the_o meridian_n construc_n ¦_o tio_fw-la 27_o from_o the_o give_v day_n in_o the_o calendar_n and_o note_v the_o day_n of_o the_o month_n against_o it_o than_o number_n the_o day_n between_o that_o day_n and_o the_o give_v day_n and_o you_o have_v the_o answer_n so_o if_o the_o day_n be_v the_o last_o of_o february_n exam._n or_o the_o first_o of_o march_n consider_v the_o sun_n set_v that_o day_n by_o the_o instrument_n which_o be_v 40._o m_o past_o 5._o this_o double_v make_v the_o length_n of_o the_o day_n 11._o hour_n 20._o m_o then_o from_o the_o last_o of_o february_n account_n 7._o gr_n and_o a_o half_a and_o it_o will_v point_v out_o the_o fifteen_o of_o march_n at_o which_o time_n the_o sun_n seat_v at_o 10._o m_o past_o 6_o which_o double_v make_v 12_o hour_n 20._o m_o so_o the_o fifteen_o of_o march_n the_o length_n of_o the_o day_n be_v a_o hour_n long_o than_o it_o be_v the_o first_o of_o march_n and_o the_o difference_n of_o time_n only_o but_o 15._o day_n but_o if_o the_o number_n of_o day_n be_v account_v to_o or_o from_o the_o sun_n enter_v into_o the_o tropical_a point_n it_o will_v be_v more_o than_o 35._o day_n before_o the_o day_n will_v be_v a_o hour_n long_o or_o short_a exam._n so_o if_o from_o the_o ten_o of_o june_n we_o shall_v account_v 7._o gr_n and_o a_o half_a among_o the_o meridian_n from_o that_o meridian_n that_o meet_v with_o the_o ten_o of_o june_n it_o will_v fall_v out_o at_o the_o 16_o day_n of_o july_n at_o which_o time_n the_o day_n will_v be_v a_o hour_n short_a than_o it_o be_v the_o ten_o of_o june_n and_o the_o interval_n of_o time_n more_o than_o twice_o as_o much_o as_o the_o former_a viz._n 39_o day_n pro._n 21_o eight_o to_o find_v the_o inequality_n of_o time_n in_o equal_a mounthes_n or_o equal_a number_n of_o day_n this_o proposition_n at_o the_o first_o seem_v as_o a_o paradox_n yet_o by_o this_o instrument_n may_v easy_o be_v resolve_v and_o so_o consequent_o from_o mathematical_a principle_n demonstrate_v not_o only_o the_o inequality_n of_o equal_a month_n but_o also_o the_o inequality_n of_o natural_a day_n now_o a_o day_n natural_a according_a to_o the_o general_a definition_n be_v one_o revolution_n of_o the_o aequator_fw-la or_o primum_fw-la mobile_a that_o be_v from_o sun_n rise_v to_o sun_n rise_v or_o it_o be_v the_o time_n wherein_o the_o sun_n pass_v by_o the_o meridian_n and_o come_v to_o the_o meridian_n again_o common_o take_v for_o 24._o hour_n but_o be_v cause_n that_o in_o that_o intervale_n of_o time_n the_o sun_n pass_v from_o the_o meridian_n and_o come_v to_o the_o meridian_n again_o the_o sun_n move_v according_a to_o his_o natural_a motion_n secundum_fw-la antiquiorum_fw-la traditionem_fw-la near_o a_o degree_n more_o or_o less_o therefore_o the_o natural_a day_n shall_v be_v some_o what_o long_o or_o short_a than_o 24._o hour_n viz._n by_o so_o much_o as_o the_o difference_n of_o right_a ascension_n of_o that_o degree_n of_o the_o ecliptic_a come_v to_o that_o the_o sun_n be_v in_o and_o see_v the_o degree_n of_o the_o ecliptic_a among_o themselves_o have_v not_o the_o same_o difference_n of_o right_a ascension_n that_o the_o other_o degree_n have_v notwithstanding_o the_o degree_n of_o the_o ecliptic_a among_o themselves_o be_v equal_a the_o one_o to_o the_o other_o the_o sun_n motion_n ender_v those_o degree_n be_v sometime_o quick_a and_o sometime_o slow_a it_o will_v necessary_o follow_v that_o the_o sun_n will_v move_v more_o or_o less_o until_o the_o sun_n can_v touch_v the_o meridian_n which_o be_v the_o limit_n or_o term_v of_o the_o sun_n diurnal_a revolution_n as_o before_o this_o difference_n and_o inequality_n of_o time_n in_o natural_a day_n may_v by_o calculation_n be_v give_v from_o day_n to_o day_n but_o because_o it_o be_v so_o insensible_a little_a in_o a_o day_n hardly_o by_o a_o instrument_n of_o this_o nature_n can_v be_v see_v but_o by_o a_o number_n of_o day_n compare_v with_o another_o number_n of_o day_n it_o will_v evident_o appear_v so_o exam._n if_o it_o be_v require_v how_o much_o the_o month_n of_o december_n be_v long_o than_o the_o month_n of_o march_n in_o the_o first_o of_o which_o month_n the_o sun_n motion_n be_v quick_a be_v about_o the_o perigeum_n then_o at_o other_o constru_n ¦_o ctio_fw-la 28_o time_n now_o both_o of_o which_o month_n have_v equal_a number_n of_o day_n viz._n 31._o find_v the_o right_a ascension_n for_o the_o beginning_n and_o end_v of_o mar._n viz._n 350.0_o the_o difer_n of_o right_a ascension_n for_o the_o month_n of_o mar._n be_v 29.30_o the_o difference_n between_o these_o be_v 5._o gr_n 19_o 30._o begin_v and_o end_v of_o dece_fw-la viz._n 257._o ¾_n the_o difer_n of_o right_a ascension_n for_o the_o month_n of_o dece_fw-la be_v 34._o 30._o 292._o ¼_n which_o 5._o gr_n be_v convert_v into_o time_n by_o allow_v 4_o minute_n to_o a_o degree_n make_v about_o 20._o m_o and_o so_o much_o be_v the_o month_n of_o december_n long_a than_o the_o month_n of_o march_n notwithstanding_o both_o of_o these_o month_n contain_v equal_a number_n of_o day_n pro._n 22_o nine_o to_o find_v the_o degree_n of_o the_o aequator_fw-la in_o the_o horizon_n by_o supposs_v the_o degree_n of_o the_o ecliptic_a in_o the_o horizon_n notatio_fw-la if_o the_o degree_n give_v be_v in_o the_o northern_a part_n of_o the_o ecliptic_n the_o oblique_a ascension_n be_v less_o than_o the_o constru_n ¦_o ctio_fw-la 29_o right_a ascension_n vel_fw-la contra_fw-la get_v therefore_o first_o the_o right_a ascension_n of_o the_o point_n give_v by_o the_o sixth_o pro._n and_o the_o difference_n of_o ascension_n by_o the_o 2._o pro._n for_o that_o take_v from_o the_o right_a ascension_n give_v the_o degree_n of_o the_o aequinoctial_a in_o the_o horizon_n but_o if_o the_o give_v degree_n have_v be_v in_o a_o southren_n sign_n the_o difference_n of_o ascention_n must_v be_v add_v to_o the_o right_a ascension_n so_o have_v you_o the_o degree_n of_o the_o aequator_fw-la in_o the_o horizon_n ten_o to_o find_v the_o degree_n of_o pro._n 23_o the_o ecliptic_a in_o the_o horizon_n by_o suppose_v the_o degree_n of_o the_o aequator_fw-la in_o the_o horizon_n this_o be_v but_o the_o converse_v of_o the_o former_a only_a constru_n ¦_o ctio_fw-la 30_o consider_v the_o correspondent_a quarter_n of_o the_o aequinoctial_a to_o these_o of_o the_o ecliptic_a eleven_o to_o find_v the_o degree_n of_o pro._n 24_o medium_fw-la coeli_fw-la or_o the_o degree_n of_o the_o ecliptic_a in_o the_o meridian_n by_o sup_z sing_v any_o degree_n of_o the_o ecliptic_a in_o the_o horizon_n seek_v the_o degree_n of_o the_o aequator_fw-la in_o the_o horizon_n constru_n ¦_o ctio_fw-la 31_o by_o the_o 22._o pro._n subtract_v 90._o from_o it_o if_o the_o number_n be_v too_o little_o add_v a_o whole_a circle_n to_o it_o than_o the_o degree_n of_o the_o ecliptic_a opposite_a to_o the_o remainder_n be_v the_o answer_n but_o note_v that_o if_o the_o remainder_n be_v between_o 270._o and_o 360._o the_o opposite_a point_n belong_v to_o the_o last_o quarter_n of_o the_o ecliptic_n if_o the_o remainder_n be_v between_o 180._o and_o 270._o then_o it_o respect_v the_o 3_o quarter_n of_o the_o ecliptic_a if_o the_o remainder_n be_v between_o 90._o and_o 180._o it_o have_v reference_n to_o the_o second_o quarter_n etc._n etc._n but_o if_o the_o degree_n of_o the_o ecliptic_a in_o the_o horizon_n be_v require_v by_o know_v the_o degree_n of_o the_o in_o ecliptic_a the_o meridian_n this_o be_v only_o but_o the_o converse_n of_o the_o former_a &_o constru_n ¦_o ctio_fw-la 23_o be_v thus_o perform_v first_o seek_v the_o right_a ascension_n of_o the_o give_v degree_n of_o medium_fw-la coeli_fw-la &_o add_v thereto_o 90._o gr_n by_o account_v it_o from_o the_o former_a right_a ascension_n &_o note_v the_o sun_n place_v opposite_a thereto_o for_o the_o difference_n of_o ascension_n of_o this_o last_o degree_n be_v subtract_v from_o the_o former_a degree_n of_o the_o aequator_fw-la in_o the_o horizon_n if_o it_o be_v a_o degree_n of_o the_o southren_n sign_n otherwise_o add_v give_v the_o degree_n of_o the_o ecliptic_a in_o the_o horizon_n demand_v twelve_o to_o find_v the_o horoscope_n pro._n 25_o or_o the_o degree_n ascendant_n or_o descendant_n and_o the_o nonagessima_fw-la degree_n at_o any_o hour_n first_o note_v the_o right_a ascension_n for_o the_o day_n give_v constru_n ¦_o ctio_fw-la 33_o according_a to_o the_o 6._o pro._n which_o be_v the_o degree_n of_o the_o aequator_fw-la in_o the_o meridian_n at_o 12._o of_o the_o clock_n unto_o which_o degree_n add_v 90._o so_o have_v you_o the_o degree_n of_o the_o aequator_fw-la in_o the_o horizon_n at_o 12._o of_o the_o clock_n then_o consider_v how_o many_o hour_n the_o give_v hour_n want_v of_o 12._o or_o be_v past_o 12._o
in_o the_o northern_a sign_n that_o be_v from_o the_o 10_o of_o march_n to_o the_o 13_o of_o september_n therefore_o lay_v the_o index_n to_o the_o east_n or_o aequinoctial_a point_n note_v with_o e._n or_o 40._o &_o 50._o in_o the_o limb_n so_o have_v you_o instant_o at_o once_o without_o far_a rectification_n both_o the_o altitude_n and_o hour_n of_o the_o sun_n come_v east_n or_o west_n above_o the_o horizon_n for_o all_o or_o any_o of_o the_o day_n above_o specify_v so_o the_o parallel_n of_o any_o day_n of_o the_o month_n meet_v with_o the_o edge_n of_o the_o index_n give_v the_o sun_n altitude_n in_o the_o index_n and_o the_o meridian_n meet_v therewith_o show_v the_o hour_n exam._n so_o if_o it_o be_v the_o second_o of_o may_n or_o the_o 22._o of_o july_n the_o parallel_n belong_v to_o those_o day_n meet_v with_o the_o index_n near_o about_o 23._o gr_n 17._o m_o and_o there_o also_o meet_v with_o that_o point_n the_o hour_n line_n of_o 7_o and_o 5._o which_o show_v that_o when_o the_o sun_n be_v 23._o gr_n 17._o m_o high_a either_o upon_o the_o second_o of_o may_n or_o the_o 22._o of_o july_n then_o the_o sun_n will_v be_v due_a east_n or_o west_n and_o that_o will_v happen_v to_o be_v at_o 7_o of_o the_o clock_n in_o the_o forenoon_n and_o 5._o of_o the_o clock_n in_o the_o afternoon_n pro._n 8_o eight_o to_o find_v the_o distance_n of_o the_o sun_n rise_v or_o set_v any_o day_n of_o the_o year_n from_o the_o east_n or_o west_n call_v the_o sun_n amplitude_n constru_n ¦_o ctio_fw-la 12_o lay_v the_o index_n to_o the_o day_n of_o the_o month_n for_o the_o time_n give_v &_o the_o edge_n of_o it_o in_o the_o limb_n of_o the_o instrument_n shall_v show_v the_o amplitude_n require_v so_o if_o the_o day_n be_v the_o 13_o exam._n of_o october_n the_o number_n of_o degree_n from_o the_o point_n of_o east_n note_v with_o 40._o 50._o unto_o the_o index_n be_v 18._o gr_n 40._o m._n which_o be_v the_o sun_n amplitude_n for_o the_o give_v day_n viz._n the_o 13_o day_n of_o october_n nine_o to_o know_v the_o sun_n meridional_a pro._n 9_o altitude_n or_o the_o sun_n depression_n under_o the_o horizon_n at_o midnight_n here_o or_o in_o any_o latitude_n for_o any_o day_n in_o the_o year_n lay_v the_o index_n unto_o the_o hour_n of_o 12_o and_o where_o constru_n ¦_o ctio_fw-la 11_o the_o parallel_n of_o the_o day_n of_o the_o month_n meet_v that_o therewith_o shall_v be_v the_o sun_n meridional_a altitude_n so_o if_o it_o be_v the_o 13_o day_n of_o october_n as_o before_o exam._n the_o parallel_n for_o that_o day_n be_v 11._o gr_n and_o a_o half_a from_o the_o equator_fw-la south_n this_o cross_v the_o index_n in_o 27._o gr_n which_o be_v the_o sun_n meridional_a altitude_n that_o day_n now_o for_o the_o sun_n depression_n at_o midnight_n here_o be_v to_o be_v note_v that_o any_o degree_n of_o the_o ecliptic_a be_v at_o any_o time_n so_o much_o below_o the_o horizon_n as_o his_o opposite_a degree_n in_o the_o ecliptic_a be_v above_o the_o horizon_n at_o the_o same_o time_n constru_n ¦_o ctio_fw-la 12_o therefore_o where_o the_o contrary_a parallel_n of_o the_o sun_n viz._n 11._o gr_n and_o a_o half_a north_n meet_v with_o the_o index_n in_o the_o hour_n of_o 12._o that_o shall_v be_v the_o sun_n meridional_a depression_n at_o midnight_n the_o say_v 13_o day_n of_o october_n pro._n 10_o ten_o to_o find_v the_o time_n of_o daybreak_a and_o end_n of_o twilight_n with_o the_o position_n of_o the_o sun_n under_o the_o horizon_n for_o any_o time_n this_o proposition_n have_v reference_n to_o the_o sun_n depression_n under_o the_o horizon_n for_o it_o be_v say_v to_o be_v day_n break_v or_o twilight_n to_o end_n when_o the_o sun_n be_v 18._o gr_n under_o the_o horizon_n therefore_o the_o construction_n in_o this_o will_v be_v thus_o constru_n ¦_o ctio_fw-la 13_o account_v 18._o gr_n on_o the_o index_n then_o move_v the_o index_n until_o that_o degree_n meet_v with_o the_o contrary_a parallel_n of_o declination_n for_o the_o day_n give_v so_o the_o meridian_n or_o houreline_n that_o meet_v therewith_o shall_v be_v the_o hour_n of_o day_n break_v require_v exam._n so_o if_o the_o day_n be_v the_o 10._o of_o april_n the_o parallel_n of_o declination_n for_o that_o day_n be_v north_n ii_o gr_n and_o a_o half_n which_o i_o seek_v out_o one_o the_o other_o side_n of_o the_o aequator_fw-la viz._n ii_o gr_n and_o a_o half_a south_n declination_n and_o mark_v where_o the_o 18_o gr_n of_o the_o index_n meet_v therewith_o for_o there_o also_o be_v the_o hour_n of_o day_n break_v viz._n with_o in_o 20._o m._n of_o 3._o in_o the_o morning_n and_o 20._o m._n past_o 9_o for_o the_o end_n of_o twilight_n the_o say_v 10_o of_o april_n also_o the_o index_n in_o the_o horizon_n at_o that_o instant_a show_v the_o position_n of_o the_o sun_n under_o the_o horizon_n viz._n near_o 48_o gr_n 10._o m._n to_o the_o north_n of_o the_o east_n but_o if_o the_o day_n have_v be_v the_o 13_o of_o october_n the_o hour_n of_o daybreake_n have_v be_v 2_o minute_n before_o 5._o and_o twilight_n will_v have_v end_v 2._o m._n after_o 7._o eleven_o to_o find_v the_o inequallitie_n pro._n 11_o of_o time_n between_o day_n break_v and_o sun_n rise_v for_o any_o day_n of_o the_o year_n assign_v by_o the_o first_o construction_n for_o the_o day_n give_v constructio_fw-la 14_o find_v the_o time_n of_o sun_n rise_v and_o by_o the_o former_a 13_o construction_n the_o hour_n and_o time_n of_o day_n break_v belong_v to_o those_o day_n then_o compare_v the_o time_n between_o the_o sun_n rise_v and_o day_n break_v of_o the_o one_o with_o that_o of_o the_o other_o so_o the_o difference_n of_o those_o two_o shall_v be_v the_o difference_n of_o time_n require_v example_n  _fw-fr  _fw-fr  _fw-fr h._n m._n  _fw-fr h._n m._n  _fw-fr so_n on_o the_o ten_o of_o march_n the_o sun_n rise_v be_v at_o 6._o 00_o the_o time_n between_o day_n break_v and_o sun_n rise_v be_v 2._o 0_o the_o difference_n be_v 12._o m._n day_n break_n be_v at_o 4._o 00_o docemb_v the_o sun_n rise_v it_o at_o 8._o 12_o 2._o 12_o day_n break_v be_v at_o 6._o 00_o the_o difference_n be_v 1._o ho._n 22._o m._n may_v the_o sun_n rise_v be_v at_o 4._o 11_o 3._o 34_o day_n break_v at_o 12_o 37_o so_o the_o difference_n of_o time_n between_o day_n break_v and_o sun_n rise_v the_o 10_o of_o december_n be_v near_o a_o quarter_n of_o a_o hour_n long_o than_o that_o of_o the_o 10_o of_o march_n but_o more_o than_o a_o hour_n and_o half_o long_a between_o day_n break_v and_o sun_n rise_v the_o 10_o of_o may_n than_o the_o 10_o of_o march_n pro._n 12_o twelfe_o to_o find_v the_o hour_n and_o altitude_n of_o the_o sun_n come_v upon_o a_o decline_a wall_n any_o day_n of_o the_o year_n ☞_o ☞_o see_v the_o declination_n of_o plain_n or_o wall_n be_v account_v from_o the_o point_n of_o east_n or_o west_n in_o the_o horizon_n as_o the_o sun_n amplitude_n be_v the_o number_v of_o they_o therefore_o shall_v be_v alike_o in_o the_o limb_n of_o the_o instrument_n now_o admit_v the_o declination_n of_o a_o plain_a or_o wall_n to_o be_v 22._o gr_n the_o operation_n constru_n ¦_o ctio_fw-la 15_o will_v be_v thus_o the_o index_n be_v set_v thereto_o you_o may_v instant_o see_v at_o what_o hour_n the_o sun_n will_v come_v upon_o the_o plain_a for_o any_o day_n in_o the_o year_n for_o where_o the_o parallel_n of_o the_o day_n of_o the_o month_n cross_v the_o index_n among_o the_o houreline_n which_o index_n represent_v the_o plain_a that_o be_v the_o hour_n of_o the_o sun_n come_v upon_o the_o plain_a and_o the_o degree_n in_o the_o index_n give_v the_o sun_n altitude_n examp._n so_o if_o the_o sun_n be_v in_o the_o tropic_n of_o ♋_o the_o tropic_n meet_v with_o the_o index_n almost_o within_o 5_o m._n of_o 9_o in_o the_o morning_n and_o at_o that_o time_n the_o sun_n come_v upon_o the_o plain_a and_o there_o the_o tropic_n cut_v also_o the_o index_n in_o 45._o gr_n 40._o m._n which_o be_v the_o sun_n altitude_n at_o that_o time_n that_o the_o sun_n will_v glance_v or_o begin_v to_o shine_v upon_o the_o plain_a as_o for_o the_o time_n of_o the_o sun_n continuance_n on_o the_o plain_a as_o be_v specify_v in_o the_o index_n or_o table_n account_v the_o declination_n on_o the_o other_o side_n of_o the_o east_n point_n and_o lay_v the_o index_n thereto_o so_o the_o edge_n of_o it_o in_o the_o tropic_n of_o ♋_o will_n point_n out_o at_o what_o hour_n the_o sun_n go_v of_o the_o plain_a viz._n at_o 6._o of_o the_o clock_n &_o 38._o m_o near_o if_o the_o declination_n be_v west_n as_o here_o it_o
the_o instrument_n be_v a_o part_n of_o the_o horizon_n the_o parallel_n meridian_n &_o vertical_a circle_n that_o be_v contain_v or_o may_v be_v describe_v in_o our_o latitude_n sufficient_o necessary_a induce_v any_o one_o in_o the_o understanding_n of_o the_o use_n of_o it_o that_o be_v but_o indifferent_o verse_v in_o the_o linament_n and_o principle_n of_o the_o globe_n what_o to_o speak_v and_o what_o to_o answer_v in_o a_o proposition_n without_o far_a direction_n and_o have_v have_v this_o horizontall_a quadrant_n for_o many_o year_n past_a as_o a_o pocket_n instrument_n diverse_a about_o this_o kingdom_n be_v importunate_a with_o i_o for_o to_o have_v it_o or_o to_o publish_v the_o use_n of_o it_o see_v its_o great_a facility_n and_o expedition_n in_o comparison_n of_o such_o pocket_n instrument_n as_o be_v now_o use_v here_o or_o in_o foreign_a part_n i_o be_v willing_a at_o last_o after_o i_o have_v give_v order_n for_o the_o make_n of_o four_o of_o these_o instrument_n in_o silver_n for_o several_a noble_a personage_n to_o disburden_v myself_o of_o transcribe_v the_o use_n of_o the_o instrument_n and_o table_n for_o the_o make_n of_o it_o to_o satisfy_v those_o which_o be_v importunate_a and_o to_o let_v other_o that_o be_v studious_a in_o mathematical_a practice_n also_o participate_v of_o it_o now_o what_o i_o have_v deliver_v upon_o the_o accommodate_v of_o the_o instrument_n thus_o the_o make_v thereof_o with_o the_o use_n that_o i_o have_v deliver_v in_o this_o tractat_fw-la upon_o it_o follow_v i_o acknowledge_v due_a to_o none_o inferior_a assistant_n but_o to_o my_o own_o industry_n search_n and_o labour_n and_o that_o 64._o 65._o and_o 66._o page_n of_o the_o book_n of_o the_o sector_n before_o specify_v in_o which_o be_v only_o show_v the_o 2._o 3._o 19_o 22._o 25._o and_o 30._o proposition_n of_o the_o index_n or_o table_n follow_v as_o use_n of_o the_o say_a projection_n but_o i_o have_v extend_v they_o to_o many_o more_o and_o abundant_o and_o plentiful_o supply_v the_o obscurity_n of_o that_o scheme_n or_o diagramme_n there_o draw_v as_o for_o a_o general_a good_a in_o the_o use_n of_o this_o horizantal_n quadrant_n i_o deliver_v therefore_o first_o the_o make_n of_o it_o first_o by_o the_o sector_n somewhat_o different_a from_o that_o of_o master_n gunter'_v second_o by_o geometry_n and_o last_o i_o show_v a_o three_o way_n how_o it_o may_v be_v project_v and_o make_v by_o my_o mathematical_a ring_n and_o by_o number_n which_o i_o have_v calculate_v and_o accommodate_v to_o that_o end_n in_o table_n for_o more_o exactness_n part_v of_o the_o general_a scope_n and_o use_v of_o which_o instrument_n i_o deliver_v in_o the_o index_n or_o table_n follow_v a_o index_n or_o table_n of_o the_o use_n of_o the_o horizontall_a quadrant_n viz_o of_o the_o horizon_n line_n of_o shadow_n calendar_n parallel_n aequator_fw-la ecliptic_a houreline_n index_n 1_o by_o the_o horizon_n to_o show_v 1._o the_o sun_n or_o star_n altitude_n at_o any_o time_n pag._n 53._o 2._o at_o any_o day_n of_o the_o year_n how_o far_o the_o sun_n rise_v or_o set_v from_o the_o true_a east_n or_o west_n pag._n 28._o 3._o the_o sun_n azimuth_n and_o altitude_n at_o any_o hour_n for_o any_o day_n pag._n 62._o 4._o the_o meridian_n line_n upon_o any_o appearance_n of_o the_o sun_n pag._n 55._o 5._o the_o uncertainty_n of_o time_n by_o note_v the_o shadow_n of_o thing_n pag._n 63._o 6._o the_o site_n of_o a_o building_n or_o cost_v of_o a_o place_n pag._n 57_o 7._o the_o variation_n of_o the_o needle_n pag._n 59_o 8._o the_o declination_n of_o a_o wall_n or_o plain_a the_o sun_n shine_v thereon_o pag._n 71._o 9_o the_o inclination_n of_o a_o plain_a and_o to_o place_v a_o plain_a horizontall_a pag._n 89._o 2._o by_o the_o line_n of_o shadow_n be_v have_v 10._o at_o what_o hour_n in_o any_o day_n of_o the_o year_n the_o shadow_n of_o a_o altitude_n be_v equal_a double_a triple_a etc._n etc._n unto_o it_o pag._n 35._o 11._o instant_o the_o hour_n of_o the_o day_n the_o azimuth_n and_o altitude_n of_o the_o sun_n with_o the_o meridian_n line_n without_o observation_n or_o sight_n of_o the_o sun_n by_o know_v the_o proportion_n between_o the_o length_n of_o a_o shadow_n upon_o a_o horizontall_a plain_a &_o that_o which_o cast_v the_o shadow_n pag._n 67._o 12._o at_o any_o hour_n a_o altitude_n of_o the_o sun_n or_o azimuth_n what_o proportion_n shadow_n have_v to_o their_o body_n pag._n 37._o 13._o whether_o and_o altitude_n be_v above_o or_o below_o the_o jewel_n of_o the_o eye_n &_o how_o much_o 14._o the_o height_n of_o a_o altitude_n accessible_a or_o in_o accessible_a pag._n 100_o 101._o 15._o the_o measure_n of_o any_o part_n of_o altitude_n not_o approchable_a pag._n 102._o 3._o by_o the_o calendar_n be_v know_v 16._o the_o inequality_n of_o time_n in_o equal_a month_n or_o equal_a number_n of_o day_n pag._n 44._o 17._o what_o number_n of_o day_n will_v make_v the_o day_n and_o hour_n long_o or_o short_a at_o any_o time_n pag._n 43._o 18._o the_o hour_n of_o the_o sun_n rise_v set_v with_o the_o length_n of_o the_o day_n at_o any_o time_n pag._n 23._o 19_o what_o day_n be_v alike_o in_o length_n &_o what_o day_n the_o sun_n rise_v in_o the_o one_o shall_v be_v the_o sun_n set_v in_o the_o other_o pag._n 24._o 20._o the_o inequality_n of_o time_n between_o day_n break_v and_o sun_n rise_v pag._n 41._o 4._o by_o the_o parallel_n to_o search_v out_o 21._o at_o any_o day_n the_o sun_n declination_n pag._n 24_o 22._o the_o latitude_n of_o a_o place_n or_o hight_v of_o the_o pole_n above_o the_o horizon_n pag._n 60._o 23._o at_o what_o hour_n in_o any_o day_n the_o sun_n azimuth_n and_o altitude_n will_v be_v equal_a and_o how_o much_o the_o altitude_n &_o azimuth_n will_v be_v pag._n 42._o 5._o by_o the_o aequator_fw-la be_v see_v 24._o the_o sun_n equal_a motion_n right_a ascention_n and_o oblique_a ascension_n pag._n 26._o 6._o by_o the_o ecliptic_a to_o give_v 25._o the_o sun_n place_n at_o any_o time_n of_o the_o year_n pag._n 25._o 26._o the_o degree_n of_o the_o aequator_fw-la in_o the_o horizon_n by_o suppose_v the_o degree_n of_o the_o ecliptic_a in_o the_o horizon_n pag_n 46._o 27._o the_o degree_n of_o the_o ecliptic_a in_o the_o horizon_n by_o suppose_v the_o degree_n of_o the_o aequator_fw-la in_o the_o horizon_n pag._n 47._o 28._o the_o degree_n of_o medium_fw-la coeli_fw-la or_o the_o degree_n of_o the_o ecliptic_a in_o the_o meridian_n by_o suppose_v the_o degree_n of_o the_o ecliptic_a in_o the_o horizon_n well_fw-mi contra_fw-la pag._n 47._o 29._o the_o horoscope_n or_o the_o degree_n ascendant_n '_o or_o descendant_n and_o the_o nonagessima_fw-la degree_n at_o any_o hour_n pag._n 49._o 30._o what_o angle_n the_o ecliptic_a make_v with_o the_o horizon_n or_o the_o altitude_n of_o the_o nonagessima_fw-la degree_n and_o what_o azimuth_n it_o be_v in_o at_o any_o hour_n pag._n 50._o 7._o by_o the_o hour_n line_n to_o find_v 31._o the_o hour_n of_o the_o day_n and_o azimuth_n of_o the_o sun_n pag._n 54._o 32._o the_o hour_n of_o the_o day_n agreeable_a to_o any_o altitude_n or_o azimuth_n pag._n 39_o 33._o the_o sun_n difference_n of_o ascension_n for_o any_o day_n pag._n 23._o 34._o the_o quarter_n of_o the_o year_n and_o day_n of_o the_o month_n hour_n of_o the_o day_n meridian-line_n and_o azimuth_n of_o the_o sun_n if_o it_o be_v forget_v pag._n 64._o 8._o by_o the_o index_n adjoin_v with_o other_o line_n you_o have_v 35._o at_o what_o hour_n &_o altitude_n the_o sun_n will_v be_v due_a east_n at_o any_o day_n of_o the_o year_n pag._n 27._o 36._o the_o sun_n azimuth_n &_o hour_n without_o observation_n pag._n 58._o 37._o the_o time_n of_o daybreak_a or_o end_n of_o twilight_n for_o any_o day_n in_o the_o year_n pag._n 30._o 38._o the_o height_n or_o depression_n of_o the_o sun_n in_o the_o meridian_n for_o any_o day_n in_o the_o year_n here_o or_o for_o any_o latitude_n pag._n 29._o 39_o the_o sun_n depression_n &_o azimuth_n at_o any_o hour_n of_o the_o night_n assign_v pag._n 40._o 40._o the_o hour_n of_o the_o day_n to_o our_o antipode_n by_o suppose_v the_o sun_n depression_n under_o the_o horizon_n pag._n 42._o 41._o what_o hour_n &_o altitude_n the_o sun_n come_v upon_o a_o decline_a wall_n any_o day_n in_o the_o year_n &_o how_o long_o the_o sun_n shine_v thereon_o pag._n 32._o 42._o at_o what_o hour_n and_o altitude_n the_o sun_n must_v have_v to_o be_v opposite_a or_o perpendicular_a to_o a_o declination_n plain_a pag._n 33._o 43_o the_o declination_n of_o a_o wall_n by_o see_v the_o sun_n beginning_n to_o shine_v thereon_o or_o go_v from_o it_o pag._n 69._o 44._o the_o hour_n &_o altitude_n of_o a_o star_n come_v to_o the_o meridian_n at_o
21._o 19_o 25._o 24._o 35._o 2._o 38._o 37._o 20._o 41._o and_o 42._o as_o follow_v the_o day_n of_o the_o month_n know_v to_o find_v 1._o the_o hour_n of_o sun_n rise_v set_v and_o length_n of_o the_o day_n 2._o the_o sun_n difference_n of_o ascention_n 3._o the_o sun_n declination_n 4._o what_o day_n be_v alike_o in_o length_n and_o what_o day_n the_o sun_n rise_v in_o the_o one_o shall_v be_v the_o sun_n set_v in_o the_o other_o 5._o the_o sun_n place_n or_o degree_n in_o the_o ecliptic_a 6._o the_o sun_n right_a ascension_n and_o oblique_a ascension_n 7._o the_o hour_n and_o altitude_n of_o the_o sun_n come_v east_n or_o west_n 8._o the_o distance_n of_o the_o sun_n rise_v or_o set_v from_o the_o east_n or_o west_n 9_o the_o height_n or_o depression_n of_o the_o sun_n in_o the_o meridian_n here_o or_o for_o any_o latitude_n 10._o the_o time_n of_o day_n break_v and_o end_n of_o twilight_n 11._o the_o inequality_n of_o time_n between_o day_n break_v and_o sun_n rise_v 12._o the_o hour_n and_o altitude_n of_o the_o sun_n come_v upon_o any_o decline_a wall_n 13._o at_o what_o hour_n and_o altitude_n the_o sun_n must_v have_v to_o be_v opposite_a or_o perpendicular_a to_o a_o decline_a wall_n first_o to_o find_v the_o time_n of_o sun_n pro._n 1_o rise_v or_o set_v and_o length_n of_o the_o day_n for_o any_o day_n of_o the_o year_n seek_v the_o day_n of_o the_o month_n in_o the_o calendar_n constru_n ¦_o ctio_fw-la 1_o and_o the_o hour_n line_n that_o meet_v therewith_o show_v the_o time_n of_o sun_n rise_v or_o set_v so_o if_o the_o day_n of_o the_o month_n be_v the_o 13._o exam._n of_o october_n the_o parallel_n that_o meet_v therewith_o be_v the_o hour_n viz._n 7._o of_o the_o clock_n at_o which_o time_n the_o sun_n rise_v the_o same_o hour_n be_v note_v also_o with_o 5._o which_o be_v the_o time_n of_o sun_n set_v that_o day_n this_o double_a make_n 10._o the_o length_n of_o the_o day_n require_v second_o to_o find_v the_o difference_n pro._n 2_o of_o ascention_n for_o any_o day_n of_o the_o year_n mark_v what_o meridian_n meet_v with_o the_o day_n constru_n ¦_o ctio_fw-la 2_o of_o the_o month_n in_o the_o calendar_n as_o suppose_v the_o day_n to_o be_v the_o former_a 13._o of_o october_n which_o be_v the_o hour_n line_n of_o 7._o and_o 5._o as_o before_o and_o account_v the_o number_n of_o meridian_n to_o the_o hour_n of_o 6._o so_o have_v you_o 15._o gr_n or_o a_o hour_n which_o be_v the_o difference_n of_o ascension_n for_o the_o 13._o day_n of_o october_n require_v pro._n 3_o three_o to_o find_v the_o sun_n declination_n for_o any_o day_n constru_n ¦_o ctio_fw-la 3_o mark_v what_o parallel_n of_o declination_n meet_v with_o the_o day_n of_o the_o month_n in_o the_o calendar_n and_o account_v how_o many_o degree_n it_o be_v from_o the_o equinoctial_a so_o have_v you_o the_o sun_n declination_n for_o that_o day_n exam._n so_o if_o the_o day_n be_v the_o last_o of_o august_n the_o parallel_n that_o meet_v therewith_o be_v the_o 5_o from_o the_o equator_fw-la and_o somuch_o be_v the_o sun_n declination_n that_o day_n viz._n 5._o gr_n north_n declination_n pro._n 4_o four_o to_o find_v what_o day_n in_o the_o year_n be_v alike_o in_o length_n and_o what_o day_n the_o sun_n rise_v in_o the_o one_o shall_v be_v the_o sun_n set_v in_o the_o other_o constru_n ¦_o ctio_fw-la 4_o for_o the_o first_o note_z that_o the_o day_n between_o the_o 10_o of_o december_n and_o the_o 11_o of_o june_n be_v day_n of_o increase_n and_o the_o rest_n be_v day_n of_o decrease_v now_o right_a against_o any_o day_n of_o decrease_n in_o the_o calendar_n be_v the_o day_n of_o increase_n which_o day_n be_v equal_a one_o to_o the_o other_o exam._n so_o the_o 19_o day_n of_o may_n be_v against_o the_o 4._o of_o july_n at_o which_o time_n the_o sun_n rise_v and_o set_v alike_o without_o sensible_a error_n viz._n 4._o of_o the_o clock_n and_o therefore_o those_o day_n be_v of_o equal_a length_n and_o so_o of_o other_o for_o the_o second_o to_o 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the_o former_a parallel_n of_o the_o 13_o of_o october_n meet_v with_o the_o ecliptic_a in_o the_o begin_n of_o â™_o and_o ♓_o but_o which_o of_o these_o be_v the_o sun_n place_n the_o quarter_n of_o the_o year_n may_v easy_o tell_v you_o viz._n â™_o which_o be_v the_o sun_n place_n or_o the_o degree_n in_o the_o ecliptic_a for_o that_o day_n pro._n 6_o six_o to_o find_v the_o sun_n right_a ascension_n and_o oblique_a ascension_n at_o any_o time_n constru_n ¦_o ctio_fw-la 7_o consider_v what_o meridean_a meet_v with_o the_o sun_n place_n in_o the_o ecliptic_a for_o the_o day_n give_v and_o mark_v the_o number_n of_o meridian_n in_o the_o equator_fw-la for_o the_o meridian_n be_v number_v in_o the_o equator_fw-la as_o be_v say_v before_o in_o the_o description_n so_o have_v you_o the_o sun_n right_a ascension_n but_o here_o note_n that_o the_o degree_n in_o the_o ecliptic_a be_v number_v forward_o and_o backward_o in_o the_o ecliptic_a unto_o 360._o gr_n upon_o this_o instrument_n so_o be_v the_o right_a ascension_n of_o those_o degree_n also_o number_v forward_o and_o backward_o in_o the_o aequator_fw-la for_o the_o right_a ascension_n of_o any_o degree_n in_o the_o ecliptic_a be_v that_o degree_n of_o the_o aequator_fw-la which_o be_v opposite_a unto_o it_o the_o succession_n of_o the_o sign_n consider_v so_o if_o the_o sun_n be_v in_o the_o begin_n of_o â™_o the_o right_a ascension_n be_v near_o 208._o degree_n for_o the_o meridian_n that_o pass_v by_o the_o begin_n of_o â™_o be_v account_v in_o the_o equator_fw-la from_z ♈_o and_o be_v within_o 6._o m_o of_o 28._o gr_n now_o the_o right_a ascension_n of_o ♋_o be_v 90._o gr_n and_o the_o beginning_n the_o of_o ♎_o be_v 180._o gr_n and_o from_o the_o begin_n of_o ♎_o to_o the_o beginning_n â™_o be_v within_o 6._o m_o of_o 28._o gr_n as_o before_o all_o be_v which_o put_v together_o make_v near_o 208._o gr_n the_o right_a ascension_n of_o the_o sun_n the_o 13_o day_n of_o october_n to_o find_v the_o sun_n oblique_a ascension_n at_o any_o time_n note_v that_o the_o difference_n of_o ascension_n be_v the_o constru_n ¦_o ctio_fw-la 8_o difference_n always_o between_o the_o right_a ascension_n of_o the_o sun_n and_o the_o oblique_a ascension_n thereof_o therefore_o the_o right_a ascension_n know_v by_o the_o last_o direction_n &_o the_o difference_n of_o ascension_n by_o the_o second_o direction_n the_o oblique_a ascension_n be_v easy_o have_v by_o addition_n or_o substraction_n thus_o if_o the_o sun_n be_v in_o a_o southern_a sign_n than_o the_o oblique_a ascension_n be_v great_a than_o the_o right_a ascension_n by_o so_o much_o as_o the_o difference_n of_o ascention_n come_v to_o but_o if_o the_o sun_n be_v in_o a_o northern_a sign_n the_o oblique_a ascension_n be_v so_o much_o less_o which_o difference_n of_o ascension_n as_o before_o by_o the_o 2_o pro_fw-la for_o the_o say_v 13_o of_o october_n be_v 15._o gr_n this_o ad_fw-la unto_o the_o right_a ascension_n of_o the_o begin_n of_o â™_o viz._n 208._o gr_n make_v 223._o gr_n the_o sun_n oblique_a ascension_n for_o the_o begin_n of_o â™_o on_o the_o 13_o day_n of_o october_n but_o if_o the_o sun_n have_v be_v in_o the_o begin_n of_o ♉_o the_o oblique_a ascension_n will_v have_v be_v only_o near_o 13._o gr_n viz._n 12._o gr_n 54._o m._n seven_o to_o find_v the_o sun_n altitude_n pro._n 7_o and_o hour_n of_o the_o sun_n come_v east_n or_o west_n any_o day_n of_o the_o year_n above_o the_o horizon_n here_o note_v that_o this_o proposition_n hold_v in_o use_n constru_n ¦_o ctio_fw-la 9_o only_o for_o that_o time_n of_o the_o sun_n be_v
be_v suppose_v which_o add_v to_o the_o time_n of_o the_o sun_n come_v on_o the_o plain_a make_v 9_o hour_n 33._o m_o &_o so_o long_a the_o sun_n shine_v on_o the_o plain_a thirteen_o to_o find_v at_o what_o pro._n 13_o hour_n and_o altitude_n the_o sun_n must_v have_v to_o be_v opposite_a or_o perpendicular_a to_o a_o decline_a plain_n any_o day_n in_o the_o year_n let_v a_o plain_a decline_n from_o the_o east_n point_n towards_o the_o south_n 22._o example_n gr_n account_v this_o in_o the_o limb_n constru_n ¦_o ctio_fw-la 16_o from_o the_o hour_n of_o 12._o and_o lay_v the_o index_n thereto_o so_o the_o parallel_n that_o cross_v the_o index_n do_v show_v the_o sun_n altitude_n and_o the_o meridian_n meet_v therewith_o give_v the_o hour_n at_o which_o time_n the_o sun_n will_v be_v opposite_a to_o the_o plain_a so_o have_v you_o at_o one_o instant_a for_o every_o day_n in_o the_o year_n at_o what_o hour_n and_o altitude_n the_o sun_n will_v be_v opposite_a to_o the_o plain_a  _fw-fr gr_fw-fr m._n as_o admit_v the_o day_n be_v these_o decem._n the_o ten_o the_o sun_n place_n at_o which_o time_n be_v in_o ♑_o and_o the_o hour_n of_o the_o sun_n be_v opposite_a to_o the_o plain_a that_o day_n will_v be_v at_o 40-m_a past_a 1_o and_o the_o sun_n altitude_n at_o that_o time_n will_v be_v 12.12_o march_n ♈_o 14_o m._n past_a 1._o 36.25_o june_n ♋_o 48_o m._n past_o 12_o 60.45_o thus_o touch_v the_o resolution_n of_o the_o former_a 13_o use_n of_o the_o aforesaid_a table_n or_o index_n which_o have_v reference_n only_o to_o the_o knowledge_n of_o the_o day_n of_o the_o month_n there_o be_v 13._o other_o use_n of_o the_o foresay_a index_n or_o table_n viz._n the_o 10._o 12._o 32._o 39_o 40._o 23._o 17._o 16._o 26._o 27._o 28._o 29._o 30._o which_o have_v no_o dependence_n upon_o the_o sight_n of_o the_o sun_n of_o which_o the_o 6_o first_o be_v resolve_v only_o by_o know_v the_o day_n of_o the_o month_n and_o the_o other_o 7._o be_v as_o follow_v viz_o by_o know_v the_o day_n of_o the_o month_n to_o find_v 1._o at_o what_o hour_n the_o shadow_n of_o a_o altitude_n be_v equal_a double_a triple_a etc._n etc._n unto_o it_o 2._o at_o any_o hour_n and_o altitude_n of_o the_o sun_n or_o azimuth_n what_o proportion_n shadow_n have_v to_o their_o body_n 3._o the_o hour_n of_o the_o day_n agreeable_a to_o any_o altitude_n or_o azimuth_n 4._o the_o sun_n depression_n and_o azimuth_n at_o any_o hour_n of_o the_o night_n assign_v 5._o the_o hour_n of_o the_o day_n to_o our_o antipode_n by_o supose_v the_o sun_n depression_n under_o the_o horizon_n 6._o at_o what_o hour_n in_o any_o day_n the_o sun_n azimuth_n and_o altitude_n will_v be_v equal_a and_o how_o much_o the_o altitude_n and_o azimuth_n will_v be_v to_o find_v 7._o what_o number_n of_o day_n will_v make_v the_o day_n a_o hour_n long_o or_o short_a at_o any_o time_n 8._o thâ—_n inequallitie_n of_o time_n in_o equal_a month_n or_o equal_a number_n of_o day_n 9_o the_o degree_n of_o the_o aequator_fw-la in_o the_o horizon_n by_o suppose_v any_o degree_n of_o the_o ecliptic_a in_o the_o horizon_n 10._o the_o degree_n of_o the_o ecliptic_a in_o the_o horizon_n by_o suppose_v the_o degree_n of_o the_o equator_fw-la in_o the_o horizon_n 11._o the_o degree_n of_o medium_fw-la coeli_fw-la or_o the_o degree_n of_o the_o ecliptic_a in_o the_o meridian_n by_o suppose_v the_o degree_n of_o the_o ecliptic_a in_o the_o horizon_n vel_fw-la contra_fw-la 12._o the_o horoscope_n or_o the_o degree_n ascendant_n or_o descendâ—nt_n and_o the_o nonagessima_fw-la degree_n at_o any_o hour_n 13._o what_o angle_n the_o ecliptic_a make_v with_o the_o horizon_n or_o the_o altitude_n of_o the_o nonagessima_fw-la degree_n &_o what_o azimuth_n it_o be_v in_o at_o any_o hour_n first_o to_o find_v the_o proportion_n of_o pro._n 14_o shadow_n to_o their_o altitude_n at_o any_o time_n as_o if_o it_o be_v require_v the_o 20_o of_o april_n declara_fw-la ∣_o tio_fw-la at_o what_o hour_n of_o the_o day_n and_o how_o high_a the_o sun_n must_v be_v either_o in_o the_o forenoon_n or_o afternoon_n that_o the_o shadow_n of_o a_o man_n or_o any_o altitude_n shall_v be_v equal_a unto_o his_o height_n double_a triple_a quadruple_a quintuple_a etc._n etc._n constru_n ¦_o ctio_fw-la 17_o lay_v the_o index_n unto_o the_o number_n in_o the_o line_n of_o shadow_n viz._n to_o 1._o 2._o 3._o 4._o 5._o etc._n etc._n and_o wheresoever_o any_o of_o those_o division_n in_o the_o line_n of_o shadow_n meet_v with_o the_o index_n among_o the_o degree_n there_o it_o show_v what_o height_n the_o sun_n must_v have_v to_o make_v the_o shadow_n equal_a double_a triple_a etc._n etc._n to_o the_o altitude_n exam._n so_o lay_v the_o index_n upon_o 1_o in_o the_o line_n of_o shadow_n it_o meet_v with_o 45._o gr_n in_o the_o index_n &_o so_o high_a the_o sun_n must_v be_v to_o make_v the_o shadow_n of_o a_o man_n or_o any_o thing_n equal_a to_o his_o height_n upon_o a_o horizontall_a plain_a then_o move_v the_o index_n to_o and_o fro_o until_o the_o say_v 45._o gr_n in_o the_o index_n meet_v with_o the_o parallel_n of_o the_o day_n month_n viz_o the_o 20._o of_o april_n so_o the_o hour_n line_n that_o meet_v therewith_o be_v the_o hour_n of_o the_o day_n that_o the_o shadow_n of_o a_o man_n or_o other_o altitude_n will_v be_v equal_a to_o his_o height_n or_o altitude_n viz_o near_o 10._o of_o the_o clock_n in_o the_o forenoon_n or_o 2._o of_o the_o clock_n in_o the_o afternoon_n  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr forenoon_n afternoon_n  _fw-fr  _fw-fr  _fw-fr gr_fw-fr m._n  _fw-fr ho._n m._n ho._n m._n and_o according_a to_o the_o same_o direction_n when_o shadow_n be_v double_a the_o altitude_n will_v be_v 26._o 33_o and_o the_o hour_n the_o say_v 20._o of_o april_n will_v be_v 7._o 37_o 4._o 23_o triple_a 18._o 26_o 6._o 43_o 5._o 17_o quadruple_a 14._o 2_o 6._o 16_o 5._o 44_o quintuple_a 11._o 19_o 5._o 58_o 6._o 02_o sextuple_a 9_o 27_o 5._o 46_o 6._o 14_o septuple_a 8._o 7_o 5._o 37_o 6._o 23_o octuple_a 7._o 7_o 5._o 31_o 6._o 29_o nâ—nocuple_n 6._o 20_o 5._o 25_o 6._o 35_o decuple_n 5._o 43_o 5._o 21_o 6._o 39_o vigecuple_n 2._o 51_o 5._o 2_o 6._o 58_o second_o to_o find_v what_o proportion_n pro._n 15_o shadow_n have_v to_o their_o body_n at_o any_o hour_n in_o the_o day_n azimuth_n or_o altitude_n of_o the_o sun_n asign_v if_o the_o hour_n be_v know_v or_o suppose_v move_v the_o constru_n ¦_o ctio_fw-la 18_o index_n until_o it_o meet_v with_o the_o hour_n in_o the_o parallel_n of_o the_o day_n of_o the_o month_n so_o the_o intersection_n of_o that_o parallel_n with_o the_o index_n be_v the_o sun_n altitude_n and_o the_o edge_n of_o the_o index_n in_o the_o limb_n will_v show_v the_o sun_n azimuth_n then_o move_v the_o index_n until_o the_o degree_n of_o altitude_n intersect_v the_o line_n of_o shadow_n so_o shall_v you_o have_v the_o proportion_n of_o shadow_n to_o their_o body_n require_v so_o if_o on_o the_o 11_o of_o april_n at_o 7._o exam._n of_o the_o clock_n in_o the_o forenoon_n if_o the_o sun_n shine_v it_o be_v require_v what_o proportion_n the_o shadow_n of_o a_o man_n shall_v bear_v to_o his_o height_n or_o the_o shadow_n of_o a_o altitude_n to_o the_o altitude_n the_o parallel_n that_o belong_v to_o the_o give_v day_n be_v near_o 12._o gr_n mark_v where_o this_o parallel_n meet_v with_o the_o give_v hour_n of_o 7._o and_o bring_v the_o index_n to_o it_o so_o have_v you_o the_o sun_n height_n at_o that_o hour_n viz_o 18._o gr_n 26._o m_o and_o the_o edge_n of_o the_o index_n in_o the_o limb_n of_o the_o instrument_n shall_v give_v the_o azimuth_n viz_o 4._o gr_n from_o the_o east_n then_o move_v the_o index_n until_o the_o degree_n of_o the_o sun_n altitude_n viz_o 18._o gr_n 26._o m_o meet_v with_o the_o line_n of_o shadow_n which_o will_v be_v in_o 3_o which_o show_v that_o at_o 7._o of_o the_o clock_n in_o the_o forenone_o the_o say_v 11_o of_o april_n the_o shadow_n of_o a_o man_n or_o the_o shadow_n of_o a_o altitude_n shall_v be_v triple_a to_o his_o height_n the_o like_a will_v be_v at_o 5._o of_o the_o clock_n in_o the_o afternoon_n for_o equal_a distance_n of_o the_o sun_n from_o the_o meridian_n the_o same_o day_n without_o sensible_a error_n will_v give_v equal_a altitude_n of_o the_o sun_n and_o equal_a altitude_n of_o the_o sun_n do_v produce_v equal_a shadow_n upon_o horizontall_a plain_n constru_n ¦_o ctio_fw-la 19_o second_o if_o the_o position_n or_o azimuth_n of_o the_o sun_n be_v know_v or_o suppose_v which_o admit_v 4_o gr_n from_o the_o east_n towards_o the_o south_n lay_v the_o index_n unto_o it_o in_o the_o limb_n
&_o mark_v what_o degree_n in_o the_o index_n the_o parallel_n meet_v with_o which_o be_v with_o 18._o gr_n 26._o m_o so_o have_v you_o the_o sun_n altitude_n in_o the_o index_n then_o move_v the_o index_n until_o the_o degree_n meet_v with_o the_o line_n of_o shadow_n so_o have_v you_o the_o proportion_n of_o shadow_n require_v at_o that_o instant_n viz_o triple_a as_o before_o constru_n ¦_o ctio_fw-la 20_o three_o if_o the_o sun_n height_n be_v know_v or_o suppose_v which_o admit_v 18._o gr_n 26._o m_o account_v it_o in_o the_o index_n and_o move_v the_o index_n until_o that_o degree_n meet_v with_o the_o line_n of_o shadow_n so_o where_o it_o intersect_v the_o line_n of_o the_o shadow_n there_o you_o have_v the_o proportion_n of_o shadow_n to_o their_o body_n at_o that_o instant_n of_o time_n require_v which_o will_v be_v triple_a as_o before_o so_o the_o 10_o of_o april_n if_o the_o hour_n be_v 7._o or_o the_o altitude_n 18._o g._n 26._o m_o or_o the_o azimuth_n 4._o gr_n from_o the_o east_n towards_o the_o south_n the_o proportion_n of_o shadow_n to_o their_o body_n will_v be_v triple_a three_o to_o find_v the_o hour_n of_o the_o pro._n 16_o day_n agreeable_a to_o any_o altitude_n or_o azimuth_n for_o any_o day_n of_o the_o year_n propose_v for_o the_o first_o account_v the_o sun_n altitude_n in_o the_o constru_n ¦_o ctio_fw-la 21_o index_n and_o move_v it_o to_o and_o fro_o until_o that_o degree_n meet_v with_o the_o parallel_n of_o the_o day_n of_o the_o month_n so_o the_o meridian_n that_o pass_v by_o that_o point_n shall_v be_v the_o hour_n require_v thus_o if_o the_o day_n be_v the_o ten_o of_o march_n exam._n the_o sun_n be_v that_o day_n in_o the_o aequinoctial_a &_o the_o altitude_n suppose_v to_o be_v 32._o gr_n 37._o m_o this_o i_o seek_v out_o upon_o the_o index_n and_o move_v the_o index_n till_o that_o degree_n meet_v with_o the_o aequator_fw-la so_o the_o meridian_n or_o hour_n circle_n that_o pass_v thereby_o be_v the_o hour_n viz._n 10._o of_o the_o clock_n in_o the_o forenoon_n or_o 2._o of_o the_o clock_n in_o the_o afternoon_n and_o if_o you_o move_v the_o index_n soft_o along_o as_o the_o degree_n of_o the_o sun_n altitude_n in_o the_o index_n intersect_v the_o aequator_fw-la and_o so_o of_o any_o parallel_n so_o the_o meridian_n that_o meet_v therewith_o be_v the_o hour_n of_o the_o day_n agreeable_a to_o that_o altitude_n for_o the_o second_o to_o find_v the_o hour_n constru_n ¦_o ctio_fw-la 22_o of_o the_o day_n agreeable_a to_o any_o azimuth_n as_o suppose_v it_o be_v 36._o gr_n 35._o m_o exam._n from_o the_o south_n move_v the_o index_n in_o the_o limb_n unto_o this_o azimuth_n know_v or_o suppose_v so_o where_o the_o index_n cross_v the_o parallel_n for_o the_o day_n give_v there_o the_o meridian_n that_o meet_v therewith_o show_v the_o hour_n of_o the_o day_n viz_o 10._o of_o the_o clock_n in_o the_o forenoon_n or_o 2_o in_o the_o afternoon_n as_o before_o and_o if_o you_o move_v the_o index_n soft_o along_o as_o the_o index_n pass_v by_o any_o azimuth_n in_o the_o limb_n so_o the_o edge_n of_o the_o index_n shall_v intersect_v the_o parallel_n of_o declination_n for_o the_o day_n of_o the_o month_n in_o the_o hour_n of_o the_o day_n agreeable_a to_o that_o azimuth_n by_o which_o proposition_n and_o the_o last_o glass_n may_v be_v easy_o place_v to_o burn_v according_a to_o the_o sun_n azimuth_n or_o hour_n assign_v pro._n 17_o four_o to_o find_v the_o sun_n depression_n &_o position_n under_o the_o horizon_n at_o any_o hour_n of_o the_o night_n with_o the_o hour_n of_o the_o day_n to_o our_o antipode_n by_o suppose_v the_o sun_n any_o number_n of_o degree_n under_o the_o horizon_n constru_n ¦_o ctio_fw-la 23_o by_o the_o 11_o construction_n it_o be_v say_v that_o any_o degree_n of_o the_o ecliptic_a be_v asmuch_o below_o the_o horizon_n at_o any_o time_n as_o his_o opposite_a degree_n be_v above_o the_o horizon_n at_o the_o same_o time_n therefore_o if_o the_o index_n be_v lay_v to_o the_o like_a parallel_n on_o the_o contrary_a side_n of_o the_o aequator_fw-la that_o meet_v with_o the_o give_v hour_n the_o intersection_n in_o the_o index_n shall_v show_v you_o the_o degree_n of_o the_o sun_n depression_n under_o the_o horizon_n at_o that_o hour_n so_o if_o at_o 10_o of_o the_o clock_n at_o night_n the_o say_v 13_o of_o october_n it_o be_v require_v to_o find_v the_o sun_n depression_n under_o the_o horizon_n exam._n consider_v the_o declination_n or_o the_o sun_n parallel_n for_o that_o day_n which_o be_v 11._o gr_n and_o a_o half_a south_n which_o declination_n i_o seek_v in_o the_o other_o side_n of_o the_o aequator_fw-la and_o mark_v where_o it_o meet_v with_o the_o hour_n of_o 10._o unto_o which_o i_o lay_v the_o index_n so_o the_o edge_n thereof_o in_o the_o limb_n show_v the_o sun_n azimuth_n to_o be_v never_o 42_o gr_n 30._o m_o from_o the_o south_n and_o the_o parallel_n intersection_n that_o meet_v with_o the_o index_n give_v the_o sun_n depression_n viz._n near_o 43._o gr_n and_o so_o much_o be_v the_o sun_n below_o the_o horizon_n and_o in_o that_o position_n the_o 13_o of_o october_n at_o 10._o of_o the_o clock_n at_o night_n but_o if_o it_o be_v require_v at_o what_o hour_n of_o the_o night_n the_o sun_n will_v touch_v the_o vertical_a circle_n of_o east_n and_o west_n under_o the_o horizon_n lay_v the_o index_n to_o the_o point_n of_o east_n and_o mark_n constru_n ¦_o ctio_fw-la 24_o where_o about_o the_o contrary_a palleâ—_n meet_v with_o the_o index_n for_o there_o you_o have_v both_o the_o hour_n and_o the_o degree_n of_o the_o sun_n depression_n so_o the_o day_n be_v as_o before_o the_o 13_o of_o october_n exam._n &_o the_o declination_n south_n 11._o gr_n and_o a_o half_a this_o account_n amongst_o the_o north_n declination_n &_o it_o meet_v with_o the_o index_n in_o 38_o m_o past_o 6._o the_o hour_n of_o the_o sun_n be_v west_n and_o with_o all_o the_o sun_n depression_n at_o the_o same_o time_n be_v near_o 14._o gr_n and_o 50._o m._n pro._n 18_o five_o to_o find_v the_o hour_n of_o the_o day_n to_o our_o antipode_n by_o suppose_v the_o sun_n depression_n under_o the_o horizon_n constru_n ¦_o ctio_fw-la 25_o consider_v the_o declination_n for_o the_o day_n and_o move_v the_o index_n to_o and_o fro_o until_o the_o degree_n of_o the_o sun_n depression_n in_o the_o index_n meet_v with_o the_o like_a parallel_n or_o the_o other_o side_n of_o the_o aequator_fw-la so_o the_o hour_n that_o meet_v therewith_o be_v the_o hour_n of_o the_o day_n to_o our_o antipode_n exam._n so_o if_o on_o the_o 20_o of_o april_n we_o shall_v suppose_v the_o sun_n to_o be_v 13._o gr_n under_o the_o horizon_n &_o desire_v to_o know_v the_o hour_n to_o our_o antipode_n the_o parallel_n of_o declension_n for_o that_o day_n be_v 15._o gr_n north_n now_o in_o the_o index_n account_v 13._o degree_n and_o move_v it_o to_o and_o fro_o until_o the_o say_v thirteen_o degree_n in_o the_o index_n meet_v with_o the_o 15_o parallel_v of_o 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♋_o exam_n the_o index_n be_v move_v to_o and_o fro_o until_o there_o be_v like_o degree_n in_o the_o index_n and_o in_o the_o limb_n which_o will_v be_v near_o 16._o gr_n 45._o m_o and_o there_o the_o hour_n that_o meet_v therewith_o be_v 12._o m_o after_o 6._o in_o the_o forenoon_n at_o which_o hour_n the_o eleven_o of_o june_n the_o sun_n azimuth_n and_o altitude_n will_v be_v equal_a viz._n near_o 16._o gr_n 45._o m_o as_o before_z seven_o to_o find_v what_o number_n pro._n 20_o of_o day_n any_o time_n of_o the_o year_n will_v make_v the_o day_n a_o hour_n long_o or_o short_a account_v 7._o gr_n and_o a_o half_a among_o
which_o convert_v into_o measure_n and_o account_v eastward_o or_o westward_o according_a to_o the_o hour_n give_v from_o the_o former_a point_n of_o the_o aequator_fw-la in_o the_o horizon_n at_o 12._o will_v give_v the_o degree_n of_o the_o aequator_fw-la in_o the_o horizon_n at_o the_o hour_n propose_v then_o by_o the_o 23._o pro._n i_o seek_v out_o the_o degree_n of_o the_o ecliptic_a in_o the_o horizon_n answerable_a to_o the_o degree_n of_o the_o aequator_fw-la so_o have_v you_o the_o degree_n ascendant_n from_o which_o account_n 90._o gr_n or_o 3_o sign_n so_o have_v you_o the_o degree_n of_o the_o nonagessima_fw-la point_n in_o the_o horizon_n but_o if_o you_o reckon_v 6._o sign_n from_o the_o ascendant_n you_o have_v the_o desendant_fw-fr degree_n of_o the_o ecliptic_a in_o the_o west_n of_o the_o horizon_n pro._n 26_o thirteen_o to_o find_v what_o angle_n the_o ecliptic_a make_v with_o the_o horizon_n or_o the_o altitude_n of_o the_o nonagessima_fw-la degree_n of_o the_o ecliptic_a above_o the_o horizon_n and_o what_o azimuth_n it_o be_v in_o at_o any_o hour_n according_a to_o the_o last_o pro._n sinde_v the_o degree_n constru_n ¦_o ctio_fw-la 34_o ascendant_n and_o the_o nonagessima_fw-la degree_n then_o by_o the_o 24._o pro._n find_v what_o degree_n of_o the_o ecliptic_a be_v in_o the_o meridian_n answerable_a to_o the_o degree_n of_o the_o ecliptic_a in_o the_o horizon_n so_o shall_v you_o know_v on_o which_o side_n of_o the_o meridian_n the_o nonagessima_fw-la degree_n be_v &_o how_o far_o from_o the_o meridian_n then_o if_o that_o index_n be_v lay_v upon_o the_o hour_n of_o 12_o where_o the_o parallel_n of_o the_o nonagessima_fw-la degree_n cross_v it_o that_o shall_v be_v the_o height_n of_o it_o if_o it_o be_v in_o the_o meridian_n account_v therefore_o from_o the_o meridian_n or_o hour_n of_o 12._o in_o the_o aequator_fw-la the_o number_n of_o degree_n between_o the_o nonagessima_fw-la degree_n and_o the_o degree_n of_o the_o ecliptic_a in_o the_o meridian_n &_o mark_v where_o that_o meridian_n meet_v with_o the_o parallel_n of_o the_o of_o the_o nonagessima_fw-la degree_n lay_v the_o index_n thereto_o so_o have_v you_o the_o altitude_n of_o the_o nonagessima_fw-la degree_n in_o the_o index_n and_o the_o azimuth_n in_o the_o horizon_n or_o limb_n of_o the_o instrument_n there_o be_v yet_o the_o 48._o 49._o 50._o 9_o 13._o 14._o and_o 15_o use_n of_o the_o say_a index_n or_o table_n which_o have_v no_o relation_n to_o the_o sun_n sight_n or_o observation_n in_o there_o operation_n and_o resolution_n and_o shall_v have_v follow_v these_o 26._o use_n that_o have_v be_v deliver_v but_o i_o refer_v they_o to_o the_o end_n of_o this_o tractat_fw-la as_o for_o these_o use_n of_o the_o instrument_n which_o depend_v upon_o the_o sun_n sight_n or_o observation_n they_o be_v these_o 13._o follow_a viz._n the_o 1._o 31._o 4._o 6._o 36._o 7._o 22._o 3._o 5._o 34._o 11._o 43._o and_o 8_o viz._n to_o show_v 1._o the_o sun_n or_o star_n altitude_n above_o the_o horizon_n at_o any_o time_n 2._o the_o hour_n of_o the_o day_n and_o azimuth_n of_o the_o sun_n 3._o the_o meridian_n line_n upon_o any_o appearance_n of_o the_o sun_n 4._o the_o sit_v of_o a_o building_n or_o cost_v of_o a_o place_n 5._o the_o sun_n azimuth_n and_o hour_n without_o observation_n 6._o the_o variation_n of_o the_o needle_n 7._o the_o latitude_n of_o a_o place_n or_o height_n of_o the_o pole_n above_o the_o horizon_n 8._o the_o sun_n azimuth_n and_o altitude_n at_o any_o hour_n 9_o the_o uncertainetie_n of_o time_n by_o note_v the_o shadow_n of_o thing_n 10._o the_o quarter_n of_o the_o year_n and_o day_n of_o the_o month_n with_o the_o hour_n azimuth_n and_o the_o meridian_n line_n 11._o instant_o the_o hour_n of_o the_o day_n the_o azimuth_n and_o altitude_n of_o the_o sun_n with_o the_o meridional_a line_n without_o observation_n or_o sight_n of_o the_o sun_n by_o know_v the_o proportion_n between_o the_o length_n of_o a_o shadow_n upon_o a_o horizontal_a plain_n and_o that_o which_o do_v cast_v the_o shadow_n 12._o the_o declination_n of_o a_o wall_n by_o see_v the_o sun_n beginning_n to_o shine_v thereon_o or_o go_v from_o it_o 13._o the_o declination_n of_o a_o wall_n the_o sun_n shine_v thereon_o first_o how_o to_o observe_v the_o sun_n or_o pro._n 27_o star_n altitude_n above_o the_o horizon_n at_o any_o time_n lift_v up_o the_o edge_n of_o the_o instrument_n to_o the_o eye_n constru_n ¦_o ctio_fw-la 35_o so_o that_o the_o sight_n which_o be_v at_o the_o limb_n or_o circumference_n of_o the_o quadrant_n be_v next_o the_o eye_n and_o the_o index_n to_o hang_v perpendicular_a and_o to_o play_v easy_o by_o the_o side_n thereof_o then_o move_v the_o quadrant_n up_o and_o down_o until_o you_o may_v through_o both_o sight_n see_v the_o centre_n or_o middle_n of_o the_o sun_n or_o star_n so_o the_o index_n in_o the_o limb_n shall_v fall_v upon_o the_o degree_n of_o the_o sun_n or_o star_n altitude_n above_o the_o horizon_n at_o that_o time_n or_o without_o look_v at_o the_o sun_n the_o altitude_n thereof_o may_v be_v thus_o find_v hold_v the_o quadrant_n constru_n ¦_o ctio_fw-la 36_o that_o the_o index_n may_v hang_v perpendicular_a or_o be_v vertical_a as_o before_o then_o move_v about_o the_o instrument_n until_o the_o edge_n of_o it_o be_v opposite_a to_o the_o body_n of_o the_o sun_n now_o suppose_v the_o instrument_n to_o hang_v thus_o upon_o his_o centre_n soft_o lift_v up_o the_o edge_n thereof_o which_o be_v towards_o the_o sun_n until_o you_o see_v the_o beam_n of_o the_o sun_n pass_v through_o both_o sight_n than_o the_o index_n in_o the_o limb_n shall_v give_v the_o sun_n altitude_n as_o before_o pro._n 28_o second_o how_o to_o find_v the_o hour_n of_o the_o day_n and_o azimuth_n of_o the_o sun_n upon_o any_o appearance_n of_o the_o sun_n constru_n ¦_o ctio_fw-la 37_o by_o the_o last_o pro._n observe_v or_o take_v the_o sun_n altitude_n and_o account_n it_o on_o the_o index_n then_o seek_v for_o the_o parallel_n of_o the_o day_n of_o the_o month_n for_o the_o day_n present_a &_o move_v the_o index_n until_o that_o degree_n of_o altitude_n in_o the_o edge_n of_o the_o index_n meet_v with_o the_o parallel_n of_o the_o day_n so_o the_o meridian_n that_o meet_v with_o that_o degree_n of_o altitude_n in_o the_o index_n shall_v be_v the_o hour_n of_o the_o day_n require_v &_o the_o edge_n of_o the_o index_n in_o the_o limb_n of_o the_o instrument_n shall_v likewise_o show_v the_o sun_n azimuth_n belong_v to_o that_o hour_n so_o if_o upon_o the_o last_o of_o august_n the_o sun_n altitude_n in_o the_o forenoon_n shall_v be_v observe_v and_o find_v to_o be_v 30._o exam._n gr_n &_o a_o half_a seek_v this_o altitude_n out_o upon_o the_o index_n &_o move_v the_o index_n until_o the_o degree_n of_o altitude_n meet_v with_o the_o parallel_n for_o the_o day_n of_o the_o month_n give_v viz._n the_o five_o parallel_n from_o the_o aequator_fw-la northward_o so_o the_o houreline_n that_o meet_v also_o with_o the_o 30._o gr_n &_o a_o half_a in_o the_o index_n be_v the_o hour_n viz._n near_o 9_o &_o that_o shall_v be_v the_o hour_n of_o the_o day_n at_o that_o instant_n &_o the_o edge_n of_o the_o index_n in_o the_o limb_n cut_v near_o 35._o gr_n and_o 30._o m_o from_o the_o point_n of_o east_n towards_o the_o south_n and_o so_o much_o be_v the_o sun_n azimuth_n at_o that_o time_n three_o how_o to_o find_v the_o meridian_n pro._n 29_o line_n and_o the_o true_a point_n of_o north_n &_o south_n east_n and_o west_n upon_o any_o appearance_n of_o the_o sun_n according_a to_o the_o 27._o pro._n first_o observe_v the_o constru_n ¦_o ctio_fw-la 38_o sun_n altitude_n above_o the_o horizon_n and_o by_o the_o last_o construction_n find_v the_o sun_n azimuth_n agreeable_a to_o that_o altitude_n let_v the_o index_n and_o rest_n at_o that_o degree_n and_o erect_v the_o prependicular_a at_o the_o end_n of_o the_o index_n then_o hold_v the_o plain_a or_o face_n of_o the_o quadrant_n parallel_v to_o the_o horizon_n move_v the_o instrument_n circular_a until_o the_o shadow_n of_o the_o say_v perpendicular_a fall_n by_o the_o side_n of_o the_o index_n and_o so_o the_o hoverline_n of_o 12_o or_o the_o edge_n of_o the_o instrument_n which_o be_v parallel_n unto_o it_o which_o be_v the_o north_n and_o south_n edge_n of_o the_o instrument_n shall_v represent_v the_o meridian_n line_n and_o point_v out_o the_o north_n and_o south_n in_o the_o horizon_n of_o the_o world_n by_o the_o term_n thereof_o and_o the_o other_o straight_o edge_n of_o the_o instrument_n which_o be_v perpendicular_a unto_o that_o edge_n be_v the_o east_n and_o west_n edge_n of_o the_o instrument_n and_o denote_v or_o show_v the_o line_n of_o east_n and_o west_n in_o the_o
horizon_n of_o the_o world_n but_o this_o may_v be_v more_o accurate_o do_v if_o you_o place_v the_o back_n of_o the_o instrument_n down_o upon_o a_o horizontall_a plain_a and_o the_o edge_n of_o the_o index_n be_v at_o the_o degree_n of_o the_o sun_n azimuth_n observe_v and_o the_o perpendicular_a erect_v at_o the_o end_n of_o the_o index_n as_o before_o then_o move_v the_o instrument_n as_o it_o so_o lie_v until_o the_o shadow_n of_o the_o perpendicular_a fall_n by_o the_o side_n of_o the_o index_n so_o the_o meridian_n of_o the_o instrument_n shall_v be_v in_o the_o meridian_n of_o the_o world_n and_o every_o point_n and_o degree_n in_o the_o limb_n of_o the_o instrument_n shall_v point_v out_o and_o be_v opposite_a and_o represent_v his_o like_a degree_n in_o the_o horizon_n of_o the_o world_n constru_n ¦_o ctio_fw-la 39_o but_o here_o note_v that_o this_o construction_n serve_v only_o but_o for_o the_o forenoon_n observation_n for_o if_o the_o practice_n be_v in_o the_o afternone_o the_o way_n to_o find_v the_o meridian_n line_n may_v be_v thus_o have_v find_v the_o sun_n azimuth_n as_o before_o lay_v the_o index_n upon_o the_o hour_n line_n of_o 12._o and_o erect_v the_o perpendicular_a at_o the_o end_n thereof_o and_o move_v the_o instrument_n about_o circular_a until_o the_o shadow_n of_o the_o say_v perpendicular_a fall_n by_o the_o side_n of_o the_o index_n for_o than_o if_o the_o edge_n of_o the_o index_n be_v move_v unto_o the_o sun_n azimuth_n before_o know_v the_o edge_n of_o the_o index_n shall_v represent_v the_o meridian_n line_n &_o 90._o gr_n far_o shall_v be_v the_o point_n of_o east_n and_o the_o centre_n of_o the_o instrument_n the_o point_n of_o west_n therefore_o if_o upon_o the_o plain_a that_o the_o instrument_n lie_v upon_o you_o make_v a_o mark_n at_o the_o edge_n of_o the_o index_n which_o be_v in_o the_o meridian_n as_o before_o and_o another_o mark_v right_a under_o the_o centre_n and_o so_o place_v the_o north_n and_o south_n edge_n of_o the_o instrument_n unto_o these_o two_o point_n then_o every_o degree_n in_o the_o horizon_n or_o limb_n of_o the_o instrument_n shall_v point_v out_o as_o before_o his_o opposite_a or_o â—ike_a degree_n in_o the_o horizon_n of_o the_o world_n four_o how_o to_o find_v the_o sit_v pro._n 30_o of_o a_o building_n or_o cost_v of_o a_o place_n by_o the_o last_o pro._n find_v out_o or_o draw_v the_o meridian_n constru_n ¦_o ctio_fw-la 40_o line_n and_o place_v the_o north_n and_o south_n edge_n of_o the_o instrument_n unto_o it_o if_o the_o building_n or_o place_n lie_v in_o the_o eastern_a semicircle_n of_o the_o world_n but_o if_o it_o lie_v in_o the_o western_a semicircle_n then_o let_v the_o east_n &_o west_n edge_n of_o the_o instrument_n be_v place_v upon_o the_o meridian_n line_n so_o the_o eye_n be_v over_o the_o centre_n of_o the_o instrument_n and_o behold_v the_o place_n let_v the_o index_n be_v move_v until_o it_o be_v also_o with_o the_o visual_a line_n 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observe_v you_o have_v the_o point_n of_o the_o compass_n which_o the_o place_n or_o object_n bear_v from_o you_o pro._n 31_o five_o to_o find_v the_o sun_n azimuth_n and_o hour_n without_o observation_n the_o meridian_n line_n be_v draw_v first_o upon_o a_o constru_n ¦_o ctio_fw-la 41_o plain_n according_a to_o the_o former_a direction_n consider_v if_o it_o be_v in_o the_o forenoon_n or_o afternoon_n if_o in_o the_o forenoon_n then_o let_v the_o north_n and_o south_n edge_n of_o the_o instrument_n be_v place_v unto_o the_o meridian_n line_n but_o if_o it_o be_v in_o the_o afternoon_n than_o set_v the_o edge_n of_o east_n &_o west_n of_o the_o instrument_n unto_o the_o meridian_n line_n and_o let_v the_o instrument_n rest_v there_o then_o erect_v the_o perpendicular_a at_o the_o end_n of_o the_o index_n &_o move_v the_o index_n about_o until_o the_o shadow_n of_o the_o perpendicular_a fall_n by_o the_o side_n of_o the_o index_n so_o the_o edge_n of_o the_o index_n will_v among_o the_o degree_n in_o the_o limb_n show_v the_o sun_n azimuth_n at_o that_o time_n and_o where_o the_o edge_n of_o the_o index_n meet_v with_o the_o parallel_n of_o the_o day_n of_o the_o month_n that_o be_v the_o hour_n of_o the_o day_n at_o that_o time_n but_o if_o the_o axis_n be_v rectify_v then_o there_o be_v no_o need_n of_o a_o meridian_n line_n to_o be_v draw_v for_o this_o instrument_n will_v with_o great_a facility_n find_v out_o his_o own_o meridian_n by_o move_v it_o to_o and_o fro_o until_o the_o shadow_n of_o the_o perpendicular_a which_o be_v over_o the_o centre_n of_o the_o instrument_n intersect_v the_o same_o hour_n in_o the_o parallel_n of_o the_o day_n of_o the_o month_n that_o the_o axis_n do_v among_o the_o common_a hour_n so_o that_o hour_n shall_v be_v the_o hour_n of_o the_o day_n for_o that_o instant_n and_o the_o shadow_n of_o the_o say_v perpendicular_a cut_v the_o limb_n or_o extend_v unto_o it_o do_v there_o show_v the_o sun_n azimuth_n and_o so_o the_o meridian_n of_o the_o instrument_n at_o that_o position_n shall_v be_v in_o the_o meridian_n of_o the_o world_n require_v six_o to_o find_v the_o variation_n pro._n 32_o of_o the_o needle_n by_o the_o twenty_o nine_o pro._n upon_o a_o even_o plain_a parallel_n to_o the_o horizon_n draw_v the_o meridian_n line_n &_o constru_n ¦_o ctio_fw-la 42_o place_n the_o north_n &_o south_n line_n of_o the_o card_n direct_o over_o the_o say_a meridian_n line_n so_o the_o number_n of_o degree_n that_o the_o needle_n cut_v in_o the_o card_n from_o the_o north_n and_o south_n line_n of_o the_o card_n that_o shall_v be_v the_o variation_n of_o the_o needle_n require_v otherwise_o it_o may_v be_v find_v thus_o near_o unto_o the_o centre_n of_o the_o index_n upon_o the_o index_n may_v a_o small_a brosse_n pin_n be_v so_o place_v that_o it_o may_v be_v erect_v perpendicular_a to_o the_o centre_n of_o the_o instrument_n and_o half_a a_o inch_n above_o it_o let_v a_o needle_n by_o place_v upon_o this_o pin_n then_o lay_v the_o east_n and_o west_n edge_n of_o the_o instrument_n to_o the_o meridian_n line_n &_o when_o the_o needle_n rest_v move_v the_o index_n until_o the_o edge_n of_o it_o be_v direct_o under_o the_o needle_n so_o the_o edge_n of_o the_o index_n in_o the_o limb_n of_o the_o instrument_n shall_v point_v out_o or_o show_v the_o needle_n variation_n require_v pro._n 33_o seven_o to_o find_v the_o latitude_n of_o a_o place_n or_o the_o pole_n hight_v above_o the_o horizon_n constru_n ¦_o ctio_fw-la 43_o first_o draw_v the_o meridian_n line_n upon_o some_o plain_n by_o help_n of_o the_o 38._o construction_n then_o erect_v the_o prependicular_a at_o the_o end_n of_o the_o index_n and_o place_v the_o north_n and_o south_n edge_n of_o the_o instrument_n to_o the_o meridian_n line_n so_o draw_v upon_o the_o plain_a and_o move_v also_o the_o index_n until_o the_o edge_n thereof_o touch_v the_o hour_n of_o 12._o let_v the_o instrument_n rest_n at_o this_o position_n then_o mark_v diligent_o about_o noon_n or_o 12._o of_o the_o clock_n when_o the_o shadow_n of_o the_o perpendicular_a do_v fall_v by_o the_o edge_n of_o the_o index_n for_o then_o the_o sun_n be_v in_o the_o meridian_n at_o which_o time_n according_a to_o the_o 27._o pro._n observe_v or_o take_v the_o sun_n height_n which_o be_v his_o meridian_n altitude_n for_o that_o day_n and_o by_o the_o 3._o pro._n find_v the_o sun_n declination_n agreeable_a to_o that_o day_n and_o add_v it_o to_o the_o sun_n meridional_a altitude_n observe_v if_o it_o be_v south_n declination_n otherwise_o subtract_v it_o from_o the_o former_a meridional_a altitude_n so_o have_v you_o the_o height_n of_o the_o aequinoctial_a above_o the_o horizon_n that_o take_v from_o 90._o give_v the_o depression_n of_o
the_o south_n pole_n under_o the_o horizon_n which_o be_v always_o equal_a to_o the_o elevation_n of_o the_o north_n pole_n above_o the_o horizon_n so_o if_o upon_o the_o ten_o of_o april_n exam._n the_o meridian_n altitude_n shall_v be_v find_v to_o be_v 50._o gr_n the_o declination_n belong_v to_o that_o day_n by_o the_o 3._o pro._n be_v 11._o gr_n and_o a_o half_a north_n which_o be_v subtract_v according_a to_o the_o former_a direction_n leave_v 38._o gr_n 30._o m_o the_o height_n of_o the_o aequinoctial_a above_o the_o horizon_n &_o that_o take_v from_o 90._o leaf_n 51._o gr_n 30._o m_o the_o depression_n of_o the_o south_n pole_n under_o the_o horizon_n or_o the_o elevation_n of_o the_o north_n pole_n above_o the_o horizon_n for_o the_o height_n of_o the_o aequinoctial_a know_v the_o compliment_n thereof_o be_v always_o the_o latitude_n of_o the_o place_n or_o height_n of_o the_o pole_n and_o here_o note_v general_o that_o the_o height_n of_o the_o pole_n and_o aequinoctial_a together_o do_v always_o make_v a_o quadrant_n or_o 90._o gr_n therefore_o the_o height_n of_o one_o of_o they_o be_v know_v the_o height_n of_o the_o other_o be_v also_o know_v and_o further_a here_o note_v that_o if_o the_o sun_n have_v north_n declination_n the_o sun_n be_v so_o much_o high_a than_o the_o aequinoctial_a at_o none_o that_o day_n by_o so_o much_o as_o his_o declination_n come_v to_o but_o if_o the_o sun_n have_v south_n declination_n than_o the_o sun_n be_v low_a than_o the_o aequinoctial_a that_o day_n at_o noon_n by_o so_o much_o as_o his_o declination_n come_v to_o by_o which_o you_o may_v easy_o gether_o when_o to_o add_v or_o subtract_v the_o sun_n declination_n to_o or_o from_o the_o sun_n meridianall_a altitude_n to_o get_v the_o height_n of_o aequator_fw-la which_o know_v the_o pole_n height_n can_v be_v unknown_a pro._n 34_o eight_o to_o find_v the_o sun_n azimuth_n and_o altitude_n for_o any_o hour_n constru_n ¦_o ctio_fw-la 44_o mark_n where_o the_o parallel_n for_o the_o day_n of_o the_o month_n meet_v with_o the_o give_v hour_n and_o bring_v the_o edge_n of_o the_o index_n thereto_o so_o the_o degree_n that_o the_o edge_n of_o the_o index_n cut_v in_o the_o limb_n of_o the_o instrument_n that_o shall_v be_v the_o sun_n azimuth_n and_o the_o degree_n that_o the_o hour_n cut_v in_o the_o index_n that_o shall_v be_v the_o sun_n altitude_n require_v so_o if_o upon_o the_o ten_o of_o december_n at_o nine_o of_o the_o clock_n in_o the_o morning_n exam._n the_o sun_n azimuth_n and_o altitude_n be_v require_v mark_v first_o where_o the_o tropic_a of_o capricorn_n which_o be_v the_o parallel_n for_o that_o day_n give_v meet_v with_o the_o give_v hour_n of_o nine_o and_o bring_v the_o index_n thereto_o so_o the_o edge_n of_o it_o in_o the_o limb_n point_v out_o near_o 40._o gr_n and_o a_o half_a &_o so_o much_o be_v the_o sun_n azimuth_n from_o the_o south_n at_o nine_o of_o the_o clock_n in_o the_o forenoon_n the_o say_v ten_o of_o december_n and_o the_o hour_n line_n meet_v with_o the_o index_n show_v near_o 5._o gr_n 25._o m._n so_o much_o be_v the_o sun_n altitude_n at_o that_o time_n now_o if_o you_o move_v the_o index_n soft_o along_o as_o the_o edge_n of_o it_o pass_v by_o any_o hour_n for_o any_o day_n of_o the_o year_n so_o the_o edge_n of_o the_o index_n in_o the_o limb_n of_o the_o instrument_n show_v the_o sun_n azimuth_n and_o the_o intersection_n of_o the_o parallel_n with_o the_o index_n shall_v show_v the_o sun_n altitude_n belong_v to_o that_o hour_n nine_o to_o show_v the_o uncertainty_n pro._n 35_o of_o time_n by_o note_v the_o shadow_n of_o thing_n it_o be_v usual_o note_v by_o some_o that_o when_o the_o shadow_n of_o the_o edge_n of_o a_o window_n door_n wall_n or_o such_o like_a shall_v touch_v such_o or_o such_o mark_n that_o it_o shall_v be_v then_o such_o or_o such_o a_o hour_n of_o the_o day_n and_o so_o constant_o to_o hold_v for_o all_o the_o year_n this_o observation_n be_v far_o from_o truth_n and_o the_o principal_n of_o astronomy_n and_o may_v be_v easy_o contradict_v by_o such_o which_o have_v but_o indifferent_a judgement_n in_o the_o nature_n of_o shadow_n and_o the_o sun_n passage_n by_o the_o meridian_n and_o vertical_a circle_n of_o the_o heaven_n for_o by_o how_o much_o great_a the_o propinquity_n of_o the_o sun_n approachment_n be_v unto_o the_o zenith_n or_o vertical_a point_n by_o so_o much_o the_o more_o shall_v the_o hour_n or_o time_n be_v various_a in_o one_o and_o the_o same_o azimuth_n so_o in_o the_o last_o pro._n the_o azimuth_n of_o the_o sun_n the_o ten_o of_o december_n at_o nine_o of_o the_o clock_n in_o the_o forenoon_n be_v find_v to_o be_v 40._o gr_n and_o a_o half_a exam_n and_o the_o sun_n distance_n from_o the_o zenith_n at_o that_o time_n be_v near_o 84._o gr_n 35._o m_o now_o admit_v the_o sun_n distance_n from_o the_o zenith_n the_o ten_o of_o june_n be_v but_o 32._o gr_n 35._o m_o the_o sun_n be_v in_o the_o same_o azimuth_n the_o hour_n will_v be_v half_a a_o hour_n past_o 10._o for_o the_o index_n be_v lay_v to_o the_o hour_n of_o 9_o in_o the_o tropic_n of_o ♑_o which_o be_v the_o sun_n parallel_n for_o the_o say_v ten_o of_o december_n and_o it_o cut_v the_o constru_n ¦_o ctio_fw-la 45_o parallel_n of_o the_o sun_n motion_n in_o the_o inequality_n of_o time_n and_o so_o the_o compliment_n of_o the_o former_a 32._o gr_n 35._o m_o in_o the_o index_n meet_v with_o the_o tropic_n of_o ♋_o which_o be_v the_o sun_n parallel_n for_o the_o ten_o of_o june_n in_o half_a a_o hour_n past_o 10._o so_o that_o it_o evident_o appear_v that_o the_o shadow_n of_o a_o perpendicular_a thing_n on_o the_o ten_o of_o december_n denote_v the_o hour_n of_o the_o day_n to_o be_v 9_o of_o the_o clock_n the_o same_o shadow_n the_o ten_o of_o june_n shall_v represent_v half_o a_o hour_n past_o 10._o so_o the_o error_n shall_v be_v a_o hour_n and_o a_o half_a but_o if_o you_o move_v the_o index_n unto_o the_o hour_n of_o 9_o belong_v to_o the_o ten_o of_o june_n the_o index_n shall_v point_v you_o out_o in_o the_o limb_n near_o 68_o gr_n of_o azimuth_n for_o that_o hour_n which_o at_o 9_o of_o the_o clock_n the_o ten_o of_o december_n be_v but_o 40._o gr_n &_o a_o half_a so_o the_o difference_n of_o azimuth_n in_o one_o and_o the_o same_o hour_n shall_v be_v 27._o gr_n and_o a_o half_a &_o the_o time_n as_o before_o a_o hour_n and_o a_o half_a which_o difference_n be_v sufficient_a to_o confirm_v the_o point_n ten_o to_o find_v the_o quarter_n of_o pro._n 36_o the_o year_n and_o day_n of_o the_o month_n if_o it_o be_v forget_v constru_n ¦_o ctio_fw-la 46_o at_o any_o appearance_n of_o the_o sun_n by_o the_o 27._o pro._n take_v the_o sun_n altitude_n then_o place_v the_o north_n and_o south_n edge_n of_o the_o instrument_n unto_o the_o meridian_n line_n former_o draw_v if_o in_o the_o forenoon_n otherwise_o place_v the_o east_n and_o west_n edge_n of_o instrument_n to_o the_o meridian-line_n and_o erect_v the_o prependicular_a at_o the_o end_n of_o the_o index_n then_o move_v the_o index_n to_o and_o fro_o until_o the_o shadow_n of_o the_o prependicular_a fall_n by_o the_o side_n of_o the_o index_n so_o the_o parallel_n that_o meet_v with_o the_o degree_n of_o the_o sun_n observe_v altitude_n in_o the_o edge_n of_o the_o index_n parallel_n in_o the_o calendar_n that_o shall_v show_v the_o day_n of_o the_o month_n require_v so_o if_o exam._n upon_o a_o certain_a day_n in_o the_o year_n the_o sun_n altitude_n be_v observe_v and_o find_v to_o be_v 36._o gr_n have_v place_v the_o edge_n of_o the_o instrument_n to_o the_o meridian_n line_n and_o rectify_v the_o index_n then_o move_v the_o index_n until_o the_o shadow_n of_o the_o prependicular_a fall_n by_o the_o edge_n of_o the_o instrument_n let_v the_o instrument_n rest_n at_o this_o position_n and_o account_v the_o former_a 36._o gr_n upon_o the_o index_n which_o degree_n meet_v with_o the_o hour_n in_o the_o aequator_fw-la and_o also_o that_o intersect_v the_o calendar_n in_o the_o ten_o of_o march_n &_o the_o thirteen_o of_o september_n but_o which_o of_o these_o day_n be_v the_o day_n of_o the_o month_n the_o next_o day_n observation_n of_o the_o sun_n upon_o the_o same_o hour_n will_v help_v you_o for_o if_o the_o sun_n altitude_n besound_v to_o be_v great_a than_o the_o day_n of_o the_o month_n inquire_v after_o it_o be_v the_o ten_o of_o march_z because_o the_o sun_n from_o the_o ten_o of_o december_n unto_o the_o eleven_o of_o june_n do_v every_o day_n at_o one_o &_o the_o same_o hour_n ascend_v but_o if_o the_o sun_n altitude_n be_v find_v to_o be_v
less_o than_o the_o former_a day_n observation_n specify_v be_v than_o the_o day_n require_v be_v the_o thirteen_o of_o september_n because_o that_o from_o the_o eleven_o of_o june_n unto_o the_o ten_o of_o december_n the_o sun_n altitude_n every_o day_n do_v sensible_o diminish_v at_o one_o and_o the_o same_o hour_n ☞_o ☞_o but_o here_o be_v to_o be_v note_v that_o if_o there_o be_v no_o meridional_a line_n than_o the_o prependicular_a over_o the_o constru_n ¦_o ctio_fw-la 47_o centre_n and_o the_o axis_n of_o the_o index_n be_v erect_v place_v down_o the_o back_n of_o the_o instrument_n upon_o a_o horizontall_a plain_a and_o move_v the_o instrument_n to_o and_o fro_o until_o the_o shadow_n of_o the_o axis_n meet_v with_o the_o same_o hour_n below_o the_o tropic_n among_o the_o common_a hour_n that_o the_o shadow_n of_o the_o prependicular_a over_o the_o centre_n of_o the_o instrument_n meet_v with_o on_o the_o face_n of_o the_o instrument_n for_o then_o the_o parallel_n that_o cross_v or_o meet_v with_o the_o shadow_n of_o the_o prependicular_a and_o the_o hour_n will_v in_o the_o calendar_n show_v the_o day_n of_o the_o month_n require_v and_o so_o then_o the_o meridian_n of_o the_o instrument_n shall_v be_v in_o the_o meridian_n of_o the_o world_n and_o every_o point_n or_o degree_n in_o the_o horizon_n of_o the_o instrument_n it_o shall_v point_v out_o his_o like_a or_o opposite_a degree_n in_o the_o horizon_n of_o the_o world_n constru_n ¦_o ctio_fw-la 48_o or_o otherwise_o it_o may_v be_v do_v thus_o take_v the_o sun_n altitude_n then_o immediate_o by_o some_o watch_n clock_z or_o sundial_n learn_v the_o hour_n of_o the_o day_n and_o move_v the_o index_n to_o and_o fro_o until_o the_o sun_n altitude_n in_o the_o index_n meet_v with_o the_o former_a hour_n so_o the_o parallel_n that_o meet_v therewith_o shall_v show_v the_o day_n of_o the_o month_n in_o the_o calendar_n require_v then_o have_v the_o day_n of_o the_o month_n you_o have_v the_o quarter_n of_o the_o year_n for_o from_o the_o ten_o of_o march_n unto_o the_o eleven_o of_o june_n be_v the_o spring_n quarter_n from_o the_o eleven_o of_o june_n to_o the_o thirteen_o of_o september_n be_v the_o summer_n quarter_n from_o the_o thirteen_o of_o september_n to_o the_o ten_o of_o december_n be_v the_o autummuall_a quarter_n and_o from_o the_o ten_o of_o december_n unto_o the_o ten_o of_o march_n be_v the_o winter_n quarter_n eleventh_o to_o find_v the_o hour_n of_o pro._n 37_o the_o day_n the_o azimuth_n and_o altitude_n of_o the_o sun_n with_o the_o meridional_a line_n without_o observation_n or_o sight_n of_o the_o sun_n by_o know_v the_o proportion_n between_o the_o length_n of_o a_o shadow_n upon_o a_o horizontal_a plain_n and_o that_o which_o cast_v the_o shadow_n first_o let_v the_o thing_n that_o cast_v the_o shadow_n or_o constru_n ¦_o ctio_fw-la 59_o something_o equal_v in_o length_n unto_o it_o be_v divide_v into_o ten_o equal_a part_n and_o each_o of_o those_o part_n subdive_v into_o ten_o other_o equal_a part_n which_o thing_n so_o divide_v shall_v represent_v a_o common_a scale_n then_o measure_v the_o shadow_n with_o the_o scale_n and_o mark_v how_o often_o the_o shadow_n be_v long_o than_o the_o scale_n and_o the_o decimall_n part_n if_o there_o be_v any_o so_o have_v you_o the_o proportion_n between_o the_o shadow_n and_o that_o which_o do_v cast_v the_o shadow_n and_o then_o be_v it_o resolve_v accor_v to_o the_o converse_n of_o the_o fifteen_o pro._n exam._n admit_v some_o one_o upon_o the_o 12._o of_o february_n or_o on_o the_o nine_o of_o october_n hold_v a_o staff_n prependicular_a as_o a_o b_o or_o suppose_v it_o to_o be_v part_n of_o the_o coin_n of_o a_o house_n or_o edge_n of_o a_o window_n or_o such_o like_a shall_v cast_v a_o shadow_n as_o b_o c_o which_o be_v note_v or_o draw_v and_o have_v divide_v the_o staff_n or_o thing_n as_o before_o and_o shall_v then_o measure_v the_o shadow_n as_o b_o c_o by_o the_o say_a staff_n or_o scale_n and_o find_v it_o to_o be_v contain_v therein_o three_o time_n and_o 6_o parts_z or_o 6_o decimal_n the_o porportion_n of_o the_o gnomon_n or_o scale_v a_o b_o to_o the_o shadow_n b_o c_o will_v be_v as_o 1_o to_o 3._o and_o 6_o 10._o construc_fw-fr ¦_o tio_fw-la 50_o move_v therefore_o the_o index_n to_o and_o fro_o until_o the_o edge_n of_o it_o mere_a with_o 3._o and_o 6_o 10_o in_o the_o line_n of_o shadow_n so_o have_v you_o the_o degree_n of_o the_o sun_n altitude_n at_o that_o instant_n in_o the_o index_n viz._n 15._o gr_n and_o ½_n then_o seek_v out_o the_o parallel_n for_o the_o 12._o of_o february_n or_o the_o nine_o of_o october_n the_o day_n give_v which_o be_v near_o the_o ten_o degree_n from_o the_o aequator_fw-la south_n move_v the_o index_n until_o the_o former_a 15._o gr_n and_o ½_n in_o the_o index_n meet_v with_o the_o say_a parallel_n for_o the_o day_n so_o have_v you_o the_o hour_n belong_v to_o that_o time_n which_o will_v be_v near_o 42_o m_o past_o 8._o in_o the_o morning_n or_o 18._o m_o past_o 3_o in_o the_o after_o noon_n and_o the_o edge_n of_o the_o index_n in_o the_o limb_n of_o the_o instrument_n show_v the_o sun_n azimuth_n also_o at_o that_o instant_n viz_o near_o 39_o gr_n 12._o m_o from_o the_o east_n towards_o the_o south_n now_o for_o the_o meridional_a line_n this_o may_v be_v do_v constru_n ¦_o ctio_fw-la 51_o at_o any_o time_n after_o if_o the_o azimuth_n be_v not_o forget_v for_o if_o the_o centre_n of_o the_o instrument_n be_v lay_v down_o upon_o any_o part_n of_o the_o shadow_n b_o c_o and_o so_o the_o instrument_n to_o be_v move_v upon_o his_o centre_n until_o the_o say_a shadow_n b_o c_o former_o draw_v cut_v the_o edge_n of_o the_o limb_n in_o the_o aforesaid_a azimuth_n of_o 39_o gr_n 30._o m_o than_o the_o meridian_n of_o the_o instrument_n shall_v be_v in_o the_o meridian_n of_o the_o world_n and_o if_o that_o shadow_n be_v from_o a_o window_n or_o building_n the_o position_n of_o the_o instrument_n shall_v denote_v the_o position_n of_o the_o window_n or_o building_n twelve_o to_o find_v the_o declination_n pro._n 38_o of_o a_o wall_n by_o see_v the_o sun_n beginning_n to_o shine_v thereon_o or_o go_v from_o it_o by_o the_o 27._o pro._n take_v the_o height_n of_o the_o sun_n and_o constru_n ¦_o ctio_fw-la 52_o by_o the_o 28._o pro._n find_v the_o sun_n azimuth_n for_o the_o altitude_n so_o the_o azimuth_n thus_o find_v shall_v be_v the_o declination_n of_o the_o plain_a require_v for_o the_o declination_n of_o any_o perpendicular_a plain_n be_v account_v from_o the_o point_n of_o east_n west_n north_n or_o south_n in_o the_o horizon_n as_o the_o sun_n azimuth_n be_v therefore_o whatsoever_o plain_n be_v in_o the_o plain_a of_o any_o virticall_a circle_n that_o plain_o be_v as_o far_o from_o any_o of_o the_o cardinal_n point_v of_o the_o horizon_n as_o the_o sun_n be_v at_o that_o time_n &_o so_o the_o sun_n be_v in_o that_o virticall_a circle_n shall_v necessary_o glance_v upon_o the_o plain_a and_o therefore_o look_v what_o the_o sun_n azimuth_n be_v at_o that_o instant_n such_o shall_v be_v the_o declination_n of_o the_o plain_a require_v thirteen_o to_o find_v the_o declination_n pro._n 39_o of_o a_o plain_a upon_o any_o appearance_n of_o the_o sun_n thus_o for_o the_o construction_n of_o the_o aforesaid_a 13._o use_n which_o do_v depend_v upon_o the_o sun_n observation_n the_o 48._o 49._o 50._o 9_o 13._o 14._o and_o 15_o use_n of_o the_o index_n or_o table_n against_o page_n the_o first_o shall_v have_v follow_v but_o before_o i_o speak_v of_o they_o it_o will_v not_o be_v inconvenient_a that_o i_o apply_v the_o instrument_n unto_o the_o resolution_n of_o the_o 44._o 45._o 46._o &_o 47._o use_n of_o the_o aforesaid_a index_n or_o table_n which_o have_v reference_n to_o night_n observation_n upon_o such_o star_n which_o be_v or_o may_v be_v place_v on_o the_o face_n of_o the_o instrument_n between_o the_o two_o tropicke_n or_o under_o the_o tropic_n of_o cancer_n according_a to_o there_o declination_n and_o right_a ascension_n which_o be_v these_o follow_v the_o name_n of_o the_o star_n decli_n rec_n the_o name_n of_o the_o star_n decli_n rec._n g._n m._n h._n m._n g.m._n g.m._n h._n m_o g._n m._n exit_fw-la alae_fw-la pegasi_fw-la 13.9_o n._n 23.54_o 1._o 30._o coâ—_n hydrae_fw-la 7.5_o a_o 9_o 10._o 42.45_o pri_fw-la ♈_o â—1_n 40_o n._n 1.46_o 26._o 30._o cor_fw-la leonis_fw-la 13.45_o b._n 9_o 48._o 33.00_o oculus_fw-la ♉_o 15.42_o n._n 4.15_o 63.45_o cauda_fw-la ♌_o 16.38_o b_o 11.30_o 7.26_o pri_fw-la singuli_fw-la ori._n 0._o 17._o s._n 5._o 13._o 78.15_o spica_fw-la â™_o 9_o â—0_n m._n 13._o 5._o 16.15_o canis_fw-la maior_fw-la 16_o 1â—_n s._n 6._o 30._o 82.15_o
but_o if_o from_o the_o say_v 7_o hour_n and_o 24._o m_o the_o say_z 6_o hour_n 15._o m_o be_v take_v there_o will_v rest_v 1._o hour_n 9_o m_o and_o so_o much_o before_o 12._o of_o the_o clock_n at_o noon_n do_v oculus_fw-la ♉_o rise_v that_o be_v 51._o m_o after_z 10_o of_o the_o clock_n and_o so_o consequent_o if_o the_o say_v 7._o hour_n and_o 24._o m_o be_v add_v unto_o the_o hour_n of_o the_o star_n be_v in_o the_o meridian_n viz._n 6._o of_o the_o clock_n and_o 15._o m_o as_o before_z the_o say_a star_n will_v set_v at_o 39_o m_o past_o 1_o in_o the_o morning_n last_o if_o at_o any_o hour_n between_o the_o rise_n of_o the_o star_n and_o the_o set_n thereof_o it_o be_v require_v at_o what_o position_n and_o altitude_n the_o star_n be_v in_o it_o be_v thus_o do_v account_v to_o the_o give_v hour_n from_o the_o hour_n of_o the_o star_n rise_v set_v or_o be_v in_o the_o meridian_n constru_n ¦_o ctio_fw-la 56_o in_o the_o parallel_n of_o the_o star_n declination_n and_o lay_v the_o index_n thereto_o so_o the_o edge_n of_o it_o in_o the_o limb_n of_o the_o instrument_n shall_v show_v the_o star_n azimuth_n or_o position_n and_o where_o the_o parallel_n of_o the_o star_n declination_n cross_v the_o edge_n of_o the_o index_n that_o shall_v be_v the_o star_n altitude_n at_o that_o hour_n so_o if_o on_o the_o say_v 6_o of_o february_n at_o 11._o exam._n of_o the_o clock_n at_o night_n it_o be_v require_v in_o what_o position_n or_o azimuth_n oculus_fw-la ♉_o be_v in_o and_o also_o how_o high_a above_o the_o horizon_n i_o make_v or_o suppose_v the_o hour_n of_o 12._o to_o be_v the_o aforesaid_a 6._o of_o the_o clock_n and_o 15._o m_o for_o at_o that_o hour_n as_o before_o oculus_fw-la ♉_o be_v in_o the_o mridian_n and_o from_o thence_o in_o the_o star_n parallel_v of_o declination_n i_o account_v until_o i_o come_v unto_o 11._o of_o the_o clock_n viz._n that_o be_v 4._o hour_n and_o 45._o m_o from_o 12._o and_o lay_v the_o index_n thereto_o so_o the_o edge_n of_o the_o index_n in_o the_o limb_n point_v out_o 4._o gr_n 24._o m_o and_o so_o far_a oculus_fw-la ♉_o be_v distant_a from_o the_o west_n at_o 11._o of_o the_o clock_n at_o night_n and_o the_o parallel_n of_o the_o star_n declination_n meet_v with_o the_o index_n in_o 24._o gr_n near_o which_o be_v the_o star_n altitude_n at_o that_o hour_n require_v pro._n 42_o three_o to_o find_v in_o any_o night_n of_o the_o year_n in_o what_o part_n of_o the_o horizon_n any_o of_o the_o star_n on_o the_o instrument_n rise_v or_o set_v and_o at_o what_o hour_n and_o altitude_n a_o star_n will_v be_v due_a east_n or_o west_n constru_n ¦_o ctio_fw-la 57_o for_o the_o first_o mark_v where_o the_o parallel_n of_o the_o star_n declination_n cross_v the_o horizon_n or_o calendar_n lay_v the_o edge_n of_o the_o index_n hereto_o so_o the_o number_n of_o degree_n between_o the_o edge_n of_o the_o index_n and_o the_o point_n of_o east_n or_o west_n upon_o the_o limb_n of_o the_o instrument_n show_v the_o distance_n of_o the_o star_n rise_v from_o the_o east_n or_o west_n so_o if_o it_o be_v require_v in_o what_o part_n of_o the_o horizon_n oculus_fw-la ♉_o rise_v exam._n mark_v where_o the_o parallel_n of_o the_o star_n declination_n cross_v the_o horizon_n and_o lay_v the_o edge_n of_o the_o index_n thereto_o so_o it_o cut_v the_o limb_n of_o the_o instrument_n from_o the_o east_n near_o 26._o gr_n and_o so_o far_a oculus_fw-la ♉_o rise_v from_o the_o east_n towards_o the_o north._n for_o the_o second_o to_o find_v the_o time_n of_o a_o star_n come_v east_n or_o west_n by_o the_o 40_o pro._n consider_v at_o what_o hour_n the_o star_n constru_n ¦_o ctio_fw-la 58_o be_v in_o the_o meridian_n then_o lay_v the_o edge_n of_o the_o index_n to_o the_o point_n of_o east_n and_o west_n and_o account_v in_o the_o parallel_n of_o the_o star_n declination_n the_o number_n of_o hour_n between_o the_o edge_n of_o the_o index_n and_o the_o hour_n of_o 12._o which_v be_v take_v from_o the_o hour_n of_o the_o star_n be_v in_o the_o meridian_n give_v the_o hour_n of_o the_o star_n come_v east_n but_o add_v unto_o the_o hour_n of_o the_o star_n be_v in_o the_o meridian_n show_v the_o hour_n of_o the_o star_n be_v west_n so_o if_o it_o be_v demand_v at_o what_o hour_n exam._n upon_o the_o 6_o of_o february_n cor_n ♌_o will_v be_v due_a east_n or_o west_n and_o what_o altitude_n the_o star_n shall_v then_o have_v first_o lay_v the_o edge_n of_o the_o index_n to_o the_o point_n of_o east_n and_o west_n &_o wheresoever_o the_o parallel_n of_o the_o star_n declination_n cross_v the_o edge_n of_o the_o index_n that_o shall_v be_v the_o star_n altitude_n viz._n near_o 17._o gr_n 45._o m_o then_o account_v the_o number_n of_o hour_n in_o the_o parallel_n of_o the_o star_n declination_n between_o the_o edge_n of_o the_o index_n and_o the_o hour_n of_o 12._o which_o be_v near_o 5._o hour_n and_o 12._o m_o which_o take_v from_o the_o hour_n of_o the_o star_n be_v in_o the_o meridian_n which_o by_o the_o 40_o pro._n be_v at_o 11._o of_o the_o clock_n &_o 48._o m_o at_o night_n rest_v 6_o hour_n and_o 36._o m_o but_o if_o the_o say_v 5._o hour_n and_o 12._o m_o be_v add_v unto_o the_o say_v 11._o hour_n and_o 48._o m_o it_o make_v 17._o hour_n from_o which_o 12._o be_v take_v leaf_n 5_o hour_n so_o upon_o the_o 6_o of_o february_n cor_n ♌_o shall_v be_v due_a east_n at_o 36._o m_o past_o 6_o at_o night_n and_o due_a west_n at_o 5_o of_o the_o clock_n in_o the_o morning_n and_o the_o star_n altitude_n be_v either_o east_n or_o west_n be_v near_o 17._o gr_n 45._o m_o as_o be_v require_v pro._n 43_o four_o upon_o the_o sight_n or_o appearance_n of_o any_o of_o the_o aforesaid_a star_n to_o find_v the_o azimuth_n thereof_o and_o the_o hour_n of_o the_o night_n by_o the_o 40_o pro._n for_o the_o day_n give_v find_v the_o constru_n ¦_o ctio_fw-la 59_o hour_n of_o the_o star_n come_v to_o the_o meridâ—â—_n then_o by_o the_o 27._o pro._n take_v the_o star_n height_n 〈◊〉_d account_n that_o height_n in_o the_o index_n theâ—_n 〈…〉_o index_n until_o the_o degree_n of_o the_o starred_a 〈…〉_o the_o index_n meet_v with_o the_o parallâ—_n 〈…〉_o declination_n so_o the_o edge_n of_o the_o 〈…〉_o show_v the_o star_n azimuth_n and_o the_o meridian_n that_o meet_v with_o the_o degree_n of_o the_o altitude_n in_o the_o index_n shall_v show_v you_o the_o hour_n that_o the_o star_n want_v to_o be_v in_o the_o meridian_n or_o be_v past_o the_o meridian_n which_o add_v or_o subtract_v from_o the_o hour_n of_o the_o star_n be_v in_o the_o meridian_n give_v the_o hour_n of_o the_o night_n require_v so_o if_o the_o day_n be_v the_o 26_o of_o july_n exam._n and_o if_o aquila_n shall_v be_v observe_v to_o be_v on_o the_o west_n of_o the_o meridian_n 29._o gr_n 20._o m_o high_a above_o the_o horizon_n this_o i_o seek_v out_o upon_o the_o index_n and_o move_v the_o index_n to_o and_o fro_o until_o the_o say_v 29._o gr_n 20._o m_o meet_v with_o the_o parallel_n of_o declination_n of_o aquila_n so_o the_o edge_n of_o the_o index_n in_o the_o limb_n do_v point_n out_o the_o star_n azimuth_n from_o the_o south_n viz._n 63._o gr_n 12._o m_o and_o the_o meridian_n that_o meet_v with_o the_o aforesaid_a degree_n of_o altitude_n be_v the_o time_n of_o the_o star_n distance_n from_o the_o meridian_n viz._n near_o 3._o hour_n and_o 28._o m_o this_o add_v unto_o the_o hour_n of_o aquilas_fw-la be_v in_o the_o meridian_n which_o by_o the_o 40_o pro._n be_v at_o 10._o of_o the_o clock_n &_o 32._o m_o at_o night_n make_v 14._o hour_n or_o 2_o of_o the_o clock_n in_o the_o morning_n so_o if_o aquila_n be_v observe_v the_o 26_o of_o july_n to_o be_v 29._o gr_n 20._o m_o high_a to_o the_o west_n of_o the_o meridian_n than_o the_o position_n or_o azimuth_n of_o that_o star_n from_o the_o meridian_n be_v 63._o gr_n 12._o m_o and_o the_o hour_n at_o that_o instant_n be_v at_o 2._o of_o the_o clock_n in_o the_o morning_n thus_o touch_v the_o resolution_n of_o the_o aforesaid_a 44._o 45._o 46._o and_o 47_o pro._n of_o the_o aforesaid_a index_n or_o table_n which_o do_v belong_v to_o astronomical_a observation_n the_o last_o use_v now_o follow_v viz._n 48._o 49._o 50._o 9_o 13._o 14._o and_o 15_o use_n of_o the_o index_n or_o table_n which_o be_v only_o proper_a to_o geometrical_a practice_n viz._n to_o show_v 1._o how_o to_o measure_v the_o quantity_n of_o a_o angle_n or_o to_o take_v the_o distance_n of_o two_o star_n 2._o how_o to_o measure_v distance_n and_o