Selected quad for the lemma: hand_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
hand_n	left_a	right_a	string_n	8,078	5	13.9494	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A48262	Mathematicall recreations. Or, A collection of many problemes, extracted out of the ancient and modern philosophers as secrets and experiments in arithmetick, geometry, cosmographie, horologiographie, astronomie, navigation, musick, opticks, architecture, statick, mechanicks, chemistry, water-works, fire-works, &c. Not vulgarly manifest till now. Written first in Greeke and Latin, lately compi'ld in French, by Henry Van Etten, and now in English, with the examinations and augmentations of divers modern mathematicians whereunto is added the description and use of the generall horologicall ring: and the double horizontall diall. Invented and written by William Oughtred.; Récréation mathématique. English.	Oughtred, William, 1575-1660. aut	1653 (1653)	Wing L1790; ESTC R217635	140,825	339

have_v his_o head_n and_o foot_n upward_o problem_n xxv_o of_o a_o ladder_n by_o which_o two_o man_n ascend_v at_o one_o time_n the_o more_o they_o ascend_v the_o more_o they_o shall_v be_v asunder_o notwithstanding_o one_o be_v as_o high_a as_o another_o this_o be_v most_o evident_a that_o if_o there_o be_v a_o ladder_n half_a on_o this_o side_n of_o the_o centre_n of_o the_o earth_n and_o the_o other_o half_n on_o the_o other_o side_n and_o that_o two_o at_o the_o centre_n of_o the_o world_n at_o one_o instant_n be_v to_o ascend_v the_o one_o towards_o we_o and_o the_o other_o towards_o our_o antipode_n they_o shall_v in_o ascend_v go_v far_a and_o far_o one_o from_o another_o notwithstanding_o both_o of_o they_o be_v of_o like_a height_n problem_n xxvi_o how_o it_o be_v that_o a_o man_n have_v but_o a_o rod_n or_o pole_n of_o land_n do_v brag_v that_o he_o may_v in_o a_o right_a line_n pass_v from_o place_n to_o place_n above_o 3000_o mile_n the_o open_n of_o this_o be_v easy_a 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be_v add_v by_o that_o which_o multiply_v so_o than_o your_o quotient_n shall_v be_v equal_a to_o his_o remainder_n wherefore_o without_o ask_v he_o any_o thing_n you_o shall_v tell_v he_o what_o do_v remain_v which_o will_v seem_v strange_a to_o he_o that_o know_v not_o the_o cause_n for_o example_n suppose_v he_o think_v 7_o which_o multiply_v by_o 5_o make_v 35_o to_o which_o add_v 10_o make_v 45_o which_o divide_v by_o 5_o yield_v 9_o from_o which_o if_o you_o take_v away_o one_o the_o number_n think_v because_o the_o multiplier_n divide_v by_o the_o divisor_n give_v the_o quotient_a 1_o the_o rest_n will_v be_v two_o which_o will_v be_v also_o prove_v if_o 10_o the_o number_n which_o be_v add_v be_v divide_v by_o 5_o viz._n 2._o problem_n xxix_o of_o the_o play_n with_o two_o several_a thing_n it_o be_v a_o pleasure_n to_o see_v and_o consider_v how_o the_o science_n of_o number_n do_v furnish_v we_o not_o only_o 〈…〉_z recreate_v the_o spirit_n but_o also_o 〈…〉_z knowledge_n of_o admirable_a thing_n 〈…〉_z measure_n be_v show_v in_o this_o 〈…〉_z the_o mean_a time_n to_o produce_v always_o some_o of_o they_o suppose_v that_o a_o man_n hold_v divers_a thing_n in_o his_o hand_n as_o gold_n and_o ●ilver_n and_o in_o one_o hand_n he_o hold_v the_o gold_n and_o in_o the_o other_o hand_n he_o hold_v the_o silver_n to_o know_v subtle_o and_o by_o way_n of_o divination_n or_o artificial_o in_o which_o hand_n the_o gold_n or_o silver_n be_v attribute_v t●_n the_o gold_n or_o suppose_v it_o have_v a_o certain_a price_n and_o so_o likewise_o attribute_v to_o the_o silver_n another_o price_n conditional_o that_o the_o one_o be_v odd_a and_o the_o other_o even_o as_o for_o example_n bid_v h●m_n that_o the_o gold_n be_v value_v at_o 4_o crown_n or_o shilling_n and_o the_o silver_n at_o ●_o crown_n or_o 3_o shilling_n or_o any_o other_o number_n so_o that_o one_o be_v odd_a and_o the_o other_o even_o as_o before_o then_o bid_v he_o triple_a that_o which_o be_v in_o the_o 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which_o 9_o without_o ask_v any_o qustion_n and_o this_o seem_v most_o subtle_a yet_o deliver_v howsoever_o differ_v little_a from_o the_o former_a and_o be_v thus_o perform_v take_v private_o to_o yourself_o also_o two_o number_n the_o one_o even_o and_o the_o other_o odd_a as_o 4._o and_o 3._o then_o bid_v peter_n that_o he_o double_v the_o number_n which_o he_o take_v and_o do_v you_o private_o double_v also_o your_o great_a number_n then_o bid_v john_n to_o triple_a the_o number_n which_o he_o have_v and_o do_v you_o the_o like_a upon_o your_o last_o number_n add_v your_o two_o product_n together_o &_o mark_v if_o it_o be_v even_o or_o odd_a then_o bid_v the_o two_o party_n put_v their_o number_n together_o and_o bid_v they_o take_v the_o half_a of_o it_o which_o if_o they_o can_v do_v then_o immediate_o tell_v peter_n he_o take_v 10._o and_o john_n 9_o because_o the_o aggregate_v of_o the_o double_a of_o 4._o and_o the_o triple_a of_o 3._o make_v odd_a and_o such_o will_v be_v the_o aggregate_v or_o sum_n of_o the_o double_a of_o peter_n number_n and_o john_n number_n if_o peter_n have_v take_v 10._o if_o otherwise_o than_o they_o may_v have_v take_v half_a and_o so_o john_n shall_v have_v take_v 10._o and_o peter_n 9_o as_o suppose_v peter_n have_v take_v 10._o the_o double_a be_v 20._o and_o the_o triple_a of_o 9_o the_o other_o ●umber_n be_v 27._o which_o put_v together_o make_v 47._o odd_a in_o like_a manner_n the_o double_a of_o your_o number_n conceive_v in_o mind_n viz._n 4._o make_v 8._o and_o the_o triple_a of_o the_o 3._o the_o other_o number_n make_v 9_o which_o set_v together_o make_v 17._o odd_a now_o you_o can_v take_v the_o half_a of_o 17_o nor_o 47._o which_o argue_v that_o peter_n have_v the_o great_a number_n for_o otherwise_o the_o double_a of_o 9_o be_v 18._o &_o the_o triple_a of_o 10._o be_v 30._o which_o set_v together_o make_v 48._o the_o half_a of_o it_o may_v be_v take_v therefore_o in_o such_o case_n peter_n the_o take_v less_o number_n and_o john_n the_o great_a and_o this_o be_v do_v clean_o carry_v much_o grace_n with_o it_o problem_n xxxi_o how_o to_o describe_v a_o circle_n that_o shall_v touch_v 3_o point_n place_v howsoever_o upon_o a_o plain_a if_o they_o be_v not_o in_o a_o right_a line_n let_v the_o three_o point_n be_v a.b.c._n put_v one_o foot_n of_o the_o compass_n upon_o a._n and_o describe_v a_o arch_n of_o a_o circle_n at_o pleasure_n and_o place_v at_o b._n across_o that_o arch_n in_o the_o two_o point_n e._n and_o f._n and_o place_v in_o c._n across_o the_o arch_n in_o g._n and_o h._n then_o lay_v a_o ruler_n upon_o g.h._n and_o draw_v

as_o they_o will_v be_v if_o there_o be_v a_o liquid_a substance_n in_o the_o glass_n hence_o they_o have_v a_o assure_a proof_n to_o conclude_v that_o the_o hollow_v of_o the_o glass_n be_v total_o empty_a problem_n xl._o if_o any_o one_o shall_v hold_v in_o each_o hand_n as_o many_o piece_n of_o money_n as_o in_o the_o other_o how_o to_o find_v how_o much_o there_o be_v bid_v he_o that_o hold_v the_o money_n that_o he_o put_v out_o of_o one_o hand_n into_o the_o other_o what_o number_n you_o think_v convenient_a provide_v that_o it_o may_v be_v do_v this_o do_v bid_v he_o that_o out_o of_o the_o hand_n that_o he_o put_v the_o other_o number_n into_o that_o he_o take_v out_o of_o it_o as_o many_o as_o remain_v in_o the_o other_o hand_n and_o put_v it_o into_o that_o hand_n for_o then_o be_v assure_v that_o in_o the_o hand_n which_o be_v put_v the_o first_o take_v away_o there_o will_v be_v find_v just_o the_o double_a of_o the_o number_n take_v away_o at_o the_o first_o example_n 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the_o other_o two_o then_o bid_v he_o throw_v these_o two_o dice_n and_o mark_v how_o many_o point_v a_o pair_n be_v upward_o which_o add_v unto_o the_o former_a sum_n then_o put_v one_o of_o these_o dice_n away_o not_o change_v the_o side_n mark_v the_o point_n which_o be_v under_o the_o other_o dice_n and_o add_v it_o to_o the_o former_a sum_n last_o throw_v that_o one_o dice_n and_o whatsoever_o appear_v upward_o add_v it_o unto_o the_o former_a sum_n and_o let_v the_o dice_n remain_v thus_o this_o do_v come_v to_o the_o table_n note_v what_o point_n do_v appear_v upward_o upon_o the_o three_o dice_n which_o add_v private_o together_o and_o unto_o it_o add_v ●1_n or_o 3_o time_n 7_o so_o this_o addition_n or_o sum_n shall_v be_v equal_a to_o the_o sum_n which_o the_o party_n private_o make_v of_o all_o the_o operation_n which_o he_o former_o make_v as_o if_o he_o shall_v throw_v three_o dice_n and_o there_o shall_v appear_v upward_o 5_o 3_o 2._o the_o sum_n of_o they_o be_v 10._o and_o set_v one_o of_o they_o apart_o as_o 5._o unto_o 10_o add_v the_o point_n which_o be_v under_o 3_o and_o 2_o which_o be_v 4_o and_o 5_o and_o it_o make_v 19_o then_o cast_v these_o two_o dice_n suppose_v there_o shall_v appear_v 4_o and_o 1_o this_o add_v unto_o 19_o make_v 24._o and_o set_v one_o of_o these_o two_o dice_n apart_o as_o the_o 4._o unto_o the_o former_a 24_o i_o add_v the_o number_n of_o point_n which_o be_v under_o the_o other_o dice_n viz._n under_o 1_o that_o be_v 6_o which_o make_v 30._o last_o of_o all_o i_o throw_v that_o one_o dice_n and_o suppose_v there_o do_v appear_v 2_o which_o i_o add_v to_o the_o former_a 30_o and_o it_o make_v 32_o then_o leave_v the_o 3_o dice_n thus_o the_o point_n which_o be_v upward_o will_v be_v these_o 5_o 4_o 2_o unto_o which_o add_v secret_o 21_o as_o before_o be_v say_v so_o have_v you_o 32_o the_o same_o number_n which_o he_o have_v and_o in_o the_o same_o manner_n you_o may_v practice_v with_o 4_o 5_o 6_o or_o many_o 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the_o intention_n of_o archimedes_n be_v not_o upon_o contrary_a metal_n enclose_v in_o 〈…〉_z box_n but_o consist_v of_o compare_v metta●●●_n simple_a in_o the_o water_n one_o with_o another_o therefore_o the_o inference_n be_v false_a and_o absurd_a problem_n xliii_o two_o globe_n of_o diverse_a metal_n as_o one_o gold_n and_o the_o other_o copper_n yet_o of_o equal_a weight_n be_v put_v into_o a_o box_n as_o bg_n to_o find_v in_o which_o end_n the_o gold_n or_o copper_n be_v this_o be_v discover_v by_o the_o change_n of_o the_o place_n of_o the_o two_o bowles_n or_o globe_n

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to_o shoot_v at_o he_o this_o can_v be_v for_o no_o object_n whatsoever_o present_v to_o a_o concave_a glass_n if_o it_o be_v not_o near_o to_o the_o grass_n than_o the_o eye_n be_v it_o come_v not_o out_o to_o the_o sight_n of_o the_o party_n therefore_o he_o need_v not_o fear_v that_o which_o be_v say_v to_o be_v behind_o his_o back_n and_o come_v out_o of_o the_o glass_n for_o if_o it_o do_v come_v out_o it_o must_v then_o necessary_o be_v before_o his_o face_n so_o in_o a_o concave_a glass_n who_o centre_n be_v far_o remote_a of_o a_o sword_n stick_v or_o such_o like_a be_v present_v to_o the_o glass_n it_o shall_v total_o be_v see_v to_o come_v forth_o of_o the_o glass_n and_o all_o the_o hand_n that_o hold_v it_o and_o here_o general_o note_v that_o if_o a_o image_n be_v see_v to_o issue_v out_o of_o the_o glass_n to_o come_v towards_o the_o face_n of_o any_o one_o that_o stand_v by_o the_o object_n shall_v be_v likewise_o see_v to_o thrust_v towards_o that_o face_n in_o the_o 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in_o obscurity_n or_o shadow_v or_o else_o it_o will_v not_o be_v see_v to_o cast_v light_n in_o the_o night_n to_o a_o place_n remote_a with_o a_o candle_n place_v in_o the_o point_n of_o concourse_n or_o inflammation_n be_v one_o of_o the_o most_o notable_a property_n which_o can_v be_v show_v in_o a_o concave_a glass_n for_o if_o in_o the_o point_n of_o inflammation_n of_o a_o parabolicall_a section_n a_o candle_n be_v place_v the_o light_n will_v be_v reflect_v by_o parallel_a line_n as_o a_o column_n or_o cylinder_n but_o in_o the_o spherical_a section_n it_o be_v defective_a in_o part_n the_o beam_n be_v not_o unite_v in_o one_o point_n

a_o line_n and_o place_v a_o ruler_n upon_o e._n and_o f._n cut_v the_o other_o line_n in_o k_o so_o k_o be_v the_o centre_n of_o the_o circumference_n of_o a_o circle_n which_o will_v pass_v by_o the_o say_v three_o point_n a.b.c._n or_o it_o may_v be_v invert_v have_v a_o circle_n draw_v to_o find_v the_o centre_n of_o that_o circle_n make_v 3._o point_n in_o the_o circumference_n and_o then_o use_v the_o same_o way_n so_o shall_v you_o have_v the_o centre_n a_o thing_n most_o facile_a to_o every_o practitioner_n in_o the_o principle_n of_o geometry_n problem_n xxxii_o how_o to_o change_v a_o circle_n into_o a_o square_a form_n m●ke_v a_o circle_n upon_o pasteboard_n or_o other_o material_a as_o the_o circle_n a.c.d.e._n of_o which_o a._n be_v the_o centre_n then_o cut_v it_o into_o 4_o quarter_n and_o dispose_v they_o so_o that_o a._n at_o the_o centre_n of_o the_o circle_n may_v always_o be_v at_o the_o angle_n of_o the_o square_n and_o so_o the_o four_o quarter_n of_o the_o circle_n be_v place_v so_o it_o will_v make_v a_o perfect_a square_n who_o side_n a.a._n be_v equal_a to_o the_o diameter_n b.d._n now_o here_o be_v to_o be_v note_v that_o the_o square_n be_v great_a than_o the_o circle_n by_o the_o vacuity_n in_o the_o middle_n viz._n m._n problem_n xxxiii_o with_o one_o and_o the_o same_o compass_n and_o at_o one_o and_o the_o same_o extent_n or_o open_v how_o to_o describe_v many_o circle_n concentricall_a that_o be_v great_a or_o lesser_a one_o than_o another_o it_o be_v not_o without_o cause_n that_o many_o admire_v how_o this_o proposition_n be_v to_o be_v resolve_v yea_o in_o the_o judgement_n of_o some_o it_o be_v think_v impossible_a who_o consider_v not_o the_o industry_n of_o a_o ingenious_a geometrician_n who_o make_v it_o possible_a and_o that_o most_o facile_a sundry_a way_n for_o in_o the_o first_o place_n if_o you_o make_v a_o circle_n upon_o a_o fine_a plain_n and_o upon_o the_o centre_n of_o that_o circle_n a_o small_a peg_n of_o 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take_v together_o and_o the_o line_n ad.ae._n be_v equal_a to_o the_o diameter_n bc._n because_o of_o the_o same_o distance_n or_o extent_n of_o open_v the_o compass_n it_o follow_v that_o the_o diameter_n e.d._n and_o all_o his_o circle_n together_o be_v much_o less_o than_o the_o diameter_n and_o the_o circle_n bc._n which_o be_v to_o be_v perform_v problem_n xxxiv_o any_o number_n under_o 10._o be_v think_v upon_o to_o find_v what_o number_n they_o be_v let_v the_o first_o number_n be_v double_v and_o unto_o it_o add_v 5._o and_o multiply_v that_o sum_n by_o 5._o and_o unto_o it_o add_v 10._o and_o unto_o this_o product_n add_v the_o next_o number_n think_v upon_o multiply_v this_o same_o again_o by_o 10._o and_o add_v unto_o it_o the_o next_o number_n and_o so_o proceed_v now_o if_o he_o declare_v the_o last_o sum_n mark_v if_o he_o think_v but_o upon_o one_o figure_n for_o then_o subtract_v only_o 35._o from_o it_o and_o the_o first_o figure_n in_o the_o place_n of_o ten_o be_v the_o number_n think_v upon_o if_o he_o think_v upon_o two_o figure_n then_o subtract_v also_o the_o say_a ●5_n from_o his_o last_o sum_n and_o the_o two_o figure_n which_o remain_v be_v the_o number_n think_v upon_o if_o he_o think_v upo●_n three_o figure_n then_o subtract_v 350._o and_o then_o the_o first_o three_o figure_n be_v the_o number_n think_v upon_o etc._n etc._n so_o if_o one_o think_v upon_o these_o number_n 5.7.9.6_o double_a the_o first_o make_v 1●_n to_o which_o add_v 5._o make_v 15._o this_o multiply_v by_o 5._o make_v 75._o to_o which_o add_v 1●_n make_v 85._o to_o this_o add_v the_o next_o number_n viz._n 7._o make_v 92._o this_o multiply_v by_o 10._o make_v 920._o to_o which_o add_v the_o next_o number_n viz._n 9_o make_v 929._o which_o multiply_v by_o 10._o make_v 9290._o to_o which_o add_v 6._o make_v 9296._o from_o which_o subtract_v 3500._o rest_v 5796._o the_o four_o number_n think_v upon_o now_o because_o the_o two_o last_o figure_n be_v like_o the_o two_o number_n think_v upon_o to_o conceal_v this_o bid_v he_o take_v the_o half_a of_o it_o or_o put_v first_o 12._o or_o any_o other_o number_n to_o it_o and_o then_o it_o will_v not_o be_v so_o open_a problem_n xxxv_o of_o the_o play_n with_o the_o ring_n among_o a_o company_n of_o 9_o or_o 10._o person_n one_o of_o they_o have_v a_o ring_n or_o such_o like_a to_o find_v out_o in_o which_o hand_n upon_o which_o finger_n &_o joint_n it_o be_v this_o will_v cause_v great_a astonishment_n to_o ignorant_a spirit_n which_o will_v make_v they_o believe_v that_o he_o that_o do_v it_o work_v by_o magic_n or_o witchcraft_n but_o in_o effect_v it_o be_v nothing_o else_o but_o a_o nimble_a act_n of_o arithmetic_n found_v upon_o the_o precedent_a problem_n for_o first_o it_o be_v suppose_v that_o the_o person_n stand_v or_o sit_v in_o order_n that_o one_o be_v first_o the_o next_o second_o etc._n etc._n likewise_o there_o must_v be_v imagine_v that_o of_o these_o two_o hand_n the_o one_o be_v first_o and_o the_o other_o second_o and_o also_o of_o the_o five_o finger_n the_o one_o be_v first_o the_o next_o be_v second_v and_o last_o of_o the_o joint_n the_o one_o be_v as_o 1._o the_o other_o be_v as_o 2._o the_o other_o as_o 3._o etc._n etc._n from_o whence_o it_o appear_v that_o in_o perform_v this_o play_n there_o be_v nothing_o else_o to_o be_v do_v than_o to_o think_v 4._o number_n for_o example_n if_o the_o four_o person_n have_v the_o ring_n in_o his_o left_a hand_n and_o upon_o the_o five_o finger_n and_o three_o joint_n and_o i_o will_v divine_v and_o find_v it_o out_o thus_o i_o will_v proceed_v as_o in_o the_o 34_o problem_n in_o cause_v he_o to_o double_v the_o first_o number_n that_o be_v the_o number_n of_o person_n which_o be_v 4._o and_o it_o make_v 8._o to_o which_o add_v 5._o make_v 13._o this_o multiply_v by_o 5._o make_v 65._o put_v 10._o to_o it_o make_v 75._o unto_o this_o put_v ●_o for_o the_o number_n belong_v to_o the_o left_a hand_n and_o so_o it_o make_v 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