Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	east_n	point_n	west_n	1,970	5	9.4719	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A29761	The description and use of the trianguler quadrant being a particular and general instrument, useful at land or sea, both for observation and operation : more universally useful, portable and convenient, than any other yet discovered, with its uses in arithmetick, geometry, superficial and solid, astronomy, dyalling, three wayes, gaging, navigation, in a method not before used / by John Brown, philomath.	Brown, John, philomath.	1671 (1671)	Wing B5041; ESTC R15524	175,812	507

shall_v be_v the_o sine_fw-la of_o the_o sun_n declination_n require_v for_o that_o distance_n from_o the_o next_o equinoctial-point_n by_o the_o 1_o sy_n rule_n abovesaid_a by_o the_o sector_n take_v 23-31_a from_o the_o sin_n make_v it_o a_o =_o in_o the_o sine_fw-la of_o 90_o then_o the_o =_o sine_fw-la of_o the_o sun_n distance_n from_o the_o next_o equinoctial-point_n shall_v be_v the_o sine_fw-la of_o the_o sun_n declination_n example_n as_o before_o rule_n the_o 1_o st_z use_v xiii_o the_o sun_n declination_n be_v give_v to_o find_v his_o true_a place_n or_o distance_n from_o ♈_o or_o ♎_o the_o two_o equinoctial_a point_n lay_v the_o thread_n to_o the_o declination_n count_v in_o the_o degree_n from_o 600_o particular_o and_o in_o the_o line_n of_o the_o sun_n place_n be_v his_o true_a place_n require_v example_n when_o the_o sun_n declination_n be_v 12_o degree_n northward_o the_o day_n increase_v than_o the_o sun_n will_v be_v 31_o deg_n and_o 23_o min._n from_o ♈_o or_o 1_o deg_n 23_o min._n in_o ♉_o his_o true_a place_n require_v as_o sine_fw-la of_o 23-31_a the_o sun_n great_a declination_n t._n to_o sine_fw-la of_o 90_o so_o sine_fw-la of_o 12-00_a the_o sun_n present_a declination_n to_o sine_fw-la of_o sun_n distance_n from_o ♈_o or_o ♎_o 31-23_a which_o by_o consider_v the_o time_n of_o the_o year_n give_v his_o true_a place_n by_o look_v on_o the_o month_n and_o line_n of_o sun_n place_n on_o the_o quadrantal-side_n take_v the_o sine_fw-la of_o the_o present_a declination_n generally_n make_v it_o a_o =_o sine_fw-la in_o the_o great_a declination_n lay_v the_o thread_n to_o nd_o and_o on_o the_o degree_n the_o thread_n shall_v give_v the_o sun_n distance_n from_o ♈_o or_o ♎_o require_v example_n as_o before_o make_v sine_fw-la of_o the_o give_v sun_n declination_n sector_n a_o =_o sine_fw-la in_o the_o sun_n great_a declination_n then_o =_o sine_fw-la of_o 90_o measure_v from_o the_o centre_n be_v the_o =_o sine_fw-la of_o the_o sun_n distance_n from_o ♈_o or_o ♎_o require_v or_o count_v 30_o deg_n for_o one_o sign_n and_o the_o centre_n for_o the_o next_o equinoctial-point_n and_o 90_o for_o the_o two_o tropic_n of_o cancer_n and_o capricorn_n ♋_o ♑_o use_v fourteen_o the_o sun_n place_n or_o day_n of_o the_o month_n and_o great_a declination_n give_v to_o find_v his_o right_a ascension_n from_o the_o same_o equinoctial_a lay_v the_o thread_n to_o the_o day_n of_o the_o month_n quadr._n or_o place_n give_v and_o in_o the_o line_n of_o the_o sun_n right_a ascension_n you_o have_v his_o right_a ascension_n in_o degree_n or_o hour_n and_o minute_n count_v 4_o minute_n for_o every_o degree_n example_n on_o the_o 9th_o of_o april_n near_o night_n the_o sun_n be_v then_o enter_v ♉_o the_o sun_n right_a ascension_n will_v be_v 1_o hour_n 52_o min._n or_o 28_o degree_n of_o right_a ascension_n distant_a from_o ♈_o as_o the_o sine_fw-la of_o 90_o t._n to_o the_o sine_fw-la compliment_n of_o the_o sun_n great_a declination_n or_o c.s._n of_o 23-31_a count_v backward_o from_o 90_o which_o will_v be_v at_o the_o sine_fw-la of_o 66-29′_a so_o be_v the_o tangent_fw-la of_o the_o sun_n distance_n from_o the_o next_o equinoctial-point_n to_o the_o tangent_fw-la of_o the_o sun_n right_a ascension_n from_o the_o same_o equinoctial-point_n generally_n take_v the_o cousin_a of_o the_o great_a declination_n from_o the_o centre_n downward_o be_v the_o sine_fw-la of_o 66-29′_a make_v it_o a_o =_o sine_fw-la of_o 90_o lay_v the_o thread_n to_o nd_o and_o note_v what_o degree_n and_o minuit_fw-la it_o cut_v for_o this_o be_v fix_v to_o this_o proportion_n then_o take_v the_o tangent_fw-la of_o the_o sun_n distance_n from_o the_o next_o equinoctial-point_n from_o the_o centre_n at_o 600_o on_o the_o degree_n towards_o the_o end_n and_o lay_v it_o on_o the_o sin_n from_o the_o centre_n downward_o and_o note_v the_o point_n where_o it_o stay_v for_o the_o nd_o from_o thence_o to_o the_o thread_n shall_v be_v the_o tangent_fw-la of_o the_o sun_n right_a ascension_n require_v note_v that_o if_o the_o sun_n distance_n from_o ♈_o or_o ♎_o be_v above_o 45_o degree_n than_o the_o tangent_n on_o the_o loose-piece_n be_v to_o be_v use_v instead_o of_o the_o tangent_n on_o the_o moveable-leg_n or_o by_o sines_n only_o thus_o or_o take_v sine_fw-la of_o the_o present_a sun_n declination_n make_v it_o a_o =_o in_o the_o sine_fw-la of_o the_o sun_n great_a declination_n and_o lay_v the_o thread_n to_o nd_o then_o take_v =_o cousin_a of_o the_o sun_n great_a declination_n and_o make_v it_o a_o =_o in_o cousin_a of_o the_o sun_n present_a declination_n and_o lay_v the_o thread_n to_o nd_o and_o in_o the_o degree_n it_o cut_v the_o sun_n right_a ascension_n require_v make_v cousin_a of_o 23-31_a sector_n viz._n the_o right_a sine_fw-la of_o 66-29_a a_o =_o sine_fw-la of_o 90_o than_o the_o =_o tangent_fw-la of_o the_o sun_n distance_n from_o ♈_o or_o ♎_o be_v the_o =_o tangent_fw-la of_o the_o sun_n right_a ascension_n from_o the_o same_o point_n of_o ♈_o or_o ♎_o as_o at_o 30_o from_o ♈_o it_o be_v 28_o degree_n or_o 1_o hour_n and_o 52_o minute_n from_o ♈_o near_o use_v xv._n have_v the_o sun_n right_a ascension_n and_o great_a declination_n to_o find_v the_o angle_n of_o the_o ecliptic_a and_o meridian_n as_o sine_fw-la 90_o to_o sine_fw-la 23-31_a sine_fw-la so_o be_v the_o cousin_a of_o the_o sun_n right_a ascension_n to_o the_o cousin_a of_o the_o angle_n of_o the_o ecliptic_a and_o meridian_n lay_v the_o thread_n to_o 23-31_a quadr._n count_v on_o the_o degree_n from_o the_o head_n then_o count_v the_o cousin_a of_o the_o right_a ascension_n from_o the_o centre_n downward_o or_o the_o sine_fw-la from_o 90_o upward_o and_o take_v the_o nd_o from_o thence_o to_o the_o thread_n and_o measure_v it_o from_o the_o centre_n and_o it_o shall_v reach_v to_o the_o cousin_a of_o the_o angle_n require_v example_n the_o right_a ascention_n be_v 30_o degree_n or_o 2_o hour_n the_o angle_n shall_v be_v 69-50_a sector·_n make_v the_o right_a sine_fw-la of_o 23-31_a a_o =_o sine_fw-la of_o 90_o then_o the_o =_o cousin_a of_o 30_o viz._n =_o 60_o shall_v make_v the_o sine_fw-la of_o 69-50_a the_o angle_n of_o the_o ecliptic_a and_o meridian_n use_v xvi_o have_v the_o latitude_n and_o declination_n of_o the_o sun_n or_o star_n to_o find_v the_o sun_n or_o star_n amplitude_n at_o rise_v or_o set_v quadr._n take_v the_o sun_n declination_n from_o the_o particular_a scale_n of_o sines_n and_o lay_v it_o from_o 6_o in_o the_o hour_n or_o azimuth-line_n and_o it_o shall_v give_v the_o amplitude_n from_o south_n as_o it_o be_v figure_v or_o from_o east_n or_o west_n count_v from_o 90_o observe_v to_o turn_v the_o compass_n the_o same_o way_n from_o 90_o or_o 6_o as_o the_o declination_n be_v northward_o or_o southwards_o example_n the_o sun_n declination_n be_v 10_o degree_n northward_o the_o sun_n amplitude_n or_o line_n be_v 106-12_a from_o the_o south_n or_o 16-12_a from_o the_o east-point_n sines_n as_o cousin_a of_o the_o latitude_n to_o s._n 90_o so_o be_v s._n of_o the_o sun_n declination_n to_o s._n of_o the_o amplitude_n general_o take_v the_o sine_fw-la of_o the_o sun_n declination_n make_v it_o a_o =_o in_o the_o cousin_a of_o the_o latitude_n and_o lay_v the_o thread_n to_o the_o near_a distance_n sector_n and_o on_o the_o degree_n the_o thread_n shall_v show_v the_o true_a amplitude_n require_v make_v the_o right_a sine_fw-la of_o the_o sun_n declination_n a_o =_o in_o cousin_a latitude_n then_o =_o 90_o take_v and_o measure_v from_o the_o centre_n give_v the_o amplitude_n or_o line_n use_v xvii_o have_v the_o same_o amplitude_n and_o declination_n to_o find_v the_o latitude_n as_o s._n of_o the_o sun_n amplitude_n sine_fw-la to_o s._n the_o sun_n declination_n so_o be_v s_o 90_o to_o cousin_a latitude_n take_v the_o sine_fw-la of_o the_o sun_n declination_n quadr._n set_v one_o point_n in_o the_o sine_fw-la of_o the_o sun_n amplitude_n lay_v the_o thread_n to_o nd_o and_o on_o the_o degree_n it_o show_v the_o compliment_n of_o the_o latitude_n require_v example_n the_o declination_n be_v 20_o degree_n and_o the_o amplitude_n 33-15_a the_o compliment_n of_o the_o latitude_n will_v be_v 38-28_a count_v from_o the_o head_n toward_z the_o end_n make_v the_o right_n sine_fw-la of_o the_o sun_n declination_n sector_n a_o =_o sine_fw-la in_o the_o sun_n amplitude_n then_o the_o =_o sine_fw-la of_o 90_o shall_v be_v the_o cousin_a of_o the_o latitude_n require_v use_v xviii_o have_v the_o latitude_n and_o sun_n declination_n to_o find_v his_o altitude_n at_o east_n or_o west_n common_o call_v the_o vertical-circle_n or_o azimuth_n of_o east_n or_o west_n take_v the_o sun_n declination_n from_o the_o particular_a line_n of_o sines_n q._n set_v one_o point_n in_o 90_o on_o the_o

azimuth-line_n and_o lay_v the_o thread_n to_o the_o nd_o and_o on_o the_o degree_n it_o show_v the_o altitude_n require_v count_v from_o 600_o towards_o the_o end_n as_o s._n latitude_n s._n of_o 90_o s._n so_o s._n of_o sun_n declination_n to_o s._n sun_n height_n at_o east_n or_o west_n quad._n take_v the_o sine_fw-la of_o the_o sun_n declination_n make_v it_o a_o =_o in_o the_o sine_fw-la of_o the_o latitude_n and_o lay_v the_o thread_n to_o nd_o and_o on_o the_o degree_n it_o shall_v show_v the_o sun_n altitude_n at_o east_n and_o west_n require_v example_n declination_n 10._o latitude_n 51-32_a the_o altitude_n be_v 12_o degree_n and_o 50_o minute_n as_o s._n of_o the_o sun_n declination_n to_o =_o s._n of_o latitude_n sector_n so_o be_v the_o =_o s._n of_o 90_o to_o s._n of_o vertical_a altitude_n use_v xix_o have_v the_o latitude_n and_o sun_n declination_n to_o find_v the_o time_n when_o the_o sun_n will_v be_v due_a east_n or_o west_n have_v get_v the_o altitude_n by_o the_o last_o rule_n take_v it_o from_o the_o particular_a sine_fw-la q._n then_o lay_v the_o thread_n to_o the_o sun_n declination_n count_v on_o the_o degree_n then_o set_v one_o point_n in_o the_o hour-line_n so_o as_o the_o other_o turn_v about_o shall_v but_o just_a touch_n the_o thread_n and_o the_o compass-point_n shall_v stay_v at_o the_o hour_n and_o minuit_fw-la of_o time_n require_v as_o tangent_fw-la latitude_n to_o sine_fw-la 90_o t._n so_o be_v the_o tangent_fw-la of_o the_o sun_n declination_n to_o cousin_a of_o the_o hour_n or_o as_o sine_fw-la 90_o to_o tangent_fw-la sun_n declination_n so_o be_v co-tangent-latitude_n to_o cousin_a of_o the_o hour_n from_o noon_n example_n latitude_n 51-32_a declination_n 10_o the_o sun_n will_v be_v due_a east_n at_o 6-32_a and_o west_n at_o 5-28_a take_v the_o tangent_fw-la of_o the_o latitude_n on_o the_o loose-piece_n quad._n count_v from_o 60_o towards_o the_o moveable-leg_n or_o else_o from_o 600_o on_o the_o moving-leg_n or_o degree_n according_a as_o the_o latitude_n be_v above_o or_o under_o 45_o degree_n and_o lay_v it_o from_o the_o centre_n downward_o and_o note_v the_o point_n where_o it_o end_v then_o take_v from_o the_o same_o tangent_fw-la the_o tangent_fw-la of_o the_o sun_n declination_n and_o set_v one_o foot_n in_o the_o point_n last_o note_v lie_v the_o thread_n to_o nd_o than_o the_o =_o sine_fw-la of_o 90_o shall_v be_v the_o sine_fw-la of_o the_o hour_n from_o 6._o or_o by_o the_o sin_n only_o work_v thus_o take_v the_o sine_fw-la of_o the_o sun_n declination_n make_v it_o a_o =_o in_o sine_fw-la of_o the_o latitude_n lay_v the_o thread_n to_o nd_o then_o take_v nd_o from_o the_o cousin_a latitude_n to_o the_o thread_n then_o set_v one_o foot_n in_o the_o cousin_a of_o the_o sun_n declination_n lay_v the_o thread_n to_o nd_o and_o on_o the_o degree_n it_o give_v the_o hour_n from_o noon_n as_o it_o be_v figure_v or_o the_o hour_n from_o 6_o count_v from_o the_o head_n count_v 4_o minute_n for_o every_o degree_n make_v the_o small_a tangent_fw-la of_o the_o latitude_n if_o above_o 45_o sector_n take_v from_o the_o centre_n a_o =_o sine_fw-la of_o 90_o then_o the_o tangent_fw-la of_o the_o sun_n declination_n take_v from_o the_o same_o small_a tangent_fw-la and_o carry_v paralle_o till_o it_o stay_v in_o like_a sin_n shall_v be_v the_o sine_fw-la of_o the_o hour_n from_o 6._o or_o as_o before_o by_o sines_n only_o make_v sine_fw-la declination_n a_o =_o sine_fw-la latitude_n then_o take_v =_o cousin_a latitude_n and_o make_v it_o a_o =_o cousin_a of_o the_o sun_n declination_n then_o take_v =_o 90_o and_o lay_v it_o from_o the_o centre_n it_o give_v the_o sine_fw-la of_o the_o hour_n from_o 6._o use_v xx._n have_v the_o latitude_n and_o sun_n declination_n to_o find_v the_o ascentional_a difference_n or_o the_o sun_n rise_v and_o set_v and_o oblique_a ascension_n lay_v the_o thread_n to_o the_o day_n of_o the_o month_n or_o to_o the_o sun_n declination_n or_o true_a place_n q._n or_o to_o his_o right_a ascension_n for_o the_o thread_n be_v lay_v to_o any_o one_o of_o they_o be_v then_o also_o lay_v to_o all_o the_o rest_n then_o in_o the_o azimuth-line_n it_o cut_v the_o ascentional_a difference_n if_o it_o you_o count_v from_o 90_o or_o the_o sun_n rise_v as_o you_o count_v the_o morning_n hour_n or_o his_o set_v count_v the_o afternoon_n hour_n the_o oblique_a ascension_n be_v find_v out_o for_o the_o six_o northern_a sign_n oblique-ascention_n or_o summer_n half-year_n by_o substract_v the_o sun_n difference_n of_o ascension_n out_o of_o the_o sun_n right_a ascension_n but_o for_o the_o other_o winter-half_a year_n or_o six_o southern_a sign_n it_o be_v find_v by_o add_v the_o sun_n difference_n of_o ascension_n to_o his_o right_a ascension_n this_o sum_n in_o winter_n and_o the_o remainder_n as_o abovesaid_a in_o summer_n shall_v be_v the_o sun_n oblique_a ascension_n require_v tan._n as_o co-tangent_a lat._n to_o sine_fw-la 90_o to_o be_v the_o tangent_fw-la of_o the_o sun_n declination_n to_o the_o sine_fw-la of_o the_o sun_n ascentional_a difference_n quad._n take_v the_o co-tangent_a latitude_n from_o the_o loose_a or_o moveable-piece_n as_o it_o be_v above_o or_o under_o 45_o degree_n make_v it_o a_o =_o in_o sine_fw-la 90_o lay_v the_o thread_n to_o nd_o then_o take_v the_o tangent_fw-la of_o the_o sun_n declination_n from_o the_o same_o tangent_n and_o carry_v it_o =_o till_o it_o stay_v in_o the_o part_n that_o the_o other_o foot_n turn_v about_o will_v but_o just_a touch_n the_o thread_n which_o part_n shall_v be_v the_o sine_fw-la of_o the_o sun_n ascentional_a difference_n require_v or_o ●hus_o by_o sines_n only_o make_v the_o sine_fw-la of_o declination_n a_o =_o cousin_a of_o the_o latitude_n lay_v the_o thread_n to_o nd_o then_o take_v the_o =_o sine_fw-la of_o latitude_n make_v it_o a_o =_o in_o cousin_a of_o the_o declination_n and_o lay_v the_o thread_n to_o nd_o and_o on_o the_o degree_n it_o shall_v cut_v the_o sun_n ascentional-difference_n require_v which_o be_v turn_v into_o time_n by_o count_v 4_o minute_n for_o every_o degree_n and_o add_v to_o or_o take_v from_o 6_o gives_z the_o sun_n rise_v in_o summer_n or_o winter_n make_v the_o co-tangent_a latitude_n sector_n a_o =_o sine_fw-la of_o 90_o then_o take_v tangent_fw-la of_o the_o sun_n declination_n and_o carry_v it_o =_o till_o it_o stay_v in_o like_a part_n viz._n the_o sine_fw-la of_o the_o sun_n ascentional_a difference_n require_v example_n otherwise_o as_o sine_fw-la 90_o to_o =_o tangent_fw-la 38-28_a so_o be_v =_o tangent_fw-la of_o 23-31_a the_o sun_n great_a declination_n to_o the_o sine_fw-la of_o the_o sun_n great_a ascentional_a difference_n 33_o deg_n and_o 12_o min._n use_v xxi_o the_o latitude_n and_o sun_n declination_n give_v to_o find_v the_o sun_n meridian_n altitude_n when_o the_o latitude_n and_o declination_n be_v both_o alike_o viz._n both_o north_n or_o both_o south_n then_o subtract_v the_o declination_n out_o of_o the_o latitude_n or_o the_o less_o from_o the_o great_a and_o the_o remainder_n shall_v be_v the_o compliment_n of_o the_o sun_n meridian_n altitude_n but_o when_o they_o be_v unlike_a then_o add_v they_o together_o and_o the_o sum_n shall_v be_v the_o compliment_n of_o the_o meridian_n altitude_n the_o contrary_a work_n serve_v when_o the_o compliment_n of_o the_o latitude_n and_o declination_n be_v give_v to_o find_v the_o meridian_n altitude_n lay_v the_o thread_n to_o the_o declination_n count_v on_o the_o degree_n from_o 600_o the_o right_a way_n towards_o the_o head_n for_o north_n and_o towards_o the_o end_n for_o south_n declination_n then_o take_v the_o near_a distance_n from_o the_o center-prick_a at_o 12_o in_o the_o hour-line_n to_o the_o thread_n this_o distance_n measure_v on_o the_o particular-line_n of_o sines_n shall_v show_v the_o sun_n meridian-altitude_n require_v use_v xxi_o the_o latitude_n and_o hour_n from_o the_o midnight_n meridian_n give_v to_o find_v the_o angle_n of_o the_o sun_n position_n viz._n the_o angle_n between_o the_o hour_n and_o azimuth-line_n in_o the_o centre_n of_o the_o sun_n t._n as_o sine_fw-la 90_o to_o cousin_a of_o the_o latitude_n so_o be_v the_o sine_fw-la of_o the_o hour_n from_o midnight_n to_o the_o sine_fw-la of_o the_o angle_n of_o position_n example_n as_o sine_fw-la 90_o to_o cousin_a latitude_n 38-28_a so_o be_v the_o cousin_a of_o the_o hour_n from_o midnight_n 120_o for_o which_o you_o must_v use_v 60_o to_o 32-34_a the_o angle_n of_o position_n q._n take_v the_o distance_n from_o the_o hour_n to_o the_o 90_o azimuth_n on_o the_o hour-line_n and_o measure_v it_o in_o the_o particular_a sin_n and_o it_o shall_v show_v the_o angle_n of_o position_n require_v this_o hold_v in_o the_o equinoctial_a take_v cousin_a latitude_n quad_n make_v it_o a_o =_o in_o sine_fw-la 90_o then_o take_v