Selected quad for the lemma: day_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
day_n	half_a	hour_n	quarter_n	7,627	5	11.1436	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A34005	The sector on a quadrant, or A treatise containing the description and use of four several quadrants two small ones and two great ones, each rendred many wayes, both general and particular. Each of them accomodated for dyalling; for the resolving of all proportions instrumentally; and for the ready finding the hour and azimuth universally in the equal limbe. Of great use to seamen and practitioners in the mathematicks. Written by John Collins accountant philomath. Also An appendix touching reflected dyalling from a glass placed at any reclination.	Collins, John, 1625-1683.; Lyon, John, professor of mathematics. Appendix touching reflective dialling.; Sutton, Henry, mathematical instrument maker.	1659 (1659)	Wing C5382; ESTC R32501	226,510	415

to_o proportion_n out_o a_o sine_fw-la to_o a_o lesser_a radius_fw-la which_o will_v find_v the_o point_n of_o entrance_n the_o next_o will_v be_v to_o find_v the_o altitude_n or_o depression_n at_o 6._o the_o three_o will_v be_v to_o enter_v the_o sum_n or_o difference_n of_o the_o sin_n of_o the_o altitude_n or_o depression_n at_o 6_o at_o the_o point_n of_o entrance_n and_o to_o lay_v the_o thread_n to_o the_o other_o foot_n but_o i_o shall_v demonstrate_v it_o from_o other_o ground_n 1._o to_o find_v the_o time_n of_o sun_n rising_n or_o set_v take_v the_o declination_n from_o the_o lesser_a sine_fw-la and_o enter_v it_o at_o the_o declination_n in_o the_o scale_n of_o entrance_n lay_v the_o thread_n to_o the_o other_o foot_n according_a to_o near_a distance_n and_o it_o show_v the_o time_n of_o rise_v or_o set_v in_o the_o equal_a limb._n so_o when_o the_o sun_n have_v 13_o of_o south_n declination_n he_o rise_v at_o 8′_n past_o 7_o in_o the_o morning_n f●re_o and_o set_v at_o 52′_n past_o 4_o in_o the_o afternoon_n 2._o to_o find_v the_o true_a time_n of_o the_o day_n in_o summer_n or_o northwardly_a declination_n take_v the_o distance_n between_o the_o altitude_n in_o the_o great_a sine_fw-la and_o the_o declination_n in_o the_o lesser_a sine_fw-la in_o winter_n take_v the_o declination_n in_o the_o lesser_a sine_fw-la and_o with_o your_o compass_n add_v it_o to_o the_o altitude_n in_o the_o great_a sine_fw-la these_o extent_n enter_v at_o the_o declination_n in_o the_o scale_n of_o entrance_n and_o lay_v the_o thread_n to_o the_o other_o foot_n according_a to_o near_a distance_n and_o in_o the_o equal_a limb_n it_o will_v lie_v over_o the_o true_a time_n of_o the_o day_n in_o summer_n when_o the_o declination_n in_o the_o fit_a scale_n be_v above_o the_o altitude_n the_o hour_n be_v find_v from_o 6_o towards_o midnight_n when_o below_o it_o towards_o noon_n example_n when_o the_o sun_n have_v 13_o of_o north_n declination_n his_o altitude_n be_v 39_o 10′_n will_v be_v a_o quarter_n past_o 9_o in_o the_o morning_n or_o 3_o quarter_n past_o 2_o in_o the_o afternoon_n and_o when_o he_o have_v the_o same_o south_n declination_n his_o altitude_n be_v 16_o 14′_n the_o time_n of_o the_o day_n will_v be_v find_v the_o same_o the_o converse_n will_v find_v the_o sun_n altitude_n on_o all_o hour_n by_o this_o fit_a scale_n which_o i_o shall_v handle_v the_o general_a way_n 3._o to_o find_v the_o amplitude_n take_v the_o declination_n from_o the_o great_a sine_fw-la and_o enter_v it_o at_o the_o begin_n of_o the_o scale_n of_o entrance_n lay_v the_o thread_n to_o the_o other_o foot_n according_a to_o near_a distance_n and_o it_o show_v it_o in_o the_o limb._n when_o the_o sun_n have_v 13_o of_o declination_n his_o amplitude_n will_v be_v 21_o 12′_n 4._o to_o find_v the_o azimuth_n of_o the_o sun_n in_o summer_n take_v the_o distance_n between_o the_o altitude_n in_o the_o lesser_a sine_fw-la and_o the_o declination_n in_o the_o great_a in_o winter_n or_o south_n declination_n take_v the_o declination_n from_o the_o great_a sine_fw-la and_o add_v it_o to_o the_o altitude_n in_o the_o lesser_a sine_fw-la with_o your_o compass_n these_o extent_n enter_v at_o the_o altitude_n in_o the_o scale_n of_o entrance_n and_o lay_v the_o thread_n to_o the_o other_o foot_n according_a to_o near_a distance_n and_o in_o the_o equal_a limb_n it_o show_v the_o azimuth_n from_o the_o east_n or_o west_n in_o summer_n when_o the_o altitude_n fall_v below_o the_o declination_n the_o azimuth_n be_v find_v from_o the_o east_n or_o west_n northwards_o when_o above_o it_o southwards_o so_o when_o the_o sun_n have_v 13_o of_o north_n declination_n his_o altitude_n be_v 43_o 50′_n the_o azimuth_n will_v be_v find_v to_o be_v 45_o from_o east_n or_o west_n southwards_o and_o when_o he_o have_v the_o same_o south_n declination_n his_o altitude_n be_v 14_o 50′_n he_o shall_v have_v the_o same_o azimuth_n these_o scale_n be_v fit_v to_o give_v the_o altitude_n at_o six_o and_o the_o vertical_a altitude_n by_o inspection_n against_o the_o declination_n in_o the_o great_a lesser_a sine_fw-la stand_v the_o vertical_a altitude_n or_o depression_n altitude_n or_o depression_n at_o six_o when_o the_o hour_n or_o azimuth_n fall_v near_a noon_n mind_n against_o what_o arch_n of_o the_o line_n of_o sines_n the_o point_n of_o entrance_n fall_v the_o thread_n may_v be_v lay_v to_o the_o like_a arch_n in_o the_o limb_n and_o the_o respective_a extent_n enter_v parallel_o between_o the_o scale_n and_o the_o thread_n and_o the_o answer_v find_v in_o the_o line_n of_o sines_n but_o we_o have_v a_o better_a remedy_n by_o help_n of_o the_o verse_v sine_fw-la of_o 90_o put_v through_o the_o whole_a limb._n the_o joint_a use_n of_o the_o fit_v scale_n with_o the_o verse_v sine_fw-la of_o 90_o in_o the_o limb._n in_o the_o follow_a proposition_n i_o shall_v make_v no_o use_n of_o the_o lesser_a sine_fw-la of_o the_o fit_v scale_n get_v the_o summer_n and_o winter_n meridian_n altitude_n by_o sum_v and_o difference_v the_o declination_n and_o the_o compliment_n of_o the_o latitude_n which_o may_v be_v do_v with_o compass_n in_o the_o equal_a limb_n by_o apply_v the_o chord_n of_o the_o declination_n both_o way_n from_o the_o co-latitude_n to_o find_v the_o hour_n of_o the_o day_n in_o winter_n take_v the_o distance_n between_o the_o meridian_n altitude_n and_o the_o give_v altitude_n out_o of_o the_o great_a sine_fw-la of_o the_o fit_a scale_n and_o as_o before_o enter_v it_o at_o the_o declination_n in_o the_o scale_n of_o entrance_n lay_v the_o thread_n to_o the_o other_o foot_n according_a to_o near_a distance_n and_o in_o the_o verse_v sine_fw-la of_o 90_o it_o show_v the_o hour_n from_o noon_n so_o if_o the_o sun_n have_v 13_o of_o south_n declination_n the_o meridian_n altitude_n be_v 25_o 28′_n if_o the_o give_v altitude_n be_v 17_o 44′_n the_o time_n of_o the_o day_n will_v be_v half_a a_o hour_n past_o 9_o in_o the_o morning_n or_o as_o much_o after_o 2_o in_o the_o afternoon_n to_o find_v the_o hour_n of_o the_o day_n in_o summer_n take_v the_o distance_n between_o the_o summer_n meridian_n altitude_n and_o the_o propose_a altitude_n and_o if_o this_o extent_n be_v less_o than_o the_o distance_n of_o the_o declination_n in_o the_o scale_n of_o entrance_n from_o the_o centre_n enter_v it_o at_o the_o declination_n in_o the_o say_a scale_n and_o lay_v the_o thread_n to_o the_o other_o foot_n it_o will_v in_o the_o verse_v sine_fw-la of_o 90_o show_v the_o hour_n from_o noon_n if_o the_o sun_n have_v 23_o 31′_n of_o north_n declination_n his_o meridian_n altitude_n will_v be_v 61_o 59′_n if_o his_o give_a altitude_n be_v 47_o 51′_n the_o time_n of_o the_o day_n will_v be_v a_o quarter_n past_o 9_o in_o the_o morning_n or_o three_o quarter_n of_o a_o hour_n past_o 2_o in_o the_o afternoon_n if_o the_o extent_n be_v large_a than_o the_o distance_n of_o the_o point_n of_o entrance_n to_o wit_n the_o distance_n of_o the_o declination_n in_o the_o scale_n of_o entrance_n from_o the_o centre_n the_o hour_n must_v be_v find_v from_o midnight_n in_o this_o case_n with_o your_o compass_n add_v the_o sine_fw-la of_o the_o winter_n meridian_n altitude_n take_v from_o the_o great_a sine_fw-la of_o the_o fit_a scale_n to_o the_o sine_fw-la of_o the_o altitude_n in_o the_o say_a scale_n and_o enter_v the_o say_v whole_a extent_n at_o the_o point_n of_o entrance_n as_o before_o and_o in_o the_o verse_v sine_fw-la of_o 90_o the_o thread_n will_v show_v the_o hour_n from_o midnight_n when_o the_o sun_n have_v 23_o 31′_n of_o north_n declination_n if_o his_o altitude_n be_v 5_o 24′_n the_o time_n of_o the_o day_n will_v be_v half_a a_o hour_n past_o 4_o in_o the_o morning_n or_o half_o a_o hour_n past_o 7_o in_o the_o evening_n the_o winter_n meridian_n altitude_n to_o this_o declination_n be_v 14_o 57′_n when_o the_o hour_n in_o these_o example_n fall_v near_o noon_n the_o extent_n of_o the_o compass_n may_v be_v double_v or_o tripled_a and_o a_o ark_n first_o find_v in_o the_o limb_n then_o if_o the_o thread_n be_v lay_v over_o the_o like_a ark_n from_o the_o other_o edge_n it_o will_v according_o in_o the_o verse_v sin_n double_v or_o tripled_a show_v the_o time_n seek_v and_o the_o like_a may_v be_v do_v for_o the_o azimuth_n to_o find_v the_o azimuth_n of_o the_o sun_n in_o winter_n get_v the_o ark_n of_o difference_n between_o the_o sun_n altitude_n and_o the_o compliment_n of_o the_o latitude_n and_o in_o the_o great_a sine_fw-la of_o the_o fit_a scale_n take_v the_o distance_n between_o the_o say_a ark_n and_o the_o sun_n declination_n and_o enter_v one_o foot_n of_o this_o extent_n at_o the_o altitude_n in_o the_o scale_n of_o entrance_n lay_v the_o

of_o the_o sun_n altitude_n propose_v in_o like_a manner_n may_v be_v draw_v all_o the_o other_o parallel_n of_o altitude_n desire_v which_o will_v show_v the_o sun_n altitude_n or_o the_o proportion_n of_o any_o shadow_n to_o its_o altitude_n at_o any_o appearance_n of_o the_o sun_n reflex_n thereon_o to_o draw_v the_o jewish_a or_o old_a unequal_a hour-line_n to_o any_o recline_a glass_n on_o any_o plane_n whatsoever_o that_o the_o sunbeam_n will_v be_v reflect_v on_o here_o note_v that_o the_o jewish_a hour-line_n be_v great_a circle_n first_o by_o the_o rule_v former_o give_v draw_v two_o reflect_a parallel_n of_o declination_n of_o 16_o d._n 55′_n the_o one_o be_v near_o the_o summer_n and_o the_o other_o near_o the_o winter-tropick_n for_o when_o the_o sun_n have_v that_o declination_n the_o day_n be_v 15_o hour_n long_o in_o the_o summer_n and_o 9_o in_o the_o winter_n then_o as_o be_v former_o direct_v situate_v a_o thread_n just_a between_o the_o eye_n and_o those_o three_o point_n in_o the_o say_v reflect_v dial_n as_o be_v express_v in_o the_o ensue_a table_n so_o may_v you_o thereby_o draw_v all_o or_o any_o of_o those_o jewish_a hour-line_n desire_v which_o will_v at_o any_o appearance_n of_o the_o spot_n by_o the_o reflex_n of_o the_o glass_n among_o those_o hour-line_n show_v how_o many_o of_o the_o equal_a hour_n be_v pass_v since_o sunrising_n as_o be_v desire_v now_o in_o this_o latitude_n of_o 51_o deg_n 30′_n if_o the_o parallel_n of_o the_o sun_n declination_n be_v draw_v both_o when_o the_o day_n be_v 9_o and_o 15_o hour_n long_o that_o be_v when_o it_o be_v 16_o d._n 55′_n any_o of_o those_o jewish_a hour-line_n will_v intersect_v the_o common_a hour-line_n either_o upon_o the_o hour_n half_a hour_n or_o quarter_n and_o such_o a_o declination_n may_v be_v find_v that_o it_o shall_v so_o do_v in_o any_o latitude_n desire_v unequal_a hour_n 15_o h._n m_o equ_n h._n 9_o h._n m._n 0_o 4_o 30_o 6_o 7_o 30_o 1_o 5_o 45_o 7_o 8_o 15_o 2_o 7_o 00_o 8_o 9_o 00_o 3_o 8_o 15_o 9_o 9_o 45_o 4_o 9_o 30_o 10_o 10_o 30_o 5_o 10_o 45_o 11_o 11_o 15_o 6_o 12_o 00_o 12_o 12_o 00_o unequ_n hour_n 15_o h._n m._n equ_n h._n 9_o h._n m._n  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 7_o 1_o 15_o 1_o 0_o 45_o 8_o 2_o 30_o 2_o 1_o 30_o 9_o 3_o 45_o 3_o 2_o 15_o 10_o 5_o 00_o 4_o 3_o 00_o 11_o 6_o 15_o 5_o 3_o 45_o 12_o 7_o 30_o 6_o 4_o 30_o to_o draw_v the_o circle_n of_o position_n to_o any_o recline_a glass_n on_o any_o plane_n whatsoever_o that_o the_o sunbeam_n will_v be_v reflect_v on_o note_v that_o all_o circle_n of_o position_n be_v great_a circle_n of_o the_o sphere_n and_o do_v always_o intersect_v each_o other_o in_o that_o point_n of_o the_o reflect_v meridian_n which_o touch_v the_o reflect_v horizon_n which_o may_v be_v call_v the_o common_a intersection_n which_o say_v circle_n of_o position_n be_v reckon_v upon_o the_o reflect_v equinoctial_a both_o way_n from_o the_o say_a meridian_n down_o to_o the_o say_a horizon_n the_o horizon_n eastward_o be_v the_o cuspis_fw-la of_o the_o first_o house_n and_o the_o horizon_n westward_o be_v the_o cuspis_fw-la of_o the_o seven_o house_n and_o the_o reflect_v meridian_n the_o cuspis_fw-la of_o the_o ten_o house_n so_o that_o those_o meridian-planes_a who_o reclination_n be_v 60_o degree_n westward_n be_v measure_v from_o the_o meridian_n in_o the_o equinoctial_a lie_v in_o the_o cuspis_fw-la of_o the_o eight_o house_n and_o 30_o degr_n westward_o lie_v in_o the_o cuspis_fw-la of_o the_o nine_o house_n and_o 30_o deg_n eastward_o in_o the_o cuspis_fw-la of_o the_o eleven_o house_n and_o 60_o deg_n eastward_o in_o the_o cuspis_fw-la of_o the_o twelve_o house_n which_o be_v all_o the_o house_n above_o the_o horizon_n now_o to_o draw_v any_o circle_n of_o position_n or_o the_o cuspis_fw-la of_o any_o house_n on_o any_o ceiling_n or_o wall_n to_o any_o recline_a glass_n be_v do_v as_o follow_v first_o fasten_v a_o thread_n in_o such_o sort_n within_o the_o room_n as_o that_o it_o may_v interpose_v between_o the_o eye_n and_o the_o say_v common_a point_n of_o intersection_n on_o the_o wall_n or_o ceiling_n and_o also_o between_o that_o point_n where_o the_o reflect_a hour-line_n of_o 4_o be_v 60_o deg_n westward_o from_o the_o say_a meridian_n intersect_v the_o reflect_a equinoctial_a also_o on_o the_o ceiling_n whereby_o point_n may_v be_v make_v at_o every_o bend_n or_o angle_n of_o the_o wall_n or_o ceiling_n to_o which_o the_o thread_n so_o situate_v may_v also_o interpose_v by_o which_o point_v the_o reflect_v cuspis_fw-la of_o the_o eight_o house_n may_v be_v draw_v in_o like_a manner_n may_v the_o cuspis_fw-la of_o any_o other_o house_n above_o the_o horizon_n as_o the_o 9_o the_o or_o 10_o the_o which_o be_v the_o meridian_n or_o medium_fw-la coell_n or_o 11_o the_o or_o 12_o the_o be_v draw_v also_o for_o if_o as_o before_o the_o say_a thread_n be_v again_o so_o fasten_v within_o the_o room_n as_o that_o it_o may_v also_o interpose_v between_o the_o eye_n and_o the_o say_v common_a point_n of_o intersection_n and_o also_o those_o point_n where_o the_o reflect_a hour-line_n of_o 2_o be_v 30_o deg_n westward_o from_o the_o say_a meridian_n do_v cut_v the_o reflect_v equinoctial_a whereby_o may_v be_v draw_v the_o reflect_v cuspis_fw-la of_o the_o nine_o house_n or_o where_o the_o reflect_v hour-line_n of_o 10_o be_v also_o 30_o deg_n eastward_o from_o the_o meridian_n do_v also_o cut_v the_o say_v reflect_v equinoctial_a whereby_o may_v be_v draw_v the_o cuspis_fw-la of_o the_o 11_o the_o house_n or_o where_o the_o reflect_a hour-line_n of_o 8_o be_v 60_o deg_n eastward_o from_o the_o meridian_n do_v also_o cut_v the_o say_v reflect_v equinoctial_a whereby_o may_v be_v draw_v the_o cuspis_fw-la of_o the_o 12_o the_o house_n the_o horizon_n always_o be_v the_o cuspis_fw-la of_o the_o first_o and_o seven_o house_n and_o the_o meridian_n the_o cuspis_fw-la of_o the_o ten_o house_n or_o medium_fw-la coeli_fw-la wherein_o general_o it_o be_v to_o be_v note_v that_o in_o all_o plane_n which_o cut_v the_o common_a intersection_n of_o the_o meridian_n and_o horizon_n as_o do_v the_o horizontal_n and_o also_o all_o meridian_n plane_n both_o direct_a and_o recline_a these_o circle_n of_o position_n be_v all_o parallel_n to_o the_o meridian_n and_o therefore_o parallel_v each_o to_o other_o for_o look_v what_o respect_n the_o hour-line_n in_o all_o direct_a or_o recline_a polar_a plane_n or_o direct_a meridian_n planes_n have_v to_o the_o axis_n of_o the_o world_n such_o respect_n have_v the_o circle_n of_o position_n in_o all_o horizontal_n or_o direct_a meridian_n or_o recline_a meridian_n planes_n to_o the_o axis_n of_o the_o prime_n vertical_a for_o as_o the_o hour-line_n in_o the_o first_o be_v all_o parallel_n to_o the_o axis_n of_o the_o equinoctial_a in_o who_o pole_n they_o meet_v so_o the_o circle_n of_o position_n in_o the_o second_o be_v all_o parallel_n to_o the_o axis_n of_o the_o prime_n vertical_a in_o who_o pole_n they_o also_o meet_v the_o reason_n why_o glass_n reflect_v a_o double_a spot_n be_v because_o they_o be_v polish_a on_o both_o side_n which_o may_v be_v remedy_v with_o a_o pumex-stone_n those_o that_o desire_v to_o read_v more_o of_o this_o subject_n may_v see_v what_o be_v write_v by_o kircher_n in_o primitiis_fw-la gnomicae_fw-la catoptricae_n and_o since_o he_o by_o magnan_n and_o other_o vale_fw-la finis_fw-la

concentric_a to_o the_o limb_n to_o keep_v the_o other_o at_o a_o certainty_n in_o stretch_v and_o the_o other_o to_o be_v rectify_v for_o use_v to_o rectify_v the_o bead._n lay_v the_o thread_n over_o the_o day_n of_o the_o month_n in_o its_o proper_a circle_n and_o if_o the_o season_n wherein_o the_o quadrant_n be_v to_o be_v use_v be_v in_o the_o winter_n half_a year_n set_v the_o bead_n by_o remove_v it_o to_o the_o winter_n ecliptic_a but_o in_o summer_n let_v it_o be_v set_v to_o the_o low_a or_o summer_n ecliptic_a and_o then_o it_o be_v fit_v for_o use_n one_o caution_n in_o rectify_v the_o bead_n be_v to_o be_v give_v and_o that_o be_v in_o summer_n time_n if_o it_o be_v require_v to_o find_v the_o hour_n and_o azimuth_n of_o the_o sun_n by_o the_o projection_n before_o the_o hour_n of_o 6_o in_o the_o morning_n or_o after_o it_o in_o the_o evening_n or_o which_o be_v all_o one_o when_o the_o sun_n have_v less_o altitude_n than_o he_o have_v at_o 6_o of_o the_o clock_n then_o 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may_v conclude_v if_o his_o observe_a altitude_n be_v less_o upon_o the_o same_o day_n and_o the_o hour_n and_o azimuth_n seek_v the_o bead_n must_v be_v set_v to_o the_o winter_n ecliptic_a and_o the_o operation_n perform_v in_o the_o revert_v tail_n here_o it_o may_v be_v note_v also_o that_o the_o exact_a way_n of_o rectify_v the_o bead_n will_v be_v either_o from_o a_o table_n of_o the_o sun_n declination_n lay_v the_o thread_n over_o the_o same_o in_o the_o graduated_a circle_n or_o from_o his_o true_a place_n lay_v it_o over_o the_o same_o in_o the_o proper_a ecliptic_a or_o from_o his_o right_a ascension_n count_v in_o the_o limb._n or_o last_o from_o his_o meridian_n altitude_n on_o the_o right_a edge_n of_o the_o quadrant_n for_o these_o do_v mutual_o give_v each_o other_o the_o bead_n be_v rectify_v to_o the_o respective_a ecliptic_a as_o before_o for_o example_n to_o find_v the_o sun_n declination_n the_o thread_n lay_v over_o the_o day_n of_o the_o month_n intersect_v it_o upon_o that_o circle_n whereon_o it_o be_v graduate_v which_o in_o the_o summer_n half_a year_n be_v to_o be_v account_v on_o this_o side_n the_o equinoctial_a north_n and_o in_o the_o winter-half_a year_n south_n so_o lay_v the_o thread_n over_o the_o 27_o day_n of_o april_n it_o intersect_v the_o circle_n of_o declination_n at_o 17_o degree_n and_o so_o much_o be_v the_o sun_n declination_n to_o find_v the_o sun_n true_a place_n the_o thread_n lie_v as_o before_o show_v it_o on_o the_o respective_a ecliptic_a so_o the_o thread_n lie_v over_o the_o 17_o of_o april_n will_v cut_v the_o summer_n ecliptic_a in_o 17_o 7_o m_o of_o taurus_n or_o in_o 12_o 53_o m_o of_o leo_n which_o agree_v to_o the_o 26_o day_n of_o july_n or_o thereabouts_o the_o thread_n intersect_v both_o these_o day_n at_o once_o and_o the_o opposite_a point_n of_o the_o ecliptic_a hereto_o be_v 17d●_o m_o in_o scorpio_n about_o the_o 20_o of_o october_n and_o 12_o 53_o m_o of_o aquarius_n about_o the_o 22_o of_o 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the_o night_n by_o the_o quadrant_n we_o need_v no_o more_o than_o 12_o hour_n of_o ascension_n for_o either_o sun_n or_o star_n and_o the_o limb_n be_v according_o number_v from_o the_o left_a edge_n towards_o the_o right_n from_o 1_o to_z 6_o in_o a_o small_a figure_n and_o thence_o back_o again_o to_o 12_o and_o the_o other_o figure_n be_v the_o compliment_n of_o these_o to_o 12._o so_o that_o when_o the_o sun_n be_v depart_v from_o the_o equator_fw-la towards_o the_o tropic_n his_o right_a ascension_n be_v always_o less_o than_o 6_o hour_n and_o the_o compliment_n of_o it_o more_o but_o when_o he_o be_v return_v from_o the_o tropic_n towards_o the_o equator_fw-la it_o be_v always_o more_o than_o 6_o hour_n and_o the_o compliment_n of_o it_o less_o the_o odd_a minute_n be_v to_o be_v take_v from_o the_o limb_n where_o each_o degree_n be_v divide_v into_o 4_o part_n each_o part_n signify_v a_o minute_n of_o time_n and_o to_o know_v whether_o the_o sun_n do_v depart_v from_o or_o return_v towards_o the_o equator_fw-la be_v very_o visible_a by_o the_o progress_n and_o regress_n of_o the_o day_n of_o the_o month_n as_o they_o be_v denominate_v on_o the_o quadrant_n example_n so_o the_o thread_n lay_v over_o 17_o of_o declination_n which_o will_v be_v about_o the_o 27_o april_n the_o sun_n right_a ascension_n will_v be_v 44_o 37_o m_o in_o time_n 2_o h_o 58′_n 26_o july_n the_o sun_n right_a ascension_n will_v be_v 135_o 23_o in_o time_n 9_o 2_o 20_o october_n the_o sun_n right_a ascension_n will_v be_v 224_o 37_o in_o time_n 2_o 58_o 22_o january_n the_o sun_n right_a ascension_n will_v be_v 315_o 23_o in_o time_n 9_o 2_o but_o here_o the_o latter_a 12_o hour_n be_v omit_v such_o proposition_n as_o require_v the_o use_n of_o the_o bead_n be_v to_o find_v the_o sun_n amplitude_n or_o coast_n of_o rise_v and_o set_v from_o the_o true_a east_n or_o west_n bring_v the_o bead_n be_v rectify_v to_o either_o of_o the_o ecliptic_o it_o matter_n not_o which_o to_o either_o of_o the_o orison_n and_o the_o thread_n will_v intersect_v the_o amplitude_n seek_v upon_o both_o alike_o example_n the_o sun_n declination_n be_v 17_o north_n or_o south_n the_o sun_n amplitude_n will_v be_v find_v to_o be_v 28_o 2m._o the_o amplitude_n before_o find_v for_o the_o summer_n half_a year_n be_v to_o be_v account_v from_o east_n or_o west_n northwards_o and_o in_o the_o winter_n half_a year_n from_o thence_o southwards_o to_o find_v the_o time_n of_o the_o sun_n rise_v or_o set_v the_o thread_n lie_v in_o the_o same_o position_n as_o in_o the_o former_a proposition_n intersect_v the_o ascensional_a difference_n in_o the_o limb_n which_o may_v there_o be_v count_v either_o in_o degree_n or_o time_n example_n so_o the_o bead_n lie_v upon_o the_o horizon_n be_v rectify_v to_o 17_o of_o declination_n the_o thread_n intersect_v the_o limb_n at_o 22_o 38_o m_o which_o be_v 1_o h_o 30_o m_o of_o time_n and_o so_o it_o show_v the_o time_n of_o sun_n rise_v in_o summer_n or_o set_v in_o winter_n to_o be_v at_o half_a a_o hour_n past_o 4_o and_o his_o rise_n in_o winter_n and_o set_v in_o summer_n to_o be_v at_o half_a a_o hour_n past_o 7._o to_o find_v the_o length_n of_o the_o day_n or_o night_n the_o time_n of_o the_o sun_n rise_v and_o set_v be_v one_o of_o they_o the_o compliment_n of_o the_o other_o to_o 12_o hour_n so_o that_o one_o of_o they_o be_v know_v the_o other_o will_v be_v find_v by_o substraction_n the_o time_n of_o sun_n set_v be_v equal_a to_o half_a the_o length_n of_o the_o day_n and_o this_o double_v give_v the_o whole_a length_n of_o the_o day_n in_o

take_v the_o altitude_n mind_n what_o ark_n in_o the_o particular_a sine_fw-la the_o thread_n cut_v add_v the_o sine_fw-la of_o that_o ark_n to_o the_o sine_fw-la of_o the_o declination_n and_o enter_v that_o extent_n at_o the_o declination_n in_o the_o scale_n of_o entrance_n lay_v the_o thread_n to_o the_o other_o foot_n according_a to_o near_a distance_n and_o in_o the_o equal_a limb_n it_o show_v the_o hour_n from_o six_o so_o if_o the_o declination_n be_v 13_o d._n south_n and_o the_o sun_n altitude_n 14_o d._n 38_o m._n the_o thread_n in_o the_o particular_a sine_fw-la will_v cut_v 18_o d._n 49_o m._n and_o true_a time_n of_o the_o day_n will_v be_v 9_o in_o the_o morning_n or_o 3_o in_o the_o morning_n to_o find_v the_o time_n of_o the_o day_n for_o north_n declination_n have_v observe_v what_o ark_n the_o thread_n in_o take_v the_o altitude_n hang_v over_o in_o the_o particular_a sine_fw-la take_v the_o distance_n between_o the_o sine_fw-la of_o the_o say_a ark_n and_o the_o sine_fw-la of_o the_o declination_n and_o enter_v that_o extent_n at_o the_o declination_n in_o the_o scale_n of_o entrance_n the_o thread_n in_o the_o limb_n show_v the_o hour_n from_o six_o example_n if_o the_o sun_n declination_n be_v 23_o d._n 31_o m._n north_n and_o his_o altitude_n 39_o d._n the_o arch_n in_o the_o particular_a sine_fw-la will_v be_v 53_o d._n 32_o m._n and_o the_o time_n of_o the_o day_n will_v be_v about_o 3_o quarter_n past_o 3_o in_o the_o afternoon_n or_o a_o quarter_n past_o 8_o in_o the_o morning_n when_o the_o altitude_n be_v more_o than_o the_o latitude_n the_o thread_n will_v hang_v over_o a_o secant_fw-la in_o the_o particular_a scale_n this_o happen_v not_o till_o the_o sun_n have_v more_o than_o 13_o d._n of_o north_n declination_n in_o this_o case_n take_v the_o distance_n between_o the_o secant_fw-la before_o the_o begin_n of_o the_o scale_n of_o entrance_n and_o the_o sine_fw-la of_o the_o declination_n at_o the_o end_n of_o the_o same_o and_o 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ars_fw-la anaclastica_fw-la finis_fw-la the_o description_n and_o use_v of_o a_o general_z quadrant_n with_o the_o horizontal_n projection_n upon_o it_o invert_v write_a and_o publish_v by_o john_n collins_n accountant_a and_o student_n in_o the_o mathematics_n london_n print_v anno_fw-la m._n dc_o lviii_o the_o description_n of_o the_o horizontal_n quadrant_n this_o denomination_n be_v attribute_v to_o it_o because_o it_o be_v derive_v from_o the_o horizontal_n projection_n invert_v of_o the_o fore-side_n on_o the_o right_a edge_n be_v a_o line_n of_o natural_a sin_n on_o the_o left_a edge_n a_o line_n of_o versed-sines_n both_o these_o line_n issue_n from_o the_o centre_n where_o they_o concur_v and_o make_v a_o right_a angle_n and_o between_o they_o and_o the_o circular_a line_n in_o the_o limb_n be_v the_o projection_n include_v which_o consist_v of_o divers_a portion_n and_o arke_n of_o circle_n of_o the_o parallel_n of_o declination_n these_o be_v portion_n of_o circle_n that_o cross_v the_o quadrant_a oblique_o from_o the_o left_a edge_n towards_o the_o right_n to_o describe_v they_o observe_v that_o the_o left_a edge_n of_o the_o quadrant_a be_v call_v the_o meriridian_n line_n and_o that_o every_o degree_n or_o parallel_n of_o the_o sun_n declination_n if_o continue_v about_o will_v cross_v the_o meridian_n in_o two_o opposite_a point_n the_o one_o below_o the_o centre_n towards_o the_o limb_n and_o the_o other_o above_o and_o beyond_o the_o centre_n of_o the_o quadrant_a the_o distance_n between_o these_o two_o point_n be_v the_o diameter_n of_o the_o say_a parallel_n and_o the_o semidiameter_n will_v be_v the_o centre_n point_v it_o will_v be_v necessary_a in_o the_o first_o place_n to_o limit_v the_o outwardmost_a parallel_n of_o declination_n which_o may_v be_v do_v in_o the_o meridian_n line_n at_o any_o point_n assume_v the_o distance_n of_o this_o assume_v point_n from_o the_o centre_n in_o any_o latitude_n must_v represent_v the_o tangent_fw-la of_o a_o compound_n ark_n make_v by_o add_v half_o the_o great_a meridian_n altitude_n to_o 45_o deg._n which_o for_o london_n must_v be_v the_o tangent_fw-la of_o 76_o degr._fw-la and_o to_o the_o radius_fw-la of_o this_o tangent_fw-la mus_fw-la the_o follow_a work_n be_v fit_v in_o like_a manner_n the_o semidiameter_n of_o all_o other_o parallel_n that_o fall_v below_o the_o centre_n be_v limit_v by_o prick_v down_o the_o tangent_n of_o arke_n frame_v by_o add_v half_o the_o meridian_n altitude_n suitable_a to_o each_o declination_n continual_o to_o 45_o degr._fw-la now_o to_o limit_v the_o semidiameter_n above_o or_o beyond_o the_o centre_n only_o prick_v off_o the_o respective_a tangent_n of_o half_a the_o sun_n midnight_n depression_n from_o the_o centre_n the_o other_o way_n retain_v the_o former_a radius_fw-la by_o this_o mean_n there_o will_v be_v find_v two_o respective_a point_n limit_v the_o diameter_n of_o each_o parallel_n which_o have_v the_o centre_n will_v be_v easy_o find_v fall_v in_o the_o middle_n of_o each_o diameter_n but_o to_o do_v this_o arithmetical_o first_o find_v the_o ark_n compound_v of_o half_a the_o sun_n meridian_n altitude_n and_o 45_o degr._fw-la as_o before_o and_o to_o the_o tangent_fw-la thereof_o add_v the_o tangent_fw-la of_o half_a the_o sun_n midnight_n depression_n observe_v that_o the_o sun_n midnight_n depression_n in_o winter-summer_n be_v equal_a to_o his_o meridian_n altitude_n in_o summer-winter_n his_o declination_n be_v alike_o in_o quantity_n though_o in_o different_a hemisphere_n the_o half_a sum_n of_o these_o two_o tangent_n be_v the_o respective_a semidiameter_n seek_v and_o be_v prick_v in_o the_o meridian_n line_n either_o way_n from_o the_o former_a point_n limit_v the_o diameter_n will_v find_v the_o centre_n or_o without_o limit_v those_o point_n for_o the_o diameter_n first_o get_v the_o difference_n between_o the_o tangent_n of_o those_o arke_n that_o limit_v they_o on_o either_o side_n and_o the_o half_a sum_n abovesaid_a the_o say_a difference_n prick_v from_o the_o centre_n of_o the_o quadrant_a in_o the_o meridian_n line_n find_v the_o respective_a centre_n of_o those_o parallel_n the_o say_v half_a sum_n be_v the_o respective_a semidiameter_n wherewith_o they_o be_v to_o be_v describe_v of_o the_o line_n or_o index_n of_o altitude_n this_o be_v no_o other_o than_o a_o single_a prick_v line_n stand_v next_o the_o meridian_n line_n or_o leave_v edge_n of_o the_o quadrant_a to_o which_o the_o bead_n must_v be_v continual_o rectify_v when_o either_o the_o hour_n or_o azimuth_n be_v find_v by_o help_n of_o the_o projection_n to_o graduate_v it_o add_v half_o the_o altitude_n respective_o whereto_o the_o index_n be_v to_o be_v fit_v to_o 45_o degr._fw-la and_o prick_v down_o the_o tangent_n of_o these_o compound_n arke_v from_o the_o centre_n example_n to_o graduate_v the_o index_n for_o 40_o degr._fw-la of_o altitude_n the_o half_a thereof_o be_v 20_o which_o add_v to_o 45_o degr._fw-la make_v 65_o degr._fw-la which_o take_v from_o a_o tangent_fw-la to_o the_o former_a radius_fw-la and_o prick_v from_o the_o centre_n give_v the_o point_n where_o the_o index_n be_v to_o be_v graduate_v with_o 40_o degree_n hence_o it_o be_v evident_a that_o where_o the_o division_n of_o the_o index_n begin_v mark_v 0_o the_o distance_n of_o that_o point_n from_o the_o centre_n be_v equal_a to_o the_o common_a radius_fw-la of_o the_o tangent_n because_o this_o quadrant_a as_o all_o natural_a projection_n have_v a_o revert_v tail_n the_o graduation_n of_o the_o index_n be_v continue_v above_o the_o hozontal_n point_n 0_o towards_o the_o centre_n to_o 30_o degr._fw-la 40′_n as_o much_o as_o be_v the_o sun_n great_a vertical_a altitude_n in_o this_o latitude_n and_o the_o graduation_n of_o the_o index_n be_v set_v off_o from_o the_o centre_n by_o prick_v down_o the_o tangent_n of_o the_o arke_n of_o difference_n

the_o day_n example_n let_v the_o declination_n be_v suppose_v 23_o deg_n 31′_n north_n and_o the_o altitude_n 38_o deg_n 59′_n the_o near_a distance_n from_o the_o sine_fw-la thereof_o to_o the_o thread_n lay_v over_o the_o secant_fw-la of_o 3●_n deg_n 31′_n will_v reach_v be_v turn_v twice_o over_o from_o 3●_n d._n 31′_n in_o the_o annex_v tangent_fw-la near_o the_o centre_n to_o 33_o deg_n 45′_n in_o the_o sin_n alias_o to_o 56_o d._n 15′_n count_v as_o a_o verse_v sine_fw-la show_v the_o time_n of_o the_o day_n to_o be_v a_o quarter_n past_o 8_o in_o the_o morning_n or_o three_o quarter_n past_o three_o in_o the_o afternoon_n 3_o to_o find_v the_o sun_n altitude_n on_o all_o hour_n take_v the_o distance_n between_o the_o hour_n and_o the_o declination_n in_o the_o fit_a scale_n and_o enter_v it_o down_o the_o line_n of_o sin_n from_o the_o centre_n then_o lay_v the_o thread_n over_o the_o cousin_n of_o the_o declination_n in_o the_o limb_n the_o near_a distance_n to_o it_o shall_v be_v the_o sine_fw-la of_o the_o altitude_n seek_v example_n thus_o whee_fw-mi the_o sun_n have_v 13_o deg_n of_o south_n declination_n count_v it_o in_o that_o part_n of_o the_o annex_v tangent_fw-la near_a the_o limb_n if_o then_o it_o be_v require_v to_o find_v the_o sun_n altit_fw-fr for_o the_o hour_n of_o 10_o or_o 2_o by_o the_o former_a prescription_n the_o altitude_n will_v be_v find_v 10_o d._n 25′_n 4_o to_o find_v the_o sun_n amplitude_n take_v the_o sine_fw-la of_o the_o declination_n from_o the_o line_n of_o the_o sin_n and_o apply_v it_o to_o the_o fit_a scale_n where_o the_o annex_v tangent_fw-la begin_v and_o either_o way_n it_o will_v reach_v to_o the_o sine_fw-la of_o the_o amplitude_n example_n so_o when_o the_o sun_n have_v 15_o deg_n of_o declination_n his_o amplitude_n will_v be_v find_v to_o be_v 24_o deg_n 35′_n 5_o to_o find_v the_o azimuth_n or_o true_a coast_n of_o the_o sun_n here_o we_o likewise_o introduce_v the_o radius_fw-la in_o the_o latter_a proportion_n 1_o in_o winter_n lay_v the_o thread_n to_o the_o secant_fw-la of_o the_o altitude_n in_o the_o limb_n and_o from_o the_o sine_fw-la of_o the_o declination_n take_v the_o near_a distance_n to_o it_o the_o say_a extent_n enter_v twice_o forward_o from_o the_o altitude_n in_o the_o annex_v tangent_fw-la and_o it_o will_v reach_v to_o the_o verse_v sine_fw-la of_o the_o azimuth_n from_o the_o south_n example_n so_o when_o the_o sun_n have_v 15_o deg_n of_o south_n declination_n if_o his_o altitude_n be_v 15_o deg_n the_o near_a distance_n from_o the_o sine_fw-la thereof_o to_o the_o thread_n lay_v over_o the_o secant_fw-la of_o 15_o degree_n shall_v reach_v in_o the_o fit_a scale_n from_o the_o annex_v tangent_fw-la of_o 15_o deg_n be_v twice_o repeat_v forward_o to_o the_o verse_v sine_fw-la of_o 39_o deg_n 50′_n for_o the_o sun_n azimuth_n from_o the_o south_n 2_o in_o summer_n when_o the_o altitude_n be_v less_o than_o 40_o deg_n enter_v the_o former_a extent_n from_o the_o sine_fw-la of_o the_o declination_n to_o the_o thread_n lay_v over_o the_o secant_fw-la of_o the_o altitude_n twice_o backward_o from_o the_o altitude_n in_o the_o annex_v tangent_fw-la and_o it_o will_v reach_v to_o the_o verse_v sine_fw-la of_o the_o azimuth_n from_o the_o south_n example_n so_o if_o the_o sun_n have_v 15_o deg_n of_o north_n declination_n and_o his_o altitude_n be_v 30_o deg_n the_o prescribe_a extent_n double_v shall_v reach_v from_o the_o annex_v tangent_fw-la of_o 30_o deg_n to_o the_o verse_v sine_fw-la of_o 75_o deg_n 44′_n for_o the_o sun_n azimuth_n from_o the_o south_n 3_o in_o summer_n when_o the_o altitude_n be_v more_o than_o 40_o deg_n and_o less_o than_o 60_o deg_n apply_v the_o extent_n from_o the_o sine_fw-la of_o the_o declination_n to_o the_o thread_n lay_v over_o the_o secant_fw-la of_o the_o altitude_n once_o to_o the_o discontinue_v tangent_fw-la place_v a_o cross_a the_o quadrant_a from_o the_o altitude_n backward_o mind_v how_o far_o it_o reach_v just_a against_o the_o like_a ark_n in_o the_o annex_v tangent_fw-la stand_v the_o verse_v sine_fw-la of_o the_o azimuth_n from_o the_o south_n 4_o when_o the_o altitude_n be_v more_o than_o 60_o deg_n this_o fit_a scale_n be_v of_o worst_a performance_n however_o the_o defect_n of_o the_o secant_fw-la may_v be_v supply_v by_o vary_v the_o proportion_n 6_o to_o find_v the_o sun_n altitude_n on_o all_o azimuth_n just_o against_o the_o azimuth_n propose_v stand_v the_o sun_n altitude_n in_o the_o equator_fw-la suitable_a thereto_o which_o be_v the_o first_o ark_n find_v by_o calculation_n when_o we_o treat_v of_o this_o subject_n and_o the_o second_o ark_n be_v to_o be_v find_v by_o a_o proportion_n in_o sin_n wrought_v upon_o the_o quadrant_a this_o quadrant_a be_v also_o particular_o fit_v for_o give_v the_o hour_n and_o azimuth_n in_o the_o equal_a limb_n the_o sine_fw-la of_o 90_o deg_n make_v equal_a to_o the_o sine_fw-la if_o 51_o deg_n 32′_n give_v the_o altitude_n of_o the_o sun_n or_o star_n at_o six_o for_o if_o the_o thread_n be_v lay_v over_o the_o declination_n count_v in_o the_o say_v sine_fw-la it_o show_v the_o altitude_n seek_v in_o the_o limb_n so_o when_o the_o sun_n have_v 13_o deg_n of_o declination_n his_o altitude_n or_o depression_n at_o 6_o be_v 10_o deg_n 9′_n it_o also_o give_v the_o vertical_a altitude_n if_o the_o declination_n be_v count_v in_o the_o limb_n seek_v what_o ark_n it_o cut_v in_o that_o particular_a sine_fw-la when_o the_o sun_n have_v 13_o deg_n of_o declination_n his_o vertical_a altitude_n or_o depression_n be_v 16_o deg_n 42′_n to_o find_v the_o hour_n of_o the_o day_n have_v find_v the_o altitude_n of_o the_o sun_n or_o star_n at_o six_o take_v the_o distance_n between_o the_o sine_fw-la thereof_o in_o the_o line_n sines_n and_o the_o altitude_n give_v and_o enter_v one_o foot_n of_o that_o extent_n at_o the_o declination_n in_o the_o scale_n of_o entrance_n lay_v the_o thread_n to_o the_o other_o foot_n according_a to_o near_a distance_n it_o will_v show_v the_o hour_n from_o six_o in_o the_o limb_n example_n when_o the_o sun_n have_v 13_o deg_n of_o declination_n his_o altitude_n or_o depression_n at_o six_o will_v be_v 10_o deg_n 9′_n if_o the_o declination_n be_v north_n and_o the_o altitude_n of_o the_o sun_n be_v 24_o deg_n 5′_n the_o time_n of_o the_o day_n will_v be_v half_o a_o hour_n past_o 7_o in_o the_o morning_n or_o as_o much_o past_o 4_o in_o the_o afternoon_n in_o winter_n when_o the_o sun_n have_v south_n declination_n as_o also_o for_o such_o star_n as_o have_v south_n declination_n the_o sine_fw-la of_o their_o altitude_n must_v be_v add_v to_o the_o sine_fw-la of_o their_o depression_n at_o six_o and_o that_o whole_a extent_n enter_v as_o before_o when_o the_o sun_n have_v the_o same_o south_n declination_n if_o his_o altitude_n be_v 11_o deg_n 7′_n the_o time_n of_o the_o day_n will_v be_v half_a a_o hour_n past_o 8_o in_o the_o morning_n or_o 30_o min._n past_o 3_o in_o the_o afternoon_n to_o find_v the_o azimuth_n of_o the_o sun_n or_o star_n lay_v the_o thread_n over_o their_o altitude_n in_o the_o particular_a sine_fw-la fit_v to_o the_o latitude_n and_o in_o the_o equal_a limb_n it_o show_v a_o four_o ark_n when_o the_o declination_n be_v north_n take_v the_o distance_n in_o the_o line_n of_o sin_n between_o that_o four_o ark_n and_o the_o declination_n and_o enter_v one_o foot_n of_o that_o extent_n at_o the_o altitude_n in_o the_o scale_n of_o entrance_n lay_v the_o thread_n to_o the_o other_o foot_n and_o in_o the_o equal_a limb_n it_o show_v the_o azimuth_n from_o the_o east_n or_o west_n example_n when_o the_o altitude_n be_v 44_o deg_n 39′_n the_o arch_n find_v in_o the_o equal_a limb_n will_v be_v 33_o deg_n 20′_n then_o if_o the_o declination_n be_v 23_o deg_n 31′_n north_n the_o distance_n in_o the_o line_n of_o sin_n between_o it_o and_o the_o say_a ark_n be_v enter_v at_o 44_o deg_n 39′_n in_o the_o scale_n of_o entrance_n the_o thread_n be_v lay_v to_o the_o other_o foot_n will_v show_v the_o azimuth_n to_o be_v 20_o deg_n from_o the_o east_n or_o west_n but_o if_o the_o declination_n be_v south_n add_v with_o your_o compass_n the_o sine_fw-la thereof_o to_o the_o sine_fw-la of_o the_o four_o ark_n and_o enter_v that_o whole_a extent_n as_o before_o and_o the_o thread_n will_v show_v the_o azimuth_n in_o the_o equal_a limb_n example_n when_o the_o altitude_n be_v 12d_o 13′_n the_o four_o arch_n will_v be_v find_v to_o be_v 9_o degree_n 32_o minute_n then_o admit_v the_o declination_n to_o be_v 13_o degree_n south_n whereto_o add_v the_o sine_fw-la of_o the_o four_o ark_n the_o whole_a will_v be_v equal_a to_o the_o sine_fw-la of_o 22_o deg_n 41_o minute_n and_o

limb._n so_o likewise_o the_o table_n for_o put_v on_o the_o lesser_a sin_n be_v make_v by_o halfe_v the_o natural_a sin_n and_o then_o seek_v what_o ark_v correspond_v thereto_o in_o the_o natural_a sin_n aforesaid_a those_o that_o think_v these_o line_n to_o many_o may_v very_o well_o want_v the_o verse_v sin_n so_o oft_o repeat_v and_o they_o that_o will_v admit_v of_o a_o radius_fw-la of_o 6_o or_o 7_o inch_n may_v have_v the_o line_n of_o line_n superficies_n and_o solid_n put_v on_o in_o the_o limb_n on_o the_o foreside_n and_o the_o segment_n quadrature_n equated_a body_n metal_n and_o inscribe_v body_n or_o other_o line_n at_o pleasure_n put_v on_o upon_o the_o backside_n as_o have_v be_v already_o do_v upon_o some_o quadrant_n now_o to_o the_o use_n the_o use_v of_o the_o projection_n of_o the_o almanac_n before_o the_o projection_n can_v be_v use_v the_o day_n of_o the_o month_n the_o sun_n place_n or_o declination_n must_v be_v know_v but_o these_o be_v common_o give_v by_o the_o knowledge_n thereof_o now_o this_o almanac_n will_v as_o much_o help_n to_o the_o obtain_n hereof_o as_o any_o other_o common_a almanac_n it_o consist_v of_o a_o rectangular_a oblong_n or_o long_a square_n divide_v into_o 7_o column_n in_o the_o breadth_n to_o represent_v 7_o day_n of_o the_o week_n account_v the_o lord_n day_n first_o and_o length_n way_n into_o 9_o column_n the_o two_o uppermost_o represent_v the_o month_n of_o the_o year_n account_v march_n the_o first_o the_o five_o middlemost_a the_o respective_a day_n of_o each_o month_n and_o the_o two_o undermost_a some_o certain_a leap_n year_n posit_v in_o such_o column_n as_o that_o thereby_o may_v be_v know_v by_o inspection_n what_o day_n of_o the_o week_n the_o first_o of_o march_n happen_v upon_o in_o the_o say_a leap_n year_n the_o contrivance_n hereof_o own_v its_o original_n from_o my_o worthy_a friend_n mr._n michael_n darie_n for_o the_o due_a place_n of_o the_o month_n over_o the_o column_n of_o day_n take_v the_o follow_a rule_n in_o his_o own_o word_n first_o have_v march_n assign_v to_o lead_v the_o round_a the_o rest_n of_o the_o month_n be_v easy_o after_o find_v if_o that_o you_o take_v the_o compliment_n in_o day_n to_o 35_o of_o a_o place_v month_n always_o and_o count_v it_o from_o its_o place_n with_o due_a progression_n it_o show_v you_o where_o the_o next_o month_n take_v possession_n thus_o place_v the_o month_n of_o march_n first_o then_o if_o i_o will_v place_v april_n or_o the_o second_o month_n march_n have_v 31_o day_n the_o compliment_n thereof_o to_o 35_o be_v 4_o then_o count_v four_o column_n from_o the_o place_n of_o march_n it_o fall_v upon_o the_o 5_o column_n where_o the_o figure_n 2_o be_v place_v for_o the_o 2_o month_n than_o april_n be_v place_v if_o i_o will_v place_n may_v i_o take_v 30_o the_o number_n of_o day_n in_o april_n from_o 35_o there_o rest_v 5_o and_o count_v 5_o column_n from_o the_o place_n of_o april_n where_o it_o end_v which_o be_v in_o the_o 3_o column_n the_o figure_n 3_o be_v place_v for_o the_o 3_o month_n or_o month_n of_o may._n the_o next_o thing_n to_o be_v know_v be_v on_o what_o day_n of_o the_o week_n the_o first_o day_n of_o march_n fall_v upon_o which_o be_v continual_o to_o be_v remember_v in_o use_v the_o almanac_n this_o for_o some_o leap_v year_n to_o come_v may_v be_v know_v by_o count_v in_o what_o column_n the_o say_v leap_v year_n be_v grave_v thus_o in_o anno_fw-la 1660_o the_o first_o of_o march_n fall_v upon_o a_o thursday_n because_o 60_o be_v grave_v in_o the_o 5_o column_n that_o be_v the_o five_o day_n of_o the_o week_n but_o for_o a_o general_a rule_n take_v it_o in_o these_o word_n to_o the_o number_n two_o add_v the_o year_n of_o our_o lord_n and_o a_o four_o part_n thereof_o neglect_v the_o odd_a remainder_n when_o there_o be_v any_o the_o amount_v divide_v by_o 7_o the_o remainder_n when_o the_o division_n be_v finish_v show_v the_o number_n of_o direction_n or_o day_n of_o the_o week_n on_o which_o the_o first_o day_n of_o march_n fall_v account_v the_o lord_n day_n the_o first_o but_o if_o nothing_o remain_v it_o fall_v on_o a_o saturday_n  _fw-fr 2_o  _fw-fr example_n for_o the_o year_n 1657_o the_o even_o four_o thereof_o 414_o  _fw-fr 2073_o 296_o quotient_n 7_o 1_o remain_v  _fw-fr by_o this_o rule_n there_o will_v be_v find_v to_o remain_v one_o for_o the_o year_n of_o our_o lord_n 1657_o whence_o it_o follow_v that_o the_o first_o day_n of_o march_n fall_v on_o the_o first_o day_n of_o the_o week_n alias_o the_o lord_n day_n in_o that_o year_n so_o in_o anno_fw-la 1658_o there_o remain_v 2_o for_o monday_n in_o 1659._o rest_v 3_o for_o tuesday_n in_o 1660_o rest_n 5_o for_o thursday_n so_o that_o hence_o it_o may_v be_v observe_v that_o every_o 4_o year_n the_o first_o of_o march_n proceed_v 5_o day_n upon_o which_o supposition_n the_o former_a rule_n be_v build_v say_v then_o as_o 4_o to_z 5_o or_o as_o 1_o to_o 1¼_n so_o be_v the_o year_n of_o the_o lord_n propound_v to_o the_o number_n of_o day_n the_o first_o of_o march_n have_v proceed_v in_o all_o that_o tract_n cause_v by_o the_o odd_a day_n in_o each_o year_n and_o the_o access_n of_o the_o day_n for_o the_o leap_v year_n this_o number_n divide_v by_o 7_o the_o remainder_n show_v the_o fractionate_a part_n of_o a_o week_n above_o whole_a one_o which_o the_o say_a day_n have_v proceed_v which_o will_v not_o agree_v with_o the_o day_n of_o the_o week_n the_o first_o of_o march_n fall_v upon_o according_a to_o common_a tradition_n unless_o the_o number_n two_o be_v add_v thereto_o which_o argue_v that_o the_o first_o of_o march_n as_o we_o now_o account_v the_o day_n of_o the_o week_n fall_v upon_o monday_n or_o the_o second_o day_n of_o the_o week_n in_o the_o year_n of_o our_o lord_n nativity_n this_o be_v only_o for_o illustration_n of_o the_o former_a rule_n be_v to_o show_v that_o the_o add_v of_o the_o even_o four_o part_n of_o the_o year_n of_o our_o lord_n thereto_o work_v the_o proportion_n of_o 4_o to_o 5._o the_o use_n of_o this_o almanac_n be_v to_o know_v for_o ever_o on_o what_o day_n of_o the_o week_n any_o day_n of_o the_o month_n fall_v upon_o remember_v on_o what_o day_n of_o the_o week_n the_o first_o day_n of_o march_n fall_v upon_o in_o the_o year_n propound_v which_o do_v then_o begin_v in_o the_o use_n of_o this_o almanac_n and_o not_o soon_o or_o late_a as_o upon_o new-year_n day_n or_o quarter_n day_n all_o the_o figure_n represent_v the_o day_n of_o the_o month_n do_v also_o represent_v the_o same_o day_n of_o the_o week_n in_o the_o respective_a month_n under_o which_o they_o stand_v and_o the_o converse_n the_o month_n be_v assign_v all_o the_o figure_n that_o stand_v as_o day_n under_o it_o inform_v you_o what_o day_n of_o the_o say_a month_n the_o week_n day_n shall_v be_v the_o same_o as_o it_o be_v upon_o the_o first_o day_n of_o march_n and_o then_o by_o a_o due_a progression_n it_o will_v be_v easy_a to_o find_v upon_o what_o day_n of_o the_o month_n any_o day_n of_o the_o week_n fall_v as_o well_o as_o by_o a_o common_a almanac_n without_o the_o trouble_n of_o always_o one_o and_o sometime_o two_o dominical_a letter_n quite_o shun_v in_o this_o almanac_n by_o begin_v the_o year_n the_o first_o of_o march_n and_o so_o the_o odd_a day_n for_o leap_n year_n be_v introduce_v between_o the_o end_n of_o the_o old_a and_o the_o beginning_n of_o the_o new-year_n example_n in_o anno_fw-la 1657._o look_v for_o the_o figure_n 10_o in_o the_o column_n for_o month_n for_o the_o month_n of_o december_n under_o it_o i_o find_v 6_o 13_o 20_o 27_o now_o the_o first_o of_o march_n be_v the_o lord_n day_n i_o conclude_v also_o that_o these_o respective_a day_n in_o december_n be_v likewise_o on_o the_o lord_n day_n and_o from_o hence_o collect_v that_o christmas_n day_n which_o be_v always_o the_o 25_o of_o that_o month_n happen_v on_o a_o friday_n use_v of_o the_o projection_n this_o projection_n be_v no_o other_o than_o a_o four_o part_n of_o stofler_n particular_a astrolabe_n fit_v for_o the_o latitude_n of_o london_n invert_v that_o be_v the_o summer_n tropic_n and_o altitude_n etc._n etc._n turn_v downward_o towards_o the_o limb_n whereas_o in_o his_o astrolabe_n they_o be_v place_v upward_o towards_o the_o centre_n thus_o the_o quadrant_n thereof_o make_v be_v render_v most_o useful_a and_o accurate_a when_o there_o be_v most_o occasion_n for_o it_o before_o the_o projection_n can_v be_v use_v the_o bead_n must_v be_v rectify_v and_o because_o the_o thread_n and_o bead_n may_v stretch_v there_o may_v be_v two_o bead_n the_o one_o set_v to_o some_o circle_n

limb_n from_o it_o may_v be_v take_v off_o sin_n tangent_n or_o secant_v as_o be_v do_v from_o the_o limb_n and_o therein_o the_o hour_n and_o azimuth_n find_v general_o by_o help_n of_o the_o line_n of_o sin_n on_o the_o left_a edge_n as_o be_v large_o show_v in_o the_o use_n of_o this_o quadrant_a beside_o its_o use_n in_o dyall_v only_o when_o such_o a_o instrument_n be_v make_v apart_o it_o will_v be_v more_o convenient_a to_o have_v the_o line_n of_o sines_n to_o be_v set_v on_o the_o right_a edge_n and_o the_o diameter_n number_v also_o by_o its_o compliment_n this_o diameter_n or_o double_a tangent_fw-la or_o hipotenusal_a line_n be_v first_o divide_v on_o all_o the_o other_o line_n may_v from_o it_o by_o the_o same_o table_n that_o serve_v to_o graduate_v they_o from_o the_o equal_a limb_n be_v likewise_o inscribe_v and_o here_o let_v i_o put_v a_o period_n to_o the_o use_n of_o this_o quadrant_a gloria_fw-la deo_fw-la the_o description_n of_o a_o universal_a small_a pocket_n quadrant_n this_o quadrant_a have_v only_o one_o face_n on_o the_o right_a edge_n from_o the_o centre_n be_v place_v a_o line_n of_o sin_n divide_v into_o degree_n and_o half_a degree_n up_o to_o 60_o d._n afterward_o into_o whole_a degree_n to_o 80_o d._n on_o the_o left_a edge_n issue_v a_o line_n of_o 10_o equal_a part_n from_o the_o centre_n be_v precise_a 4_o inch_n long_o each_o part_n be_v divide_v into_o 10_o subdivision_n and_o each_o subdivision_n into_o half_n these_o two_o line_n make_v a_o right_a angle_n at_o the_o centre_n and_o between_o they_o include_v a_o projection_n of_o the_o sphere_n for_o the_o latitude_n of_o london_n above_o the_o projection_n be_v put_v on_o in_o quadrant_n of_o circle_n a_o line_n of_o declination_n 4_o quadrant_n for_o the_o day_n of_o the_o month_n above_o they_o the_o name_n of_o 5_o star_n with_o their_o right_a ascension_n grave_v against_o they_o and_o a_o general_a almanac_n beneath_o the_o projection_n be_v put_v on_o in_o quadrant_n of_o circle_n a_o particular_a sine_fw-la and_o secant_fw-la so_o call_v because_o it_o be_v particular_a to_o the_o latitude_n of_o london_n below_o that_o the_o quadrat_fw-la and_o shadow_n below_o that_o a_o line_n of_o tangent_n to_o 45_o d._n last_o of_o all_o the_o equal_a limb_n on_o the_o left_a edge_n be_v place_v the_o dial_a scale_n of_o hour_n 4_o inch_n long_o outwardmost_a on_o the_o right_a edge_n a_o line_n of_o latitude_n fit_v thereto_o within_o the_o line_n of_o sin_n close_o abut_a thereto_o be_v place_v a_o small_a scale_n call_v the_o scale_n of_o entrance_n beginning_n against_o 52_o d._n 35_o min._n of_o the_o sin_n number_v to_o 60_o d._n the_o line_n of_o sin_n that_o issue_v from_o the_o centre_n shall_v for_o a_o particular_a use_n have_v be_v continue_v long_o to_o wit_n to_o a_o secant_fw-la of_o 28_o d._n because_o this_o can_v not_o be_v admit_v the_o say_v secant_fw-la be_v place_v outward_a at_o the_o end_n of_o the_o scale_n of_o entrance_n towards_o the_o limb_n and_o as_o much_o of_o the_o sine_fw-la as_o be_v needful_a place_v at_o its_o due_a distance_n at_o the_o other_o end_n of_o the_o scale_n of_o entrance_n of_o the_o use_n of_o the_o say_v quadrant_a the_o almanac_n have_v be_v large_o speak_v to_o in_o pag._n 12_o and_o 13_o also_o again_o in_o the_o use_n of_o the_o horizontal_n quadrant_a pag._n 11_o 12._o the_o quadrat_fw-la and_o shadow_n from_o pag._n 35_o to_o 44._o the_o line_n of_o latitude_n and_o scale_n of_o hour_n pag._n 250._o again_o from_o page_n to_o 262_o to_o 274_o also_o the_o line_n of_o sin_n equal_a part_n and_o tangent_n in_o other_o part_n of_o the_o book_n the_o use_n of_o the_o projection_n this_o projection_n be_v only_o fit_v for_o find_v the_o hour_n in_o the_o limb_n and_o not_o the_o azimuth_n all_o the_o circular_a line_n on_o it_o be_v parallel_n of_o altitude_n or_o depression_n except_o the_o ecliptic_a and_o horizon_n the_o ecliptic_a be_v know_v by_o the_o character_n of_o the_o sign_n and_o the_o horizon_n lie_v beneath_o it_o be_v number_v with_o 10_o 20_o 30_o 40._o the_o parallel_n of_o altitude_n be_v the_o winter_n parallel_v of_o stofler_n astrolable_a and_o be_v number_v from_o the_o horizon_n upward_o towards_o the_o centre_n the_o parallel_n of_o depression_n which_o supply_v the_o use_n of_o stofler_n summer_n altitude_n be_v number_v downward_o from_o the_o top_n of_o the_o projection_n towards_o the_o limb_n to_o find_v the_o time_n of_o sun_n rise_v and_o his_o amplitude_n lay_v the_o thread_n over_o the_o day_n of_o the_o month_n and_o set_v the_o bead_n to_o the_o ecliptic_a then_o carry_v the_o thread_n and_o bead_n to_o the_o horizon_n and_o the_o thread_n in_o the_o limb_n show_v the_o time_n of_o rise_v and_o the_o bead_n on_o the_o horizon_n the_o quantity_n of_o the_o amplitude_n example_n so_o on_o the_o second_o of_o august_n the_o sun_n declination_n be_v 15_o d_o his_o amplitude_n will_v be_v 24_o d._n 35_o min._n and_o the_o time_n of_o rise_a 41′_n past_o 4_o in_o the_o morning_n to_o find_v the_o hour_n of_o the_o day_n have_v take_v the_o sun_n altitude_n and_o rectify_v the_o bead_n as_o before_o show_v if_o the_o sun_n have_v south_n declination_n bring_v the_o bead_n to_o that_o parallel_n of_o altitude_n on_o which_o the_o sun_n height_n be_v observe_v among_o those_o parallel_n that_o be_v number_v upward_o towards_o the_o centre_n and_o the_o thread_n in_o the_o limb_n show_v the_o time_n of_o the_o day_n eample_n so_o when_o the_o sun_n have_v 15_o d._n of_o south_n declination_n as_o about_o 28_o of_o january_n if_o his_o altitude_n be_v 15_o deg_n the_o time_n of_o the_o day_n will_v be_v 39_o m._n past_o 2_o in_o the_o afternoon_n or_o 21_o m._n past_o 9_o in_o the_o morning_n but_o in_o the_o summer_n half_a year_n bring_v the_o bead_n to_o lie_v on_o those_o parallel_n that_o be_v number_v downward_o to_o the_o limb_n and_o the_o thread_n show_v therein_o the_o time_n of_o the_o day_n seek_v example_n if_o on_o the_o second_o of_o august_n his_o declination_n be_v 15_o d._n his_o altitude_n be_v 40_o d._n the_o true_a time_n of_o the_o day_n will_v be_v 8_o m._n past_o 9_o in_o the_o morning_n or_o 52_o m._n past_o 2_o in_o the_o afternoon_n if_o the_o bead_n will_v not_o meet_v with_o the_o altitude_n give_v among_o those_o parallel_n that_o run_v donwnwards_o towards_o the_o right_a edge_n than_o it_o must_v be_v bring_v to_o those_o parallel_n that_o lie_v below_o the_o horizon_n downward_o towards_o the_o left_a edge_n and_o the_o thread_n in_o the_o limb_n show_v the_o time_n of_o the_o day_n before_o six_o in_o the_o morning_n or_o after_o it_o in_o the_o evening_n in_o summer_n example_n when_o the_o sun_n have_v 15_o d._n of_o north_n declination_n as_o on_o the_o second_o of_o august_n if_o his_o altitude_n be_v 5_o d._n the_o time_n of_o the_o day_n will_v be_v 44_o m._n before_o 6_o in_o the_o morning_n or_o after_o it_o in_o the_o evening_n of_o the_o general_a line_n on_o this_o quadrant_a the_o line_n of_o sin_n on_o the_o right_a edge_n be_v general_a for_o find_v either_o the_o hour_n or_o the_o azimuth_n in_o the_o equal_a limb_n or_o in_o the_o say_a line_n of_o sin_n as_o i_o have_v large_o show_v in_o page_n 231_o for_o find_v the_o hour_n also_o for_o find_v the_o sun_n altitude_n on_o all_o hour_n as_o in_o page_n 234_o for_o find_v the_o azimuth_n from_o page_n 237_o to_o pag._n 2.9_o though_o this_o quadrant_a have_v neither_o secant_v nor_o verse_v sin_n as_o the_o rest_n have_v yet_o both_o may_v be_v easy_o supply_v let_v it_o be_v require_v to_o work_v this_o proportion_n as_o the_o cousin_a of_o the_o declination_n be_v to_o the_o secant_fw-la of_o the_o latitude_n so_o be_v the_o difference_n of_o the_o sin_n of_o the_o sun_n meridian_n and_o give_v altitude_n to_o the_o verse_v sine_fw-la of_o the_o hour_n from_o noon_n before_o or_o after_o six_o the_o hour_n may_v be_v find_v from_o midnight_n by_o the_o proportion_n in_o page_n 230._o let_v the_o radius_fw-la of_o the_o sin_n be_v assume_v to_o represent_v the_o secant_fw-la of_o the_o latitude_n the_o radius_fw-la to_o that_o secant_fw-la will_v be_v the_o cousin_n of_o the_o latitude_n then_o lay_v the_o thread_n to_o the_o compliment_n of_o the_o declination_n in_o the_o limb_n count_v from_o right_a edge_n and_o take_v the_o near_a distance_n to_o it_o i_o say_v that_o extent_n shall_v be_v the_o cousin_n of_o the_o declination_n to_o the_o radius_fw-la of_o the_o secant_fw-la enter_v this_o at_o 90_o d._n of_o the_o line_n of_o sin_n lay_v the_o thread_n to_o the_o other_o foot_n according_a to_o near_a distance_n then_o in_o the_o sin_n take_v the_o

repair_n to_o the_o month_n you_o be_v in_o and_o those_o figure_n that_o stand_v against_o it_o show_v you_o what_o day_n of_o the_o say_a month_n the_o week_n day_n shall_v be_v the_o same_o as_o it_o be_v the_o first_o day_n of_o march._n example_n for_o the_o year_n 1660_o have_v find_v that_o the_o first_o day_n of_o march_n happen_v upon_o a_o thursday_n look_v into_o the_o column_n against_o june_n and_o february_n you_o will_v find_v that_o the_o seven_o 14_o 21th_o and_o 28_o day_n of_o those_o month_n be_v thursday_n whence_o it_o may_v be_v conclude_v if_o need_n be_v that_o the_o quarter_n day_n or_o 24_o day_n of_o june_n that_o year_n happen_v on_o the_o lord_n day_n of_o the_o epact_n the_o epact_n be_v a_o number_n carry_v on_o in_o account_n from_o year_n to_o year_n towards_o a_o new_a change_n and_o be_v 11_o day_n and_o some_o odd_a time_n beside_o cause_v by_o reason_n of_o the_o moon_n motion_n which_o change_v 12_o time_n in_o a_o year_n solar_a and_o run_v also_o this_o 11_o day_n more_o towards_o a_o new_a change_n the_o use_n of_o it_o serve_v to_o find_v the_o moon_n age_n and_o thereby_o the_o time_n of_o high_a water_n to_o know_v the_o moon_n age_n add_v to_o the_o day_n of_o the_o month_n the_o epact_n and_o so_o many_o day_n more_o as_o be_v month_n from_o march_n to_o the_o month_n you_o be_v in_o including_z both_o month_n the_o sum_n if_o less_o than_o 30_o be_v the_o moon_n age_n if_o more_o subtract_v 30_o and_o the_o residue_n in_o the_o moon_n age_n prope_fw-la verum_fw-la example_n the_o epact_n for_o the_o year_n 1658_o be_v 6_o and_o let_v it_o be_v require_v to_o know_v the_o moon_n age_n the_o 28_o of_o july_n be_v the_o five_o month_n from_o march_n both_o inclusive_a 6_o 28_o 5_o the_o sum_n of_o these_o three_o number_n be_v 39_o whence_o reject_v 30_o the_o remainder_n be_v 9_o for_o the_o moon_n age_n seek_v the_o former_a rule_n serve_v when_o the_o month_n have_v 31_o day_n but_o if_o the_o month_n have_v but_o 30_o day_n or_o less_o take_v away_o but_o 29_o and_o the_o residue_n be_v her_o age_n to_o find_v the_o time_n of_o the_o moon_n come_v to_o south_n multiply_v the_o moon_n age_n by_o 4_o and_o divide_v by_o 5_o the_o quotient_n show_v it_o every_o unit_fw-la that_o remain_v be_v in_o value_n twelve_o minute_n of_o time_n and_o because_o when_o the_o moon_n be_v at_o the_o full_a or_o 15_o day_n old_a she_o come_v to_o south_n at_o the_o hour_n of_o 12_o at_o midnight_n for_o ease_v in_o multiplication_n and_o division_n when_o her_o age_n exceed_v 15_o day_n reject_v 15_o from_o it_o example_n so_o when_o the_o moon_n be_v 8_o day_n old_a she_o come_v to_o south_n at_o 24_o minute_n past_o six_o of_o the_o clock_n which_o be_v know_v her_o rise_n or_o set_v may_v be_v rude_o guess_v at_o to_o be_v six_o hour_n more_o or_o less_o before_o she_o be_v south_n and_o her_o set_n as_o much_o after_o but_o in_o regard_n of_o the_o vary_a of_o her_o declination_n no_o general_a certain_a rule_n for_o the_o memory_n can_v be_v give_v here_o it_o may_v be_v note_v that_o the_o first_o 15_o day_n of_o the_o moon_n age_n she_o come_v to_o the_o meridian_n after_o the_o sun_n be_v to_o the_o eastward_o of_o he_o and_o the_o late_a 15_o day_n she_o come_v to_o the_o meridian_n before_o the_o sun_n be_v to_o the_o westward_n of_o he_o to_o find_v the_o time_n of_o high_a water_n to_o the_o time_n of_o the_o moon_n come_v to_o south_n add_v the_o time_n of_o high_a water_n on_o the_o change_n day_n proper_a to_o the_o place_n to_o which_o the_o question_n be_v suit_v the_o sum_n show_v the_o time_n of_o high_a water_n for_o example_n there_o be_v add_v in_o a_o table_n of_o the_o time_n of_o high_a water_n at_o london_n which_o any_o one_o may_v cast_v up_o by_o memory_n according_a to_o these_o rule_n it_o be_v to_o be_v note_v that_o spring_n tide_n high_a wind_n and_o the_o moon_n in_o her_o quarter_n cause_v some_o variation_n from_o the_o time_n here_o express_v moon_n age_n moon_n south_n tide_n london_n day_n ho._n mi._n ho._n mi_fw-mi 0 15_n 12_o 3_o 00_o 1 16_n 12_o 48_o 3_o 48_o 2 17_n 1_o 36_o 4_o 36_o 3 18_n 2_o 24_o 5_o 24_o 4 19_n 3_o 12_o 6_o 12_o 5 20_n 4_o  _fw-fr 7_o 00_o 6 21_n 4_o 48_o 7_o 48_o 7 22_n 5_o 36_o 8_o 36_o 8 23_n 6_o 24_o 9_o 24_o 9 24_n 7_o 12_o 10_o 12_o 10 25_n 8_o 00_o 11_o 00_o 11 26_n 8_o 48_o 11_o 48_o 12 27_n 9_o 36_o 12_o 36_o 13 28_n 10_o 24_o 1_o 24_o 14 29_n 11_o 12_o 2_o 12_o this_o rule_n may_v in_o some_o measure_n satisfy_v and_o serve_v for_o vulgar_a use_n for_o such_o as_o have_v occasion_n to_o go_v by_o water_n and_o but_o that_o there_o be_v spare_v room_n to_o grave_n on_o the_o epact_n nothing_o at_o all_o shall_v have_v be_v say_v thereof_o a_o table_n show_v the_o hour_n and_o minute_n to_o be_v add_v to_o the_o time_n of_o the_o moon_n come_v to_o south_n for_o the_o place_n follow_v be_v the_o time_n of_o high_a water_n on_o the_o change_n day_n  _fw-fr h._n m._n quinborough_n southampton_n portsmouth_n isle_n of_o wight_n beachie_n the_o spit_n kentish_a knock_n half_a tide_n at_o dunkirk_n 00_o  00_n rochester_n maulden_n aberdeen_n redban_n west_n end_n of_o the_o nowre_n black_a tail_n 00_o  45_n gravesend_n downes_n rumney_n silly_a half_a tide_n blackness_n ramkins_n semhead_n 1_o  30_n dundee_n st._n andrew_n lixborne_n st._n lucas_n bel_n isle_n holy_a isle_n 2_o  15_n london_n tinmouth_n hartlepoole_n whitby_n amsterdam_n gascoigne_n britain_n galizia_n 3_o  00_n barwick_n flamborough_n head_n bridlington_n bay_n ostend_n flushing_n bourdeaux_n fountnesse_n 3_o  45_n scarborough_n quarter_n tide_n lawrenas_n mountsbay_n severne_n king_n sale_n corke-haven_n baltamoor_n dungarvan_n calais_n creek_n bloy_v seven_o isle_n 4_o  30_n falmouth_n foy_n humber_n moonles_a newcastle_n dartmouth_n torbay_n caldy_n garnesey_n st._n mallow_n abrowrath_n lizard_n 5_o  15_n plymouth_n weymouth_n hull_n lin_n lundy_n antwerp_n holmes_n of_o bristol_n st._n david_n head_n concalo_fw-la saint_n malo_n 6_o  00_n bristol_n foulnes_n at_o the_o start_n 6_o  45_n milford_n bridg-water_n exwater_n land_n end_n waterford_n cape_n clear_a abermorick_n texel_n 7_o  20_n portland_n peterperpont_n harflew_v hague_n st._n magnus_n sound_v dublin_n lambay_n mackuels_n castle_n 8_o  15_n poole_n s._n helen_n man_n isle_n catnes_n orkney_n fair_a isle_n dunbar_n kildien_n basse_fw-fr island_n the_o casquer_n deep_o at_o half_a tide_n 9_o  _fw-fr needles_n oxford_n laysto_n south_n and_o north_n foreland_n 9_o  45_n yarmouth_n dover_n harwich_n in_o the_o frith_n bullen_n saint_n john_n de_fw-fr luce_fw-fr calais_n ride_v 10_o  30_n rye_n winchelsea_n gorend_a rivers_n mouth_n of_o thames_n fair_a isle_n rhodes_n 11_o  15_n to_o find_v the_o epact_n for_o ever_o in_o order_n hereto_o first_o find_v out_o the_o prime_a number_n divide_v the_o year_n of_o the_o lord_n by_o 19_o the_o residue_n after_o the_o division_n be_v finish_v be_v augment_v by_o a_o unit_fw-la be_v the_o prime_n seek_v and_o if_o nothing_o remain_v the_o prime_n be_v a_o unit._n to_o find_v the_o epact_n multiply_v the_o prime_n by_o 11_o the_o product_n be_v the_o epact_n seek_v if_o less_o than_o 30_o but_o if_o it_o be_v more_o the_o residue_n of_o the_o product_v divide_v by_o 30_o be_v the_o epact_n seek_v there_o note_v that_o the_o prime_n change_v the_o first_o of_o january_n and_o the_o epact_n the_o first_o of_o march_n otherwise_o have_v once_o obtain_v the_o epact_n add_v 11_o so_o it_o the_o sum_n if_o less_o than_o 30_o be_v the_o epact_n for_o the_o next_o year_n if_o more_o reject_v 30_o and_o the_o residue_n be_v the_o epact_n seek_v caution_n when_o the_o epact_n be_v find_v to_o be_v 29_o for_o any_o year_n the_o next_o year_n follow_v it_o will_v be_v 11_o and_o not_o 10_o as_o the_o rule_n will_v suggest_v a_o table_n of_o the_o epact_n belong_v to_o the_o respective_a prime_n pr._n 1_o 2_o 3_o 4_o 5_o 6_o 7_o 8_o 9_o 10_o 11_o 12_o 13_o 14_o 15_o 16_o 17_o 18_o 19_o ep._n 11_o 22_o 3_o 14_o 25_o 6_o 17_o 28_o 9_o 20_o 1_o 12_o 23_o 4_o 15_o 26_o 7_o 18_o 29_o the_o prime_a number_n call_v the_o golden_a number_n be_v the_o number_n of_o 19_o year_n in_o which_o space_n the_o moon_n make_v all_o variety_n of_o her_o change_n as_o if_o she_o change_v on_o a_o certain_a day_n of_o the_o month_n on_o a_o certain_a year_n she_o shall_v not_o change_v the_o same_o day_n of_o the_o month_n again_o till_o 19_o year_n after_o and_o then_o it_o do_v not_o happen_v upon_o the_o same_o hour_n of_o the_o day_n yet_o the_o difference_n do_v not_o cause_v

59_o 17_o 04_o 31_o 15_o 03_o 17_o 21_o day_n november_n ☉_o r._n a._n ☉_o decl._n h._n m._n d._n m._n 1_o 15_o 07_o 17_o 38_o 2_o 15_o 11_o 17_o 54_o 3_o 15_o 15_o 18_o 10_o 4_o 15_o 19_o 18_o 26_o 5_o 15_o 23_o 18_o 41_o 6_o 15_o 27_o 18_o 56_o 7_o 15_o 31_o 19_o 11_o 8_o 15_o 36_o 19_o 26_o 9_o 15_o 40_o 19_o 40_o 10_o 15_o 45_o 19_o 53_o 11_o 15_o 49_o 20_o 07_o 12_o 15_o 53_o 20_o 19_o 13_o 15_o 58_o 20_o 32_o 14_o 16_o 02_o 20_o 44_o 15_o 16_o 07_o 20_o 56_o 16_o 16_o 11_o 21_o 08_o 17_o 16_o 15_o 21_o 19_o 18_o 16_o 19_o 21_o 29_o 19_o 16_o 23_o 21_o 39_o 20_o 16_o 28_o 21_o 49_o 21_o 16_o 32_o 21_o 58_o 22_o 16_o 36_o 22_o 08_o 23_o 16_o 40_o 22_o 16_o 24_o 16_o 44_o 22_o 24_o 25_o 16_o 49_o 22_o 32_o 26_o 16_o 53_o 22_o 39_o 27_o 16_o 57_o 22_o 46_o 28_o 17_o 02_o 22_o 52_o 29_o 17_o 06_o 22_o 58_o 30_o 17_o 11_o 23_o 03_o 31_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr day_n december_n ☉_o r._n a._n ☉_o decl._n h._n m._n d._n m._n 1_o 17_o 15_o 23_o 08_o 2_o 17_o 20_o 23_o 13_o 3_o 17_o 25_o 23_o 17_o 4_o 17_o 29_o 23_o 20_o 5_o 17_o 34_o 23_o 23_o 6_o 17_o 38_o 23_o 26_o 7_o 17_o 42_o 23_o 28_o 8_o 17_o 47_o 23_o 29_o 9_o 17_o 51_o 23_o 30_o 10_o 17_o 56_o 23_o 31_o 11_o 18_o 00_o 23_o 31½_n 12_o 18_o 05_o 23_o 31_o 13_o 18_o 09_o 23_o 30_o 14_o 18_o 14_o 23_o 29_o 15_o 18_o 19_o 23_o 27_o 16_o 18_o 24_o 23_o 25_o 17_o 18_o 28_o 23_o 22_o 18_o 18_o 33_o 23_o 19_o 19_o 18_o 37_o 23_o 15_o 20_o 18_o 41_o 23_o 11_o 21_o 18_o 45_o 23_o 07_o 22_o 18_o 49_o 23_o 02_o 23_o 18_o 54_o 22_o 56_o 24_o 18_o 58_o 22_o 50_o 25_o 19_o 03_o 22_o 43_o 26_o 19_o 07_o 22_o 36_o 27_o 19_o 11_o 22_o 29_o 28_o 19_o 16_o 22_o 21_o 29_o 19_o 20_o 22_o 13_o 30_o 19_o 25_o 22_o 04_o 31_o 19_o 30_o 21_o 55_o a_o rectify_v table_n for_o the_o sun_n declination_n  _fw-fr year_n year_n year_n  _fw-fr 1657_o 1661._o 1665_o 1669_o 1673_o 1659._o 1663._o 1667_o 1671_o 1675_o 1660_o 1664_o 1668_o 1672_o 1676_o month_n min._n min._n min._n january_n 3_o s_o 2_o a_o 5_o a_o 4_o s_z 3_o a_o 7_o a_o 5_o s_z 4_o a_o 9_o a_o february_n 5_o s_z 5_o a_o 10_o a_o 5_o s_z 5_o a_o 11_o a_o 6_o s_z 5_o a_o 11_o a_o march_z 6_o s_z 5_o a_o 13_o s_z 5_o a_o 5_o s_z 12_o a_o 5_o a_o 5_o s_z 12_o a_o april_n 5_o a_o 5_o s_z 11_o a_o 5_o a_o 5_o s_z 10_o a_o 4_o a_o 4_o s_z 9_o a_o may_v 4_o a_o 4_o s_z 8_o a_o 3_o a_o 3_o s_z 6_o a_o 2_o a_o 2_o s_z 4_o a_o june_n 1_o a_o 1_o s_o 2_o a_o 0_o s_o 0_o a_o 0_o s_o 1_o s_z 1_o a_o 3_o s_o july_n 2_o s_z 2_o a_o 5_o s_z 3_o s_z 3_o a_o 7_o s_z 4_o s_z 4_o a_o 9_o s_o august_n 5_o s_z 5_o a_o 10_o s_z 5_o s_z 5_o a_o 11_o s_z 6_o s_z 5_o a_o 12_o s_o september_n 6_o s_z 5_o a_o 13_o s_z 6_o a_o 5_o s_z 13_o a_o 6_o a_o 5_o s_z 12_o a_o october_n 6_o a_o 5_o s_z 12_o a_o 5_o a_o 5_o s_z 11_o a_o 4_o a_o 5_o s_z 9_o a_o novem._n 3_o a_o 4_o s_z 7_o a_o 2_o a_o 3_o s_z 5_o a_o 1_o a_o 2_o s_z 3_o a_o decemb._n 0_o a_o 1_o s_z 1_o a_o 1_o s_o 0_o a_o 1_o s_z 2_o s_z 1_o a_o 3_o s_z the_o use_n of_o the_o rectify_v table_n note_v that_o the_o minute_n under_o the_o respective_a year_n be_v to_o be_v add_v or_o substract_v to_o or_o from_o the_o sun_n declination_n in_o the_o former_a table_n as_o be_v note_v with_o the_o letter_n a_o or_o s_o and_o also_o note_v that_o the_o first_o figure_n in_o each_o month_n stand_v for_o the_o first_o 10_o day_n of_o the_o month_n and_o the_o second_o for_o the_o second_o 10_o day_n &_o the_o three_o for_o the_o last_o 10_o day_n except_o in_o march_n or_o september_n which_o in_o march_n will_v be_v the_o first_o 9_o day_n only_o and_o in_o september_n the_o first_o 12_o day_n example_n i_o will_v know_v the_o sun_n declination_n the_o 15_o day_n of_o may_n 1668._o now_o because_o this_o day_n of_o the_o month_n fall_v in_o the_o second_o 10_o day_n i_o look_v in_o the_o table_n under_o the_o year_n 1663._o and_o right_a against_o may_v you_o shall_v find_v that_o in_o the_o second_o place_n of_o the_o month_n stand_v 6_o a_o which_o show_v i_o that_o i_o must_v add_v 6_o minute_n to_o the_o sun_n declination_n in_o the_o former_a table_n 21_o degree_n 5_o min._n that_o stand_v against_o the_o 15_o day_n of_o may_n and_o then_o i_o find_v that_o the_o sun_n will_v have_v 21_o deg_n 11_o min._n of_o north_n declination_n and_o so_o for_o the_o rest_n which_o will_v never_o differ_v above_o two_o minute_n from_o the_o truth_n but_o seldom_o so_o much_o and_o for_o the_o most_o part_n true_a note_v that_o the_o former_a table_n of_o the_o sun_n declination_n be_v fit_v exact_o for_o the_o year_n 1666._o by_o the_o rule_n mr._n wright_n give_v in_o his_o correction_n of_o error_n and_o from_o his_o table_n and_o may_v indifferent_o serve_v for_o the_o year_n 1658_o 1662._o 1670_o 1674_o without_o any_o sensible_a error_n and_o the_o table_n of_o right_a ascension_n will_v not_o vary_v a_o minute_n of_o time_n in_o many_o year_n finis_fw-la error_n in_o the_o horizontal_n quadrant_n page_n 5_o line_n 6_o in_o a_o italian_a letter_n shall_v not_o have_v be_v distinct_a nor_o in_o another_o letter_n from_o the_o former_a line_n page_n 5._o line_n 9_o for_o quarter_n read_v half_a p._n 5._o l._n 13._o r._n of_o a_o quadrant_a p._n 11._o l._n 7._o r._n 63_o d._n 26′_n p._n 19_o l._n 7._o r._n the_o same_o day_n to_o p._n 23._o l._n 17._o r._n and_o end_n at_o 32′_n past_o 9_o p._n 27._o l._n 7._o for_o n_o r_o r._n n_o z._n p._n 28._o l._n 4._o r._n in_o the_o parallel_n p._n 30._o l._n 9_o &_o l._n 10._o r._n 23_o d._n 31′_n p._n 38._o l._n 4._o r._n be_v to_o the_o sine_fw-la p._n 50._o l._n 5._o r._n whereof_o the_o diameter_n a_o appendix_n touch_v reflective_a dial_v by_o john_n lyon_n professor_n of_o this_o or_o any_o other_o part_n of_o the_o mathematics_n near_o somerset_n house_n in_o the_o strand_n london_n print_v anno_fw-la domini_fw-la 1658._o direct_v dial_v by_o a_o hole_n or_o nodus_fw-la to_o draw_v a_o dial_n under_o any_o window_n that_o the_o sun_n shine_v upon_o by_o help_n of_o a_o thread_n fasten_v in_o any_o point_n of_o the_o direct_a axis_n find_v in_o the_o ceiling_n and_o a_o hole_n in_o any_o pane_n of_o glass_n or_o a_o knob_v or_o nodus_fw-la upon_o any_o side_n of_o the_o window_n or_o window-post_n constructio_fw-la first_o draw_v on_o pasteboard_n or_o other_o material_a a_o horizontal_n dial_n for_o the_o latitude_n propose_v then_o by_o help_n of_o the_o sun_n azimuth_n which_o may_v be_v find_v by_o help_n of_o a_o general_a quadrant_n at_o any_o time_n or_o by_o know_v the_o true_a hour_n of_o the_o day_n with_o the_o help_n of_o the_o say_v horizontal_n dial_n and_o draw_v that_o true_a meridian_n from_o the_o hole_n or_o nodus_fw-la propose_v both_o above_o on_o the_o ceiling_n and_o below_o on_o the_o wall_n and_o floor_n of_o the_o room_n so_o that_o if_o a_o right_a line_n be_v extend_v from_o the_o say_a hole_n or_o nodus_fw-la by_o any_o point_n in_o any_o of_o those_o line_n it_o will_v be_v in_o the_o meridian_n circle_n of_o the_o world_n to_o find_v a_o point_n in_o the_o direct_a axis_n of_o the_o world_n which_o will_v ever_o fall_v to_o be_v in_o the_o say_a meridian_n in_o which_o point_n the_o end_n of_o a_o thread_n be_v to_o be_v fasten_v first_o fix_v the_o end_n of_o a_o thread_n or_o small_a silk_n in_o the_o centre_n of_o the_o hole_n or_o nodus_fw-la and_o move_v the_o other_o end_n thereof_o up_o or_o down_o in_o the_o say_a meridian_n former_o draw_v on_o the_o ceiling_n or_o wall_n until_o by_o apply_v the_o side_n of_o a_o quadrant_n to_o that_o thread_n it_o be_v find_v to_o be_v elevate_v equal_a to_o the_o latitude_n of_o the_o place_n so_o be_v that_o thread_n direct_o situate_v parallel_n to_o the_o axis_n of_o the_o world_n and_o the_o point_n where_o the_o end_n of_o that_o thread_n touch_v the_o meridian_n either_o on_o the_o ceiling_n or_o wall_n be_v that_o point_n in_o the_o direct_a axis_n seek_v for_o wherein_o fix_v one_o end_n of_o a_o thread_n which_o thread_n will_v be_v of_o present_a use_n in_o project_v of_o hour-point_n in_o any_o place_n propose_v then_o to_o find_v the_o hour-point_n

the_o sine_fw-la of_o the_o angle_n at_o i._n to_o its_o opposite_a side_n b_o h_n the_o sine_fw-la of_o the_o altitude_n so_o be_v the_o radius_fw-la or_o the_o angle_n at_o h._n to_z b_o i_o h_z difference_n of_o the_o verse_v sine_fw-la of_o the_o semidiurnal_a ark_n and_o of_o the_o hour_n seek_v in_o the_o parallel_n of_o declination_n and_o by_o consequence_n so_o be_v the_o secant_fw-la of_o the_o declination_n to_o the_o say_a difference_n in_o the_o common_a radius_fw-la as_o we_o have_v else_o where_o note_v if_o this_o difference_n be_v subtract_v from_o the_o verse_v sine_fw-la of_o the_o semidiurnal_a ark_n there_o will_v remain_v e_o b_o the_o verse_v sine_fw-la of_o the_o hour_n from_o noon_n the_o like_a hold_n if_o perpendicular_o be_v let_v fall_n from_o any_o other_o parallel_n of_o declination_n from_o the_o same_o scheme_n it_o also_o follow_v as_o the_o cousin_n of_o the_o latitude_n be_v to_o the_o secant_fw-la of_o the_o declination_n so_o be_v the_o sine_fw-la of_o the_o meridian_n altitude_n to_o the_o verse_v sine_fw-la of_o the_o semidiurnal_a ark_n here_o observe_v the_o like_a proportion_n between_o the_o two_o latter_a term_n as_o between_o the_o two_o former_a which_o may_v be_v of_o use_n on_o a_o sector_n if_o the_o scheme_n be_v consider_v not_o as_o fit_v to_o a_o peculiar_a question_n for_o find_v the_o hour_n but_o as_o have_v three_o side_n to_o find_v a_o angle_n it_o will_v be_v find_v upon_o such_o a_o consideration_n in_o relation_n to_o the_o change_n of_o side_n that_o the_o proportion_n for_o the_o azimuth_n follow_v be_v no_o other_o than_o the_o same_o proportion_n apply_v to_o other_o side_n of_o the_o triangle_n and_o so_o we_o need_v have_v no_o other_o trouble_n to_o come_v by_o a_o proportion_n for_o the_o azimuth_n but_o it_o also_o follow_v from_o the_o same_o scheme_n in_o the_o triangle_n c_o d_o a_o and_o c_o k_n g_o and_o c_o z_o n_o the_o first_o operation_n will_v be_v to_o find_v a_o d_o and_o g_z k_o and_o n_o ●_o in_o all_o which_o the_o proportion_n will_v hold_v as_o the_o radius_fw-la to_o the_o tangent_fw-la of_o the_o latitude_n or_o as_o the_o cotangent_fw-la of_o the_o latitude_n to_o radius_fw-la so_o be_v the_o tangent_fw-la of_o the_o altitude_n to_o the_o say_v respective_a quantity_n which_o when_o the_o altitude_n be_v less_o than_o the_o compliment_n of_o the_o latitude_n be_v the_o sin_n of_o the_o sun_n azimuth_n from_o the_o vertical_a belong_v to_o the_o propose_a altitude_n when_o the_o sun_n be_v in_o the_o equinoctial_a or_o have_v no_o declination_n the_o next_o proportion_n will_v be_v as_o the_o cousin_n of_o the_o latitude_n be_v to_o the_o secant_fw-la of_o the_o altitude_n so_o be_v the_o sine_fw-la of_o the_o declination_n to_o the_o difference_n seek_v be_v a_o 4_o proportional_a hereby_o we_o may_v find_v a_o b_o in_o the_o winter_n triangle_n a_o g_o b_o which_o add_v to_o a_o d_o the_o sum_n be_v the_o sine_fw-la of_o the_o azimuth_n from_o the_o vertical_a consequent_o w_n b_o be_v the_o verse_v sine_fw-la of_o the_o azimuth_n from_o the_o noon_n meridian_n also_o we_o find_v g_o l_o in_o the_o summer_n triangle_n l_o m_o g_o when_o the_o altitude_n be_v less_o than_o the_o compliment_n of_o the_o latitude_n which_o add_v to_o s_o g_o the_o sum_n s_o l_o be_v the_o verse_v sine_fw-la of_o the_o azimuth_n from_o the_o south_n likewise_o we_o may_v find_v n_o r_o in_o the_o triangle_n r_o o_fw-fr n_o and_o by_o subtract_v it_o from_o n_o z_o the_fw-mi will_v remain_v r_z z_o and_o consequent_o q_o r_z the_o verse_v sine_fw-la of_o the_o azimuth_n from_o the_o meridian_n in_o summer_n when_o the_o altitude_n be_v great_a than_o the_o co-latitude_n and_o for_o star_n that_o come_v to_o the_o meridian_n between_o the_o zenith_n and_o the_o elevate_v pole_n we_o may_v find_v n_o c_o in_o the_o triangle_n n_o c_o d_o where_o it_o hold_v as_o the_o sine_z of_o the_o angle_n at_o n_o the_o compliment_n of_o the_o latitude_n to_o its_o opposite_a side_n c_o d_o the_o prick_a line_n the_o sine_fw-la of_o the_o declination_n so_o be_v the_o radius_fw-la to_o n_o c_o the_o parallel_n of_o altitude_n the_o azimuth_n seek_v the_o latter_a proportion_n lie_v so_o evident_a it_o need_v not_o be_v speak_v to_o if_o what_o be_v say_v before_o for_o the_o hour_n be_v regard_v and_o the_o former_a proportion_n lie_v as_o the_o cousin_n of_o the_o latitude_n the_o sine_fw-la of_o the_o angle_n at_o a._n to_o its_o opposite_a side_n d_o c_o the_o sine_z of_o the_o altitude_n so_o be_v the_o sine_fw-la of_o the_o latitude_n the_o angle_n at_o c._n to_o its_o opposite_a side_n a_o d_o in_o the_o parallel_n of_o altitude_n and_o in_o stead_n of_o the_o cousin_n and_o sine_fw-la of_o the_o latitude_n we_o may_v take_v the_o radius_fw-la and_o the_o tangent_fw-la of_o the_o latitude_n another_o analogy_n will_v be_v require_v to_o reduce_v it_o to_o the_o common_a radius_fw-la as_o the_o cousin_n of_o the_o altitude_n to_o radius_fw-la so_o the_o four_o before_o find_v in_o a_o parallel_n to_o the_o like_a quantity_n to_o the_o common_a radius_fw-la these_o analogy_n or_o proportion_n be_v reduce_v into_o one_o by_o multiply_v the_o term_n of_o each_o proportion_n and_o then_o free_v from_o needless_a affection_n will_v produce_v the_o proportion_n at_o first_o deliver_v the_o use_v of_o the_o say_a scale_n we_o have_v before_o note_v that_o if_o two_o term_n of_o a_o proportion_n be_v fix_v and_o natural_a line_n thereto_o fit_v of_o a_o equal_a length_n that_o if_o any_o three_o term_n be_v seek_v in_o the_o former_a line_n the_o four_o term_n will_v be_v find_v in_o the_o other_o line_n by_o inspection_n as_o stand_v against_o the_o three_o so_o here_o in_o this_o scale_n which_o consist_v of_o two_o line_n the_o one_o a_o annex_v tangent_fw-la the_o other_o a_o line_n of_o sines_n continue_v both_o way_n the_o radius_fw-la of_o the_o sin_n be_v first_o fitt_v the_o tangent_fw-la annex_v must_v be_v of_o such_o a_o radius_fw-la as_o that_o 38_o deg_n 28′_n of_o it_o may_v be_v equal_a in_o length_n to_o the_o radius_fw-la of_o the_o sine_fw-la to_o which_o it_o be_v adjoin_v and_o then_o look_v for_o the_o declination_n in_o the_o tangent_fw-la just_a against_o it_o stand_v the_o time_n of_o rise_v from_o six_o or_o ascentional_a difference_n or_o the_o semidiurnal_a ark_n if_o the_o same_o be_v account_v from_o the_o other_o end_n as_o a_o verse_v sine_fw-la so_o if_o the_o sun_n altitude_n be_v give_v and_o account_v in_o the_o tangent_fw-la just_a against_o it_o stand_v the_o sun_n azimuth_n when_o he_o be_v in_o the_o equinoctial_a upon_o the_o like_a altitude_n and_o thus_o the_o point_n n_o will_v be_v find_v in_o the_o tangent_fw-la at_o the_o altitude_n when_o it_o be_v more_o than_o the_o colatitude_n 1_o a_o example_n for_o find_v the_o time_n of_o the_o sun_n rise_v if_o the_o declination_n be_v 13_o deg_n look_v for_o it_o in_o the_o annex_v tangent_fw-la and_o just_a against_o it_o in_o the_o hour_n scale_n stand_v 16_o deg_n 53′_n the_o ascentional_a difference_n in_o time_n 1_o hour_n 7½_n min._n show_v that_o the_o sun_n rise_v so_o much_o before_o and_o set_v so_o much_o after_o 6_o in_o summer_n and_o in_o winter_n rise_v so_o much_o after_o and_o set_v before_o 6_o for_o this_o ark_n may_v be_v find_v on_o either_o side_n of_o six_o where_o the_o declination_n begin_v each_o way_n 2_o to_o find_v the_o time_n of_o the_o day_n to_o perform_v this_o proposition_n we_o divide_v the_o other_o proportion_n into_o two_o by_o introduce_v the_o radius_fw-la in_o the_o middle_a as_o the_o radius_fw-la be_v to_o the_o secant_fw-la of_o the_o declination_n so_o be_v the_o sine_fw-la of_o the_o altitude_n to_o a_o four_o again_o as_o the_o cousin_n of_o the_o latitude_n to_o radius_fw-la so_o the_o four_o before_o find_v to_o the_o difference_n of_o the_o verse_v sin_n of_o the_o semidiurnal_a ark_n and_o of_o the_o hour_n seek_v the_o former_a of_o these_o proportion_n must_v be_v wrought_v upon_o the_o quadrant_a the_o latter_a be_v remove_v by_o fit_v the_o radius_fw-la of_o the_o sin_n that_o give_v the_o answer_n equal_a in_o length_n to_o the_o cousin_n of_o the_o latitude_n wherefore_o to_o find_v the_o time_n of_o the_o day_n lay_v the_o thread_n to_o the_o secant_fw-la of_o the_o declination_n in_o the_o limb_n and_o from_o the_o sine_fw-la of_o the_o altitude_n take_v the_o near_a distance_n to_o it_o and_o because_o the_o secant_fw-la be_v make_v but_o to_o half_a the_o common_a radius_fw-la set_v down_o one_o foot_n of_o this_o extent_n at_o the_o declination_n in_o the_o annex_v tangent_fw-la and_o enter_v the_o say_a extent_n twice_o forward_o and_o it_o will_v show_v the_o time_n of_o