Selected quad for the lemma: world_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
world_n	circle_n	pass_v	pole_n	1,949	5	11.4508	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A42708	Syntaxis mathematica, or, A construction of the harder problemes of geometry with so much of the conicks as is therefore requisite and other more ordinary and usefull propositions inter-mixed, and tables to several purposes / by Tho. Gibson.	Gibson, Thomas, 17th/18th cent.	1665 (1665)	Wing G677; ESTC R28671	95,056	272

43_o  _fw-fr 40_o 51_o  _fw-fr 11_o 45_o 24_o 9_o 37_o 52_o 53_o 24_o 70_o 59_o  _fw-fr 39_o 52_o  _fw-fr 11_o 55_o 24_o 27_o 38_o 15_o 53_o 46_o 71_o 13_o  _fw-fr 38_o 53_o  _fw-fr 12_o 5_o 24_o 43_o 38_o 37_o 54_o 8_o 71_o 28_o  _fw-fr 37_o 54_o  _fw-fr 12_o 13_o 25_o 2_o 38_o 58_o 54_o 29_o 71_o 41_o  _fw-fr 36_o 55_o  _fw-fr 12_o 22_o 25_o 18_o 39_o 19_o 54_o 49_o 71_o 54_o  _fw-fr 35_o these_o table_n need_v no_o explanation_n the_o use_n of_o they_o be_v evident_a but_o if_o they_o prove_v not_o satisfactory_a for_o want_v of_o calculation_n for_o further_a degree_n of_o elevation_n or_o for_o want_v of_o half_n and_o quarter_n of_o degree_n or_o the_o like_a of_o hour_n they_o be_v as_o i_o have_v they_o out_o of_o kercherus_n his_o ars_fw-la magna_fw-la nevertheless_o i_o will_v show_v the_o make_n of_o they_o whereby_o any_o man_n may_v fit_v they_o for_o his_o own_o purpose_n and_o for_o his_o place_n if_o it_o happen_v without_o these_o limit_n by_o his_o own_o calculation_n as_o follow_v first_o for_o the_o table_n a._n radius′_n t._n c._n elevation″_n t._n c′_n declination′_n b″_n this_o b_o be_v the_o sine_z compliment_n of_o the_o angle_n at_o the_o pole_n which_o show_v the_o hour_n from_o noon_n in_o winter_n and_o the_o hour_n from_o midnight_n in_o summer_n wherein_o the_o sun_n rise_v have_v declination_n which_o declination_n be_v ready_a in_o table_n the_o make_n of_o which_o shall_v be_v show_v anon_o and_o also_o the_o table_n of_o the_o sun_n declination_n at_o the_o end_n hereof_o shall_v ensue_v the_o angle_n at_o the_o pole_n so_o find_v be_v divide_v by_o 15._o show_n in_o winter_n the_o semidiurnal_a arch_n in_o hour_n which_o be_v have_v by_o the_o first_o work_v in_o degree_n and_o minute_n and_o in_o summer_n the_o seminocturnal_a who_o compliment_n to_o 180_o degree_n or_o to_o 12_o hour_n be_v the_o thing_n require_v here_o all_o the_o time_n from_o the_o vernal_a to_o the_o autumnal_a aequinoctial_a be_v call_v summer_n second_o for_o the_o table_n b._n s._n c._n elevation′_n s._n declination″_n radius′_n s._n c._n azimuth″_n which_o azimuth_n be_v compare_v with_o 90_o d._n difference_n be_v the_o amplitude_n example_n for_o elevation_n 40._o initio_fw-la ♊_o to_n radius_fw-la log_n 10000000_o add_v sine_fw-la declination_n 20._o 13′_n log_n 09538537_o sum_n 19538537_o subtract_v sine_fw-la compliment_n elevation_n remain_v sine_fw-la compliment_n azimuth_n which_o compliment_n here_o be_v the_o amplitude_n 9654283_o the_o arch_n belong_v to_o sine_fw-la 9654283._o being_n seek_v in_o the_o canon_n be_v 26._o 48′_n which_o be_v the_o amplitude_n require_v where_o the_o elevation_n be_v 40_o degree_n three_o for_o the_o table_n c._n first_o to_o find_v any_o horizontal_a arch_n for_o any_o hour_n as_o for_o example_n 3_o or_o 9_o radius′_n t._n of_o the_o hour_n in_o degree_n that_o be_v here_o t._n 45″_n sine_fw-la elevation′_n t._n of_o the_o arch_a required″_n or_o else_o t._n c._n 45′_n r″_n s._n elevation′_n t._n arch_a required″_n second_o in_o a_o prime_n vertical_a radius′_n t._n hour″_n s._n c._n elevation′_n t._n of_o the_o arch″_n it_o be_v at_o first_o in_o the_o symbol_n chap._n 1._o advertise_v that_o the_o letter_n s._n and_o t._n or_o s._n c._n and_o t_o c._n signify_v the_o sine_fw-la and_o tangent_fw-la or_o sine_fw-la compliment_n and_o tangent_fw-la compliment_n of_o a_o arch_n or_o angle_n and_o work_v by_o the_o logarithme_n of_o the_o sin_n and_o tangent_n the_o former_a analogisme_n happen_v not_o but_o in_o their_o stead_n certain_a aequality_n or_o aequation_n as_o follow_v for_o the_o table_n a._n tc_n elevation_n +_o tc_n declination_n =_o rad_n +_o b._n which_o b_o be_v the_o cousin_a of_o the_o thing_n require_v that_o be_v of_o the_o angle_n at_o the_o pole_n which_o divide_v by_o 15_o gives_z the_o time_n for_o the_o table_n b._n rad_n +_o s._n declination_n =_o sc_n elevation_n +_o sc_n azimuth_n for_o the_o table_n c._n s._n elevation_n +_o t._n the_o hour_n =_o radius_fw-la +_o t._n the_o arch_n or_o more_o ready_o thus_o tc_n hour′_n r″_n s._n elevat′_n t._n of_o arch_n from_o the_o substile″_n it_o must_v still_o be_v remember_v that_o r_o stand_v for_o radius_fw-la the_o elevation_n be_v always_o take_v for_o the_o height_n of_o the_o pole_n above_o the_o horizon_n which_o horizon_n be_v the_o dial_n plane_n in_o other_o plane_n as_o the_o prime_n vertical_a and_o all_o other_o vertical_o the_o height_n of_o the_o pole_n above_o the_o plane_n must_v be_v use_v have_v therefore_o find_v that_o call_v it_o p_o or_o else_o call_v the_o declination_n q_o then_o s._n q_o +_o s._n elevat_fw-la =_o r_o +_o s._n p._n and_o r_o +_o s_o p_o =_o tc_n the_o hour_n +_o t_o the_o arch_n of_o that_o hour_n distance_n from_o the_o substile_a so_o after_o still_o till_o all_o the_o hour_n be_v find_v this_o late_a work_n must_v be_v repeat_v whereas_o we_o use_v tc_n the_o hour_n and_o t._n the_o arch_n by_o the_o hour_n be_v always_o mean_v the_o angle_n at_o the_o pole_n or_o the_o space_n there_o include_v between_o any_o hour_n and_o the_o substile_a as_o 15d_o for_o 1_o 30d_o for_o 2_o etc._n etc._n the_o arch_n be_v the_o distance_n of_o any_o hour_n from_o the_o substile_a measure_v in_o the_o arch_n of_o a_o circle_n who_o centre_n be_v the_o centre_n of_o the_o dial_n when_o it_o be_v project_v upon_o the_o plane_n to_o find_v the_o declination_n of_o a_o place_n the_o declination_n be_v a_o arch_n of_o a_o great_a circle_n pass_v through_o the_o pole_n of_o the_o world_n and_o the_o centre_n of_o the_o place_n who_o declination_n be_v seek_v intercept_v between_o the_o say_a centre_n and_o the_o aequator_fw-la if_o the_o place_n have_v no_o latitude_n that_o be_v if_o it_o be_v in_o the_o ecliptic_a the_o near_a distance_n from_o aries_n or_o libra_n be_v give_v call_v it_o b._n then_o r′_n s._n 23d_o 32_o m″_n s._n b′_n s._n e″_n and_o e_o be_v the_o declination_n require_v work_v by_o the_o natural_a sin_n second_o if_o the_o place_n have_v latitude_n that_o be_v give_v or_o find_v in_o table_n and_o the_o right_a angle_n which_o the_o circle_n of_o latitude_n make_v with_o the_o ecliptic_a for_o all_o circle_n of_o latitude_n do_v so_o as_o the_o circle_n of_o declination_n do_v with_o the_o aequator_fw-la and_o the_o next_o distance_n to_o aries_n or_o libra_n be_v also_o give_v 1_o then_o if_o the_o place_n lie_v betwixt_o the_o ecliptic_a and_o the_o aequator_fw-la call_v the_o near_a distance_n to_o ♈_o or_o ♎_o b_o as_o before_z and_o the_o latitude_n give_v c._n it_o be_v logarichmical_o s._n c_o +_o r_o =_o s_o b_o +_o s_o a_o &_o a_o be_v a_o angle_n which_o be_v take_v out_o of_o 23._o 32′_n leave_v a_o angle_n which_o angle_n call_v d_o then_z s_z b_o +_o s_o d_o =_o r_o +_o s_o e._n and_o e_o be_v the_o declination_n require_v 2_o if_o the_o place_n lie_v betwixt_o the_o ecliptic_a and_o the_o pole_n the_o angle_n a_o find_v as_o before_o must_v be_v add_v to_o 23._o 32′_n and_o call_v the_o sum_n f_o then_z s_z b_o +_o s_o f_o =_o r_o +_o s_o e_o etc._n etc._n 3_o last_o let_v the_o place_n lie_v betwixt_o the_o aequator_fw-la and_o the_o other_o pole_n then_z s_z c_o +_o r_o =_o s_o b_o +_o s_o a_o and_o from_o a_o subtract_v 23._o 32′_n call_v the_o rest_n g._n then_o s_o b_o +_o s_o g_o =_o r_o +_o s_o e_o and_z e_z the_o declination_n to_o find_v the_o right_a ascension_n of_o a_o place_n if_o it_o be_v in_o the_o ecliptic_a as_o the_o sun_n be_v let_v the_o near_a distance_n from_o aries_n be_v call_v still_o b._n and_o work_v by_o logarithm_n it_o be_v r_o +_o sc_fw-la 23._o 32′_n =_o =_o tc_n b_o +_o t_o a._n and_o a_o be_v the_o right_a ascension_n 2_o if_o the_o place_n have_v latitude_n call_v it_o still_o c_o and_o let_v the_o declination_n find_v with_o latitude_n as_o before_o be_v call_v q._n then_o sc_n b_o +_o r_o =_o sc_fw-la q_o +_o sc_fw-la a_o and_o a_o be_v the_o right_a ascension_n or_o between_o ♋_o and_o ♎_o the_o compliment_n of_o it_o to_o find_v the_o ascensional_a difference_n thus_o t._n elevation_n +_o t._n declination_n =_o r_o +_o s.y._n and_o y_o be_v the_o ascensional_a difference_n to_o find_v the_o oblique_a ascension_n in_o the_o southern_a sign_n add_v the_o ascensional_a difference_n to_o the_o right_a ascension_n or_o in_o the_o northern_a sign_n subtract_v the_o same_o from_o the_o right_a ascension_n the_o sum_n in_o winter_n and_o the_o remainder_n in_o summer_n be_v the_o oblique_a ascension_n that_o which_o have_v be_v last_o say_v concern_v the_o declination_n right_a ascension_n ascensional_a diffeence_n and_o oblique_a