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 â™_o 11-31_a ♈_o ♎_o 0-00_a ♓_o â™_o 11-31_a â™’_o â™_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
think_v may_v fit_v the_o plain_n set_v off_o the_o point_n g_o then_o make_v give_v radius_fw-la of_o 45_o tang._n set_v off_o on_o ab_fw-la from_o a_o the_o tang._n of_o the_o style_n elevation_n to_o f_o and_o draw_v the_o line_n fg_v as_o a_o obscure_a line_n then_o come_v to_o the_o dial_n plain_a and_o measure_n from_o the_o centre_n to_o the_o place_n on_o the_o substile-line_n where_o you_o will_v have_v your_o remote_a line_n of_o the_o sign_n ♋_o or_o ♑_o to_o pass_n and_o take_v this_o distance_n between_o your_o compass_n and_o carry_v it_o in_o above_z or_o below_o the_o line_n fg_v first_o draw_v and_o produce_v to_o ♋_o or_o ♑_o till_o you_o find_v one_o point_v to_o stay_v in_o a_o ♋_o and_o the_o other_o in_o agnostus_n so_o as_o to_o draw_v a_o line_n =_o to_o fg_n first_o draw_v if_o that_o do_v not_o fit_a than_o deal_n fg_n and_o draw_v this_o =_o to_o it_o in_o its_o stead_n to_o fit_a and_o fill_v the_o plain_a with_o the_o tropic_n to_o your_o mind_n to_o make_v they_o large_a and_o yet_o convenient_a then_o note_n the_o point_n g_z represent_v the_o centre_n of_o the_o dial_n agnostus_n be_v the_o length_n of_o the_o style_n from_o the_o centre_n to_o the_o nodus_fw-la a_o perpendicule_a let_v fall_v from_o a_o to_o fg_n show_v the_o point_n h_n gh_n be_v the_o measure_n on_o the_o substile-line_n on_o the_o plain_a from_o the_o centre_n to_o the_o horizontal-line_n ha_o be_v the_o perpendicule_a height_n of_o the_o style_n a_o the_o apex_n or_o top_n of_o the_o style_n or_o nodus_fw-la to_o give_v the_o shadow_n then_o draw_v a_o line_n from_o g_o =_o to_o ab_fw-la as_o lk_v and_o any_o where_o between_o ab_fw-la draw_v lm_o =_o to_o agnostus_n and_o wheresoever_o fg_n cut_v lm_o make_v a_o mark_n as_o at_o m_n then_o make_v lm_o a_o =_o sine_fw-la of_o 90_o degree_n and_o the_o sector_n so_o set_v take_v out_o the_o sine_fw-la compliment_n of_o the_o ark_n at_o the_o pole_n for_o every_o hour_n and_o lay_v they_o from_o l_o towards_o m_n on_o the_o line_n lm_o and_o to_o all_o those_o point_n draw_v line_n from_o g_o and_o mark_v they_o with_o 12_o 1_o 2_o 3_o 4_o etc._n etc._n as_o in_o the_o table_n or_o else_o take_v the_o measure_n from_o g_o to_o f_o and_o lay_v it_o on_o the_o dial_n from_o the_o centre_n on_o the_o substile_a and_o draw_v that_o line_n precise_o perpendicule_a to_o the_o substile_a for_o the_o true_a equinoctial-line_n on_o the_o plain_a then_o the_o measure_n from_o the_o centre_n of_o the_o dial_n to_o the_o cross_v of_o every_o hour-line_n and_o the_o equinoctial-line_n take_v and_o lay_v from_o g_o to_o the_o line_n ab_fw-la give_v point_n to_o draw_v the_o hour-line_n on_o the_o trygon_n as_o in_o the_o figure_n wherein_o you_o may_v note_v that_o if_o the_o substile_n happen_v to_o fall_v on_o a_o even_o whole_a or_o half_a hour_n than_o one_o line_n will_v serve_v on_o both_o side_n of_o the_o substile_a but_o if_o not_o you_o must_v draw_v as_o many_o more_o and_o set_v figure_n to_o they_o to_o avoid_v confusion_n then_o i_o say_v that_o the_o several_a distance_n from_o g_o to_o the_o cross_n of_o those_o hour-line_n last_o draw_v on_o the_o trygon_n and_o the_o sign_n be_v lay_v on_o their_o correspondent_a hour-line_n from_o the_o centre_n of_o the_o dial_n shall_v give_v point_n in_o those_o hour-line_n to_o draw_v the_o sign_n of_o the_o zodiac_n with_o a_o thin_a rule_n that_o will_v bend_v to_o those_o hyperbolic_a section_n the_o same_o way_n serve_v to_o draw_v the_o parallel_n of_o the_o length_n of_o the_o day_n if_o you_o lay_v the_o distunce_n from_o g_z the_o cross_n of_o the_o prick_v line_n and_o hour_n on_o the_o trygon_n and_o be_v as_o true_a as_o any_o other_o way_n by_o calculation_n which_o must_v afterward_o be_v perform_v by_o protraction_n in_o this_o manner_n thus_o you_o have_v the_o way_n to_o proportion_v the_o height_n of_o the_o style_n to_o fit_v the_o plain_n and_o the_o place_n of_o the_o horizontal-line_n in_o all_o erect-dials_n which_o be_v always_o perpendicule_a to_o 12_o and_o draw_v through_o that_o point_n across_o the_o plain_n and_o this_o way_n of_o draw_v the_o sign_n be_v general_a in_o all_o plain_n whatsoever_o that_o will_v admit_v they_o ii_o to_o find_v the_o horizontal-line_n in_o all_o manner_n of_o plain_n first_o the_o horizontal-plain_a can_v have_v none_o nor_o many_o other_o both_o recline_a and_o incline_v who_o reclination_n or_o inclination_n be_v above_o the_o compliment_n of_o the_o sun_n meridian_n altitude_n in_o ♑_o if_o the_o style_n have_v any_o considerable_a altitude_n in_o all_o other_o plain_n the_o best_a mechanic_n way_n be_v thus_o the_o dial_n be_v set_v in_o or_o as_o in_o his_o place_n apply_v the_o moveing-leg_n to_o the_o top_n of_o the_o style_n &_o one_o corner_n of_o it_o to_o the_o plain_a and_o at_o the_o same_o time_n let_v the_o thread_n play_v even_o on_o 600_o and_o the_o corner_n at_o the_o plain_n will_v make_v as_o many_o mark_n as_o you_o please_v to_o draw_v it_o by_o otherwise_o note_n that_o wheresoever_o the_o hour-line_n of_o 6_o and_o the_o equinoctial-line_n do_v meet_v there_o be_v one_o point_n then_o find_v at_o what_o hour_n and_o minute_n the_o sun_n do_v rise_v or_o set_v at_o in_o the_o begin_n of_o any_o other_o whole_a sign_n most_o remote_a from_o the_o first_o point_n and_o that_o shall_v be_v another_o and_o so_o as_o many_o as_o you_o please_v to_o draw_v that_o line_n by_o this_o be_v general_a for_o all_o plain_n to_o find_v that_o point_n by_o the_o trianguler-quadrant_n lay_v the_o thread_n to_o the_o sign_n give_v and_o in_o the_o hour-line_n be_v the_o hour_n and_o minute_n require_v thus_o the_o sun_n be_v in_o ♈_o rise_v and_o set_v at_o 6_o or_o 1_o quarter_n of_o a_o minute_n before_o or_o after_o and_o in_o ♉_o at_o just_a 5_o and_o set_v at_o 7_o in_o ♊_o at_o 9_o minute_n after_o 4_o or_o set_v 9_o minute_n before_o 8_o the_o like_a for_o winter_n sign_n iii_o to_o draw_v the_o old_a unequal_a hour_n the_o unequal_a jewish_a or_o planetary_a hour_n divide_v the_o day_n be_v it_o long_o or_o short_a into_o 12_o equal_a hour_n for_o the_o draw_v of_o which_o in_o the_o equinoctial_a the_o common_a hour_n give_v point_n for_o the_o tropic_n do_v thus_o divide_v the_o number_n of_o minute_n in_o the_o long_a and_o short_a day_n by_o 12_o viz._n divide_v 986_o the_o minute_n in_o one_o day_n in_o ♋_o at_o london_n by_z 12_o the_o quotient_n be_v 82_o ½_o and_o divide_v 454_o the_o number_n of_o minute_n in_o one_o day_n at_o london_n in_o ♑_o and_o the_o quotient_n shall_v be_v 37′_n ¾_n then_o if_o you_o fasten_v a_o index_n or_o lay_v a_o rule_n to_o the_o centre_n and_o to_o every_o 1_o hour_n and_o 22′_n ½_o in_o ♋_o from_o 12_o and_o to_o every_o 37′_n ¾_n in_o ♑_o it_o shall_v give_v point_n to_o draw_v the_o jewish_a or_o planetary_a hour_n require_v according_a to_o this_o table_n thus_o make_v for_o london_n by_o the_o line_n of_o number_n against_o 12_o set_n 6_o and_o the_o rest_n in_o order_n as_o the_o day_n proceed_v for_o our_o 12_o be_v the_o 6_o hour_n according_a to_o the_o jew_n to_o make_v this_o table_n ready_o by_o the_o line_n of_o number_n a_o table_n to_o divide_v the_o planetary_a hour_n in_o ♋_o and_o in_o ♑_o for_o london_n 51-32_a latitude_n h_o ♑_o m_o how_o h_o ♋_o m_o 8_o 43_o 1_o 5_o 10_o 9_o 28_o 2_o 6_o 31_o 10_o 16_o 3_o 7_o 52_o 10_o 44_o 4_o 9_o 15_o 11_o 22_o 5_o 10_o 37_o 12_o 00_o 6_o 12_o 00_o 12_o 37_o 7_o 1_o 22_o 1_o 15_o 8_o 2_o 44_o 1_o 53_o 9_o 4_o 06_o 2_o 31_o 10_o 5_o 29_o 3_o 8_o 11_o 6_o 51_o 3_o 47_o 12_o 8_o 13_o extend_v the_o compass_n from_o 16-26_a the_o length_n of_o the_o long_a day_n in_o hour_n and_o minute_n to_o 1_o the_o same_o extent_n shall_v reach_v the_o contrary_a way_n from_o 60_o to_o 986_o the_o number_n of_o minute_n in_o one_o day_n or_o rather_o as_o 1_o hour_n to_o 60_o minute_n so_o be_v 16_o hour_n 26′_n to_o 986_o minute_n then_o as_o 1_o to_o 82_o minute_n ¼_n so_o be_v 2_o to_o 164_o minute_n ½_o so_o be_v 3_o to_o 246_o minute_n ¾_n or_o you_o may_v say_v as_o 12_o to_z 1_o so_o be_v 986_o to_o 82-2_a the_o minute_n in_o 1_o hour_n which_o proper_o be_v one_o hour_n 22_o minute_n the_o length_n of_o one_o hour_n in_o cancer_n then_o the_o second_o hour_n be_v 2_o hour_n 44_o ½_o the_o three_o hour_n be_v 4_o hour_n and_o 6′_n ¾_n from_o 12_o and_o so_o for_o the_o rest_n as_o in_o the_o forego_n table_n for_o london_n but_o if_o you_o draw_v the_o parallel_n of_o
horologiographia_fw-la or_o the_o art_n of_o dyall_v be_v the_o second_o book_n of_o the_o use_n of_o the_o trianguler-quadrant_n show_v the_o natural_a artificial_a and_o instrumental_a way_n of_o make_v of_o sun-dials_n on_o any_o flat_a superficies_n with_o plain_a and_o easy_a direction_n to_o discover_v their_o nature_n and_o affection_n by_o the_o horizontal_a projection_n with_o the_o way_n of_o draw_v the_o usual_a ornament_n on_o any_o plain_n also_o a_o familiar_a easy_a way_n to_o draw_v those_o line_n on_o the_o ceiling_n of_o a_o room_n by_o the_o triangule_a quadrant_n also_o the_o use_n of_o the_o same_o instrument_n in_o navigation_n both_o for_o observation_n and_o operation_n perform_v the_o use_n of_o several_a sea-instrument_n still_o in_o use_n by_o john_n brown_n philomath_n london_n print_v by_o john_n derby_n for_o john_n wingfield_n and_o be_v to_o be_v sell_v at_o his_o house_n in_o crutched-fryer_n and_o by_o john_n brown_a at_o the_o sphere_n and_o sundial_n in_o the_o minory_n and_o by_o john_n seller_n at_o the_o hermitage-stair_n in_o wapping_n 1671._o to_o the_o courteous_a reader_n thou_o have_v here_o present_v to_o thy_o view_n courteous_a reader_n in_o this_o second_o part_n a_o plain_a discourse_n of_o dial_v both_o natural_a artificial_a &_o instrumental_a natural_a i_o call_v it_o from_o the_o plain_a illustration_n thereof_o by_o the_o armilary_n sphere_n of_o brass_n herein_o describe_v or_o by_o the_o poor-man_n dial-sphear_n as_o i_o fancy_n to_o call_v it_o be_v only_o a_o move_a horizontal-dial_n and_o a_o move_a plain_n according_a to_o the_o figure_n thereof_o in_o the_o book_n annex_v whereby_o all_o the_o ark_n angle_n situation_n and_o affection_n be_v very_o plain_o represent_v to_o a_o ordinary_a capacity_n artificial_a i_o call_v it_o from_o the_o lively_a delineation_n of_o the_o horizontal-projection_n the_o fit_a in_o my_o opinion_n for_o the_o make_v plain_o the_o mystery_n of_o dial_v instrumental_a i_o call_v it_o from_o the_o apply_v of_o the_o trianguler-quadrant_n to_o the_o ready_a resolve_v all_o the_o arithmetical_a and_o astronomical_a work_n needful_a thereunto_o and_o that_o to_o competent_a exactness_n as_o in_o the_o first_o part_n and_o also_o in_o this_o second_o part_n be_v sufficient_o see_v in_o find_v the_o requisite_n and_o delineat_v the_o hour-line_n to_o small_a part_n exact_o &_o speedy_o by_o the_o natural_a sin_n tangent_n and_o secant_v on_o the_o sector_n and_o quadrant_n also_o the_o ready_a way_n of_o find_v the_o sun_n altitude_n hour_n azimuth_n angle_n of_o the_o plain_a and_o any_o such_o business_n relate_v to_o dyall_v as_o in_o the_o first_o part_n be_v large_o treat_v on_o further_o in_o this_o second_o part_n you_o have_v table_n of_o the_o sun_n declination_n to_o every_o day_n of_o the_o year_n 1_o 2_o &_o 3_o after_o the_o bissextile_a as_o near_o as_o any_o extent_n also_o a_o short_a but_o plain_a direction_n how_o to_o use_v the_o trianguler-quadrant_n at_o any_o manner_n of_o way_n of_o observation_n use_v at_o sea_n as_o backward_o or_o forward_o as_o the_o davis-quadrant_n and_o the_o cross-staff_n be_v use_v also_o as_o gunter_n bow_n be_v use_v both_o for_o the_o sun_n or_o star_n a_o figure_n of_o the_o stereographick_a projection_n pag_n â—_o the_o print_n of_o the_o line_n of_o number_n as_o you_o see_v here_o insert_v be_v in_o part_n according_a to_o mr._n windgates_n as_o to_o a_o single_a and_o break_a line_n of_o number_n but_o the_o addition_n of_o the_o line_n of_o the_o fractional_a part_n of_o a_o pound_n and_o the_o several_a gage-point_n be_v never_o before_o use_v as_o i_o know_v of_o but_o do_v much_o ease_n &_o expedite_v the_o operation_n by_o the_o line_n of_o number_n sin_n and_o tangent_n also_o these_o scale_n of_o reduction_n be_v convenient_a for_o the_o find_v the_o decimal-fraction_n equal_a to_o the_o other_o sexagenary-fraction_n and_o be_v agreeable_a to_o those_o table_n in_o mr._n windgates_n book_n of_o arithmetic_n pag._n 82._o also_o note_n that_o the_o figure_n of_o the_o rule_n at_o the_o begin_n of_o the_o book_n past_v on_o a_o board_n be_v the_o very_a same_o with_o that_o speak_v of_o chap._n xv._n use_v 28._o pag._n 397_o of_o the_o first_o part_n and_o will_v work_v all_o question_n wrought_v by_o the_o trianguler-quadrant_n to_o exercise_v they_o that_o be_v out_o of_o the_o way_n to_o have_v they_o make_v and_o may_v serve_v as_o good_a direction_n to_o the_o young_a instrument-maker_n though_o these_o be_v make_v too_o too_o small_a a_o radius_fw-la to_o arrive_v at_o exactness_n the_o like_a may_v i_o say_v of_o the_o gunters-line_n in_o the_o figure_n annex_v yet_o as_o large_a as_o the_o book_n will_v bear_v thus_o i_o have_v give_v you_o a_o brief_a account_n of_o my_o present_a thought_n about_o this_o matter_n and_o somewhat_o more_o particular_o in_o the_o first_o part_n disclaim_v all_o boast_n or_o vain_a ostentation_n know_v that_o at_o the_o next_o impression_n it_o may_v be_v amend_v in_o many_o place_n i_o shall_v rest_v and_o remain_v ready_a to_o make_v amends_o in_o the_o make_n of_o these_o or_o any_o other_o mathematical_a instrument_n at_o my_o house_n at_o the_o sphere_n and_o sundial_n in_o the_o great_a minories_n john_n browne_n february_n 16._o 1670._o chap._n i._n the_o use_n of_o the_o triangule_a quadrant_n in_o make_v of_o dial_n svn-dials_n may_v be_v make_v on_o any_o plain_a and_o all_o kind_n of_o plain_n be_v either_o flat_a as_o horizontal_a or_o upright_o or_o lean_v the_o horizontal_a have_v two_o face_n the_o one_o behold_v the_o zenith_n call_v the_o horizontal-plain_a the_o other_o behold_v the_o nadir_n as_o the_o ceiling_n of_o a_o room_n be_v the_o upright_a plain_n be_v those_o that_o make_v right_a angle_n with_o the_o horizon_n and_o do_v behold_v neither_o the_o zenith_n or_o nadir_n but_o be_v parallel_n to_o they_o the_o lean_v plain_n be_v of_o two_o sort_n general_o the_o one_o call_v recliner_n behold_v the_o zenith_n the_o other_o sort_n call_v incliner_n behold_v the_o nadir_n as_o the_o outside_n and_o inside_n of_o a_o roof_n of_o a_o house_n may_v represent_v the_o two_o last_o sort_n viz._n upright_a and_o lean_v may_v be_v direct_a or_o decline_a viz._n behold_v the_o south_n or_o north_n or_o east_n or_o west_n point_v of_o the_o horizon_n or_o decline_a therefrom_o viz._n decline_a from_o south_n or_o north_n towards_o the_o east_n or_o west_n all_o which_o plain_n be_v lively_o represent_v by_o a_o sphere_n make_v for_o that_o purpose_n in_o brass_n or_o pasteboard_n or_o by_o the_o projection_n of_o the_o sphere_n in_o plano_n thus_o equal_a to_o the_o radius_fw-la of_o the_o small_a tangent_n describe_v the_o circle_n eswn_n represent_v the_o horizon_n cross_v it_o precise_o in_o the_o the_o centre_n z_o with_o the_o line_n sn_a and_o ewe_n denote_v the_o point_n of_o south_n and_o north_n east_n and_o west_n then_o count_v the_o small_a tangent_fw-la on_o the_o sector-side_n double_o as_o thus_o call_z 5_o 10_o &_o 10_o 20_o &_o 20_o 40_o &_o 30_o 60_o &_o 40_o 80_o &_o 45_o 90_o etc._n etc._n lay_v off_o from_o z_o towards_o saint_n the_o compliment_n of_o the_o sun_n meridian_n altitude_n in_o ♋_o in_o ♈_o and_o ♑_o for_o those_o point_n on_o the_o meridian-line_n between_o z_o and_o s_o and_o consequent_o the_o half_a tangent_fw-la of_o the_o compliment_n of_o the_o sun_n meridian_n altitude_n in_o every_o degree_n of_o declination_n if_o you_o proceed_v so_o far_o then_o for_o the_o intersection_n of_o all_o those_o line_n and_o parallel_n of_o declination_n on_o the_o north-side_n of_o the_o meridian_n observe_v that_o the_o same_o number_n of_o degree_n and_o minute_n that_o any_o point_n be_v above_o the_o horizon_n on_o the_o south_n part_n of_o the_o meridian_n in_o summer_n just_o so_o many_o degree_n and_o minute_n be_v his_o opposite_a parallel_n in_o winter_n below_o the_o horizon_n as_o thus_o for_o example_n the_o sun_n be_v in_o ♋_o or_o 23_o deg_n 31_o min._n of_o declination_n north_n have_v for_o his_o meridian_n altitude_n 62_o degree_n and_o so_o many_o degree_n be_v his_o opposite_a parallel_n of_o 23-31_a or_o ♑_o below_o the_o north_n part_n of_o the_o horizon_n at_o midnight_n as_o thus_o let_v the_o centre_n at_o the_o begin_n of_o the_o line_n of_o tangent_n represent_v the_o centre_n z_o and_o let_v the_o tangent_fw-la of_o 45_o represent_v the_o horizon_n in_o the_o scheam_n viz._n s._n and_o n._n then_o as_o the_o distance_n from_o s._n to_o ♑_o be_v 15_o deg_n take_v from_o 45_o towards_o 0_o and_o lay_v from_o s._n to_o ♑_o inward_o towards_o the_o centre_n z_o as_o the_o distance_n be_v take_v from_o the_o tangent_fw-la of_o 45_o towards_o the_o begin_n of_o the_o line_n of_o tangent_n that_o represent_v the_o centre_n so_o the_o point_n cancer_n from_o n._n
sector_n be_v set_v to_o the_o small_a tangent_fw-la and_o by_o turn_v 4_o time_n you_o have_v the_o remainder_n of_o the_o great_a tangent_fw-la above_o 45_o when_o the_o sector_n be_v set_v to_o the_o great_a line_n of_o 45_o as_o in_o the_o polar_a dial._n or_o else_o alter_v the_o sector_n to_o the_o radius_fw-la of_o 45_o in_o the_o great_a tangent_fw-la that_o go_v but_o to_o 45_o and_o take_v out_o the_o =_o tangent_n of_o 30_o and_o lay_v it_o from_o 6_o both_o way_n for_o 4_o &_o 8_o and_o the_o =_o tangent_fw-la of_o 15_o and_o lay_v it_o from_o 6_o both_o way_n for_o 7_o &_o 5._o and_o last_o by_o all_o those_o point_n draw_v line_n =_o to_o 6_o for_o the_o hour-line_n require_v and_o number_v the_o east-dial_n with_o the_o morning-hour_n and_o the_o west_n with_o the_o afternoon-hour_n the_o style_n be_v to_o be_v a_o plate_n or_o a_o upright_a point_n the_o top_n of_o who_o edge_n or_o point_n be_v to_o be_v equal_a to_o the_o tangent_fw-la of_o 45_o as_o the_o sector_n stand_v to_o prick_v down_o the_o hour-line_n 4._o to_o draw_v the_o horizontal-plain_a the_o four_o plain_n next_o in_o a_o natural_a order_n of_o easiness_n to_o apprehend_v as_o i_o judge_v be_v the_o horizontal_a dial_n that_o lie_v with_o its_o plain_a =_o to_o the_o horizon_n and_o the_o zenith_n be_v the_o pole_n thereof_o represent_v by_o the_o primitive_a circle_n s.n.e.w._n in_o the_o general_a scheam_n wherein_o only_o the_o hour_n ark_n and_o style_n be_v require_v the_o style_n elevation_n be_v always_o equal_a to_o the_o latitude_n and_o therefore_o give_v the_o substile_a be_v always_o in_o the_o hour_n 12_o be_v the_o meridian-line_n the_o hour-line_n be_v find_v by_o this_o general_a canon_n as_o the_o sine_fw-la of_o 90_o the_o right_a angle_n pn_n 1_o general-scheam_a to_o the_o sine_fw-la of_o pn_n a_o side_n always_o equal_a to_o the_o latitude_n or_o style_n elevation_n 51-30_a so_o be_v the_o tangent_fw-la of_o the_o angle_n np_n 1_o 15_o or_o np_v 2_o 30_o etc._n etc._n the_o angle_n at_o the_o pole_n to_o the_o tangent_fw-la of_o n_o 1_o a_o side_n or_o n_o 2_o a_o second_o side_n the_o several_a hour-arks_a on_o the_o plain_a require_v find_v by_o the_o artificial_a sin_n and_o tangent_n as_o fast_o as_o one_o can_v write_v they_o down_o thus_o the_o extent_n of_o the_o compass_n from_o the_o sine_fw-la of_o 90_o the_o sine_fw-la of_o the_o latitude_n 51-30_a be_v lay_v the_o same_o way_n from_o the_o tangent_fw-la of_o 15_o shall_v reach_v to_o the_o tangent_fw-la of_o 11-50_a and_o if_o you_o turn_v the_o compass_n the_o other_o way_n from_o the_o tangent_fw-la of_o 15_o it_o shall_v give_v the_o tangent_fw-la of_o 71-6_a for_o the_o hour_n of_o 5_o as_o well_o as_o 11_o which_o number_n be_v gather_v into_o a_o table_n and_o lay_v off_o by_o chord_n or_o sin_n in_o a_o semicircle_n shall_v be_v the_o true_a hour-point_n to_o draw_v the_o line_n by_o but_o i_o shall_v not_o insist_v further_o thereon_o but_o show_v how_o to_o draw_v it_o more_o ready_o and_o as_o true_o by_o the_o sector_n thus_o first_o draw_v a_o straight_a line_n in_o the_o meridian_n if_o the_o plain_n be_v fix_v for_o 12_o as_o the_o line_n ab_fw-la then_o design_v a_o point_n in_o that_o line_n to_o serve_v for_o a_o centre_n as_o at_o c_o then_o on_o the_o centre_n c_o erect_v a_o perpendiculer-line_n to_o ab_fw-la and_o draw_v it_o through_o the_o centre_n c_o for_o the_o two_o 6_o a_o clock_n hour-line_n as_o the_o line_n de_fw-fr then_o draw_v two_o line_n equal_o distant_a from_o and_o =_o to_o the_o first_o line_n ab_fw-la on_o either_o side_n as_o large_a as_o the_o plain_n will_v give_v leave_n as_o df_n and_o eglantine_n which_o may_v common_o serve_v for_o margin_n to_o put_v the_o figure_n in_o then_o take_v the_o distance_n cd_o and_o make_v it_o a_o =_o secant_fw-la of_o 00_o and_o take_v out_o the_o =_o secant_fw-la of_o the_o compliment_n of_o the_o latitude_n and_o lay_v it_o from_o d_o to_o f_o and_o from_o e_z to_z g_z on_o the_o two_o parallel-line_n and_o draw_v the_o line_n fg._n then_o last_o for_o prick_v down_o the_o style_n note_v that_o the_o =_o tangent_fw-la of_o 38-30_a the_o compliment_n of_o the_o latitude_n as_o the_o sector_n stand_v for_o the_o noon_n hour_n lay_v from_o d_o to_o h_n gives_z a_o point_n to_o draw_v it_o true_o by_o or_o the_o sine_fw-la of_o 51-30_a the_o latitude_n lay_v from_o b_o at_o near_a distance_n about_o h_n as_o the_o sector_n stand_v for_o the_o morning-hour_n will_v do_v as_o well_o the_o style_n be_v to_o be_v a_o plate_n or_o a_o bend_a wire_n cut_v or_o bend_a according_a to_o the_o angle_n hcb_n and_o erect_v perpendicular_o on_o the_o line_n 12_o so_o long_o as_o the_o sun_n be_v 62_o degree_n high_a may_v cause_v the_o shadow_n thereof_o to_o reach_v the_o hour_n of_o 12_o and_o then_o set_v due_o north_n &_o south_n and_o horizontal_a the_o shadow_n will_v show_v the_o true_a hour_n of_o the_o day_n note_v the_o figure_n note_v also_o that_o a_o horizontal_a dial_n draw_v for_o any_o one_o latitude_n may_v serve_v for_o any_o other_o latitude_n north_n or_o south_n elevate_a or_o depress_v the_o style_n till_o it_o look_v to_o the_o pole-point_n that_o be_v by_o make_v it_o to_o recline_v northward_o or_o southward_o as_o much_o as_o the_o difference_n of_o the_o latitude_n viz._n that_o the_o dial_n be_v make_v for_o and_o that_o wherein_o it_o be_v to_o be_v use_v shall_v be_v 5._o to_o draw_v a_o north_n or_o south_n plain_a the_o next_o plain_n to_o this_o and_o most_o like_o it_o be_v the_o direct_a north_n and_o south_n dial_n who_o plain_a lie_n =_o to_o the_o prime_n virtical_a or_o circle_n of_o east_n and_o west_n and_o its_o pole_n in_o the_o south_n and_o north_n part_n of_o the_o horizon_n and_o represent_v by_o the_o line_n ezw_n in_o the_o general_a scheam_n who_o style_n be_v always_o equal_a to_o the_o compliment_n of_o the_o latitude_n as_o the_o horizontal_n be_v equal_a to_o the_o latitude_n and_o consequent_o give_v the_o hour_n ark_v on_o the_o plain_a be_v find_v by_o the_o former_a canon_n viz._n as_o the_o sine_fw-la of_o 90_o viz._n the_o angle_n pze_v be_v to_o the_o sine_fw-la of_o the_o side_n pz_n the_o co-latitude_n or_o style_n elevation_n the_o ark_n on_o the_o plain_a find_v as_o before_o by_o artificial_a sin_n and_o tangent_n and_o be_v draw_v into_o a_o table_n to_o be_v lay_v off_o by_o chord_n or_o sines_n or_o by_o the_o sector_n thus_o draw_v a_o perpendiculer-line_n for_o the_o substile_a or_o 12_o a_o clock_n line_n and_o in_o that_o line_n design_v a_o point_n for_o a_o centre_n as_o the_o point_n a_o in_o the_o line_n ab_fw-la through_o which_o point_n a_o draw_v another_o line_n cross_v the_o former_a at_o right_a angle_n for_o a_o horizontal-line_n and_o the_o two_o six_o as_o you_o do_v in_o the_o horizontal_a then_o on_o each_o side_n and_o equi-distant_a from_o 12_o make_v two_o line_n =_o to_o ab_fw-la as_o marginal-line_n as_o cf_n and_o de_fw-fr the_o distance_n ad_fw-la of_o the_o parallel_n make_v a_o =_o secant_fw-la of_o 00_o and_o take_v out_o the_o =_o secant_fw-la of_o 51-30_a the_o latitude_n of_o the_o place_n and_o lay_v it_o from_o c_o to_o f_o and_o from_o d_o to_z e_z and_o draw_v the_o line_n fe_o then_o make_v df_n a_o tangent_fw-la of_o 45_o and_o lay_v off_o the_o hour_n and_o quarter_n as_o you_o do_v in_o the_o horizontal_a in_o all_o respect_n also_o make_v bf_o a_o =_o tangent_fw-la of_o 45_o and_o lay_v off_o the_o =_o tangent_n of_o every_o hour_n and_o quarter_n if_o you_o please_v from_o b_o both_o way_n toward_z e_z and_o f_o and_o by_o those_o point_n draw_v line_n for_o the_o hour_n require_v the_o angle_n of_o the_o style_n may_v be_v lay_v off_o by_o sines_n tangent_n or_o chord_n as_o before_o be_v show_v to_o the_o quantity_n of_o the_o compliment_n of_o the_o latitude_n and_o may_v be_v a_o plate_n or_o wyre_n as_o you_o please_v as_o the_o angle_n gab._n the_o north_n dial_n be_v the_o same_o with_o the_o south_n for_o manner_n of_o make_v only_o the_o noon-hour_n be_v neglect_v and_o the_o morning_n and_o evening-hour_n both_o before_o and_o after_o 6_o on_o each_o side_n only_o insert_v and_o the_o centre_n of_o the_o dial_n for_o that_o cause_n appoint_v in_o the_o middle_n of_o the_o plain_a and_o not_o on_o the_o upper-part_n as_o in_o the_o south_n and_o the_o stile-point_n upward_o as_o in_o the_o south_n it_o point_v downward_o note_v the_o figure_n 6._o to_o draw_v the_o hour_n on_o a_o direct_a recliner_n the_o next_o plain_n to_o be_v consider_v be_v also_o direct_v but_o not_o erect_a or_o upright_o but_o lean_v from_o
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 oâ—_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
if_o you_o please_v shall_v give_v point_n enough_o to_o draw_v the_o dial_n and_o also_o the_o tropic_n and_o azimuth_n and_o altitude_n also_o if_o it_o be_v convenient_a to_o mark_v it_o or_o to_o any_o other_o altitude_n you_o mind_n to_o have_v at_o that_o azimuth_n all_o at_o once_o or_o at_o most_o with_o two_o slip_n of_o the_o thread_n the_o italian_a babylonish_n or_o jewish-hour_n as_o easy_o draw_v by_o point_n find_v in_o the_o other_o line_n also_o on_o the_o meridian-line_n you_o may_v add_v the_o day_n of_o the_o month_n or_o any_o thing_n that_o depend_v on_o the_o sun_n meridian_n altitude_n which_o work_n be_v well_o do_v and_o draw_v with_o smooth_a line_n and_o well_o ornament_v will_v be_v a_o comely_a &_o pleasant_a ornament_n to_o a_o ceiling_n and_o far_o cheap_a than_o some_o fret_v ceiling_n be_v do_v and_o more_o useful_a last_o when_o all_o be_v do_v to_o put_v the_o glass_n in_o right_n the_o foil_n be_v first_o rub_v off_o to_o to_o cause_v it_o to_o give_v but_o one_o spot_n let_v the_o superficies_n of_o the_o glass_n lie_v just_a so_o high_a as_o the_o centre_n of_o the_o quadrant_n be_v in_o the_o draw_v the_o line_n and_o put_v some_o putty_n under_o it_o and_o the_o sun_n shine_v make_v it_o to_o play_v right_a on_o the_o true_a hour_n altitude_n and_o azimuth_n or_o if_o it_o be_v just_a at_o noon_n then_o bend_v it_o on_o the_o putty_n with_o your_o finger_n till_o it_o fall_v just_a on_o the_o meridian_n and_o day_n of_o the_o month_n also_o in_o the_o meridian-line_n also_o note_n that_o look_v what_o altitude_n the_o sun_n have_v at_o any_o time_n the_o same_o will_v the_o reflect_a altitude_n be_v at_o the_o same_o time_n if_o the_o glass_n lie_v true_a which_o two_o observator_n at_o the_o same_o time_n may_v carful_o prove_v the_o make_n of_o the_o table_n of_o the_o sun_n altitude_n and_o azimuth_n be_v very_o large_o show_v in_o the_o 15_o chapter_n use_v the_o 37th_o and_o 38th_o where_o you_o have_v way_n both_o general_a and_o particular_a for_o any_o one_o or_o more_o latitude_n the_o figure_n explain_v a_o the_o place_n on_o the_o transum_fw-la for_o the_o glass_n to_o lie_v on_o and_o in_o the_o midst_n thereof_o one_o point_n in_o the_o ray_n of_o the_o quadrant_n be_v to_o play_v ih_o a_o piece_n of_o wood_n to_o be_v nail_v fast_o at_o h_n and_o i_o for_o the_o other_o point_n to_o play_v in_o at_o g_o l_o the_o hole_n for_o the_o plummet_n to_o play_v in_o be_v cut_v through_o the_o thin_a quadrant_n b_o and_o c_z the_o end_n of_o the_o semicircle_n nail_v on_o the_o transum_fw-la or_o stool_n k_o the_o hole_n in_o the_o quadrant_n for_o the_o semi-circular-ring_n to_o pass_v through_o fe_o the_o post_n of_o the_o window_n d_o the_o beginning_n of_o the_o degree_n on_o the_o semicircle_n be_o a_o thread_n extend_v from_o the_o centre_n of_o the_o quadrant_n to_o the_o ceiling_n thus_o you_o have_v the_o usual_a way_n of_o dial_v in_o a_o competent_a measure_n plain_o and_o practical_o handle_v which_o may_v be_v useful_a to_o many_o a_o learner_n and_o i_o hope_v will_v be_v as_o well_o accept_v as_o with_o freewill_n though_o with_o little_a ability_n and_o less_o leisure_n ready_o impart_v a_o table_n of_o the_o sun_n azimuth_n from_o the_o south_n at_o every_o hour_n and_o quarter_n 51-32_a  _fw-fr ♋_o ♊_o ♌_o ♉_o â™_o ♈_o ♎_o ♓_o â™_o â™’_o â™_o ♑_o  _fw-fr d._n m._n d._n m._n d._n m_o d._n m_o d._n m_o d._n m_o d._n m_o 12_o 00_o 00_o 00_o 00_o 00_o 00_o 00_o 00_o 00_o 00_o 00_o 00_o 00_o 00_o  _fw-fr 07_o 10_o 05_o 53_o 5_o 37_o 4_o 55_o 03_o 54_o 03_o 53_o 3_o 52_o  _fw-fr 14_o 22_o 13_o 24_o 11_o 10_o 9_o 40_o 07_o 57_o 07_o 40_o 7_o 10_o  _fw-fr 21_o 27_o 19_o 53_o 16_o 44_o 14_o 13_o 12_o 11_o 11_o 10_o 10_o 37_o 11_o 1_o 27_o 54_o 26_o 00_o 22_o 13_o 18_o 52_o 16_o 22_o 14_o 45_o 14_o 13_o  _fw-fr 34_o 14_o 32_o 01_o 27_o 32_o 23_o 22_o 20_o 15_o 18_o 17_o 17_o 38_o  _fw-fr 40_o 12_o 37_o 40_o 32_o 41_o 27_o 41_o 24_o 06_o 21_o 53_o 20_o 59_o  _fw-fr 45_o 39_o 43_o 04_o 37_o 32_o 32_o 08_o 29_o 44_o 26_o 30_o 24_o 25_o 10_o 2_o 50_o 51_o 47_o 57_o 42_o 05_o 36_o 24_o 31_o 50_o 28_o 52_o 27_o 49_o  _fw-fr 55_o 31_o 52_o 41_o 47_o 04_o 40_o 30_o 35_o 35_o 32_o 18_o 31_o 00_o  _fw-fr 61_o 43_o 57_o 11_o 50_o 51_o 44_o 26_o 39_o 10_o 35_o 39_o 34_o 17_o  _fw-fr 64_o 11_o 61_o 18_o 54_o 33_o 48_o 13_o 42_o 36_o 38_o 50_o 37_o 34_o 9_o 3_o 68_o 10_o 65_o 16_o 58_o 47_o 51_o 56_o 46_o 02_o 42_o 04_o 40_o 36_o  _fw-fr 71_o 52_o 69_o 56_o 62_o 33_o 55_o 33_o 49_o 25_o 45_o 16_o 43_o 40_o  _fw-fr 75_o 26_o 72_o 37_o 66_o 10_o 58_o 59_o 52_o 43_o 48_o 21_o 46_o 42_o  _fw-fr 78_o 48_o 76_o 05_o 69_o 38_o 62_o 22_o 55_o 55_o 51_o 22_o 49_o 40_o 8_o 4_o 82_o 00_o 79_o 20_o 72_o 57_o 65_o 40_o 59_o 00_o 54_o 22_o  _fw-fr  _fw-fr 85_o 08_o 82_o 42_o 76_o 12_o 68_o 53_o 62_o 08_o  _fw-fr  _fw-fr  _fw-fr 88_o 10_o 85_o 38_o 79_o 23_o 72_o 06_o 65_o 12_o  _fw-fr  _fw-fr  _fw-fr 91_o 09_o 87_o 50_o 82_o 28_o 75_o 03_o 68_o 12_o  _fw-fr  _fw-fr 7_o 5_o 94_o 05_o 91_o 34_o 85_o 30_o 78_o 06_o 71_o 10_o  _fw-fr  _fw-fr  _fw-fr 96_o 51_o 94_o 25_o 88_o 27_o 81_o 09_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 99_o 38_o 97_o 16_o 91_o 25_o 84_o 06_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 102_o 25_o 100_o 07_o 94_o 22_o 87_o 04_o  _fw-fr  _fw-fr  _fw-fr 6_o 6_o 105_o 08_o 102_o 54_o 97_o 12_o 90_o 00_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 107_o 52_o 104_o 58_o 100_o 02_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 110_o 36_o 108_o 26_o 103_o 00_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 113_o 18_o 111_o 14_o 105_o 54_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 5_o 7_o 116_o 03_o 114_o 03_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 118_o 50_o 116_o 54_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 121_o 41_o 119_o 47_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 124_o 29_o 122_o 37_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 4_o 8_o 127_o 24_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 130_o 28_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr a_o table_n of_o the_o sun_n altitude_n at_o every_o hour_n and_o quarter_n in_o each_o sign_n for_o 51-32_a  _fw-fr ♋_o ♊_o ♌_o ♉_o â™_o ♈_o ♎_o ♓_o â™_o â™’_o â™_o ♑_o  _fw-fr d._n m_o d._n m_o d._n m_o d._n m_o d._n m_o d._n m_o d._n m_o 12_o 62_o 90_o 58_o 42_o 50_o 00_o 38_o 28_o 27_o 00_o 18_o 18_o 14_o 59_o  _fw-fr 61_o 50_o 58_o 34_o 49_o 52_o 38_o 24_o 26_o 54_o 18_o 13_o 14_o 55_o  _fw-fr 61_o 25_o 58_o 09_o 49_o 31_o 38_o 07_o 26_o 40_o 18_o 00_o 14_o 38_o  _fw-fr 60_o 41_o 57_o 29_o 49_o 00_o 37_o 38_o 26_o 15_o 17_o 37_o 14_o 20_o 11_o 59_o 43_o 56_o 34_o 48_o 12_o 36_o 58_o 25_o 40_o 17_o 06_o 13_o 52_o  _fw-fr 58_o 32_o 55_o 26_o 47_o 10_o 36_o 07_o 24_o 02_o 16_o 26_o 13_o 10_o  _fw-fr 57_o 04_o 54_o 06_o 46_o 02_o 35_o 06_o 23_o 59_o 15_o 38_o 12_o 35_o  _fw-fr 55_o 29_o 52_o 36_o 44_o 38_o 33_o 56_o 22_o 58_o 14_o 49_o 11_o 30_o 10_o 53_o 45_o 50_o 55_o 43_o 12_o 32_o 37_o 21_o 51_o 13_o 38_o 10_o 36_o  _fw-fr 51_o 52_o 49_o 07_o 41_o 33_o 31_o 10_o 20_o 33_o 12_o 27_o 9_o 20_o  _fw-fr 49_o 54_o 47_o 12_o 39_o 46_o 29_o 36_o 19_o 10_o 11_o 09_o 8_o 9_o  _fw-fr 47_o 50_o 45_o 12_o 37_o 56_o 27_o 54_o 17_o 35_o 9_o 44_o 6_o 41_o 9_o 45_o 42_o 43_o 06_o 36_o 00_o 26_o 07_o 15_o 58_o 8_o 13_o 5_o 16_o  _fw-fr 43_o 30_o 40_o 57_o 33_o 55_o 24_o 14_o 14_o 14_o 9_o 49_o 3_o 41_o  _fw-fr 41_o 16_o 38_o 45_o 31_o 50_o 22_o 16_o 12_o 27_o 4_o 54_o 2_o 04_o  _fw-fr 39_o 00_o 36_o 30_o 29_o 40_o 20_o 14_o 10_o 32_o 3_o 07_o 0_o 17_o 8_o 36_o 41_o 34_o 13_o 27_o 31_o 18_o 08_o 8_o 35_o 1_o 15_o  _fw-fr  _fw-fr 34_o 22_o 31_o 55_o 25_o 09_o 15_o 59_o 6_o 30_o  _fw-fr  _fw-fr  _fw-fr 32_o 02_o 29_o 13_o 22_o 56_o 13_o 46_o 4_o 27_o  _fw-fr  _fw-fr  _fw-fr 29_o 42_o 27_o 16_o 20_o 37_o 11_o 33_o 2_o 17_o  _fw-fr  _fw-fr 7_o 27_o 23_o 24_o 56_o 18_o 18_o 09_o 17_o 0_o 06_o  _fw-fr  _fw-fr  _fw-fr 25_o 03_o 22_o 36_o 15_o 58_o 06_o 58_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 22_o 45_o 20_o 16_o 13_o 38_o 04_o 40_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 20_o 28_o 17_o 58_o 11_o 18_o 02_o 20_o  _fw-fr  _fw-fr  _fw-fr 6_o 18_o 11_o 15_o 41_o 09_o 00_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 â—â—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 compleâ—ment_n thereof_o and_o to_o be_v call_v the_o upper_a semicircle_n or_o circle_n always_o perpendicuâ—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 â—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 â™_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
the_o equinoctial_a stand_v for_o 51-30_a latitude_n and_o the_o account_n will_v end_v at_o 62_o degree_n the_o sun_n meridian_n altitude_n at_o that_o declination_n northwards_o but_o if_o it_o have_v be_v 23-30_a south_n declination_n then_o count_v as_o much_o from_o the_o equinoctial_a downward_o and_o the_o count_n will_v end_v at_o 15_o degree_n for_o the_o sun_n meridian_n altitude_n at_o 23-30_a south_n declination_n use_v v._o the_o sun_n declination_n and_o latitude_n be_v give_v to_o find_v the_o sun_n rise_v or_o set_v and_o amplitude_n east_n or_o west_n count_n the_o sun_n declination_n on_o the_o hour-circle_n towards_o his_o proper_a pole_n that_o be_v south-declination_n towards_o the_o south-pole_n and_o north-declination_n towards_o the_o north-pole_n and_o thereunto_o lie_v the_o thread_n that_o be_v fasten_v in_o the_o centre_n then_o bring_v the_o hour-circle_n and_o thread_n both_o together_o till_o the_o thread_n touch_v the_o horizon_n then_o the_o thread_n on_o the_o horizon_n show_v the_o amplitude_n and_o the_o divided-side_n of_o the_o hour-circle_n show_v the_o sun_n rise_v and_o set_v on_o the_o equinoctial_a count_v the_o meridian_n always_o 12_o and_o the_o 2_o east_n and_o west-point_n 6_o and_o 15_o degr_n for_o a_o hour_n and_o every_o deg_n 4_o min._n example_n june_n 11._o declination_n 23-30_a the_o sun_n rise_v at_o 13′_n before_o 4_o and_o the_o amplitude_n be_v near_o 40_o deg_n again_o april_n 10._o declination_n 11-30_a the_o amplitude_n be_v 18-30_a from_o the_o east_n to_o the_o north_n and_o rise_v at_o 5_o the_o hour-circle_n cut_v 15_o degree_n on_o the_o equinoctial_a use_v vi_o the_o declination_n &_o latitude_n &_o sun_n altitude_n give_v to_o find_v both_o hour_n &_o azimuth_n rectify_v the_o sphere_n and_o set_v the_o plain_a horizontal_a that_o be_v level_v or_o parallel_v to_o the_o horizon_n then_o apply_v the_o thread_n to_o the_o declination_n count_v the_o right_a way_n on_o the_o hour-circle_n then_o turn_v the_o hour-circle_n and_o upper_a semicircle_n about_o till_o the_o thread_n cut_v the_o degree_n of_o altitude_n in_o the_o upper_a semicircle_n and_o the_o hour-circle_n show_v the_o hour_n in_o the_o equinoctial_a and_o the_o semicircle_n cut_v the_o sun_n azimuth_n in_o the_o deg_n on_o the_o horizon_n or_o plain_n example_n declination_n 10_o latitude_n 51-30_a and_o the_o sun_n altitude_n 30_o the_o hour_n will_v be_v 8-27_a and_o the_o azimuth_n 66_o from_o south_n eastward_n if_o in_o the_o morning_n or_o the_o contrary_a if_o in_o the_o afternoon_n use_v vii_o the_o hour_n or_o azimuth_n and_o the_o sun_n declination_n give_v to_o find_v the_o altitude_n the_o sphere_n rectify_v as_o before_o and_o the_o hour_n be_v give_v set_v the_o hour-circle_n to_o the_o hour_n on_o the_o equinoctial_a then_o bring_v the_o thread_n to_o the_o declination_n count_v on_o the_o hour-circle_n then_o bring_v the_o upper_a semicircle_n till_o the_o fore-side_n do_v just_o touch_v the_o thread_n and_o the_o thread_n on_o the_o semicircle_n shall_v show_v the_o altitude_n require_v and_o on_o the_o horizon_n the_o azimuth_n at_o that_o hour_n and_o altitude_n but_o if_o the_o azimuth_n be_v first_o give_v then_o set_v the_o upper_a semicircle_n thereunto_o count_v on_o the_o fix_a horizon_n then_o the_o thread_n lay_v to_o the_o declination_n on_o the_o hour-circle_n and_o turn_v about_o till_o it_o touch_v the_o upper_a semicircle_n there_o it_o show_v the_o altitude_n and_o the_o hour-circle_n on_o the_o equinoctial_a show_v the_o hour_n use_v viii_o to_o find_v the_o sun_n height_n in_o the_o vertical-circle_n set_a the_o upper_a semicircle_n to_o the_o east_n or_o west-point_n or_o 90_o degree_n of_o azimuth_n then_o lay_v the_o thread_n to_o the_o declination_n on_o the_o hour-circle_n and_o then_o bring_v it_o and_o the_o thread_n together_o till_o it_o just_a touch_n the_o upper_a semicircle_n and_o it_o shall_v there_o show_v the_o altitude_n at_o east_n or_o west_n require_v example_n at_o 10_o degree_n declination_n north_n it_o will_v be_v east_n at_o 16_o degree_n of_o altitude_n use_v ix_o to_o find_v the_o sun_n altitude_n at_o 6._o set_a the_o hour-circle_n to_o 6_o on_o the_o equinoctial_a and_o the_o thread_n to_o the_o declination_n then_o bring_v the_o semicircle_n to_o the_o thread_n and_o it_o show_v the_o altitude_n at_o 6_o require_v example_n at_o 23-30_a declination_n the_o altitude_n 18-15_a above_o the_o horizon_n in_o north-declination_n and_o as_o much_o under_o in_o south-declination_n for_o you_o must_v observe_v that_o the_o sure_a work_n be_v from_o the_o upper_a or_o divided-side_n of_o the_o ring_n on_o every_o occasion_n to_o use_v it_o use_v x._o to_o find_v the_o hour_n of_o the_o day_n when_o the_o sun_n shine_v rectify_v the_o sphere_n and_o set_v the_o plain_a parallel_n to_o the_o equinoctial-circle_n then_o set_v the_o meridian-circle_n due_a north_n and_o south_n and_o the_o shadow_n of_o the_o axis_n shall_v on_o the_o plain_a show_v the_o true_a hour_n or_o otherwise_o thus_o at_o the_o true_a place_n of_o the_o sun_n declination_n on_o the_o hour-circle_n make_v a_o mark_n or_o stick_v the_o point_n of_o a_o pin_n then_o turn_v the_o sphere_n about_o till_o the_o shadow_n of_o that_o mark_n fall_v on_o the_o centre_n the_o sphere_n stand_v horizontal_a as_o near_o as_o may_v be_v than_o the_o hour-circle_n shall_v on_o the_o equinoctial_a show_v the_o hour_n of_o the_o day_n require_v note_v a_o small_a bead_n or_o knot_n on_o the_o thread_n will_v do_v the_o business_n as_o well_o as_o may_v be_v thus_o any_o the_o like_a question_n may_v be_v wrought_v for_o the_o star_n or_o the_o manner_n of_o raise_v the_o canon_n for_o any_o spherical_a triangle_n whatever_o to_o work_v the_o same_o exact_o by_o the_o logarithm_n as_o thus_o suppose_v i_o will_v make_v the_o canon_n or_o proposition_n to_o find_v the_o sun_n height_n in_o the_o vertical_a circle_n at_o any_o declination_n first_o the_o sphere_n be_v rectify_v and_o the_o plate_n set_v horizontal_a bring_v the_o upper_a semicircle_n to_o the_o east-point_n and_o lay_v the_o thread_n to_o the_o declination_n on_o the_o hour-circle_n bring_v it_o and_o the_o thread_n together_o till_o it_o just_a touch_n the_o upper_a semicircle_n the_o ring_n or_o circle_n so_o stand_v and_o be_v great_a circle_n of_o the_o sphere_n there_o be_v constitute_v a_o spherical-triangle_n in_o this_o form_n wherein_o you_o have_v zae_n 51-30_a the_o latitude_n the_o angle_n at_o the_o equinoctial_a and_o see_fw-mi 90_o the_o upper_a semicircle_n and_o ab_fw-la 23-30_a the_o declination_n part_n of_o the_o hour-circle_n to_o find_v be_v part_n of_o the_o upper_a semicircle_n now_o this_o be_v a_o rightangled_n spherical-triangle_n and_o the_o part_n which_o be_v give_v be_v one_o right_a angle_n viz._n the_o angle_n at_o a_o and_o the_o side_n ab_fw-la the_o sun_n declination_n and_o the_o angle_n at_o e_o 51-30_a to_o find_v the_o side_n be_v now_o the_o sin_n of_o the_o side_n of_o spherical-triangle_n be_v proportional_a to_o the_o sin_n of_o their_o opposite_a angle_n and_o the_o contrary_n therefore_o as_o the_o sine_fw-la of_o the_o triangle_n bea_fw-mi 51-30_a be_v to_o the_o sine_fw-la of_o the_o side_n ab_fw-la 23-30_a so_n be_v the_o sine_fw-la of_o the_o angle_n bae_n 90-00_a to_o the_o sine_fw-la of_o be_v 30-39_a and_o the_o like_a for_o any_o other_o as_o by_o compare_v the_o rule_n in_o mr._n norwood_n trigonometry_n and_o the_o circle_n of_o the_o sphere_n together_o the_o use_n and_o convenience_n thereof_o will_v evident_o appear_v unto_o you_o only_o note_n this_o plain_a observation_n that_o the_o side_n of_o a_o rightangled_n triangle_n which_o subtend_v the_o right_a angle_n be_v most_o proper_o call_v the_o hypothenusa_n the_o other_o which_o you_o make_v or_o suppose_v radius_fw-la the_o base_a the_o other_o the_o perpendicule_a or_o more_o short_a the_o hypothenusa_n and_o leg_n therefore_o if_o the_o hypothenusa_n and_o one_o leg_n be_v give_v the_o proportion_n be_v wrought_v by_o sines_n alone_o but_o if_o the_o two_o leg_n be_v give_v and_o first_o and_o second_o in_o the_o question_n than_o the_o proportion_n be_v wrought_v by_o sines_n and_o tangent_n together_o as_o for_o example_n as_o the_o sine_z of_o ♈_o ♋_o 90-00_a to_o the_o sine_z of_o ♋_o ae_n 23-31_a so_o be_v the_o sine_z of_o ♈_o ♉_o 30-00_a to_o the_o sine_z of_o ♉_o r_o 11-31_a the_o sun_n declination_n in_o ♉_o again_o second_o as_o the_o sine_z of_o ♈_o ae_n 90-00_a to_o the_o tangent_fw-la of_o ae_n ♋_o 23-31_a so_o be_v the_o sine_z of_o ♈_o r_o 27-54_a to_o the_o tangent_fw-la of_o r_o ♉_o 11-31_a the_o declination_n as_o before_o  _fw-fr but_o if_o the_o one_o acute_a angle_n and_o his_o opposite_a leg_n or_o side_n be_v give_v than_o the_o proportion_n be_v make_v by_o sines_n only_o as_o in_o the_o forego_n example_n again_o in_o vertical_a
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
count_v the_o fiducial_a line_n in_o which_o the_o leg-center-pin_n stand_v always_o for_o the_o meridian_n of_o one_o place_n and_o some_o where_o in_o that_o line_n according_a to_o the_o latitude_n thereof_o count_v the_o leg-center_n the_o pole_n of_o the_o world_n and_o the_o index_n be_v hang_v thereon_o by_o the_o tangent_n prick_v down_o the_o latitude_n there_o i_o say_v knock_v in_o a_o pin_n to_o stay_v a_o thread_n for_o one_o place_n then_o on_o the_o degree_n count_v the_o difference_n of_o longitude_n from_o the_o head-leg_n and_o lay_v the_o index_n to_o it_o and_o bring_v the_o thread_n fasten_v as_o before_z till_o on_o the_o index_n it_o cut_v the_o degree_n and_o part_n of_o the_o other_o latitude_n and_o there_o make_v the_o thread_n fast_o with_o another_o pin_n in_o the_o loose-piece_n then_o if_o you_o move_v the_o index_n to_o any_o degree_n of_o longitude_n between_o those_o place_n the_o thread_n shall_v cut_v on_o the_o index_n the_o degree_n of_o latitude_n that_o answer_v unto_o it_o or_o if_o you_o make_v the_o thread_n cut_v any_o degree_n of_o latitude_n the_o index_n give_v the_o longitude_n require_v for_o that_o latitude_n note_v if_o the_o latitude_n be_v small_a as_o between_z 10_o and_o 30_o the_o small_a tangent_n be_v most_o convenient_a but_o if_o it_o be_v between_o 40_o and_o 80_o the_o great_a tangent_fw-la line_n be_v best_a note_v that_o two_o thread_n and_o a_o pair_n of_o compass_n may_v serve_v but_o the_o index_n be_v much_o better_a and_o quick_a in_o operation_n example_n let_v the_o two_o place_n be_v the_o summer-island_n and_o the_o lizard-point_n the_o same_o example_n that_o you_o find_v in_o mr._n norwood_n pag._n 126_o and_o in_o mr._n phillip_n geometrical-seaman_n pag._n 55._o that_o you_o may_v the_o more_o ready_o compare_v the_o truth_n thereof_o by_o their_o operation_n the_o latitude_n of_o the_o lizard_n point_n be_v 50_o degree_n the_o longitude_n be_v 10._o the_o latitude_n of_o the_o summer_n island_n be_v 32-25_a the_o longitude_n be_v 300._o the_o difference_n of_o longitude_n be_v 70_o as_o be_v compute_v by_o their_o observation_n then_o hang_v or_o put_v the_o center-hole_n of_o the_o index_n over_o the_o leg-center-pin_n and_o count_v the_o fiducial-line_n on_o the_o head-leg_n for_o the_o meridian_n of_o one_o place_n count_v on_o the_o tangent_fw-la line_n on_o the_o index_n the_o co-tangent_a of_o one_o latitude_n as_o suppose_v the_o latitude_n of_o the_o lizard-point_n the_o centre_n always_o count_v as_o 90_o and_o there_o knock_v in_o a_o pin_n in_o a_o small_a hole_n to_o hang_v a_o thread_n on_o then_o count_v 70_o degree_n the_o difference_n in_o longitude_n on_o the_o degree_n from_o the_o head-leg_n and_o there_o stay_v it_o then_o draw_v the_o thread_n put_v over_o the_o first_o pin_n till_o it_o cut_v the_o compliment_n of_o the_o other_o latitude_n and_o by_o help_n of_o another_o pin_n stay_v it_o there_o which_o you_o may_v convenient_o do_v by_o one_o of_o the_o sliding-sight_n then_o the_o thread_n be_v so_o lay_v slide_v the_o index_n to_o every_o single_a degree_n or_o five_o degree_n of_o longitude_n and_o then_o the_o thread_n shall_v show_v on_o the_o index_n the_o co-tangent_a of_o the_o latitude_n answerable_a to_o that_o degree_n of_o longitude_n as_o in_o the_o table_n annex_v also_o if_o you_o will_v have_v equal_a degree_n of_o latitude_n and_o will_v find_v the_o longitude_n according_a to_o it_o then_o slide_v the_o index_n to_o and_o fro_o till_o the_o thread_n cut_v on_o the_o index_n a_o even_a degree_n of_o latitude_n then_o on_o the_o degree_n you_o have_v the_o difference_n of_o longitude_n from_o either_o place_n also_o note_n that_o the_o draw_v of_o one_o line_n only_o on_o the_o triangule_a instrument_n in_o the_o beginning_n according_a to_o the_o direction_n of_o lay_v of_o the_o thread_n with_o the_o thread_n and_o compass_n will_v perform_v this_o work_n also_o the_o table_n long_o d.l._n latitude_n 300_o 09_o 32_o 25_o 305_o 05_o 35_o 52_o 310_o 10_o 38_o 51_o 315_o 15_o 41_o 24_o 320_o 20_o 43_o 34_o 325_o 25_o 45_o 24_o 330_o 30_o 46_o 54_o 335_o 35_o 48_o 07_o 340_o 40_o 49_o 04_o 345_o 45_o 49_o 47_o 350_o 50_o 50_o 15_o 355_o 55_o 50_o 31_o 360_o 60_o 50_o 33_o 05_o 65_o 50_o 23_o 10_o 70_o 50_o 00_o if_o this_o work_n fit_v not_o any_o case_n that_o may_v happen_v there_o be_v another_o way_n mention_v in_o page_n 75_o of_o the_o geometrical_a seaman_n by_o the_o steriographick_a projection_n and_o that_o scheam_n be_v draw_v the_o same_o way_n as_o the_o horizontal-projection_n for_o dyall_v be_v and_o somewhat_o easy_o and_o any_o two_o point_n give_v in_o a_o circle_n you_o may_v draw_v a_o great_a circle_n to_o cut_v they_o and_o the_o first_o circle_n into_o two_o equal-part_n by_o the_o direction_n in_o page_z 15_o and_o the_o application_n thereof_o you_o have_v very_o plain_o in_o mr._n phillip_n his_o book_n to_o which_o i_o refer_v you_o have_v say_v more_o than_o at_o first_o i_o intend_v which_o be_v chief_o the_o use_n thereof_o in_o observation_n only_o so_o for_o the_o present_a i_o conclude_v this_o discourse_n and_o shall_v endeavour_v a_o further_a advantage_n in_o the_o next_o impression_n according_a as_o time_n and_o opportunity_n shall_v offer_v farewell_o the_o end_n of_o the_o second_o part._n the_o table_n of_o the_o thing_n contain_v in_o this_o second_o part._n the_o definition_n and_o kind_n of_o dial_n page_n 7_o direction_n to_o draw_v the_o scheam_n 9_o to_o draw_v line_n to_o represent_v the_o several_a sort_n of_o plain_n in_o the_o scheam_n 13_o to_o draw_v a_o scheam_n particular_o for_o one_o dial_n 14_o to_o draw_v the_o equinoctial_a dial_n 19_o to_o try_v when_o a_o plain_a lie_v equinoctial_a 20_o to_o draw_v a_o polar-dial_n 21_o to_o draw_v a_o erect_a east_n or_o west-dial_n 24_o to_o draw_v a_o horizontal-dial_n 27_o the_o demonstration_n of_o the_o canon_n for_o hour_n ib._n to_o draw_v a_o direct_a erect_a south_n or_o north-dial_n 30_o to_o draw_v a_o direct_a recliner_n 33_o the_o use_n of_o the_o figure_n 35_o to_o draw_v a_o direct_a east_n or_o west_n recliner_n 37_o to_o make_v the_o table_n of_o ark_n at_o the_o pole_n 42_o to_o refer_v those_o dial_n to_o a_o new_a latitude_n and_o a_o new_a declination_n wherein_o they_o may_v become_v erect_a decliner_n 46_o to_o find_v the_o requisite_n by_o the_o scheam_n ibid._n to_o find_v the_o declination_n of_o a_o plain_a by_o the_o needle_n or_o by_o the_o sun_n 49_o to_o take_v off_o a_o angle_n or_o set_v the_o sector_n to_o any_o angle_n require_v 53_o precept_n to_o find_v the_o declination_n by_o the_o sun_n and_o example_n also_o of_o the_o same_o 58_o to_o draw_v a_o erect_a declining-dial_n 62_o the_o proportion_n for_o the_o requisite_n of_o erect_a decliner_n 64_o to_o find_v the_o requisite_n three_o way_n 66_o to_o draw_v the_o erect_a south_n decliner_n 67_o to_o draw_v the_o line_n on_o a_o north_n decliner_n 70_o to_o draw_v the_o hour-line_n on_o a_o plain_a that_o decline_v above_o 60_o degree_n 73_o of_o decline_a recline_a plain_n 77_o the_o first_o sort_n of_o south_n recliner_n 79_o the_o second_o sort_n of_o south_n recliner_n be_v polar_n 90_o the_o three_o sort_n of_o south-recliners_a 98_o the_o first_o sort_n of_o north_n recliner_n 106_o the_o second_o sort_n of_o north_n recliner_n be_v equinoctial_a 114_o the_o three_o sort_n of_o north_n recliner_n 119_o of_o incline_v diâ—ls_n 126_o to_o find_v the_o useful_a hour_n in_o all_o plain_n 130_o to_o draw_v the_o mathematical_a ornament_n on_o all_o sort_n of_o dial_n 134_o to_o draw_v the_o tropic_n or_o length_n of_o the_o day_n 136_o to_o make_v the_o trygon_n 138_o to_o draw_v the_o planetary_a or_o jewish_a hour_n 142_o to_o draw_v the_o italian_a hour_n 144_o to_o draw_v the_o babylonish_n hour_n 145_o to_o draw_v the_o azimuth_n line_n 146_o to_o draw_v the_o almicanter_n 154_o to_o draw_v the_o circle_n of_o position_n or_o house_n 160_o to_o draw_v the_o hour_n and_o all_o the_o rest_n on_o the_o ceiling_n of_o a_o room_n 165_o the_o figure_n of_o the_o instrument_n explain_v 166_o a_o table_n of_o the_o sun_n azimuth_n at_o every_o hour_n and_o quarter_n in_o the_o whole_a sign_n 168_o a_o table_n of_o the_o sun_n altitude_n the_o same_o time_n 169_o the_o description_n and_o use_v of_o the_o armilary-sphear_n for_o dyall_v several_a way_n 172_o the_o description_n and_o use_v of_o the_o poor-man_n dial-sphear_n for_o dyall_v and_o several_a uses_n thereof_o 203_o how_o to_o remedy_n several_a inconvenience_n in_o the_o use_n of_o the_o gunter_n rule_n 220_o the_o use_n and_o a_o further_a description_n of_o the_o trianguler-quadrant_n for_o navigation_n or_o observation_n at_o sea_n 227_o for_o a_o fore-observation_n with_o