Selected quad for the lemma: day_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
day_n	hour_n	minute_n	pole_n	5,045	5	12.8170	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A29756	The description and use of a joynt-rule fitted with lines for the finding the hour of the day and azimuth of the sun, to any particular latitude, or, to apply the same generally to any latitude : together with all the uses of Gunters quadrant applyed thereunto ... / contriv'd & written by J. Brown, philomath.	Brown, John, philomath.	1661 (1661)	Wing B5038; ESTC R33265	55,838	193

declination_n of_o 12_o principal_a fix_a star_n in_o the_o heaven_n most_o of_o which_o be_v insert_v on_o the_o rule_n or_o if_o room_n will_v allow_v all_o of_o they_o  _fw-fr r._n asc._n declina_fw-la star_n name_n h._n m._n deg._n m._n pleyade_n or_o 7_o star_n 03_o 24_o 23_o 20_o bulls-eye_n 04_o 16_o 15_o 48_o orion_n girdle_n 05_o 18_o 01_o 195_o little_a dog_n 07_o 20_o 06_o 08_o lion_n heart_n 09_o 50_o 13_o 40_o lion_n tail_n 11_o 30_o 16_o 30_o arcturus_n 14_o 00_o 21_o 04_o vulture_n heart_n 19_o 33_o 08_o 00_o dolphin_n head_n 20_o 30_o 14_o 52_o pegasus_n mouth_n 21_o 27_o 08_o 19_o fomahant_n 22_o 39_o 31_o 17_n pegasus_n lower_v wing_n 23_o 55_o 13_o 19_o  _fw-fr 1_o  _fw-fr 3_o  _fw-fr 5_o 7_o 4_o  _fw-fr  _fw-fr 6_o  _fw-fr 8_o  _fw-fr  _fw-fr  _fw-fr month_n 9_o  _fw-fr 11_o  _fw-fr 2_o 10_o 12_o  _fw-fr 1_o 2_o 3_o 4_o 5_o 6_o 7_o  _fw-fr 8_o 9_o 10_o 11_o 12_o 13_o 14_o day_n 15_o 16_o 17_o 18_o 19_o 20_o 21_o  _fw-fr 22_o 23_o 24_o 25_o 26_o 27_o 28_o  _fw-fr 29_o 30_o 31_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr weekday_n s_o m_o t_o w_n t_o f_o sat_n dom._n letter_n d_o c_o b_o a_o g_o f_o e_o leap_n year_n 68_o 80_o 64_o 76_o 60_o 72_o 84_o exact_v 26_o 9_o 12_o 25_o 28_o 11_o 23_o the_o description_n and_o use_v of_o a_o joynt-rule_a chap._n i._n the_o description_n of_o the_o line_n on_o the_o rule_n as_o it_o be_v make_v only_o for_o one_o latitude_n and_o for_o the_o find_v the_o hour_n of_o the_o day_n only_o first_o open_v the_o joint_a of_o the_o rule_n then_o upon_o the_o head-leg_n be_v next_o to_o your_o right_a hand_n you_o have_v a_o line_n beginning_n at_o the_o hole_n which_o be_v the_o centre_n of_o the_o quadrantal_a line_n and_o divide_v from_o thence_o downward_o towards_o the_o head_n into_z as_o many_o degree_n as_o the_o sun_n great_a altitude_n in_o that_o latitude_n will_v be_v which_o with_o we_o at_o london_n be_v to_o 62_o degree_n which_o line_n i_o call_v the_o scale_n of_o altitude_n divide_v to_o whole_a half_n and_o sometime_o quarter_n of_o degree_n 2._o second_o on_o the_o other_o leg_n and_o next_o to_o the_o inside_n be_v the_o line_n of_o hour_n usual_o divide_v into_o hour_n quarter_n and_o every_o five_o minute_n begin_v at_o the_o head_n with_o 4_o and_o so_o proceed_v to_o 5_o 6_o 7_o 8_o 9_o 10_o 11_o and_o 12_o at_o the_o end_n and_o then_o back_o again_o with_o 1_o 2_o 3_o 4_o 5_o 6_o 7_o 8_o for_o the_o morning_n and_o afternoon_n hour_n 3._o next_o to_o this_o be_v a_o calendar_n of_o month_n and_o day_n in_o two_o line_n the_o uppermost_a contain_v that_o half_a year_n the_o day_n lengthen_v in_o and_o the_o lowermost_a the_o shorten_n day_n as_o by_o the_o name_n of_o the_o month_n may_v appear_v the_o name_n of_o every_o month_n stand_v in_o the_o month_n and_o at_o the_o begin_n of_o the_o month_n and_o all_o but_o the_o two_o month_n that_o have_v the_o long_a and_o the_o short_a day_n viz._n june_n and_o december_n be_v divide_v into_o single_a day_n the_o ten_o day_n have_v a_o figure_n 10_o or_o a_o point_n or_o prick_v on_o the_o head_n of_o the_o stroke_n and_o the_o five_o only_o a_o long_a stroke_n without_o a_o prick_n and_o the_o beginning_n of_o every_o month_n a_o long_a stroke_n and_o every_o single_a day_n all_o alike_o of_o one_o shortness_n according_a to_o the_o usual_a manner_n of_o distinguish_v on_o line_n 4._o and_o last_o you_o have_v a_o line_n of_o degree_n for_o so_o they_o be_v most_o proper_o call_v and_o they_o be_v the_o same_o with_o the_o equal_a limb_n on_o quadrant_n and_o serve_v for_o the_o same_o use_n viz._n for_o take_v of_o altitude_n or_o horizontal_a angle_n and_o be_v divide_v usual_o to_o whole_a and_o half_a degree_n of_o the_o quadrant_a and_o figure_v with_o 30_o 40_o 50_o 600_o 7010_o 8020_o and_o 90_o just_a on_o the_o head_n cut_v the_o centre_n or_o point_n where_o the_o scale_n of_o altitude_n and_o the_o line_n of_o hour_n meet_v which_o point_n for_o distinction_n sake_n i_o call_v the_o rectify_v point_n and_o the_o reckon_n on_o this_o line_n as_o to_o take_v of_o altitude_n be_v thus_o at_o the_o number_n 600_o be_v the_o beginning_n then_o towards_o the_o head_n count_v 10_o 20_o 30_o where_o the_o 90_o be_v then_o begin_v at_o the_o end_n again_o &_o count_v as_o the_o figure_n show_v you_o to_o 90_o at_o the_o head_n as_o before_z chap_n ii_o the_o use_v of_o the_o rule_n follow_v 1._o to_o rectify_v or_o set_v the_o rule_n to_o his_o true_a angle_n open_v the_o rule_n to_o 60_o degree_n which_o be_v do_v thus_o indifferent_o make_v the_o line_n on_o the_o head_n and_o the_o line_n on_o the_o other_o leg_n meet_v in_o a_o straight_a line_n then_o be_v the_o scale_n of_o altitude_n and_o the_o line_n of_o hour_n set_v to_o a_o angle_n of_o 60_o degree_n the_o rectify_v point_n be_v the_o centre_n of_o that_o angle_n or_o to_o do_v it_o more_o exact_o do_v thus_o put_v one_o point_n of_o a_o pair_n of_o compass_n into_o the_o rectify_v point_n then_o open_a the_o other_o to_o 10_o 20_o 30_o or_o 40_o on_o the_o scale_n of_o altitude_n the_o compass_n so_o open_v and_o the_o point_n yet_o remain_v in_o the_o rectify_v point_n turn_v the_o other_o to_o that_o margenal_a line_n in_o the_o line_n of_o hour_n that_o cut_v the_o rectify_v point_n and_o there_o stay_v it_o then_o remove_v the_o point_n that_o be_v fix_v in_o the_o rectify_v point_n and_o open_a or_o shut_v the_o rule_n till_o the_o point_n of_o the_o compass_n will_v touch_v 10_o 20_o 30_o or_o 40_o be_v the_o point_n you_o set_v the_o compass_n too_o in_o the_o scale_n of_o altitude_n in_o the_o innermost_a line_n that_o cut_v the_o centre_n and_o the_o rectify_v point_n then_o be_v it_o set_v exact_o to_o 60_o degree_n and_o fit_v for_o observation_n 2._o to_o find_v the_o sun_n altitude_n at_o any_o time_n put_v a_o pin_n in_o the_o centre_n hole_n at_o the_o upper_a end_n of_o the_o scale_n of_o altitude_n and_o on_o the_o pin_n hang_v a_o thread_n and_o plummet_n then_o if_o the_o sun_n be_v low_a that_o be_v to_o say_v under_o 25_o degree_n high_a as_o in_o the_o winter_n it_o will_v always_o be_v then_o lift_v up_o the_o movable_a leg_n where_o the_o month_n and_o the_o degree_n be_v till_o the_o shadow_n of_o the_o end_n fall_v just_a on_o the_o meeting_n of_o that_o leg_n with_o the_o head_n than_o the_o thread_n shall_v show_v the_o sun_n altitude_n count_v from_o 600_o towards_o the_o head_n either_o 10_o 20_o 25_o or_o any_o degree_n between_o but_o if_o the_o sun_n be_v above_o 25_o or_o 30_o degree_n high_a lift_v up_o the_o head_n leg_n till_o the_o shadow_n of_o that_o play_n as_o before_o or_o make_v the_o shadow_n of_o the_o pin_n in_o the_o centre_n hole_n play_v on_o the_o innermost_a line_n of_o the_o scale_n of_o altitude_n where_o the_o pin_n stand_v than_o the_o thread_n will_v fall_v on_o the_o degree_n and_o part_n of_o a_o degree_n that_o his_o true_a altitude_n shall_v be_v but_o if_o the_o sun_n be_v in_o a_o cloud_n and_o can_v not_o be_v see_v so_o as_o to_o give_v a_o shadow_n then_o look_v up_o along_o by_o the_o head-leg_n or_o movable_a leg_n just_a against_o the_o middle_n of_o the_o round_a body_n of_o the_o sun_n and_o the_o thread_n play_v even_o by_o the_o degree_n shall_v show_v the_o true_a altitude_n require_v the_o like_a must_v you_o do_v for_o a_o star_n or_o any_o other_o object_n who_o altitude_n you_o will_v find_v 3._o have_v find_v the_o sun_n altitude_n and_o the_o day_n of_o the_o month_n to_o find_v the_o hour_n of_o the_o day_n whatsoever_o you_o find_v the_o altitude_n to_o be_v take_v the_o same_o off_o from_o the_o line_n of_o altitude_n from_o the_o centre_n downward_o with_o a_o pair_n of_o compass_n then_o lay_v the_o thread_n be_v put_v over_o the_o pin_n on_o the_o day_n of_o the_o month_n than_o put_v one_o foot_n of_o the_o compass_n in_o the_o line_n of_o hour_n in_o that_o line_n that_o cut_v the_o rectify_v point_n and_o carry_v it_o further_o off_o or_o nigh_o till_o the_o other_o foot_n of_o the_o compass_n be_v turn_v about_o will_v just_o touch_v the_o thread_n at_o the_o near_a distance_n than_o the_o point_n of_o the_o compass_n on_o the_o line_n of_o hour_n shall_v show_v the_o true_a hour_n and_o minute_n of_o the_o day_n require_v example_n on_o the_o 2._o of_o july_n 1._o i_o observe_v the_o altitude_n in_o the_o morning_n and_o i_o find_v it_o to_o be_v 30_o degree_n high_a then_o lay_v the_o thread_n on_o the_o day_n of_o

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 win●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 sh●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 ●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 ●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

the_o day_n of_o her_o change_n but_o far_o more_o ready_o and_o as_o exact_o by_o the_o line_n of_o number_n or_o rule_n of_o three_o say_v if_o 29._o 540._o require_v 360._o what_o 6_o facit_fw-la 73_o 1_o 4_o that_o be_v 2_o signs_z 13_o degree_n 15_o minute_n to_o be_v add_v to_o 14_o degree_n in_o ♌_o and_o it_o make_v 27_o 1_o 4_o in_o ♎_o the_o moon_n place_n for_o that_o day_n or_o thus_o multiply_v the_o moon_n age_n by_o 4_o divide_v the_o product_n by_o 10_o the_o quotient_n show_v the_o sign_n and_o the_o remainder_n multiply_v by_o 3_o sheweth_z the_o degree_n which_o you_o must_v add_v to_o the_o sun_n place_n on_o the_o day_n require_v and_o it_o shall_v be_v the_o moon_n true_a place_n require_v for_o that_o day_n of_o her_o age._n example_n july_n 27._o the_o sun_n and_o moon_n be_v in_o leo_n 14_o degr_n 0._o august_n 2._o being_n 6_o day_n add_v the_o moon_n motion_n 2._o 13_o 9_o '_o make_v be_v count_v virgo_fw-la ♍_o libra_n ♎_o 27_o deg_n 9_o the_o place_n require_v which_o on_o the_o rule_n you_o may_v count_v without_o all_o this_o work_n or_o trouble_v but_o for_o plainness_n sake_n i_o be_o constrain_v so_o to_o do_v or_o thus_o prop._n 3._o to_o find_v the_o moon_n hour_n to_o do_v this_o you_o must_v do_v the_o work_n of_o the_o second_o chapter_n and_o second_o and_o three_o proposition_n where_o note_n that_o the_o moon_n place_v find_v be_v to_o be_v use_v as_o the_o day_n of_o the_o month_n or_o sun_n declination_n example_n the_o moon_n be_v 27_o degree_n in_o libra_n and_o 20_o degree_n high_a i_o find_v the_o our_o to_o be_v 31_o '_o pass_v 9_o if_o on_o the_o east-side_n or_o 29_o '_o pass_v 2_o if_o on_o the_o westside_n ●f_n the_o meridian_n prop._n 4._o to_o find_v the_o true_a hour_n of_o the_o night_n have_v find_v the_o moon_n hour_n as_o before_o consider_v the_o moon_n age_n then_o say_v by_o the_o line_n of_o number_n or_o rule_n of_o three_o if_o 29._o 540_o part_n require_v 24_o what_o shall_v 6_o day_n require_v facit_fw-la 4_o hour_n and_o 52_o minute_n which_o take_v from_o 9_o 31._o rest_n ●_o 29._o the_o true_a time_n require_v example_n moon_n hour_n 9_o 31_o time_n to_o be_v sub_v ●_o 52_o true_a time_n remain_v 3_o 39_o the_o time_n require_v this_o work_n be_v do_v more_o ready_o by_o the_o two_o line_n fit_v for_o that_o purpose_n for_o look_v for_o 6_o the_o moon_n age_n in_o one_o and_o you_o shall_v find_v ●_o hour_n 52_o minute_n the_o time_n to_o be_v substract_v in_o the_o other_o chap._n vii_o to_o find_v the_o hour_n of_o the_o night_n by_o the_o fix_a star_n for_o the_o do_n of_o this_o i_o have_v make_v choice_n of_o twelve_o principal_a fix_a star_n all_o within_o the_o two_o tropic_n many_o more_o may_v be_v add_v but_o these_o will_v very_o well_o serve_v the_o turn_n the_o name_n of_o they_o and_o their_o right_a ascension_n in_o hour_n and_o minute_n be_v set_v on_o the_o rule_n and_o the_o star_n be_v place_v in_o his_o true_a declination_n on_o or_o among_o the_o month_n and_o for_o to_o know_v the_o star_n next_o to_o a_o tutor_n a_o celestial_a globe_n or_o a_o nocturnal_a of_o all_o the_o chief_a star_n from_o the_o pole_n to_o the_o equinoctial_a and_o to_o be_v have_v at_o the_o sundial_n in_o the_o mi●nories_n be_v the_o best_a the_o use_n whereof_o do_o follow_v first_o know_v the_o star_n you_o observe_v then_o observe_v his_o altitude_n and_o lay_v the_o thread_n on_o the_o star_n by_o the_o second_o chapter_n second_o and_o three_o proposition_n get_v the_o star_n hour_n than_o out_o of_o the_o righ●_n ascension_n of_o the_o star_n take_v the_o righ●_n ascension_n of_o the_o sun_n find_v by_o the_o five_o proposition_n of_o the_o three_o chapter_n for_o that_o day_n and_o note_v the_o difference_n for_o this_o difference_n add_v to_o the_o star_n hour_n find_v shall_v show_v the_o hour_n o●_n the_o night_n example_n on_o the_o first_o of_o november_n i_o observe_v the_o altitude_n of_o the_o bulls-eye_n and_o find_v it_o to_o be_v 30._o then_o by_o second_o and_o three_o of_o the_o second_o chapter_n i_o find_v the_o hour_n to_o be_v 7._o 54_o past_o the_o meridian_n the_o sun_n right_a ascension_n that_o day_n find_v to_o be_v 15_o hour_n 8_o minute_n the_o star_n right_a ascension_n be_v 4_o hour_n 16_o minute_n which_o take_v the_o great_a from_o the_o least_o by_o add_v of_o 24_o hour_n re●_n 13._o 08._o then_o 7._o 54._o the_o star_n hou●_n add_v make_v 21._o 02._o from_o which_o taking_n 12_o hour_n rest_v 9_o 02._o the_o hour_n o●_n the_o night_n require_v for_o more_o plainness_n note_v the_o work_n of_o two_o or_o thre●_n example_n star_n right_a ascension_n be_v set_v on_o the_o rule_n 4_o 16_o sun_n right_a asc._n nou._n 1._o 15_o 08_o substraction_n being_n make_v by_o add_v 24_o remain_v 13_o 08_o to_o which_o you_o must_v add_v the_o star_n hour_n find_v 7_o 54_o then_o the_o remainder_n take_v away_o 12_o hour_n be_v 9_o 02_o the_o true_a hour_n again_o may_v 15_o by_o arcturus_n at_o 50_o 0_o '_o high_a westward_n the_o right_a asc._n of_o arcturus_n be_v 14h●_o 0_o '_o sun_n right_n asc._n may_v 15._o be_v 4_o 10_o the_o right_a asc._n of_o the_o sun_n take_v from_o the_o r._n asc._n of_o the_o star_n rest_n ●_o 50_o the_o star_n hour_n at_o 50_o degr_n high_a find_v to_o be_v 02_o 13_o which_o be_v add_v to_o the_o difference_n before_o make_v 1●_n 03_o or_o 11_o 03._o again_o january_n 5._o by_o the_o great-dog_n at_o 15_o degree_n high_a east_n the_o right_a asc._n of_o great-dog_n be_v 06-29_a the_o right_n asc._n of_o the_o sun_n be_v 19_o 50_o substr_n make_v by_o add_v 24_o h._n be_v 10-39_a star_n hour_n at_o 15_o degr_n high_a be_v 9_o 32_o ant_n m._n or_o p._n septen_n which_o add_v to_o the_o difference_n find_v and_o 12_o substract_v remain_v 8._o 11_o '_o for_o the_o true_a hour_n of_o the_o night_n require_v to_o be_v find_v and_o so_o of_o any_o other_o star_n se●_n down_o in_o the_o rule_n as_o by_o the_o trial_n and_o practise_n will_v prove_v easy_a and_o ready_a to_o the_o ingenuous_a practitioner_n but_o by_o the_o line_n of_o 24_o or_o twice_o 12_o hour_n and_o the_o help_n of_o a_o pair_n of_o compass_n you_o may_v perform_v it_o without_o write_v it_o down_o thus_o take_v the_o righ●_n ascension_n of_o the_o sun_n out_o of_o that_o lin●_n of_o hour_n between_o your_o compass_n be_v always_o count_v under_o 12_o an●_n set_v the_o same_o from_o the_o right_a ascension_n of_o the_o star_n towards_o a_o lesser_a number_n o●_n the_o beginning_n of_o the_o hour_n and_o th●_n point_n shall_v stay_v at_o the_o remainder_n that_o be_v to_o be_v add_v to_o the_o star_n hour_n find_v then_o open_a the_o compass_n from_o thence_o to_o the_o begin_n of_o the_o hour_n and_o add_v that_o to_o the_o star_n hour_n find_v and_o it_o shall_v reach_v to_o the_o hour_n of_o the_o night_n require_v example_n feb._n 6._o 1660._o by_o arcturus_n 20_o degree_n high_a take_v 10_o hour_n 1_o minute_n between_o your_o compass_n and_o set_v it_o from_o 14_o hour_n or_o 2_o hour_n beyond_o 12_o and_o it_o shall_v stay_v at_o 3._o 59_o then_o take_v 3._o 59_o and_o add_v it_o to_o 6._o 24_o the_o star_n hour_n at_o 20_o degree_n high_a and_o it_o shall_v be_v 10._o 23_o the_o hour_n of_o the_o night_n require_v chap._n viii_o to_o find_v the_o amplitude_n or_o azimuth_n of_o the_o fix_a star_n also_o their_o rise_n set_v and_o sothe_v 1._o first_o for_o the_o amplitude_n take_v the_o star_n declination_n from_o the_o particular_a scale_n of_o altitude_n and_o lay_v it_o from_o 90_o in_o the_o azimuth-line_n and_o it_o shall_v show_v his_o amplitude_n from_o east_n or_o west_n towards_o south_n or_o north_n according_a to_o the_o declination_n and_o time_n of_o day_n morning_n or_o evening_n the_o same_o work_n be_v for_o the_o sun_n example_n the_o bulls-eye_n have_v 25._o 54_o degree_n of_o amplitude_n so_o have_v the_o sun_n at_o 15_o degree_n 48_o minute_n of_o declination_n 2._o to_o find_v the_o azimuth_n work_n as_o you_o do_v for_o the_o sun_n at_o the_o same_o declination_n the_o star_n have_v by_o chapter_n 5._o and_o you_o shall_v have_v your_o desire_n example_n december_n 24._o at_o 6_o degree_n high_a by_o the_o bulls-eye_n i_o find_v the_o azimuth_n to_o be_v 107._o 53._o from_o the_o south_n 3_o to_o find_v the_o star_n rise_v and_o set_v lay_v the_o thread_n on_o the_o star_n among_o the_o month_n and_o in_o the_o line_n of_o hour_n it_o show_v the_o star_n rise_v and_o set_v as_o you_o count_v for_o the_o sun_n but_o yet_o note_v this_o be_v

day_n in_o this_o latitude_n will_v be_v find_v to_o be_v 109_o degree_n want_v of_o south_n or_o pole_n of_o the_o place_n therefore_o unlike_o sign_n and_o to_o be_v add_v and_o they_o make_v up_o 119_o degree_n who_o compliment_n to_o 180_o be_v 61_o for_o 61_o and_o 119_o add_v make_v up_o 180_o therefore_o this_o plain_n decline_v 61_o degree_n from_o the_o north_n towards_o the_o east_n again_o the_o same_o day_n in_o the_o afternoon_n i_o find_v the_o azimuth_n past_o the_o south_n or_o meridian_n of_o the_o place_n 30_o degree_n and_o at_o the_o same_o time_n the_o sun_n want_v in_o come_v to_o the_o meridian_n or_o pole_n of_o the_o plain_a 10_o degree_n here_o by_o addition_n i_o find_v the_o declination_n to_o be_v 40_o degree_n south-west_n note_v what_o i_o have_v say_v in_o these_o three_o example_n be_v general_a at_o all_o time_n but_o if_o it_o be_v a_o fair_a day_n and_o time_n and_o opportunity_n serve_v to_o come_v either_o just_a at_o 12_o a_o clock_n when_o the_o sun_n be_v the_o meridian_n or_o pole_n of_o the_o place_n or_o just_o when_o the_o sun_n be_v in_o the_o meridian_n or_o pole_n of_o the_o plain_a than_o your_o work_n be_v only_o thus_o first_o if_o you_o come_v to_o observe_v at_o 12_o then_o apply_v your_o rule_n to_o the_o wall_n and_o hold_v up_o the_o thread_n and_o plummet_n how_o much_o so_o ever_o the_o sun_n want_v or_o be_v past_o the_o pole_n of_o the_o plain_a that_o be_v the_o declination_n if_o it_o be_v pass_v it_o be_v east-ward_n if_o it_o want_v it_o be_v south-west-ward_n if_o neither_o a_o just_a south_n plain_a and_o then_o the_o pole_n or_o meridian_n of_o place_n and_o plain_n be_v the_o same_o but_o second_o if_o you_o come_v when_o the_o sun_n be_v just_a in_o the_o pole_n of_o the_o plain_a than_o whatsoever_o you_o find_v the_o sun_n azimuth_n to_o be_v that_o be_v the_o declination_n if_o it_o want_v of_o south_n it_o decline_v east-ward_n if_o it_o be_v past_a it_o decline_v westward_n thus_o i_o have_v copious_o and_o yet_o very_o brief_o show_v you_o the_o most_o artificial_a way_n of_o get_v the_o declination_n of_o any_o wall_n howsoever_o situate_v note_v if_o the_o sun_n be_v above_o 15_o degree_n want_v of_o the_o meridian_n of_o the_o plain_a your_o rule_n will_v prove_v defective_a in_o take_v the_o plain_n meridian_n when_o the_o centre_n leg_n be_v next_o the_o wall_n than_o you_o must_v turn_v the_o other_o leg_n to_o the_o wall_n and_o then_o you_o find_v a_o supply_n for_o all_o angle_n to_o 45_o degree_n past_o the_o plain_a but_o for_o the_o supply_n of_o the_o rest_n which_o be_v 45_o degree_n do_v thus_o open_v the_o rule_n till_o the_o great_a line_n of_o tangent_n &_o the_o outside_n of_o the_o leg_n make_v a_o right_a angle_n for_o which_o on_o the_o head_n you_o may_v make_v a_o mark_n for_o the_o ready_a set_n then_o make_v the_o inside_n of_o the_o leg_n at_o the_o end_n of_o 45_o as_o a_o centre_n the_o tangent_n on_o the_o other_o leg_n supply_v very_o large_o the_o defect_n of_o the_o otherside_n or_o if_o you_o set_v on_o the_o box_n and_o needle_n on_o the_o rule_n and_o open_a or_o shut_v the_o rule_n till_o the_o shadow_n of_o the_o thread_n show_v just_a 12_o than_o the_o angle_n the_o sector_n stand_v at_o be_v the_o compliment_n of_o what_o the_o sum_n want_v or_o be_v past_o the_o meridian_n or_o pole_n of_o the_o plain_a chap._n fourteen_o to_o draw_v a_o vertical_a decline_a plain_n to_o any_o declination_n first_o draw_v a_o perpendicular-line_n for_o 12_o as_o a_o b_o then_o design_v a_o point_n in_o that_o line_n for_o the_o centre_n as_o c_o at_o the_o upper_a end_n if_o it_o be_v a_o south_n plain_a or_o contrary_a if_o it_o be_v a_o north_n plain_a then_o on_o that_o centre_n describe_v a_o arch_n of_o a_o circle_n on_o that_o side_n of_o 12_o which_o be_v contrary_a to_o the_o plain_n declination_n as_o d_o e_z and_o in_o that_o arch_n lie_v off_o from_o 12_o the_o substile_a and_o on_o that_o the_o style_n height_n and_o the_o hour_n of_o 6_o be_v find_v by_o the_o ten_o chapter_n and_o draw_v those_o line_n from_o c_o the_o centre_n then_o draw_v two_o parallel_n to_o 12_o as_o in_o the_o direct_a south_n then_o fit_a the_o distance_n of_o the_o parallel_n in_o the_o secant_fw-la of_o the_o declination_n and_o take_v the_o secant_fw-la of_o the_o latitude_n and_o set_v it_o from_o the_o centre_n c_o on_o the_o line_n of_o 12_o to_o f_o and_o on_o the_o parallel_n from_o 6_o to_z g_z and_o draw_v a_o line_n by_o those_o two_o point_n f_o and_o g_o to_o cut_v the_o other_o parallel_n in_o h_n then_o have_v you_o find_v 6_o 3_o and_o 9_o then_o fit_a 6_o g_o in_o the_o tangent_fw-la of_o 45_o and_o prick_v off_o 15_o 30_o and_o the_o respective_a quarter_n both_o way_n from_o 6_o for_o the_o morning_n and_o afternoon_n hour_n then_o fit_a f_o g_o in_o 45_o and_o lay_v off_o the_o same_o point_n from_o f_o both_o way_n for_o 10_o 11_o 1_o and_o 2_o and_o the_o quarter_n also_o if_o you_o please_v and_o those_o shall_v be_v point_n to_o draw_v the_o hour-line_n by_o the_o stile_n must_v be_v set_v perpendicular_a over_o the_o substile_a to_o the_o angle_n find_v by_o the_o rule_n in_o the_o ten_o chapter_n and_o then_o the_o dial_n shall_v show_v the_o true_a hour_n of_o the_o day_n be_v draw_v fit_a to_o his_o proper_a declination_n another_o way_n to_o perform_v this_o geometrical_o for_o all_o erect_a dial_n with_o centre_n when_o you_o have_v draw_v a_o line_n of_o 12_o and_o appoint_v a_o centre_n make_v a_o geometrical_a square_n on_o that_o side_n 12_o as_o the_o stile_n must_v stand_v on_o as_o a_o b_o c_o d_o the_o perpendicular_a side_n of_o which_o square_a may_v also_o be_v the_o parallel_n as_o before_o again_o fit_v the_o side_n of_o the_o square_n in_o the_o cousin_n of_o the_o latitude_n and_o take_v out_o the_o sine_fw-la of_o the_o latitude_n and_o fit_a that_o over_o in_o the_o sine_fw-la of_o 90_o then_o take_v out_o the_o 〈◊〉_d sine_fw-la of_o the_o declination_n and_o lay_v it_o from_o d_o to_z g_z for_o the_o hour_n of_o 6_o and_o draw_v the_o line_n a_o g_o for_o the_o 6_o a_o clock_n hour_n line_n then_o again_o fit_v the_o side_n of_o the_o square_n or_o the_o distance_n of_o the_o parallel_n in_o the_o other_o way_n when_o you_o want_v a_o secant_fw-la or_o your_o secant_fw-la too_o little_a in_o the_o sine_fw-la of_o 90_o and_o take_v out_o the_o cousin_n of_o the_o declination_n fit_a that_o in_o the_o cousin_n of_o the_o latitude_n then_o take_v out_o the_o sine_fw-la of_o 90_o and_o lay_v it_o from_o the_o centre_n on_o the_o line_n of_o 12_o and_o 〈◊〉_d 6_o in_o the_o side_n of_o the_o square_n and_o by_o those_o two_o point_n draw_v the_o contingent_a line_n and_o then_o fit_a those_o point_n or_o distance_n in_o the_o tangent_fw-la of_o 45_o and_o lay_v down_o the_o hour_n as_o in_o the_o former_a part_n of_o this_o chapter_n but_o if_o you_o want_v the_o hour_n before_o 9_o in_o west-decliners_a or_o the_o hour_n after_o 3_o in_o east-decliners_a and_o the_o 6_o fall_v too_o high_a above_o the_o horizontal_a line_n on_o that_o side_n you_o may_v supply_v this_o defect_n thus_o take_v the_o measure_n with_o your_o compass_n from_o 3_o to_o 4_o and_o 5_o upward_o in_o the_o west-decliners_a or_o from_o 9_o to_o 7_o and_o 8_o in_o east-decliners_a and_o lay_v it_o upward_o from_o 9_o or_o 3_o on_o the_o deficient_a side_n in_o the_o parallel_n as_o it_o shall_v have_v be_v from_o 6_o downward_o in_o south_n or_o upward_o in_o north_n plain_n and_o you_o shall_v see_v all_o your_o defective_a point_n to_o be_v complete_o supply_v whereunto_o draw_v the_o hour-line_n according_o chap._n xv_o to_o draw_v the_o hour-line_n on_o a_o upright_a decline_a dial_n decline_v above_o 60_o degree_n in_o all_o erect_a decliner_n the_o way_n of_o find_v the_o stile_n substile_a 6_o and_o 12_o and_o inclination_n of_o meridian_n be_v the_o same_o but_o when_o you_o come_v to_o protract_v or_o lay_v down_o the_o hour-line_n you_o shall_v find_v they_o come_v so_o close_o together_o as_o they_o will_v be_v useless_a unless_o the_o stile_n be_v augment_v the_o usual_a way_n for_o do_v of_o which_o be_v to_o draw_v the_o dial_n on_o a_o large_a floor_n and_o then_o cut_v off_o so_o much_o and_o at_o such_o a_o distance_n as_o best_o serve_v your_o turn_n but_o this_o be_v not_o always_o to_o be_v affect_v for_o want_v of_o conveniency_n and_o large_a instrument_n it_o may_v very_o artificial_o be_v do_v by_o a_o natural_a tangent_fw-la of_o 75_o or_o 80_o degree_n fit_v on_o the_o leg_n of_o a_o

the_o description_n and_o use_v of_o a_o joynt-rule_a fit_v with_o line_n for_o the_o find_v the_o hour_n of_o the_o day_n and_o azimuth_n of_o the_o sun_n to_o any_o particular_a latitude_n or_o to_o apply_v the_o same_o general_o to_o any_o latitude_n together_o with_o all_o the_o use_n of_o gunter_n quadrant_a apply_v thereunto_o as_o sunrising_n declination_n amplitude_n true_a place_n right_a ascension_n and_o the_o hour_n of_o the_o night_n by_o the_o moon_n or_o fix_v star_n a_o speedy_a and_o easy_a way_n of_o find_v of_o altitude_n at_o one_o or_o two_o station_n also_o the_o way_n of_o make_v any_o kind_n of_o erect_a sundial_n to_o any_o latitude_n or_o declination_n by_o the_o same_o rule_n with_o the_o description_n and_o use_v of_o several_a line_n for_o the_o mensuration_n of_o superficies_n and_o solid_n and_o of_o other_o line_n usual_o put_v on_o carpenter_n rule_n also_o the_o use_n of_o mr._n whites_n rule_n for_o measure_v of_o board_n and_o timber_n round_o and_o square_a with_o the_o manner_n of_o use_v the_o serpentine-line_n of_o number_n sin_n tangent_n and_o verse_v sin_n contrive_v &_o write_v by_o j._n brown_n philom_o london_n print_v by_o t._n i._n for_o i._o brown_n and_o h._n sutton_n and_o sell_v at_o their_o house_n in_o the_o minory_n &_o thredneedle-street_n 1661._o to_o the_o reader_n courteous_a reader_n among_o the_o multitude_n of_o book_n which_o be_v print_v and_o publish_v in_o this_o scribble_a age_n some_o serious_a some_o seditious_a some_o discover_v or_o savour_v of_o art_n other_o of_o ignorance_n possible_o every_o one_o endeavour_v to_o bring_v their_o male_n among_o the_o rest_n of_o the_o crowd_n i_o like_o the_o widow_n throw_v in_o my_o mite_n if_o it_o be_v or_o seem_v to_o be_v little_a it_o be_v like_o the_o giver_n and_o therefore_o i_o presume_v will_n of_o some_o be_v accept_v as_o little_a as_o it_o be_v and_o as_o little_a worth_n as_o it_o be_v it_o be_v like_a enough_o to_o be_v challenge_v but_o i_o shall_v endeavour_v to_o prevent_v prejudice_n by_o the_o follow_a discourse_n have_v for_o some_o time_n be_v inquire_v to_o find_v out_o a_o way_n whereby_o workman_n may_v on_o their_o rule_n their_o constant_a companion_n have_v a_o way_n easy_o and_o exact_o to_o find_v the_o hour_n of_o the_o day_n and_o sun_n altitude_n and_o azimuth_n and_o the_o like_a and_o have_v at_o several_a time_n for_o several_a man_n at_o their_o request_n use_v one_o and_o the_o other_o contrivance_n to_o find_v the_o hour_n as_o that_o of_o the_o cillender_n quadrant_n or_o the_o like_a as_o the_o altitude_n by_o a_o tangent_fw-la on_o the_o inside_n of_o a_o square_a or_o joynt-rule_n and_o the_o line_n of_o sin_n on_o the_o flat_a side_n but_o still_o one_o inconvenience_n or_o other_o of_o trouble_n in_o add_v of_o compliment_n or_o difficulty_n of_o take_v of_o aititude_n or_o trouble_v to_o the_o memory_n do_v accrue_v to_o the_o work_n or_o else_o the_o radius_fw-la be_v small_a and_o so_o much_o the_o more_o short_a of_o exactness_n at_o last_o there_o come_v to_o my_o sight_n a_o quadrant_n make_v by_o mr._n thomson_n and_o as_o i_o be_v inform_v be_v first_o draw_v or_o contrive_v to_o that_o form_n by_o mr_n samuel_n foster_n that_o ingenious_a artist_n and_o laborious_a student_n and_o reader_n of_o the_o mathematics_n in_o gresham_n college_n and_o consider_v of_o the_o ease_n and_o speed_n in_o the_o use_n thereof_o i_o set_v myself_o to_o the_o contrive_v thereof_o to_o a_o more_o portable_a form_n at_o last_o take_v some_o pain_n in_o delineat_v one_o and_o another_o in_o several_a form_n and_o inquire_v after_o the_o use_v thereof_o and_o in_o effect_n have_v do_v as_o mr._n gunter_n with_o stoffler_n astrolabe_n and_o nepeirs_n logarithm_n and_o as_o mr._n oughtre_v with_o gunter_n rule_n to_o a_o slide_n and_o circular_a form_n and_o as_o my_o father_n thomas_n brown_n into_o a_o serpentine_a form_n or_o as_o mr._n windgate_n in_o his_o rule_n of_o froportion_n and_o as_o of_o late_a mr._n collins_n with_o mr._n gunter_n sector_n on_o a_o quadrant_n so_o may_v this_o not_o unfit_o be_v call_v the_o quadrant_n on_o a_o sector_n and_o in_o fine_a the_o invention_n will_v be_v value_v for_o the_o learned_a author_n sake_n and_o never_o a_o whit_n the_o worse_a for_o the_o new_a contriver_n sake_n for_o first_o hereby_o it_o be_v make_v large_a in_o little_a room_n and_o as_o well_o on_o wood_n as_o on_o brass_n which_o be_v a_o incommunicable_a property_n to_o broad_a quadrant_n though_o of_o never_o so_o good_a matter_n as_o experience_a workman_n know_v right_a well_o and_o by_o a_o tangent_fw-la of_o 30_o degree_n lay_v together_o be_v get_v all_o kind_n of_o angle_n or_o altitude_n under_o 90_o degree_n and_o to_o be_v afford_v for_o a_o low_a price_n in_o comparison_n of_o other_o instrument_n which_o will_v not_o perform_v the_o same_o operation_n any_o better_a have_v make_v some_o joynt-rule_n in_o the_o manner_n follow_v and_o expose_v they_o to_o sale_n i_o have_v be_v many_o time_n solicit_v to_o write_v somewhat_o of_o the_o use_n and_o now_o at_o last_o after_o near_o a_o year_n suspense_n have_v commit_v the_o follow_a discourse_n to_o public_a view_n partly_o to_o save_v the_o labour_n of_o tedious_a transcribing_n and_o also_o to_o make_v so_o useful_a cheap_a and_o exact_v a_o instrument_n if_o it_o be_v true_o make_v to_o be_v more_o know_v or_o occupy_v in_o which_o business_n i_o desire_v to_o disclaim_v all_o vainglorious_a ostentation_n and_o therefore_o have_v naked_o and_o plain_o assert_v the_o manner_n how_o and_o why_o it_o come_v to_o be_v publish_v to_o the_o world_n by_o i_o it_o be_v a_o mechanical_a thing_n and_o mechanical_o apply_v and_o of_o mechanical_a man_n will_v be_v humanical_o accept_v i_o doubt_v not_o have_v begin_v to_o write_v i_o can_v not_o break_v off_o so_o short_a and_o abrupt_o as_o at_o first_o i_o do_v intend_v to_o do_v therefore_o have_v add_v this_o short_a discourse_n of_o ordinary_a dyall_n the_o exact_a method_n of_o which_o i_o find_v in_o no_o other_o author_n that_o ever_o i_o meet_v with_o and_o indeed_o i_o have_v not_o time_n to_o read_v many_o yet_o i_o dare_v presume_v that_o for_o speed_n ease_n convenience_n and_o exactness_n inferior_a to_o none_o especial_o the_o way_n of_o make_v far_o decline_v dial_n as_o for_o other_o decline_a reclining_a dial_n i_o refer_v you_o to_o other_o author_n or_o to_o a_o discourse_n thereof_o by_o itself_o if_o i_o find_v encouragement_n and_o ability_n to_o perform_v the_o same_o a_o copy_n whereof_o i_o have_v have_v a_o long_a time_n by_o i_o write_v by_o a_o very_a ingenious_a artist_n the_o demonstration_n of_o which_o dial_n be_v most_o excellent_o and_o easy_o show_v by_o the_o figure_n insert_v page_n 77._o as_o for_o the_o other_o part_n for_o take_v of_o altitude_n and_o angle_n it_o may_v also_o be_v very_o convenient_o do_v if_o the_o rule_n be_v fit_v to_o a_o three-leg_n staff_n with_o a_o small_a ball-socket_n to_o set_v it_o level_n or_o upright_o as_o other_o surveighing-instrument_n be_v as_o will_v be_v ample_o find_v if_o a_o trial_n be_v make_v thereof_o that_o of_o ma●er_a white_n be_v rule_n be_v a_o thing_n that_o have_v give_v very_o good_a content_n to_o several_a gentleman_n in_o the_o county_n of_o essex_n suffolk_n and_o norfolk_z and_o indeed_o be_v a_o very_a neat_a and_o accurate_a way_n of_o operation_n well_o become_v a_o gentleman_n for_o while_o a_o workman_n shall_v take_v measure_n his_o rule_n keep_v the_o count_n of_o length_n or_o breadth_n and_o have_v the_o length_n first_o give_v the_o gird_v or_o squareness_n be_v no_o soon_o agree_v on_o but_o you_o have_v the_o content_a without_o pen_n or_o compass_n as_o for_o the_o other_o line_n as_o decimal-board_n and_o timber-measure_n inch_n and_o foot_n in_o the_o way_n of_o reduction_n girt-measure_n circle_n diameter_n circumference_n square_n inscribe_v and_o equal_a the_o use_n of_o they_o will_v be_v very_o grateful_a to_o many_o a_o learner_n last_o this_o brief_a touch_n of_o the_o serpentine-line_n i_o make_v bold_a to_o assert_v to_o see_v if_o i_o can_v draw_v out_o a_o performance_n of_o that_o promise_n that_o have_v be_v so_o long_o unperformed_a by_o the_o promiser_n thereof_o these_o collection_n courteous_a reader_n i_o have_v print_v at_o my_o friend_n and_o my_o own_o proper_a charge_n and_o if_o they_o prove_v to_o be_v as_o i_o do_v hope_n they_o will_v of_o public_a benefit_n i_o shall_v enjoy_v my_o expectation_n and_o be_v ready_a at_o all_o time_n to_o serve_v you_o further_o as_o i_o may_v in_o these_o or_o other_o mathematical_a instrument_n at_o my_o house_n at_o the_o sundial_a in_o the_o minory_n and_o remain_v to_o you_o much_o oblige_v february_n 8_o 1660._o

john_n brown_n a_o table_n of_o the_o thing_n contain_v in_o this_o book_n chap._n i._n page_z the_o description_n of_o the_o rule_n for_o the_o hour_n only_o 1._o 2._o 3_o chap._n ii_o to_o rectify_v or_o set_v the_o rule_n to_o his_o true_a angle_n for_o observation_n 4_o to_o find_v the_o sun_n altitude_n 5_o to_o find_v the_o hour_n of_o the_o day_n 6_o to_o find_v the_o sun_n rise_v and_o set_v 7_o to_o find_v a_o level_n or_o perpendicular_a 7_o chap._n iii_o a_o further_a description_n of_o the_o rule_n for_o hour_n and_o azimuth_n general_o 10_o 11_o 12_o chap._n four_o to_o find_v the_o sun_n declination_n 13_o to_o find_v the_o sun_n true_a place_n and_o right_a ascension_n 14_o to_o find_v the_o sun_n amplitude_n 14_o chap._n v._n to_o find_v the_o sun_n azimuth_n at_o any_o altitude_n and_o declination_n in_o this_o particular_a latitude_n in_o summer_n 16_o to_o find_v the_o azimuth_n in_o winter_n and_o equinoctial_a 17_o 18_o chap._n vi_o to_o find_v the_o hour_n of_o the_o night_n by_o the_o moon_n 19_o to_o find_v the_o moon_n age_n 20_o to_o find_v the_o moon_n place_n 21_o to_o find_v the_o moon_n hour_n by_o the_o 11_o chap._n 2_o and_o 3_o proposition_n 23_o to_o find_v the_o true_a hour_n of_o the_o night_n thereby_o 24_o chap._n vii_o to_o find_v the_o hour_n of_o the_o night_n by_o the_o sixed_a star_n 25_o three_o example_n thereof_o 26_o 27_o 28_o chap._n viii_o to_o find_v the_o amplitude_n azimuth_n rise_v and_o so●●hing_v of_o the_o fix_a star_n and_o example_n thereof_o in_o page_n 29_o 30_o 31_o 32_o chap._n ix_o to_o find_v the_o hour_n and_o azimuth_n etc._n etc._n in_o any_o latitude_n 33_o to_o find_v the_o sun_n rise_v set_v and_o ascentional_a difference_n ibid._n to_o find_v his_o amplitude_n in_o any_o latitude_n 34_o to_o find_v the_o sun_n altitude_n at_o six_o in_o any_o latitude_n 35_o to_o find_v the_o hour_n when_o the_o sun_n be_v in_o the_o equinoctial_a 36_o to_o find_v the_o hour_n in_o any_o latitude_n altitude_n and_o declination_n 37_o to_o find_v the_o sun_n azimuth_n in_o any_o latitude_n at_o any_o declination_n and_o altitude_n in_o summer_n 38_o to_o find_v the_o same_o in_o winter_n 39_o chap._n x._o to_o find_v the_o inclination_n of_o meridian_n substile_a stile_n and_o angle_n between_o 12_o and_o 6_o for_o erect_v decliner_n three_o way_n one_o particular_a and_o two_o general_n 40_o to_o find_v the_o substile_a style_v elevation_n inclination_n of_o meridian_n 41_o to_o find_v the_o angle_n between_o 12_o and_o 6_o for_o a_o particular_a latitude_n 42_o to_o perform_v the_o same_o in_o general_n for_o any_o latitude_n by_o the_o general_a scale_n of_o altitude_n 43_o 44_o five_o canon_n to_o find_v the_o same_o by_o the_o artificial_a sin_n and_o ta●gents_n and_o how_o to_o work_v they_o on_o the_o rule_n 45_o 46_o chap._n xi_o to_o draw_v a_o horizontal_a dyal_n to_o any_o latitude_n 47_o to_o draw_v a_o vertical_a direct_a north_n or_o south_n dial_n to_o any_o latitude_n 48_o 49_o to_o draw_v a_o direct_a erect_a east_n or_o west_n dial_n 50_o 51_o chap._n xiii_o to_o find_v the_o declination_n of_o a_o plain_n 52_o to_o do_v it_o by_o the_o needle_n 53_o 54_o to_o find_v the_o quantity_n of_o a_o angle_n the_o sector_n or_o rule_n stand_v at_o 55_o a_o example_n of_o the_o work_n 56_o to_o find_v a_o declination_n by_o the_o sun_n at_o any_o time_n 57_o 58_o some_o precept_n and_o example_n for_o the_o same_o 59_o 60_o 61_o to_o find_v a_o declination_n at_o two_o choice_n particular_a time_n viz._n when_o the_o sun_n be_v in_o the_o meridian_n of_o place_n or_o plain_a 62_o 63_o how_o to_o supply_v a_o deficiency_n in_o one_o line_n of_o the_o rule_n by_o another_o line_n on_o the_o rule_n 64_o chap._n xiiii_o to_o draw_v a_o vertical_a decline_a dial_n to_o any_o declination_n and_o latitude_n 65_o to_o perform_v it_o another_o way_n 66_o 67_o to_o supply_v a_o defect_n on_o the_o parallel_n contingent_a 68_o chap._n xv._n to_o draw_v the_o hour-line_n on_o a_o upright_a decline_a dial_n decline_v above_o 60_o degree_n 96_o to_o make_v the_o table_n for_o the_o hour_n 70_o to_o find_v the_o substile_a style_v augmentation_n and_o radius_fw-la to_o fit_a and_o fill_v the_o plain_a with_o any_o certain_a number_n of_o hour_n 71_o 72_o 73_o 74_o 75_o a_o advertisement_n relate_v to_o decline_a recline_a plain_n 76_o 77_o 78_o 79_o chap._n xvi_o to_o find_v a_o perpendicular_a altitude_n at_o one_o or_o two_o stationi_fw-la 80_o to_o do_v it_o at_o one_o station_n 81_o to_o perform_v it_o at_o two_o station_n 82_o 83_o 84_o to_o work_v it_o by_o the_o sector_n line_n 85_o 86_o chap._n xvii_o the_o use_n of_o several_a line_n insert_v on_o rule_n for_o the_o use_n of_o several_a workman_n for_o the_o mensuration_n of_o superficial_a and_o solid_a measure_n and_o reduction_n etc._n etc._n 87_o the_o use_n of_o inch_n and_o foot_n measure_v lay_v together_o in_o give_v the_o price_n of_o one_o to_o know_v the_o price_n of_o a_o hundred_o or_o the_o contrary_a 88_o the_o use_n in_o buy_v of_o timber_n know_v the_o price_n of_o a_o load_n or_o 50_o foot_n to_o know_v the_o price_n of_o one_o foot_n or_o the_o contrary_a 89_o 90._o the_o like_a work_n for_o the_o great_a hundred_o or_o 112_o l._n to_o the_o c._n 90_o 91_o the_o use_n of_o the_o line_n of_o decimal_a board_n measure_v 92_o the_o use_n of_o the_o line_n of_o decimal_a timber_n measure_v 93_o the_o use_n of_o the_o line_n of_o decimal_a yard_n measure_v 94_o or_o that_o which_o agree_v with_o foot_n and_o inch_n 95_o the_o use_n of_o the_o line_n of_o decimal_n round_o or_o gird_a measure_n 96_o the_o use_n of_o the_o line_n of_o decimal_n solid_a measure_n by_o the_o diameter_n 97_o the_o table_n of_o decimal_n superficial_a under_o measure_n 98_o 99_o the_o table_n for_o decimal_n solid_a under_o measure_n 100_o 101_o the_o table_n of_o under-yard_n measure_n for_o foot_n measure_n or_o inch_n 102_o 103_o the_o table_n of_o under_o gird_v measure_n to_o inch_n 104_o the_o table_n of_o under_o diameter_n measure_n to_o inch_n and_o quarter_n 105_o a_o table_n of_o brick_n measure_v 106_o the_o use_n of_o the_o line_n of_o circumference_n diameter_n and_o square_n equal_a and_o inscribe_v 108_o chap._n xviii_o the_o use_n of_o mr._n whites_n rule_v or_o the_o slide_a rule_n in_o arithmetic_n and_o measure_v superficial_a and_o solid_a measure_n from_o 110_o to_o 118_o chap_n xix_o to_o find_v hour_n and_o azimnth_n by_o that_o sector_n to_o find_v the_o azimuth_n by_o have_v latitude_n sun_n declination_n and_o altitude_n cemplement_n and_o the_o hour_n from_o noon_n 119_o to_o find_v the_o hour_n by_o have_v the_o same_o compliment_n and_o the_o azimuth_n from_o south_n 120_o have_v the_o compliment_n of_o the_o latitude_n and_o altitude_n and_o the_o sun_n distance_n from_o the_o pole_n to_o find_v the_o sun_n azimuth_n 121_o have_v the_o same_o compliment_n to_o find_v the_o hour_n by_o the_o sector_n 122_o have_v latitude_n declination_n meridian_n and_o present_a altitude_n to_o find_v the_o hour_n of_o the_o day_n 123_o have_v latitude_n declination_n and_o altitude_n to_o find_v the_o sun_n azimuth_n at_o one_o operation_n by_o the_o sector_n 124_o have_v the_o length_n of_o the_o shadow_n to_o find_v the_o altitude_n and_o the_o contrary_a 126_o have_v latitude_n and_o declination_n to_o find_v the_o sun_n rise_v and_o set_v 127_o to_o find_v the_o sun_n altitade_fw-la at_o any_o hour_n general_o 129_o to_o find_v when_o the_o sun_n shall_v be_v due_a east_n or_o west_n 130_o to_o find_v the_o quesita_fw-la in_o erect_v dial_n 131_o 132._o chap._n xx._n the_o use_n of_o the_o serpentine_a line_n the_o description_n thereof_o 134_o 135_o 136_o 137_o some_o observation_n in_o the_o use_n thereof_o 138._o 139_o 140_o to_o find_v the_o hour_n of_o the_o day_n thereby_o according_a to_o mr._n gunter_n 142_o to_o find_v the_o hour_n thereby_o according_a to_o mr._n collins_n 145_o to_o find_v the_o azimuth_n thereby_o mr._n collins_n his_o way_n 146_o to_o find_v the_o azimuth_n mr._n gunter'_v way_n 148_o to_o find_v the_o hour_n and_o azimnth_n at_o one_o operation_n by_o help_n of_o the_o natural_a sin_n and_o verse_v sin_n 149_o to_o 154_o to_o find_v the_o sun_n altitude_n at_o any_o hour_n or_o azimuth_n 155_o 156_o to_o find_v the_o hour_n by_o have_v the_o azimuth_n and_o the_o contrary_a 157_o five_o other_o useful_a proposition_n 159_o to_o square_a and_o cube_fw-la a_o number_n and_o to_o find_v the_o square_n and_o cube_fw-la root_n of_o a_o number_n 162_o 163_o to_o work_n question_n of_o interest_n and_o annuity_n 164_o the_o use_n of_o the_o everlasting_a almanac_n 167_o the_o right_a ascension_n and_o

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 hour●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 horizontal_a part_n for_o the_o same_o thread_n be_v a_o stile_n for_o that_o also_o also_o on_o the_o bottom_n let_v there_o be_v a_o rabbit_n or_o grove_n make_v to_o fit_v the_o leg_n of_o the_o rule_n or_o sector_n so_o as_o be_v press_v into_o it_o it_o may_v not_o fall_v off_o from_o the_o rule_n if_o your_o hand_n shall_v shake_v or_o you_o cease_v to_o hold_v it_o there_o this_o be_v so_o fit_v the_o use_n follow_v in_o their_o order_n put_v your_o box_n and_o needle_n on_o that_o leg_n of_o the_o rule_n that_o will_v be_v most_o fit_a for_o your_o purpose_n and_o also_o the_o north_n end_n of_o the_o needle_n towards_o the_o wall_n if_o it_o be_v a_o south_n wall_n and_o the_o contrary_a if_o a_o north_n as_o the_o play_v of_o the_o needle_n will_v direct_v you_o better_a than_o the_o way_n how_o in_o a_o thousand_o word_n then_o open_a or_o close_o the_o rule_n till_o the_o needle_n play_v right_a over_o the_o north_n and_o south-line_n in_o the_o bottom_n of_o the_o box_n 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

rule_n so_o set_v on_o a_o board_n and_o draw_v two_o line_n by_o the_o leg_n of_o the_o sector_n and_o find_v the_o angle_n by_o a_o line_n of_o chord_n second_o more_o speedy_o and_o artificial_o thus_o by_o the_o line_n of_o sines_n be_v draw_v to_o 2._o 4_o or_o 6_o degree_n asunder_o the_o sector_n so_o set_v take_v the_o parallel_n sine_fw-la of_o 30_o and_o 30_o and_o measure_v it_o on_o the_o lateral_a sin_n from_o the_o centre_n and_o it_o shall_v reach_v to_o the_o sine_fw-la of_o half_a the_o angle_n the_o line_n of_o sin_n stand_v at_o be_v more_o by_o 2_o 4_o or_o 6_o degree_n then_o the_o sector_n stand_v at_o because_o it_o be_v draw_v one_o two_o or_o three_o degree_n from_o the_o inside_n or_o else_o take_v the_o latteral_a sine_fw-la of_o 30_o from_o the_o centre_n and_o keep_v one_o foot_n fix_v in_o 30_o turn_v the_o other_o till_o it_o cross_v the_o line_n of_o sin_n on_o that_o line_n next_o the_o inside_n and_o count_v from_o 90_o it_o shall_v touch_v at_o the_o angle_n the_o line_n of_o sin_n standsat_n be_v two_o degree_n more_o than_o the_o sector_n stand_v at_o the_o line_n be_v draw_v so_o will_v be_v as_o i_o conceive_v most_o convenien_a take_v a_o example_n i_o come_v to_o a_o south-east-wall_n and_o put_v my_o box_n and_o needle_n on_o my_o rule_n with_o the_o cross_n or_o north-end_n of_o the_o needle_n towards_o the_o wall_n and_o the_o rule_n be_v apply_v ●lat_a to_o the_o wall_n on_o the_o edge_n thereof_o on_o the_o even_a place_n thereof_o and_o hold_v level_a so_o as_o the_o needle_n may_v play_v well_o with_o the_o head_n of_o the_o rule_n towards_o your_o right_a hand_n as_o you_o shall_v find_v it_o to_o be_v in_o a_o east-wall_n most_o convenient_a then_o i_o open_v or_o close_o the_o rule_n till_o the_o needle_n play_v right_a over_o the_o north_n and_o south_n line_n in_o the_o bottom_n of_o the_o box_n then_o have_v get_v the_o angle_n take_v off_o the_o box_n or_o if_o you_o put_v it_o on_o the_o other_o side_n that_o labour_n may_v be_v save_v i_o take_v the_o parallel_n sine_fw-la of_o 30_o and_o measure_v it_o from_o the_o centre_n it_o reach_v suppose_v to_o the_o sine_fw-la of_o 20_o then_o be_v the_o line_n of_o sin_n at_o a_o angle_n of_o 40_o degree_n but_o the_o sector_n at_o two_o degree_n less_o viz._n 38_o degree_n who_o compliment_n 52_o be_v the_o declination_n then_o to_o consider_v which_o way_n mind_n thus_o first_o it_o be_v south_n because_o the_o sun_n be_v in_o the_o south_n shine_v on_o the_o wall_n second_o consider_v the_o sun_n be_v in_o the_o east_n it_o shine_v also_o on_o the_o wall_n therefore_o it_o be_v east_n plain_a thus_o have_v you_o get_v the_o denomination_n which_o way_n and_o also_o the_o quantity_n how_o much_o that_o way_n or_o if_o you_o take_v the_o latteral_a sine_fw-la of_o 30_o from_o the_o centre_n and_o turn_v the_o point_n of_o the_o compass_n from_o 30_o towards_o 90_o on_o the_o other_o leg_n you_o shall_v find_v it_o to_o reach_v to_o the_o sine_fw-la of_o 50_o degree_n who_o compliment_n count_v from_o 90_o be_v 40_o or_o rather_o 38_o for_o the_o reason_n before-said_a or_o else_o add_v 2_o to_o 50_o and_o you_o have_v the_o angle_n require_v without_o complement_n of_o it_o be_v the_o true_a declination_n seek_v for_o thus_o by_o the_o needle_n you_o may_v get_v the_o declination_n of_o any_o wall_n which_o in_o cloudy_a weather_n may_v stand_v you_o in_o good_a stead_n or_o to_o examine_v a_o observation_n by_o the_o sun_n as_o to_o the_o mis-counting_a or_o mistake_v therein_o but_o for_o exactness_n the_o sun_n be_v always_o the_o best_a because_o the_o needle_n though_o never_o so_o good_a may_v be_v draw_v aside_o by_o iron_n in_o the_o wall_n and_o also_o by_o some_o kind_n of_o brick_n therefore_o not_o to_o be_v too_o much_o trust_v unto_o to_o find_v a_o declination_n by_o the_o sun_n first_o open_v the_o rule_n to_o a_o angle_n of_o 60_o degree_n as_o you_o do_v to_o find_v the_o hour_n of_o the_o day_n and_o put_v a_o pin_n in_o the_o hole_n and_o hang_v the_o thread_n and_o plummet_n on_o the_o pin_n also_o you_o must_v have_v another_o thread_n somewhat_o long_o and_o grosser_n than_o that_o for_o the_o hour_n in_o a_o readiness_n for_o your_o use_n then_o apply_v the_o head_n leg_n to_o the_o wall_n if_o the_o sun_n be_v come_v on_o the_o plain_a and_o hold_v the_o rule_n horizontal_a or_o level_a then_o hold_v up_o the_o long_a thread_n till_o the_o shadow_n fall_v right_a over_o the_o pin_n or_o the_o centre_n hole_n at_o the_o same_o instant_n the_o shadow_n shall_v show_v on_o the_o degree_n how_o much_o the_o sun_n want_v of_o come_v to_o be_v just_a against_o the_o plain_a which_o i_o call_v the_o meridian_n or_o pole_n of_o the_o plain_a which_o number_n you_o must_v write_v down_o thus_o as_o suppose_v it_o fall_v on_o 40_o write_v down_o 40-00_a want_n then_o as_o soon_o as_o may_v be_v take_v the_o sun_n true_a altitude_n and_o write_v that_o down_o also_o with_o which_o you_o must_v find_v the_o sun_n azimuth_n then_o subtract_v the_o great_a out_o of_o the_o less_o and_o the_o remainder_n be_v the_o declination_n require_v but_o for_o a_o general_a rule_n take_v this_o if_o the_o sun_n do_v want_n of_o come_v to_o the_o meridian_n of_o the_o place_n and_o also_o want_v of_o come_v to_o the_o meridian_n of_o the_o plain_a than_o you_o must_v always_o subtract_v the_o great_a number_n out_o of_o the_o less_o whether_o it_o be_v forenoon_n or_o afternoon_n so_o likewise_o when_o the_o sun_n be_v pass_v the_o meridian_n and_o past_o the_o plain_a also_o but_o if_o the_o sign_n be_v unlike_a that_o be_v to_o say_v one_o past_o the_o plain_n or_o meridian_n and_o the_o other_o want_n either_o of_o the_o plain_a or_o meridian_n than_o you_o must_v add_v they_o together_o and_o the_o sum_n be_v the_o declination_n from_o the_o south_n which_o rule_n for_o better_a tenaciousness_n sake_n take_v in_o this_o homely_a rhyme_n sign_n both_o alike_o substraction_n do_v require_v but_o unlike_a sign_n addition_n do_v desire_v the_o further_a illustration_n by_o two_o or_o three_o example_n suppose_v on_o the_o first_o of_o may_n in_o the_o forenoon_n i_o come_v and_o apply_v the_o rule_n be_v open_v to_o his_o angle_n of_o 60_o degree_n to_o the_o wall_n viz._n the_o head_n leg_n or_o the_o leg_n where_o the_o centre_n be_v and_o hold_v up_o my_o thick_a thread_n and_o plummet_n so_o as_o the_o shadow_n of_o it_o cross_v the_o centre_n and_o at_o the_o same_o instant_n also_o on_o 60_o degree_n than_o i_o say_v the_o sun_n want_v 60_o deg_n of_o come_v to_o the_o meridian_n of_o the_o plain_a at_o the_o same_o instant_n or_o as_o soon_o as_o possible_a i_o can_v i_o take_v the_o sun_n altitude_n as_o before_o be_v show_v and_o set_v that_o down_o which_o suppose_v it_o to_o be_v 20_o degree_n then_o by_o the_o rule_v before_o get_v the_o sun_n azimuth_n for_o that_o day_n and_o altitude_n which_o in_o our_o example_n will_v be_v find_v to_o be_v 94_o degree_n from_o the_o south_n or_o meridian_n then_o in_o regard_n the_o sign_n be_v both_o alike_o i._n e._n want_n if_o you_o subtract_v one_o out_o of_o the_o other_o there_o remain_v 34_o the_o declination_n require_v but_o for_o the_o right_a denomination_n which_o way_n either_o north_n or_o south_n towards_o either_o east_n or_o west_n observe_v this_o plain_a rule_n first_o if_o the_o sun_n come_v to_o the_o meridian_n or_o pole_n of_o the_o plain_a before_o it_o come_v to_o the_o meridian_n or_o pole_n of_o the_o place_n than_o it_o be_v always_o a_o east-plain_a but_o if_o the_o contrary_a it_o be_v a_o west-plain_a that_o be_v to_o say_v if_o the_o sun_n come_v to_o the_o meridian_n or_o pole_n of_o the_o place_n before_o it_o come_v to_o the_o meridian_n or_o pole_n of_o the_o plain_a than_o it_o be_v a_o west-plain_a also_o if_o the_o sum_n or_o remainder_n after_o addition_n or_o substraction_n be_v under_o 90_o it_o be_v a_o south-plain_a but_o if_o it_o be_v above_o 90_o it_o be_v a_o north-plain_a also_o note_n that_o when_o the_o sum_n or_o remainder_n be_v above_o 90_o than_o the_o compliment_n to_o 180_o be_v always_o the_o declination_n from_o the_o north_n towards_o either_o east_n or_o west_n so_o that_o according_a to_o these_o rule_n in_o our_o example_n it_o be_v 34_o degree_n southeast_n again_o in_o the_o morning_n june_n 13._o i_o apply_v my_o rule_n to_o the_o wall_n and_o i_o find_v the_o sun_n be_v pass_v the_o pole_n or_o meridian_n of_o the_o plain_a 10_o degree_n and_o the_o altitude_n at_o the_o same_o time_n 15_o degree_n the_o azimuth_n at_o that_o altitude_n and_o

else_o as_o before_o as_o the_o right_a sine_fw-la of_o the_o compliment_n of_o the_o sun_n declination_n be_v to_o the_o parallel_n sine_fw-la of_o the_o azimuth_n so_o be_v the_o right_a sine_fw-la of_o coaltitude_n to_o the_o parallel_n sine_fw-la of_o the_o hour_n from_o noon_n count_v as_o before_o prop._n 3._o have_v the_o compliment_n of_o the_o latitude_n sun_n altitude_n and_o declination_n to_o find_v the_o sun_n azimuth_n from_o the_o north_n part_n of_o the_o horizon_n 1._o first_o of_o the_o compliment_n of_o the_o latitude_n and_o sun_n present_a altitude_n find_v the_o difference_n 2._o and_o second_o count_n it_o on_o the_o line_n of_o sin_n from_o 90_o towards_o the_o centre_n 3._o take_v the_o distance_n from_o thence_o to_o the_o sine_fw-la of_o the_o sun_n declination_n but_o note_v when_o the_o latitude_n and_o declination_n differ_v as_o in_o winter_n you_o must_v count_v the_o declination_n beyond_o the_o centre_n and_o you_o must_v call_v it_o the_o sun_n distance_n from_o the_o pole_n 4._o four_o make_v that_o distance_n a_o parallel_n sine_fw-la in_o the_o compliment_n of_o the_o latitude_n 5._o five_o then_o take_v out_o the_o parallel_n sine_fw-la of_o 90._o 6._o and_o sixthly_a make_v it_o a_o parallel_n sine_fw-la in_o the_o coaltitude_n 7._o seven_o than_o the_o sector_n so_o set_v take_v out_o parallel_n radius_fw-la or_o sine_fw-la of_o 90._o and_o eighthly_a measure_v it_o on_o the_o line_n of_o sin_n from_o 90_o towards_o and_o if_o need_v be_v beyond_o the_o centre_n and_o it_o shall_v reach_v to_o the_o verse_v sine_fw-la of_o the_o sun_n azimuth_n from_o the_o north_n or_o if_o you_o count_v the_o other_o way_n from_o the_o south_n note_v that_o in_o work_v of_o these_o if_o the_o line_n of_o sin_n be_v too_o big_a than_o you_o have_v two_o or_o three_o small_a sin_n on_o the_o rule_n where_o on_o to_o begin_v and_o end_v the_o work_n example_n latitude_n 51._o 32_o declination_n 18_o 30_o altitude_n 48._o 12_o you_o shall_v find_v the_o azimuth_n to_o be_v 130_o from_o the_o north_n or_o 50_o from_o the_o south_n prop._n 4._o have_v the_o compliment_n of_o the_o latitude_n and_o declination_n or_o sun_n distance_n from_o the_o pole_n and_o the_o sun_n altitude_n give_v to_o find_v the_o hour_n from_o east_n or_o west_n or_o else_o from_o noon_n 1._o first_o of_o the_o compliment_n of_o the_o latitude_n and_o sun_n distance_n from_o the_o pole_n find_v the_o difference_n 2._o count_n this_o from_o the_o sine_fw-la of_o 9●_n towards_o the_o centre_n 3._o take_v the_o distance_n from_o thence_o to_o the_o sine_fw-la of_o the_o sun_n altitude_n 4._o make_v that_o distance_n a_o parallel_n sine_fw-la of_o the_o compliment_n of_o the_o latitude_n 5._o take_v out_o the_o parallel_n sine_fw-la of_o 90_o degree_n and_o 6._o make_v that_o a_o parallel_n sine_fw-la in_o the_o codeclination_n than_o 7._o take_v out_o the_o parallel_n sine_fw-la o●_n 90_o again_o and_o 8._o measure_v it_o from_o the_o sine_fw-la of_o 90_o towards_o the_o centre_n and_o it_o shall_v show_v the_o verse_v sine_fw-la of_o the_o hour_n from_o the_o north_n or_o the_o sine_fw-la of_o the_o hour_n from_o east_n or_o west_n or_o if_o you_o reckon_v from_o 90_o the_o hour_n from_o noon_n require_v example_n latitude_n 51._o 32_o declination_n north_n 20._o 14_o altitude_n 50._o 55_o you_o shall_v find_v the_o hour_n from_o the_o north_n to_o be_v 10_o hour_n or_o 10_o a_o clock_n in_o the_o forenoon_n or_o 4_o hour_n past_o 6_o or_o two_o short_a of_o noon_n according_a to_o each_o proper_a reckon_n prop._n 5._o have_v the_o latitude_n the_o compliment_n of_o the_o sun_n declination_n the_o sun_n present_a altitude_n and_o meridian_n altitude_n for_o that_o day_n to_o find_v the_o hour_n make_v the_o lateral_a secant_fw-la of_o the_o latitude_n a_o parallel_n sine_fw-la in_o the_o codeclination_n then_o take_v the_o distance_n from_o the_o sun_n meridian_n altitude_n to_o his_o present_a altitude_n and_o lay_v it_o from_o the_o cer_n on_o both_o side_n of_o the_o line_n of_o sin_n and_o take_v the_o parallel_a distance_n between_o those_o two_o point_n and_o measure_v it_o from_o 90_o on_o a_o line_n of_o sin_n of_o the_o same_o radius_fw-la the_o secant_v be_v as_o the_o small_a adjoin_v sine_fw-la be_v and_o it_o shall_v show_v the_o verse_v sine_fw-la of_o the_o hour_n from_o noon_n or_o the_o right_a sine_z before_o or_o after_o 6_o towards_o noon_n or_o night_n prop._n 6._o have_v the_o latitude_n declination_n and_o sun_n altitude_n to_o find_v the_o sun_n azimuth_n take_v the_o latteral_a secant_fw-la of_o the_o latitude_n and_o make_v it_o a_o parallel_n in_o the_o compliment_n of_o the_o altitude_n then_o take_v the_o distance_n between_o the_o sun●_n of_o the_o complement●_n of_o of_o museum_fw-la the_o latitude_n and_o altitude_n if_o under_o 90_o and_o the_o son_n declination_n and_o lay_v it_o from_o the_o centre_n on_o the_o line_n of_o sin_n that_o parallel_a distance_n take_v and_o measure_v on_o the_o sin_n of_o the_o same_o radius_fw-la the_o secant_fw-la be_v from_o 90_o shall_v show_v the_o verse_v sine_fw-la of_o the_o azimuth_n from_o noon_n but_o if_o the_o sum_n of_o the_o colatitude_n and_o coaltitude_n exceed_v 90_o then_o take_v the_o excess_n above_o 90_o out_o of_o the_o natural_a sine_fw-la from_o the_o centre_n towards_o 90_o and_o add_v that_o to_o the_o sine_fw-la of_o the_o sun_n declination_n towards_o 90_o and_o then_o the_o parallel_n distance_n between_o those_o two_o point_n shall_v be_v the_o azimuth_n require_v from_o noon_n but_o when_o the_o latitude_n and_o declination_n be_v unlike_a as_o with_o we_o in_o the_o northern_a part_n in_o winter_n than_o you_o must_v take_v the_o declination_n out_o of_o the_o excess_n or_o the_o lesser_a out_o of_o the_o great_a and_o lay_v the_o rest_n from_o the_o centre_n and_o the_o parallel_a distance_n shall_v be_v verse_v sine_fw-la of_o the_o azimuth_n from_o noon_n example_n at_o 18_o 15_o altitude_n latitude_n 51_o 32_o declination_n 13_o 15_o south_n the_o sum_n of_o the_o colatitude_n and_o the_o coaltitude_n be_v 109._o 37_o then_o count_v the_o centre_n for_o 90_o the_o right_a sine_fw-la of_o 10_o for_o a_o 100_o and_o 19_o for_o 109_o and_o 37_o minute_n forward_a there_o set_v the_o point_n of_o the_o compass_n then_o take_v from_o thence_o to_o the_o right_n sine_fw-la of_o the_o declination_n and_o lay_v this_o distance_n from_o the_o centre_n on_o the_o line_n of_o sin_n and_o the_o parallel_a space_n between_o be_v the_o verse_v sine_fw-la of_o the_o azimuth_n require_v prop._n 7._o have_v the_o length_n of_o the_o shadow_n of_o any_o object_n stand_v perpendicular_a and_o the_o length_n of_o that_o object_n to_o find_v the_o altitude_n take_v the_o tangent_fw-la of_o 45_o and_o make_v it_o a_o parallel_n in_o the_o length_n of_o the_o shadow_n in_o the_o line_n of_o line_n than_o the_o parallel_n distance_n between_o the_o length_n of_o the_o object_n that_o cast_v the_o shadow_n take_v from_o the_o line_n of_o line_n and_o measure_v on_o the_o line_n of_o tangent_n from_o the_o centre_n shall_v reach_v to_o the_o sun_n altitude_n require_v example_n if_o the_o object_n be_v 40_o part_n long_o and_o the_o shadow_n 80_o part_n the_o altitude_n will_v be_v find_v to_o be_v 26._o 35._o but_o if_o you_o have_v the_o altitude_n and_o shadow_n and_o will_v know_v the_o height_n of_o the_o object_n then_o work_v thus_o take_v the_o length_n of_o the_o shadow_n out_o of_o the_o line_n of_o line_n or_o any_o other_o equal_a part_n and_o make_v it_o a_o parallel_n tangent_fw-la of_o 45_o then_o take_v out_o the_o parallel_n tangent_fw-la of_o the_o sun_n altitude_n and_o measure_v it_o on_o the_o line_n of_o line_n or_o the_o same_o equal_a part_n and_o it_o shall_v show_v the_o length_n of_o the_o object_n that_o cause_v the_o shadow_n the_o same_o rule_n do_v serve_v in_o take_v of_o altitude_n by_o the_o rule_n as_o in_o the_o 18_o chapter_n account_v the_o measure_n from_o the_o station_n to_o the_o object_n the_o length_n of_o the_o shadow_n and_o the_o sun_n altitude_n the_o angle_n at_o the_o base_a prop._n 8._o to_o find_v the_o sun_n rise_v and_o set_v in_o any_o latitude_n take_v the_o latteral_a cotangent_fw-la of_o the_o latitude_n make_v it_o a_o parallel_n in_o the_o sin_n of_o 90_o and_o 90_o then_o take_v the_o latteral_a tangent_fw-la of_o the_o sun_n declination_n and_o carry_v it_o parallel_v in_o the_o sin_n till_o it_o stay_v in_o like_a sin_n that_o sine_fw-la shall_v be_v the_o asentional_a difference_n between_o six_o and_o the_o time_n of_o rise_v before_o or_o after_o 6_o count_v 15_o degree_n to_o a_o hour_n prop._n 9_o to_o find_v the_o amplitude_n in_o any_o latitude_n take_v the_o latteral_a sine_fw-la of_o 90_o and_o make_v it_o a_o parallel_n

and_o this_o be_v fix_v for_o one_o day_n then_o in_o summer_n time_n or_o north_n declination_n by_o help_n of_o the_o line_n of_o natural_a sin_n in_o the_o second_o line_n find_v the_o difference_n between_o the_o sun_n present_a altitude_n and_o the_o latitude_n at_o 6_o but_o in_o winter_n or_o southern_n signs_z or_o declination_n add_v the_o two_o altitude_n together_o in_o this_o manner_n lay_v one_o leg_n of_o the_o index_n to_o the_o natural_a sine_fw-la of_o the_o altitude_n at_o 6_o and_o the_o other_o to_o the_o altitude_n propose_v the_o two_o leg_n so_o set_v bring_v one_o of_o they_o viz_o the_o right_a to_o the_o begin_n of_o the_o line_n of_o natural_a sin_n and_o the_o other_o shall_v stay_v at_o the_o difference_n require_v but_o in_o winter_n set_v one_o leg_n to_o the_o begin_n of_o the_o sin_n and_o open_v the_o other_o to_o the_o height_n at_o 6_o or_o rather_o depression_n under_o the_o horizon_n at_o 6_o which_o be_v all_o one_o at_o like_a declination_n north_n and_o south_n then_o set_v the_o first_o leg_n to_o the_o present_a altitude_n of_o the_o sun_n and_o the_o other_o shall_v show_v the_o sine_fw-la of_o the_o sum_n of_o both_o add_v together_o which_o sum_n or_o difference_n be_v thus_o to_o be_v use_v lay_v the_o left_a leg_n to_o the_o cousin_n of_o the_o declination_n and_o the_o other_o to_o the_o secant_fw-la of_o the_o latitude_n count_v beyond_o 90_o as_o far_o as_o the_o secant_fw-la of_o 9_o 40_o or_o rather_o lay_v the_o left_a leg_n on_o the_o cousin_a of_o the_o latitude_n and_o the_o other_o to_o the_o secant_fw-la of_o the_o sun_n declination_n than_o the_o first_o leg_n lay_v on_o the_o sine_fw-la of_o the_o sum_n in_o winter_n or_o difference_n in_o summer_n shall_v cause_v the_o other_o leg_n to_o fall_v on_o the_o sine_fw-la of_o the_o hour_n from_o 6_o towards_o noon_n in_o winter_n and_o summer_n except_o the_o altitude_n in_o summer_n be_v less_o than_o the_o altitude_n at_o 6_o than_o it_o be_v the_o hour_n from_o 6_o towards_o midnight_n prop._n 3._o have_v the_o latitude_n sun_n altitude_n and_o declination_n to_o find_v the_o sun_n azimuth_n from_o east_n or_o west_n lat._n 51._o 32._o declin_n 23._o 30._o alt._n 49_o 56._o first_o you_o must_v get_v the_o sun_n altitude_n or_o depression_n in_o the_o vertical_a circle_n by_o this_o cannon_n lay_v the_o first_o leg_n to_o the_o sine_fw-la of_o the_o latitude_n and_o the_o second_o to_o the_o sine_fw-la of_o 90_o and_o you_o shall_v find_v they_o both_o to_o be_v on_o the_o same_o line_n than_o the_o first_o leg_n lay_v on_o the_o sine_fw-la of_o the_o declination_n shall_v cause_v the_o second_o be_v carry_v with_o the_o first_o without_o move_v the_o angle_n first_o set_v to_o fall_v on_o the_o sine_fw-la of_o 30._o 39_o the_o sun_n altitude_n in_o the_o vertical_a circle_n with_o which_o you_o must_v do_v as_o you_o do_v before_o with_o the_o altitude_n at_o 6_o and_o the_o present_a altitude_n to_o find_v the_o sum_n and_o difference_n by_o help_n of_o the_o line_n of_o natural_a tangent_n than_o this_o proportion_n hold_v lay_v the_o first_o leg_n to_o the_o cousin_n of_o the_o altitude_n by_o count_v the_o altitude_n from_o 20_o and_o the_o second_o leg_n to_o the_o tangent_fw-la of_o the_o latitude_n and_o observe_v which_o way_n and_o the_o turn_v between_o then_o the_o first_o leg_n remove_v and_o lay_v to_o the_o sine_fw-la of_o the_o sum_n before_o find_v in_o winter_n or_o the_o difference_n in_o summer_n shall_v cause_v the_o second_o leg_n to_o fall_v on_o the_o sine_fw-la of_o the_o azimuth_n of_o the_o sun_n from_o east_n or_o west_n towards_o noon_n if_o winter_n and_o also_o in_o summer_n when_o the_o sun_n altitude_n be_v more_o than_o his_o altitude_n at_o the_o vertical_a circle_n but_o if_o less_o from_o the_o east_n or_o west_n towards_o north_n or_o midnight_n meridian_n thus_o in_o our_o example_n it_o will_v be_v find_v to_o be_v the_o sine_fw-la of_o 30_o degree_n or_o 60_o from_o the_o south_n the_o sine_fw-la of_o the_o difference_n be_v find_v to_o be_v 14._o 49._o prop._n 4._o to_o find_v the_o azimuth_n according_a to_o mr._n gunter_n by_o have_v the_o latitude_n sun_n altitude_n and_o declination_n give_v first_o by_o the_o sun_n declination_n get_v his_o distance_n from_o the_o pole_n which_o in_o summer_n or_o north_n declination_n be_v always_o the_o compliment_n of_o the_o declination_n likewise_o in_o south_n latitude_n and_o south_n declination_n but_o when_o the_o latitude_n and_o declination_n be_v unlike_a than_o you_o must_v add_v 90_o to_o the_o declination_n and_o the_o sum_n be_v the_o distance_n from_o the_o elevate_v pole_n having_n find_v the_o distance_n from_o the_o pole_n add_v that_o and_o the_o compliment_n of_o the_o latitude_n and_o sun_n altitude_n together_o find_v the_o difference_n between_o their_o half_a sum_n and_o the_o sun_n distance_n from_o the_o pole_n than_o the_o proportion_n will_v be_v thus_o as_o in_o this_o example_n 13_o declination_n 41._o 53._o alt._n lat._n 51._o 32._o lay_v one_o leg_n on_o the_o sine_fw-la of_o 90_o and_o the_o other_o to_o the_o sine_fw-la of_o 38_o 28_o be_v so_o set_v remove_v the_o first_o leg_n to_o the_o sine_fw-la compliment_n of_o the_o altitude_n 48._o 07._o and_o the_o second_o leg_n shall_v fall_v on_o a_o four_o sine_fw-la which_o will_v be_v find_v to_o be_v 27._o 36._o then_o set_v the_o first_o or_o left_a leg_n to_o 27._o 36._o the_o four_o sine_fw-la and_o the_o second_o to_o 81._o 47._o the_o sine_fw-la of_o the_o half_a sum_n then_o remove_v the_o first_o leg_n to_o the_o sine_fw-la of_o the_o difference_n shall_v cause_v the_o second_o to_o show_v two_o circle_n low_o the_o verse_v sine_fw-la of_o 130_o the_o azimuth_n require_v be_v count_v from_o the_o north_n part_n of_o the_o horizon_n who_o compliment_n to_o 180_o from_o the_o south_n be_v 50_o degree_n two_o other_o canon_n to_o find_v the_o hour_n of_o the_o day_n and_o azimuth_n of_o the_o sun_n by_o one_o operation_n by_o help_n of_o the_o natural_a sin_n and_o first_o for_o the_o hour_n have_v the_o latitude_n the_o sun_n meridian_n and_o present_a altitude_n and_o declination_n to_o find_v the_o hour_n from_o noon_n first_o lay_v one_o leg_n to_o the_o meridian_n altitude_n in_o the_o line_n of_o natural_a sin_n and_o the_o other_o to_o the_o sine_fw-la of_o the_o altitude_n in_o the_o same_o line_n then_o bring_v the_o right_a leg_n to_o the_o begin_n of_o the_o line_n of_o sin_n and_o the_o other_o 〈…〉_z difference_n which_o difference_n 〈…〉_z keep_v then_o lay_v one_o leg_n on_o the_o 〈◊〉_d the_o declination_n and_o the_o other_o 〈◊〉_d secant_fw-la of_o the_o latitude_n and_o note_v the_o turn_n between_o or_o rather_o lay_v the_o first_o leg_n to_o the_o cousin_n of_o the_o latitude_n and_o the_o other_o to_o the_o secant_fw-la of_o the_o declination_n than_o the_o leg_n be_v so_o set_v bring_v the_o first_o or_o left_a leg_n to_o the_o sine_fw-la of_o the_o difference_n first_o find_v and_o the_o other_o leg_n shall_v show_v the_o verse_v sine_fw-la of_o the_o hour_n from_o noon_n if_o the_o verse_v sin_n have_v be_v set_v thus_o i._n e._n the_o verse_v sine_fw-la of_o 90_o against_o the_o sine_fw-la of_o 90_o as_o in_o some_o instrument_n it_o be_v but_o to_o remedy_v this_o defect_n do_v thus_o keep_v the_o right_a leg_n there_o and_o open_v the_o other_o to_o the_o verse_v sine_fw-la of_o 0._o or_o sine_fw-la of_o 90_o and_o note_v the_o turn_n between_o then_o lay_v the_o leg_n that_o be_v on_o the_o sine_fw-la of_o 90_o or_o verse_v sine_fw-la of_o 0_o to_o the_o verse_v sine_fw-la of_o 90_o and_o the_o other_o leg_n shall_v show_v the_o verse_v sine_fw-la of_o the_o hour_n from_o noon_n count_v from_o 90._o example_n at_o 45_o 13_o degree_n altitude_n declination_n north_n 23_o 32._o latitude_n 51_o 32_o the_o meridian_n altitude_n be_v 62_o be_v find_v by_o add_v colatitude_n and_o declination_n together_o and_o in_o southern_a declination_n by_o substraction_n then_o the_o natural_a sine_fw-la of_o 45._o 42_o take_v from_o 62_o shall_v be_v the_o sine_fw-la of_o 9_o 38._o then_o as_o the_o cousin_n of_o the_o latitude_n 38._o 28_o be_v to_o the_o secant_fw-la of_o declination_n 23._o 32_o so_o be_v the_o sine_fw-la of_o 9_o 38._o to_o the_o sine_fw-la of_o 17._o 05_o or_o verse_v sine_fw-la of_o 45_o if_o they_o be_v place_v and_o number_v as_o in_o some_o instrument_n they_o be_v but_o to_o help_v i●_n in_o this_o say_v as_o the_o verse_v sine_fw-la of_o 0_o be_v to_o the_o verse_n of_o 114._o 26_o so_o be_v the_o verse_v sine_fw-la of_o 90_o to_o the_o verse_v sine_fw-la of_o 135_o who_o compliment_n to_o 180_o be_v the_o angle_n or_o hour_n from_o noon_n require_v second_o

for_o the_o sun_n azimuth_n have_v the_o latitude_n declination_n and_o sun_n altitude_n to_o find_v the_o azimuth_n from_o south_n or_o north._n first_o add_v the_o compliment_n of_o the_o coaltitude_n and_o colatitude_n together_o then_o if_o the_o sum_n be_v under_o 90_o take_v the_o distance_n between_o the_o cousin_n of_o it_o and_o the_o sine_z of_o the_o declination_n in_o the_o line_n of_o natural_a sin_n and_o measure_v it_o in_o the_o line_n of_o sin_n from_o the_o beginning_n and_o it_o shall_v give_v the_o sine_fw-la of_o the_o difference_n but_o if_o the_o sum_n exceed_v 90_o then_o when_o the_o latitude_n and_o declination_n be_v alike_o add_v the_o excess_n to_o the_o declination_n but_o if_o contrary_a subtract_v one_o out_o of_o other_o and_o measure_v the_o sum_n or_o remainder_n from_o the_o begin_n of_o the_o sin_n you_o have_v the_o difference_n which_o you_o must_v keep_v then_o lay_v the_o first_o or_o left_a leg_n to_o the_o cousin_n of_o the_o altitude_n and_o the_o second_o to_o the_o secant_fw-la of_o the_o latitude_n or_o else_o lay_v the_o first_o to_o the_o cousin_n of_o the_o latitude_n and_o the_o other_o to_o the_o secant_fw-la of_o the_o altitude_n and_o more_o the_o turn_n between_o then_o lay_v the_o first_o leg_n to_o the_o sine_fw-la of_o the_o difference_n before_o find_v and_o the_o other_o shall_v show_v the_o verse_v sine_fw-la of_o the_o azimuth_n from_o noon_n require_v if_o the_o verse_v sin_n be_v set_v as_o before_o be_v express_v that_o be_v to_o say_v 90_o of_o right_a sin_n and_o verse_v sin_n together_o and_o number_v forward_o as_o the_o sin_n be_v but_o in_o the_o use_n of_o this_o instrument_n the_o remedy_n aforesaid_a supply_v the_o defect_n example_n at_o 10._o 19_o altitude_n 23._o 32._o declination_n 51._o 32._o latitude_n to_o find_v the_o azimuth_n the_o sum_n of_o the_o coaltitude_n and_o co-latitude_n be_v 118.09_o the_o excess_n above_o 90_o with_o right_a sine_fw-la of_o declination_n add_v be_v 60._o 30_o find_v by_o natural_a sin_n then_o say_v as_o the_o cousin_n of_o latitude_n to_o the_o secant_fw-la of_o altitude_n so_o be_v the_o sine_fw-la of_o the_o difference_n 60._o 30_o to_o the_o verse_v sine_fw-la of_o the_o azimuth_n but_o here_o to_o the_o verse_v sine_fw-la of_o a_o ark_n beyond_o radius_fw-la unknown_a then_o as_o the_o verse_v sine_fw-la of_o 0_o to_o that_o ark_n so_o be_v the_o verse_v sine_fw-la of_o 90_o to_o the_o ver_fw-la sine_fw-la of_o 60_o the_o azimuth_n from_o noon_n who_o compliment_n to_o 180_o be_v 125_o the_o azimuth_n from_o sonth_n require_v have_v be_v so_o large_a in_o these_o i_o shall_v in_o the_o rest_n contract_v myself_o as_o to_o the_o repetition_n and_o only_o give_v the_o canon_n for_o the_o proposition_n follow_v the_o way_n of_o work_v be_v the_o same_o in_o all_o other_o as_o in_o these_o before_o rehearse_v and_o note_v also_o what_o be_v to_o be_v do_v by_o the_o serpentine-line_n be_v to_o be_v do_v by_o the_o three_o same_o line_n of_o number_n sin_n and_o tangent_n on_o the_o edge_n of_o the_o sector_n by_o alter_v the_o term_n leg_n to_o to_o the_o point_n of_o the_o compass_n the_o canon_n follow_v prop_n 4._o have_v latitude_n declination_n and_o hour_n give_v to_o find_v the_o sun_n altitude_n at_o that_o hour_n or_o quarter_n and_o first_o for_o the_o hour_n of_o 6._o as_o the_o sine_fw-la of_o 90_o to_o the_o sine_fw-la of_o the_o latitude_n 51._o 30_o so_o be_v the_o sine_fw-la of_o the_o declination_n 23._o 30_o to_o the_o sine_fw-la of_o the_o altitude_n at_o 6._o 18._o 13._o second_o for_o all_o hour_n in_o the_o equinoctial_a as_o the_o radius_fw-la or_o sine_fw-la of_o 90_o to_o the_o cousin_n of_o the_o latitude_n 51._o 32_o so_o be_v the_o sine_fw-la of_o the_o sun_n distance_n from_o 6_o in_o hour_n and_o minute_n be_v turn_v into_o degree_n and_o minute_n 30_o for_o 8._o or_o 4_o to_o the_o sine_fw-la of_o the_o altitude_n of_o the_o sun_n at_o the_o time_n require_v 18._o 07_o but_o for_o all_o other_o time_n say_v as_o the_o sine_fw-la of_o 90_o to_o the_o cotangent_fw-la of_o the_o latitude_n 38._o 28._o so_o be_v the_o sine_fw-la of_o the_o sun_n distance_n from_o 6_o 30_o 0_o to_o the_o tangent_fw-la of_o the_o 4_o ark_n 21_o 40._o which_o four_o ark_n must_v be_v take_v out_o of_o the_o sun_n distance_n from_o the_o pole_n 66_o 21_o in_o cancer_n leave_v a_o residue_n 44_o 48_o which_o be_v call_v a_o five_o ark_n but_o for_o the_o hour_n before_o and_o after_o 6_o you_o must_v add_v the_o four_o ark_n to_o the_o sun_n distance_n from_o the_o pole_n and_o the_o sum_n be_v the_o five_o ark_n then_o say_v as_o the_o cousin_n of_o the_o four_o ark_n 78_o 20_o be_v to_o the_o sine_fw-la of_o the_o latitude_n 51_o 32_o so_o be_v the_o cousin_n of_o the_o residue_n 45_o 12_o to_o the_o sine_fw-la of_o the_o sun_n altitude_n at_o 8_o 36_o 42_o at_o that_o declination_n prop._n 6._o have_v the_o latitude_n declination_n and_o azimuth_n to_o find_v the_o sun_n altitude_n at_o that_o azimuth_n and_o first_o to_o find_v the_o sun_n altitude_n at_o any_o azimuth_n in_o the_o aequator_fw-la then_o as_o the_o sine_fw-la of_o 90_o to_o the_o cousin_n of_o the_o sun_n azimuth_n from_o the_o south_n 50_o 0_o so_o be_v the_o cotangent_fw-la of_o the_o latitude_n 38_o 28_o to_o the_o tangent_fw-la of_o 27_o 03_o the_o sun_n altitude_n at_o that_o azimuth_n require_v second_o to_o find_v it_o at_o all_o other_o time_n do_v thus_o as_o the_o sine_fw-la of_o the_o latitude_n 51_o 32_o to_o the_o sine_fw-la of_o the_o sun_n declination_n 23_o 32_o so_o be_v the_o cousin_n of_o the_o sun_n altitude_n in_o the_o aequator_fw-la at_o the_o same_o azimuth_n from_o the_o vertical_a viz._n 30_o to_o the_o sine_fw-la of_o a_o four_o ark_n 28_o 16._o which_o four_o ark_n must_v be_v add_v to_o the_o sun_n altitude_n at_o the_o aequator_fw-la in_o all_o azimuth_n under_o 90_o from_o the_o meridian_n where_o the_o latitude_n and_o declination_n be_v alike_o but_o in_o azimuth_n more_o than_o 90_o from_o the_o meridian_n take_v the_o altitude_n in_o the_o aequator_fw-la out_o of_o the_o four_o ark_n and_o the_o sum_n or_o remainder_n shall_v be_v the_o altitude_n require_v viz._n 42_o 56._o but_o when_o the_o latitude_n and_o declination_n be_v unlike_a as_o with_o we_o in_o winter_n time_n then_o take_v the_o four_o ark_n out_o of_o the_o altitude_n at_o the_o aequator_fw-la and_o you_o shall_v have_v the_o altitude_n belong_v to_o that_o azimuth_n require_v prop._n 7._o have_v the_o hour_n from_o noon_n and_o the_o altitude_n to_o find_v the_o sun_n azimuth_n at_o that_o time_n as_o the_o cousin_n of_o the_o altitude_n to_o the_o sine_fw-la of_o the_o hour_n so_o be_v the_o cousin_n of_o the_o sun_n declination_n to_o the_o sine_fw-la of_o the_o azimuth_n require_v prop._n 8._o have_v the_o sun_n azimuth_n altitude_n and_o declination_n to_o find_v though_o hour_n of_o the_o day_n as_o the_o cousin_n of_o the_o declination_n to_o the_o sine_fw-la of_o the_o sun_n azimuth_n so_o be_v the_o cousin_n of_o the_o altitude_n to_o the_o sine_fw-la of_o the_o hour_n prop._n 9_o have_v the_o latitude_n and_o declination_n to_o find_v when_o the_o sun_n shall_v be_v due_a east_n or_o west_n as_o the_o tangent_fw-la of_o the_o latitude_n to_o the_o tangent_fw-la of_o the_o sun_n declination_n so_o be_v the_o sine_fw-la of_o 90_o to_o the_o cousin_n of_o the_o hour_n from_o noon_n prop._n 10._o have_v the_o latitude_n and_o sun_n declination_n to_o find_v the_o amplitude_n as_o the_o cousin_n of_o the_o latitude_n to_o the_o sine_fw-la of_o the_o declination_n so_o be_v the_o sine_fw-la of_o 90_o to_o the_o sine_fw-la of_o the_o amplitude_n from_o the_o east_n or_o west_n towards_o north_n or_o south_n according_a to_o the_o time_n of_o the_o day_n and_o year_n prop._n 11._o the_o latitude_n and_o declination_n give_v to_o find_v the_o time_n of_o the_o sun_n rise_v before_o or_o after_o 6._o as_o the_o cotangent_fw-la of_o the_o latitude_n to_o the_o sine_fw-la of_o 90_o so_o be_v the_o tangent_fw-la of_o the_o sun_n declination_n to_o the_o sine_fw-la of_o the_o sun_n ascentional_a difference_n between_o the_o hour_n of_o 6_o and_o the_o sun_n rise_v prop._n 12._o have_v the_o sun_n place_n to_o find_v his_o declination_n and_o the_o contrary_n as_o the_o sine_fw-la of_o 90_o to_o the_o sun_n distance_n from_o the_o next_o equinoctial_a point_n so_o be_v the_o sine_fw-la of_o the_o sun_n great_a declination_n to_o the_o sine_fw-la of_o his_o present_a declination_n require_v prop._n 13._o the_o great_a and_o present_a declination_n give_v to_o find_v the_o sun_n right_a ascension_n as_o the_o tangent_fw-la of_o the_o great_a declination_n to_o the_o sine_fw-la of_o 90_o so_o