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
A29762	Horologiographia, or, The art of dyalling being the second book of the use of the trianguler-quadrant : shewing the natural, artificial, and instrumental way, of making of sun-dials, on any flat superficies, with plain and easie directions, to discover their nature and affections, by the horizontal projection : with the way of drawing the usual ornaments on any plain : also, a familiar easie way to draw those lines on the ceiling of a room, by the trianguler quadrant : also, the use of the same instrument in navigation, both for observation, and operation : performing the use of several sea-instruments still in use / by John Brown, philomath.	Brown, John, philomath.	1671 (1671)	Wing B5042; ESTC R17803	103,467	309

but_o when_o the_o sun_n be_v in_o the_o equinoctial_a it_o behold_v the_o south-plain_a at_o the_o rise_n be_v at_o 6_o a_o clock_n in_o the_o morning_n and_o shine_v on_o it_o all_o day_n till_o sun_n set_v be_v at_o 6_o at_o night_n and_o then_o the_o north_n dial_n be_v useless_a 2._o for_o a_o declining-plain_a suppose_v 30_o degree_n southeast_n first_o set_v the_o scheam_n in_o his_o right_a situation_n for_o a_o southeast_n plain_a then_o if_o you_o count_v 30_o degree_n from_o saint_n towards_o e_o for_o the_o pole_n of_o the_o plain_a and_o 30_o degree_n from_o w_n towards_o saint_n or_o from_o e_z toward_z n_o and_o draw_v that_o line_n that_o shall_v represent_v the_o plain_a than_o you_o shall_v find_v that_o the_o sun_n be_v in_o cancer_n will_v begin_v to_o shine_v on_o this_o plain_a just_a a_o quarter_n before_o 5_o in_o the_o morning_n and_o continue_v till_o near_o half_a a_o hour_n after_o 2._o but_o about_o the_o middle_n of_o january_n it_o will_v shine_v on_o it_o till_o a_o quarter_n after_o 4_o viz._n till_o sun_n set_v and_o all_o the_o hour_n after_o 2_o belong_v to_o the_o northwest_n plain_a that_o decline_v 30_o degree_n and_o one_o hour_n in_o the_o morning_n also_o viz._n from_o a_o quarter_n before_o till_o three_o quarter_n after_o 4._o the_o like_a work_n serve_v for_o any_o decliner_n whatsoever_o in_o any_o latitude_n 3._o but_o for_o decliner_n and_o recliner_n draw_v a_o long_a line_n as_o ab_fw-la and_o cross_v it_o with_o a_o perpendicule_a in_o the_o centre_n c_o and_o lay_v off_o from_o c_o towards_o a_o and_o b_o the_o tangent_fw-la of_o 45_o or_o the_o semi-tangent_a of_o 90_o equal_a to_o the_o largeness_n of_o your_o scheam_n then_o lay_v off_o the_o semi-tangent_a of_o the_o reclination_n from_o c_o to_o d_o up_z and_o down_o both_o way_n then_o take_v out_o the_o secant_fw-la of_o the_o compliment_n of_o the_o reclination_n which_o will_v be_v a_o radius_fw-la to_o draw_v the_o ark_n adb_n which_o paper_n you_o must_v cut_v out_o and_o apply_v the_o two_o point_n of_o the_o paper_n adbd_v to_o the_o two_o point_n of_o declination_n of_o the_o plain_a note_v in_o the_o scheam_n with_o a_o and_o b_o that_o be_v put_v a_o to_o a_o and_o b_o to_z b_o then_o the_o round_a or_o convex-edge_n of_o the_o paper_n represent_v the_o recline_a plain_n and_o the_o same_o edge_n on_o the_o other_o part_n next_o the_o horizon_n southwards_o represent_v the_o south-west_n incliner_n example_n suppose_v i_o make_v the_o paper_n adb_n to_o recline_v 35-50_a the_o reclination_n of_o the_o equinoctial-plain_a then_o first_o set_v the_o scheam_n right_a before_o you_o in_o its_o right_a situation_n and_o put_v the_o point_v a_o in_o the_o paper_n on_o a_o on_o the_o scheam_n and_o b_o in_o the_o paper_n to_o b_o on_o the_o scheam_n i_o shall_v find_v it_o to_o be_v even_o with_o the_o recline_a circle_n aeb_n then_o follow_v the_o tropic_a of_o cancer_n i_o find_v that_o it_o shine_v on_o the_o north_n recliner_n from_o the_o rise_n till_o near_o 2_o at_o which_o time_n it_o leave_v the_o north-recline_a decline_v eastward_o and_o begin_v to_o shine_v upon_o the_o opposite_a plain_n viz._n the_o south-west_n incliner_n decline_v 55-0_a and_o recline_v 35-50_a and_o so_o continue_v till_o sunset_n but_o note_n that_o if_o the_o line_n that_o represent_v the_o plain_a cut_v the_o tropic_a twice_o as_o the_o line_n ewe_n for_o a_o north-plain_a then_o though_o the_o sun_n leave_v the_o plain_a in_o the_o morning_n it_o will_v shine_v on_o it_o again_o in_o the_o afternoon_n note_v also_o that_o a_o north-east_n recliner_n be_v represent_v by_o the_o other_o convex-edge_n of_o the_o paper_n as_o here_o a_o north-east_n decliner_n 55_o and_o incline_v 35-50_a the_o sun_n will_v shine_v but_o till_o 3_o quarter_n after_o 8_o in_o cancer_n but_o in_o capricorn_n it_o shine_v till_o half_a a_o hour_n after_o 9_o and_o come_v no_o more_o on_o it_o that_o day_n and_o note_v always_o that_o when_o it_o leave_v any_o plain_a that_o then_o it_o begin_v to_o shine_v on_o his_o opposite_a as_o here_o the_o opposite_a to_o this_o north-east_n incliner_n be_v the_o south-west_n recliner_n be_v represent_v by_o the_o same_o line_n or_o circle_n adb_n that_o the_o north_n recliner_n be_v only_o you_o must_v count_v that_o side_n of_o the_o line_n next_o to_o the_o horizon_n the_o inclining-plain_a and_o that_o side_n next_o the_o zenith_n the_o reclining-plain_a for_o the_o line_n that_o represent_v it_o have_v no_o breadth_n can_v be_v no_o otherwise_o distinguish_v unless_o you_o will_v make_v a_o material_a armilary_n sphere_n of_o pasteboard_n or_o brass_n as_o the_o follow_a discourse_n do_v plain_o demonstrate_v in_o these_o several_a operation_n for_o the_o better_a conceive_n of_o these_o mathematical_a excercitation_n thus_o you_o have_v the_o way_n of_o make_v all_o manner_n of_o sun_n dial_n upon_o any_o plain_a superficies_n the_o axis_n of_o the_o world_n be_v the_o suppose_a style_n to_o all_o these_o plain_n as_o for_o those_o curiosity_n of_o upright_a style_n and_o eliptical_a dial_n and_o draw_v of_o dial_n by_o the_o horizontal_a or_o equinoctial_a dial_n you_o have_v they_o in_o the_o work_v of_o mr._n samuel_n foster_n and_o other_o and_o in_o kerkers_n ars_fw-la magna_fw-la etc._n etc._n but_o i_o intend_v not_o a_o volumn_n of_o shadow_n but_o only_o a_o further_a improvement_n of_o the_o trianguler-quadrant_n as_o you_o will_v see_v in_o the_o next_o chapter_n of_o draw_v the_o furniture_n or_o ornament_n of_o dial_n which_o be_v but_o seldom_o use_v i_o shall_v here_o crave_v a_o apology_n for_o the_o brevity_n therein_o fear_v lest_o that_o to_o the_o young_a practitioner_n it_o may_v seem_v somewhat_o hard_a to_o conceive_v though_o to_o the_o exercise_v in_o these_o matter_n it_o may_v be_v plain_a enough_o then_o for_o a_o conclusion_n you_o shall_v have_v a_o easy_a mechanic_n way_n to_o draw_v a_o dial_n on_o the_o ceiling_n of_o a_o room_n that_o lie_v flat_a or_o horizontal_a which_o will_v be_v very_o good_a for_o painter_n or_o plasterer_n to_o ornament_n a_o room_n withal_o and_o be_v not_o yet_o treat_v on_o that_o way_n as_o ever_o i_o read_v of_o chap._n viii_o to_o furnish_v any_o dial_n with_o the_o usual_a mathematical_a ornament_n by_o the_o trianguler-quadrant_n as_o parallel_n of_o the_o sun_n declination_n or_o the_o sun_n place_n or_o length_n of_o the_o day_n to_o find_v the_o horizontal_a and_o virtical_a line_n and_o point_n to_o draw_v the_o azimuth_n and_o almicanter_n the_o jewish_a italian_a &_o babylonish_n hour_n and_o 12_o house_n on_o any_o plain_a before_o mention_v 1._o to_o draw_v the_o tropic_n or_o parallel_n of_o the_o sun_n declination_n or_o the_o length_n of_o the_o day_n artificial_a on_o any_o dial._n but_o note_n that_o if_o it_o be_v a_o perpendicule_a style_n who_o upper_a point_n or_o apex_n be_v to_o be_v the_o nodus_fw-la to_o give_v the_o shadow_n than_o you_o must_v strain_v a_o thread_n very_o hard_o or_o apply_v a_o rule_n for_o the_o present_a whereon_o to_o rest_v the_o moving-leg_n on_o instead_o of_o the_o axis_n or_o else_o you_o may_v do_v it_o thus_o as_o mr._n gunter_n show_v first_o to_o make_v the_o trygon_n if_o the_o rule_n or_o quadrant_n prove_v too_o large_a for_o your_o small_a dial._n on_o a_o sheet_n of_o pasteboard_n or_o slate_n draw_v a_o long_a straight_a line_n as_o ab_fw-la to_o which_o line_n erect_v two_o perpendiculer_o one_o at_o the_o upper_a and_o the_o other_o at_o the_o low_a end_n as_o cd_o and_o of_o then_o make_v ab_fw-la a_o tangent_fw-la of_o 45_o degree_n then_o have_v first_o make_v these_o little_a table_n that_o follow_v by_o the_o trianguler-quadrant_n which_o be_v only_o the_o sun_n declination_n at_o his_o entrance_n into_o the_o whole_a sign_n or_o at_o a_o even_a half-hour_n of_o rise_v lay_v of_o both_o way_n from_o b_o the_o tangent_n of_o the_o sun_n declination_n at_o ♈_o ♉_o ♊_o ♋_o as_o in_o the_o table_n follow_v and_o draw_v line_n to_o these_o point_n from_o the_o centre_n a_o as_o in_o the_o figure_n annex_v and_o then_o set_v the_o mark_n to_o they_o and_o this_o be_v the_o trigon_n figure_n i._n sun_n declination_n for_o the_o parallel_n of_o the_o length_n of_o the_o day_n hour_n declin_n 16-26_a 23-31_a 16-0_a 21-41_a 15-0_a 16-55_a 14_o 11-37_a 13_o 5-53_a 12_o 0-00_a 11_o 5-53_a 10_o 11-37_a 9_o 16-55_a 8_o 21-41_a 7-34_a 23-31_a for_o the_o sign_n of_o the_o zodiac_n sign_n declin_n ♋_o 23-31_a ♌_o ♊_o 20-14_a ♉_o ♍_o 11-31_a ♈_o ♎_o 0-00_a ♓_o ♏_o 11-31_a ♒_o ♐_o 20-14_a ♑_o 23-31_a declination_n 5-0_a 100l_a 15-0_a 20-0_a 23-31_a both_o way_n then_o from_o the_o centre_n a_o any_o way_n on_o the_o line_n cd_o at_o such_o a_o convenient_a distance_n as_o you_o

5_o n_o 30_o dolphin_n head_n 3_o 307_o 53_o 20_o 32_o 15_o 0_o n._n 31_o pegassus_n mouth_n 1_o 321_o 50_o 21_o 27_o 8_o 19_o n_o 32_o pomahant_n 3_o 339_o 30_o 22_o 38_o 31_o 17_o s._n 33_o pegassus_n lower_v wing_n 2_o 358_o 50_o 23_o 55_o 13_o 22_o n._n as_o for_o example_n to_o find_v the_o sun_n declination_n for_o the_o year_n 1670_o on_o the_o 12_o day_n of_o may_n first_o if_o you_o divide_v 70_o be_v the_o ten_o only_o of_o the_o year_n of_o our_o lord_n by_o 4_o reject_v the_o 100_o s_o you_o shall_v find_v 2_o as_o a_o remainder_n which_o note_v it_o to_o be_v the_o second_o after_o leap-year_n and_o if_o 0_o remain_n than_o it_o be_v leap-year_n then_o look_v in_o the_o table_n of_o declination_n for_o 1666_o the_o second_o after_o leap-year_n as_o the_o year_n 1670_o be_v and_o find_v the_o month_n in_o the_o head_n of_o the_o table_n and_o the_o day_n on_o one_o side_n and_o in_o the_o meeting-point_n you_o shall_v find_v 20_o deg_n 31_o min._n for_o the_o declination_n on_o that_o day_n at_o noon_n require_v or_o if_o you_o use_v the_o triangule_a quadrant_n extend_v the_o thread_n from_o the_o centre_n over_o the_o 12_o of_o may_n and_o you_o shall_v find_v it_o to_o cut_v in_o the_o degree_n just_a 20_o deg_n 31_o min._n the_o true_a declination_n for_o that_o year_n and_o day_n note_v that_o if_o you_o have_v occasion_n to_o use_v the_o declination_n before_o noon_n then_o observe_v that_o the_o difference_n between_o stroke_n and_o stroke_n be_v the_o difference_n of_o declination_n for_o one_o day_n and_o by_o consequence_n one_o half_a of_o that_o space_n for_o half_a a_o day_n and_o a_o quarter_n for_o a_o quarter_n of_o a_o day_n etc._n etc._n as_o thus_o for_o example_n suppose_v i_o will_v have_v the_o sun_n declination_n the_o 18_o of_o august_n 1666_o at_o 6_o in_o the_o morning_n here_o you_o must_v note_v that_o the_o 18_o stroke_n from_o the_o begin_n of_o august_n represent_v the_o 18_o day_n at_o noon_n just_a now_o the_o time_n require_v be_v 6_o hour_n before_o noon_n lay_v the_o thread_n one_o four_o part_n of_o the_o distance_n for_o one_o day_n towards_o the_o 17_o day_n and_o then_o in_o the_o degree_n the_o thread_n shall_v cut_v on_o 9-43′_a whereas_o at_o noon_n just_a it_o will_v be_v but_o 9-38_a and_o the_o next_o or_o 19_o day_n at_o noon_n it_o be_v 9_o degree_n 16_o min._n and_o 3_o quarter_n of_o a_o min._n as_o the_o three_o prick_n thus_o ..._o in_o the_o table_n do_v plain_o show_v but_o by_o the_o rule_n a_o minute_n be_v as_o much_o as_o can_v be_v see_v and_o so_o near_o with_o care_n may_v you_o come_v note_v also_o far_o that_o if_o you_o shall_v use_v it_o in_o place_n that_o be_v 4_o hour_n 6_o or_o 8_o 10_o or_o 12_o hour_n more_o eastward_o or_o westward_o in_o longitude_n the_o same_o rule_n will_v tell_v you_o the_o minute_n to_o be_v add_v in_o western-longitude_n or_o to_o be_v substract_v in_o eastern-longitude_n as_o reason_n and_o experience_n will_v dictate_v unto_o you_o with_o due_a consideration_n for_o if_o be_v eastward_n the_o sun_n come_v to_o the_o meridian_n of_o that_o place_n before_o it_o come_v to_o the_o meridian_n of_o london_n then_o lay_v the_o thread_n as_o in_o morning_n hour_n but_o if_o the_o place_n be_v to_o the_o westward_n where_o it_o come_v late_a then_o lay_v the_o thread_n so_o many_o hour_n beyond_o the_o noon-stroke_n for_o london_n as_o the_o place_n have_v hour_n of_o western-longitude_n more_o than_o london_n count_v 15_o degree_n for_o a_o hour_n and_o 4_o minute_n for_o every_o degree_n and_o then_o shall_v you_o have_v the_o declination_n to_o one_o minute_n of_o the_o very_a truth_n but_o if_o it_o happen_v to_o be_v the_o leap-year_n or_o the_o first_o or_o three_o year_n after_o the_o leap-year_n than_o thus_o suppose_v for_o the_o 5_o of_o october_n 1671_o be_v the_o three_o after_o leap-year_n i_o will_v have_v the_o declination_n first_o if_o you_o lay_v the_o thread_n over_o the_o 5_o of_o october_n in_o the_o degree_n it_o give_v 08_o deg_n 42_o minute_n for_o the_o declination_n in_o the_o second_o year_n after_o leap-year_n then_o because_o this_o be_v the_o three_o year_n look_v in_o the_o rectifying-table_n for_o the_o 5_o of_o october_n and_o there_o you_o find_v s._n 4_o for_o subtract_v 4_o minute_n and_o a_o half_a from_o 8-42_a rest_v 8-38_a the_o true_a declination_n require_v for_o the_o 5_o of_o october_n 1671._o the_o like_a work_n serve_v for_o any_o other_o day_n or_o year_n but_o for_o every_o 5_o and_o 10_o day_n you_o have_v the_o declination_n set_v down_o in_o a_o table_n for_o all_o 4_o year_n to_o prove_v and_o try_v the_o truth_n of_o your_o operation_n and_o by_o that_o and_o the_o line_n of_o number_n or_o the_o rule_n of_o three_o you_o may_v continue_v it_o to_o every_o day_n by_o this_o proportion_n as_o 5_o day_n or_o 120_o hour_n to_o the_o difference_n of_o declination_n in_o the_o table_n between_o one_o 5_o day_n and_o another_o so_o be_v any_o part_n of_o 5_o day_n or_o 120_o hour_n to_o the_o difference_n in_o declination_n to_o be_v add_v or_o substract_v to_o the_o 5_o day_n declination_n immediate_o foregoing_a the_o day_n require_v example_n suppose_v for_o the_o 18_o of_o february_n 1669_o the_o first_o after_o leap-year_n i_o will_v know_v the_o declination_n by_o the_o table_n make_v to_o every_o 5_o day_n only_o on_o the_o 20_o of_o february_n i_o find_v 6-53_a ½_o on_o the_o 15_o day_n 8-47_a the_o difference_n between_o they_o be_v 1-53_a ½_o then_o the_o extent_n of_o the_o compass_n from_o 5_o the_o number_n of_o day_n to_o 1-53_a the_o minute_n difference_n count_v proper_o every_o 10_o for_o 6_o minute_n shall_v reach_v from_o 3_o the_o day_n from_o 15_o towards_o 18_o to_o 1_o degree_n 7_o minute_n and_o a_o half_a which_o take_v from_o 8-47′_a the_o declination_n for_o the_o 15_o day_n leave_v 7_o degree_n 38_o minute_n and_o a_o half_a the_o true_a declination_n for_o the_o 18_o day_n of_o february_n in_o the_o first_o after_o leap-year_n or_o by_o the_o line_n of_o number_n thus_o the_o extent_n from_o 5_o the_o difference_n in_o day_n to_o 113_o ½_o the_o difference_n in_o min._n for_o 5_o day_n shall_v reach_v from_o 3_o the_o difference_n in_o day_n to_o 68_o the_o difference_n in_o minute_n for_o 3_o day_n to_o be_v add_v or_o substract_v according_a to_o the_o increase_n or_o decrease_v of_o the_o declination_n at_o that_o time_n of_o the_o year_n prove_v thus_o if_o you_o subtract_v 5′_n ½_o from_o 7_o deg_n 44_o ..._o the_o declination_n in_o the_o second_o year_n there_o remain_v 7_o deg_n 38′_n ½_o the_o declination_n for_o the_o 18_o of_o february_n 1669._o these_o table_n may_v serve_v very_o well_o for_o 30_o year_n and_o not_o differ_v 6_o minute_n in_o declination_n about_o the_o equinoctial_a where_o the_o difference_n be_v most_o and_o in_o june_n and_o december_n not_o at_o all_o to_o be_v perceive_v thus_o you_o may_v by_o the_o rule_n and_o rectify_v table_n find_v the_o sun_n declination_n to_o a_o minute_n at_o any_o time_n without_o the_o trouble_n of_o calculation_n chap._n iu._n the_o use_n of_o the_o trianguler-quadrant_n in_o the_o operative_a part_n of_o navigation_n use_v i._o to_o find_v how_o many_o league_n or_o miles_n answer_v to_o one_o degree_n of_o longitude_n in_o any_o latitude_n between_o the_o equinoctial_a and_o pole_n first_o it_o be_v convenient_a to_o be_v resolve_v how_o many_o league_n or_o mile_n be_v in_o one_o degree_n in_o the_o meridian_n or_o equinoctial_a which_o mr._n norwood_n and_o mr._n collins_n have_v state_v about_o 24_o league_n or_o 72_o mile_n or._n if_o you_o keep_v the_o old_a number_n make_v the_o mile_n great_a viz._n 60_o mile_n or_o 20_o league_n then_o the_o proportion_n by_o the_o number_n sin_n and_o tangent_n run_v thus_o as_o sine_fw-la 90_o to_o 20_o on_o the_o number_n for_o league_n so_o be_v cousin_a of_o the_o latitude_n to_o the_o league_n on_o the_o number_n contain_v in_o one_o degree_n of_o longitude_n in_o that_o latitude_n but_o in_o miles_n to_o have_v the_o answer_n work_v thus_o as_o sine_fw-la 90_o to_o 60_o on_o number_n so_o cousin_a latitude_n to_o the_o number_n of_o mile_n example_n latitude_n 51°_n 32′_n as_o sine_fw-la 90_o to_o 60_o so_o sine_fw-la 38-28_a to_o 37_o mile_n 30_o 100_o but_o by_o the_o trianguler-quadrant_n or_o sector_n work_v thus_o take_v the_o latteral_a 20_o for_o league_n or_o 60_o for_o mile_n from_o the_o line_n of_o line_n from_o the_o centre_n downward_o and_o make_v it_o a_o parallel_n in_o the_o sine_fw-la of_o 90_o lay_v the_o thread_n to_o the_o near_a distance_n then_o the_o near_a distance_n

the_o length_n of_o the_o day_n in_o the_o dial_n you_o shall_v find_v these_o hour_n to_o cross_v the_o even_a hour-line_n and_o quarter_n in_o the_o parallel_n for_o 15_o and_o 9_o hour_n as_o well_o as_o in_o the_o equinoctial_a iv._o to_o draw_v the_o italian_a or_o babylonish-hour_n first_o draw_v the_o common_a hour_n and_o the_o parallel_n of_o the_o sign_n or_o rather_o the_o length_n of_o the_o day_n then_o note_n that_o these_o hour-line_n meet_v with_o the_o common_a hour_n in_o the_o equinoctial_a only_o the_o italian_n who_o account_n from_o sunsetting_a call_v our_o 12_o in_o the_o equinoctial_a 18_o and_o the_o babylonian_n who_o reckon_v from_o the_o sunrising_n call_v our_o 12_o in_o the_o equinoctial_a 6_o hour_n then_o to_o mark_v these_o in_o the_o tropic_n do_v thus_o but_o if_o you_o draw_v the_o parallel_n of_o the_o length_n of_o the_o day_n than_o you_o shall_v find_v the_o 18_o hour_n after_o sun_n set_v to_o cut_v the_o hour-line_n of_o 10_o in_o the_o parallel_n of_o the_o day_n be_v 8_o hour_n long_o and_o 12_o in_o the_o parallel_n of_o 12_o hour_n long_o and_o the_o common_a hour-line_n of_o 2_o in_o the_o parallel_n of_o 16_o hour_n long_o and_o so_o successive_o for_o the_o rest_n for_o so_o many_o hour_n from_o the_o last_o sunsetting_a for_o from_o 6_o the_o last_o night_n in_o the_o equinoctial_a to_o 12_o this_o noon_n be_v 18_o hour_n but_o in_o ♑_o from_o 47′_n after_o 3_o at_o sunset_n to_o the_o next_o noon_n be_v 20_o hour_n and_o 13′_n as_o in_o the_o figure_n forego_v but_o for_o the_o babylonish-hour_n who_o reckon_v by_o equal_a hour_n from_o the_o sun_n rising_n as_o before_o count_v 2_o hour_n and_o 13_o minute_n after_o 6_o in_o ♑_o and_o 2_o hour_n and_o 13′_n before_o 6_o in_o ♋_o and_o just_o 6_o in_o ♈_o and_o that_o shall_v draw_v the_o line_n of_o the_o sun_n rise_v then_o count_v 3_o hour_n and_o 13′_n after_o 6_o in_o ♑_o and_o 7_o in_o ♈_o and_o 1_o hour_n 13′_n before_o 6_o in_o ♋_o and_o that_o shall_v be_v the_o first_o hour_n after_o sun_n rise_v and_o so_o successive_o till_o night_n but_o if_o you_o use_v the_o parallel_n of_o the_o length_n of_o the_o day_n the_o work_n be_v easy_a for_o then_o 5_o 7_o and_o 09_o in_o the_o parallel_n of_o 16_o 12_o and_o 8_o hour_n shall_v be_v point_n for_o the_o first_o from_o sunrising_n and_o 6_o 8_o and_o 10_o shall_v show_v the_o second_o hour_n from_o sunrising_n and_o so_o forward_o as_o in_o the_o table_n follow_v v._o to_o draw_v the_o azimuth-line_n for_o all_o erect-dials_n both_o direct_a or_o decliner_n deal_v with_o the_o declination_n of_o the_o plain_a as_o you_o do_v with_o the_o inclination_n of_o meridian_n and_o at_o the_o meridian_n or_o 12_o set_v the_o plain_n declination_n and_o then_o for_o rumb_n take_v 11_o deg_n 15′_n as_o often_o as_o you_o can_v and_o what_o the_o last_o number_n want_v of_o 11-15_a set_v on_o the_o other_o side_n of_o the_o substile_a and_o to_o that_o add_v 11-15_a till_o you_o have_v enough_o as_o in_o the_o table_n annex_v for_o a_o dial_n who_o declination_n be_v 35_o degree_n westward_n then_o make_v the_o perpendicule_a height_n of_o the_o style_n radius_fw-la or_o tangent_fw-la of_o 45_o and_o on_o the_o horizontal-line_n lie_v off_o the_o =_o tangent_n of_o the_o rumb_n last_o make_v in_o the_o table_n from_o the_o foot_n of_o the_o style_n their_o right_a way_n and_o draw_v line_n through_o those_o point_n all_o parallel_n to_o 12_o for_o the_o rumb_n or_o virtical_a circle_n require_v on_o the_o meridian_n write_v south_n and_o the_o rest_n in_o their_o due_a order_n to_o draw_v the_o azimuth_n or_o virtical-circle_n on_o recline_v or_o inclining-plain_n point_n d._n m_o s._n e._n 80_o 00_o s._n e._n by_o s._n 68_o 45_o s._n s._n e._n 57_o 30_o s._n by_o e._n 46_o 15_o south_n 35_o 00_o s._n by_o w._n 23_o 45_o s._n s._n w._n 12_o 30_o s._n w._n by_o s._n 1_o 15_o substile_fw-fr  _fw-fr s._n w._n 10_o 00_o s.w._n b._n w._n 21_o 15_o w._n s._n w._n 32_o 30_o w._n by_o s._n 43_o 45_o west_n 55_o 00_o w._n by_o n._n 66_o 15_o w._n n._n w._n 77_o 30_o n._n w._n b._n w._n 88_o 45_o n._n w._n  _fw-fr in_o all_o recline_a or_o incline_v plain_n these_o azimuth_n virtical_a circle_n or_o rumb_n do_v meet_v in_o a_o point_n call_v the_o vertical_a point_n find_v in_o the_o meridian_n or_o 12_o a_o clock_n line_n right_o over_o in_o incliner_n or_o under_o in_o recliner_n the_o apex_n or_o top_n of_o the_o style_n that_o be_v to_o give_v the_o shadow_n when_o set_v in_o its_o right_a place_n right_a over_o the_o substile-line_n and_o as_o far_o off_o the_o foot_n of_o the_o style_n be_v a_o point_n in_o the_o substile_a square_n or_o perpendicule_a to_o the_o apex_n or_o top_n of_o the_o style_n in_o a_o vertical_a line_n draw_v through_o the_o foot_n of_o the_o style_n =_o to_o the_o perpendicule_a line_n of_o the_o plain_a as_o the_o co-tangent_a of_o the_o reclination_n make_v the_o perpendicule_a height_n of_o the_o style_n to_o be_v radius_fw-la or_o tangent_fw-la of_o 45_o degree_n also_o the_o co-tangent_a of_o the_o reclination_n of_o the_o plain_a to_o the_o same_o radius_fw-la lay_v from_o the_o foot_n of_o the_o style_n in_o the_o same_o virtical-line_n shall_v give_v the_o point_n in_o the_o vertical-line_n to_o draw_v the_o horizontal-line_n by_o for_o a_o rule_n lay_v to_o this_o point_n and_o the_o cross_v the_o equinoctial-line_n and_o hour_n of_o 6_o shall_v draw_v the_o true_a horizontal-line_n then_o make_v the_o distance_n between_o this_o point_n and_o the_o meeting_n of_o the_o equinoctial_a and_o 6_o a_o =_o tangent_fw-la of_o the_o west_n or_o east_n azimuth_n in_o the_o table_n and_o then_o the_o sector_n be_v set_v to_o lay_v off_o all_o the_o rest_n by_o take_v the_o =_o tangent_n of_o the_o number_n in_o the_o table_n and_o lay_v they_o from_o the_o vertical-point_n in_o the_o horizontal-line_n both_o way_n on_o the_o horizontal-line_n for_o from_o hence_o you_o may_v note_v that_o the_o sun_n be_v in_o the_o equinoctial_a do_v rise_v and_o set_v near_o 6_o and_o also_o do_v rise_v near_o the_o east-point_n and_o set_v near_o the_o west_n therefore_o the_o same_o point_n in_o the_o dial_n must_v be_v for_o the_o hour_n 6_o in_o the_o morning_n and_o the_o east_n aximuth_n or_o the_o hour_n 6_o at_o night_n and_o the_o west_n azimuth_n according_a as_o the_o plain_n decline_v eastward_n or_o westward_n then_o right_a line_n draw_v from_o the_o vertical-point_n in_o the_o meridian_n and_o to_o all_o these_o point_n in_o the_o horizontal-line_n shall_v be_v the_o azimuth-line_n require_v a_o thus_o for_o example_n in_o the_o figure_n annex_v be_v the_o three_o sort_n of_o south-recliners_a before-going_a decline_a 35_o degree_n south-west_n and_o recline_v 60_o degree_n ch_n be_v the_o substile_a cg_n the_o style_n h_n the_o foot_n of_o the_o style_n ik_fw-mi the_o vertical-line_n draw_v through_o the_o foot_n of_o the_o style_n he_o the_o vertical-point_n in_o the_o cross_n of_o 12_o and_o the_o vertical-line_n and_o yet_o right_a under_o g_o the_o apex_n consider_v the_o reclination_n and_o the_o raise_n of_o g_o the_o apex_n square_a or_o perpendicule_a to_o h_n the_o foot_n of_o the_o style_n then_o i_o say_v a_o plumb-line_n let_v fall_v from_o g_o will_v rest_v in_o ay_o the_o vertical-point_n the_o dial_n be_v set_v in_o its_o due_a place_n then_o gh_o the_o perpendicule_a height_n make_v a_o =_o tangent_fw-la of_o 45_o he_o be_v the_o co-tangent_a of_o the_o reclination_n viz._n 30_o and_o hk_v the_o tangent_fw-la o●_n the_o reclination_n 60_o be_v the_o vertical-point_n in_o the_o horizontal-line_n from_o whence_o to_o lay_v the_o =_o tangent_n of_o the_o rumb_n in_o the_o table_n last_o make_v into_o the_o horizontal-line_n then_o line_n draw_v from_o the_o vertical-point_n i_o to_o those_o point_n in_o the_o horizontal-line_n shall_v be_v the_o rumb_n or_o point_n of_o the_o compass_n vertical_a circle_n or_o azimuth_n require_v otherwise_o when_o you_o have_v make_v the_o table_n of_o the_o angle_n at_o the_o zenith_n as_o before_o you_o may_v by_o this_o canon_n make_v table_n of_o angle_n at_o the_o vertical-point_n between_o the_o vertical-line_n and_o the_o rumb_n to_o be_v draw_v on_o the_o plain_a as_o the_o sine_fw-la of_o 90_o to_o the_o cousin_a of_o reclination_n or_o inclination_n so_o the_o tangent_fw-la of_o the_o angle_n at_o zenith_n to_o the_o tangent_fw-la at_o the_o vertical_a this_o table_n be_v make_v you_o may_v set_v one_o point_n in_o the_o vertical-point_n and_o describe_v a_o circle_n to_o any_o radius_fw-la and_o therein_o prick_v off_o from_o the_o vertical-line_n the_o several_a chord_n of_o the_o rumb_n as_o in_o the_o

00_o 00_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 15_o 56_o 13_o 25_o 06_o 41_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 13_o 44_o 11_o 11_o 04_o 23_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 11_o 35_o 8_o 59_o 02_o 08_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 5_o 9_o 32_o 6_o 50_o 00_o 06_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 7_o 23_o 4_o 44_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 5_o 26_o 2_o 41_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 3_o 36_o 0_o 41_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 4_o 1_o 32_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr the_o description_n and_o some_o use_v of_o the_o sphere_n for_o dial_v and_o for_o the_o better_a understanding_n of_o the_o general_a and_o particular_a scheme_n next_o the_o foot_n and_o semicircle_n frame_v for_o support_v of_o it_o you_o may_v consider_v 1._o the_o fix_a horizon_n to_o which_o the_o foot_n be_v fasten_v with_o 4_o screw_n number_v and_o divide_v into_o 360_o degree_n or_o four_o 90_o deg_n who_o count_n begin_v at_o the_o dividee_n side_n of_o the_o meridian-circle_n 2._o the_o meridian_n circle_n who_o fore-side_n at_o the_o nadir-point_n stand_v in_o the_o centre_n of_o the_o foot_n this_o be_v also_o divide_v into_o 4_o 90_o s_o and_o begin_v to_o be_v number_v at_o the_o south_n and_o north_n part_n of_o the_o horizon_n upward_o towards_o the_o zenith_n and_o downward_o towards_o the_o nadir_n which_o circle_n be_v always_o fix_v as_o the_o horizon_n be_v 3._o the_o equinoctial_a circle_n make_v fast_o at_o the_o east_n and_o west_n point_v of_o the_o horizon_n move_v up_o and_o down_o upon_o the_o meridian-circle_n according_a to_o the_o elevation_n of_o the_o equinoctial_a in_o any_o latitude_n this_o be_v divide_v ●●kewise_o into_o four_o 90_o s_o &_o number_v from_o the_o meridian_n each_o way_n to_o the_o east_n and_o west_n point_v of_o the_o horizon_n 4._o on_o the_o meridian_n circle_n be_v set_v 2_o movable_a pole_n to_o be_v elevate_v or_o depress_v fit_a to_o the_o latitude_n of_o any_o place_n on_o the_o fiducial-edge_n of_o which_o be_v fasten_v the_o thread_n represent_v the_o axis_n of_o the_o world_n at_o any_o elevation_n of_o the_o pole_n 5._o on_o the_o 2_o pole_n point_n be_v fasten_v the_o hour_n circle_n which_o delineate_v or_o represent_v the_o motion_n of_o the_o sun_n or_o any_o fix_a star_n move_v in_o its_o suppose_a diurnal_a motion_n about_o the_o pole_n of_o the_o world_n and_o may_v not_o improper_o be_v call_v the_o movable_a meridian_n circle_n or_o hour_n circle_n divide_v as_o before_o 6._o the_o movable_a horizon_n that_o move_v about_o to_o any_o azimuth_n and_o slide_v or_o move_v in_o the_o fix_a horizon_n 7._o the_o plain_a fix_v in_o 2_o opposite_a point_n to_o the_o move_a horizon_n be_v set_v either_o horizontal_a when_o it_o lie_v parallel_v to_o the_o fix_a horizon_n or_o erect_v when_o perpendicule_a thereunto_o or_o set_v to_o any_o reclination_n or_o inclination_n by_o help_n of_o the_o semicircle_n of_o reclination_n fasten_v to_o the_o backside_n of_o the_o plain_a in_o the_o 2_o pole_n thereof_o 8._o you_o have_v the_o upper_a move_a semicircle_n in_o turn_v about_o of_o which_o whatever_o degree_n the_o fore-side_n of_o the_o semicircle_n cut_v the_o perpendiculer-point_n cut_v the_o comple●ment_n thereof_o and_o to_o be_v call_v the_o upper_a semicircle_n or_o circle_n always_o perpendicu●ler_n to_o the_o plain_a 9_o there_o aught_o to_o be_v a_o thread_n fasten_v in_o the_o centre_n of_o the_o plain_a to_o be_v extend_v to_o any_o altitude_n or_o azimuth_n require_v thus_o much_o for_o description_n repeat_v again_o in_o short_a thus_o the_o horizon_n the_o meridian_n the_o equinoctial_a circle_n the_o 2_o pole_n point_n and_o axis_n the_o hour_n circle_n or_o movable_a meridian_n the_o movable_a horizon_n the_o plain_a the_o semicircle_n of_o reclination_n the_o upper_a semicircle_n and_o the_o thread_n note_v also_o every_o circle_n be_v divide_v into_o 4_o time_n 90_o and_o number_v the_o most_o useful_a way_n also_o on_o the_o plain_n be_v set_v the_o 12_o month_n and_o every_o single_a day_n on_o which_o every_o respective_a day_n if_o you_o extend_v the_o thread_n then_o in_o the_o degree_n be_v the_o sun_n right_a ascension_n in_o degree_n on_o the_o innermost_a circle_n the_o same_o in_o hour_n and_o quarter_n from_o the_o next_o equinoctial-point_n on_o the_o line_n of_o declination_n his_o mean_a declination_n on_o the_o line_n of_o ●he_n sun_n place_n his_o mean_a true_a place_n sufficient_o true_a for_o any_o illustration_n in_o mathematical_a practice_n the_o use_v whereof_o in_o some_o part_n follow_v 1._o to_o rectify_v the_o sphere_n to_o any_o latitude_n count_v the_o elevation_n of_o the_o pole_n on_o the_o meridian_n circle_n from_o the_o horizon_n upward_o and_o downward_o from_o the_o north_n and_o south_n part_n of_o the_o horizon_n and_o there_o make_v fast_o with_o the_o help_n of_o the_o small_a screw_n the_o fiducial-edge_n of_o the_o pole_n point_n carry_v the_o hour_n circle_v fix_v upon_o they_o than_o the_o pole_n be_v right_o elevate_v 2._o count_n the_o compliment_n of_o the_o pole_n elevation_n on_o the_o meridian_n from_o the_o south_n part_n of_o the_o horizon_n and_o to_o it_o set_v the_o divide_a side_n of_o the_o equinoctial_a circle_n then_o be_v that_o rectify_v also_o in_o the_o northern_a hemisphere_n or_o in_o the_o southern_a if_o you_o call_v the_o north_n pole_n the_o south_n pole_n 3._o extend_v the_o thread_n or_o axis_n pass_v through_o the_o centre_n to_o the_o south_n pole_n and_o there_o make_v it_o fast_o and_o then_o the_o sphere_n be_v rectify_v for_o many_o use_v in_o that_o latitude_n use_v i._o the_o day_n of_o the_o month_n be_v give_v to_o find_v the_o sun_n true_a place_n lay_v the_o thread_n in_o the_o centre_n of_o the_o plain_a on_o the_o day_n of_o the_o month_n and_o in_o the_o line_n of_o the_o sun_n place_n you_o have_v his_o place_n example_n on_o the_o 5_o of_o november_n it_o be_v 23_o degree_n in_o ♐_o or_o if_o the_o sun_n place_n be_v give_v look_v for_o that_o and_o just_a against_o it_o in_o the_o month_n be_v the_o day_n require_v example_n the_o sun_n place_n be_v 15_o degree_n ♌_o i_o look_v for_o it_o in_o the_o line_n of_o his_o place_n and_o just_a against_o it_o i_o find_v july_n 28_o day_n use_v ii_o to_o find_v his_o declination_n any_o day_n look_v for_o the_o day_n give_v and_o right_a against_o it_o in_o the_o line_n of_o declination_n be_v his_o due_a declination_n require_v example_n august_n the_o 5_o the_o declination_n be_v 14_o degree_n 5_o minute_n from_o the_o next_o equinoctial-point_n viz._n ♎_o note_v in_o the_o northern_a sin_n or_o summertime_n the_o sun_n have_v north_n declination_n or_o in_o southern_a sin_n or_o winter-month_n the_o sun_n have_v south_n declination_n or_o if_o you_o have_v the_o sun_n declination_n find_v that_o in_o the_o line_n declination_n and_o right_a against_o it_o in_o the_o month_n be_v the_o day_n require_v example_n 21_o degree_n south_n declination_n begin_v from_o the_o equinoctial_a towards_o the_o winter_n solstice_n i_o find_v novemb_n 15._o the_o like_a work_n have_v be_v if_o the_o sun_n place_n have_v be_v give_v to_o find_v his_o declination_n use_v iii_o the_o day_n give_v to_o find_v the_o sun_n rightascention_n this_o be_v usual_o reckon_v from_o ♈_o to_o ♈_o round_a in_o 24_o hour_n but_o twice_o 12_o be_v as_o useful_a and_o then_o it_o be_v thus_o find_v the_o day_n among_o the_o month_n and_o day_n and_o just_a against_o it_o in_o the_o time_n of_o hour_n be_v the_o sun_n right_a ascension_n but_o note_n it_o be_v not_o right_o figure_v for_o this_o use_n count_v onward_o from_o ♈_o or_o the_o 10_o of_o march_n to_o the_o 13_o of_o septemb_n and_o from_o thence_o to_o aries_n again_o likewise_o the_o degree_n be_v to_o be_v reckon_v from_o ♈_o onward_o as_o the_o month_n proceed_v example_n on_o the_o 12_o of_o may_n what_o be_v the_o sun_n right_a ascension_n lay_v the_o thread_n on_o the_o 12_o of_o may_n and_o in_o the_o line_n of_o hour_n it_o cut_v 9-57′_a count_v from_o aries_n onward_o or_o in_o degree_n 59-15_a count_v as_o before_o thus_o if_o any_o one_o of_o these_o 4_o general_a thing_n be_v give_v the_o other_o may_v be_v find_v use_v iu._n the_o sun_n declination_n and_o latitude_n be_v give_v to_o find_v the_o sun_n meridian_n altitude_n the_o sphere_n be_v rectify_v count_v the_o declination_n on_o the_o meridian_n from_o the_o equinoctial_a that_o way_n the_o declination_n be_v either_o north_n or_o south_n and_o where_o the_o count_v end_n there_o be_v the_o meridian_n altitude_n require_v for_o that_o day_n or_o declination_n example_n june_n 11._o declination_n 23-30′_a count_v 23-30_a from_o 38-30_a the_o place_n where_o