Selected quad for the lemma: cause_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
cause_n	account_n	account_v	action_n	36	3	6.7445	4	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

full_a so_o in_o c_o there_o be_v now_o but_o 1_o pint_n 5_o in_o b_o and_o 2_o in_o a_o pour_v all_o that_o be_v in_o b_o into_o a_o then_o pour_v the_o wine_n which_o be_v in_o c_o into_o b_o so_o there_o be_v in_o c_o nothing_o in_o b_o only_a 1_o pint_n and_o in_o 7_o a_o 7_o pint_n last_o out_o of_o a_o fill_v the_o pot_n c_o so_fw-mi there_o will_v remain_v in_o a_o 4_o pint_n or_o be_v but_o half_a full_a then_o if_o the_o liquor_n in_o c_o be_v pour_v into_o b_o it_o will_v be_v the_o other_o half_o in_o like_a manner_n may_v be_v take_v the_o half_a of_o a_o vessel_n which_o contain_v 12_o pint_n by_o have_v but_o the_o measure_n 5_o and_o 7_o or_o 5_o and_o 8._o now_o such_o other_o may_v be_v propose_v but_o we_o omit_v many_o in_o one_o and_o the_o same_o nature_n problem_n x._o to_o make_v a_o stick_n stand_v upon_o the_o tip_n of_o one_o finger_n without_o fall_v fasten_v the_o edge_n of_o two_o knife_n or_o such_o like_a of_o equal_a poise_n at_o the_o end_n of_o the_o stick_n lean_v out_o somewhat_o from_o the_o stick_n so_o that_o they_o may_v counterpoise_v one_o another_o the_o stick_n be_v sharp_a at_o the_o end_n and_o hold_v upon_o the_o top_n of_o the_o finger_n will_v there_o rest_v without_o support_v if_o it_o fall_v it_o must_v fall_v together_o and_o that_o perpendicular_a or_o plumb-wise_a or_o it_o must_v fall_v side-wise_a or_o before_o one_o another_o in_o the_o first_o manner_n it_o can_v for_o the_o centre_n of_o gravity_n be_v support_v by_o the_o top_n of_o the_o finger_n and_o see_v that_o each_o part_n by_o the_o knife_n be_v counterpoise_v it_o can_v fall_v sidewise_o therefore_o it_o can_v fall_v no_o wise_a in_o like_a manner_n may_v great_a piece_n of_o timber_n as_o joist_n &c_n &c_n be_v support_v if_o unto_o one_o of_o the_o end_n be_v apply_v convenient_a proportional_a counterpoise_n yea_o a_o lance_n or_o pike_n may_v stand_v perpendicular_a in_o the_o air_n upon_o the_o top_n of_o one_o finger_n or_o place_v in_o the_o midst_n of_o a_o court_n by_o help_n of_o his_o centre_n of_o gravity_n examination_n this_o proposition_n seem_v doubtful_a for_o to_o imagine_v absolute_o that_o a_o pike_n or_o such_o like_a arm_v with_o two_o knife_n or_o other_o thing_n shall_v stand_v upright_o in_o the_o air_n and_o so_o remain_v without_o any_o other_o support_n see_v that_o all_o the_o part_n have_v a_o infinite_a difference_n of_o propensity_n to_o fall_v and_o it_o be_v without_o question_n that_o a_o staff_n so_o accommodate_v upon_o his_o centre_n of_o gravity_n but_o that_o it_o may_v incline_v to_o some_o one_o part_n without_o some_o remedy_n be_v apply_v and_o such_o as_o be_v here_o specify_v in_o the_o problem_n will_v not_o warrant_v the_o thing_n nor_o keep_v it_o from_o fall_v and_o if_o more_o knife_n shall_v be_v place_v about_o it_o it_o shall_v cause_v it_o to_o fall_v more_o swift_o forasmuch_o as_o the_o superior_a part_n by_o reason_n of_o the_o centrical_a motion_n be_v make_v more_o ponderous_a and_o therefore_o less_o in_o rest_n to_o place_v therefore_o this_o prop_n real_o let_v the_o two_o knife_n or_o that_o which_o be_v for_o counterpoise_v be_v long_o always_o then_o the_o staff_n and_o so_o it_o will_v hang_v together_o as_o one_o body_n and_o it_o will_v appear_v admirable_a if_o you_o place_v the_o centre_n of_o gravity_n near_o the_o side_n of_o the_o top_n of_o the_o finger_n or_o point_n for_o it_o will_v then_o hang_v horizontall_a and_o seem_v to_o hang_v only_o by_o a_o touch_n yet_o more_o strange_a if_o you_o turn_v the_o point_n or_o top_n of_o the_o finger_n upside_o down_o problem_n xi_o how_o a_o millstone_n or_o other_o ponderosity_n may_v be_v support_v by_o a_o small_a needle_n without_o break_v o●_n any_o wise_a bow_v the_o same_o let_v a_o needle_n be_v set_v perpendicular_a to_o the_o horizon_n and_o the_o centre_n of_o gravity_n of_o the_o stone_n be_v place_v on_o the_o top_n of_o the_o needle_n it_o be_v evident_a that_o the_o stone_n can_v fall_v forasmuch_o as_o it_o hang_v in_o aequilibra_n or_o be_v counterpoyse_v in_o all_o part_n alike_o and_o moreover_o it_o can_v bow_v the_o needle_n more_o on_o the_o one_o side_n then_o on_o the_o other_o the_o needle_n will_v not_o therefore_o be_v either_o break_a or_o bow_v if_o otherwise_o then_o the_o part_n of_o the_o needle_n must_v penetrate_v and_o sink_v one_o with_o another_o that_o which_o be_v absurd_a and_o impossible_a to_o nature_n therefore_o it_o shall_v be_v support_v the_o experiment_n which_o be_v make_v upon_o trencher_n plate_n or_o such_o like_o lesser_a thing_n do_v make_v it_o most_o credible_a in_o great_a body_n but_o here_o especial_o be_v to_o be_v note_v that_o the_o needle_n ought_v to_o be_v uniform_a in_o matter_n and_o figure_n and_o that_o it_o be_v erect_v perpendicular_a to_o the_o horizon_n and_o last_o that_o the_o centre_n of_o gravity_n be_v exact_o find_v problem_n xii_o to_o make_v three_o knife_n hang_v and_o move_v upon_o the_o point_n of_o a_o needle_n fit_a the_o three_o knife_n in_o form_n of_o a_o balance_n and_o hold_v a_o needle_n in_o your_o hand_n and_o place_v the_o back_n of_o that_o knife_n which_o lie_v crosswise_o to_o the_o other_o two_o upon_o the_o point_n of_o the_o needle_n as_o the_o figure_n here_o show_v you_o for_o then_o in_o blow_v soft_o upon_o they_o they_o will_v easy_o turn_v and_o move_v upon_o the_o point_n of_o the_o needle_n with_o ●ou_n fall_v problem_n xiii_o to_o find_v the_o weight_n of_o smoke_n which_o be_v exhale_v of_o any_o combustible_a body_n whatsoever_o let_v it_o be_v suppose_v that_o a_o great_a heap_n of_o faggot_n or_o a_o load_n of_o straw_n weigh_v 500_o pound_n shall_v be_v fire_v it_o be_v evident_a that_o this_o gross_a substance_n will_v be_v all_o invert_v into_o smoke_n and_o ash_n now_o it_o seem_v that_o the_o smoke_n weigh_v nothing_o see_v it_o be_v of_o a_o thin_a substance_n now_o dilate_v in_o the_o air_n notwithstanding_o if_o it_o be_v gather_v and_o reduce_v into_o the_o thick_a that_o it_o be_v at_o first_o it_o will_v be_v sensible_o weighty_a weigh_v therefore_o the_o ash_n which_o admit_v 50_o pound_n now_o see_v that_o the_o rest_n of_o the_o matter_n be_v not_o lose_v but_o be_v exhale_v into_o smoke_n it_o must_v necessary_o be_v that_o the_o rest_n of_o the_o weight_n to_o wit_n 450_o pound_n must_v be_v the_o weight_n of_o the_o smoke_n require_v examination_n now_o although_o it_o be_v thus_o deliver_v yet_o here_o may_v be_v note_v that_o a_o ponderosity_n in_o his_o own_o medium_n be_v not_o weighty_a for_o thing_n be_v say_v to_o be_v weighty_a when_o they_o be_v out_o of_o their_o place_n or_o medium_n and_o the_o difference_n of_o such_o gravity_n be_v according_a to_o the_o motion_n the_o smoke_n therefore_o certain_o be_v light_n be_v in_o its_o true_a medium_n the_o air_n if_o it_o shall_v change_v his_o medium_n then_o will_v we_o change_v our_o discourse_n problem_n xvi_o many_o thing_n be_v dispose_v circular_a or_o otherwise_o to_o find_v which_o of_o they_o any_o one_o think_v upon_o suppose_v that_o have_v rank_v 10_o thing_n as_o abcdefghik_n circular_a as_o the_o figure_n show_v and_o that_o one_o have_v touch_v or_o think_v upon_o g_o which_o be_v the_o 7_o ask_v the_o party_n at_o what_o letter_n he_o will_v begin_v to_o account_v for_o account_n he_o must_v otherwise_o it_o can_v be_v do_v which_o suppose_v at_o e_z which_o be_v the_o 5_o place_n then_o add_v secret_o to_o this_o 5_o 10_o which_o be_v the_o number_n of_o the_o circle_n and_o it_o make_v 15_o bid_v he_o account_v 15_o backward_a from_o e_z beginning_z his_o account_n with_o that_o number_n he_o think_v upon_o so_o at_o e_z he_o shall_v account_v to_o himself_o 7_o at_z d_o account_n 8_o at_z c_o account_n 9_o etc._n etc._n so_o the_o account_n of_o 15_o will_v exact_o fall_v upon_o g_o the_o thing_n or_o number_n think_v upon_o and_o so_o of_o other_o but_o to_o conceal_v it_o the_o more_o you_o may_v will_v the_o party_n from_o e_z to_o account_v 25_o 35_o etc._n etc._n and_o it_o will_v be_v the_o same_o there_o be_v some_o that_o use_v this_o play_n at_o card_n turn_v upside_o down_o as_o the_o ten_o simple_a card_n with_o the_o king_n and_o queen_n the_o king_n stand_v for_o 12_o and_o the_o queen_n for_o 11_o and_o so_o know_v the_o situation_n of_o the_o card_n and_o think_v a_o certain_a hour_n of_o the_o day_n cause_n the_o party_n to_o account_v from_o what_o card_n he_o please_v with_o this_o proviso_n that_o when_o you_o see_v where_o he_o intend_v to_o account_v set_v 12_o to_o that_o number_n so_o in_o count_v as_o

before_o the_o end_n of_o the_o account_n shall_v fall_v upon_o the_o card_n which_o shall_v denote_v or_o show_v the_o hour_n think_v upon_o which_o be_v turn_v up_o will_v give_v grace_n to_o the_o action_n and_o wonder_v to_o those_o that_o be_v ignorant_a in_o the_o cause_n problem_n xv._n how_o to_o make_v a_o door_n or_o gate_n which_o shall_v open_v on_o both_o side_n all_o the_o skill_n and_o subtlety_n of_o this_o rest_v in_o the_o artificial_a disposer_n of_o four_o plate_n of_o iron_n two_o at_o the_o high_a end_n and_o two_o at_o the_o low_a end_n of_o the_o gate_n so_o that_o one_o side_n may_v move_v upon_o the_o hook_n or_o hinge_n of_o the_o post_n and_o by_o the_o other_o end_n may_v be_v make_v fast_o to_o the_o gate_n and_o so_o move_v upon_o these_o hinge_n the_o gate_n will_v open_v upon_o one_o side_n with_o the_o aforesaid_a plate_n or_o hook_n of_o iron_n and_o by_o help_n of_o the_o other_o two_o plate_n will_v open_v upon_o the_o other_o side_n problem_n xvi_o to_o show_v how_o a_o ponderosity_n or_o heavy_a thing_n may_v be_v support_v upon_o the_o end_n of_o a_o staff_n or_o such_o like_a upon_o a_o table_n and_o nothing_o hold_v or_o touch_v it_o take_v a_o pale_a which_o have_v a_o handle_n and_o fill_v it_o full_a of_o water_n or_o at_o pleasure_n then_o take_v a_o staff_n or_o stick_v which_o may_v not_o roll_v upon_o the_o table_n as_o aec_fw-la and_o place_v the_o handle_n of_o the_o pale_a upon_o the_o staff_n then_o place_v another_o staff_n or_o stick_v under_o the_o staff_n ce_fw-fr which_o may_v reach_v from_o the_o bottom_n of_o the_o pale_a unto_o the_o former_a staff_n ce_fw-fr perpendicular_a wise_a which_o suppose_v fg_v then_o shall_v the_o pale_a of_o water_n hang_v without_o fall_v for_o if_o it_o fall_v it_o must_v fall_v perpendicular_o or_o plumbe_v wise_a and_o that_o can_v be_v see_v the_o staff_n ce_fw-fr support_v it_o it_o be_v parallel_n to_o the_o horizon_n and_o sustain_v by_o the_o table_n and_o it_o be_v a_o thing_n admirable_a that_o if_o the_o staff_n ce_fw-fr be_v alone_a from_o the_o table_n and_o that_o end_n of_o the_o staff_n which_o be_v upon_o the_o table_n be_v great_a and_o heavy_a than_o the_o other_o it_o will_v be_v constrain_v to_o hang_v in_o that_o nature_n examination_n now_o without_o some_o experience_n of_o this_o problem_n a_o man_n will_v acknowledge_v either_o a_o possibility_n or_o impossibity_n therefore_o it_o be_v that_o very_a touchstone_n of_o knowledge_n in_o any_o thing_n to_o discourse_v first_o if_o a_o thing_n be_v possible_a in_o nature_n and_o then_o if_o it_o can_v be_v bring_v to_o experience_n and_o under_o sense_n without_o see_v it_o do_v at_o the_o first_o this_o proposition_n seem_v to_o be_v absurd_a and_o impossible_a notwithstanding_o be_v support_v with_o two_o stick_n as_o the_o figure_n declare_v it_o be_v make_v facile_a for_o the_o horizontall_a line_n to_o the_o edge_n of_o the_o table_n be_v the_o centre_n of_o motion_n and_o pass_v by_o the_o centre_n of_o gravity_n which_o necessary_o support_v it_o problem_n xvii_o of_o a_o deceitful_a bowl_n to_o play_v withal_o make_v a_o hole_n in_o one_o side_n of_o the_o bowl_n and_o cast_v melt_a lead_n therein_o and_o then_o make_v up_o the_o hole_n close_o that_o the_o knavery_n or_o deceit_n be_v not_o perceive_v you_o will_v have_v pleasure_n to_o see_v that_o notwithstanding_o the_o bowl_n be_v cast_v direct_o to_o the_o play_n how_o it_o will_v turn_v away_o side-wise_a for_o that_o on_o that_o part_n of_o the_o bowl_n which_o be_v heavy_a upon_o the_o one_o side_n then_o on_o the_o other_o it_o never_o will_v go_v true_o right_a if_o artificial_o it_o be_v not_o correct_v which_o will_v hazard_v the_o game_n to_o those_o which_o know_v it_o not_o but_o if_o it_o be_v know_v that_o the_o leady_a side_n in_o roll_a be_v always_o under_o or_o above_o it_o may_v go_v indifferent_o right_a if_o otherwise_o the_o weight_n will_v carry_v it_o always_o side-wise_a problem_n xviii_o to_o part_v a_o apple_n into_o 2.4_o or_o 8._o like_a part_n without_o break_v the_o rind_n pass_v a_o needle_n and_o thread_n under_o the_o kind_n of_o the_o apple_n and_o then_o round_o it_o with_o divers_a turn_n until_o you_o come_v to_o the_o place_n where_o you_o begin_v then_o draw_v out_o the_o thread_n gentle_o and_o part_v the_o apple_n into_o as_o many_o part_n as_o you_o think_v convenient_a and_o so_o the_o part_n may_v be_v take_v out_o between_o the_o part_n of_o the_o rind_n and_o the_o rind_n remain_v always_o whole_a problem_n xix_o to_o find_v a_o number_n think_v upon_o without_o ask_v of_o any_o question_n certain_a operation_n be_v do_v bid_v he_o add_v to_o the_o number_n think_v as_o admit_v 15_o half_a of_o it_o if_o it_o may_v be_v if_o not_o the_o great_a half_n that_o exceed_v the_o other_o but_o by_o a_o unite_v which_o be_v 8_o and_o it_o make_v 23._o second_o unto_o this_o 23._o add_v the_o half_a of_o it_o if_o it_o may_v be_v if_o not_o the_o great_a half_n viz._n 12._o make_v 35._o in_o the_o mean_a time_n note_v that_o if_o the_o number_n think_v upon_o can_v be_v half_v at_o the_o first_o time_n as_o here_o it_o can_v then_o for_o it_o keep_v 3_o in_o the_o memory_n if_o at_o the_o second_o time_n it_o will_v not_o be_v equal_o half_v reserve_v 2_o in_o memory_n but_o if_o at_o both_o time_n it_o can_v not_o be_v equal_o halve_v then_o may_v you_o together_o reserve_v five_o in_o memory_n this_o do_v cause_v he_o from_o the_o last_o sum_n viz._n 35._o to_o subtract_v the_o double_a of_o the_o number_n think_v viz._n 30._o rest_n 5._o will_v he_o to_o take_v the_o half_a of_o that_o if_o he_o can_v if_o not_o reject_v 1._o and_o then_o take_v the_o half_a of_o the_o rest_n which_o keep_v in_o your_o memory_n then_o will_v he_o to_o take_v the_o half_a again_o if_o he_o can_v if_o not_o take_v one_o from_o it_o which_o reserve_v in_o your_o memory_n and_o so_o perpetual_o halve_a until_o 1._o remain_n for_o then_o mark_v how_o many_o half_n there_o be_v take_v for_o the_o first_o half_a account_n 2_o for_o the_o second_o 4_o for_o the_o three_o 8_o etc._n etc._n and_o add_v unto_o those_o number_n the_o one_o be_v which_o you_o reserve_v in_o memory_n so_o there_o be_v 5_o remain_v in_o this_o proposition_n there_o be_v 2_o halfing_n for_o which_o last_n account_v 4_o but_o because_o it_o can_v not_o exact_o be_v halve_v without_o reject_v of_o 1._o i_o add_v the_o 1_o therefore_o to_o this_o 4_o makes_z 5_o which_o half_a or_o sum_n always_o multiply_v by_o 4_o make_v 20._o from_o which_o subtract_v the_o first_o 3_o and_o 2_o because_o the_o half_n can_v not_o be_v former_o add_v leave_v 15_o the_o number_n think_v upon_o other_o example_n the_o number_n think_v upon_o the_o number_n think_v 12_o the_o half_a of_o it_o 6_o the_o sum_n 18_o the_o half_a of_o it_o 9_o the_o sum_n of_o it_o 27_o the_o double_a of_o the_o number_n 24_o which_o take_v away_o rest_v 3_o the_o half_a of_o it_o 1_o for_o which_o account_n 2_o and_o 1_o put_v to_o it_o because_o the_o 3_o can_v not_o be_v half_v make_v 3_o this_o multiply_v by_o 4_o make_v 12_o the_o number_n think_v 79_o the_o great_a half_n 40_o 3_o the_o sum_n 119_o the_o great_a half_n of_o which_o be_v 60_o 2_o the_o sum_n of_o it_o be_v 179_o the_o double_a of_o 79_o be_v 158_o which_o take_v from_o it_o rest_v 21_o the_o lesser_a half_n 10._o which_o halue_fw-mi  _fw-fr the_o half_a of_o this_o be_v 5_o which_o make_v  _fw-fr the_o half_a of_o this_o be_v 2_o which_o be_v 10_o  _fw-fr the_o half_a of_o this_o be_v 1_o with_o 10_o and_o 11_o be_v 21._o  _fw-fr this_o 21_o which_o be_v the_o double_a of_o the_o last_o half_a with_o the_o remainder_n be_v multiply_v by_o 4._o make_v 84_o from_o which_o take_v the_o aforesaid_a 3_o and_o 2_o ●●st_n 79_o the_o number_n think_v upon_o  _fw-fr problem_n xx._n how_o to_o make_v a_o uniform_a &_o a_o inflexible_a body_n to_o pass_v through_o two_o small_a hole_n of_o divers_a form_n as_o one_o be_v circular_a and_o the_o other_o square_n quadrangular_a and_o triangular-wise_a yet_o so_o that_o the_o hole_n shall_v be_v exact_o fill_v this_o problem_n be_v extract_v from_o geometrical_a observation_n and_o seem_v at_o the_o first_o somewhat_o obscure_a yet_o that_o which_o may_v be_v extract_v in_o this_o nature_n will_v appear_v more_o difficult_a and_o admirable_a now_o in_o all_o geometrical_a practice_n the_o lesser_a or_o easy_a problem_n do_v always_o make_v way_n to_o facilitate_v the_o great_a and_o the_o aforesaid_a problem_n be_v thus_o resolve_v take_v a_o cone_n or_o round_a