Selected quad for the lemma: book_n

Word A Word B Word C Word D Occurrence Frequency Band MI MI Band Prominent
book_n concern_v time_n write_v 2,871 5 5.4131 4 true
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
A44011 Seven philosophical problems and two propositions of geometry by Thomas Hobbes of Malmesbury ; with an apology for himself and his writings. Hobbes, Thomas, 1588-1679. 1682 (1682) Wing H2259; ESTC R28663 37,975 99

There is 1 snippet containing the selected quad. | View original text

its_o own_o side_n so_o that_o the_o unit_fw-la which_o be_v before_o sometime_o a_o line_n sometime_o a_o square_a be_v now_o a_o cube_n b._n it_o can_v be_v no_o otherwise_o when_o you_o so_o apply_v arithmetic_n to_o geometry_n as_o to_o number_v the_o line_n of_o a_o plain_a or_o the_o plain_n of_o a_o cube_n a._n in_o the_o next_o place_n i_o find_v that_o the_o cube_n of_o die_v be_v equal_a to_o 45_o want_v the_o square_a root_n of_o 1622._o what_o be_v that_o 45_o line_n or_o square_n or_o cube_n b._n cube_n cube_n of_o dv_o a._n then_o if_o you_o add_v to_o 45_o cube_n of_o dv_o the_o square_a root_n of_o 1682_o the_o sum_n will_v be_v 45_o cube_n of_o dv_o and_o if_o you_o add_v to_o the_o cube_n of_o die_v the_o same_o root_n of_o 1682_o the_o sum_n will_v be_v the_o cube_n of_o die_v plus_fw-la the_o square_a root_n of_o 1682._o and_o these_o two_o sum_n must_v be_v equal_a b._n they_o must_v so_o a._n but_o the_o square_a root_n of_o 1682_o be_v a_o line_n add_v nothing_o to_o a_o cube_n therefore_o the_o cube_n alone_o of_o die_v which_o he_o say_v be_v equal_a almost_o to_o 4._o cube_n of_o dv_o be_v equal_a to_o 45_o cube_n of_o the_o same_o dv_o b._n all_o these_o impossibility_n do_v necessary_o follow_v the_o confound_a of_o arithmetic_n and_o geometry_n a._n i_o pray_v you_o let_v i_o see_v the_o operation_n by_o which_o the_o cube_n of_o die_v that_o be_v the_o cube_n of_o 3_o want_v the_o root_n of_o 2_o be_v find_v equal_a to_o 45_o want_v the_o square_a root_n of_o 1682._o a_o detection_n of_o the_o absurd_a use_n of_o arithmetic_n as_o it_o be_v now_o apply_v to_o geometry_n b._n here_o it_o be_v 3_o r._n 2._o 3_o r._n 2._o r._n 18_o ✚_o two_o 9_o r._n 18_o 9_o r._n 72_o ✚_o 2._o 3_o r._n 2._o r._n 162_o ✚_o 12_o r._n 8._o 27_o r._n 648_o ✚_o 6_o 27_o r._n 658_o r._n 162_o ✚_o 18_o r._n 8._o a._n why_o for_o two_o root_n of_o 18_o do_v you_o put_v the_o root_n of_o 72._o b._n because_o 2_o root_n of_o 18_o be_v equal_a to_o one_o root_n of_o 4_o time_n 18_o which_o be_v 72._o a._n next_o we_o have_v that_o the_o root_n of_o 2_o multiply_v into_o 2_o make_v the_o root_n of_o 8._o how_o be_v that_o true_a b._n do_v it_o not_o make_v 2_o root_n of_o 2_o and_o be_v not_o br_n the_o root_n of_o 2_o and_o 2_o br_n equal_a to_o the_o diagonal_a and_o be_v not_o the_o diagonal_a the_o root_n of_o a_o square_a equal_a to_o 8_o square_n of_o dv_o a._n it_o be_v true_a but_o here_o the_o root_n of_o 8_o be_v put_v for_o the_o cube_n of_o the_o root_n of_o 2._o can_v a_o line_n be_v equal_a to_o a_o cube_n b._n no._n but_o here_o we_o be_v in_o arithmetic_n again_o and_o 8_o be_v a_o cubique_a number_n a._n how_o do_v the_o root_n of_o 2_o multiply_v into_o the_o root_n of_o 72_o make_v 12_o b._n because_o it_o make_v the_o root_n of_o 2_o time_n 72_o that_o be_v to_o say_v the_o root_n of_o 144_o which_o be_v 12._o a._n how_o do_v 9_o root_n of_o 2_o make_v the_o root_n of_o 162_o b._n because_o it_o make_v the_o root_n of_o 2_o square_n of_o 9_o that_o be_v the_o root_n of_o 162._o a._n how_o do_v 3_o root_n of_o 72_o make_v the_o root_n of_o 648_o b._n because_o it_o make_v the_o root_n of_o 9_o time_n 72_o that_o be_v of_o 648._o a._n for_o the_o total_a sum_n i_o see_v 27_o and_o 18_o which_o make_v 45._o therefore_o the_o root_n of_o 648_o together_o with_o the_o root_n of_o 162●_n and_o of_o 8_o which_o be_v to_o be_v deduct_v from_o 45_o aught_o to_o be_v equal_a to_o the_o root_n of_o 1682._o b._n so_o they_o be_v for_o 648_o multiply_v by_o 162_o make_v 104976_o of_o which_o the_o double_a root_n be_v 648_o and_o 648_o and_o 162_o add_v together_o make_v 810._o therefore_o the_o root_n of_o 948_o add_v to_o the_o root_n of_o 162_o make_v the_o root_n of_o 1459_o again_o 1458_o into_o 8_o be_v 11664._o the_o double_a root_n whereof_o be_v 216._o the_o sum_n of_o 1458_o and_o 8_o add_v together_o be_v 1466._o the_o sum_n of_o 1466_o and_o 216_o be_v 1682_o and_o the_o root_n the_o root_n of_o 1682._o a._n i_o see_v the_o calculation_n in_o number_n be_v right_n though_o false_a in_o line_n the_o reason_n whereof_o can_v be_v no_o other_o than_o some_o difference_n between_o multiply_a number_n into_o line_n or_o plain_n and_o multiply_a line_n into_o the_o same_o line_n or_o plain_n b._n the_o difference_n be_v manifest_a for_o when_o you_o multiply_v a_o number_n into_o line_n the_o product_n be_v line_n as_o the_o number_n 2_o multiply_v into_o 3_o line_n be_v no_o more_o than_o 3_o line_n 2_o time_n tell_v but_o if_o you_o multiply_v line_n into_o line_n you_o make_v plain_n and_o if_o you_o multiply_v line_n into_o plain_n you_o make_v solid_a body_n in_o geometry_n there_o be_v but_o three_o dimension_n length_n superficies_n and_o body_n in_o arithmetic_n there_o be_v but_o one_o and_o that_o be_v number_n or_o length_n which_o you_o will_n and_o though_o there_o be_v some_o number_n call_v plain_a other_o solid_a other_o plano-solid_a other_o square_a other_o cubique_fw-la other_o square-square_a other_o quadrato-cubique_a other_o cubi-cubique_a etc._n etc._n yet_o be_v all_o these_o but_o one_o dimension_n namely_o number_n or_o a_o file_n of_o thing_n number_v a._n but_o see_v this_o way_n of_o calculation_n by_o number_n be_v so_o apparent_o false_a what_o be_v the_o reason_n this_o calculation_n come_v so_o near_o the_o truth_n b._n it_o be_v because_o in_o arithmetic_n unit_v be_v not_o nothing_o and_o therefore_o have_v breadth_n and_o therefore_o many_o line_n set_v together_o make_v a_o superficies_n though_o their_o breadth_n be_v insensible_a and_o the_o great_a the_o number_n be_v into_o which_o you_o divide_v your_o line_n the_o less_o sensible_a will_v be_v your_o error_n a._n archimedes_n to_o find_v a_o straight_a line_n equal_a to_o the_o circumferrence_n of_o a_o circle_n use_v this_o may_n of_o extract_a root_n and_o it_o be_v the_o way_n also_o by_o which_o the_o table_n of_o sines_n secant_v and_o tangent_n have_v be_v calculate_v be_v they_o all_o cut_n b._n as_o for_o archimedes_n there_o be_v no_o man_n that_o do_v more_o admire_v he_o then_o i_o do_v but_o there_o be_v no_o man_n that_o can_v err._n his_o reason_n be_v good_a but_o he_o add_v all_o other_o geometricans_n before_o and_o after_o he_o have_v have_v two_o principle_n that_o cross_a one_o another_o when_o they_o be_v apply_v to_o one_o and_o the_o same_o science_n one_o be_v that_o a_o point_n be_v no_o part_n of_o a_o line_n which_o be_v true_a in_o geometry_n where_o a_o part_n of_o a_o line_n when_o it_o be_v call_v a_o point_n be_v not_o reckon_v another_o be_v that_o a_o unit_fw-la be_v part_n of_o a_o number_n which_o be_v also_o true_a but_o when_o they_o reckon_v by_o arethmetick_n in_o geometry_n there_o a_o unit_fw-la be_v sometime_o part_n of_o a_o line_n sometime_o a_o part_n of_o a_o square_a and_o sometime_o part_v of_o a_o cube_n as_o for_o the_o table_n of_o sines_n secant_v and_o tangent_n i_o be_o not_o the_o first_o that_o find_v fault_n with_o they_o yet_o i_o deny_v not_o but_o they_o be_v true_a enough_o for_o the_o reckon_n of_o acre_n in_o a_o map_n of_o land_n a._n what_o a_o deal_n of_o labour_n have_v be_v lose_v by_o they_o that_o be_v professor_n of_o geometry_n have_v read_v nothing_o else_o to_o their_o auditor_n but_o such_o stuff_n as_o this_o you_o have_v here_o see_v and_o some_o of_o they_o have_v write_v great_a book_n of_o it_o in_o strange_a character_n such_o as_o in_o troublesome_a time_n a_o man_n will_v suspect_v to_o be_v a_o cypher_n b._n i_o think_v you_o have_v see_v enough_o to_o satisfy_v you_o that_o what_o i_o have_v write_v heretofore_o concern_v the_o quadrature_n of_o the_o circle_n and_o of_o other_o figure_n make_v in_o imitation_n of_o the_o parabola_fw-la have_v not_o be_v yet_o confute_v a._n i_o see_v you_o have_v wrest_v out_o of_o the_o hand_n of_o our_o antagonist_n this_o weapon_n of_o algebra_n so_o as_o they_o can_v never_o make_v use_n of_o it_o again_o which_o i_o consider_v as_o a_o thing_n of_o much_o more_o consequence_n to_o the_o science_n of_o geometry_n then_o either_o of_o the_o duplication_n of_o the_o cube_n or_o the_o find_n of_o two_o mean_v proportional_n or_o the_o quadrature_n of_o a_o circle_n or_o all_o these_o problem_n put_v together_o finis_fw-la book_n write_v by_o this_o author_n and_o print_v for_o william_n crook_n 1_o de_fw-fr mirabilibus_fw-la pecci_n in_o quarto_fw-la latin_n in_o octavo_n in_o english_a and_o lantin_n 2_o three_o paper_n to_o the_o royal_a society_n against_o dr._n wallis_n 3_o lumathematica_fw-la 4_o prima_fw-la partis_fw-la doctrinae_fw-la wallisianae_n de_fw-la motu_fw-la censura_fw-la brevis_fw-la 5_o resetum_fw-la geometricum_fw-la sive_fw-la propositiones_fw-la aliquot_fw-la frustra_fw-la antehac_fw-la tentatae_fw-la 6_o principia_fw-la &_o poblemata_fw-la aliquot_fw-la geometrica_fw-la ante_fw-la desperata_fw-la nunc_fw-la breviter_fw-la explicata_fw-la &_o demonstrata_fw-la 7_o quadratura_fw-la circuli_fw-la cubatio_n sphere_n duplicatio_fw-la cubi_n breviter_fw-la demonstrata_fw-la 8_o consideration_n on_o his_o loyalty_n reputation_n religion_n and_o manner_n by_o himself_o 9_o de_fw-fr principio_fw-la &_o ratione_fw-la geometry_n 20_o the_o travel_n of_o vlise_n translate_v from_o homer_n 11_o epistol_n ad_fw-la dr._n wood._n 12_o the_o translation_n of_o all_o homer_n work_n into_o english_a 13_o the_o epitome_n of_o the_o civil_a war_n of_o enland_n from_o 1640_o to_o 1660._o 14_o aristotle_n rhetoric_n translate_v into_o english_a by_o he_o with_o his_o own_o rhetoric_n to_o it_o 15_o a_o dialogue_n betwixt_o a_o student_n in_o the_o common-law_n of_o england_n and_o a_o philosopher_n in_o which_o be_v set_v forth_o the_o error_n in_o some_o practice_n 16_o a_o narration_n of_o heresy_n and_o the_o punishment_n thereof_o 17_o ten_o dialogue_n of_o natural_a philosophy_n 18_o a_o poem_n in_o latin_a of_o his_o life_n 19_o idem_fw-la the_o same_o in_o english_a 20_o his_o life_n write_v in_o latin_a part_n by_o himself_o and_o the_o rest_n by_o dr._n r._n b._n wherein_o be_v contain_v the_o most_o material_a part_n of_o his_o life_n 21_o seven_o philosophical_a problem_n and_o two_o proposition_n of_o geometry_n with_o a_o apology_n for_o himself_o and_o his_o write_n dedicate_v to_o the_o king_n in_o the_o year_n 1662._o