Selected quad for the lemma: day_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
day_n	rise_v	set_v	sun_n	12,892	5	7.7156	4	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A40034	Posthuma Fosteri the description of a ruler, upon which is inscribed divers scales: and the uses thereof: invented and written by Mr. Samuel Foster, late professor of astronomie in Gresham-Colledg. By which the most usual propositions in astronomy, navigation, and dialling, are facily performed. Also, a further use of the said scales in deliniating of far declining dials; and of those that decline and recline, three severall wayes. With the deliniating of all horizontall dials, between 30 and 60 gr. of latitude, without drawing any lines but the houres themselves.	Foster, Samuel, d. 1652.	1654 (1654)	Wing F1635A; ESTC R218296	23,210	71

52_o if_o you_o take_v the_o tangent_fw-la thereof_o out_o of_o the_o scale_n of_o tangent_n and_o set_v it_o upon_o the_o horizon_n from_o c_o to_o l_o the_o point_n l_o shall_v be_v the_o centre_n of_o the_o circle_n ntz._n or_o the_o secant_n of_o 49_o gr._n 52_o 52_o being_n set_v from_o t_o that_o also_o shall_v give_v you_o the_o centre_n alas_o before_o the_o centre_n of_o the_o hour-circle_n be_v find_v in_o the_o same_o manner_n for_o the_o hour_n from_o the_o meridian_n be_v 31_o gr._n 28_o 28_o if_o you_o take_v the_o tangent_fw-la thereof_o our_o of_o your_o scale_n it_o shall_v reach_v from_o c_o to_o r_o the_o point_n r_o be_v the_o centre_n of_o the_o hour-circle_n musp_o or_o the_o secant_n of_o 31_o gr._n 28_o 28_o be_v set_v from_o v_o shall_v give_v the_o point_n r_o for_o the_o centre_n of_o the_o same_o hour_n and_o in_o this_o manner_n may_v any_o hour_n or_o azimuth_n whatsoever_o be_v draw_v many_o other_o proposition_n in_o astronomy_n may_v be_v wrought_v upon_o this_o projection_n and_o indeed_o any_o of_o the_o 28_o cales_fw-la of_o spherical_a trigonometry_n may_v by_o this_o kind_n of_o projection_n be_v easy_o illustrate_v and_o resolve_v which_o will_v clear_o inform_v the_o fancy_n in_o the_o resolve_n of_o spherical_a triangle_n a_o example_n or_o two_o for_o practice_n shall_v be_v 1._o to_o find_v the_o sun_n amplitude_n in_o this_o projection_n the_o amplitude_n from_o the_o east_n or_o west_n be_v represent_v by_o the_o line_n cx_o take_v therefore_o the_o distance_n cx_o in_o your_o compass_n and_o apply_v it_o to_o the_o line_n of_o tangent_n count_v every_o degree_n of_o the_o tangent_n to_o be_v two_o degree_n and_o where_o it_o rest_v that_o shall_v be_v the_o amplitude_n from_o the_o east_n or_o west_n which_o will_v be_v find_v to_o be_v 33_o gr._n 22x_fw-la or_o if_o you_o lay_v a_o ruler_n upon_o z_o and_o x_o it_o will_v cut_v the_o circle_n in_o y_o and_o the_o distance_n ny_o be_v measure_v on_o the_o line_n of_o chord_n shall_v give_v the_o amplitude_n also_o 2._o to_o find_v the_o distance_n of_o the_o sun_n from_o the_o zenith_n the_o distance_n of_o the_o sun_n from_o the_o zenith_n be_v the_o ark_n z_o s_o therefore_o to_o find_v the_o quantity_n thereof_o you_o must_v first_o find_v the_o pole_n of_o the_o circle_n ns_o z_o which_o be_v do_v after_o this_o manner_n lay_v a_o ruler_n from_o z_o to_o t_o and_o it_o will_v cut_v the_o circle_n in_o a_o then_o take_v in_o your_o compass_n a_o quadrant_a of_o the_o outward_a circle_n and_o set_v it_o from_o a_o to_o b_o then_o lay_v a_o ruler_n from_o z_o to_o b_o and_o it_o shall_v cut_v the_o horizon_n in_fw-la e_fw-la which_o point_n e_fw-it be_v the_o pole_n of_o the_o circle_n ztn._n now_o to_o measure_v the_o ark_n z_o s_o you_o must_v lay_v a_o ruler_n upon_o e_fw-la and_o s_o which_o will_v cut_v the_o outward_a circle_n in_o the_o point_n a_o so_o shall_v a_o z_o be_v measure_v upon_o the_o line_n of_o chord_n give_v you_o the_o quantity_n of_o degree_n contain_v in_o the_o ark_n z_o s_o which_o will_v be_v 40_o equal_a to_o the_o compliment_n of_o the_o sun_n altitude_n this_o latter_a proposition_n be_v insert_v rather_o to_o show_v how_o the_o ark_n of_o any_o great_a circle_n of_o the_o sphere_n the_o side_n of_o all_o spherical_a triangle_n be_v such_o may_v be_v measure_v then_o for_o any_o need_n there_o be_v to_o find_v the_o distance_n of_o the_o sun_n from_o the_o zenith_n for_o that_o may_v have_v be_v more_o easy_o effect_v it_o be_v only_o the_o compliment_n of_o the_o sun_n altitude_n but_o according_a to_o this_o operation_n may_v the_o side_n of_o any_o spherical_a triangle_n whatsoever_o be_v measure_v the_o line_n of_o sine_n also_o will_v project_v the_o analemma_n as_o master_n gunter_n show_v if_o this_o proposition_n be_v add_v how_o to_o divide_v any_o line_n give_v into_o such_o part_n as_o the_o scale_n of_o sine_n be_v divide_v which_o proposition_n may_v be_v do_v by_o that_o which_o be_v set_v down_o in_o the_o 1_o chapt._n for_o if_o ad_fw-la mn_z c_o be_v part_n or_o division_n make_v equal_a to_o those_o upon_o the_o scale_n of_o sine_n and_o ce_fw-fr be_v a_fw-fr line_n in_o the_o same_o manner_n to_o be_v divide_v after_o you_o have_v prepare_v your_o work_n as_o be_v there_o prescribe_v you_o need_v only_o to_o take_v the_o least_o distance_n between_o the_o point_n c_o nm_fw-la d_n and_o the_o line_n ae_o and_o insert_v the_o same_o into_o your_o give_a line_n so_o shall_v the_o division_n thereof_o be_v proportional_a to_o the_o line_n of_o sine_n chap._n vii_o of_o the_o line_n of_o versed-sines_n the_o general_a use_n of_o this_o scale_n be_v principal_o to_o resolve_v these_o two_o spherical_a case_n first_o by_o have_v three_o side_n of_o a_o spherical_a triangle_n to_o find_v a_o angle_n second_o by_o have_v two_o side_n and_o the_o angle_n comprehend_v to_o find_v the_o three_o side_n according_a to_o which_o two_o general_a case_n you_o shall_v find_v particular_a example_n namely_o the_o first_o and_o three_o section_n of_o this_o chapter_n suitable_a to_o the_o first_o case_n and_o the_o 5_o section_n answerable_a to_o the_o second_o sect._n 1._o to_o find_v the_o sun_n azimuth_n first_o find_v the_o sum_n and_o difference_n of_o the_o compliment_n of_o your_o latitude_n and_o compliment_n of_o the_o sun_n altitude_n then_o have_v make_v ab_o equal_v to_o the_o length_n of_o the_o whole_a scale_n count_v upon_o the_o same_o scale_n the_o sum_n and_o difference_n before_o find_v after_o this_o take_v with_o your_o compass_n the_o distance_n from_o the_o sun_n place_n to_o the_o sum_n and_o set_v one_o foot_n of_o that_o extent_n upon_o b_o with_o the_o other_o describe_v the_o ark_n cd_o so_o again_o take_v the_o distance_n upon_o the_o scale_n from_o the_o sun_n place_n to_o the_o difference_n and_o with_o that_o extent_n upon_o the_o centre_n a_o describe_v the_o ark_n ef_o which_o do_v draw_v the_o straight_a line_n de_o so_o as_o it_o may_v just_o touch_v those_o two_o ark_n cut_v the_o line_n ab_o in_fw-la g_o so_o shall_v bg_o be_v measure_v upon_o the_o scale_n from_o the_o beginning_n of_o it_o show_v the_o azimuth_n from_o the_o south_n and_o ag_o measure_a upon_o the_o same_o scale_n will_v give_v the_o azimuth_n from_o the_o north_n sect._n 2._o to_o find_v the_o amplitude_n of_o the_o sun_n rise_v or_o set_v if_o you_o suppose_v the_o sun_n to_o be_v in_o the_o horizon_n or_o 00_o gr._n high_a and_o so_o the_o compliment_n of_o the_o altitude_n to_o be_v 90_o and_o if_o upon_o these_o supposition_n you_o work_v as_o in_o the_o last_o section_n be_v show_v then_o shall_v bg_o give_v the_o gradual_a distance_n of_o the_o sun_n rise_v or_o set_v from_o the_o south_n ag_o from_o the_o north_n and_o from_o the_o midst_n of_o the_o line_n to_o g_o be_v the_o amplitude_n from_o east_n or_o west_n sect._n 3._o to_o find_v the_o hour_n of_o the_o day_n make_v ab_o equal_a to_o the_o whole_a scale_n as_o before_o and_o count_v from_o the_o beginning_n of_o the_o scale_n to_o the_o sun_n place_n what_o number_n of_o degree_n there_o be_v the_o same_o number_n show_v the_o gradual_a distance_n of_o the_o sun_n from_o the_o north_n pole_n of_o this_o distance_n and_o the_o compliment_n of_o your_o latitude_n find_v the_o sum_n and_o difference_n and_o count_v they_o both_o upon_o the_o scale_n as_o be_v do_v before_o then_o again_o count_v thereon_o also_o the_o compliment_n of_o the_o sun_n altitude_n upon_o which_o point_n set_v one_o foot_n of_o your_o compass_n extend_v the_o other_o to_o the_o forename_a sum_n and_o with_o that_o extent_n upon_o the_o centre_n b_o describe_v the_o ark_n cd_o again_o set_v one_o foot_n of_o your_o compass_n upon_o the_o compliment_n of_o the_o sun_n altitude_n extend_v the_o other_o to_o the_o forename_a difference_n and_o with_o that_o extent_n upon_o the_o centre_n a_o describe_v the_o ark_n ef._n last_o draw_v the_o straight_a line_n de_o which_o only_o touch_v the_o two_o former_a ark_n may_v cut_v the_o line_n ab_o in_fw-la g_o so_o shall_v ag_o measure_v on_o the_o scale_n from_o the_o beginning_n of_o it_o give_v the_o degree_n of_o the_o sun_n distance_n from_o the_o south_n these_o may_v be_v turn_v into_o hour_n count_v 15_o gr._n for_o one_o hour_n and_o 1_o gr._n for_o 4_o minute_n of_o a_o hour_n sect._n 4._o to_o find_v the_o semidiurnal_a and_o seminocturnall_a ark_n if_o you_o suppose_v the_o sun_n altitude_n to_o be_v 00_o gr._n and_o so_o the_o compliment_n of_o it_o to_o be_v 90_o and_o then_o work_v as_o be_v direct_v in_o the_o 3._o sect._n of_o this_o chap._n then_o shall_v ag_o give_v

the_o semidiurnal_a ark_n and_o bg_o the_o seminocturnall_a ark_n each_o of_o these_o turn_v into_o hour_n and_o minute_n and_o double_v will_v give_v the_o length_n of_o the_o day_n and_o night_n sect._n 5._o the_o sun_n place_n be_v assign_v in_o any_o point_n of_o the_o ecliptic_a to_o find_v his_o altitude_n at_o all_o hour_n by_o this_o may_v table_n of_o the_o sun_n altitude_n be_v make_v to_o all_o hour_n the_o sun_n be_v in_o any_o sign_n of_o the_o zodiac_n whereby_o many_o particular_a instrument_n for_o find_v the_o hour_n of_o the_o day_n may_v be_v make_v as_o ring_n quadrant_n cylinder_n and_o such_o like_a this_o always_o and_o then_o only_o happen_v when_o the_o sum_n find_v at_o first_o be_v great_a than_o 90_o gr._n look_v then_o how_o much_o it_o be_v beyond_o for_o so_o many_o degree_n be_v the_o sun_n below_o the_o horizon_n at_o that_o hour_n of_o the_o night_n or_o which_o be_v all_o one_o so_o many_o degree_n be_v the_o sun_n elevate_v above_o the_o horizon_n in_o that_o sign_n or_o point_n of_o the_o ecliptic_a which_o be_v so_o much_o on_o the_o other_o part_n of_o the_o equinoctial_a that_o be_v if_o the_o sun_n place_n give_v be_v the_o beginning_n of_o taurus_n or_o virgo_n and_o your_o compass_n suppose_v at_o the_o 9th_o hour_n go_v beyond_o the_o 90th_o gr._n of_o the_o scale_n you_o shall_v there_o see_v how_o low_o the_o sun_n be_v under_o the_o horizon_n at_o 9_o a_o clock_n at_o night_n or_o at_o 3_o in_o the_o morning_n and_o the_o same_o also_o show_v how_o high_a the_o sun_n be_v at_o 9_o in_o the_o morning_n or_o at_o 3_o afternoon_n if_o his_o place_n be_v in_o the_o entrance_n of_o scorpio_n or_o pisces_fw-la which_o two_o sign_n be_v so_o much_o beyond_o the_o equinoctial_a on_o the_o other_o part_n as_o taurus_n and_o virgo_n be_v on_o this_o side_n sect._n 6._o all_o proportion_n in_o sine_n alone_o where_o the_o radius_fw-la stand_v first_o may_v be_v wrought_v upon_o this_o scale_n without_o any_o protraction_n at_o all_o the_o manner_n of_o the_o work_n will_v best_o appear_v by_o a_o example_n let_v the_o proportion_n set_v down_o before_o in_o sine_n alone_o be_v here_o repeat_v the_o term_n stand_v thus_o as_o the_o radius_fw-la to_o the_o sine_fw-la of_o 23½_o so_o the_o sine_fw-la of_o 10_o to_o the_o sine_fw-la of_o what_o take_v the_o sum_n and_o difference_n of_o the_o second_o and_o three_o ark_n the_o sum_n be_v 33½_n the_o difference_n be_v 13½_o count_v these_o both_o upon_o the_o scale_n and_o there_o take_v their_o distance_n apply_v the_o same_o to_o the_o middle_n of_o the_o scale_n so_o as_o that_o the_o same_o number_n of_o degree_n may_v be_v above_o 90_o that_o be_v below_o so_o shall_v the_o degree_n either_o above_o or_o below_o be_v about_o 4_o and_o this_o be_v the_o sine_fw-la require_v for_o a_o four_o proportional_a to_o the_o former_a chap._n viii_o how_o to_o work_v proportion_n in_o sine_n and_o tangent_n by_o the_o line_n of_o versed-sines_n and_o ⊙_o let_v the_o sine_n give_v or_o require_v be_v measure_v out_o of_o ⊙_o and_o let_v they_o be_v set_v upon_o the_o radius_fw-la from_o a_o to_o ac_o or_o ae_o let_v the_o tangent_n give_v or_o require_v be_v measure_v out_o of_o the_o verse_a scale_n from_o 90_o to_o 00_o or_o to_o 180_o which_o be_v 90_o chord_n belong_v to_o 90_o equal_a part_n of_o the_o semicircle_n abdp_n and_o the_o same_o tangent_n must_v ever_o be_v set_v upon_o the_o circle_n from_o a_o as_o ab_o ad_fw-la then_o draw_v a_o right_a line_n through_o the_o first_o and_o three_o of_o the_o give_a term_n as_o from_o b_o and_o c_o to_o o_o and_o another_o right_a line_n from_o o_o to_o d_o or_o to_o e._o so_o the_o four_o term_v require_v shall_v be_v either_o the_o sine_fw-la ae_o or_o the_o tangent_fw-la ad_fw-la each_o to_o be_v measure_v in_o its_o proper_a scale_n the_o further_a use_n of_o this_o line_n be_v show_v afterwards_o in_o the_o make_n of_o decline_a recline_a dial_n chap._n ix._o to_o find_v the_o declination_n of_o a_o plain_n to_o effect_v this_o there_o be_v require_v two_o observation_n the_o first_o be_v of_o the_o horizontal_a distance_n of_o the_o sun_n from_o the_o pole_n of_o the_o plain_a the_o second_o be_v of_o the_o sun_n altitude_n thereby_o to_o get_v the_o azimuth_n and_o these_o two_o observation_n must_v be_v make_v at_o one_o instant_a of_o time_n as_o near_o as_o may_v be_v that_o the_o part_n of_o the_o work_n may_v agree_v together_o the_o better_a 1_o for_o the_o horizontal_a distance_n of_o the_o sun_n from_o the_o pole_n of_o the_o plain_a apply_v one_o edge_n of_o a_o quadrant_n to_o the_o plain_a so_o that_o the_o other_o may_v be_v perpendicular_a to_o it_o and_o the_o limb_n may_v be_v towards_o the_o sun_n and_o hold_v the_o whole_a quadrant_n horizontal_a as_o near_o as_o you_o can_v conjecture_v then_o hold_v a_o thread_n and_o plummet_n at_o full_a liberty_n so_o that_o the_o shadow_n of_o the_o thread_n may_v pass_v through_o the_o centre_n and_o limb_n of_o the_o quadrant_n observe_v then_o the_o degree_n cut_v off_o by_o the_o shadow_n of_o the_o thread_n and_o number_v they_o from_o that_o side_n of_o the_o quadrant_n that_o stand_v square_a to_o the_o plain_a for_o those_o degree_n be_v the_o distance_n require_v 2_o at_o the_o same_o instant_n observe_v the_o altitude_n of_o the_o sun_n these_o two_o will_v help_v you_o to_o the_o plain_n declination_n by_o the_o rule_n follow_v first_o by_o have_v the_o altitude_n you_o may_v find_v the_o azimuth_n by_o the_o 1._o sect._n of_o the_o 8._o chap._n then_o by_o compare_v the_o azimuth_n and_o distance_n together_o you_o may_v find_v the_o plain_n declination_n in_o this_o manner_n when_o you_o make_v your_o observation_n of_o the_o sun_n horizontal_a distance_n mark_v whether_o the_o shadow_n of_o the_o thread_n fall_v between_o the_o south_n and_o that_o side_n of_o the_o quadrant_n which_o be_v perpendicular_a to_o the_o plain_a for_o 1._o if_o the_o shadow_n fall_n between_o they_o than_o the_o distance_n and_o azimuth_n add_v together_o do_v make_v the_o declination_n of_o the_o plain_a and_o in_o this_o case_n the_o declination_n be_v upon_o the_o same_o coast_n whereon_o the_o sun_n azimuth_n be_v 2._o if_o the_o shadow_n fall_v not_o between_o they_o than_o the_o difference_n of_o the_o distance_n and_o azimuth_n be_v the_o declination_n of_o the_o plain_a and_o if_o the_o azimuth_n be_v the_o great_a of_o the_o two_o than_o the_o plain_a decline_v to_o the_o same_o coast_n whereon_o the_o azimuth_n be_v otherwise_o if_o the_o distance_n be_v the_o great_a than_o the_o plain_a decline_v to_o the_o contrary_a coast_n to_o that_o whereon_o the_o sun_n azimuth_n be_v note_v here_o further_o that_o the_o declination_n so_o find_v be_v always_o account_v from_o the_o south_n and_o that_o all_o declination_n be_v number_v from_o either_o south_n or_o north_n towards_o either_o east_n or_o west_n and_o must_v not_o exceed_v 90_o gr._n 1._o if_o therefore_o the_o number_n of_o declination_n exceed_v 90_o you_o must_v take_v the_o residue_n of_o that_o number_n to_o 180_o gr._n and_o the_o same_o shall_v be_v the_o declination_n of_o the_o plain_a from_o the_o north_n 2._o if_o the_o number_n of_o declination_n do_v exceed_v 180_o gr._n than_o the_o excess_n above_o 180_o give_v the_o plain_n declination_n from_o the_o north_n towards_o that_o coast_n which_o be_v contrary_a to_o the_o coast_n whereon_o the_o sun_n be_v and_o here_o note_v that_o wheresoever_o in_o this_o chapter_n the_o use_n of_o a_o quadrant_n be_v require_v the_o scale_n of_o chord_n will_v effect_v the_o same_o if_o upon_o a_o piece_n of_o plain_a board_n you_o describe_v a_o quadrant_n who_o side_n may_v be_v parallel_n to_o the_o edge_n of_o the_o board_n upon_o which_o you_o may_v set_v off_o the_o horizontal_a distance_n and_o altitude_n which_o will_v perform_v the_o work_n thereof_o when_o a_o quadrant_n be_v not_o at_o hand_n chap._n x._o of_o dial_n to_o draw_v upright_o decline_a dial_n by_o the_o line_n of_o sine_n and_o tangent_n the_o declination_n of_o the_o plain_a be_v find_v by_o the_o last_o chap._n upon_o your_o plain_n describe_v a_o rectangled_a parallelogram_n in_o which_o let_v the_o side_n ab_o and_o cd_o be_v perpendicular_a to_o the_o horizon_n and_o each_o of_o they_o equal_a to_o the_o tangent_fw-la of_o your_o latitude_n and_o let_v ac_o and_o bd_o be_v equal_a each_o of_o they_o to_o the_o cotangent_n of_o your_o latitude_n and_o let_v bd_o be_v prolong_v if_o need_v be_v then_o take_v that_o side_n of_o the_o parallelogram_n for_o the_o hour_n of_o 12_o which_o look_v towards_o that_o coast_n unto_o which_o the_o plain_n decline_v as_o here_o namely_o the_o side_n ab_o