the_o month_n and_o take_v 30_o degree_n from_o the_o scale_n of_o altitude_n and_o put_v one_o point_n in_o the_o line_n of_o hour_n till_o the_o other_o point_n turn_v about_o will_v but_o just_a touch_n the_o thread_n and_o i_o find_v it_o to_o 23_o minute_n past_o 7_o but_o if_o it_o have_v be_v in_o the_o afternoon_n it_o will_v have_v be_v 37_o minute_n past_o 4._o 2._o again_o on_o the_o ten_o of_o august_n in_o the_o afternoon_n at_o 20_o degree_n high_a i_o take_v 20_o degree_n from_o the_o scale_n of_o altude_n and_o lay_v the_o thread_n on_o the_o day_n of_o the_o month_n viz._n the_o ten_o aforesaid_a count_v from_o the_o name_n at_o the_o begin_n of_o august_n towards_o september_n and_o carry_v the_o compass_n in_o the_o line_n of_o hour_n till_o the_o other_o point_n do_v but_o just_a touch_n the_o thread_n and_o you_o shall_v find_v it_o to_o be_v 54_o minute_n past_o 4_o a_o clock_n 3._o again_o on_o the_o 11._o of_o december_n at_o 15_o degree_n high_a work_v as_o before_o and_o you_o shall_v find_v it_o to_o be_v just_a 12_o a_o clock_n but_o to_o work_v this_o you_o must_v lay_v the_o rule_n down_o on_o something_o and_o extend_v the_o thread_n beyond_o the_o rule_n for_o the_o nigh_a distance_n will_v happen_v on_o the_o outside_n of_o the_o rule_n 4._o again_o on_o the_o 11_o of_o june_n at_o noon_n i_o find_v the_o altitude_n to_o be_v 62_o degree_n high_a then_o lay_v the_o thread_n on_o the_o 10_o the_o or_o 11_o the_o of_o june_n for_o then_o a_o day_n be_v unsensible_a and_o work_v as_o before_o you_o shall_v find_v the_o point_n of_o the_o compass_n to_o stay_v at_o just_a 12_o a_o clock_n the_o time_n require_v for_o that_o altitude_n 4._o to_o find_v the_o sun_n rise_v any_o day_n in_o the_o year_n lay_v the_o thread_n on_o the_o day_n of_o the_o month_n and_o in_o the_o line_n of_o hour_n it_o show_v the_o true_a hour_n and_o minute_n of_o the_o sun_n rise_v or_o set_v for_o the_o rise_n count_v the_o morning_n hour_n and_o for_o the_o set_n count_v the_o evening_n hour_n 5._o to_o find_v if_o any_o place_n lie_v level_a or_o nor_o open_v the_o rule_n to_o his_o true_a angle_n of_o 60_o degree_n than_o set_v the_o movable_a leg_n upon_o the_o place_n you_o will_v make_v level_a and_o if_o the_o thread_n play_v just_a on_o 60_o degree_n it_o be_v a_o true_a level_a place_n or_o else_o not_o 6._o to_o try_v if_o any_o thing_n be_v upright_o or_o not_o hang_v a_o thread_n and_o plummet_n on_o the_o centre_n than_o ap_o the_o head_n leg_n of_o the_o rule_n to_o the_o wall_n or_o post_n and_o if_o it_o be_v upright_o the_o thread_n will_v play_v just_a on_o the_o innermost_a line_n of_o the_o scale_n of_o altitude_n or_o else_o not_o chap._n iii_o a_o further_a description_n of_o the_o rule_n to_o make_v it_o to_o show_v the_o sun_n azimuth_n declination_n true_a place_n right_a ascention_n and_o the_o hour_n of_o day_n or_o night_n in_o this_o or_o any_o other_o lattitude_n 1._o first_o in_o stead_n of_o the_o scale_n of_o altitude_n to_o 62_o degree_n there_o be_v one_o put_v to_o 90_o degree_n in_o that_o place_n and_o that_o of_o 62_o be_v put_v by_o in_o some_o other_o place_n where_o it_o may_v serve_v as_o well_o 2._o the_o line_n of_o hour_n have_v a_o double_a margin_n viz_o one_o for_o hour_n and_o the_o other_o for_o azimuth_n &_o then_o every_o 5_o the_o minute_n be_v more_o proper_o make_v 4_o or_o else_o every_o 2_o minute_n and_o in_o a_o large_a rule_n to_o every_o quarter_n of_o a_o degree_n of_o azimuth_n or_o to_o every_o single_a minute_n of_o time_n 3._o the_o degree_n ought_v to_o be_v reckon_v after_o 3_o manner_n of_o way_n first_o as_o before_o be_v express_v second_o from_o 60_o towards_o the_o end_n with_o 10_o 20_o 30_o 40_o 50_o 60_o etc._n etc._n to_o be_v so_o account_v in_o find_v the_o azimuch_o for_o a_o particular_a latitude_n and_o and_o three_o from_o the_o head_n or_o 90_o towards_o the_o end_n with_o 10_o 20_o 30_o 40_o 50_o 60_o 70_o 80_o etc._n etc._n for_o the_o general_a find_v of_o hour_n and_o azimuth_n in_o any_o latitude_n and_o many_o other_o problem_n of_o the_o sphere_n beside_o to_o which_o may_v be_v add_v where_o room_n will_v allow_v a_o line_n of_o hour_n begin_v at_o 6_o at_o the_o head_n and_o 12_o at_o the_o end_n but_o reckon_v 15_o degree_n for_o a_o hour_n and_o 4_o minute_n for_o every_o degree_n it_o may_v do_v as_o well_o without_o it_o 4._o to_o the_o calendar_n of_o month_n and_o day_n be_v add_v a_o line_n of_o the_o sun_n true_a place_n in_o the_o zodiac_n or_o where_o room_n fail_v the_o character_n of_o the_o twelve_o sign_n put_v on_o that_o day_n of_o the_o month_n the_o sun_n enter_v into_o it_o and_o count_v every_o day_n for_o a_o degree_n may_v indifferent_o serve_v for_o the_o use_v it_o be_v chief_o intend_v for_o 5._o under_o that_o be_v a_o line_n of_o the_o sun_n right_a ascension_n to_o hour_n and_o quarter_n at_o least_o or_o rather_o every_o five_o minute_n number_v thus_o 12_o and_o 24_o right_n under_o ♈_o and_o ♎_o or_o the_o ten_o of_o march_n and_o so_o forward_o to_o the_o ten_o of_o june_n or_o ♋_o where_o stand_v 6_o then_o backward_o to_o 12_o where_o you_o begin_v then_o backward_o still_o to_o the_o eleven_o of_o december_n with_o 13_o 14_o 15_o 16_o 17_o 18_o to_o ♑_o then_z from_o thence_o forward_o to_o 24_o where_o you_o first_o begin_v but_o when_o you_o be_v straighten_v for_o room_n as_o on_o most_o ordinary_a rule_n you_o will_v be_v than_o it_o may_v very_o well_o suffice_v to_o have_v a_o point_n or_o stroke_n show_v when_o the_o sun_n shall_v gradual_o get_v a_o hour_n of_o right_a ascension_n and_o from_o that_o for_o every_o day_n count_v four_o minute_n of_o time_n till_o it_o have_v increase_v to_o a_o hour_n more_o and_o this_o computation_n will_v serve_v very_o well_o and_o in_o stead_n of_o say_v 13_o 14_o 15_o hour_n of_o right_a ascension_n say_v 1_o 2_o 3_o etc._n etc._n which_o will_v perform_v the_o work_n as_o well_o and_o reduce_v the_o time_n to_o more_o proper_a term_n 6._o there_o be_v fit_v two_o line_n one_o contain_v 24_o hour_n and_o the_o other_o 29_o day_n and_o about_o 13_o hour_n and_o they_o serve_v to_o find_v the_o time_n of_o the_o moon_n come_v to_o the_o south_n before_o or_o after_o the_o sun_n and_o by_o that_o the_o time_n of_o high-water_n at_o london-bridge_n or_o any_o other_o place_n as_o be_v ordinary_a chap._n iu._n the_o use_v follow_v in_o order_n 1._o to_o find_v the_o sun_n declination_n lay_v the_o thread_n on_o the_o day_n of_o the_o month_n then_o in_o the_o line_n of_o degree_n you_o have_v the_o declination_n from_o march_v the_o ten_o towards_o the_o head_n be_v the_o declination_n northward_o the_o other_o way_n be_v southward_o as_o by_o the_o time_n of_o the_o year_n be_v discover_v example_n on_o the_o ten_o of_o april_n it_o be_v 11_o 48_o '_o toward_z the_o north_n but_o on_o the_o ten_o of_o october_n it_o be_v 10_o 30_o '_o toward_z the_o south_n 2._o as_o the_o thread_n be_v so_o lay_v on_o the_o day_n of_o the_o month_n in_o the_o line_n of_o the_o sun_n place_n it_o show_v that_o and_o in_o the_o line_n of_o the_o sun_n right_a ascension_n his_o right_a ascension_n also_o only_o you_o must_v give_v it_o its_o due_a order_n of_o reckon_n as_o thus_o it_o begin_v at_o ♈_o aries_n and_o so_o proceed_v to_o ♋_o then_z back_o again_o to_o ♑_o at_o the_o eleven_o of_o december_n then_o forward_o again_o to_o ♈_o aries_n where_o you_o begin_v 3._o to_o find_v the_o sun_n right_a ascension_n in_o hour_n and_o minute_n lay_v the_o thread_n as_o before_o on_o the_o day_n of_o the_o month_n and_o in_o the_o line_n of_o right_a ascension_n you_o have_v the_o hour_n and_o minute_n require_v compute_v right_o according_a to_o the_o time_n of_o the_o year_n that_o be_v begin_v at_o the_o ten_o of_o march_n or_o ♈_o aries_n and_o so_o reckon_v forward_o and_o backward_o as_o the_o month_n go_v example_n on_o the_o ten_o of_o april_n the_o sun_n place_n be_v 1_o degree_n in_o ♉_o taurus_n and_o the_o sun_n right_a ascension_n 1_o hour_n 55_o minute_n on_o the_o ten_o of_o october_n 27_o 1_o 4_o in_o ♎_o libra_n and_o his_o right_a ascension_n be_v 13_o hour_n and_o 42_o minute_n 4._o to_o find_v the_o sun_n amplitude_n at_o rise_v or_o set_v take_v the_o sun_n declination_n out_o of_o the_o particular_a scale_n of_o altitude_n and_o lay_v it_o the_o same_o way_n as_o the_o declination_n be_v from_o 90_o in_o the_o azimuth_n scale_n and_o it_o shall_v show_v
the_o amplitude_n from_o the_o east_n or_o west_n count_v from_o 90._o example_n may_v the_o ten_o it_o be_v 33._o 37._o chap._n v._n have_v the_o sun_n declination_n or_o day_n of_o the_o month_n to_o find_v the_o azimuth_n at_o any_o altitude_n require_v for_o that_o day_n first_o find_v the_o sun_n declination_n by_o the_o first_o proposition_n of_o the_o four_o chapter_n then_o take_v that_o out_o of_o the_o particular_a scale_n of_o altitude_n or_o scale_v to_o 62_o degree_n than_o whatsoever_o the_o altitude_n shall_v happen_v to_o be_v count_v the_o same_o on_o the_o degree_n from_o 60_o towards_o the_o end_n of_o the_o rule_n according_a to_o the_o second_o manner_n of_o count_v in_o the_o three_o proposition_n of_o the_o three_o chapter_n and_o thereunto_o lie_v the_o thread_n than_o the_o compass_n set_v to_o the_o declination_n carry_v one_o point_n along_o the_o line_n of_o hour_n on_o the_o same_o side_n of_o the_o thread_n the_o declination_n be_v that_o be_v to_o say_v if_o the_o day_n of_o the_o month_n or_o declination_n be_v on_o the_o right_a side_n the_o aequinoctial_a then_o carry_v the_o compass_n on_o the_o right_a side_n but_o if_o the_o declination_n be_v on_o the_o south_n side_n that_o be_v towards_o the_o end_n count_v from_o the_o ten_o of_o march_n or_o aries_n or_o libra_n then_o carry_v the_o compass_n along_o the_o line_n of_o hour_n and_o azimuth_n on_o the_o left_a side_n of_o the_o thread_n as_o all_o winâ—er_a time_n it_o will_v be_v and_o have_v set_v the_o compass_n to_o the_o least_o distance_n to_o the_o thread_n it_o shâ—ll_v stay_v at_o the_o sun_n true_a azimuth_n from_o the_o south_n require_v count_v as_o the_o figure_n be_v number_v or_o from_o east_n or_o west_n count_v from_o 90._o example_n 1._o on_o the_o ten_o of_o july_n i_o desire_v to_o find_v the_o sun_n azimuth_n at_o any_o altitude_n first_o on_o that_o day_n i_o find_v the_o sun_n declination_n to_o be_v 20._o 45_o which_o number_n count_v from_o the_o begin_n of_o the_o particular_a scale_n of_o altitude_n towards_o 62_o and_o that_o distance_n take_v between_o your_o compass_n then_o be_v they_o set_v for_o all_o that_o day_n then_o suppose_v the_o sun_n height_n to_o be_v ten_o degree_n lay_v the_o thread_n on_o 10_o count_v from_o 60_o towards_o the_o left_a end_n then_o carry_v the_o compass_n on_o the_o right_a side_n of_o the_o thread_n because_o it_o be_v summer_n or_o north_n declination_n on_o the_o line_n of_o azimuth_n it_o shall_v show_v 110._o 40_o the_o azimuth_n from_o the_o south_n require_v but_o if_o you_o count_v from_o 90_o it_o be_v but_o 20._o 40._o from_o the_o east_n or_o west_n point_v northward_o according_a to_o the_o time_n of_o the_o day_n either_o morning_n or_o evening_n example_n 2._o again_o on_o the_o 14._o of_o november_n or_o the_o 6._o of_o january_n when_o the_o sun_n have_v the_o same_o declination_n southward_o and_o the_o same_o altitude_n to_o work_v this_o you_o must_v lay_v the_o rule_n down_o on_o something_o then_o lay_v the_o thread_n on_o the_o altitude_n count_v from_o 60_o towards_o the_o end_n as_o before_o and_o carry_v the_o compass_n on_o the_o southside_n of_o the_o aequinoctial_a along_o the_o azimuth-line_n till_o the_o other_o point_n do_v but_o just_a touch_n the_o thread_n and_o it_o shall_v stay_v at_o 36._o 45_o the_o azimuth_n from_o south_n require_v if_o it_o be_v morning_n it_o want_v of_o come_v to_o south_n if_o it_o be_v afternoon_n it_o be_v pass_v the_o south_n example_n 3._o but_o if_o the_o sun_n be_v in_o the_o aequinoctial_a and_o have_v no_o declination_n than_o it_o be_v but_o lay_v the_o thread_n to_o the_o altitude_n and_o in_o the_o line_n of_o azimuth_n the_o thread_n shall_v show_v the_o true_a azimuth_n require_v as_o for_o instance_n at_o 00_o degree_n of_o altitude_n the_o azimuth_n be_v 90_o at_o 10_o degree_n it_o be_v 77._o 15_o at_o 20_o degree_n 62._o 45_o at_o 30_o degree_n high_a 43._o 15_o at_o 35_o degree_n high_a 28._o 10_o at_o 38_o degree_n 28_o '_o high_z it_o be_v just_a south_n as_o by_o practice_n may_v plain_o appear_v but_o if_o the_o sun_n altitude_n be_v above_o 45_o than_o the_o degree_n will_v go_v beyond_o the_o end_n of_o the_o rule_n to_o supply_v this_o defect_n do_v thus_o subtract_v 45_o out_o of_o the_o number_n you_o will_v have_v and_o double_a the_o remainder_n then_o lay_v the_o rule_n down_o with_o some_o piece_n of_o the_o same_o thickness_n in_o a_o straight_a line_n with_o the_o movable_a leg_n then_o take_v the_o distance_n from_o the_o tangent_fw-la of_o the_o remainder_n double_v count_v from_o 60_o to_o the_o end_n of_o the_o rule_n in_o the_o line_n next_o the_o edge_n to_o the_o centre_n lay_v that_o distance_n in_o the_o same_o straight_a line_n from_o the_o tangent_fw-la double_v and_o that_o shall_v be_v the_o tangent_fw-la of_o the_o angle_n above_o 45_o whereunto_o you_o must_v lay_v the_o thread_n for_o the_o find_v the_o azimuth_n when_o the_o sun_n be_v above_o 45_o degree_n high_a chap._n vi_o to_o find_v the_o hour_n of_o the_o night_n by_o the_o moon_n first_o by_o the_o help_n of_o a_o almanac_n get_v the_o true_a time_n of_o the_o new_a moon_n then_o compute_v her_o true_a place_n at_o that_o time_n which_o be_v always_o the_o place_n of_o the_o sun_n very_o nigh_o at_o the_o hour_n and_o minute_n of_o conjunction_n then_o compute_v how_o many_o day_n old_a the_o moon_n be_v then_o by_o the_o line_n of_o number_n say_v if_o 29_o day_n 13_o hour_n or_o on_o the_o line_n 29._o 540_o require_v 860_o degree_n or_o 12_o sign_n what_o shall_v â—ny_v less_o number_n of_o day_n and_o part_n of_o a_o day_n require_v the_o answer_n will_v be_v the_o moon_n true_a place_n at_o that_o age_n have_v â—ound_v her_o true_a place_n then_o take_v her_o altitude_n and_o lay_v the_o thread_n on_o the_o moon_n place_v find_v and_o work_v as_o you_o do_v for_o the_o sun_n and_o note_v what_o hour_n you_o find_v then_o consider_v if_o it_o be_v new_a moon_n the_o hour_n you_o find_v be_v thentrue_a hour_n likewise_o in_o the_o full_a but_o if_o it_o be_v before_o or_o after_o you_o must_v subtract_v by_o the_o line_n of_o number_n thus_o if_o 29_o day_n 540_o part_n require_v 24_o hour_n what_o shall_v any_o number_n of_o day_n and_o part_n require_v the_o answer_n be_v what_o you_o must_v take_v away_o from_o the_o moon_n hour_n find_v to_o make_v the_o true_a hour_n of_o the_o night_n which_o be_v require_v but_o for_o more_o plainness_n sake_n i_o will_v reduce_v these_o operation_n to_o so_o many_o proposition_n before_o i_o come_v to_o a_o example_n prop._n 1._o to_o find_v the_o moon_n age._n first_o it_o be_v most_o ready_o and_o exact_o do_v by_o a_o ephemerides_n such_o a_o one_o as_o you_o find_v in_o mr._n lilly_n almanac_n or_o as_o to_o her_o age_n only_o in_o any_o book_n or_o sheet-almanack_n but_o you_o may_v do_v it_o indifferent_o by_o the_o epact_n thus_o by_o the_o rule_n of_o the_o 152_o page_n in_o the_o appendix_n to_o the_o carpenter_n rule_n add_v the_o epact_n the_o month_n and_o the_o day_n of_o the_o month_n together_o and_o the_o sum_n if_o under_o 30_o be_v the_o moon_n age_n but_o if_o above_o consider_v if_o the_o month_n have_v 30_o or_o 31_o day_n then_o subtract_v 29_o or_o 30_o out_o and_o the_o remainder_n be_v the_o moon_n age_n in_o day_n example_n august_n 2._o 1660._o epact_n 28._o month_n 6._o day_n 2._o add_v make_n 36._o now_o august_n or_o six_o month_n have_v 31_o day_n therefore_o 30_o being_n take_v away_o 6_o day_n remain_v for_o the_o moon_n age_n require_v prop._n 2._o to_o find_v the_o moon_n place_n by_o the_o ephemerides_n aforesaid_a in_o mr._n lilly_n almanac_n you_o have_v it_o ser_fw-mi down_o every_o day_n in_o the_o year_n but_o to_o find_v it_o by_o the_o rule_n do_v thus_o count_n six_o day_n back_o from_o august_n 2._o viz._n to_o july_n 27._o there_o lay_v the_o thread_n and_o in_o the_o line_n of_o the_o sun_n place_n you_o have_v the_o moon_n place_v require_v be_v then_o near_o alike_o then_o in_o regard_n the_o moon_n go_v fast_a than_o the_o sun_n that_o be_v to_o say_v in_o 29_o day_n 13_o hour_n 12_o sign_n or_o 360_o degree_n in_o 3_o day_n 1_o sign_n 6_o degr_n 34_o min._n 20_o sec._n in_o one_o day_n o_o sign_n 12_o degr_n 11_o min._n 27_o sec._n in_o one_o hour_n 30_o min._n 29_o sec._n or_o half_o a_o minute_n add_v the_o sign_n and_o degree_n and_o minute_n the_o moon_n have_v go_v in_o so_o many_o day_n and_o hour_n if_o you_o know_v they_o together_o and_o the_o sun_n shall_v be_v the_o moon_n true_a place_n be_v add_v to_o what_o she_o have_v on_o
not_o the_o time_n in_o common_a hour_n but_o be_v thus_o find_v add_v the_o compliment_n of_o the_o sun_n ascension_n and_o the_o star_n right_a ascension_n and_o the_o star_n hour_n last_o find_v together_o and_o the_o sun_n if_o less_o than_o 12_o or_o the_o remain_z 12_o be_v substract_v shall_v be_v the_o time_n of_o his_o rise_n in_o common_a hour_n but_o for_o his_o set_n add_v the_o star_n set_v last_o find_v to_o the_o other_o number_n and_o the_o sum_n or_o difference_n shall_v be_v the_o set_n example_n for_o the_o bulls-eye_n on_o the_o 23_o of_o december_n it_o rise_v at_o 2_o in_o the_o afternoon_n and_o set_v at_o 4._o 46_o in_o the_o morning_n 4._o to_o find_v the_o time_n of_o the_o sothe_v of_o any_o star_n on_o the_o rule_n or_o any_o other_o who_o right_a ascension_n and_o declination_n be_v know_v subtract_v the_o sun_n right_a ascension_n from_o the_o star_n increase_v by_o 24_o when_o you_o can_v do_v without_o and_o the_o remainder_n if_o less_o than_o 12_o be_v the_o time_n require_v in_o the_o afternoon_n or_o night_n before_o 12_o but_o if_o there_o remain_v more_o than_o 12_o subtract_v 12_o and_o the_o residue_n be_v the_o time_n from_o midnight_n to_o midday_n follow_v example_n lyons-heart_n on_o the_o ten_o of_o march_n the_o sun_n ascension_n be_v 0_o 2_o '_o lyons-heart_n whole_a right_a asc_n be_v 9_o 50_o '_o time_z of_o sothe_v be_v 9_o 48_o '_o at_o night_n 5._o to_o find_v how_o long_o any_o star_n will_v be_v above_o the_o horizon_n lay_v the_o thread_n to_o the_o star_n and_o in_o the_o hour-line_n it_o show_v the_o ascensional_a difference_n count_v from_o 90_o then_o note_n if_o the_o star_n have_v north_n declination_n add_v that_o to_o 6_o hour_n and_o the_o sum_n be_v half_a the_o time_n if_o south_n subtract_v it_o from_o 6_o and_o the_o residue_n be_v half_a the_o time_n and_o the_o compliment_n of_o each_o to_o 24_o be_v double_v be_v the_o whole_a nocturnal_a arch_n under_o the_o horizon_n example_n for_o the_o bulls-eye_n his_o ascensional_a difference_n will_v be_v find_v to_o be_v one_o hour_n 23_o minute_n which_o add_v to_o 6_o hour_n and_o double_a make_v 14._o 46_o the_o diurnal_a ark_n of_o the_o star_n and_o the_o residue_n from_o 24_o be_v 9_o 14._o for_o the_o nocturnal_a ark_n or_o the_o time_n of_o its_o be_v under_o the_o horizon_n chap._n ix_o to_o perform_v the_o foregoing_a work_n in_o any_o latitude_n as_o rise_v amplitude_n ascensional_a difference_n latitude_n hour_n and_o azimuth_n wherein_o i_o shall_v give_v only_o the_o rule_n and_o leave_v out_o the_o example_n for_o brevity_n sake_n 1._o for_o the_o rise_n and_o set_v and_o ascensional_a difference_n be_v all_o one_o do_v thus_o take_v the_o sun_n declination_n out_o of_o the_o general_a scale_n of_o altitude_n than_o set_v one_o foot_n of_o the_o compass_n in_o the_o colatitude_n on_o the_o same_o scale_n and_o with_o the_o other_o lie_v the_o thread_n to_o the_o nigh_a distance_n then_o the_o thread_n so_o lay_v take_v the_o nigh_a distance_n from_o the_o latitude_n to_o the_o thread_n with_o that_o distance_n set_v one_o foot_n in_o the_o sun_n declination_n count_v from_o 90_o towards_o the_o centre_n and_o the_o thread_n lay_v to_o the_o near_a distance_n shall_v in_o the_o degree_n show_v the_o ascensional_a difference_n require_v count_v from_o 90_o at_o the_o head_n towards_o the_o end_n of_o the_o rule_n and_o if_o you_o reduce_v those_o degree_n and_o minute_n to_o time_n you_o have_v the_o rise_n and_o set_v before_o and_o after_o 6_o according_a to_o the_o declination_n and_o time_n of_o the_o year_n 2._o to_o find_v the_o sun_n amplitude_n take_v the_o sun_n declination_n and_o set_v one_o foot_n in_o the_o colatitude_n with_o the_o other_o lie_v the_o thread_n to_o the_o near_a distance_n and_o on_o the_o degree_n it_o show_v the_o sun_n amplitude_n at_o rise_v or_o set_v count_v as_o beâ—ore_v from_o 90_o to_o the_o left_a end_n of_o the_o rule_n 3._o have_v amplitude_n and_o declination_n to_o find_v the_o latitude_n take_v the_o declination_n from_o the_o general_a scale_n and_o set_v one_o foot_n in_o the_o amplitude_n the_o thread_n lay_v to_o the_o near_a distance_n in_o the_o line_n of_o degree_n it_o show_v the_o compliment_n of_o the_o latitude_n require_v or_o the_o converse_n 4._o have_v latitude_n sun_n declination_n and_o altitude_n to_o find_v the_o height_n at_o 6_o and_o then_o at_o any_o other_o time_n of_o the_o day_n and_o year_n count_n the_o declination_n in_o the_o degree_n from_o 90_o towards_o the_o end_n thereto_o lay_v the_o thread_n the_o least_o distance_n from_o which_o to_o the_o latitude_n in_o the_o general_a scale_n shall_v be_v the_o sun_n height_n at_o 6_o in_o the_o summer_n or_o his_o depression_n in_o the_o winter_n the_o compass_n stand_v at_o this_o distance_n take_v measure_n on_o the_o general_a scale_n of_o altitude_n from_o the_o begin_n at_o the_o pin_n towards_o 90_o keep_v one_o point_n there_o open_v the_o other_o to_o the_o sun_n altitude_n thus_o have_v you_o substract_v the_o height_n at_o 6_o out_o of_o the_o sun_n altitude_n but_o in_o winter_n you_o must_v add_v the_o depression_n at_o 6_o which_o be_v all_o one_o at_o the_o same_o declination_n with_o his_o height_n at_o 6_o in_o summer_n and_o that_o be_v do_v thus_o put_v one_o point_n of_o the_o compass_n so_o set_v in_o the_o general_a scale_n to_o the_o sun_n altitude_n then_o turn_v the_o other_o outward_n towards_o 90_o there_o keep_v it_o then_o open_a the_o compass_n to_o the_o begin_n of_o the_o scale_n then_o have_v you_o add_v it_o to_o the_o sun_n altitude_n have_v this_o distance_n set_v one_o foot_n in_o the_o colatitude_n on_o the_o general_a scale_n lay_v the_o thread_n to_o the_o near_a distance_n the_o thread_n so_o lay_v take_v the_o near_a distance_n from_o 90_o to_o the_o thread_n than_o set_v one_o foot_n in_o the_o declination_n count_v from_o 90_o and_o on_o the_o degree_n it_o show_v the_o hour_n from_o 6_o reckon_v from_o the_o head_n or_o from_o 12_o count_v from_o the_o end_n of_o the_o rule_n i_o shall_v make_v all_o more_o plain_a by_o make_v three_o proposition_n of_o it_o thus_o prop._n 1._o to_o find_v the_o hour_n in_o the_o aequinoctial_a take_v the_o altitude_n from_o the_o begin_n of_o the_o general_a scale_n of_o altitude_n and_o set_v one_o foot_n in_o the_o colatitude_n the_o thread_n lay_v to_o the_o near_a distance_n with_o the_o other_o foot_n in_o the_o degree_n shall_v show_v the_o hour_n from_o 6_o count_v from_o 90_o and_o allow_v for_o every_o 15_o 1_o hour_n and_o 4_o min_fw-mi for_o every_o degree_n prop._n 2._o to_o find_v it_o at_o just_a 6._o be_v before_o express_v by_o the_o converse_n of_o the_o first_o part_n of_o the_o four_o which_o i_o shall_v again_o repeat_v prop._n 3._o to_o find_v it_o at_o any_o time_n do_v thus_o count_n the_o sun_n declination_n in_o the_o degree_n thereunto_o lay_v the_o thread_n the_o least_o distance_n to_o which_o from_o latitude_n in_o the_o general_a scale_n shall_v be_v the_o sun_n altitude_n at_o 6_o which_o distance_n in_o summer_n you_o must_v subtract_v from_o but_o in_o winter_n you_o must_v add_v to_o the_o sun_n present_a altitude_n have_v that_o distance_n set_v one_o foot_n in_o the_o coaltitude_n with_o the_o other_o lie_v the_o thread_n to_o the_o near_a distance_n take_v again_o the_o near_a distance_n from_o 90_o to_o the_o thread_n than_o set_v one_o foot_n in_o the_o sun_n diclination_n count_v from_o 90_o and_o lay_v the_o thread_n to_o the_o near_a distance_n and_o in_o the_o degree_n it_o shall_v show_v the_o hour_n require_v example_n at_o 10_o declination_n north_n and_o 30_o high_a latitude_n 51._o 32_o the_o hour_n be_v find_v to_o be_v 8._o 25_o count_v 90_o for_o 6_o and_o so_o forward_o again_o at_o 20_o degree_n of_o declination_n south_n and_o 10_o degree_n of_o altitude_n i_o find_v the_o hour_n in_o the_o same_o latitude_n to_o be_v 17_o minute_n past_o 9_o have_v latitude_n delination_n and_o altitude_n to_o find_v the_o sun_n azimuth_n take_v the_o sine_fw-la of_o the_o declination_n put_v one_o foot_n in_o the_o latitude_n the_o thread_n lay_v to_o the_o near_a distance_n in_o the_o degree_n it_o show_v the_o sun_n height_n at_o due_a east_n or_o west_n which_o you_o must_v in_o summer_n subtract_v from_o the_o sun_n altitude_n as_o before_o on_o the_o general_a scale_n of_o altitude_n with_o which_o distance_n put_v one_o foot_n in_o the_o colatitude_n and_o lay_v the_o thread_n to_o the_o near_a distance_n then_o take_v the_o near_a distance_n from_o the_o sine_fw-la of_o the_o latitude_n fit_a that_o again_o in_o the_o colatitude_n and_o the_o thread_n lay_v to_o the_o heere_v
degree_n on_o the_o other_o side_n of_o the_o rule_n and_o lay_v off_o 15_o 30_o and_o 45_o for_o every_o whole_a hour_n or_o every_o 3_o degree_n and_o 45_o minute_n for_o every_o quarter_n from_o d_o and_o e_z toward_z f_o and_o g_o for_o 7_o 8_o 9_o and_o for_o 3_o 4_o and_o 5_o a_o clock_n hour_n point_v last_o set_v c_o d_o or_o b_o e_z in_o the_o tangent_fw-la of_o 45_o and_o lay_v the_o same_o point_n of_o 15_o 30_o 45_o both_o way_n from_o b_o or_o 12_o for_o 10_o 11_o and_o 1_o 2_o and_o to_o all_o those_o point_n draw_v line_n for_o the_o true_a hour-line_n require_v for_o lay_v down_o the_o style_v height_n if_o you_o take_v the_o latitude_n compliment_n out_o of_o the_o tangent-line_n as_o the_o sector_n stand_v to_o prick_v the_o noon_n hour_n and_o set_v it_o on_o the_o line_n d_o f_o or_o e_o g_o from_o d_o or_o e_z downward_o from_o d_o to_o h_n it_o will_v show_v you_o where_o to_o draw_v c_o h_n for_o the_o style_n then_o to_o those_o line_n set_v figure_n and_o plant_v the_o dial_n horizontal_a and_o the_o style_v perpendicular_a and_o right_a north_n and_o south_n and_o it_o shall_v show_v when_o the_o sun_n shine_v the_o true_a hour_n of_o the_o day_n note_v well_o the_o figure_n follow_v chap._n xii_o to_o draw_v a_o vertical_a direct_v south_n or_o north_n dyal_n first_o draw_v a_o perpendicular_a line_n for_o 12_o a_o clock_n then_o in_o that_o line_n at_o the_o upper_a end_n in_o the_o south_n plain_a and_o at_o the_o low_a end_n in_o a_o north_n plain_a appoint_v a_o place_n for_o the_o centre_n through_o which_o point_n across_o it_o at_o right_a angle_n a_o horizontall_a dial_n a_o south_n dial_n for_o 6_o and_o 6_o as_o you_o do_v in_o the_o horizontal_a plain_n as_o the_o line_n a_o b_o and_o c_o d_o on_o each_o side_n 12_o make_v two_o parallel_n as_o in_o the_o horizontal_a then_o take_v a_o d_o the_o parallel_n and_o fit_v it_o in_o the_o sine_fw-la of_o the_o latitude_n compliment_n and_o take_v out_o the_o sine_fw-la of_o 90_o and_o 90_o and_o lay_v it_o in_o the_o parallel_n from_o d_o and_o c_o to_z e_z and_o f_o and_o draw_v the_o line_n e_o f_o then_o make_v d_o e_z and_o b_o e_o tangent_n of_o 45_o and_o lay_v down_o the_o hour_n as_o you_o do_v in_o the_o horizontal_a and_o you_o shall_v have_v point_n whereby_o to_o draw_v the_o hour_n line_n for_o the_o north_n you_o must_v turn_v the_o hour_n both_o way_n for_o 4_o 5_o 8_o and_o 7_o in_o the_o morning_n and_o 4_o 5_o 7_o and_o 8_o at_o night_n the_o height_n of_o the_o stile_n must_v be_v the_o tangent_fw-la of_o the_o compliment_n of_o the_o of_o the_o latitude_n when_o the_o sector_n be_v set_v to_o lay_v off_o the_o hour_n from_o d_o as_o here_o it_o be_v lay_v down_o from_o c_o to_o g_z and_o draw_v the_o line_n a_o g_o for_o the_o stile_n for_o illustration_n sake_n note_v the_o figure_n chap._n xii_o to_o draw_v a_o erect_a east_n or_o west_n dial._n first_o by_o the_o five_o proposition_n of_o the_o second_o chapter_n draw_v a_o horizontal_a line_n as_o the_o line_n a_o b_o at_o the_o upper_a part_n of_o the_o plain_a then_o at_o one_o three_o part_n of_o the_o line_n a_o b_o from_o a_o the_o right_a end_n if_o it_o be_v a_o east_n plain_a or_o from_o b_o the_o left_a end_n if_o it_o be_v a_o west_n plain_a appoint_v the_o centre_n c_o from_o which_o point_n c_z draw_v the_o semicircle_n a_o e_o d_o and_o fit_a that_o radius_fw-la in_o the_o sine_fw-la of_o 30_o degree_n which_o in_o the_o chord_n be_v 60_o degree_n then_o take_v out_o the_o sine_fw-la of_o half_a the_o latitude_n and_o lay_v it_o from_o a_o to_o e_o and_o draw_v the_o line_n c_o e_z for_o six_o in_o the_o morning_n on_o the_o east_n or_o the_o contrary_a way_n for_o the_o west_n then_o lay_v the_o sine_fw-la of_o half_a the_o compliment_n of_o the_o latitude_n from_o d_o to_o f_o and_o draw_v the_o line_n c_o f_o for_o the_o contingent_a or_o equinoctial_a line_n to_o which_o line_n you_o must_v draw_v another_o line_n parallel_n as_o far_o a_o east_n dial_n a_o west_n dial_n asunder_o as_o the_o plain_n will_v give_v leave_n then_o take_v the_o near_a distance_n from_o a_o to_o the_o six_o a_o clock_n line_n or_o more_o or_o less_o as_o you_o best_o fancy_v and_o fit_v it_o in_o the_o tangent_fw-la of_o 45_o degree_n and_o prick_v down_o all_o the_o hour_n and_o quarter_n on_o both_o the_o equinoctial_a line_n both_o way_n from_o six_o and_o they_o shall_v be_v point_n whereby_o to_o draw_v the_o hoor_fw-mi line_n by_o but_o for_o the_o two_o hour_n of_o 10_o and_o 11_o there_o be_v a_o lesser_a tangent_fw-la beginning_n at_o 45_o and_o proceed_v to_o 75_o which_o use_v thus_o fit_v the_o space_n from_o six_o to_o three_o in_o the_o little_a tangent_fw-la of_o 45_o and_o then_o and_o then_o lie_v of_o 60_o in_o the_o little_a tangent_n from_o 6._o to_o 10_o and_o the_o tangent_fw-la of_o 75_o from_o 6_o to_o 11_o and_o the_o respective_a quarter_n also_o if_o you_o please_v so_o have_v you_o all_o the_o hourâ—s_n in_o the_o east_n or_o west_n dial_n the_o distance_n from_o six_o to_o nine_o or_o from_o six_o to_o three_o in_o the_o west_n be_v the_o height_n of_o the_o stile_n in_o the_o east_n and_o west_n dial_n and_o must_v stand_v in_o the_o six_o a_o clock_n line_n and_o parallel_v to_o the_o plain_a chap._n xiii_o to_o find_v the_o declination_n of_o any_o plain_a for_o the_o find_n of_o the_o declination_n of_o a_o plain_a the_o most_o usual_a and_o easy_a way_n be_v by_o a_o magnetical_a needle_n fit_v according_a to_o mr._n fail_v way_n in_o the_o index_n of_o a_o declinatory_n or_o in_o a_o square_a box_n with_o the_o 90_o degree_n of_o a_o quadrant_a on_o the_o two_o side_n or_o by_o a_o needle_n fit_v on_o the_o index_n of_o a_o quadrant_a after_o all_o which_o way_n you_o may_v have_v they_o at_o the_o sign_n of_o the_o sphere_n and_o sundial_n in_o the_o minory_n make_v by_o john_n brown_n but_o the_o work_n may_v be_v very_o ready_o and_o exact_o perform_v by_o the_o rule_n either_o by_o the_o sun_n or_o needle_n in_o this_o manner_n follow_v of_o which_o two_o way_n that_o by_o the_o sun_n be_v always_o the_o best_a and_o most_o exact_a and_o artificial_a and_o the_o other_o not_o to_o be_v use_v if_o i_o may_v advise_v but_o when_o the_o other_o fail_v by_o the_o sun_n not_o shine_v or_o as_o a_o proof_n or_o confirmation_n of_o the_o other_o and_o first_o by_o the_o needle_n because_o the_o easy_a for_o this_o purpose_n you_o must_v have_v a_o needle_n well_o touch_v with_o the_o loadstone_n of_o about_o three_o or_o four_o inch_n long_o and_o fit_v into_o a_o box_n somewhat_o broad_a than_o one_o of_o the_o leg_n of_o the_o sector_n with_o a_o lid_n to_o open_v and_o shut_v and_o on_o the_o inside_n of_o the_o lid_n may_v be_v draw_v a_o south_n erect_v dial_n and_o a_o wire_n to_o set_v the_o lid_n upright_o and_o a_o thread_n to_o be_v the_o gnomon_n or_o stile_n to_o that_o dial_n it_o will_v not_o be_v a_o miss_n also_o to_o extend_v the_o line_n on_o the_o 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then_o the_o compliment_n of_o the_o angle_n that_o the_o sector_n stand_v at_o which_o may_v always_o be_v under_o 90_o degree_n be_v the_o declination_n of_o the_o plain_a but_o if_o it_o happen_v to_o stand_v at_o any_o angle_n above_o 90_o than_o the_o quantity_n thereof_o above_o 90_o be_v the_o declination_n of_o the_o wall_n to_o find_v the_o quantity_n of_o the_o angle_n the_o sector_n stand_v at_o may_v be_v do_v two_o way_n first_o by_o protraction_n by_o lay_v down_o the_o
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the_o tangent_fw-la of_o the_o present_a declination_n to_o the_o right_a ascension_n require_v only_o you_o must_v regard_v to_o give_v it_o a_o right_a account_n by_o consider_v the_o time_n of_o the_o year_n and_o how_o many_o 90_n past_a pror_n 14._o to_o find_v a_o altitude_n by_o the_o length_n and_o shadow_n of_o any_o perpendicular_a object_n lay_v the_o hair_n on_o one_o leg_n to_o the_o length_n of_o the_o shadow_n find_v on_o the_o line_n of_o number_n and_o the_o hair_n of_o the_o other_o leg_n to_o the_o length_n of_o the_o object_n that_o cause_v the_o shadow_n find_v on_o the_o same_o line_n of_o the_o number_n then_o observe_v the_o line_n between_o and_o which_o way_n when_o the_o leg_n be_v so_o set_v bring_v the_o first_o of_o they_o to_o the_o tangent_fw-la of_o 45_o and_o the_o other_o leg_n shall_v â—hew_v on_o the_o line_n of_o tangent_n so_o many_o turn_n between_o and_o the_o same_o way_n the_o tangent_fw-la of_o the_o altitude_n require_v thus_o may_v you_o 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