o thing_n as_o arithmetical_a proportion_n or_o not_o notwithstanding_o that_o on_o all_o occasion_n you_o speak_v of_o arithmetical_o proportional_n yes_o this_o be_v it_o that_o make_v you_o think_v that_o proportion_n universal_o and_o proportion_n geometrical_a be_v the_o same_o and_o yet_o to_o say_v you_o can_v tell_v whether_o they_o be_v the_o same_o or_o not_o it_o be_v no_o wonder_n therefore_o if_o in_o such_o confusion_n of_o the_o understanding_n you_o apprehend_v not_o that_o the_o proportion_n of_o two_o to_o five_o and_o nine_o to_o twelve_o be_v the_o same_o for_o you_o be_v blind_v by_o see_v that_o they_o be_v not_o the_o same_o proportion_n geometrical_a nor_o do_v it_o help_v you_o that_o i_o say_v the_o difference_n be_v the_o proportion_n fâ—â—_n by_o difference_n you_o may_v if_o you_o will_v have_v understand_v the_o act_n of_o differ_v at_o the_o second_o article_n you_o note_v for_o a_o fault_n in_o method_n that_o after_o i_o have_v use_v the_o word_n antecedent_n and_o consequent_a of_o a_o proportion_n in_o some_o of_o the_o precedent_a chapter_n i_o define_v they_o afterward_o i_o do_v not_o believe_v you_o say_v this_o against_o your_o knowledge_n but_o that_o the_o eagerness_n of_o your_o malice_n make_v you_o oversee_v therefore_o go_v back_o again_o to_o the_o three_o article_n of_o chap._n 11._o where_o have_v define_v correlative_n i_o add_v these_o word_n of_o which_o the_o first_o be_v call_v the_o antecedent_n the_o second_o the_o consequent_a this_o be_v but_o a_o oversight_n though_o such_o as_o in_o i_o you_o will_v not_o have_v excuse_v at_o the_o thirteen_o article_n you_o find_v fault_n with_o that_o i_o say_v that_o the_o proportion_n of_o inequality_n whether_o it_o be_v of_o excess_n or_o of_o defect_n be_v quantity_n but_o the_o proportion_n of_o equality_n be_v not_o quanty_a whether_o that_o which_o you_o say_v