one_o day_n variation_n in_o 300_o year_n as_o be_v observe_v by_o mr._n philip_n the_o use_v of_o the_o quadrant_n without_o rectify_v the_o bead_n nothing_o can_v be_v perform_v by_o this_o projection_n except_o find_v the_o sun_n meridian_n altitude_n be_v show_v upon_o the_o index_n by_o the_o intersection_n of_o the_o parallel_n of_o declination_n therewith_o also_o the_o time_n when_o the_o sun_n will_v be_v due_a east_n or_o west_n trace_v the_o parallel_n of_o declination_n to_o the_o right_a edge_n of_o the_o projection_n and_o the_o hour_n it_o there_o intersect_v in_o most_o case_n to_o be_v due_o estimate_v show_v the_o time_n seek_v thus_o when_o the_o sun_n have_v 21_o deg_n of_o north_n declination_n we_o shall_v find_v that_o he_o will_v be_v due_a east_n or_o west_n about_o three_o quarter_n of_o a_o hour_n past_o 4_o in_o the_o afternoon_n or_o a_o quarter_n past_o 7_o in_o the_o morning_n the_o declination_n be_v to_o be_v find_v on_o the_o backside_n of_o the_o quadrant_a by_o lay_v the_o thread_n over_o the_o day_n of_o the_o month_n to_o rectify_v the_o bead._n lay_v the_o thread_n upon_o the_o graduated_a index_n and_o set_v the_o bead_n to_o the_o observe_v or_o give_v altitude_n and_o when_o the_o altitude_n be_v nothing_o or_o when_o the_o sun_n be_v in_o the_o horizon_n set_v the_o bead_n to_o the_o cypher_n on_o the_o graduated_a index_n which_o afterward_o be_v carry_v without_o stretch_v to_o the_o parallel_n of_o declination_n the_o thread_n in_o the_o limb_n show_v the_o amplitude_n or_o azimuth_n and_o the_o bead_n among_o the_o hour_n show_v the_o true_a time_n of_o the_o day_n example_n upon_o the_o 24_o of_o april_n the_o sun_n declination_n will_v be_v find_v to_o 16_o deg_n north._n now_o to_o find_v his_o amplitude_n and_o the_o time_n of_o his_o rise_n lay_v the_o thread_n over_o the_o graduated_a index_n set_v the_o bead_n to_o the_o begin_n of_o the_o graduation_n of_o the_o index_n and_o bring_v it_o without_o stretch_v to_o the_o parallel_n of_o declination_n above_o be_v 16_o d_o and_o the_o thread_n in_o the_o limb_n will_v lie_v over_o 26_o deg_n 18′_n for_o the_o sun_n amplitude_n or_o coast_n of_o rise_v to_o the_o northward_o of_o the_o east_n and_o the_o bead_n among_o the_o hour_n show_v 24_o minute_n past_o 4_o for_o the_o time_n of_o sun_n rise_v which_o double_v give_v the_o length_n of_o the_o night_n 8_o hour_n 49_o min._n in_o like_a manner_n the_o time_n of_o set_v double_v give_v the_o length_n of_o the_o day_n the_o same_o to_o find_v the_o hour_n and_o azimuth_n let_v the_o give_v altitude_n be_v 45_o degree_n have_v rectify_v the_o bead_n to_o the_o say_a altitude_n on_o the_o index_n and_o bring_v it_o to_o the_o intersect_n the_o parallel_n of_o declination_n the_o thread_n lie_v over_o 50_o degree_n 48′_n for_o the_o sun_n azimuth_n from_o the_o south_n and_o the_o bead_n among_o the_o hour_n show_v the_o time_n of_o the_o day_n to_o be_v 41_o minute_n past_o 9_o in_o the_o morning_n or_o 19_o minute_n past_o two_o in_o the_o afternoon_n another_o example_n wherein_o the_o operation_n will_v be_v upon_o the_o revert_v tail_n let_v the_o altitude_n be_v 3_o deg_n 30′_n and_o the_o declination_n 16_o deg_n north_n as_o before_o to_o know_v when_o to_o rectify_v the_o bead_n to_o the_o upper_a or_o nether_a altitude_n will_v be_v no_o matter_n of_o difficulty_n for_o if_o the_o bead_n be_v set_v to_o the_o nether_a altitude_n will_v not_o meet_v with_o the_o parallel_n of_o declination_n than_o set_v it_o to_o the_o upper_a altitude_n and_o it_o will_v meet_v with_o winter_n parallel_n of_o like_a declination_n which_o in_o this_o case_n supply_v the_o turn_n so_o in_o this_o example_n the_o bead_n be_v set_v to_o the_o upper_a altitude_n of_o 3_o deg_n 30′_n and_o carry_v to_o the_o winter_n parallel_n of_o declination_n the_o thread_n in_o the_o limb_n will_v fall_v upon_o 68_o deg_n 28′_n for_o the_o sun_n azimuth_n from_o the_o north_n and_o the_o bead_n among_o the_o hour_n show_v the_o time_n of_o the_o day_n to_o be_v either_o 5_o in_o the_o morning_n or_o 7_o at_o night_n another_o example_n admit_v the_o sun_n have_v 20_o degr_n of_o north_n declination_n as_o about_o the_o 9th_o of_o may_n and_o his_o observe_a altitude_n be_v 56_o deg_n 20′_n have_v rectify_v the_o bead_n thereto_o and_o bring_v it_o to_o intersect_v the_o parallel_n of_o 20_o deg_n among_o the_o hour_n it_o show_v the_o time_n of_o the_o day_n to_o be_v 11_o in_o the_o morning_n or_o 1_o in_o the_o afternoon_n and_o the_o azimuth_n of_o the_o sun_n to_o be_v 26_o deg_n from_o the_o south_n the_o use_v of_o the_o projection_n to_o find_v the_o sun_n altitude_n on_o all_o hour_n or_o azimuth_n will_v be_v but_o the_o converse_n of_o what_o be_v already_o say_v therefore_o one_o example_n shall_v serve_v when_o the_o sun_n have_v 45_o deg_n of_o azimuth_n from_o the_o south_n and_o his_o declination_n 13_o deg_n northwards_o lay_v the_o thread_n over_o 45_o deg_n in_o the_o limb_n and_o where_o the_o thread_n intersect_v the_o parallel_n of_o declination_n thereto_o remove_v the_o bead_n which_o carry_v to_o the_o index_n without_o stretch_v show_v 43_o deg_n 50′_n for_o the_o altitude_n seek_v likewise_o to_o the_o same_o declination_n if_o it_o be_v require_v to_o find_v the_o sun_n altitude_n for_o the_o hour_n of_o 2_o or_o 10._o lay_v the_o thread_n over_o the_o intersection_n of_o the_o hour_n propose_v with_o the_o parallel_n of_o declination_n and_o thereto_o set_v the_o bead_n which_o carry_v to_o the_o index_n show_v the_o altitude_n seek_v namely_o 44_o deg_n 31′_n the_o same_o altitude_n also_o belong_v to_o that_o azimuth_n the_o thread_n in_o the_o former_a position_n lie_v over_o in_o the_o limb_n this_o projection_n be_v of_o worst_a performance_n early_o in_o the_o morning_n or_o late_a in_o the_o evening_n about_o which_o time_n mr._n dary_n curve_v be_v of_o best_a performance_n whereto_o we_o now_o address_v ourselves_o of_o the_o curve_v line_n and_o scale_n thereto_o fit_v this_o as_o we_o have_v say_v before_o be_v the_o ingenious_a invention_n of_o m._n michael_n dary_n derive_v from_o the_o proportionalty_n of_o two_o like_v equiangle_v plain_a triangle_n accommodate_v to_o the_o latitude_n of_o london_n for_o the_o ready_a work_n of_o these_o two_o proportion_n 1._o for_o the_o hour_n 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 difference_n between_o the_o sine_fw-la of_o the_o sun_n propose_v and_o meridian_n altitude_n to_o the_o verse_v sine_fw-la of_o the_o hour_n from_o noon_n and_o the_o converse_n and_o so_o be_v the_o sine_fw-la of_o the_o sun_n meridian_n altitude_n to_o the_o verse_v sine_fw-la of_o the_o semidiurnal_a ark_n 2._o for_o the_o azimuth_n the_o curve_v be_v fit_v to_o find_v it_o from_o the_o south_n and_o not_o from_o the_o north_n and_o the_o proportion_n wrought_v upon_o it_o 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 difference_n of_o the_o verse_v sin_n of_o the_o sun_n or_o star_n distance_n from_o the_o elevate_a pole_n and_o of_o the_o sum_n of_o the_o compliment_n both_o of_o the_o latitude_n and_o altitude_n to_o the_o verse_v sine_fw-la of_o the_o azimuth_n from_o the_o noon_n meridian_n which_o will_v not_o hold_v backward_o to_o find_v the_o altitude_n on_o all_o azimuth_n because_o the_o altitude_n be_v a_o term_n involve_v both_o in_o the_o second_o and_o three_o term_n of_o the_o former_a proportion_n if_o the_o three_o term_n of_o the_o former_a proportion_n have_v not_o be_v a_o difference_n of_o sines_n or_o verse_v sin_n the_o curve_v line_n will_v have_v be_v a_o straight-line_n and_o the_o three_o term_n always_o count_v from_o one_o point_n which_o though_o in_o the_o use_n it_o may_v seem_v to_o be_v so_o here_o yet_o in_o effect_n the_o three_o term_n for_o the_o hour_n be_v always_o count_v from_o the_o meridian_n altitude_n here_o observe_v that_o the_o thread_n lie_v over_o 12_o or_o the_o end_n of_o the_o verse_v scale_n and_o over_o the_o sun_n meridian_n altitude_n in_o the_o line_n of_o altitude_n it_o will_v also_o upon_o the_o curve_v show_v the_o sun_n declination_n which_o by_o construction_n be_v so_o frame_v that_o if_o the_o distance_n from_o that_o point_n to_o the_o meridian_n altitude_n be_v make_v the_o cousin_n of_o latitude_n the_o distance_n of_o the_o say_a point_n from_o the_o end_n of_o the_o verse_v scale_n number_v with_o 12_o shall_v be_v the_o secant_fw-la of_o the_o declination_n to_o the_o same_o radius_fw-la be_v both_o in_o one_o straight-line_n by_o the_o former_a constitution_n of_o the_o thread_n and_o instead_o
reference_n to_o the_o sun_n abode_n above_o the_o horizon_n the_o time_n of_o set_v convert_v into_o degree_n be_v also_o call_v the_o semi-diurnal_a ark_n the_o time_n of_o sun_n rise_v so_o convert_v be_v call_v the_o seminocturnal_a ark_n double_v give_v the_o whole_a length_n of_o the_o night_n so_o upon_o the_o 27_o day_n of_o april_n the_o sun_n have_v 17_o of_o declination_n the_o length_n of_o the_o day_n be_v 15_o hour_n and_o the_o length_n of_o the_o night_n 9_o hour_n to_o find_v the_o sun_n altitude_n on_o all_o hour_n or_o at_o any_o time_n propose_v in_o summer_n time_n if_o the_o hour_n propose_v be_v before_o 6_o in_o the_o morning_n or_o after_o it_o in_o the_o evening_n lay_v the_o thread_n to_o the_o hour_n in_o the_o limb_n the_o bead_n be_v first_o rectify_v to_o the_o winter_n ecliptic_a and_o among_o the_o parallel_n of_o altitude_n above_o the_o upper_a horizon_n it_o show_v the_o altitude_n seek_v example_n so_o the_o sun_n have_v 16_o of_o declination_n northwards_o as_o about_o the_o 24_o of_o april_n lay_v the_o thread_n over_o the_o declination_n i_o set_v the_o bead_n to_o the_o winter_n ecliptic_a and_o if_o it_o be_v require_v to_o find_v what_o altitude_n the_o sun_n shall_v have_v at_o 36_o minute_n past_o 6_o in_o the_o afternoon_n lay_v the_o thread_n over_o the_o same_o in_o the_o limb_n and_o the_o bead_n among_o the_o parallel_n of_o altitude_n will_v fall_v upon_o 7_o at_o all_o other_o time_n the_o operation_n be_v alike_o the_o bead_n be_v rectify_v to_o that_o ecliptic_a that_o be_v proper_a to_o the_o season_n of_o the_o year_n lay_v the_o thread_n over_o the_o propose_a hour_n in_o the_o limb_n and_o the_o bead_n among_o the_o parallel_n of_o altitude_n show_v the_o altitude_n seek_v example_n so_o if_o it_o be_v require_v the_o same_o day_n to_o find_v what_o altitude_n the_o sun_n shall_v have_v at_o 19_o m_o past_o 2_o in_o the_o afternoon_n lay_v the_o thread_n in_o the_o limb_n over_o the_o time_n give_v and_o the_o bead_n among_o the_o parallel_n of_o altitude_n will_v fall_v upon_o 45_o for_o the_o altitude_n seek_v to_o find_v the_o sun_n altitude_n on_o all_o azimuth_n in_o the_o summer_n half_a year_n if_o the_o azimuth_n propound_v be_v more_o northward_o than_o the_o azimuth_n of_o the_o sun_n shall_v have_v at_o the_o hour_n of_o 6_o the_o bead_n must_v be_v rectify_v to_o the_o winter_n ecliptic_a and_o bring_v to_o the_o azimuth_n propose_v above_o the_o upper_a horizon_n and_o there_o among_o the_o parallel_n of_o altitude_n it_o show_v the_o altitude_n seek_v so_o about_o the_o 24_o of_o april_n when_o the_o sun_n declination_n be_v 16_o his_o azimuth_n at_o 6_o of_o the_o clock_n will_v be_v find_v to_o be_v 76_o 54_o m_o from_o the_o south_n then_o if_o it_o be_v require_v to_o find_v the_o sun_n altitude_n upon_o a_o azimuth_n more_o remote_a as_o upon_o 107_o from_o the_o south_n lay_v the_o thread_n over_o the_o declination_n i_o set_v the_o bead_n to_o the_o winter_n ecliptic_a and_o afterward_o carry_v it_o to_o the_o azimuth_n propose_v among_o the_o parallel_n of_o altitude_n above_o the_o upper_a horizon_n it_o fall_v upon_o 7_o for_o the_o sun_n altitude_n seek_v in_o all_o other_o case_n bring_v the_o bead_n rectify_v to_o the_o ecliptic_a proper_a to_o the_o season_n of_o the_o year_n to_o the_o azimuth_n propose_v and_o among_o the_o parallel_n of_o altitude_n it_o show_v the_o altitude_n seek_v so_o far_o the_o same_o day_n i_o set_v the_o bead_n to_o the_o summer_n ecliptic_a and_o if_o it_o be_v require_v to_o know_v what_o altitude_n the_o sun_n shall_v have_v when_o his_o azimuth_n be_v 50_o 48′_n from_o the_o meridian_n carry_v the_o bead_n to_o the_o say_a azimuth_n and_o among_o the_o parallel_n of_o altitude_n it_o will_v fall_v upon_o 45_o for_o the_o altitude_n seek_v the_o hour_n of_o the_o night_n propose_v to_o find_v the_o sun_n depression_n under_o the_o horizon_n imagine_v the_o sun_n to_o have_v as_o much_o declination_n on_o the_o other_o side_n the_o equinoctial_a as_o he_o have_v on_o the_o side_n propose_v and_o this_o case_n will_v be_v co-incident_a with_o the_o former_a of_o find_v the_o sun_n altitude_n for_o any_o time_n propose_v the_o reason_n whereof_o be_v because_o the_o sun_n be_v always_o so_o much_o below_o the_o horizon_n at_o any_o hour_n of_o the_o night_n as_o his_o opposite_a point_n in_o the_o ecliptic_a be_v above_o the_o horizon_n at_o the_o like_a hour_n of_o the_o day_n such_o proposition_n as_o depend_v upon_o the_o knowledge_n of_o the_o sun_n altititude_n be_v to_o find_v the_o hour_n of_o the_o day_n and_o the_o azimuth_n or_o true_a coast_n of_o the_o sun_n the_o sun_n altitude_n be_v take_v by_o hold_v the_o quadrant_n steady_a and_o let_v the_o sun_n beam_n to_o pass_v through_o both_o the_o sight_n at_o once_o and_o the_o thread_n hang_v at_o liberty_n show_v it_o in_o the_o equal_a limb_n if_o this_o be_v think_v unsteady_a the_o quadrant_n may_v rest_v upon_o some_o concave_a dish_n or_o pot_n into_o which_o the_o plummet_n may_v have_v room_n to_o play_v but_o for_o great_a quadrant_n there_o be_v common_o pedistall_n make_v the_o altitude_n suppose_v to_o find_v the_o hour_n of_o the_o day_n and_o the_o azimuth_n of_o the_o sun_n in_o winter_n rectify_v the_o bead_n to_o the_o winter_n ecliptic_a and_o carry_v it_o along_o among_o the_o parallel_n of_o altitude_n till_o it_o cut_v or_o intersect_v that_o parralel_n of_o altitude_n on_o which_o the_o sun_n be_v observe_v and_o the_o thread_n in_o the_o limb_n show_v the_o hour_n of_o the_o day_n and_o the_o bead_n among_o the_o azimuth_n show_v the_o azimuth_n of_o the_o sun_n example_n so_o about_o the_o 18_o of_o october_n when_o the_o sun_n declination_n be_v 13_o 20′_n south_n if_o his_o observe_a altitude_n be_v 18_o the_o true_a time_n of_o the_o day_n will_v be_v find_v to_o be_v either_o 36_o minute_n after_o 9_o or_o 24_o minute_n past_o 2_o and_o his_o azimuth_n will_v be_v 37_o degree_n from_o the_o south_n to_o find_v the_o hour_n of_o the_o day_n and_o the_o azimuth_n of_o the_o sun_n at_o any_o time_n in_o the_o summer_n half_a year_n it_o be_v before_o intimate_v that_o if_o the_o question_n be_v put_v when_o the_o sun_n have_v less_o altitude_n than_o he_o have_v at_o the_o hour_n of_o 6_o of_o the_o clock_n that_o then_o the_o operation_n must_v be_v perform_v among_o those_o parallel_n above_o the_o upper_a horizon_n in_o the_o revert_v tail_n the_o bead_n be_v rectify_v to_o the_o winter_n ecliptic_a and_o that_o it_o may_v be_v know_v what_o altitude_n the_o sun_n shall_v have_v at_o 6_o of_o the_o clock_n by_o bring_v the_o bead_n rectify_v to_o the_o summer_n ecliptic_a to_o the_o left_a edge_n of_o the_o quadrant_n so_o admit_v the_o sun_n to_o have_v 16_o of_o north_n declination_n which_o will_v be_v about_o the_o 24_o april_n i_o may_v find_v his_o altitude_n at_o 6_o of_o the_o clock_n by_o bring_v the_o bead_n rectify_v to_o the_o summer_n ecliptic_a to_o the_o left_a edge_n of_o the_o quadrant_n to_o be_v 12_o 28_o m_o whence_o i_o conclude_v if_o his_o altitude_n be_v less_o the_o bead_n must_v be_v rectify_v to_o the_o winter_n ecliptic_a and_o be_v bring_v to_o those_o parallel_n above_o the_o upper_a horizon_n and_o it_o may_v be_v note_v that_o the_o sun_n altitude_n at_o 6_o be_v always_o less_o than_o his_o declination_n example_n admit_v the_o 24_o of_o april_n aforesaid_a the_o sun_n observe_v altitude_n be_v 7_o lay_v the_o thread_n over_o the_o sun_n declination_n or_o the_o day_n of_o the_o month_n i_o rectify_v the_o bead_n to_o the_o winter_n ecliptic_a and_o bring_v it_o to_o the_o say_a parralel_n of_o altitude_n above_o the_o upper_a horizon_n and_o the_o thread_n intersect_v the_o limb_n at_o 9_o 3_o m_z show_v the_o hour_n of_o the_o day_n to_o be_v 24_o minute_n past_o 5_o in_o the_o morning_n or_o 36′_n past_o 6_o in_o the_o evening_n and_o the_o bead_n among_o the_o azimuth_n show_v the_o azimuth_n or_o coast_n of_o the_o sun_n to_o be_v 107_o from_o the_o south_n another_o example_n but_o admit_v the_o sun_n to_o have_v more_o altitude_n than_o he_o have_v at_o the_o hour_n of_o 6_o the_o operation_n notwithstanding_o differ_v not_o from_o the_o former_a but_o only_o in_o rectify_v the_o bead_n which_o must_v be_v set_v to_o the_o summer_n ecliptic_a and_o then_o carry_v to_o the_o parralel_n of_o the_o sun_n observe_v altitude_n and_o the_o thread_n will_v intersect_v the_o limb_n at_o the_o true_a time_n of_o the_o day_n and_o the_o bead_n among_o the_o azimuth_n show_v the_o true_a coast_n of_o the_o sun_n so_o upon_o the_o 24_o of_o april_n aforesaid_a the_o sun_n observe_v
difference_n of_o sin_n between_o the_o scale_n and_o the_o thread_n and_o then_o it_o will_v hold_v as_o the_o first_o term_n to_o that_o four_o so_o radius_fw-la to_o the_o sine_fw-la of_o the_o azimuth_n and_o may_v be_v either_o a_o lateral_a or_o parralel_v entrance_n according_a as_o it_o fall_v out_o and_o as_o the_o radius_fw-la be_v put_v either_o in_o the_o second_o or_o three_o place_n in_o all_o these_o direction_n the_o introducement_n of_o the_o radius_fw-la be_v suppose_v according_a to_o to_o the_o general_a advertisement_n the_o find_n of_o the_o amplitude_n this_o way_n presuppose_v the_o vertical_a altitude_n know_v and_o then_o the_o proportion_n derive_v from_o the_o analemma_n not_o from_o the_o 16_o case_n be_v as_o the_o radius_fw-la to_o the_o tangent_fw-la of_o the_o latitude_n so_o the_o sine_fw-la of_o the_o vertical_a altitude_n to_o the_o sine_fw-la of_o the_o amplitude_n so_o also_o to_o find_v the_o time_n of_o sun_n rise_v as_o the_o cousin_n of_o the_o declination_n to_o secant_fw-la of_o the_o latitude_n so_o the_o sine_fw-la of_o the_o sun_n altitude_n at_o 6_o to_o the_o sine_fw-la of_o the_o hour_n of_o rise_v from_o six_o to_o find_v the_o sun_n azimuth_n at_o six_o of_o the_o clock_n otherways_o then_o by_o the_o 16_o case_n as_o the_o cousin_n of_o the_o sun_n altitude_n at_o 6_o to_z tangent_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 altitude_n at_o 6_o and_o of_o his_o vertical_a altitude_n to_o the_o sine_fw-la of_o the_o azimuth_n from_o the_o vertical_a to_o find_v the_o time_n when_o the_o sun_n shall_v be_v due_a east_n or_o west_n as_o cousin_n of_o the_o declination_n to_o secant_fw-la of_o the_o latitude_n so_o the_o difference_n of_o the_o sin_n of_o the_o sun_n altitude_n at_o 6_o and_o of_o his_o vertical_a altitude_n to_o the_o sine_fw-la of_o the_o hour_n from_o 6_o when_o the_o sun_n shall_v be_v due_a east_n or_o west_n these_o proportion_n derive_v from_o the_o analemma_n be_v general_a both_o for_o the_o sun_n and_o star_n in_o all_o latitude_n but_o when_o the_o declination_n either_o of_o sun_n or_o star_n exceed_v the_o latitude_n of_o the_o place_n this_o proportion_n for_o find_v the_o azimuth_n can_v be_v at_o some_o time_n convenient_o perform_v on_o a_o quadrant_n but_o must_v be_v supply_v from_o another_o proportion_n whereof_o more_o hereafter_o of_o the_o hour_n and_o azimuth_n scale_n on_o the_o edge_n of_o the_o quadrant_n these_o scale_n be_v fit_v for_o the_o more_o ready_a find_v the_o hour_n and_o azimuth_n in_o one_o latitude_n be_v only_o to_o facilitate_v the_o former_a general_a way_n the_o labour_n save_v hereby_o be_v twofold_a first_o the_o sun_n declination_n be_v grave_v against_o the_o sun_n altitude_n of_o 6_o in_o the_o hour_n scale_n and_o the_o say_a declination_n continue_v at_o the_o other_o end_n of_o the_o say_a hour_n scale_n to_o give_v the_o quantity_n of_o the_o sun_n depression_n in_o winter_n equal_a to_o his_o altitude_n in_o summer_n and_o second_o they_o be_v of_o a_o fit_v length_n as_o be_v show_v in_o the_o description_n of_o the_o quadrant_n and_o thereby_o half_a the_o trouble_n by_o introduce_v the_o radius_fw-la shun_v the_o use_n of_o the_o azimuth_n scale_n the_o altitude_n and_o declination_n of_o the_o sun_n give_v to_o find_v his_o azimuth_n take_v the_o distance_n between_o the_o sun_n altitude_n in_o the_o scale_n and_o his_o declination_n in_o summer_n time_n in_o that_o scale_n that_o stand_v adjoin_v to_o the_o side_n in_o winter_n in_o that_o scale_n that_o be_v continue_v the_o other_o way_n beyond_o the_o beginning_n and_o lay_v the_o thread_n to_o the_o compliment_n of_o the_o sun_n altitude_n in_o the_o lesser_a sin_n which_o be_v double_o number_v enter_v this_o extent_n between_o the_o scale_n and_o the_o thread_n parralelly_n and_o the_o foot_n of_o the_o compass_n show_v in_o the_o line_n of_o sines_n the_o azimuth_n according_o declination_n 23_o d_o 31′_n altitude_n 47_o d_o 27′_n the_o azimuth_n thereto_o will_v be_v 25_o d_o from_o east_n or_o west_n in_o summer_n and_o if_o the_o altitude_n be_v 9_o d_o 43′_n in_o winter_n the_o azimuth_n thereto_o will_v be_v 30_o d_o either_o way_n from_o the_o meridian_n and_o so_o when_o the_o sun_n have_v no_o altitude_n lay_v the_o thread_n over_o 90_o d_o in_o the_o lesser_a sin_n and_o enter_v the_o extent_n from_o the_o begin_n of_o the_o azimuth_n scale_n to_o the_o declination_n and_o you_o will_v find_v the_o amplitude_n which_o to_o this_o declination_n will_v be_v 39_o d_o 50′_n the_o use_v of_o the_o hour_n scale_n to_o find_v the_o hour_n of_o the_o day_n take_v the_o distance_n between_o the_o sun_n altitude_n in_o the_o hour_n scale_n and_o his_o declination_n proper_a to_o the_o season_n of_o the_o year_n then_o lay_v the_o thread_n to_o the_o compliment_n of_o the_o sun_n declination_n in_o the_o lesser_a sin_n enter_v the_o former_a extent_n between_o the_o scale_n and_o the_o thread_n and_o the_o foot_n of_o the_o compass_n show_v the_o sine_fw-la of_o the_o hour_n example_n if_o the_o declination_n be_v 13_o d_o north_n and_o the_o altitude_n 37_o 13′_n take_v the_o distance_n between_o it_o in_o the_o scale_n and_o 13_o d_o in_o the_o prick_a line_n then_o lay_v the_o thread_n to_o 77_o d_o in_o the_o lesser_a sine_z enter_z that_o extent_n between_o the_o scale_n and_o the_o thread_n and_o the_o rest_a foot_n will_v show_v 45_o d_o for_o the_o hour_n from_o 6_o that_o be_v either_o 9_o in_o the_o forenoon_n or_o 3_o in_o the_o afternoon_n the_o converse_n of_o the_o former_a proposition_n will_v be_v to_o find_v the_o sun_n altitude_n on_o all_o hour_n the_o thread_n lie_v over_o the_o compliment_n of_o the_o sun_n declination_n in_o the_o lesser_a sin_n from_o the_o sine_fw-la of_o the_o hour_n take_v the_o near_a distance_n to_o it_o then_o set_v down_o one_o foot_n of_o that_o extent_n in_o the_o hour_n scale_n at_o the_o declination_n and_o the_o other_o will_v reach_v to_o the_o altitude_n example_n at_o london_n for_o these_o scale_n be_v fit_v thereto_o i_o will_v find_v the_o sun_n altitude_n at_o the_o hour_n of_o 5_o and_o at_o 7_o in_o the_o morning_n in_o summer_n when_o the_o sun_n have_v 23_o d_o 31′_n of_o declination_n here_o lay_v the_o thread_n to_o 23_o d_o 31′_n the_o sun_n declination_n from_o the_o end_n of_o the_o lesser_a sin_n be_v double_o number_v from_o the_o sine_fw-la of_o 15_o d_o take_v the_o near_a distance_n to_o it_o set_v down_o one_o foot_n of_o this_o extent_n at_o 23_o d_o 31′_n the_o declination_n it_o reach_v downward_o to_o 9_o d_o 30′_n and_o upward_o to_o 27_o d_o 23′_n the_o sun_n altitude_n at_o 5_o and_o 7_o a_o clock_n in_o the_o morning_n in_o summer_n another_o example_n let_v it_o be_v require_v to_o find_v the_o sun_n altitude_n at_o the_o hour_n of_o 10_o or_o 2_o when_o his_o declination_n be_v 23_o 31′_n both_o north_n and_o south_n the_o thread_n lie_v as_o before_o over_o the_o lesser_a sin_n take_v the_o near_a distance_n to_o it_o from_o 60_o in_o the_o sin_n the_o say_a extent_n set_v down_o at_o 23_o 31′_n in_o the_o prick_a line_n reach_v to_o 53_o d_o 44′_n for_o the_o summer_n altitude_n and_o be_v set_v down_o at_o 23_o 31′_n on_o the_o other_o or_o low_a continue_a line_n reach_v to_o 10_o 28′_n for_o the_o winter_n altitude_n the_o hour_n may_v be_v also_o sound_a in_o the_o verse_v sin_n by_o help_n of_o this_o fit_a hour_n scale_n take_v the_o distance_n between_o the_o sun_n altitude_n admit_v 36_o 42′_n and_o his_o meridian_n altitude_n to_o that_o declination_n 61_o d_o 59′_n and_o enter_v one_o foot_n of_o this_o extent_n at_o the_o sine_fw-la of_o 66_o d_o 29′_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 it_o will_v lie_v over_o the_o hour_n of_o 8_o in_o the_o morning_n or_o 4_o in_o the_o afternoon_n in_o the_o verse_v sin_n in_o the_o limb_n and_o thereby_o also_o may_v the_o time_n of_o sun_n rise_v be_v find_v by_o take_v the_o distance_n from_o 0_o to_o the_o meridian_n altitude_n and_o enter_v it_o at_o the_o cousin_n of_o the_o declination_n as_o before_o and_o the_o converse_n will_v find_v the_o sun_n altitude_n on_o all_o hour_n by_o take_v the_o distance_n from_o the_o cousin_a of_o the_o declination_n to_o the_o thread_n lay_v over_o the_o verse_v sine_fw-la of_o the_o hour_n from_o noon_n and_o the_o say_a extent_n will_v reach_v from_o the_o mridian_n altitude_n in_o the_o fit_a scale_n to_o the_o altitude_n seek_v to_o find_v the_o time_n of_o sun_n rise_v or_o set_v lay_v the_o thread_n over_o the_o compliment_n of_o the_o declination_n as_o before_o in_o the_o lesser_a sin_n
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
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 must_v the_o bead_n be_v rectify_v to_o the_o winter_n ecliptic_a and_o the_o parallel_n above_o the_o horizon_n in_o the_o revert_v tail_n be_v those_o which_o will_v come_v in_o use_n to_o find_v what_o altitude_n the_o sun_n shall_v have_v at_o 6_o of_o the_o clock_n in_o the_o summer_n half_a year_n this_o will_v be_v easy_o perform_v by_o bring_v the_o bead_n that_o be_v rectify_v to_o the_o summer_n ecliptic_a to_o the_o left_a edge_n of_o the_o quadrant_n and-there_a among_o the_o parallel_n of_o altitude_n it_o show_v what_o altitude_n the_o sun_n shall_v have_v at_o 6_o of_o the_o clock_n it_o also_o among_o the_o azimuth_n show_v what_o azimuth_n the_o sun_n shall_v have_v at_o the_o hour_n of_o 6._o example_n so_o when_o the_o sun_n have_v 17_o degree_n of_o north_n declination_n as_o about_o the_o 27_o of_o april_n his_o altitude_n at_o the_o hour_n of_o 6_o will_v be_v find_v to_o be_v 13_o 14_o m_z and_o his_o azimuth_n from_o the_o meridian_n 79_o 14_o m_o whence_o i_o 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 17dâ—_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 january_n all_o show_v at_o once_o by_o the_o thread_n position_n to_o find_v the_o sun_n right_a ascension_n lay_v the_o thread_n over_o the_o day_n of_o the_o month_n as_o before_o and_o it_o intersect_v it_o in_o the_o equal_a limb_n whence_o take_v it_o in_o degree_n and_o minute_n of_o the_o equator_fw-la whilst_o the_o sun_n be_v depart_v from_o the_o equator_fw-la towards_o the_o tropic_n it_o must_v be_v count_v as_o the_o graduation_n of_o the_o limb_n from_o the_o left_a edge_n towards_o the_o right_n but_o when_o the_o sun_n be_v return_v from_o the_o right_a edge_n towards_o the_o left_a the_o right_a ascension_n thus_o find_v must_v be_v estimate_v according_a to_o the_o season_n of_o the_o year_n from_o june_n 11_o to_o sept._n 13_o it_o must_v have_v 90_o degree_n add_v to_o it_o sep._n 13_o to_o dec._n 11_o it_o must_v have_v 180_o degree_n add_v to_o it_o dec._n 11_o to_o mar._n 10_o it_o must_v have_v 270_o degree_n add_v to_o it_o but_o in_o find_v the_o hour_n of_o 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
be_v the_o square_a of_o the_o radius_fw-la to_o the_o square_n of_o the_o tangent_fw-la of_o half_a the_o angle_n seek_v and_o by_o change_v the_o 2_o term_n into_o the_o place_n of_o the_o first_o as_o the_o rectangle_n of_o the_o sin_n of_o the_o difference_n of_o the_o leg_n from_o the_o half_a sum_n of_o the_o 3_o side_n be_v to_o the_o rectangle_n of_o the_o sin_n of_o the_o half_a sum_n of_o the_o three_o side_n and_o of_o the_o difference_n of_o the_o base_a therefrom_o so_o be_v the_o square_a of_o the_o radius_fw-la to_o the_o square_n of_o the_o cotangent_fw-la of_o half_a the_o angle_n seek_v these_o proportion_n be_v publish_v in_o order_n to_o their_o application_n to_o the_o serpentine_a line_n which_o will_v be_v accommodate_v for_o the_o sudden_a operate_n of_o any_o of_o they_o the_o axiom_n to_o be_v remember_v be_v not_o many_o the_o reader_n will_v meet_v with_o their_o demonstration_n and_o application_n in_o mr_n newtons_n trigonometry_n now_o in_o the_o press_n and_o say_v to_o be_v near_o finish_v the_o four_o proportion_n in_o plain_a triangle_n when_o three_o side_n be_v give_v to_o find_v a_o angle_n without_o the_o cadence_n of_o perpendicular_o be_v demonstrate_v in_o the_o 27_o section_n of_o the_o late_a miscellany_n of_o francis_n van_fw-mi schooten_n the_o construction_n of_o diverse_a instrument_n will_v require_v a_o table_n of_o the_o sun_n altitude_n to_o the_o hour_n and_o azimuth_n assign_v and_o for_o the_o accurate_a bound_a in_o of_o the_o line_n it_o may_v be_v a_o table_n of_o hour_n and_o azimuth_n to_o any_o altitude_n assign_v for_o the_o easy_a calculate_v whereof_o i_o be_o desire_v for_o the_o ease_n and_o benefit_n of_o the_o trade_n to_o render_v this_o part_n of_o calculation_n as_o facile_a as_o i_o can_v and_o therefore_o shall_v handle_v it_o the_o more_o large_o to_o calculate_v a_o table_n of_o hour_n to_o all_o altitude_n in_o all_o latitude_n the_o 1._o proportion_n shall_v be_v to_o find_v the_o sun_n altitude_n in_o summer_n or_o depression_n in_o winter_n at_o the_o hour_n of_o 6._o as_o the_o radius_fw-la to_o the_o sine_fw-la of_o the_o latitude_n so_o the_o sine_fw-la of_o the_o declination_n to_o the_o sine_fw-la of_o the_o altitude_n or_o depression_n seek_v this_o remain_v fix_v for_o all_o that_o day_n the_o sun_n declination_n suppose_v not_o to_o vary_v and_o then_o it_o hold_v as_o the_o cousin_n of_o the_o declination_n to_o the_o secant_fw-la of_o the_o latitude_n so_o in_o summer_n be_v the_o difference_n in_o winter_n the_o sum_n of_o the_o sin_n of_o the_o sun_n altitude_n propose_v and_o of_o his_o altitude_n or_o depression_n at_o 6_o to_o the_o sine_fw-la of_o the_o hour_n from_o 6_o towards_o noon_n in_o winter_n and_o in_o summer_n also_o when_o the_o give_v altitude_n be_v great_a than_o the_o altitude_n of_o 6_o but_o when_o it_o be_v less_o towards_o midnight_n this_o proportion_n also_o hold_v for_o calculate_v the_o horary_a distance_n of_o any_o star_n from_o the_o meridian_n in_o like_a manner_n to_o calculate_v the_o azimuth_n as_o the_o sine_fw-la of_o the_o latitude_n to_o sine_fw-la of_o the_o declination_n so_o be_v the_o radius_fw-la to_o the_o side_n of_o the_o sun_n altitude_n or_o depression_n in_o the_o prime_n vertical_a that_o be_v be_v east_n or_o west_n this_o remain_v fix_v for_o one_o day_n then_o as_o the_o cousin_n of_o the_o altitude_n to_o the_o tangent_fw-la of_o the_o latitude_n so_o in_o summer_n be_v the_o difference_n and_o in_o winter_n the_o sum_n of_o the_o sin_n of_o the_o sun_n altitude_n propose_v and_o of_o his_o vertical_a altitude_n or_o depression_n to_o the_o sine_fw-la of_o the_o azimuth_n towards_o noon_n meridian_n in_o winter_n and_o in_o summer_n also_o when_o the_o give_v altitude_n be_v great_a than_o the_o vertical_a altitude_n or_o depression_n but_o when_o it_o be_v less_o towards_o midnight_n meridian_n this_o proportion_n be_v general_a either_o for_o sun_n or_o star_n when_o the_o declination_n be_v less_o than_o the_o latitude_n of_o the_o place_n but_o when_o it_o be_v more_o say_v as_o before_o as_o the_o sine_fw-la of_o the_o latitude_n to_o the_o sine_fw-la of_o the_o declination_n so_o be_v the_o radius_fw-la to_o a_o four_o we_o may_v call_v it_o a_o secant_fw-la again_o as_o cousin_n altitude_n to_o the_o tangent_fw-la of_o the_o latitude_n so_o in_o declination_n towards_o the_o depress_v pole_n be_v the_o sum_n but_o towards_o the_o elevate_v pole_n the_o difference_n of_o this_o secant_fw-la and_o of_o the_o sine_fw-la of_o the_o sun_n or_o star_n altitude_n to_o the_o sine_fw-la of_o the_o azimuth_n from_o the_o vertical_a towards_o the_o noon_n meridian_n before_o application_n be_v make_v the_o latter_a part_n of_o these_o proportion_n be_v of_o my_o own_o peculiar_a invention_n and_o of_o very_o great_a use_n both_o for_o calculation_n and_o instrumental_o it_o will_v be_v necessary_a to_o demonstrate_v the_o same_o for_o the_o hour_n from_o the_o analemma_n have_v in_o the_o scheme_n annex_v draw_v the_o equator_fw-la and_o horizon_n the_o two_o prick_a line_n pass_v through_o the_o centre_n as_o also_o the_o prime_n vertical_a and_o axis_n the_o two_o straight_a line_n pass_v through_o the_o same_o let_v i_o x_o and_o l_o m_o represent_v two_o parallel_n of_o declination_n on_o each_o side_n the_o equator_fw-la and_o o_o x_o a_o parralel_n of_o the_o sun_n altitude_n in_o summer_n and_o p_o qui_fw-fr of_o his_o depression_n in_o winter_n at_o the_o hour_n of_o 6_o because_o these_o parallel_n pass_v through_o the_o intersection_n of_o the_o parallel_n of_o declination_n with_o the_o axis_n let_v r_o s_o be_v a_o parralel_n of_o altitude_n after_o 6_o and_o t_o v_o a_o parralel_n of_o altitude_n before_o it_o from_o the_o intersection_n of_o these_o parallel_n of_o altitude_n with_o the_o parallel_n of_o declination_n let_v fall_v perpendicular_o on_o the_o parallel_n of_o the_o sun_n altitude_n or_o depression_n at_o 6_o and_o then_o we_o shall_v have_v divers_a right_n line_v right_o angle_v triangle_n constitute_v in_o which_o we_o shall_v make_v use_n of_o the_o proportion_n of_o the_o sin_n of_o angle_n to_o their_o opposite_a side_n a_o axiom_n of_o common_a demonstration_n in_o the_o triangle_n a_o f_o e_o as_o the_o sine_fw-la of_o the_o angle_n at_o f_o the_o radius_fw-la to_o its_o opposite_a side_n a_o e_o the_o sine_z of_o the_o declination_n so_o the_o sine_fw-la of_o the_o latitude_n the_o angle_n at_o e_o to_o a_o f_o the_o sine_fw-la of_o the_o sun_n altitude_n at_o 6._o again_o in_o the_o two_o opposite_a triangle_n a_o b_o c_o the_o small_a before_o the_o great_a after_o 6._o 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_o to_o its_o opposite_a side_n b_o c_o the_o difference_n of_o the_o sin_n of_o the_o sun_n altitude_n at_o 6_o and_o of_o his_o propose_a altitude_n so_o be_v the_o radius_fw-la sine_fw-la of_o the_o angle_n at_o b_o to_z c_z a_o the_o sine_z of_o the_o hour_n from_o 6_o in_o the_o parralel_n of_o declination_n in_o the_o low_a triangle_n before_o in_o the_o upper_a after_o 6._o so_o in_o the_o winter_n or_o low_a triangle_n a_o b_o d_o c._n as_o cousin_n of_o the_o latitude_n sine_fw-la of_o the_o angle_n at_o a_o to_z b_o c_z the_o sum_n of_o the_o sin_n of_o the_o sun_n depression_n at_o 6_o b_o d_o and_o of_o his_o give_a altitude_n d_o c_o so_o be_v the_o radius_fw-la the_o sine_fw-la of_o the_o angle_n at_o b_o to_z a_o c_z the_o sine_z of_o the_o hour_n from_o 6_o towards_o noon_n in_o the_o parralel_n of_o declination_n the_o sine_fw-la of_o the_o hour_n thus_o find_v in_o a_o parralel_n be_v to_o be_v reduce_v by_o another_o analogy_n to_o the_o common_a radius_fw-la and_o that_o will_v be_v as_o the_o radius_fw-la of_o the_o parralel_n i_o a_o the_o cousin_n of_o the_o declination_n be_v to_o the_o common_a radius_fw-la e_o ae_n so_o be_v any_o other_o sine_fw-la in_o that_o parralel_n to_o the_o sine_fw-la of_o the_o say_a arch_n to_o the_o common_a radius_fw-la now_o it_o rest_v to_o be_v prove_v that_o both_o these_o analogy_n may_v be_v reduce_v into_o one_o and_o that_o will_v be_v do_v by_o bring_v the_o rectangle_n of_o the_o two_o middle_a term_n of_o the_o first_o proportion_n with_o the_o first_o term_n under_o they_o as_o a_o improper_a fraction_n to_o be_v place_v as_o a_o single_a term_n in_o the_o second_o proportion_n be_v in_o value_n the_o answer_n find_v in_o the_o parralel_n and_o then_o we_o have_v the_o rule_n of_o three_o to_o operate_v as_o it_o be_v in_o whole_a number_n and_o mix_v the_o proportion_n will_v run_v as_o the_o cousin_n of_o the_o declination_n to_o radius_fw-la so_o the_o say_v improper_a fraction_n to_o the_o answer_n and_o so_o proceed_v according_a to_o the_o
from_o six_o in_o the_o sin_n towards_o noon_n if_o the_o altitude_n fall_v beyond_o the_o star_n point_n otherwise_o towards_o midnight_n example_n for_o the_o goat_n star_n let_v its_o altitude_n be_v 40_o deg_n and_o past_o the_o meridian_n the_o hour_n of_o that_o star_n will_v be_v 44′_n from_o six_o for_o the_o compass_n fall_v upon_o the_o sine_fw-la of_o 11_o deg_n 4′_n the_o hour_n be_v towards_o noon_n meridian_n because_o the_o altitude_n be_v great_a than_o 34_o deg_n the_o point_n where_o the_o star_n be_v grave_v the_o thread_n lie_v over_o the_o star_n intersect_v the_o limb_n at_o 25_o deg_n 47′_n if_o the_o distance_n between_o the_o star_n and_o its_o altitude_n be_v enter_v at_o the_o sine_fw-la of_o that_o ark_n and_o the_o thread_n lay_v to_o the_o other_o foot_n the_o hour_n will_v be_v find_v in_o the_o equal_a limb_n the_o same_o as_o before_o for_o star_n of_o southwardly_a declination_n because_o the_o star_n point_n can_v fall_v the_o other_o way_n beyond_o the_o centre_n of_o the_o quadrant_a therefore_o the_o distance_n between_o the_o star_n point_n and_o the_o centre_n must_v be_v increase_v by_o add_v the_o sine_fw-la of_o the_o star_n altitude_n thereto_o which_o will_v fall_v more_o outward_o towards_o the_o limb_n and_o then_o that_o whole_a extent_n be_v to_o be_v enter_v as_o before_o example_n the_o virgin_n spike_n have_v 9_o deg_n 19′_n of_o south_n declination_n the_o depression_n of_o that_o star_n at_o six_o will_v be_v find_v by_o help_n of_o the_o particular_a sine_fw-la to_o be_v 7_o deg_n 17′_n and_o at_o that_o ark_n in_o the_o sin_n the_o star_n be_v grave_v if_o the_o altitude_n of_o that_o star_n be_v 20_o deg_n the_o sine_fw-la thereof_o add_v to_o the_o star_n will_v be_v equal_a to_o the_o sine_fw-la of_o 29_o deg_n 6′_n this_o whole_a extent_n enter_v at_o the_o sine_fw-la of_o 37_o deg_n 52′_n the_o ark_n of_o the_o limb_n against_o which_o the_o star_n be_v grave_v and_o the_o thread_n lay_v to_o the_o other_o foot_n the_o hour_n of_o that_o star_n if_o the_o altitude_n increase_n will_v be_v 19′_n past_o 9_o to_o find_v the_o true_a time_n of_o the_o right_n this_o must_v be_v do_v by_o turn_v the_o star_n hour_n into_o the_o sun_n hour_n or_o common_a time_n either_o by_o the_o pen_n as_o have_v be_v show_v before_o which_o may_v be_v also_o convenient_o perform_v by_o the_o back_n of_o this_o quadrant_a for_o the_o thread_n lie_v over_o the_o day_n of_o the_o month_n show_v the_o compliment_n of_o the_o sun_n ascension_n in_o the_o limb_n or_o with_o compass_n on_o the_o say_v quadrant_a of_o ascension_n the_o thread_n lie_v over_o the_o day_n of_o the_o month_n take_v the_o distance_n between_o it_o and_o the_o star_n on_o the_o say_v quadrant_a the_o say_a extent_n be_v apply_v the_o same_o way_n as_o it_o be_v take_v the_o sun_n foot_n to_o the_o star_n hour_n shall_v reach_v from_o the_o star_n hour_n to_o the_o true_a hour_n of_o the_o night_n and_o if_o one_o of_o the_o foot_n of_o the_o compass_n fall_v off_o the_o quadrant_a a_o double_a remedy_n be_v elsewhere_a prescribe_v example_n if_o on_o the_o 12_o of_o january_n the_o hour_n of_o the_o goat_n star_n be_v 16′_n past_o 5_o from_o the_o meridian_n the_o true_a time_n seek_v will_v be_v 49′_n past_o 1_o in_o the_o morning_n example_n if_o upon_o the_o three_o of_o january_n the_o hour_n of_o the_o virgin_n spike_n be_v observe_v to_o be_v 19′_n past_o 9_o the_o true_a time_n seek_v will_v be_v 45′_n past_o 2_o in_o the_o morning_n to_o find_v the_o time_n of_o a_o star_n rise_v and_o set_v the_o ascentional_a difference_n be_v grave_v against_o the_o star_n the_o virgin_n spike_n have_v 48′_n of_o ascentional_a difference_n that_o be_v to_o say_v that_o star_n hour_n of_o rise_v be_v at_o 48′_n past_o 6_o and_o set_v at_o 12′_n past_o 5_o and_o the_o true_a time_n of_o that_o star_n rise_v upon_o the_o three_o of_o january_n will_v be_v at_o 22′_n past_o 10_o at_o night_n and_o of_o its_o set_n at_o 47′_n past_o 8_o in_o the_o morning_n find_v by_o the_o former_a direction_n of_o the_o rest_n of_o the_o line_n on_o the_o back_n of_o this_o quadrant_a they_o be_v either_o such_o as_o relate_v to_o the_o motion_n of_o the_o sun_n or_o star_n or_o to_o dial_v or_o such_o as_o be_v derive_v from_o mr_n gunter'_v sector_n the_o tangent_fw-la of_o 51_o deg_n 32′_n put_v through_o the_o whole_a limb_n be_v peculiar_o fit_v to_o the_o latitude_n of_o london_n and_o will_v serve_v to_o find_v the_o time_n when_o the_o sun_n will_v be_v east_n or_o west_n as_o also_o for_o any_o of_o the_o star_n that_o have_v less_o declination_n than_o the_o place_n have_v latitude_n lay_v the_o thread_n to_o the_o declination_n count_v in_o the_o say_v tangent_fw-la and_o in_o the_o limb_n it_o show_v the_o hour_n from_o 6_o if_o reckon_v from_o the_o right_a edge_n example_n when_o the_o sun_n have_v 15_o deg_n of_o north_n declination_n the_o time_n of_o his_o be_v east_n or_o west_n will_v be_v 12_o deg_n 17′_n in_o time_n about_o 49′_n before_o or_o after_o six_o ferè_fw-la the_o sun_n place_n be_v give_v in_o the_o ecliptic_a line_n by_o lay_v the_o thread_n over_o the_o day_n of_o the_o month_n in_o the_o quadrant_a of_o ascension_n of_o which_o see_v page_n 16_o &_o 17_o of_o the_o small_a quadrant_a of_o the_o line_n relate_v to_o dial_v such_o be_v the_o line_n of_o latitude_n and_o scale_n of_o hour_n of_o which_o before_o and_o the_o line_n sol_fw-mi in_o the_o limb_n of_o which_o i_o shall_v say_v nothing_o at_o present_a it_o be_v only_o place_v there_o in_o readiness_n to_o take_v off_o any_o ark_n from_o it_o according_a to_o the_o accustom_a manner_n of_o take_v off_o line_n from_o the_o limb_n to_o any_o assign_a radius_fw-la the_o requisite_a arke_n of_o a_o upright_a decliner_n will_v be_v give_v by_o the_o particular_a line_n on_o the_o quadrant_n for_o the_o latitude_n without_o the_o trouble_n of_o proportional_a work_n 1_o the_o substiles_a distance_n from_o the_o meridian_n account_v the_o plain_n declination_n as_o a_o sine_fw-la in_o the_o fit_a hour_n scale_n on_o the_o right_a edge_n of_o the_o fore-side_n and_o just_a against_o it_o in_o the_o annex_v tangent_fw-la stand_v the_o substiles_a distance_n from_o the_o meridian_n if_o a_o upright_a plain_n decline_v 30_o deg_n the_o substiles_a distance_n will_v be_v 21_o deg_n 41_o minute_n 2_o the_o style_n height_n count_n the_o compliment_n of_o the_o plain_n declination_n in_o the_o say_v fit_v hour_n scale_v as_o a_o sine_fw-la and_o apply_v it_o with_o compass_n to_o the_o line_n of_o sin_n issue_v from_o the_o centre_n for_o the_o former_a plain_n the_o style_n height_n will_v be_v find_v 32_o deg_n 37′_n 3_o the_o inclination_n of_o meridian_n account_v the_o stilt_n height_n in_o the_o annex_v tangent_fw-la of_o the_o fit_a hour_n scale_n and_o just_a against_o it_o in_o the_o sine_fw-la stand_v the_o compliment_n of_o the_o inclination_n of_o meridians_fw-la which_o for_o the_o former_a plain_n will_v be_v find_v to_o be_v 36_o deg_n 25′_n 4_o the_o angle_n of_o 12_o and_o 6._o account_v the_o plain_n declination_n in_o the_o limb_n on_o the_o backside_n from_o the_o right_a edge_n and_o lay_v the_o thread_n over_o it_o and_o in_o the_o particular_a tangent_fw-la it_o show_v the_o angle_n between_o the_o horizon_n and_o six_o 32_o deg_n 9′_n in_o this_o example_n the_o compliment_n whereof_o be_v the_o angle_n of_o 12_o and_o 6_o namely_o 57_o deg_n 51_o min._n also_o the_o requisite_a arke_n of_o a_o direct_a east_n or_o west_n recline_v or_o incline_v dial_n may_v be_v find_v after_o the_o same_o manner_n for_o this_o latit_fw-fr 1_o the_o substiles_a distance_n account_v the_o plain_n reinclination_n in_o the_o limb_n on_o the_o backside_n from_o the_o left_a edge_n and_o in_o there_o lay_v the_o thread_n and_o in_o the_o particular_a tangent_fw-la it_o show_v the_o ark_n seek_v so_o if_o a_o east_n or_o west_n plain_o recline_v or_o incline_v 60_o deg_n the_o substiles_a distance_n will_v be_v find_v to_o be_v 32_o deg_n 12′_n 2_o the_o style_n height_n account_v the_o reinclination_n in_o the_o particular_a sine_fw-la on_o the_o foreside_n and_o in_o the_o limb_n it_o show_v the_o style_n height_n which_o for_o the_o former_a example_n will_v be_v find_v to_o be_v 42_o deg_n 41′_n 3_o the_o inclination_n of_o meridian_n the_o proportion_n be_v as_o the_o sine_fw-la of_o the_o latitude_n to_o radius_fw-la so_o be_v the_o sine_fw-la of_o the_o substiles_a distance_n to_o the_o sine_fw-la of_o the_o inclination_n of_o meridian_n when_o the_o substiles_a distance_n be_v less_o than_o the_o latitude_n of_o the_o place_n it_o may_v be_v find_v in_o the_o
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 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