Selected quad for the lemma: order_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
order_n	distance_n	foot_n	rank_n	8,037	5	11.9661	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A08582	The circles of proportion and the horizontal instrument The former shewing the maner how to work proportions both simple and compound: and the ready and easy resolving of quæstions both in arithmetic, geometrie, & astronomie: and is newly increased with an additament for navigation. All which rules may also be wrought with the penne by arithmetic, and the canon of triangles. The later teaching how to work most quæstions, which may be performed by the globe: and to delineat dialls upon any kind of plaine. Invented, and written in latine by W.O. Translated into English, and set out for the public benefit, by William Forster.	Oughtred, William, 1575-1660.; Forster, William, mathematician.; Oughtred, William, 1575-1660. Addition unto the use of the circles of proportion. aut	1633 (1633)	STC 18899B; ESTC S120820	74,822	159

the_o diligent_a practizer_n 6_o to_o find_v the_o weight_n of_o a_o sphere_n of_o tin_n at_o any_o other_o diameter_n assign_v multiply_v the_o cube_n of_o the_o diameter_n give_v by_o 1216_o if_o it_o be_v in_o inch_n measure_n or_o by_o 2101_o ⌊_o 248_o if_o the_o measure_n be_v by_o decimall_n part_n of_o a_o foot_n and_o the_o product_n will_v be_v the_o weight_n of_o that_o sphere_n and_o contrariwise_o to_o find_v the_o diameter_n of_o a_o sphere_n of_o tin_n by_o the_o weight_n give_v in_o grain_n divide_v the_o weight_n give_v in_o grain_n by_o 1216_o if_o you_o will_v have_v inch_n measure_n or_o by_o 2101_o ⌊_o 248_o if_o you_o will_v measure_v by_o decimall_n part_n of_o a_o foot_n and_o the_o quotient_n shall_v be_v the_o cube_n of_o the_o diameter_n 7._o to_o find_v the_o weight_n of_o a_o sphere_n of_o any_o mettle_n at_o any_o diameter_n give_v either_o in_o inch_n measure_n or_o in_o decimall_n part_n of_o a_o foot_n first_o by_o sect._n 6_o seek_v the_o weight_n of_o a_o sphere_n of_o tin_n at_o that_o diameter_n then_o by_o sect._n 4_o say_v as_o the_o proportional_a number_n of_o tin_n be_v to_o the_o proportional_a number_n of_o that_o other_o metal_n so_o be_v the_o weight_n of_o the_o sphere_n of_o tin_n now_o find_v to_o the_o weight_n of_o the_o sphere_n propose_v example_n suppose_v a_o sphere_n of_o iron_n who_o diameter_n be_v 3_o inch_n what_o shall_v be_v the_o weight_n thereof_o first_o the_o weight_n of_o a_o sphere_n of_o tin_n of_o 3_o inch_n diameter_n will_v be_v find_v to_o be_v 32832_o grain_n then_o say_v 1554_o ·_o 1680_o ∷_o 32832_o ·_o 35494_o ⌊_o 054_o grain_n the_o weight_n of_o the_o sphere_n propose_v 8_o to_o find_v the_o diameter_n of_o a_o sphere_n of_o any_o metal_n in_o inch_n measure_n or_o decimall_n part_n of_o a_o foot_n the_o weight_n thereof_o be_v give_v first_o by_o the_o contrary_a of_o sect._n 6_o seek_v the_o cube_n of_o the_o diameter_n of_o a_o sphere_n of_o tin_n of_o that_o weight_n then_o by_o sect._n 4_o say_v reciprocal_o as_o the_o proportional_a number_n of_o that_o other_o metal_n be_v to_o the_o proportional_a number_n of_o tin_n so_o be_v the_o cube_n of_o the_o diameter_n now_o find_v to_o the_o cube_n of_o the_o diameter_n of_o the_o sphere_n propose_v example_n a_o sphere_n of_o iron_n weigh_v 35494_o ⌊_o 0●4_n grain_n how_o many_o inch_n be_v the_o diameter_n thereof_o first_o the_o cube_n of_o the_o diameter_n of_o a_o sphere_n of_o tin_n of_o 35494_o ⌊_o 054_o grain_n weight_n will_v be_v 29_o ⌊_o 18910695_o then_o say_v reciprocal_o 1680_o ·_o 1554_o ∷_o 29_o ⌊_o 18910691_o ·_o 27_o the_o cubic_n root_n whereof_o be_v 3_o the_o diameter_n of_o a_o sphere_n of_o iron_n of_o that_o weight_n propose_v chap._n xi_o concern_v the_o order_v of_o soldier_n in_o any_o kind_n of_o rectangular_a form_n of_o battle_n 1_o battle_n be_v consider_v either_o in_o respect_n of_o the_o number_n of_o man_n or_o in_o respect_n of_o the_o form_n of_o ground_n as_o asquare_n battle_n of_o man_n be_v that_o which_o have_v a_o equal_a number_n of_o man_n both_o in_o rank_n and_o file_n though_o the_o ground_n on_o which_o they_o stand_v be_v long_o on_o the_o file_n then_o on_o the_o rank_n and_o a_o square_a battle_n of_o ground_n be_v that_o which_o have_v the_o rank_n as_o long_o as_o the_o f●le_n though_o the_o man_n in_o rank_n be_v more_o than_o in_o file_n 2._o in_o respect_n of_o the_o number_n of_o man_n it_o be_v call_v either_o asquare_n battle_n or_o a_o double_a battle_n or_o a_o battle_n of_o the_o grand_a front_n which_o be_v quadruple_a or_o a_o battle_n of_o any_o proportion_n of_o the_o number_n in_o rank_n to_o the_o number_n in_o file_n 3._o if_o it_o be_v asquare_n battle_n of_o man_n extract_v the_o quadrat_fw-la root_n out_o of_o the_o whole_a number_n of_o man_n and_o the_o same_o shall_v be_v the_o number_n of_o soldier_n to_o be_v set_v in_o a_o rank_n example_n 576_o soldier_n be_v to_o be_v martial_v in_o a_o square_a battle_n that_o so_o many_o may_v be_v in_o rank_n as_o in_o file_n take_v the_o quadrat_fw-la root_n of_o 576_o which_o be_v 24_o the_o same_o shall_v be_v the_o number_n to_o be_v place_v in_o a_o rank_n 4._o if_o it_o be_v a_o double_a battle_n of_o man_n extract_v the_o quadrat_fw-la root_n out_o of_o half_a the_o number_n of_o man_n and_o the_o same_o double_a shall_v be_v the_o number_n of_o soldier_n to_o be_v set_v in_o a_o rank_n example_n 1458_o soldier_n be_v to_o be_v place_v in_o a_o double_a battle_n so_o that_o twice_o so_o many_o may_v be_v in_o rank_a as_o in_o file_n take_v half_o the_o give_v number_n 1458_o which_o be_v 729_o the_o quadrat_fw-la root_n whereof_z be_v 27_o double_v it_o and_o you_o shall_v have_v 54_o man_n to_o be_v place_v in_o a_o rank_n 5._o if_o it_o be_v a_o quadruple_a battle_n which_o be_v call_v of_o the_o great_a front_n extract_v the_o quadrat_fw-la root_n out_o of_o one_o quarter_n of_o the_o number_n of_o man_n and_o the_o same_o quadruple_v shall_v be_v the_o number_n of_o soldier_n to_o be_v set_v in_o a_o rank_n example_n 1024_o soldier_n be_v to_o be_v martial_v into_o a_o battle_n of_o the_o grand_a front_n so_o that_o four_o time_n so_o many_o be_v in_o rank_n as_o in_o file_n take_v one_o quarter_n of_o 1024_o the_o number_n give_v which_o be_v 256_o the_o quadrat_fw-la root_n whereof_z be_v 16_o quadruple_a it_o and_o you_o shall_v have_v 64_o man_n to_o be_v place_v in_o a_o rank_n 6._o if_o a_o battle_n be_v require_v of_o any_o other_o form_n that_o be_v if_o a_o ratio_fw-la be_v give_v according_a to_o which_o the_o number_n of_o man_n in_o rank_n shall_v be_v to_o the_o number_n in_o file_n multiply_v the_o two_o term_n of_o the_o ratio_fw-la give_v then_o say_v as_o the_o product_n be_v to_o the_o quadrat_fw-la of_o the_o term_n which_o be_v for_o the_o rank_n or_o as_o the_o term_n which_o be_v for_o the_o file_n be_v to_o the_o term_n which_o be_v for_o the_o rank_n so_o be_v the_o whole_a number_n of_o soldier_n to_o the_o quadrat_fw-la of_o the_o number_n of_o man_n to_o be_v place_v in_o a_o rank_n example_n 1944_o soldier_n be_v to_o be_v martial_v so_o that_o the_o number_n of_o the_o rank_n be_v to_o the_o number_n of_o the_o file_n as_o 8_o unto_o 3_o that_o be_v for_o 8_o man_n in_o rank_n 3_o be_v to_o be_v set_v in_o file_n first_o multiply_v the_o two_o term_n of_o the_o ratio_fw-la 8_o and_o 3_o the_o product_n whereof_o be_v 24_o also_o quadrat_fw-la 8_o the_o term_n of_o the_o rank_n which_o will_v be_v 64._o then_o say_v 3_o ·_o 8_o ∷_o 1944_o ·_o 5184_o ·_o out_o of_o which_o extract_v the_o quadrat_fw-la root_n 72_o and_o it_o will_v give_v you_o the_o true_a number_n of_o the_o rank_n 7._o in_o respect_n of_o the_o form_n of_o ground_n the_o battle_n be_v either_o a_o square_a of_o ground_n or_o long_o one_o way_n then_o the_o other_o for_o the_o distance_n or_o order_n of_o soldier_n martial_v in_o array_n be_v distinguish_v either_o into_o open_a order_n or_o order_n open_v order_n be_v when_o the_o very_a centre_n of_o their_o place_n be_v distant_a 7_o foot_n asunder_o both_o in_o rank_n and_o file_n order_n be_v when_o the_o centre_n of_o their_o place_n be_v distant_a 3_o foot_n and_o a_o half_a in_o rank_n and_o so_o much_o in_o file_n or_o else_o 3_o foot_n and_o a_o half_a in_o rank_n and_o 7_o foot_n in_o file_n which_o last_o order_n and_o whatsoever_o order_n else_o there_o be_v in_o which_o the_o distance_n of_o the_o rank_n one_o from_o another_o be_v great_a than_o the_o distance_n of_o file_n cause_v that_o a_o square_a of_o man_n make_v not_o a_o square_a of_o ground_n but_o the_o ground_n be_v long_o on_o the_o file_n then_o on_o the_o rank_n 8_o if_o it_o be_v a_o square_a battle_n of_o ground_n the_o centre_n of_o the_o distance_n be_v foot_n 3½_n in_o rank_n and_o 7_o foot_n in_o file_n because_o 3½_n be_v half_a of_o 7_o the_o ratio_fw-la of_o the_o distance_n be_v as_o 1_o unto_o 2._o and_o see_v the_o number_n in_o rank_n to_o the_o number_n in_o file_n be_v reciprocal_a to_o the_o distance_n the_o ratio_fw-la of_o the_o number_n of_o man_n in_o rank_n to_o the_o number_n of_o man_n in_o file_n shall_v be_v as_o 2_o unto_o 1._o and_o so_o the_o rule_n shall_v be_v the_o same_o with_o that_o in_o sect._n 6_o namely_o as_o the_o term_n of_o the_o file_n be_v to_o the_o term_n of_o the_o rank_n so_o be_v the_o whole_a number_n of_o soldier_n to_o the_o true_a number_n of_o the_o rank_n example_n 1352_o soldier_n be_v to_o be_v set_v in_o a_o

square_a of_o ground_n that_o their_o distance_n may_v be_v foot_n 3½_n in_o rank_n and_o 7_o foot_n in_o file_n the_o ratio_fw-la of_o the_o rank_n to_o the_o file_n shall_v reciprocal_o be_v as_o 7_o to_o 3½_n that_o be_v as_o 2_o to_o 1._o say_v therefore_o 1_o ·_o 2_o ∷_o 1352_o ·_o 2704_o the_o quadrat_fw-la root_n whereof_z 52_o be_v the_o number_n of_o man_n to_o be_v set_v in_o a_o rank_n 9_o if_o a_o battle_n wherein_o the_o distance_n in_o rank_n be_v unequal_a to_o that_o in_o file_n be_v long_a one_o way_n then_o the_o other_o according_a to_o any_o ratio_fw-la give_v there_o be_v to_o be_v consider_v a_o double_a ratio_fw-la one_o reciprocal_a in_o respect_n of_o the_o distance_n the_o other_o according_a to_o the_o form_n of_o the_o ground_n wherefore_o to_o find_v the_o ratio_fw-la of_o man_n in_o rank_n to_o the_o man_n in_o file_n multiply_v the_o two_o term_n of_o the_o rank_n for_o the_o rank_n and_o the_o two_o term_n of_o the_o file_n for_o the_o file_n and_o then_o the_o rule_n shall_v be_v the_o same_o with_o that_o in_o sect._n 6_o namely_o as_o the_o term_n of_o the_o file_n be_v to_o the_o term_n of_o the_o rank_n so_o be_v the_o number_n of_o soldier_n to_o the_o quadrat_fw-la of_o the_o true_a number_n of_o the_o rank_n example_n 10290_o soldier_n be_v to_o be_v set_v in_o a_o battle_n so_o that_o they_o may_v stand_v only_o 3_o foot_n asunder_o in_o rank_n and_o 7_o foot_n in_o file_n and_o the_o length_n of_o the_o ground_n for_o the_o rank_n to_o the_o length_n of_o the_o ground_n for_o the_o file_n shall_v have_v the_o ratio_fw-la of_o 5_o unto_o 2._o first_o in_o respect_n of_o the_o distance_n the_o ratio_fw-la of_o rank_a to_o file_v reciprocal_o be_v as_o 7_o unto_o 3._o second_o in_o respect_n of_o the_o ground_n the_o ratio_fw-la of_o rank_n to_o file_v be_v as_o 5_o to_o 2._o wherefore_o by_o multiplication_n of_o like_a term_n the_o true_a ratio_fw-la of_o rank_n to_o file_n shall_v be_v 7_o ×_o 5_o to_o 3_o ×_o 2_o that_o be_v as_o 35_o to_o 6._o say_v therefore_o 6_o ·_o 35_o ∷_o 10290_o ·_o 60025_o the_o quadrat_fw-la root_n whereof_z be_v 245_o the_o number_n of_o man_n to_o be_v set_v in_o rank_n 10_o if_o 1000_o soldier_n may_v be_v lodge_v in_o a_o square_a of_o 300_o foot_n how_o many_o foot_n must_v the_o side_n of_o a_o square_a be_v which_o will_v serve_v to_o lodge_v 5000_o say_v 1000_o ·_o 5000_o ∷_o 300_o ×_o 300_o ·_o 450000_o ·_o the_o quadrat_fw-la root_n whereof_z 671_o be_v the_o square_a side_n seek_v for_o and_o this_o be_v the_o order_n for_o resolution_n of_o all_o other_o question_n of_o this_o sort_n chap._n xii_o a_o collection_n of_o the_o most_o necessary_a astronomical_a operation_n 1_o before_o we_o deliver_v the_o rule_n of_o such_o operation_n it_o will_v not_o be_v inconvenient_a to_o set_v down_o certain_a reduction_n whereof_o we_o may_v have_v frequent_a use_n to_o reduce_v sexagesime_fw-la part_n into_o decimal_n divide_v the_o sexagesime_n give_v by_o 60._o example_n how_o many_o decimal_n be_v 34′_n 12″_n here_o be_v require_v two_o reduction_n first_o of_o the_o second_o into_o decimal_n of_o minute_n then_o of_o the_o minute_n with_o their_o decimal_n into_o decimal_n of_o degree_n thus_o 60_o ·_o 1_o ∷_o 12″_n ·_o 0_o ⌊_o 2_o again_o 60_o ·_o 1_o ∷_o 34_o ⌊_o ′_o ·_o 0_o ⌊_o 57°_n wherefore_o 34′_n 12″_n be_v equal_a to_o 0_o ⌊_o 57_o of_o a_o degree_n and_o contrariwise_o to_o reduce_v decimall_n part_n of_o degree_n in_o sexagesime_n multiply_v the_o decimall_n part_v give_v by_o 60._o example_n how_o many_o sexagesime_fw-la part_n be_v 0_o ⌊_o 57°_n 1_o ·_o 60_o ∷_o 0_o ⌊_o 57°_n ·_o 34_o ⌊_o ●′_n again_o 1_o ·_o 60_o ∷_o 0_o ⌊_o 2_o ·_o 12″_n to_o reduce_v hour_n into_o degree_n multiply_v the_o hour_n with_o their_o decimall_n part_n by_o 15._o example_n how_o many_o degree_n be_v 8_o ho_o 34′_n 12″_n that_o be_v by_o the_o former_a reduction_n 8_o ⌊_o 57_o ho_o thus_o 1_o ·_o 15_o ∷_o 8_o ⌊_o 57_o ·_o 128_o ⌊_o 55_o wherefore_o hour_n 8_o 34′_n 12″_n do_v contain_v 128_o ⌊_o 55_o degree_n and_o contrariwise_o to_o reduce_v degree_n into_o hour_n divide_v the_o degree_n with_o their_o decimall_n part_n by_o 15._o example_n how_o many_o hour_n be_v in_o degree_n 128_o ⌊_o 55_o 15_o ·_o 1_o ∷_o 128_o ⌊_o 55_o ·_o 8_o ⌊_o 57_o 2_o it_o be_v to_o be_v understand_v that_o if_o four_o number_n be_v proportional_a their_o order_n may_v be_v so_o transpose_v that_o each_o of_o those_o term_n may_v be_v the_o last_o in_o proportion_n in_o this_o manner_n i._o as_o the_o first_o be_v to_o the_o second_o so_o be_v the_o three_o to_o the_o four_o ii_o as_o the_o three_o be_v to_o the_o four_o so_o be_v the_o first_o to_o the_o second_o iii_o as_o the_o second_o be_v to_o the_o first_o so_o be_v the_o four_o to_o the_o three_o four_o as_o the_o four_o be_v to_o the_o three_o so_o be_v the_o second_o to_o the_o first_o wherefore_o every_o proportion_n do_v implicit_o contain_v four_o order_n two_o descend_v and_o two_o ascend_a as_o may_v be_v see_v by_o their_o combination_n by_o one_o of_o which_o order_n if_o of_o four_o proportional_a number_n any_o three_o be_v give_v that_o other_o which_o be_v unknown_a may_v be_v find_v out_o example_n to_o find_v out_o any_o of_o these_o term_n 1_o as_o the_o sine_fw-la of_o the_o compliment_n of_o the_o sun_n declination_n 2_o be_v to_o the_o sine_fw-la of_o the_o compl_a of_o his_o altitude_n 3_o so_o be_v the_o sine_fw-la of_o the_o sun_n azumith_n from_o the_o meridian_n 4_o to_o the_o sine_fw-la of_o the_o horary_a distance_n from_o the_o meridian_n if_o the_o first_o second_o and_o three_o term_n be_v give_v the_o four_o shall_v be_v find_v out_o by_o the_o i_o order_n if_o the_o first_o three_o and_o four_o term_n be_v give_v the_o second_o shall_v be_v find_v out_o by_o the_o two_o order_n if_o the_o first_o second_o and_o four_o term_n be_v give_v the_o three_o shall_v be_v find_v out_o by_o the_o iii_o order_n if_o the_o second_o three_o and_o four_o term_n be_v give_v the_o first_o shall_v be_v find_v out_o by_o the_o four_o order_n 3._o to_o find_v out_o any_o one_o of_o these_o term_n 1_o as_o the_o radius_fw-la or_o total_a sine_fw-la 2_o be_v to_o the_o sine_fw-la of_o the_o distance_n or_o longitude_n of_o the_o sun_n in_o the_o ecliptic_a from_o the_o next_o aequinoctial_a point_n 3_o so_o be_v the_o sine_fw-la of_o the_o sun_n great_a declination_n which_o be_v the_o angle_n of_o the_o ecliptic_a with_o the_o aequinoctial_a 4_o to_z the_o sine_fw-la of_o the_o sun_n declination_n in_o that_o longitude_n 4._o to_o find_v out_o any_o one_o of_o these_o term_n 1_o as_o the_o radius_fw-la 2_o be_v to_o the_o sine_fw-la of_o the_o sun_n right_a ascension_n from_o the_o next_o equinoctial_a point_n 3_o so_o be_v the_o tangent_fw-la of_o the_o sun_n great_a declination_n 4_o to_o the_o tangent_fw-la of_o the_o sun_n declination_n in_o that_o place_n 5._o to_o find_v out_o any_o one_o of_o these_o term_n 1_o as_o the_o radius_fw-la 2_o be_v to_o the_o sine_fw-la of_o the_o compl_a of_o the_o sun_n great_a declination_n 3_o so_o be_v the_o tangent_fw-la of_o the_o longitude_n of_o the_o sun_n from_o the_o next_o equinoctial_a point_n 4_o to_o the_o tangent_fw-la of_o the_o right_a ascension_n of_o the_o sun_n from_o the_o same_o aequinoctial_a point_n 6._o to_o find_v out_o any_o one_o of_o these_o term_n 1_o as_o the_o radius_fw-la 2_o be_v to_o the_o sine_fw-la of_o the_o compl_a of_o the_o longitude_n of_o the_o sun_n from_o the_o next_o equinoctial_a point_n 3_o so_o be_v the_o tangent_fw-la of_o the_o sun_n great_a declination_n 4_o to_o the_o tangent_fw-la of_o the_o compl_a of_o the_o angle_n of_o the_o ecliptic_a with_o the_o meridian_n 7._o to_o find_v out_o any_o one_o of_o these_o term_n 1_o as_o the_o radius_fw-la 2_o be_v to_o the_o sine_fw-la of_o the_o sun_n great_a declination_n 3_o so_o be_v the_o sine_fw-la of_o the_o compl_a of_o the_o sun_n right_a ascension_n from_o the_o next_o aequinoctial_a point_n 4_o to_o the_o sine_fw-la of_o the_o compl_a of_o the_o angle_n of_o the_o ecliptic_a with_o the_o meridian_n 8._o to_o find_v out_o any_o one_o of_o these_o term_n 1_o as_o the_o sine_fw-la of_o the_o compl_a of_o the_o pole_n height_n 2_o be_v to_o the_o radius_fw-la 3_o so_o be_v the_o sine_fw-la of_o the_o sun_n declination_n 4_o to_o the_o sine_fw-la of_o the_o sun_n amplitude_n ortive_a that_o be_v the_o arch_n of_o the_o horizon_n from_o the_o place_n of_o the_o sun_n rise_v or_o set_v to_o the_o true_a east_n or_o west_n point_n 9_o