every_o common_a year_n so_o that_o in_o a_o revolution_n of_o 4._o year_n one_o day_n be_v gain_v which_o be_v add_v to_o february_n and_o therefore_o february_n have_v every_o four_o or_o leap_v year_n 29._o day_n problem_n four_o to_o find_v the_o day_n of_o the_o month_n the_o place_n of_o the_o sun_n be_v give_v as_o in_o the_o last_o problem_n it_o be_v your_o task_n to_o find_v on_o the_o horizon_n the_o day_n of_o the_o month_n first_o so_o now_o you_o must_v first_o seek_v the_o sign_n and_o degree_n the_o sun_n be_v in_o and_o against_o it_o in_o the_o circle_n of_o month_n you_o shall_v see_v the_o day_n of_o the_o month_n as_o against_o ♉_o 29._o you_o have_v may_v 10._o problem_n v._n the_o place_n of_o the_o sun_n give_v to_o find_v its_o declination_n have_v by_o the_o three_o problem_n find_v the_o sun_n place_n on_o the_o plain_a of_o the_o horizon_n you_o must_v seek_v the_o same_o degree_n in_o the_o ecliptic_a on_o the_o globe_n then_o bring_v that_o degree_n to_o 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towards_o 5_o therefore_o i_o say_v may_v 10._o the_o sun_n rise_v here_o at_o london_n at_o â…™_n which_o be_v 12._o minute_n after_o 4_o a_o clock_n in_o the_o morning_n if_o you_o double_v 4_o hour_n 12._o minute_n it_o give_v you_o the_o length_n of_o the_o night_n 8_o hour_n 24._o minute_n and_o if_o you_o subtract_v the_o length_n of_o the_o night_n 8._o hour_n 24._o minute_n from_o 24._o hour_n the_o length_n of_o day_n and_o night_n it_o leave_v the_o length_n of_o the_o day_n 15._o hour_n 36._o minute_n prob._n viii_o to_o find_v the_o hour_n of_o sun_n set._n turn_v the_o place_n of_o the_o sun_n to_o the_o west_n side_n of_o the_o horizon_n and_o the_o index_n of_o the_o hour_n circle_n show_v on_o the_o hour-circle_n the_o hour_n of_o sun_n set_v which_o on_o the_o 10_o of_o may_n aforesaid_a be_v 〈◊〉_d part_n of_o a_o hour_n after_o 〈◊〉_d 7._o a_o clock_n at_o night_n viz._n the_o sun_n set_v at_o 48._o minute_n past_o 7._o a_o clock_n prob._n ix_o to_o find_v how_o long_o it_o be_v twilight_n in_o the_o morning_n and_o evening_n twilight_n be_v that_o promiscuous_a and_o doubtful_a light_n which_o appear_v before_o the_o rise_n of_o the_o sun_n in_o the_o morning_n and_o continue_v after_o the_o set_n of_o the_o sun_n in_o the_o evening_n it_o be_v make_v by_o the_o extension_n of_o the_o sun_n beam_n into_o the_o vapour_n of_o the_o air_n when_o the_o sun_n be_v less_o than_o 18._o deg_n below_o the_o horizon_n for_o the_o sun_n ere_o it_o rise_v and_o after_o it_o set_v shoot_v forth_o its_o beam_n through_o the_o air_n and_o so_o illuminate_v the_o vapour_n of_o the_o air_n which_o illumination_n do_v by_o degree_n enlighten_v the_o horizon_n and_o spread_v through_o the_o zenith_n even_o into_o the_o west_n ere_o the_o sun_n rise_v and_o also_o continue_v above_o the_o horizon_n after_o the_o sun_n set_v now_o though_o it_o be_v twilight_n when_o the_o sun_n be_v 18._o degree_n below_o the_o horizon_n yet_o the_o duration_n of_o twilight_n be_v 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which_o be_v opposite_a to_o the_o place_n of_o the_o sun_n till_o it_o be_v elevate_v 18._o degree_n in_o the_o quadrant_n of_o altitude_n above_o the_o horizon_n in_o the_o west_n so_o shall_v the_o index_n of_o the_o hour-circle_n point_n at_o the_o hour_n that_o twilight_n begin_v then_o subtract_v the_o hour_n and_o minute_n that_o twilight_n begin_v from_o the_o hour_n and_o minute_n of_o sun_n rising_n if_o in_o the_o morning_n or_o subtract_v the_o hour_n of_o sun_n set_v from_o the_o hour_n of_o twilight_n if_o at_o night_n and_o the_o remainder_n be_v the_o length_n of_o twilight_n example_n the_o globe_n quadrant_n and_o hour-index_n be_v rectify_v as_o before_o and_o the_o sun_n place_n give_v ♉_o 29._o i_o seek_v the_o opposite_a degree_n on_o the_o globe_n after_o this_o manner_n i_o bring_v ♉_o 29._o to_o the_o meridian_n and_o observe_v what_o degree_n of_o the_o ecliptik_a the_o opposite_a part_n of_o the_o meridian_n cut_v and_o because_o i_o find_v it_o cut_v â™_o 29._o therefore_o i_o say_v â™_o 29._o be_v opposite_a to_o ♉_o 29._o have_v find_v the_o opposite_a degree_n i_o bring_v it_o into_o the_o west_n and_o also_o the_o quadrant_n of_o altitude_n and_o join_v â™_o 29._o to_o 18._o degree_n account_v upward_o on_o the_o quadrant_n so_o shall_v ♉_o 29._o be_v depress_v 18._o degree_n in_o the_o east_n side_n the_o horizon_n then_o look_v what_o hour_n the_o hour-index_n point_v at_o in_o the_o hour-circle_n i_o find_v it_o to_o be_v 1._o hor._n 8._o min._n which_o show_v that_o twilight_n begin_v at_o 8._o minute_n past_o 1._o a_o clock_n in_o the_o morning_n and_o if_o you_o subtract_v 1._o hour_n 8._o minute_n from_o 4._o hour_n 11._o minute_n the_o time_n
of_o sun_n rising_n find_v by_o the_o seven_o problem_n it_o leave_v 3._o hour_n 3._o minute_n for_o the_o length_n of_o twilight_n and_o if_o you_o double_v 1._o hour_n 8._o minute_n the_o beginning_n of_o twilight_n it_o make_v 2._o hour_n 16._o minute_n for_o the_o intermission_n of_o time_n between_o twilight_n in_o the_o evening_n and_o twilight_n in_o the_o morning_n so_o that_o may_v 10._o absolute_a night_n be_v but_o 2._o hour_n 16._o minute_n long_a here_o at_o london_n the_o reason_n why_o you_o bring_v the_o degree_n opposite_a to_o the_o sun_n place_n to_o the_o west_n be_v because_o the_o quadrant_n contain_v but_o 90._o degree_n will_v reach_v no_o low_o than_o the_o horizon_n but_o this_o problem_n require_v it_o to_o reach_v 18._o degree_n beneath_o it_o therefore_o by_o this_o help_n you_o have_v the_o proposition_n answer_v as_o well_o as_o if_o the_o quadrant_n do_v actual_o reach_v 18._o degree_n below_o the_o horizon_n this_o shift_n you_o may_v have_v occasion_n to_o make_v in_o some_o other_o problem_n if_o you_o will_v know_v when_o twilight_n end_v after_o sun_n set_v you_o shall_v find_v it_o by_o bring_v the_o degree_n of_o the_o ecliptic_a opposite_a to_o the_o place_n of_o the_o sun_n to_o 18._o degree_n of_o the_o quadrant_n of_o altitude_n on_o the_o east_n side_n the_o horizon_n for_o than_o shall_v the_o index_n of_o the_o hour-circle_n point_n at_o 10._o hour_n 52._o minute_n which_o show_v that_o it_o continue_v twilight_n till_o 52._o minute_n past_o 10._o a_o clock_n at_o night_n may_v 10._o here_o at_o london_n prob._n x._o the_o sun_n place_v give_v to_o find_v its_o amplitude_n and_o also_o to_o know_v upon_o what_o point_n of_o the_o compass_n it_o rise_v the_o globe_n etc._n etc._n rectify_v bring_v the_o sun_n place_n to_o the_o east_n side_n the_o horizon_n and_o the_o number_n of_o degree_n intercept_v between_o the_o east_n point_n of_o the_o horizon_n and_o the_o sun_n place_n be_v the_o number_n of_o degree_n of_o amplitude_n that_o the_o sun_n have_v at_o its_o rise_n and_o bear_v its_o denomination_n either_o of_o north_n or_o south_n according_a to_o its_o inclination_n to_o either_o point_n in_o the_o horizon_n or_o if_o you_o will_v know_v upon_o what_o point_n of_o the_o compass_n the_o sun_n rise_v look_v but_o in_o the_o circle_n of_o wind_n and_o against_o the_o place_n of_o the_o sun_n you_o have_v the_o name_n of_o the_o point_n of_o the_o compass_n upon_o which_o the_o sun_n rise_v example_n of_o both_o may_v 10._o the_o sun_n place_n be_v ♉_o 29._o therefore_o â—_o the_o globe_n be_v rectify_v i_o bring_v ♉_o 29._o to_o the_o east_n side_n the_o horizon_n and_o find_v it_o touch_v against_o 33_o degree_n 20._o minute_n from_o the_o east_n point_n towards_o the_o north_n therefore_o i_o say_v the_o sun_n have_v north_n amplitude_n 33_o degree_n 20._o minute_n and_o to_o know_v upon_o what_o point_n of_o the_o compass_n the_o sun_n rise_v i_o keep_v the_o globe_n to_o its_o position_n and_o look_v in_o the_o circle_n of_o wind_n in_o the_o outmost_a verge_n of_o the_o horizon_n and_o find_v the_o sun_n place_n against_o the_o wind_n name_v north_n east_n and_o by_o east_n therefore_o i_o say_v may_v 10._o here_o at_o london_n the_o sun_n rise_v upon_o the_o north_n east_n and_o by_o east_n point_n of_o the_o compass_n probl._n xi_o the_o hour_n of_o the_o day_n give_v to_o find_v the_o height_n of_o the_o sun_n the_o globe_n etc._n etc._n rectify_v turn_v about_o the_o globe_n till_o the_o index_n of_o the_o hour-circle_n point_n in_o the_o hour-circle_n to_o the_o hour_n of_o the_o day_n then_o bring_v the_o quadrant_n of_o altitude_n to_o the_o sun_n place_n in_o the_o ecliptic_a and_o the_o degree_n on_o the_o quadrant_n which_o touch_v the_o sun_n place_n shall_v be_v the_o number_n of_o degree_n of_o the_o sun_n altitude_n example_n may_v 10._o here_o at_o london_n at_o 53._o minute_n past_o 8._o a_o clock_n in_o the_o morning_n i_o will_v know_v the_o height_n of_o the_o sun_n above_o the_o horizon_n therefore_o i_o turn_v about_o the_o globe_n till_o the_o index_n of_o the_o hour-circle_n come_v to_o 53_o minute_n past_o 8._o a_o clock_n which_o be_v almost_o 9_o in_o the_o hour-circle_n and_o keep_v the_o globe_n to_o this_o position_n i_o bring_v the_o quadrant_n of_o altitude_n to_o the_o sun_n place_n viz._n 〈◊〉_d 29._o find_v by_o the_o three_o problem_n and_o because_o the_o sun_n place_n touch_v upon_o 40._o degree_n of_o the_o quadrant_n therefore_o i_o say_v may_v 10._o 53._o minute_n past_o 8._o a_o clock_n in_o the_o morning_n here_o at_o london_n the_o sun_n be_v just_a 40._o degree_n above_o the_o horizon_n or_o which_o be_v all_o one_o have_v 40._o degree_n of_o altitude_n prob._n xii_o the_o altitude_n 〈◊〉_d sun_n and_o day_n of_o the_o month_n give_v to_o find_v the_o hour_n of_o the_o day_n a_o hour_n be_v the_o 24_o part_n of_o a_o day_n and_o a_o night_n or_o the_o space_n of_o time_n that_o 15._o degree_n of_o the_o equator_fw-la take_v up_o in_o define_v pass_v through_o the_o meridian_n for_o the_o whole_a equator_fw-la which_o contain_v 360._o degree_n pass_v through_o the_o meridian_n in_o 24._o hour_n therefore_o 15._o degree_n which_o be_v the_o 24_o part_n of_o 360_o pass_v through_o in_o one_o hour_n these_o hour_n be_v vulgar_o divide_v into_o half_n quarter_n and_o half_a quarter_n but_o mathematical_o into_o minute_n second_o three_o fourths_o etc._n etc._n a_o minute_n be_v the_o 60th_o part_n of_o a_o hour_n so_o that_o 60_o minute_n make_v a_o hour_n 30_o half_o a_o hour_n 15._o a_o quarter_n of_o a_o hour_n a_o second_o be_v the_o 60th_o define_v part_n of_o a_o minute_n a_o three_o be_v the_o 60th_o part_n of_o a_o second_o a_o four_o be_v the_o 60th_o part_n of_o a_o three_o and_o so_o you_o may_v run_v on_o to_o fifths_o sixth_n seventh_n etc._n etc._n if_o you_o please_v 12._o of_o these_o hour_n make_v a_o day_n and_o 12._o more_o make_v a_o night_n so_o that_o day_n and_o night_n contain_v 24._o hour_n as_o aforesaid_a which_o be_v volgar_o number_v from_o noon_n with_o 1_o 2_o 3_o to_z 12_o at_o night_n and_o then_o begin_v again_o with_o 1_o 2_o 3_o till_o 12_o at_o noon_n but_o by_o astronomer_n they_o be_v number_v from_o noon_n with_o 1_o 2_o 3_o etc._n etc._n to_o 12._o at_o night_n and_o so_o forward_o to_o 13_o 14_o 15_o till_o 24_o which_o be_v just_o full_a noon_n the_o next_o day_n yet_o in_o this_o treatise_n i_o shall_v mention_v the_o hour_n as_o they_o be_v vulgar_o coâ—â—ted_v viz._n from_o 〈◊〉_d after_o noon_n to_o 12._o at_o night_n and_o call_v the_o hour_n after_o midnight_n by_o 1_o 2_o 3_o 4_o etc._n etc._n in_o the_o morning_n to_o 12._o at_o noon_n again_o the_o next_o day_n but_o to_o the_o operation_n the_o globe_n etc._n etc._n rectify_v bring_v the_o place_n of_o the_o son_n to_o the_o number_n of_o degree_n of_o altitude_n account_v upon_o the_o quadrant_n of_o altitude_n and_o the_o hour-index_n shall_v point_v at_o the_o hour_n in_o the_o hour-circle_n yet_o herein_o respect_n must_v be_v have_v to_o the_o fore_n or_o after_o noon_n elevation_n as_o shall_v be_v show_v in_o the_o next_o problem_n example_n may_v 10._o the_o sun_n be_v elevate_v 40._o degree_n above_o the_o horizon_n here_o at_o london_n therefore_o have_v find_v the_o place_n of_o the_o sun_n by_o the_o three_o problem_n to_o be_v â—29_n i_o move_v the_o globe_n and_o quadrant_n till_o i_o can_v join_v the_o 29._o degree_n of_o 〈◊〉_d to_o the_o 40._o deg_n upon_o the_o quadrant_n of_o altitude_n and_o then_o look_v on_o the_o hour-circle_n i_o find_v the_o index_n point_n at_o 53._o minute_n past_o 8._o a_o clock_n for_o the_o before_o noon_n elevation_n and_o at_o 3._o hour_n 7._o minute_n for_o the_o after_o noon_n elevation_n therefore_o if_o it_o be_v forenoon_n i_o say_v it_o be_v 53._o minute_n past_o 8._o a_o clock_n in_o the_o morning_n but_o if_o it_o be_v after_o noon_n i_o say_v it_o be_v 7._o minute_n past_o 3._o a_o clock_n in_o the_o after_o noon_n prob._n xiii_o how_o to_o know_v whether_o it_o be_v before_o or_o after_o noon_n have_v make_v one_o observation_n you_o must_v make_v a_o second_o a_o little_a while_n after_o the_o first_o and_o if_o the_o sun_n increase_v in_o altitude_n it_o be_v before_o noon_n but_o if_o it_o decrease_v in_o altitude_n it_o be_v after_o noon_n example_n the_o sun_n be_v at_o 8._o hor._n 53._o min._n elevate_v 40._o degr_n above_o the_o horizon_n a_o little_a while_n after_o suppose_v for_o example_n sake_n aquarter_n of_o a_o hour_n viz._n at_o 9_o hor._n 8._o min._n i_o observe_v again_o the_o height_n of_o the_o sun_n and_o find_v it_o 42._o degree_n high_a
as_o i_o can_v so_o as_o the_o spheric_a gnomon_n may_v cast_v no_o shadow_n yet_o if_o it_o do_v and_o the_o shadow_n fall_v towards_o the_o north_n pole_n then_o i_o elevate_v the_o north_n pole_n more_o till_o the_o shadow_n fall_v just_a in_o the_o middle_n of_o itself_o but_o if_o the_o shadow_n fall_v downward_o towards_o the_o south_n pole_n than_o i_o depress_v the_o north_n pole_n if_o the_o shadow_n fall_v on_o the_o east_n side_n i_o turn_v the_o globe_n on_o its_o axis_n more_o to_o the_o west_n and_o if_o the_o shadow_n fall_v to_o the_o west_n i_o turn_v the_o globe_n more_o into_o the_o east_n and_o the_o degree_n of_o the_o meridian_n which_o the_o north_n point_n of_o the_o horizon_n touch_v be_v the_o degree_n of_o the_o pole_n elevation_n which_o in_o this_o example_n be_v 51½_n the_o latitude_n of_o the_o city_n of_o london_n by_o this_o operation_n you_o have_v also_o give_v the_o hour_n of_o the_o day_n in_o the_o hour-circle_n if_o you_o keep_v the_o globe_n unmoved_a and_o the_o azimuth_n and_o almicantar_n if_o you_o apply_v but_o the_o quadrant_n of_o altitude_n to_o the_o place_n of_o the_o sun_n as_o by_o the_o 22_o and_o 23._o problem_n prob._n xix_o to_o observe_v by_o the_o globe_n the_o distance_n of_o two_o star_n you_o must_v pitch_v upon_o two_o star_n in_o the_o meridian_n and_o observe_v the_o altitude_n of_o one_o of_o they_o first_o and_o afterward_o the_o altitude_n of_o the_o other_o then_o subtract_v the_o lesser_a altitude_n from_o the_o great_a and_o the_o remainder_n shall_v be_v the_o distance_n require_v example_n march_n 7._o at_o 11._o a_o clock_n at_o night_n here_o at_o london_n i_o see_v in_o the_o meridian_n the_o two_o star_n in_o the_o foremost_a wheel_n of_o the_o wagon_n in_o the_o constellation_n of_o the_o great_a bear_n call_v by_o seaman_n the_o pointer_n because_o they_o always_o point_v towards_o the_o polestar_n therefore_o to_o observe_v the_o distance_n between_o these_o two_o star_n i_o first_o observe_v as_o by_o the_o last_o problem_n the_o altitude_n of_o the_o most_o northern_a to_o be_v 77._o degree_n 59_o minute_n and_o set_v down_o that_o number_n of_o degree_n and_o minute_n with_o a_o pen_n and_o ink_n on_o a_o paper_n or_o with_o a_o piece_n of_o chalk_n or_o a_o pencil_n on_o a_o board_n and_o afterward_o i_o observe_v the_o altitude_n of_o the_o other_o star_n which_o be_v under_o it_o as_o i_o do_v the_o first_o to_o be_v 83._o deg_n 21._o min._n and_o set_v that_o number_n of_o degree_n and_o minute_n also_o down_o under_o the_o other_o number_n of_o degree_n and_o minute_n then_o by_o substract_v the_o lesser_a from_o the_o great_a i_o find_v the_o remainder_n to_o be_v 5._o degree_n 22._o min._n which_o be_v the_o distance_n of_o the_o two_o star_n in_o the_o great_a bear_n call_v the_o pointer_n prob._n xx._n how_o you_o may_v learn_v to_o give_v a_o guess_n at_o the_o number_n of_o degree_n that_o any_o two_o star_n be_v distant_a from_o one_o another_o or_o the_o number_n of_o degree_n of_o altitude_n the_o sun_n or_o any_o star_n be_v elevate_v above_o the_o horizon_n only_o by_o look_v up_o to_o heaven_n without_o any_o instrument_n between_o the_o zenith_n and_o the_o horizon_n be_v comprehend_v a_o arch_n of_o a_o circle_n contain_v 90._o degree_n so_o that_o if_o you_o see_v any_o star_n in_o or_o near_o the_o zenith_n you_o may_v know_v that_o star_n be_v 90._o or_o near_o 90._o degree_n high_a and_o by_o so_o much_o as_o you_o may_v conceive_v it_o want_v of_o the_o zenith_n so_o much_o you_o may_v guess_v it_o want_v of_o 90._o degree_n above_o the_o horizon_n by_o this_o rule_n you_o may_v guess_v at_o a_o arch_n of_o heaven_n contain_v 90._o degree_n or_o at_o a_o arch_n of_o heaven_n contain_v 45._o degree_n if_o by_o your_o imagination_n you_o divide_v the_o whole_a arch_n into_o two_o equal_a part_n for_o than_o shall_v each_o of_o they_o contain_v 45._o degree_n and_o if_o by_o your_o imagination_n you_o divide_v the_o arch_n of_o 90._o into_o 3._o equal_a part_n each_o division_n shall_v contain_v a_o arch_n of_o 30._o degree_n etc._n etc._n but_o this_o way_n be_v a_o little_a too_o rude_a for_o guess_v at_o star_n elevate_v but_o few_o degree_n or_o for_o star_n distant_a but_o few_o degree_n from_o one_o another_o therefore_o that_o you_o may_v learn_v to_o guess_v more_o precise_o at_o distance_n in_o heaven_n you_o may_v either_o with_o a_o quadrant_n astrolabe_n or_o the_o globe_n find_v the_o exact_a distance_n of_o any_o two_o know_a star_n that_o be_v but_o few_o degree_n asunder_o and_o by_o a_o little_a revolve_v the_o distance_n of_o those_o star_n in_o your_o fancy_n you_o may_v at_o length_n so_o imprint_v their_o distance_n in_o your_o memory_n that_o you_o may_v ready_o guess_v the_o distance_n of_o other_o star_n by_o the_o distance_n of_o they_o example_n you_o may_v find_v either_o by_o the_o globe_n quadrant_n or_o asâ—rotabe_n for_o they_o all_o agree_v 3._o degree_n comprehend_v between_o the_o first_o star_n in_o orion_n girdle_n and_o the_o last_o therefore_o by_o a_o little_a 〈◊〉_d nate_v upon_o that_o distance_n you_o may_v imprint_v it_o in_o your_o fancy_n for_o 3._o degree_n and_o so_o make_v it_o applicable_a to_o other_o star_n either_o of_o the_o same_o distance_n or_o more_o or_o less_o and_o the_o pointer_n by_o the_o last_o problem_n be_v distant_a from_o one_o another_o 5._o degree_n and_o almost_o a_o half_a these_o be_v always_o above_o our_o horizon_n and_o therefore_o may_v always_o stand_v as_o a_o scale_n for_o five_o and_o a_o half_a degree_n so_o that_o by_o these_o for_o 5½_n degree_n and_o those_o in_o orion_n girdle_n for_o 3._o degree_n and_o other_o observe_v either_o of_o great_a or_o lesser_a distance_n you_o may_v according_a to_o your_o own_o judgement_n shape_v a_o guess_n if_o not_o exact_o yet_o pretty_a near_o the_o matter_n of_o truth_n when_o you_o come_v to_o other_o star_n thus_o you_o may_v exercise_v your_o fancy_n upon_o star_n find_v to_o be_v 10._o or_o 15._o degree_n asunder_o or_o more_o or_o less_o and_o with_o a_o few_o experiment_n of_o this_o nature_n enure_v your_o judgement_n to_o guess_v distance_n and_o enable_v your_o memory_n to_o retain_v your_o judgement_n this_o way_n of_o guess_v will_v be_v exact_a enough_o for_o find_v the_o hour_n of_o the_o night_n by_o the_o star_n for_o most_o common_a uses_n or_o the_o hour_n of_o the_o day_n by_o guess_v at_o the_o altitude_n of_o the_o sun_n if_o after_o you_o have_v guess_v at_o the_o altitude_n you_o shall_v work_v as_o be_v teach_v by_o prob._n 12._o for_o the_o hour_n of_o the_o day_n and_o as_o shall_v be_v teach_v in_o the_o next_o problem_n for_o the_o hour_n of_o the_o night_n prob._n xxi_o the_o day_n of_o the_o month_n and_o altitude_n of_o any_o star_n give_v to_o find_v the_o hour_n of_o the_o night_n the_o globe_n quadrant_n and_o hour_n index_n rectify_v bring_v the_o star_n on_o the_o globe_n to_o the_o same_o number_n of_o degree_n on_o the_o quadrant_n of_o altitude_n that_o it_o have_v in_o heaven_n so_o shall_v the_o index_n of_o the_o hour-circle_n point_n in_o the_o hour-circle_n at_o the_o hour_n of_o the_o night_n example_n march_n 10._o the_o altitude_n of_o arcturus_n be_v 35._o degree_n above_o the_o horizon_n here_o at_o london_n therefore_o have_v the_o globe_n quadrant_n and_o hour_n index_n rectify_v i_o bring_v arcturus_n on_o the_o globe_n to_o 35._o degree_n on_o the_o quadrant_n of_o altitude_n and_o then_o look_v in_o the_o hour-circle_n i_o find_v the_o index_n point_n at_o 10._o a_o clock_n which_o be_v the_o hour_n of_o the_o night_n prob._n xxii_o the_o place_n of_o the_o sun_n and_o hour_n of_o the_o day_n give_v to_o find_v its_o azimuth_n in_o any_o latitude_n assign_v the_o globe_n etc._n etc._n rectify_v to_o your_o latitude_n turn_v the_o globe_n till_o the_o index_n of_o the_o hour-circle_n come_v to_o the_o give_v hour_n and_o bring_v the_o quadrant_n of_o altitude_n to_o the_o place_n of_o the_o sun_n so_o shall_v the_o number_n of_o degree_n contain_v between_o the_o east_n point_n of_o the_o horizon_n and_o the_o degree_n cut_v by_o the_o quadrant_n of_o altitude_n on_o the_o horizon_n be_v the_o number_n of_o degree_n of_o the_o sun_n azimuth_n at_o that_o time_n example_n may_v 10._o at_o 53._o minute_n past_o 8._o a_o clock_n in_o the_o morning_n i_o will_v know_v the_o azimuth_n of_o the_o sun_n therefore_o the_o globe_n be_v first_o rectify_v i_o turn_v about_o the_o globe_n till_o the_o index_n of_o the_o hour-circle_n point_n to_o 53._o minute_n past_o 8._o a_o clock_n or_o which_o be_v all_o one_o within_o half_a a_o quarter_n of_o a_o hour_n of_o 9_o then_o i_o move_v
the_o quadrant_n of_o altitude_n to_o the_o degree_n the_o sun_n be_v in_o that_o day_n and_o there_o let_v it_o remain_v till_o i_o see_v how_o many_o degree_n be_v contain_v between_o the_o north_n point_n and_o the_o quadrant_n which_o in_o this_o example_n be_v 108._o deg_n 25._o min._n and_o because_o this_o distance_n from_o the_o north_n exceed_v 90._o degree_n therefore_o i_o subtract_v 90._o degree_n from_o the_o whole_a and_o the_o remain_v be_v 18._o degree_n 25._o min._n for_o the_o azimuthal_o distance_n of_o the_o sun_n from_o the_o east_n point_n towards_o the_o south_n but_o if_o it_o have_v want_v of_o 90._o degree_n from_o the_o north_n point_n than_o shall_v the_o compliment_n of_o 90._o have_v be_v the_o azimuthal_o distance_n of_o the_o sun_n from_o the_o east_n point_fw-fr prob._n xxiii_o the_o place_n of_o the_o sun_n and_o hour_n of_o the_o day_n give_v to_o find_v the_o almicantar_n of_o the_o sun_n the_o almicantars_n of_o the_o sun_n be_v upon_o the_o matter_n the_o same_o thing_n with_o the_o altitude_n of_o the_o sun_n only_o with_o this_o distinction_n the_o almicantars_n be_v circle_n parallel_v to_o the_o horizon_n describe_v by_o the_o degree_n of_o the_o quadrant_n of_o altitude_n upon_o the_o zenith_n as_o its_o centre_n by_o turn_v the_o quadrant_n round_o about_o the_o globe_n till_o it_o come_v again_o to_o its_o first_o place_n but_o the_o altitude_n be_v a_o arch_n of_o the_o vertical_a circle_n comprehend_v between_o the_o horizon_n and_o any_o point_n of_o the_o globe_n assign_v their_o agreement_n consist_v in_o this_o when_o the_o sun_n or_o any_o star_n haâ—â—_n any_o know_a almicantar_n they_o be_v say_v to_o have_v the_o same_o number_n of_o degree_n of_o altitude_n as_o if_o the_o sun_n be_v in_o the_o 20_o almicantar_n he_o have_v 20_o degree_n of_o altitude_n if_o in_o the_o 30_o almicantar_n he_o have_v 30._o degree_n of_o altitude_n etc._n etc._n now_o because_o the_o operation_n be_v the_o same_o for_o find_v the_o altitude_n and_o almicantar_n i_o shall_v refer_v you_o to_o the_o 11_o problem_n which_o show_v you_o how_o to_o find_v the_o altitude_n or_o height_n and_o by_o consequence_n the_o almicantar_n prob._n xxiv_o the_o place_n of_o the_o sun_n give_v to_o find_v what_o hour_n it_o come_v to_o the_o east_n or_o west_n and_o what_o almicantar_n it_o then_o shall_v have_v the_o globe_n quadrant_n and_o hour_n index_n rectify_v bring_v the_o quadrant_n of_o altitude_n to_o the_o east_n point_n in_o the_o horizon_n if_o you_o will_v know_v what_o hour_n it_o come_v to_o the_o east_n or_o to_o the_o west_n point_n if_o you_o will_v know_v what_o hour_n it_o come_v to_o the_o west_n then_o turn_v about_o the_o globe_n till_o the_o place_n of_o the_o sun_n come_v to_o the_o quadrant_n of_o altitude_n and_o the_o index_n of_o the_o hour_n circle_n shall_v point_v at_o the_o hour_n of_o the_o day_n which_o on_o the_o day_n aforesaid_a will_v be_v 7._o hor._n 7_o min._n in_o the_o morning_n that_o the_o sun_n come_v to_o the_o east_n and_o 4_o hor._n 53._o min._n after_o noon_n that_o the_o sun_n come_v to_o the_o west_n and_o if_o you_o then_o count_v the_o number_n of_o degree_n from_o the_o horizon_n upward_o on_o the_o quadrant_n of_o altitude_n it_o will_v show_v you_o the_o almicantar_n of_o the_o sun_n for_o that_o time_n which_o will_v both_o morning_n and_o evening_n be_v 15_o deg_n 30._o min._n as_o be_v teach_v you_o by_o the_o last_o problem_n prob._n xxv_o to_o know_v at_o any_o time_n what_o a_o clock_n it_o be_v in_o any_o other_o part_n of_o the_o earth_n the_o difference_n of_o time_n be_v reckon_v by_o the_o access_n and_o progress_n of_o the_o sun_n for_o the_o sun_n gradual_o circumvolve_v the_o earth_n in_o 24._o hour_n do_v by_o reason_n of_o the_o earth_n rotundity_n enlighten_v but_o half_a 〈…〉_z at_o one_o and_o the_o same_o moment_n of_o time_n as_o shall_v be_v show_v hereafter_o so_o that_o hereby_o it_o come_v to_o pass_v that_o when_o with_o we_o here_o in_o england_n it_o be_v 6._o a_o clock_n in_o the_o morning_n with_o those_o that_o have_v 90._o degree_n of_o longitude_n to_o the_o westward_n of_o we_o it_o be_v yet_o midnight_n with_o those_o that_o have_v 180._o degree_n of_o longitude_n from_o we_o it_o be_v evening_n and_o with_o those_o that_o have_v 90._o degree_n of_o longitude_n to_o the_o eastward_n it_o be_v noon_n so_o that_o those_o to_o the_o eastward_o have_v their_o day_n begin_v soon_o than_o we_o but_o to_o the_o westward_o their_o day_n begin_v after_o we_o therefore_o that_o you_o may_v know_v what_o hour_n it_o be_v in_o any_o place_n of_o the_o earth_n of_o what_o distance_n soever_o it_o be_v you_o must_v first_o bring_v the_o place_n of_o your_o own_o habitation_n to_o the_o meridian_n and_o the_o index_n of_o the_o hour_n circle_n to_o 12._o on_o the_o hour_n circle_n then_o bring_v the_o other_o place_n to_o the_o meridian_n and_o the_o arch_n of_o the_o hour_n circle_v comprehend_v between_o the_o hour_n 12._o and_o the_o index_n be_v the_o difference_n in_o time_n between_o the_o two_o place_n example_n london_n in_o england_n and_o surat_n in_o the_o east_n indies_n first_o i_o bring_v london_n to_o the_o meridian_n and_o turn_v the_o index_n of_o the_o hour-circle_n to_o 12_o then_o i_o turn_v the_o globe_n westward_o because_o londonâ—s_n â—s_z westward_n of_o surat_n till_o surat_n come_v to_o the_o meridian_n and_o see_v at_o what_o hour_n the_o index_n of_o the_o hour_n circle_n point_n which_o in_o this_o example_n be_v 5._o hor._n 54._o minute_n and_o because_o surat_n lie_v to_o the_o eastward_o of_o we_o so_o many_o degree_n therefore_o as_o be_v say_v before_o their_o day_n begin_v so_o much_o before_o we_o so_o that_o when_o here_o at_o london_n it_o be_v 6._o a_o clock_n in_o the_o morning_n at_o surat_n it_o will_v be_v 11._o a_o clock_n 54._o minute_n when_o with_o we_o it_o be_v 12._o a_o clock_n with_o they_o it_o will_v be_v 5_o a_o clock_n 54._o minute_n afternoon_n if_o you_o will_v know_v the_o difference_n of_o time_n between_o london_n and_o jamaica_n work_v as_o before_o you_o may_v find_v 5._o hor._n 15._o min._n but_o jamaica_n be_v to_o the_o west_n of_o london_n therefore_o their_o day_n begin_v 5._o hor._n 15._o min._n after_o we_o so_o that_o when_o with_o we_o it_o be_v noon_n with_o they_o it_o will_v be_v but_o three_o quarter_n of_o a_o hour_n past_o 6._o a_o clock_n in_o the_o morning_n and_o when_o with_o they_o it_o be_v noon_n with_o we_o it_o will_v be_v one_o quarter_n past_o 5._o a_o clock_n after_o noon_n etc._n etc._n or_o you_o may_v yet_o otherwise_o know_v the_o difference_n of_o time_n if_o you_o divide_v the_o number_n of_o degree_n of_o the_o equinoctial_a that_o pass_n through_o the_o meridian_n while_o the_o globe_n be_v move_v from_o the_o first_o place_n to_o the_o second_o by_o 15._o so_o shall_v the_o product_n give_v you_o the_o difference_n of_o hour_n and_o minute_n between_o the_o two_o place_n as_o you_o will_v find_v if_o you_o try_v either_o of_o these_o example_n or_o any_o other_o prob._n xxvi_o to_o find_v the_o right_a ascension_n of_o the_o sun_n or_o star_n the_o right_a ascension_n of_o any_o point_n on_o the_o globe_n be_v find_v by_o bring_v the_o point_n propose_v to_o the_o meridian_n and_o count_v the_o number_n of_o degree_n comprehend_v between_o the_o vernal_a colour_n and_o the_o meridian_n example_n for_o the_o sun_n june_n 1._o i_o will_v know_v the_o right_a ascension_n of_o the_o sun_n his_o place_n find_v as_o by_o the_o three_o problem_n be_v ♊_o 20._o therefore_o i_o bring_v ♊_o 20._o to_o the_o meridian_n and_o then_o the_o meridian_n cut_v the_o equinoctial_a in_o 79._o degree_n 15._o minute_n account_v from_o the_o vernal_a point_n ♈_o therefore_o i_o say_v the_o right_a ascension_n of_o the_o sun_n june_n 1._o be_v 79._o deg_n 15._o minute_n example_n for_o a_o star_n i_o take_v capella_n alius_fw-la hircus_fw-la the_o goat_n on_o auriga_n shoulder_v and_o bring_v it_o to_o the_o meridian_n and_o find_v the_o meridian_n cut_v the_o equinoctial_a count_v as_o before_o from_o the_o vernel_n point_n ♈_o in_o 73._o degree_n 58._o minute_n therefore_o i_o say_v the_o right_a ascension_n of_o hircus_fw-la be_v 73._o degree_n 58._o min._n do_v the_o like_a for_o any_o other_o point_n of_o the_o globe_n propose_v prob._n xxvii_o to_o find_v the_o declination_n of_o the_o sun_n or_o star_n the_o declination_n of_o any_o point_n on_o the_o globe_n be_v find_v by_o bring_v the_o point_n propose_v to_o the_o meridian_n and_o count_v the_o number_n of_o degree_n comprehend_v on_o the_o meridian_n between_o the_o equinoctial_a and_o the_o point_n propose_v and_o bear_v its_o denomination_n
on_o the_o meridian_n till_o the_o graduated_a edge_n cut_v the_o degree_n of_o the_o ecliptic_a the_o sun_n be_v in_o then_o i_o examine_v on_o the_o meridian_n what_o degree_n the_o upper_a end_n of_o the_o quadrant_n of_o altitude_n touch_v which_o in_o this_o example_n i_o find_v be_v 38½_n degree_n therefore_o i_o subtract_v 38½_n from_o 51½_n london_n latitude_n and_o there_o remain_v 13._o then_o count_v on_o the_o meridian_n 13._o degree_n backward_o from_o the_o place_n where_o the_o quadrant_n of_o altitude_n touch_v the_o meridian_n i_o come_v to_o 25½_n on_o the_o meridian_n northwards_o therefore_o i_o say_v in_o the_o north_n latitude_n of_o 25½_n degree_n and_o in_o the_o longitude_n of_o london_n which_o be_v in_o africa_n in_o the_o kingdom_n of_o numidia_n the_o sun_n may_v 10._o at_o 53._o minute_n past_o 8._o a_o clock_n in_o the_o morning_n have_v the_o same_o altitude_n above_o the_o horizon_n it_o have_v here_o at_o london_n the_o quadrant_n of_o altitude_n thus_o apply_v to_o the_o east_n point_n of_o the_o horizon_n make_v right_a angle_n with_o all_o point_n on_o the_o meridian_n even_o as_o all_o the_o meridian_n proceed_v from_o the_o pole_n do_v with_o the_o equator_fw-la therefore_o the_o quadrant_n be_v apply_v both_o to_o the_o east_n point_n and_o the_o sun_n place_n project_n a_o line_n to_o intersect_v the_o meridian_n perpendicular_o in_o equal_a degree_n from_o which_o intersection_n the_o sun_n have_v at_o the_o same_o time_n equal_a height_n be_v the_o degree_n few_o or_o many_o for_o those_o 5._o degree_n to_o the_o northwards_o of_o this_o intersection_n have_v the_o sun_n in_o the_o same_o height_n that_o they_o 5_o degree_n to_o the_o southwards_o have_v it_o and_o those_o 10_o 20_o 30._o degree_n more_o or_o less_o to_o the_o northwards_o have_v the_o sun_n in_o the_o same_o height_n that_o they_o have_v that_o be_v 10_o 20._o 30._o degree_n more_o or_o less_o to_o the_o southwards_o so_o that_o this_o prob._n may_v be_v perform_v another_o way_n more_o easy_o with_o your_o compass_n thus_o have_v first_o rectify_v the_o globe_n and_o hour_n index_n turn_v about_o the_o globe_n till_o the_o hour_n index_n point_n to_o the_o hour_n of_o the_o day_n then_o pitch_v one_o foot_n of_o your_o compass_n in_o the_o sun_n place_n and_o extend_v the_o other_o to_o the_o degree_n of_o latitude_n on_o the_o meridian_n which_o in_o this_o example_n be_v 51½_n degree_n north_n then_o keep_v the_o first_o foot_n of_o your_o compass_n on_o the_o degree_n of_o the_o sun_n turn_v about_o the_o other_o foot_n to_o the_o meridian_n and_o it_o will_v fall_v upon_o 25½_n as_o before_o blaew_n comment_v upon_o this_o problem_n take_v notice_n how_o gross_o they_o ere_o that_o think_v they_o can_v find_v the_o height_n of_o the_o pole_n at_o any_o hour_n of_o the_o day_n by_o the_o sun_n height_n because_o they_o do_v not_o consider_v that_o it_o be_v impossible_a to_o find_v the_o hour_n of_o the_o day_n unless_o they_o first_o know_v the_o height_n of_o the_o pole_n prob._n xlviii_o to_o find_v the_o length_n of_o the_o long_a and_o short_a artificial_a day_n or_o night_n the_o artificial_a day_n be_v that_o space_n of_o time_n which_o the_o sun_n be_v above_o the_o horizon_n of_o any_o place_n and_o the_o artificial_a night_n be_v that_o space_n of_o time_n which_o the_o sun_n be_v under_o the_o horizon_n of_o any_o place_n they_o be_v measure_v in_o the_o hour_n circle_n by_o hour_n and_o minute_n there_o be_v a_o constant_a unequallity_n of_o proportion_n in_o the_o length_n of_o these_o day_n and_o night_n which_o be_v cause_v both_o by_o the_o alteration_n of_o the_o sun_n declination_n and_o the_o difference_n of_o the_o pole_n elevation_n those_o that_o inhabit_v on_o the_o north_n side_n the_o equator_fw-la have_v their_o long_a day_n when_o the_o sun_n enter_v ♋_o and_o those_o that_o inhabit_v on_o the_o south_n side_n the_o equator_fw-la have_v their_o long_a day_n when_o the_o sun_n enter_v ♑_o but_o to_o know_v how_o long_o the_o long_a day_n be_v in_o any_o north_n or_o south_n elevation_n raise_v the_o north_n or_o south_n pole_n according_a to_o the_o elevation_n of_o the_o place_n and_o bring_v ♋_o for_o north_n elevation_n or_o ♑_o for_o south_n elevation_n to_o the_o meridian_n and_o the_o index_n of_o the_o hour_n circle_n to_o 12._o then_o turn_v the_o globe_n about_o till_o ♋_o for_o north_n elevation_n or_o ♑_o for_o south_n elevation_n come_v to_o the_o west_n side_n the_o horizon_n and_o the_o number_n of_o hour_n and_o minute_n point_v at_o on_o the_o hour_n circle_n double_v be_v the_o number_n of_o hour_n and_o minute_n of_o the_o long_a day_n the_o length_n of_o the_o night_n to_o that_o day_n be_v find_v by_o substract_v the_o length_n of_o the_o day_n from_o 24._o for_o the_o remainder_n be_v the_o length_n of_o the_o night_n the_o short_a day_n in_o that_o latitude_n be_v the_o length_n of_o the_o short_a night_n find_v as_o before_o and_o the_o long_a night_n be_v of_o the_o same_o length_n with_o the_o long_a day_n example_n i_o will_v know_v the_o length_n of_o the_o long_a day_n at_o london_n therefore_o i_o elevate_v the_o north_n pole_n 51½_n degree_n and_o bring_v ♋_o to_o the_o meridian_n and_o the_o index_n of_o the_o hour_n circle_n to_o 12._o then_o i_o turn_v ♋_o to_o the_o western_a side_n the_o horizon_n and_o find_v the_o index_n point_n at_o 8._o hour_n 18._o minute_n which_o be_v double_v make_v 16._o hour_n 36._o minute_n for_o the_o length_n of_o the_o long_a day_n here_o at_o london_n prob._n xlix_o to_o find_v how_o much_o the_o pole_n be_v raise_v or_o depress_v where_o the_o long_a day_n be_v a_o hour_n long_o or_o short_a than_o it_o be_v in_o your_o habitation_n rectify_v the_o globe_n to_o the_o latitude_n of_o your_o place_n and_o make_v a_o prick_n at_o that_o point_n of_o the_o tropic_a which_o be_v at_o the_o meridian_n i_o mean_v at_o the_o tropic_a of_n ♋_o if_o your_o habitation_n be_v on_o the_o north_n side_n the_o equator_fw-la or_o ♑_o if_o your_o habitation_n be_v on_o the_o south_n side_n the_o equator_fw-la and_o if_o you_o will_v know_v where_o the_o long_a day_n be_v just_a a_o hour_n long_o than_o it_o be_v at_o your_o habitation_n turn_v the_o globe_n to_o the_o westward_n till_o 7½_n degree_n of_o the_o equatoâ—_fw-la pass_v through_o the_o meridian_n and_o make_v there_o another_o prick_n on_o the_o tropic_a then_o turn_v about_o the_o globe_n till_o the_o first_o prick_v come_v to_o the_o horizon_n and_o move_v the_o meridian_n through_o the_o notch_n of_o the_o horizon_n till_o the_o second_o prick_n on_o the_o tropic_a come_v to_o the_o horizon_n so_o shall_v the_o arch_n of_o the_o meridian_n contain_v between_o the_o elevation_n of_o your_o place_n and_o the_o degree_n of_o the_o meridian_n at_o the_o horizon_n be_v the_o number_n of_o degree_n that_o the_o pole_n be_v elevate_v high_a than_o it_o be_v in_o your_o latitude_n example_n i_o will_v know_v in_o what_o latitude_n the_o long_a day_n be_v a_o hour_n long_o than_o it_o be_v at_o london_n therefore_o i_o rectify_v the_o globe_n to_o 51½_n deg_n and_o where_o the_o meridian_n cut_v the_o tropic_a of_n ♋_o i_o make_v a_o prick_n then_o i_o note_v what_o degree_n of_o the_o equator_fw-la be_v at_o the_o meridian_n and_o from_o that_o degree_n on_o the_o equator_fw-la count_v 7½_n degree_n to_o the_o eastward_n and_o bring_v those_o 7½_n degree_n to_o the_o meridian_n also_o and_o again_o where_o the_o meridian_n cut_v the_o tropic_a of_n ♋_o i_o make_v another_o prick_n so_o shall_v 7½_n degree_n of_o the_o tropic_n be_v contain_v between_o those_o 〈◊〉_d prick_v then_o i_o turn_v the_o globe_n about_o till_o the_o first_o prick_n come_v to_o the_o horizon_n and_o with_o a_o quill_n thrust_v between_o the_o meridian_n and_o the_o ball_n i_o fasten_v the_o globe_n in_o this_o position_n afterward_o i_o move_v the_o meridian_n through_o the_o 〈◊〉_d of_o the_o horizon_n till_o the_o second_o prick_n rise_v up_o to_o the_o horizon_n and_o then_o i_o find_v 56½_n degree_n of_o the_o meridian_n cut_v by_o the_o superficies_n of_o the_o horizon_n therefore_o i_o say_v in_o the_o latitude_n of_o 56½_n degree_n the_o long_a day_n be_v a_o hour_n long_o than_o it_o be_v here_o at_o london_n but_o if_o you_o will_v know_v in_o what_o latitude_n the_o day_n be_v a_o hour_n short_a you_o must_v make_v your_o second_o prick_n 7½_n degree_n to_o the_o westward_n of_o the_o first_o and_o after_o you_o have_v bring_v the_o first_o prick_n to_o the_o horizon_n you_o must_v depress_v the_o pole_n till_o the_o second_o prick_n descend_v to_o the_o horizon_n so_o shall_v the_o degree_n of_o the_o meridian_n at_o the_o horizon_n show_v in_o
what_o elevation_n of_o the_o pole_n the_o day_n shall_v be_v a_o hour_n short_a by_o this_o problem_n may_v be_v find_v the_o alteration_n of_o climate_n for_o as_o be_v say_v in_o the_o definition_n of_o climate_n book_n 1._o fol._n 28._o climate_n alter_v according_a to_o the_o half-hourly_a increase_n of_o the_o long_a day_n therefore_o the_o latitude_n of_o 56½_n degree_n have_v its_o day_n increase_v a_o whole_a hour_n be_v distant_a from_o the_o latitude_n of_o london_n by_o the_o space_n of_o two_o climate_n prob._n l._n the_o sun_n place_v give_v to_o find_v what_o alteration_n of_o declination_n be_v must_v have_v to_o make_v the_o day_n a_o hour_n long_o or_o short_a and_o in_o what_o number_n of_o daâ—es_n it_o will_v be_v rectify_v the_o globe_n to_o the_o latitude_n of_o the_o place_n and_o bâ—ing_v the_o sun_n place_n to_o the_o east_n side_n the_o horizon_n and_o note_n against_o what_o degree_n of_o the_o horizon_n it_o be_v then_o bring_v one_o of_o the_o colour_n to_o intersect_v the_o horizon_n in_o that_o degree_n of_o the_o horizon_n and_o at_o the_o point_n of_o intersection_n make_v a_o prick_n in_o the_o colour_n and_o observe_v what_o degree_n of_o the_o equator_fw-la be_v then_o at_o the_o meridian_n then_o turn_v the_o globe_n westward_o if_o the_o day_n shorten_v but_o eastward_n if_o they_o lengthen_v till_o 7½_n degree_n of_o the_o equator_fw-la pass_v through_o the_o meridian_n and_o where_o the_o horizon_n intersect_v the_o same_o colour_n make_v another_o prick_n in_o the_o colour_n afterward_o bring_v the_o colour_n to_o the_o meridian_n and_o count_v the_o number_n of_o degree_n between_o the_o two_o prick_n for_o so_o many_o degree_n must_v the_o sun_n declination_n alter_v to_o lengthen_v or_o shorten_v the_o day_n a_o hour_n example_n the_o sun_n place_n be_v ♉_o 10._o i_o will_v know_v how_o much_o he_o must_v alter_v his_o declination_n before_o the_o day_n be_v a_o hour_n long_o here_o at_o london_n therefore_o i_o rectify_v the_o globe_n to_o the_o latitude_n of_o london_n and_o bring_v ♉_o 10._o to_o the_o east_n side_n the_o horizon_n and_o find_v it_o against_o 24½_n degree_n from_o the_o east_n point_n therefore_o i_o bring_v one_o of_o the_o colour_n to_o this_o 24½_n degree_n and_o close_o by_o the_o edge_n of_o the_o horizon_n i_o make_v a_o prick_n with_o black_a lead_n in_o the_o colour_n then_o keep_v the_o globe_n in_o this_o position_n i_o look_v what_o degree_n of_o the_o equator_fw-la be_v then_o at_o the_o meridian_n and_o find_v 250¼_n and_o because_o the_o day_n lengthen_v i_o turn_v the_o globe_n eastward_n till_o 7½_n degree_n from_o the_o foresay_a 250¼_n pass_v through_o the_o meridian_n then_o keep_v the_o globe_n in_o this_o position_n i_o make_v another_o prick_n in_o the_o colour_n and_o bring_v this_o colour_n to_o the_o meridian_n i_o find_v a_o little_a more_o than_o 5_o degree_n of_o the_o meridian_n contain_v between_o the_o two_o prick_n therefore_o i_o say_v when_o the_o sun_n be_v in_o ♉_o 10._o degree_n he_o must_v alter_v his_o declination_n a_o little_a more_o than_o 5_o degree_n to_o make_v the_o day_n a_o hour_n long_o now_o to_o know_v in_o what_o number_n of_o day_n he_o shall_v alter_v this_o declination_n you_o must_v find_v the_o declination_n of_o the_o two_o prick_n on_o the_o colour_n as_o you_o find_v the_o sun_n declination_n by_o prob._n 5._o and_o the_o arch_n of_o the_o ecliptic_a that_o pass_v through_o the_o meridian_n while_o the_o globe_n be_v turn_v from_o the_o first_o prick_v declination_n to_o the_o second_o prick_v declination_n be_v the_o number_n of_o elliptical_a degree_n that_o the_o sun_n be_v to_o pass_v while_o he_o alter_v this_o declination_n and_o the_o degree_n of_o the_o ecliptic_a then_o at_o the_o meridian_n be_v with_o respect_n have_v to_o the_o quarter_n of_o the_o year_n the_o place_n the_o sun_n shall_v have_v when_o its_o declination_n shall_v be_v alter_v so_o much_o as_o to_o make_v the_o day_n a_o hour_n long_o thushave_v the_o sun_n first_o place_n give_v and_o its_o second_o place_n find_v you_o may_v by_o find_v those_o two_o place_n on_o the_o plain_a of_o the_o horizon_n also_o find_v the_o number_n of_o day_n comprehend_v between_o they_o as_o you_o be_v teach_v by_o the_o four_o problem_n this_o problem_n thus_o wrought_v for_o different_a time_n of_o the_o year_n will_v show_v the_o fallacy_n of_o that_o vulgar_a rule_n which_o make_v the_o day_n to_o be_v lengthen_v or_o shorten_v a_o hour_n in_o every_o fifteen_o day_n when_o as_o the_o lengthen_v or_o shorten_v of_o day_n keep_v no_o such_o equality_n of_o proportion_n for_o when_o the_o sun_n be_v near_o the_o equinoctial_a point_n the_o day_n lengthen_v or_o shorten_v very_o fast_o but_o when_o he_o be_v near_o the_o tropical_a point_n very_o slow_o prob._n li._n of_o the_o difference_n of_o civil_a and_o natural_a day_n common_o call_v the_o equation_n of_o civil_a day_n and_o how_o it_o may_v be_v find_v by_o the_o globe_n the_o civil_a day_n be_v that_o space_n of_o time_n contain_v just_o 24._o hour_n reckon_v from_o 12_o a_o clock_n on_o one_o day_n to_o 12_o a_o clock_n the_o next_o day_n in_o which_o space_n of_o time_n the_o equinoctial_a make_v upon_o the_o pole_n of_o the_o world_n a_o diurnal_a revolution_n the_o natural_a day_n be_v that_o space_n of_o time_n wherein_o the_o sun_n move_v from_o the_o meridian_n of_o any_o place_n to_o the_o same_o meridian_n again_o these_o day_n be_v at_o one_o time_n of_o the_o year_n long_o than_o at_o another_o and_o at_o all_o time_n long_o than_o the_o civil_a day_n there_o be_v but_o small_a discrepancy_n between_o they_o yet_o some_o there_o be_v make_v by_o a_o twofold_a cause_n for_o first_o the_o sun_n apparent_a motion_n be_v different_a from_o his_o true_a motion_n he_o be_v much_o slow_a in_o his_o apogeum_n than_o he_o be_v in_o his_o perigeum_n for_o when_o the_o sun_n be_v in_o his_o apogeum_n he_o scarce_o move_v 58_o minute_n from_o west_n to_o east_n in_o a_o civil_a day_n but_o when_o he_o be_v in_o his_o perigeum_n he_o move_v above_o 61_o minute_n in_o a_o civil_a day_n and_o therefore_o increase_v his_o right_a ascension_n more_o in_o equal_a time_n the_o second_o cause_n be_v the_o difference_n of_o right_a ascension_n answerable_a to_o equal_a part_n of_o the_o ecliptic_a for_o about_o ♋_o and_o ♑_o the_o difference_n of_o right_a ascension_n be_v far_o great_a than_o about_o ♈_o and_o ♎_o for_o about_o ♈_o and_o ♎_o the_o right_a ascension_n of_o 10._o degree_n be_v but_o 9_o degree_n 11._o minute_n but_o about_o ♋_o and_o ♑_o the_o right_a ascension_n of_o 10_o degree_n will_v be_v find_v to_o be_v 10._o degree_n 53._o minute_n as_o by_o the_o globe_n will_v appear_v but_o because_o of_o the_o smallness_n of_o the_o globe_n graduation_n you_o can_v actual_o distinguish_v to_o part_n near_o enough_o for_o the_o solution_n of_o this_o problem_n if_o you_o shall_v inquire_v the_o difference_n in_o length_n of_o two_o single_a day_n it_o will_v be_v requisite_a to_o take_v some_o number_n of_o day_n together_o suppose_v 20._o therefore_o find_v by_o prob._n 3._o the_o place_n of_o the_o sun_n for_o the_o beginning_n and_o end_v of_o those_o day_n you_o will_v compare_v and_o find_v the_o right_a ascension_n answerable_a to_o each_o place_n in_o the_o ecliptic_a and_o also_o the_o difference_n of_o right_a ascension_n answerable_a to_o the_o sun_n motion_n in_o each_o number_n of_o day_n then_o compare_v the_o difference_n of_o right_a ascension_n together_o and_o by_o substract_v the_o lesser_a from_o the_o great_a you_o will_v have_v the_o number_n of_o degree_n and_o minute_n of_o the_o equator_fw-la that_o have_v pass_v through_o the_o meridian_n more_o in_o one_o number_n of_o day_n then_o in_o the_o other_o number_n of_o day_n which_o degree_n of_o the_o equator_fw-la convert_v into_o time_n be_v the_o number_n of_o minute_n that_o the_o one_o number_n of_o day_n be_v long_o than_o the_o other_o number_n of_o day_n example_n i_o will_v know_v what_o difference_n of_o time_n there_o be_v in_o the_o length_n of_o the_o first_o 20._o day_n of_o december_n and_o the_o first_o 20_o day_n of_o march_n i_o find_v by_o prob._n 3._o the_o sun_n place_n december_n 1_o be_v 〈◊〉_d 19_o 45._o at_o the_o end_n of_o 20_o day_n viz._n on_o the_o 21_o day_n his_o place_n be_v 〈◊〉_d 10._o 11._o the_o sun_n place_n march_v 1._o be_v ♓_o 21._o 16._o at_o the_o 20._o day_n end_n viz._n march_n 21_o his_o place_n be_v ♈_o 11._o 3._o i_o find_v by_o prob._n 26._o the_o right_a ascension_n answerable_a to_o â™_o 19_o 45_o be_v 258._o 10._o ♑_o 10._o 11_o 280._o 25._o ♓_o 21._o 16_o 352._o 00._o ♈_o 11._o 3_o 9_o 40._o and_o
the_o difference_n of_o right_a ascension_n contain_v between_o the_o first_o day_n in_o each_o month_n and_o the_o 21_o of_o the_o same_o month_n by_o substract_v the_o lesser_a from_o the_o great_a be_v for_o 258._o 10._o and_o for_o 352._o 00._o 280._o 25._o 9_o 40._o 22._o 15_o 17._o 40._o but_o note_n because_o the_o vernal_a colour_n where_o the_o degree_n of_o right_a ascension_n begin_v and_o end_v their_o account_n be_v intercept_v be_v the_o arch_n of_o the_o sun_n motion_n from_o the_o first_o to_o the_o 21._o of_o march_n therefore_o instead_o of_o substract_v the_o lesser_a number_n of_o degree_n of_o right_a ascension_n from_o the_o great_a viz._n 9_o 40_o from_o 35._o 2._o i_o do_v for_o find_v the_o difference_n of_o the_o right_n ascensional_a arch_n of_o the_o sun_n motion_n in_o those_o 20_o day_n sustract_v the_o foresay_a 352_o degree_n from_o 360_o and_o the_o remain_v be_v 8._o which_o be_v the_o difference_n of_o right_a ascension_n from_o ♓_o 21_o 16._o to_o the_o equinoctial_a colour_n to_o which_o 8_o add_v 9_o degree_n 40_o minute_n the_o right_a ascension_n from_o the_o equinoctial_a colour_n to_o ♈_o 11._o 3._o it_o make_v 17_o degree_n 40._o minute_n for_o the_o difference_n of_o right_a ascension_n between_o ♓_o 21_o 16._o and_o ♈_o 11._o 3_o then_o i_o find_v the_o difference_n of_o this_o difference_n of_o right_a ascension_n by_o substract_v the_o less_o from_o the_o great_a viz._n 17._o 40._o from_o 22._o 15._o and_o the_o remain_v be_v 4._o degree_n 35._o minute_n for_o the_o number_n of_o degree_n and_o minute_n of_o the_o equator_fw-la that_o pass_v through_o the_o meridian_n in_o the_o first_o 20_o day_n in_o the_o month_n of_o december_n more_o than_o in_o the_o first_o 20_o day_n of_o the_o month_n of_o march_n which_o 4._o degree_n 35._o minute_n convert_v into_o time_n gives_z 19_o minute_n that_o be_v a_o quarter_n of_o a_o hour_n and_o 4_o minute_n that_o the_o first_o 20_o day_n of_o december_n aforesaid_a be_v long_o than_o the_o first_o 20_o day_n of_o march._n prob._n lii_o how_o to_o find_v the_o hour_n of_o the_o night_n when_o the_o moon_n shine_v on_o a_o sun_n dyal_n by_o help_n of_o the_o globe_n rectify_v the_o globe_n and_o find_v by_o prob._n 54._o or_o a_o ephemeris_fw-la the_o moon_n place_n at_o noon_n bring_v it_o to_o the_o meridian_n and_o the_o index_n of_o the_o hour_n circle_n to_o 12._o and_o turn_v about_o the_o globe_n till_o the_o index_n of_o the_o hour_n circle_n point_v to_o the_o same_o hour_n the_o shade_n of_o the_o moon_n fall_v on_o on_o the_o sun_n dyal_n then_o by_o prob._n 3._o find_v the_o sun_n place_n at_o noon_n and_o see_v how_o many_o degree_n of_o right_a ascension_n be_v contain_v between_o the_o sun_n place_n and_o the_o degree_n of_o the_o equator_fw-la at_o the_o meridian_n when_o the_o index_n of_o the_o hour_n circle_n be_v bring_v to_o the_o hour_n the_o moon_n shine_v on_o in_o the_o sun_n dyal_n for_o those_o number_n of_o degree_n convert_v into_o time_n shall_v be_v the_o time_n from_o noon_n or_o the_o hour_n of_o the_o night_n only_o note_n respect_n must_v be_v have_v to_o the_o motion_n of_o the_o moon_n from_o west_n to_o east_n for_o so_o swift_a be_v her_o mean_a motion_n that_o it_o be_v account_v to_o be_v above_o 12._o degree_n in_o 24._o hour_n that_o be_v 6_o degree_n in_o 12_o hour_n 3_o degree_n in_o 6_o hour_n etc._n etc._n and_o this_o also_o convert_v into_o time_n as_o aforesaid_a you_o must_v add_v proportionable_o to_o the_o time_n find_v from_o noon_n and_o the_o sum_n shall_v give_v you_o the_o true_a hour_n of_o the_o night_n example_n here_o at_o london_n i_o desire_v to_o know_v the_o hour_n of_o the_o night_n january_n 6._o this_o present_a year_n 1658._o the_o moon_n place_n find_v by_o a_o ephemeris_fw-la or_o for_o want_n of_o a_o ephemeris_fw-la by_o prob._n 54._o be_v in_o ♊_o 21._o degree_n 22_o minute_n therefore_o i_o rectify_v the_o globe_n to_o london_n latitude_n and_o bring_v ♊_o 21._o 22._o minute_n to_o the_o meridian_n and_o the_o index_n of_o the_o hour_n circle_n to_o 12._o then_o by_o prob._n 3._o i_o find_v the_o sun_n place_n in_o ♑_o 26._o degree_n 46._o minute_n and_o by_o prob._n 26._o i_o find_v his_o right_a ascension_n to_o be_v 300_o degree_n then_o i_o turn_v about_o the_o globe_n till_o the_o index_n of_o the_o hour_n circle_v point_v at_o 10_o hour_n and_o at_o the_o degree_n of_o the_o equator_fw-la at_o the_o meridian_n i_o make_v a_o prick_n then_o i_o count_v the_o number_n of_o degree_n of_o the_o equater_fw-la contain_v between_o the_o foresay_a 300_o deg_n and_o this_o prick_n and_o find_v they_o 111¼_n degree_n which_o convert_v into_o time_n by_o allow_v 15_o degree_n for_o a_o hour_n give_v 7_o hour_n 25_o minute_n time_n from_o noon_n which_o if_o the_o moon_n motion_n be_v not_o to_o be_v consider_v shall_v be_v the_o immediate_a hour_n of_o the_o night_n but_o by_o the_o rule_n aforesaid_a the_o moon_n motion_n from_o west_n to_o east_n in_o 7_o hour_n 25_o minute_n be_v 3_o degree_n 42_o minute_n and_o this_o 3_o degree_n 42_o minute_n be_v convert_v into_o time_n be_v 14_o minute_n more_o which_o be_v add_v to_o 7_o hour_n 25_o minute_n make_v 7_o hour_n 39_o minute_n for_o the_o true_a hour_n of_o the_o night_n prob._n liii_o to_o find_v the_o dominical_a letter_n the_o prime_n epact_n easter_n day_n and_o the_o rest_n of_o the_o movable_a feast_n for_o ever_o though_o these_o problem_n can_v be_v perform_v by_o the_o globe_n because_o of_o the_o several_a change_n and_o irregular_a account_n that_o their_o rule_n be_v frame_v upon_o yet_o because_o they_o be_v of_o frequent_a and_o vulgar_a use_n and_o for_o that_o the_o solution_n of_o many_o other_o question_n will_v have_v dependency_n on_o the_o knowledge_n these_o therefore_o i_o have_v think_v fit_a here_o to_o inserte_n this_o table_n of_o m_o r_o palmer_n by_o which_o you_o may_v find_v they_o all._n i_o shall_v not_o insist_v upon_o the_o reason_n of_o the_o several_a change_n of_o letter_n and_o number_n himself_o have_v already_o very_o learned_o handle_v that_o subject_n in_o his_o book_n of_o the_o catholic_n planisphear_n book_n 1_o chapter_n 11._o to_o which_o i_o refer_v you_o neither_o shall_v i_o need_v to_o give_v you_o any_o other_o instruction_n for_o find_v what_o be_v here_o propose_v than_o what_o himself_o have_v give_v in_o his_o four_o book_n chapter_n 66_o and_o part_n of_o 67._o therefore_o take_v it_o as_o he_o there_o deliver_v it_o a_o example_n shall_v serve_v here_o instead_o of_o a_o rule_n for_o the_o year_n 1657._o i_o will_v know_v all_o these_o wherefore_o i_o seek_v the_o year_n 1657._o in_o the_o table_n of_o the_o sun_n cycle_n and_o over_o against_o it_o i_o find_v 14._o for_o the_o year_n of_o the_o cycle_n of_o the_o sun_n and_o d_o for_o the_o dominical_a letter_n and_o note_v here_o that_o every_o leap-year_n have_v 2_o dominical_a letter_n as_o 1660_o have_v a_o g_z and_o the_o first_o viz._n a_o serve_v that_o year_n till_o february_n 25_o and_o the_o second_o g_z for_o the_o rest_n of_o the_o year_n and_o note_v that_o these_o letter_n go_v always_o backward_o when_o you_o count_v forward_o as_o b_o a_o then_z g_z f_o etc._n etc._n not_o f_o g_z and_o then_z a_o b_o as_o you_o may_v see_v by_o the_o table_n to_o find_v the_o age_n of_o the_o moon_n remember_v first_o that_o the_o epact_n begin_v with_o march_n which_o must_v be_v here_o account_v the_o first_o month_n then_o if_o you_o add_v to_o the_o epact_n the_o number_n of_o the_o month_n current_n and_o the_o number_n of_o the_o day_n of_o the_o month_n current_n the_o sum_n or_o the_o excess_n above_o 30_o be_v the_o moon_n age_n example_n january_n 20._o 1656._o according_a to_o the_o account_n of_o the_o church_n of_o england_n who_o begin_v the_o year_n with_o march_n 25._o which_o be_v the_o equinoctial_a day_n about_o christ_n time_n the_o epact_n be_v 14._o january_n be_v the_o 11_o the_o month_n and_o the_o 20_o the_o day_n be_v propose_v now_o add_v 14._o 11._o and_o 20._o together_o they_o make_v 45._o out_o of_o which_o i_o take_v 30._o and_o there_o remain_v 15_o the_o moon_n age_n prob._n liv._o the_o age_n of_o the_o moon_n give_v to_o find_v her_o place_n in_o the_o ecliptic_a according_a to_o her_o mean_a motion_n this_o problem_n may_v be_v perform_v exact_a enough_o for_o common_a use_n by_o the_o globe_n but_o in_o regard_n it_o only_o show_v the_o moon_n place_n in_o the_o ecliptic_a according_a to_o her_o meat_n motion_n it_o will_v often_o fail_v you_o some_o few_o degree_n of_o her_o true_a place_n the_o work_n be_v thus_o first_o set_v figure_n
the_o meridian_n cut_v the_o degree_n of_o the_o ecliptic_a on_o the_o cusp_n of_o the_o ten_o house_n the_o western_a semicircle_n of_o the_o horizon_n shall_v cut_v the_o degree_n of_o the_o ecliptic_a on_o the_o cusp_n of_o the_o seven_o house_n and_o the_o semicircle_n of_o the_o meridian_n under_o the_o horizon_n shall_v cut_v the_o degree_n of_o the_o ecliptic_a on_o the_o cusp_n of_o the_o four_o house_n if_o you_o have_v the_o day_n of_o the_o month_n you_o may_v by_o prob._n 3._o of_o the_o second_o book_n find_v the_o sun_n place_n and_o if_o you_o have_v the_o hour_n of_o the_o day_n you_o may_v by_o first_o rectify_v the_o globe_n as_o by_o prob._n 2._o of_o the_o same_o book_n turn_v about_o the_o globe_n till_o the_o index_n of_o the_o hour-circle_n point_n to_o the_o same_o hour_n in_o the_o hour-circle_n and_o you_o will_v then_o at_o the_o eastern_a semicircle_n of_o the_o horizon_n have_v the_o degree_n of_o the_o ecliptic_a that_o be_v rise_v and_o by_o consequence_n as_o aforesaid_a all_o the_o cardinal_n point_v in_o their_o respective_a place_n now_o to_o find_v what_o degree_n of_o the_o ecliptic_a occupy_v the_o cusp_n of_o the_o other_o eight_o house_n of_o heaven_n do_v thus_o the_o globe_n rectify_v as_o aforesaid_a move_v the_o semicircle_n of_o position_n upward_o till_o 30_o degree_n of_o the_o equator_fw-la shall_v be_v contain_v between_o it_o and_o the_o eastern_a semicircle_n of_o the_o horizon_n so_o shall_v the_o semicircle_n of_o position_n cut_v in_o the_o ecliptic_a the_o degree_n and_o minute_n of_o the_o ecliptic_a on_o the_o cusp_n of_o the_o twelve_o house_n and_o its_o opposite_a degree_n and_o minute_n in_o the_o ecliptic_a shall_v be_v the_o cusp_n of_o house_n the_o six_o house_n for_o you_o must_v note_v that_o if_o you_o have_v but_o the_o degree_n and_o minute_n of_o the_o ecliptic_a upon_o the_o cusp_n of_o six_o of_o the_o house_n the_o opposite_a degree_n and_o minute_n of_o the_o ecliptic_a shall_v immediate_o possess_v the_o cusp_n of_o every_o opposite_a house_n then_o move_v the_o circle_n of_o position_n over_o 30._o degree_n more_o of_o the_o equinoctial_a so_o shall_v the_o degree_n of_o the_o ecliptic_a cut_n by_o the_o circle_n of_o position_n be_v the_o degree_n of_o the_o ecliptic_a upon_o the_o cusp_n of_o the_o eleven_o house_n and_o its_o opposite_a degree_n in_o the_o ecliptic_a shall_v be_v upon_o the_o cusp_n of_o the_o five_o house_n the_o degree_n of_o the_o ecliptic_a upon_o the_o cusp_n of_o the_o ten_o and_o four_o house_n be_v find_v as_o before_o then_o remove_v the_o circle_n of_o position_n to_o the_o western_a side_n of_o the_o meridian_n and_o let_v it_o fall_v towards_o the_o horizon_n till_o 30._o degree_n of_o the_o equator_fw-la be_v contain_v between_o the_o meridian_n and_o it_o so_o shall_v the_o degree_n of_o the_o ecliptic_a cut_n by_o the_o semicircle_n of_o position_n be_v the_o degree_n of_o the_o ecliptic_a on_o the_o cuâ—p_n of_o the_o nine_o house_n and_o the_o opposite_a degree_n of_o the_o ecliptic_a shall_v be_v upon_o the_o cusp_n of_o the_o three_o house_n let_v the_o semicircle_n of_o position_n fall_v yet_o low_o till_o it_o pass_v over_o 30._o degree_n more_o of_o the_o equator_fw-la so_o shall_v the_o degree_n of_o the_o ecliptic_a cut_n by_o the_o semicircle_n of_o position_n be_v the_o degree_n of_o the_o ecliptic_a on_o the_o cusp_n of_o the_o eight_o house_n and_o the_o opposite_a degree_n of_o the_o ecliptic_a shall_v be_v upon_o the_o cusp_n of_o the_o second_o house_n the_o degree_n of_o the_o ecliptic_a on_o the_o cusp_n of_o the_o seven_o house_n and_o ascendent_n be_v find_v as_o before_o example_n i_o will_v erect_v a_o figure_n of_o heaven_n for_o july_n 27._o 5._o hour_n oâ—_n minute_n afternoon_n 1658._o in_o the_o latitude_n of_o london_n viz._n 51½_n degree_n north_n latitude_n i_o first_o place_n the_o planet_n ☊_o and_o ☋_o on_o the_o globe_n as_o by_o prob._n 55._o of_o the_o second_o book_n be_v direct_v yet_o not_o exact_o as_o i_o find_v they_o in_o the_o ephemeris_fw-la for_o that_o show_v only_o their_o place_n in_o the_o ecliptic_a at_o noon_n therefore_o i_o consider_v how_o many_o degree_n or_o minute_n each_o planet_n motion_n be_v in_o a_o whole_a day_n or_o 24._o hour_n by_o substract_v the_o elliptical_a degree_n and_o minute_n of_o the_o planet_n place_v that_o day_n at_o noon_n from_o the_o elliptical_a degree_n and_o minute_n of_o the_o planet_n place_v the_o next_o day_n at_o noon_n or_o contrary_o if_o the_o planet_n be_v retrograde_a for_o the_o remain_v of_o those_o degree_n and_o minute_n be_v the_o motion_n of_o the_o planet_n that_o day_n therefore_o proportionable_o to_o that_o motion_n i_o place_v the_o planet_n forward_o in_o the_o ecliptic_a or_o backward_o if_o it_o be_v retrograde_a as_o if_o the_o sun_n shall_v move_v forward_o 1_o degree_n that_o be_v 60_o minute_n in_o a_o whole_a day_n or_o 24_o hour_n then_o in_o 12_o hour_n he_o shall_v move_v 30_o minute_n in_o 6_o hour_n 15_o minute_n in_o 4_o hour_n 10_o minute_n in_o 1_o hour_n 2½_n minute_n and_o so_o proportionable_o for_o any_o other_o space_n of_o time_n which_o i_o consider_v before_o i_o place_v the_o planet_n on_o the_o globe_n prob._n ii_o to_o erect_v a_o figure_n of_o heaven_n according_a to_o campanus_n regiomontanus_n as_o aforesaid_a make_v the_o beginning_n of_o every_o house_n to_o be_v the_o semi_a circle_n draw_v by_o the_o side_n of_o the_o semi_a circle_n of_o position_n according_a to_o the_o succession_n of_o every_o 30_o the_o degree_n of_o the_o equator_fw-la from_o the_o horizon_n but_o camp_n 〈◊〉_d make_v it_o to_o be_v the_o semicircle_n draw_v by_o the_o side_n of_o the_o semicircle_n 〈◊〉_d position_n according_a to_o the_o succession_n of_o every_o 30_o the_o degree_n of_o 〈◊〉_d prime_a verticle_n or_o east_n azimuth_n which_o be_v represent_v by_o the_o quadrant_n of_o altitude_n place_v at_o the_o east_n point_fw-fr the_o four_o cardinal_n be_v the_o same_o both_o according_a to_o regiomontanus_n and_o campanus_n but_o the_o other_o eight_o house_n differ_v therefore_o when_o you_o will_v find_v they_o according_a to_o campanus_n rectify_v the_o globe_n and_o quadrant_n of_o altitude_n and_o bring_v the_o low_a end_n 〈◊〉_d the_o quadrant_n of_o altitude_n to_o the_o east_n point_n in_o the_o horizon_n then_o count_v from_o the_o horizon_n upward_o 30_o degree_n oâ—_n the_o quadrant_n 〈◊〉_d altitude_n and_o bring_v the_o circle_n of_o position_n to_o those_o 30_o degreeâ—_n examine_v where_o the_o circle_n of_o position_n cut_v the_o ecliptic_a which_o 〈◊〉_d the_o aforesaid_a time_n be_v in_o 〈◊〉_d 29._o 40_o for_o that_o degree_n and_o minute_n upon_o the_o cusp_n of_o the_o twelve_o house_n and_o its_o opposite_a degree_n 〈◊〉_d minute_n in_o the_o ecliptic_a viz._n ♉_o 29._o 40._o be_v upon_o the_o cusp_n of_o 〈◊〉_d six_o house_n lift_v up_o the_o circle_n of_o position_n 30_o degree_n highâ—_n upon_o the_o quadrant_n of_o altitude_n viz._n to_o 60_o degree_n and_o 〈◊〉_d circle_n of_o position_n will_v cut_v the_o ecliptic_a in_o 〈◊〉_d 15._o degree_n for_o the_o cusp_n of_o the_o eleven_o house_n and_o its_o opposite_a degree_n and_o minute_n in_o the_o ecliptic_a viz._n ♉_o 15._o be_v upon_o the_o cusp_n of_o the_o first_o house_n the_o degree_n and_o minute_n of_o the_o ecliptic_a on_o the_o cusp_n 〈◊〉_d the_o ten_o and_o four_o house_n be_v at_o the_o meridian_n then_o transfer_v the_o circle_n of_o position_n to_o the_o west_n side_n of_o the_o meridian_n and_o the_o quadrant_n of_o altitude_n to_o the_o west_n point_n in_o the_o horizon_n let_v the_o semicircle_n of_o position_n fall_v 30_o degree_n from_o the_o meridian_n on_o the_o quadrant_n of_o altitude_n and_o it_o will_v cut_v in_o the_o ecliptic_a ♎_o 16_o degree_n for_o the_o cusp_n of_o the_o nine_o house_n and_o its_o opposite_a degree_n and_o minute_n in_o the_o ecliptic_a viz._n ♈_o 16._o be_v upon_o the_o cusp_n of_o the_o three_o house_n let_v fall_v the_o circle_n of_o position_n 30_o degree_n low_a on_o the_o quadrant_n of_o altitude_n and_o it_o will_v cut_v the_o ecliptic_a in_o 〈◊〉_d 2_o degree_n for_o the_o cusp_n of_o the_o eight_o house_n and_o its_o opposite_a degree_n viz._n ♓_o 2._o degree_n be_v on_o the_o cusp_n of_o the_o second_o house_n the_o cusp_n of_o the_o seven_o and_o ascendent_n be_v the_o same_o with_o regiomontanus_n viz._n 〈◊〉_d 27._o 47_o and_o â™_o 27._o 47._o the_o figure_n follow_v prob._n iii_o to_o find_v the_o length_n of_o a_o planetary_a hour_n astrologer_n divide_v the_o artificial_a day_n be_v it_o long_o or_o short_a into_o 12_o equal_a part_n and_o the_o night_n into_o 12_o equal_a part_n these_o part_n they_o call_v planetary_a hour_n the_o first_o of_o these_o planetary_a hour_n take_v its_o
denomination_n from_o the_o planetary_a day_n and_o the_o rest_n â—re_n name_v orderly_o from_o that_o planet_n according_a to_o the_o succession_n of_o the_o planetary_a orb_n as_o if_o it_o be_v monday_n that_o be_v the_o moon_n day_n as_o by_o prob._n 42_o of_o the_o second_o â—ook_n the_o planet_n reign_v the_o first_o hour_n shall_v beâ—â—_n the_o planet_n rule_v the_o second_o hour_n shall_v be_v ♄_o the_o three_o planetary_a hour_n shall_v be_v 〈◊〉_d the_o four_o 〈◊〉_d the_o five_o ☉_o the_o six_o ♀_o the_o seven_o thou_o begin_v again_o with_o 〈◊〉_d for_o the_o eight_o planetary_a 〈◊〉_d for_o the_o nine_o and_o so_o through_o the_o whole_a day_n and_o night_n till_o the_o sun_n rise_v again_o the_o next_o day_n the_o length_n of_o this_o planetary_a hour_n be_v find_v by_o the_o globe_n thus_o the_o globe_n rectify_v bring_v the_o sun_n place_n to_o the_o east_n side_n the_o horizon_n and_o make_v a_o prick_n at_o the_o degree_n of_o the_o equator_fw-la that_o come_v to_o the_o horizon_n with_o it_o then_o remove_v the_o sun_n place_n to_o the_o meridian_n and_o count_v the_o number_n of_o degree_n of_o the_o equator_fw-la comprehend_v between_o that_o prick_n and_o the_o degree_n now_o at_o the_o horizon_n and_o divide_v that_o number_n of_o degree_n and_o minute_n by_o 6._o because_o there_o be_v 6_o planetary_a hour_n pass_v since_o noon_n and_o the_o quotient_n shall_v show_v the_o number_n of_o dâ—gâ—â—â—s_n and_o minute_n that_o pass_v through_o the_o meridian_n in_o one_o planetary_a hour_n example_n jâ—ly_o 27._o 1658._o i_o will_v know_v the_o length_n of_o the_o planetary_a 〈◊〉_d here_o at_o lonaon_n i_o rectify_v the_o globe_n and_o bring_v the_o sun_n place_v viz_o ♌_o 〈◊〉_d 50._o to_o the_o eastern_a side_n the_o horizon_n and_o find_v 115_o degree_n of_o the_o equator_fw-la come_v to_o the_o horizon_n with_o it_o to_o this_o 115_o degree_n i_o make_v a_o prick_n then_o i_o turn_v the_o sun_n place_n to_o the_o meridian_n and_o find_v 22â—_n degree_n of_o the_o equator_fw-la at_o the_o horizon_n therefore_o i_o either_o count_v the_o number_n of_o degree_n between_o the_o prick_v and_o the_o degree_n of_o the_o equator_fw-la at_o the_o horizon_n or_o else_o subâ—â—râ—ct_a the_o 〈◊〉_d from_o the_o great_a but_o both_o way_n i_o find_v 111_o degree_n of_o the_o equator_fw-la to_o pass_v through_o the_o meridian_n or_o the_o horizon_n in_o six_o planetary_a hour_n therefore_o divide_v 111._o by_o 6._o i_o 〈◊〉_d 〈◊〉_d degree_n â—0_n minute_n of_o the_o equator_fw-la to_o pass_v through_o the_o mâ—â—â—â—â—an_n in_o one_o planetary_a hour_n which_o 18._o degree_n 30_o minute_n reduce_v into_o time_n yield_v 72._o minute_n by_o account_v for_o every_o 15._o degree_n one_o hour_n for_o 1._o degree_n 4._o minute_n and_o for_o half_a a_o degree_n 〈◊〉_d minute_n of_o time_n and_o so_o proportionable_o so_o that_o the_o length_n of_o a_o planetary_a hour_n july_n 27_o be_v 1_o coâ—â—on_n hour_n and_o â—4_n minute_n here_o at_o london_n prob._n iu._n the_o length_n of_o a_o planetary_a hour_n know_v to_o find_v what_o planet_n reign_v any_o green_a hour_n of_o the_o day_n or_o night_n the_o globe_n rectify_v as_o in_o the_o last_o problem_n turn_v about_o the_o globe_n till_o the_o index_n of_o the_o hour_n circle_n point_v to_o the_o hour_n of_o the_o day_n in_o the_o hour_n circle_n then_o count_v the_o number_n of_o degree_n comprehend_v between_o the_o degree_n of_o the_o equator_fw-la at_o the_o horizon_n and_o the_o prick_n in_o the_o equator_fw-la make_v as_o in_o the_o last_o problem_n and_o reduce_v that_o number_n of_o degree_n into_o minute_n of_o time_n by_o reckon_v 4._o minute_n of_o time_n for_o every_o degree_n of_o the_o equator_fw-la reduce_v also_o the_o number_n of_o degree_n and_o minute_n that_o pass_v through_o the_o meridian_n in_o one_o planetary_a hour_n into_o minute_n by_o allow_v as_o aforesaid_a 4._o minute_n for_o every_o degree_n and_o then_o divide_v the_o 〈◊〉_d 〈◊〉_d by_o the_o second_o and_o the_o quotient_n shall_v be_v the_o number_n of_o 〈◊〉_d 〈◊〉_d since_o sun_n rising_n have_v the_o number_n of_o planetary_a hour_n since_o sun_n rising_n râ—ckon_v the_o first_o planetary_a hour_n by_o the_o â—ame_n of_o that_o planet_n that_o bear_v the_o denomination_n of_o the_o day_n the_o second_o planetary_a hour_n by_o the_o planet_n succeed_v that_o in_o order_n â—he_v thâ—â—d_v by_o the_o next_o in_o order_n and_o so_o for_o all_o the_o rest_n 〈◊〉_d you_o câ—me_v to_o the_o last_o planet_n viz._n 〈◊〉_d and_o then_o begin_v again_o with_o 〈◊〉_d and_o so_o 〈◊〉_d 〈◊〉_d etc._n etc._n 〈◊〉_d you_o have_v 〈◊〉_d so_o many_o planet_n as_o there_o be_v planetary_a hour_n siâ—ce_o mâ—â—â—â—ing_v and_o that_o planet_n the_o number_n end_v on_o shall_v be_v the_o planet_n reign_v that_o planetary_a hour_n example_n july_n 27._o 1658._o aforesaid_a i_o will_v know_v what_o planet_n rule_v at_o 5_o a_o clock_n past_o noon_n the_o length_n of_o the_o planetary_a hour_n this_o day_n â—ound_v by_o â—he_n last_o problem_n be_v 1._o hour_n 14._o minute_n therefore_o the_o globe_n rectify_v i_o bring_v the_o index_n of_o the_o hour_n circle_n to_o the_o hour_n of_o the_o day_n viz._n 5_o a_o clock_n in_o the_o hour-circle_n and_o then_o count_v the_o number_n of_o degree_n between_o the_o prick_v make_v as_o by_o the_o last_o problem_n and_o the_o degree_n of_o the_o equator_fw-la at_o the_o horizon_n and_o find_v they_o 187._o which_o i_o reduce_v into_o minute_n by_o allow_v for_o every_o degree_n 4_o minute_n and_o that_o give_v 748_o minute_n this_o 〈◊〉_d minute_n i_o divide_v by_o the_o minute_n contain_v in_o one_o planetary_a hour_n this_o day_n viz._n by_o 72._o and_o find_v 10._o hour_n 8._o minute_n which_o show_v there_o be_v 10._o planetary_a hour_n and_o 8._o minute_n past_a and_o go_v since_o sun_n rise_v therefore_o ♂_o be_v the_o planet_n after_o who_o name_n the_o day_n be_v call_v viz._n dia_n martis_n ♂_o be_v as_o aforesaid_a the_o ruler_n of_o the_o first_o planetary_a hour_n from_o he_o i_o count_v the_o planet_n succeed_v which_o be_v ☉_o for_o the_o second_o hour_n from_o ☉_o i_o count_n the_o planet_n succeed_v which_o be_v ♀_o for_o the_o three_o hour_n and_o so_o on_o to_o ♀_o and_o ☽_o and_o then_o i_o begin_v the_o round_a again_o with_o ♄_o ♃_o ♂_o and_o ☉_o till_o i_o come_v again_o too_o ♀_o which_o be_v the_o ten_o planetary_a hour_n since_o sun_n rise_v and_o the_o minute_n remain_v being_n 8._o show_n that_o there_o be_v 8._o minute_n past_a since_o she_o begin_v to_o reign_v prob._n v._n to_o find_v part_n of_o fortune_n by_o the_o globe_n count_n the_o number_n of_o degree_n and_o minute_n contain_v between_o the_o sun_n place_n and_o the_o moon_n place_n begin_n at_o the_o sun_n place_n and_o count_a according_a to_o the_o succession_n of_o sign_n till_o you_o come_v to_o the_o moon_n place_n and_o have_v find_v that_o number_n of_o degree_n and_o minute_n add_v they_o to_o the_o number_n of_o degree_n and_o minute_n ascend_v reckon_v from_o the_o first_o point_n of_o ♈_o if_o the_o sum_n exceed_v 360_o east_n away_o 360_o and_o the_o remainder_n shall_v be_v the_o number_n of_o degree_n and_o minute_n from_o the_o first_o point_n in_o 〈◊〉_d in_o which_o part_n of_o forâ—â—ne_n fall_v but_o if_o it_o do_v not_o exceed_v 360_o you_o have_v already_o the_o number_n of_o degree_n and_o minute_n from_o the_o first_o point_n of_o ♈_o in_o which_o you_o must_v place_v part_n of_o fortune_n example_n i_o will_v find_v the_o place_n of_o part_n of_o fortune_n for_o the_o time_n of_o ouâ—_n figure_n i_o seek_v the_o two_o prick_n represent_v ☉_o and_o 〈◊〉_d and_o find_v ☉_o in_o ♌_o 14._o 9_o and_o ☽_o in_o â™_o 19_o 44._o therefore_o count_v from_o the_o sun_n place_n to_o the_o moon_n place_n according_a to_o the_o succession_n of_o sign_n i_o find_v 95._o degree_n 35._o minute_n contain_v between_o they_o this_o 95._o degree_n 35._o minute_n i_o add_v to_o 267._o degree_n 47._o minute_n the_o degree_n and_o minute_n contain_v between_o the_o first_o point_n of_o ♈_o and_o the_o ascendent_n and_o they_o make_v together_o 363._o degree_n 22._o minute_n this_o exceed_v 360._o therefore_o i_o cast_v away_o 360._o and_o the_o remain_v be_v 3_o degree_n 22._o minute_n for_o the_o place_n in_o the_o ecliptic_a of_o part_n of_o fortune_n reckon_v from_o the_o first_o point_n of_o ♈_o therefore_o this_o character_n â™_o which_o represent_v part_n of_o fortune_n i_o set_v in_o its_o proper_a place_n of_o the_o figure_n as_o i_o do_v the_o planet_n prob._n vi_o to_o find_v in_o what_o circle_n of_o position_n any_o star_n or_o any_o degree_n of_o the_o ecliptic_a be_v circle_n of_o position_n be_v number_v from_o the_o horizon_n upward_o upon_o the_o quadrant_n of_o altitude_n
the_o night_n and_o day_n 42_o prob._n 8._o to_o find_v the_o hour_n of_o sun_n set._n 42_o prob._n 9_o to_o find_v how_o long_o it_o be_v twilight_n in_o the_o morning_n and_o evening_n 43_o prob._n 10._o the_o sun_n place_v give_v to_o find_v its_o amplitude_n and_o also_o to_o know_v upon_o what_o point_n of_o the_o compass_n it_o rise_v 44_o prob._n 11_o the_o hour_n of_o the_o day_n give_v to_o find_v the_o height_n of_o the_o sun_n 45_o prob._n 12._o the_o altitude_n of_o the_o sun_n and_o day_n of_o the_o month_n give_v to_o find_v the_o hour_n of_o the_o day_n fol._n 46_o prob._n 13._o how_o to_o know_v whether_o it_o be_v before_o or_o after_o noon_n 47_o how_o to_o take_v altitude_n by_o the_o quadrant_n astrolabe_n and_o crossstaff_n 47_o to_o take_v altitude_n by_o the_o astrolabe_n 50_o to_o take_v altitude_n by_o the_o crossstaff_n 51_o prob._n 14._o to_o observe_v with_o the_o globe_n the_o altitude_n of_o the_o sun_n 52_o prob._n 15._o to_o find_v the_o elevation_n of_o the_o poleâ—_n by_o the_o meridian_n altitude_n of_o the_o sun_n and_o day_n of_o the_o month_n give_v 53_o prob._n 16._o to_o take_v the_o altitude_n of_o any_o star_n above_o the_o horizon_n by_o the_o globe_n 54_o prob._n 17._o by_o the_o meridian_n altitude_n of_o any_o star_n give_v to_o find_v the_o height_n of_o the_o pole_n 54_o prob._n 18._o another_o way_n to_o find_v the_o height_n of_o the_o pole_n by_o the_o globe_n if_o the_o place_n of_o the_o sun_n be_v give_v and_o also_o to_o find_v the_o hour_n of_o the_o day_n and_o azimuth_n and_o almicanter_n of_o the_o sun_n 56_o prob._n 19_o to_o observe_v by_o the_o globe_n the_o distance_n of_o two_o star_n 57_o prob._n 20._o how_o you_o may_v learn_v to_o give_v a_o guess_n at_o the_o number_n of_o degree_n that_o any_o two_o star_n be_v distant_a from_o one_o another_o or_o the_o number_n of_o degree_n of_o altitude_n the_o sun_n or_o any_o star_n be_v elevate_v above_o the_o horizon_n only_o by_o look_v up_o to_o heaven_n without_o any_o instrument_n 58_o prob._n 21._o the_o day_n of_o the_o month_n and_o altitude_n of_o any_o star_n give_v to_o find_v the_o hour_n of_o the_o night_n 59_o prob._n 22._o the_o place_n of_o the_o sun_n and_o hour_n of_o the_o day_n give_v to_o find_v its_o azimuth_n in_o any_o latitude_n assign_v 60_o prob._n 23._o the_o place_n of_o the_o sun_n and_o hour_n of_o the_o day_n give_v to_o find_v the_o almicantar_n of_o the_o sun_n 61_o prob._n 24._o the_o place_n of_o the_o sun_n give_v to_o find_v what_o hour_n it_o come_v to_o the_o east_n or_o west_n and_o what_o almicantar_n it_o then_o shall_v have_v 61_o prob._n 25._o to_o know_v at_o any_o time_n what_o a_o clock_n it_o be_v in_o any_o other_o part_n of_o the_o earth_n 62_o prob._n 26._o to_o find_v the_o right_a ascension_n of_o the_o sun_n or_o star_n 63_o prob._n 27._o to_o find_v the_o declination_n of_o the_o sun_n or_o star_n 64_o a_o table_n of_o the_o right_a ascension_n and_o declination_n of_o 100_o select_a fix_a star_n calculate_v by_o tycho_n brahe_n for_o the_o year_n 1600_o and_o 1670._o as_o also_o their_o difference_n of_o right_a ascension_n and_o declination_n in_o 70._o year_n 65_o prob._n 28._o the_o place_n of_o the_o sun_n or_o any_o star_n give_v to_o find_v the_o right_a descension_n and_o the_o oblique_a ascension_n and_o the_o oblque_fw-fr descension_n fol._n 71_o prob._n 29._o any_o place_n on_o the_o terrestrial_a globe_n be_v give_v to_o find_v its_o antipode_n 72_o prob._n 30._o to_o find_v the_o perecij_n of_o any_o give_a place_n by_o the_o terrestrial_a globe_n 73_o prob._n 31._o to_o find_v the_o antecij_n of_o any_o give_a place_n upon_o the_o terrestrial_a globe_n 73_o prob._n 32._o to_o find_v the_o longitude_n and_o latitude_n of_o the_o star_n by_o the_o celestial_a globe_n 73_o prob._n 33._o to_o find_v the_o distance_n between_o any_o two_o place_n on_o the_o terrestrial_a globe_n 74_o prob._n 34._o to_o find_v by_o the_o terrestrial_a globe_n upon_o what_o point_n of_o the_o compass_n any_o 〈◊〉_d place_n be_v situate_a one_o from_o another_o 75_o prob._n 35._o to_o find_v by_o the_o celestial_a globe_n the_o cosmical_a rise_n and_o set_v of_o the_o star_n 76_o prob._n 36._o to_o find_v by_o the_o celestial_a globe_n the_o acronical_a rise_n and_o set_v of_o the_o star_n 77_o prob._n 37._o to_o find_v by_o the_o celestial_a globe_n the_o heliacal_a rise_n and_o set_v of_o the_o star_n 78_o prob._n 38._o to_o find_v the_o diurnal_a and_o nocturnal_a arch_n of_o the_o sun_n or_o star_n in_o any_o give_a latitude_n 79_o prob._n 39_o to_o find_v the_o azimuth_n and_o almicantar_n of_o any_o star_n 81_o prob._n 40._o to_o find_v the_o hour_n of_o the_o night_n by_o observe_v two_o know_v star_n in_o one_o azimuth_n or_o almicantar_n 81_o prob._n 41._o the_o hour_n give_v that_o any_o star_n in_o heaven_n come_v to_o the_o meridian_n to_o know_v thereby_o the_o place_n of_o the_o sun_n and_o by_o consequence_n the_o day_n of_o the_o month_n though_o it_o be_v lose_v 82_o prob._n 42._o the_o day_n of_o the_o month_n give_v to_o find_v in_o the_o circle_n of_o letter_n on_o the_o plain_a of_o the_o horizon_n the_o day_n of_o the_o week_n 83_o prob._n 43._o the_o azimuth_n of_o any_o star_n give_v to_o find_v its_o hour_n in_o any_o give_a latitude_n 84_o prob._n 44._o how_o you_o may_v learn_v to_o know_v all_o the_o star_n in_o heaven_n by_o the_o celestial_a globe_n 84_o prob._n 45._o how_o to_o hang_v the_o terrestrial_a globe_n in_o such_o a_o position_n that_o by_o the_o sun_n shine_v upon_o it_o you_o may_v with_o great_a delight_n at_o once_o behold_v the_o demonstration_n of_o many_o principle_n in_o astronomy_n and_o geography_n 89_o prob._n 46._o to_o know_v by_o the_o terrestrial_a globe_n in_o the_o zenith_n of_o what_o place_n of_o the_o earth_n the_o sâ—â—_n be_v 91_o prob._n 47._o to_o find_v in_o what_o different_a place_n of_o the_o earth_n the_o sun_n have_v the_o same_o altitude_n at_o the_o same_o time_n 92_o prob._n 48._o to_o find_v the_o length_n of_o the_o long_a and_o short_a artificial_a day_n or_o night_n 95_o prob._n 49._o to_o find_v how_o much_o the_o pole_n be_v raise_v or_o depress_v where_o the_o long_a day_n be_v a_o hour_n long_o or_o short_a than_o it_o be_v in_o your_o habitation_n 96_o prob._n 50._o the_o sun_n place_v give_v to_o find_v what_o alteration_n of_o declination_n he_o must_v have_v to_o make_v the_o day_n a_o hour_n long_o or_o short_a and_o in_o what_o number_n of_o day_n it_o will_v be_v 97_o prob._n 51._o of_o the_o difference_n of_o civil_a and_o natural_a day_n common_o call_v the_o equation_n of_o civil_a day_n and_o how_o it_o may_v be_v find_v by_o the_o globe_n 99_o prob._n 52._o how_o to_o find_v the_o hour_n of_o the_o night_n when_o the_o moon_n shine_v on_o a_o sun_n dyal_n by_o help_n of_o the_o globe_n 101_o prob._n 53._o to_o find_v the_o dominical_a letter_n the_o prime_n epact_n easter_n day_n and_o the_o rest_n of_o the_o movable_a feast_n for_o ever_o 102_o prob._n 54._o the_o age_n of_o the_o moon_n give_v to_o find_v her_o place_n in_o the_o ecliptic_a according_a to_o her_o mean_a motion_n 104_o prob._n 55._o have_v the_o longitude_n and_o latitude_n or_o right_a ascension_n and_o declination_n of_o any_o planet_n or_o comet_n to_o place_v it_o on_o the_o globe_n to_o correspond_v with_o its_o place_n in_o heaven_n 105_o the_o content_n of_o the_o three_o book_n prob._n 1._o the_o sun_n amplitude_n and_o difference_n of_o ascension_n give_v to_o find_v the_o height_n of_o the_o pole_n and_o declination_n of_o the_o sun_n 108_o prob._n 2._o the_o sun_n declination_n and_o amplitude_n give_v to_o find_v the_o pole_n elevation_n 108_o prob._n 3._o the_o sun_n declination_n and_o hour_n at_o east_n give_v to_o find_v the_o height_n of_o the_o pole_n 109_o prob._n 4._o the_o declination_n of_o the_o sun_n and_o his_o altitude_n at_o east_n give_v to_o find_v the_o height_n of_o the_o pole_n 110_o prob._n 5._o by_o the_o sun_n declination_n and_o azimuth_n at_o 6_o of_o the_o clock_n give_v to_o find_v the_o height_n of_o the_o pole_n and_o almicantar_n at_o 6._o 11â—_n prob._n 6._o by_o the_o hour_n of_o the_o night_n and_o a_o know_a star_n observe_v rise_v or_o set_v to_o find_v the_o height_n of_o the_o pole_n fol._n 112_o prob._n 7._o two_o place_n give_v in_o the_o same_o latitude_n to_o find_v the_o difference_n of_o longitude_n 112_o prob._n 8._o two_o place_n give_v in_o the_o same_o longitude_n to_o find_v the_o difference_n of_o latitude_n 113_o prob._n 9_o course_n and_o distance_n between_o two_o place_n give_v to_o find_v their_o
moon_n or_o star_n etc._n etc._n and_o for_o the_o find_v the_o azimuth_n and_o amplitude_n etc._n etc._n vi_o of_o the_o quadrant_n of_o altitude_n the_o quadrant_n of_o altitude_n be_v a_o thin_a brass_n plate_n divide_v into_o 90._o degree_n and_o mark_v upward_o with_o 10_o 20_o 30_o 40_o etc._n etc._n to_o 90._o it_o be_v rivet_v to_o a_o brass_n nut_n which_o be_v fit_v to_o the_o meridian_n and_o have_v a_o screw_n in_o it_o to_o screw_v upon_o any_o degree_n of_o the_o meridian_n when_o it_o be_v use_v it_o be_v screw_v to_o the_o zenith_n it_o be_v use_n be_v for_o measure_v the_o altitude_n find_v amplitude_n and_o azimuth_n and_o discribe_v almicantarath_n it_o will_v sometime_o stand_v you_o in_o good_a steed_n if_o the_o plate_n be_v long_o by_o the_o breadth_n of_o the_o horizon_n than_o 90._o degree_n for_o then_o that_o length_n be_v turn_v back_o will_v serve_v you_o instead_o of_o a_o index_n when_o the_o nut_n be_v screw_v to_o the_o zenith_n to_o cut_v either_o the_o degree_n or_o day_n of_o either_o style_n or_o the_o point_n of_o the_o compass_n in_o any_o of_o those_o circle_n concentrical_a to_o the_o innermost_a edge_n of_o the_o horizon_n which_o the_o ay_o can_v so_o well_o judge_v at_o vii_o of_o the_o hour_n circle_n and_o its_o index_n the_o hour_n circle_n be_v a_o small_a brazen_a circle_n fit_v on_o the_o meridian_n who_o centre_n be_v the_o pole_n of_o the_o world_n it_o be_v divide_v into_o the_o 24_o hour_n of_o the_o day_n and_o night_n and_o each_o hour_n be_v again_o divide_v into_o half_n and_o quarter_n which_o in_o a_o revolution_n of_o the_o globe_n be_v all_o point_a at_o with_o a_o index_n which_o to_o that_o purpose_n be_v fit_v on_o the_o axis_n of_o the_o globe_n the_o use_n of_o the_o hour_n circle_n be_v for_o show_v the_o time_n of_o the_o several_a mutation_n and_o configuration_n of_o celestial_a appearance_n viii_o of_o the_o nautical_a compass_n or_o box_n and_o needle_n just_o under_o the_o east_n point_n of_o the_o horizon_n upon_o the_o undermost_a plane_n be_v sometime_o fix_v a_o nautical_a compass_n who_o north_n and_o south_n line_n must_v be_v parallel_n to_o the_o north_n and_o south_n line_n of_o the_o horizon_n the_o use_n of_o it_o be_v for_o set_v the_o angle_n of_o the_o globe_n correspondent_a to_o the_o angle_n of_o the_o world_n ix_o of_o the_o semicircle_n of_o position_n this_o be_v a_o semicircle_n make_v of_o brass_n and_o divide_v into_o 180._o degree_n number_v from_o the_o equinoctial_a on_o either_o side_n with_o 10_o 20_o 30_o etc._n etc._n to_o 90._o at_o the_o two_o end_n there_o be_v a_o axis_n which_o be_v fit_v into_o the_o two_o hole_n of_o two_o small_a stud_n fix_v in_o the_o north_n and_o south_n point_v of_o the_o upper_a plane_n of_o the_o horizon_n upon_o this_o axis_n it_o be_v move_v up_o and_o down_o according_a to_o the_o intent_n of_o your_o operation_n the_o use_n of_o this_o circle_n of_o position_n be_v for_o the_o find_v the_o twelve_o astrological_a house_n of_o heaven_n and_o also_o for_o find_v the_o circle_n of_o position_n of_o any_o star_n or_o point_n in_o heaven_n thus_o much_o may_v serve_v for_o the_o lineament_n circumjacent_a to_o the_o body_n of_o the_o globe_n the_o next_o discourse_n shall_v be_v chap._n ii_o of_o the_o circle_n line_n etc._n etc._n describe_v upon_o the_o superficies_n of_o the_o globe_n beginning_n with_o the_o terrestrial_a globe_n and_o i._o of_o the_o equator_fw-la the_o equator_fw-la be_v a_o great_a circle_n encompass_v the_o very_a middle_n of_o the_o globe_n between_o the_o two_o pole_n thereof_o and_o divide_v it_o into_o two_o equal_a part_n the_o one_o the_o north_n part_n and_o the_o other_o the_o south_n part_n it_o be_v as_o all_o great_a circle_n be_v divide_v into_o 360._o equal_a part_n which_o be_v call_v degree_n upon_o this_o circle_n the_o longitude_n be_v number_v from_o east_n to_o west_n and_o from_o this_o circle_n both_o way_n viz._n north_n and_o south_n the_o latitude_n be_v reckon_v it_o be_v call_v the_o equator_fw-la because_o when_o the_o sun_n come_v to_o this_o line_n which_o be_v twice_o in_o one_o year_n to_o wit_n on_o the_o ten_o of_o march_n and_o the_o eleven_o of_o june_n the_o day_n and_o night_n be_v equate_v and_o both_o of_o one_o length_n ii_o of_o the_o meridian_n there_o be_v infinite_a of_o meridian_n for_o all_o place_n lie_v east_n or_o west_n from_o one_o another_o have_v several_a meridian_n but_o the_o meridian_n delineate_v upon_o the_o terrestrial_a globe_n be_v in_o number_n 36._o so_o that_o between_o two_o meridian_n be_v contain_v ten_o degree_n of_o the_o equator_fw-la from_o the_o first_o of_o these_o meridian_n which_o be_v divide_v into_o twice_o 90_o degree_n account_v from_o the_o equator_fw-la towards_o either_o pole_n be_v the_o begin_n of_o longitude_n which_o upon_o our_o english_a globe_n be_v at_o the_o isle_n gratiosa_fw-la one_o of_o the_o isle_n of_o the_o azore_n and_o number_v in_o the_o equator_fw-la eastward_n with_o 10_o 20_o 30_o etc._n etc._n to_o 360._o round_n about_o the_o globe_n till_o it_o end_v where_o it_o begin_v they_o be_v call_v meridian_n because_o they_o divide_v the_o day_n into_o two_o equal_a part_n for_o when_o the_o sun_n come_v to_o the_o meridian_n of_o any_o place_n it_o be_v then_o midday_n or_o full_a noon_n iii_o of_o the_o parallel_n as_o the_o meridian_n be_v infinite_a so_o be_v the_o parallel_n and_o as_o the_o meridian_n line_n delineate_v upon_o the_o globe_n be_v draw_v through_o no_o more_o than_o every_o ten_o degree_n of_o the_o equator_fw-la so_o be_v the_o parallel_n also_o delineate_v but_o upon_o every_o ten_o degree_n of_o the_o meridian_n lest_o the_o globe_n shall_v be_v too_o much_o fill_v with_o superfluity_n of_o line_n which_o may_v obscure_v the_o small_a name_n of_o place_n the_o parallel_n circle_n run_v east_n and_o west_n round_o about_o the_o globe_n even_o as_o the_o equator_fw-la only_a the_o equator_fw-la be_v a_o great_a circle_n and_o these_o be_v every_o one_o less_o than_o other_o diminish_v gradual_o till_o they_o end_v in_o the_o pole_n the_o parallel_n be_v number_v upon_o the_o meridian_n with_o 10_o 20_o 30_o etc._n etc._n to_o 90._o beginning_n in_o the_o equator_fw-la and_o end_v in_o the_o pole_n they_o be_v call_v parallel_n because_o they_o be_v parallel_v to_o the_o equator_fw-la four_o of_o the_o ecliptic_a tropic_n and_o polar_a circle_n these_o circle_n though_o they_o be_v delineate_v upon_o the_o terrestrial_a globe_n yet_o they_o be_v most_o proper_a to_o the_o celestial_a and_o therefore_o when_o i_o come_v to_o the_o celestial_a globe_n i_o shall_v define_v they_o unto_o v._o of_o the_o rhumb_n the_o rhumb_n be_v neither_o circle_n nor_o straight_a line_n but_o helispherical_a or_o spiral_n line_n they_o proceed_v from_o the_o point_n where_o we_o stand_v and_o wind_n about_o the_o globe_n till_o they_o come_v to_o the_o pole_n where_o at_o last_o they_o loose_v themselves_o they_o represent_v the_o 32_o wind_n of_o the_o compass_n their_o use_n be_v to_o show_v the_o bear_n of_o any_o two_o place_n one_o from_o another_o that_o be_v to_o say_v upon_o what_o point_n of_o the_o compass_n any_o shore_n or_o land_n lie_v from_o another_o there_o be_v many_o of_o they_o describe_v upon_o the_o globe_n for_o the_o better_a direct_v the_o eye_n from_o one_o shore_n to_o the_o other_o when_o you_o seek_v after_o the_o bear_n of_o any_o two_o land_n some_o of_o they_o where_o there_o be_v room_n for_o it_o have_v the_o figure_n of_o the_o nautical_a card_n draw_v about_o the_o centre_n or_o common_a intersection_n and_o have_v as_o all_o other_o card_n have_v for_o the_o distinction_n of_o the_o north_n point_n a_o flowerdeluce_n picture_v thereon_o they_o be_v first_o call_v rumb_n by_o the_o portugal_n and_o since_o use_v by_o latin_a author_n and_o therefore_o that_o name_n be_v continue_v by_o all_o writer_n that_o have_v occasion_n to_o speak_v of_o they_o vi_o of_o the_o land_n sea_n land_n etc._n etc._n describe_v upon_o the_o terrestrial_a globe_n the_o land_n describe_v upon_o the_o globe_n be_v bound_v with_o a_o irregular_a line_n which_o run_v turn_v and_o wind_v into_o creek_n and_o angle_n even_o as_o the_o shore_n which_o it_o represent_v do_v for_o the_o better_a distinction_n of_o land_n &c_n &c_n this_o line_n be_v culler_v close_o by_o one_o side_n thereof_o with_o divers_a colour_n as_o with_o red_a yellow_a green_a etc._n etc._n these_o colour_n distinguish_v one_o part_n of_o the_o continent_n from_o the_o other_o and_o also_o one_o island_n from_o another_o that_o side_n of_o the_o line_n which_o incompass_n the_o colour_n be_v the_o bound_n of_o the_o land_n the_o other_o side_n of_o the_o line_n which_o be_v
day_n of_o the_o month_n give_v the_o day_n of_o the_o month_n be_v march_v 20._o by_o the_o four_o prob._n you_o may_v find_v the_o place_n of_o the_o sun_n to_o be_v ♈_o 10._o therefore_o bring_v the_o place_n of_o the_o sun_n to_o the_o meridian_n and_o elevate_v it_o above_o the_o horizon_n the_o same_o number_n of_o degree_n it_o have_v in_o heaven_n so_o shall_v the_o arch_n of_o the_o meridian_n comprehend_v between_o the_o pole_n and_o the_o horizon_n be_v the_o elevation_n of_o the_o pole_n in_o your_o place_n otherwise_o the_o day_n of_o the_o month_n give_v be_v march_v 20._o so_o that_o by_o the_o four_o prob._n you_o have_v the_o sun_n place_n ♈_o 10_o and_o by_o the_o five_o the_o declination_n of_o the_o sun_n 3._o 55._o north_n therefore_o the_o declination_n be_v north_n and_o you_o on_o the_o north_n side_n the_o equator_fw-la you_o must_v subtract_v 3._o 55._o from_o the_o meridian_n altitude_n 42._o 25._o and_o there_o remain_v 38_o 30._o for_o the_o height_n of_o the_o equinoctial_a above_o the_o horizon_n but_o if_o your_o declination_n have_v be_v south_n you_o must_v have_v add_v 3_o 55._o to_o the_o meridian_n altitude_n and_o the_o sum_n will_v have_v be_v the_o elevation_n of_o the_o equinoctial_a have_v the_o elevation_n of_o the_o equinoctial_a you_o may_v easy_o have_v the_o elevation_n of_o the_o pole_n for_o the_o one_o be_v always_o the_o compliment_n of_o the_o other_o to_o 90._o thus_o the_o height_n of_o the_o equinoctial_a 38._o 30._o subtract_v from_o 90._o leaf_n 51._o 30._o for_o the_o elevation_n of_o the_o pole_n here_o at_o london_n and_o thus_o it_o follow_v that_o the_o latitude_n of_o any_o place_n from_o the_o equinoctial_a be_v always_o equal_a to_o the_o elevation_n of_o the_o pole_n for_o between_o the_o zenith_n and_o the_o equinoctial_a be_v contain_v the_o compliment_n of_o the_o height_n of_o the_o equinoctial_a above_o the_o horizon_n to_o 90._o prob._n xvi_o to_o take_v the_o altitude_n of_o any_o star_n above_o the_o horizon_n by_o the_o globe_n the_o horizon_n of_o the_o globe_n set_v parallel_v to_o the_o horizon_n of_o the_o world_n as_o before_o turn_v the_o north_n pole_n towards_o the_o star_n and_o when_o you_o can_v see_v the_o star_n through_o the_o axis_n the_o northern_a notch_n of_o the_o horizon_n will_v cut_v the_o degree_n of_o elevation_n on_o the_o meridian_n example_n april_n 19_o at_o 11._o a_o clock_n at_o night_n i_o will_v observe_v the_o altitude_n of_o spica_fw-la virgo_fw-la therefore_o i_o set_v the_o horizon_n parallel_v to_o the_o horizon_n of_o the_o world_n as_o by_o the_o second_o problem_n and_o turn_v the_o northern_a pole_n till_o it_o point_v towards_o the_o star_n then_o look_v in_o at_o the_o south_n pole_n of_o the_o globe_n through_o the_o axis_n i_o shall_v see_v the_o star_n and_o have_v on_o the_o meridian_n the_o question_n resolve_v but_o if_o it_o point_v not_o exact_o than_o i_o move_v the_o north_n pole_n upward_o or_o downward_o either_o to_o the_o right_a hand_n or_o to_o the_o left_a according_a as_o i_o may_v find_v occasion_n till_o i_o can_v see_v the_o star_n through_o the_o axis_n and_o then_o the_o edge_n of_o the_o notch_n in_o the_o horizon_n cut_v 28._o degree_n 57_o min._n on_o the_o brazen_a meridian_n therefore_o i_o say_v april_n 19_o at_o 11._o a_o clock_n at_o night_n here_o at_o london_n the_o altitude_n of_o spica_fw-la 〈◊〉_d be_v 30._o degree_n above_o the_o horizon_n prob._n xvii_o by_o the_o meridian_n altitude_n of_o any_o star_n give_v to_o find_v the_o height_n of_o the_o pole_n join_v the_o star_n to_o the_o meridian_n and_o place_n it_o to_o the_o altitude_n observe_v so_o shall_v the_o number_n of_o degree_n intercept_v between_o the_o pole_n and_o the_o horizon_n be_v the_o elevation_n of_o the_o pole_n example_n spica_fw-la virgo_fw-la be_v observe_v to_o have_v 28._o degree_n 57_o min_fw-mi meridian_n altitude_n therefore_o i_o bring_v spica_fw-la virgo_fw-la to_o the_o meridian_n and_o raise_v it_o or_o depress_v it_o high_o or_o low_o as_o i_o find_v occasion_n till_o it_o be_v just_a 28._o degree_n 57_o min._n above_o the_o horizon_n then_o i_o count_v the_o number_n of_o degree_n between_o the_o pole_n and_o the_o horizon_n and_o find_v they_o 51½_n therefore_o i_o say_v the_o elevation_n of_o the_o pole_n be_v here_o at_o london_n 51½_n yet_o note_n if_o the_o star_n who_o altitude_n you_o observe_v have_v few_o number_n of_o degree_n of_o declination_n from_o the_o pole_n than_o the_o elevation_n of_o the_o pole_n you_o may_v be_v apt_a to_o mistake_v in_o its_o come_n to_o the_o meridian_n for_o those_o star_n never_o set_v and_o therefore_o be_v twice_o visible_a in_o the_o meridian_n in_o 24._o hour_n once_o above_o the_o pole_n and_o once_o under_o the_o pole_n if_o your_o star_n have_v great_a altitude_n than_o the_o north_n star_n it_o be_v above_o the_o pole_n but_o if_o it_o have_v less_o it_o be_v below_o the_o pole_n so_o that_o if_o you_o know_v but_o whether_o it_o be_v above_o or_o below_o it_o be_v enough_o for_o so_o you_o may_v according_o raise_v it_o to_o the_o altitude_n on_o the_o meridian_n it_o have_v in_o heaven_n and_o join_v it_o to_o the_o meridian_n either_o above_o or_o beneath_o the_o pole_n as_o the_o star_n be_v place_v in_o heaven_n and_o then_o the_o arch_n of_o the_o meridian_n comprehend_v between_o the_o pole_n and_o the_o horizon_n be_v the_o elevation_n of_o the_o pole_n as_o aforesaid_a otherwise_o have_v the_o meridian_n altitude_n of_o the_o star_n you_o must_v find_v its_o declination_n by_o the_o 27._o problem_n and_o if_o the_o declination_n be_v south_n and_o you_o on_o the_o north_n side_n the_o equator_fw-la you_o must_v add_v the_o declination_n to_o the_o meridian_n altitude_n and_o the_o sum_n of_o both_o make_v the_o altitude_n of_o the_o equinoctial_a but_o if_o the_o declination_n be_v north_n and_o you_o on_o the_o north_n side_n the_o equator_fw-la you_o must_v subtract_v the_o declination_n from_o the_o meridian_n altitude_n as_o be_v teach_v by_o the_o 15._o prob._n in_o the_o example_n of_o the_o sun_n and_o the_o remainder_n be_v the_o altitude_n of_o the_o equinoctial_a then_o as_o be_v teach_v by_o the_o 15_o problem_n aforesaid_a subtract_v the_o altitude_n of_o the_o equinoctial_a from_o 90_o the_o remainder_n be_v the_o elevation_n of_o the_o pole_n in_o your_o place_n example_n by_o the_o last_o problem_n the_o meridian_n altitude_n of_o spica_fw-la virgo_fw-la be_v 28_o degree_n 57_o min_fw-mi and_o the_o declination_n of_o spica_fw-la by_o the_o 27_o problem_n be_v find_v 9_o degree_n 33._o min._n south_n therefore_o because_o the_o declination_n be_v south_n i_o add_v 9_o degree_n 33._o min._n to_o the_o meridian_n altitude_n which_o make_v 38._o deg_n 30._o min._n for_o the_o elevation_n of_o the_o equinoctial_a which_o 38._o deg_n 30._o min._n substract_v from_o 90._o leaf_n 51._o degree_n 30._o min._n for_o the_o elevation_n of_o the_o pole_n here_o at_o london_n prob._n xviii_o another_o way_n to_o find_v the_o height_n of_o the_o pole_n by_o the_o globe_n if_o the_o place_n of_o the_o sun_n be_v give_v and_o also_o to_o find_v the_o hour_n of_o the_o day_n and_o azimuth_n and_o almicantar_n of_o the_o sun_n this_o must_v be_v perform_v by_o help_n of_o a_o spheric_a gnomon_n as_o blaew_n call_v it_o which_o be_v a_o small_a pin_n or_o needle_n fix_v perpendicular_o into_o a_o small_a basis_n with_o a_o hollow_a concave_a bottom_n that_o it_o may_v stand_v upon_o the_o convexity_n of_o the_o globe_n therefore_o the_o horizon_n of_o the_o globe_n be_v set_v parallel_n to_o the_o horizon_n of_o the_o world_n as_o by_o the_o second_o problem_n the_o spheric_a gnomon_n must_v be_v set_v exact_o upon_o the_o place_n of_o the_o sun_n and_o then_o turn_v the_o globe_n about_o upon_o its_o axis_n either_o from_o east_n to_o west_n or_o contrary_o from_o west_n to_o east_n or_o else_o by_o the_o meridian_n through_o the_o notch_n of_o the_o horizon_n till_o the_o spheric_a gnomon_n cast_v no_o shadow_n on_o any_o side_n thereof_o you_o have_v on_o the_o meridian_n in_o the_o north_n point_n of_o the_o horizon_n the_o number_n of_o degree_n that_o the_o pole_n be_v elevate_v above_o the_o horizon_n example_n imagine_v the_o four_o quarter_n of_o the_o horizon_n of_o the_o globe_n correspond_v with_o the_o four_o quarter_n of_o the_o horizon_n of_o the_o world_n and_o the_o plain_a of_o the_o horizon_n of_o the_o globe_n be_v parallel_n to_o the_o plain_a of_o the_o horizon_n of_o the_o world_n the_o sun_n place_n be_v ♉_o 29¼_n which_o i_o find_v on_o the_o globe_n and_o place_v the_o spheric_a gnomon_n thereon_o then_o at_o a_o guess_n i_o move_v the_o globe_n both_o on_o its_o axis_n and_o by_o the_o meridian_n as_o near_o
quadrant_n of_o altitude_n the_o same_o degree_n on_o it_o will_v lie_v on_o both_o the_o star_n so_o shall_v the_o index_n of_o the_o hour-circle_n point_n at_o the_o hour_n of_o the_o night_n prob._n xli_o the_o hour_n give_v that_o any_o star_n in_o heaven_n come_v to_o the_o meridian_n to_o know_v thereby_o the_o place_n of_o the_o sun_n and_o by_o consequence_n the_o day_n of_o the_o month_n though_o it_o be_v lose_v bring_v the_o star_n propose_v to_o the_o meridian_n and_o turn_v the_o index_n of_o the_o hour-circle_n to_o the_o hour_n give_v then_o turn_v about_o the_o globe_n till_o the_o index_n point_n at_o the_o hour_n of_o 12_o for_o noon_n and_o the_o place_n of_o the_o sun_n in_o the_o ecliptic_a shall_v be_v cut_v by_o the_o meridian_n example_n march_n 7._o at_o 11_o aclock_o at_o night_n the_o pointer_n come_v to_o the_o meridian_n of_o london_n therefore_o i_o place_v the_o pointer_n on_o the_o celestial_a globe_n under_o the_o meridian_n and_o turn_v the_o index_n of_o the_o hour-circle_n to_o 11._o past_a noon_n afterward_o i_o turn_v back_o the_o globe_n till_o the_o index_n point_n to_o 12._o at_o noon_n then_o look_v in_o the_o ecliptic_a i_o find_v the_o meridian_n cut_v it_o in_o ♓_o 26._o 45._o minute_n therefore_o i_o say_v when_o the_o pointer_n come_v to_o the_o meridian_n at_o 11._o a_o clock_n at_o night_n the_o place_n of_o the_o sun_n be_v ♓_o 26._o 45._o have_v thus_o the_o place_n of_o the_o sun_n i_o may_v find_v the_o day_n of_o the_o month_n by_o the_o four_o problem_n and_o so_o either_o know_v the_o day_n that_o the_o pointer_n come_v to_o the_o meridian_n at_o 11._o a_o clock_n at_o night_n or_o at_o any_o other_o hour_n give_v the_o day_n of_o the_o month_n may_v also_o be_v find_v by_o the_o declination_n and_o the_o quarter_n of_o the_o ecliptic_a the_o sun_n be_v in_o give_v for_o the_o meridian_n will_v cut_v the_o degree_n of_o the_o sun_n place_n in_o the_o ecliptic_a in_o the_o parallel_n of_o declination_n so_o that_o have_v respect_n to_o the_o quarter_n of_o the_o ecliptic_a you_o will_v find_v the_o sun_n place_n and_o have_v the_o sun_n place_n you_o may_v as_o aforesaid_a find_v the_o day_n of_o the_o month_n prob._n xlii_o the_o day_n of_o the_o month_n give_v to_o find_v in_o the_o circle_n of_o letter_n on_o the_o plain_a of_o the_o horizon_n the_o day_n of_o the_o week_n the_o seven_o day_n of_o the_o week_n be_v by_o the_o idolatry_n of_o the_o ancient_a roman_a heathenish_a time_n dedicate_v to_o the_o honour_n of_o seven_o of_o their_o god_n which_o we_o call_v planet_n the_o first_o be_v the_o most_o eminent_a and_o therefore_o doubtless_o by_o they_o set_v in_o the_o first_o place_n call_v dia_n solis_n or_o the_o sun_n day_n the_o second_o dia_n luna_n the_o moon_n day_n the_o three_o dia_n martis_n the_o day_n of_o mars_n by_o we_o call_v tuesday_n the_o four_o dia_n mercurius_n mercury_n day_n by_o we_o call_v wednesday_n from_o woden_n a_o idol_n the_o saxon_n worship_v to_o who_o honour_n they_o dedicate_v that_o day_n and_o be_v by_o all_o those_o german_a nation_n still_o call_v wodensdagh_n the_o five_o dia_n jovis_n jupiter_n or_o jove_n day_n which_o doubtless_o the_o saxon_n from_o who_o probable_o we_o receive_v it_o call_v donderdagh_a because_o jupiter_n be_v the_o god_n of_o thunder_n and_o we_o either_o by_o corruption_n or_o for_o shortness_n or_o both_o call_v it_o thursday_n the_o six_o dia_n veneris_n the_o day_n of_o venus_n but_o the_o saxon_n transfer_v her_o honour_n to_o another_o of_o their_o goddess_n name_v fria_fw-la call_v it_o fridagh_o and_o we_o from_o they_o call_v it_o friday_n the_o seven_o be_v dia_n saturnis_n satyrus_n day_n the_o same_o day_n of_o the_o month_n in_o other_o year_n happen_v not_o on_o the_o same_o day_n of_o the_o week_n therefore_o the_o dominical_a letter_n for_o one_o year_n be_v not_o the_o same_o it_o be_v the_o next_o now_o because_o you_o can_v come_v to_o the_o knowledge_n of_o the_o day_n of_o the_o week_n unless_o you_o first_o know_v the_o sunday_n letter_n therefore_o have_v i_o in_o prob._n 5â—_n insert_v a_o table_n of_o m_o r_o palmer_n by_o which_o you_o may_v find_v the_o dominical_a or_o sunday_n letter_n for_o ever_o and_o have_v the_o dominical_a letter_n you_o may_v in_o the_o circle_n of_o letter_n on_o the_o horizon_n find_v it_o near_o the_o day_n of_o that_o month_n and_o count_v that_o for_o sunday_n the_o next_o under_o it_o for_o monday_n the_o next_o under_o that_o for_o tuesday_n and_o so_o in_o order_n till_o you_o come_v to_o the_o day_n of_o the_o month_n example_n i_o will_v know_v what_o day_n of_o the_o week_n june_n 1._o anno_fw-la 1658._o old_a style_n fall_v on_o i_o find_v by_o the_o table_n aforesaid_a the_o dominical_a letter_n be_v c_o then_z i_o look_v in_o the_o calendar_n of_o old_a style_n for_o june_n 1._o and_o against_o it_o i_o find_v letter_n e_o which_o because_o it_o be_v the_o second_o letter_n in_o order_n from_o c_o therefore_o it_o be_v the_o second_o day_n in_o order_n from_o sunday_n which_o be_v tuesday_n prob._n xliii_o the_o azimuth_n of_o any_o star_n give_v to_o find_v its_o hour_n in_o any_o give_a latitude_n the_o hour_n of_o a_o star_n be_v the_o number_n of_o hour_n that_o a_o star_n be_v distant_a from_o the_o meridian_n to_o find_v which_o rectify_v the_o globe_n and_o quadrant_n of_o altitude_n and_o bring_v the_o star_n propose_v to_o the_o meridian_n and_o the_o index_n of_o the_o hour-circle_n to_o 12._o then_o place_v the_o low_a end_n of_o the_o quadrant_n of_o altitude_n to_o the_o give_v azimuth_n in_o the_o horizon_n and_o turn_v the_o globe_n till_o the_o star_n come_v to_o the_o graduated_a edge_n of_o the_o quadrant_n of_o altitude_n so_o shall_v the_o index_n of_o the_o hour-circle_n point_n at_o the_o hour_n of_o the_o star_n only_o this_o caution_n you_o must_v take_v if_o the_o star_n be_v turn_v from_o the_o meridian_n towards_o the_o eastern_a side_n of_o the_o horizon_n you_o must_v subtract_v the_o number_n of_o hour_n the_o index_n point_v at_o from_o 12._o and_o the_o remainder_n shall_v be_v the_o hour_n of_o the_o star_n but_o if_o the_o star_n be_v turn_v from_o the_o meridian_n towards_o the_o west_n side_n the_o horizon_n the_o hour_n the_o index_n point_v at_o be_v without_o more_o ado_n the_o hour_n of_o the_o star_n prob._n xliv_o how_o you_o may_v learn_v to_o know_v all_o the_o star_n in_o heaven_n by_o the_o celestial_a globe_n rectify_v the_o globe_n quadrant_n hour-index_n and_o horizon_n as_o by_o prob._n 2._o then_o turn_v about_o the_o globe_n till_o the_o index_n of_o the_o hour-circle_n point_n at_o the_o hour_n of_o the_o night_n on_o the_o hour-circle_n then_o if_o every_o star_n on_o the_o globe_n have_v a_o hole_n in_o the_o midst_n and_o your_o ey_fw-mi be_v place_v in_o the_o centre_n of_o the_o globe_n you_o may_v by_o keep_v your_o ey_fw-mi in_o the_o centre_n and_o look_v through_o any_o star_n on_o the_o globe_n see_v its_o maâ—ch_n in_o heaven_n that_o be_v the_o same_o star_n in_o heaven_n which_o that_o star_n on_o the_o globe_n represent_v for_o from_o the_o centre_n of_o the_o globe_n there_o proceed_v a_o straight_a line_n through_o the_o star_n on_o the_o globe_n even_o to_o the_o same_o star_n in_o heaven_n therefore_o those_o star_n that_o be_v in_o the_o zenith_n in_o heaven_n will_v then_o be_v in_o the_o zenith_n on_o the_o globe_n those_o that_o be_v in_o the_o east_n in_o heaven_n will_v be_v in_o the_o east_n on_o the_o globe_n those_o in_o the_o west_n in_o heaven_n in_o the_o west_n on_o the_o globe_n and_o those_o star_n that_o be_v in_o any_o altitude_n in_o heaven_n will_v at_o the_o same_o time_n have_v the_o same_o altitude_n on_o the_o globe_n so_o that_o if_o you_o see_v any_o star_n in_o heaven_n who_o name_n you_o desire_v to_o know_v you_o need_v but_o observe_v its_o azimuth_n and_o altitude_n and_o in_o the_o same_o azimuth_n and_o altitude_n on_o the_o globe_n you_o may_v find_v the_o same_o star_n and_o if_o it_o be_v a_o eminent_a star_n you_o will_v find_v its_o name_n adjoin_v to_o it_o example_n december_n 10._o at_o half_a a_o hour_n past_o 9_o a_o clock_n at_o night_n here_o at_o london_n i_o see_v two_o bright_a star_n at_o a_o pretty_a distance_n one_o from_o another_o in_o the_o south_n i_o desire_v to_o know_v the_o name_n of_o they_o therefore_o have_v the_o globe_n rectify_v to_o the_o latitude_n of_o london_n and_o the_o quadrant_n of_o altitude_n screw_v to_o the_o zenith_n the_o hour-index_n also_o rectify_v and_o the_o horizon_n posit_v horizontal_o as_o by_o prob._n 2._o i_o observe_v the_o altitude_n of_o those_o star_n in_o
never_o above_o 29._o degree_n distant_a from_o the_o sun_n three_o the_o planet_n may_v be_v know_v from_o fix_a star_n by_o their_o azimuth_n and_o altitude_n observe_v as_o have_v be_v teach_v before_o for_o if_o when_o you_o have_v take_v the_o azimuth_n and_o altitude_n of_o the_o star_n in_o heaven_n you_o doubt_v to_o be_v a_o planet_n and_o you_o find_v not_o on_o the_o globe_n in_o the_o same_o azimuth_n and_o altitude_n a_o star_n appear_v to_o be_v of_o the_o same_o magnitude_n that_o that_o in_o heaven_n appear_v to_o be_v you_o may_v conclude_v that_o that_o in_o heaven_n be_v a_o planet_n yet_o notwithstanding_o it_o may_v happen_v that_o a_o planet_n may_v be_v in_o the_o same_o degree_n of_o longitude_n and_o latitude_n in_o the_o zodiac_n that_o some_o eminent_a fix_a star_n be_v in_o as_o in_o the_o degree_n and_o minute_n of_o longitude_n and_o latitude_n that_o cor_fw-la leonis_fw-la or_o the_o bull_n ey_fw-mi or_o scorpion_n heart_n be_v in_o and_o so_o may_v eclipse_v that_o star_n by_o be_v place_v between_o we_o and_o it_o but_o that_o happen_v very_o seldom_o and_o rare_o but_o if_o you_o doubt_v it_o you_o may_v apply_v yourself_o to_o some_o other_o of_o the_o precedent_n and_o subsequent_a rule_n here_o set_v down_o for_o know_v planet_n from_o fix_a star_n the_o four_o way_n be_v by_o shift_v their_o place_n for_o the_o planet_n have_v a_o continual_a motion_n do_v continual_o alter_v their_o place_n as_o ♂_o moves_z about_o half_a a_o degree_n in_o a_o day_n ♀_o a_o whole_a degree_n but_o ♃_o and_o ♄_o move_v very_a slow_o ♃_o not_o move_n above_o 5._o minute_n and_o ♄_o seldom_o above_o 2._o minute_n yet_o by_o their_o motion_n alone_o the_o planet_n may_v be_v know_v to_o be_v planet_n if_o you_o will_v precise_o observe_v their_o distance_n from_o any_o know_a fix_a star_n in_o or_o near_o the_o ecliptic_a as_o on_o this_o night_n and_o the_o next_o night_n after_o observe_v whether_o they_o retain_v the_o same_o distance_n they_o have_v the_o night_n before_o which_o if_o they_o do_v then_o be_v they_o fix_v star_n but_o if_o they_o do_v not_o then_o be_v they_o planet_n yet_o this_o caâ—â—on_n be_v to_o be_v give_v you_o in_o this_o rule_n also_o that_o the_o planet_n sometime_o be_v say_v to_o be_v stationary_a as_o not_o alter_v 1._o minute_n in_o place_n forward_o or_o backward_o in_o 6._o or_o 7._o day_n together_o therefore_o if_o you_o find_v cause_n to_o doubt_v whether_o your_o star_n be_v a_o planet_n or_o a_o fix_a star_n you_o may_v for_o the_o help_n of_o your_o understanding_n confer_v with_o some_o of_o the_o former_a rule_n unless_o you_o be_v willing_a to_o wait_v 8_o or_o 9_o day_n long_o and_o so_o by_o observation_n of_o its_o motion_n resolve_v yourself_o or_o five_o you_o may_v apply_v yourself_o to_o a_o ephemeris_fw-la for_o that_o year_n and_o see_v if_o on_o that_o day_n you_o find_v any_o planet_n in_o the_o degree_n and_o minute_n of_o the_o zodiac_n you_o see_v the_o star_n you_o question_n in_o heaven_n and_o if_o there_o be_v no_o planet_n in_o that_o degree_n of_o the_o zodiac_n you_o may_v conclude_v it_o be_v no_o planet_n but_o a_o fix_a star_n prob._n xlv_o how_o to_o hang_v the_o terrestrial_a globe_n in_o such_o a_o position_n that_o by_o the_o sun_n shine_v upon_o it_o you_o may_v with_o great_a delight_n at_o once_o behold_v the_o demonstration_n of_o many_o principle_n in_o astronomy_n and_o geography_n take_v the_o terrestrial_a ball_n out_o of_o the_o horizon_n and_o fasten_v a_o thread_n on_o the_o brazen_a meridian_n to_o the_o degree_n of_o the_o latitude_n of_o your_o place_n by_o this_o thread_n hang_v the_o globe_n in_o a_o place_n where_o the_o sun_n beam_n may_v have_v a_o free_a access_n to_o it_o then_o direct_v the_o pole_n of_o the_o globe_n to_o their_o proper_a pole_n in_o heaven_n the_o north_n pole_n to_o the_o north_n and_o the_o south_n pole_n to_o the_o south_n and_o with_o a_o thread_n fasten_v to_o either_o pole_n brace_n the_o globe_n so_o that_o it_o do_v not_o turn_v from_o his_o position_n then_o bring_v your_o habitation_n to_o the_o meridian_n so_o shall_v your_o terrestrial_a globe_n be_v rectify_v to_o correspond_v in_o all_o respect_n with_o the_o earth_n itself_o even_o as_o in_o prob._n 44._o the_o celestial_a globe_n do_v the_o pole_n of_o the_o globe_n to_o the_o pole_n of_o the_o world_n the_o meridian_n of_o the_o globe_n to_o the_o meridian_n of_o the_o world_n and_o the_o several_a region_n on_o the_o globe_n make_v correspondent_a to_o the_o same_o region_n on_o the_o earth_n so_o that_o with_o great_a delight_n you_o may_v behold_v 1._o how_o the_o counterfeit_a earth_n like_o the_o true_a one_o will_v have_v one_o hemisphere_n sun_n shine_v light_n and_o the_o other_o shadow_v and_o as_o it_o be_v dark_a by_o the_o shine_a hemisphere_n you_o may_v see_v that_o it_o be_v day_n in_o all_o place_n that_o be_v situate_a under_o it_o for_o on_o they_o the_o sun_n do_v shine_v and_o that_o it_o be_v night_n at_o the_o same_o time_n in_o those_o place_n that_o be_v situate_a in_o the_o shadow_a hemisphere_n for_o on_o they_o the_o sun_n do_v not_o shine_v and_o therefore_o they_o remain_v in_o darkness_n 2._o if_o in_o the_o middle_n of_o the_o enlighten_v hemisphere_n you_o set_v a_o spheric_a gnomon_n perpendicular_o it_o will_v project_v no_o shadow_n but_o show_v that_o the_o sun_n be_v just_a in_o the_o zenith_n of_o that_o place_n that_o be_v direct_o over_o the_o head_n of_o the_o inhabitant_n of_o that_o place_n and_o the_o point_n that_o the_o spheric_a gnomon_n stand_v on_o be_v remove_v to_o the_o meridian_n show_v the_o declination_n of_o the_o sun_n on_o the_o meridian_n for_o that_o day_n 3._o if_o you_o draw_v a_o meridian_n line_n from_o one_o pole_n to_o the_o other_o in_o all_o place_n under_o that_o line_n it_o be_v noon_n in_o those_o place_n situate_a to_o the_o west_n it_o be_v morning_n for_o with_o they_o the_o sun_n be_v east_n and_o in_o those_o place_n situate_a to_o the_o east_n it_o be_v evening_n for_o with_o they_o the_o sun_n be_v west_n 4_o note_v the_o degree_n of_o the_o equator_fw-la where_o the_o enlighten_v hemisphere_n be_v part_v from_o the_o shadow_a for_o the_o number_n of_o degree_n of_o the_o equator_fw-la intercept_v between_o that_o degree_n and_o the_o meridian_n of_o any_o place_n convert_v into_o hour_n by_o account_v for_o every_o 15._o degree_n 1._o hour_n show_v if_o the_o sun_n be_v eastward_n of_o that_o place_n how_o long_o it_o will_v be_v ere_o the_o sun_n rise_v set_v or_o come_v to_o the_o meridian_n of_o that_o place_n or_o if_o the_o sun_n be_v westward_o of_o that_o place_n how_o long_o it_o be_v since_o the_o sun_n rose_n or_o set_v or_o be_v at_o the_o meridian_n of_o that_o place_n 5._o the_o inhabitant_n of_o all_o place_n between_o the_o enlighten_v and_o shadow_v hemisphere_n behold_v the_o sun_n in_o the_o horizon_n those_o westward_n of_o the_o meridian_n semicircle_n draw_v through_o the_o middle_n of_o the_o enlighten_v hemisphere_n behold_v the_o sun_n rising_n those_o in_o the_o east_n see_v it_o set_v 6._o so_o many_o degree_n as_o the_o sun_n reach_v beyond_o either_o the_o north_n or_o south_n pole_n so_o many_o degree_n be_v the_o declination_n of_o the_o sun_n either_o northwards_o or_o southwards_o and_o in_o all_o those_o place_n comprehend_v in_o a_o circle_n describe_v at_o the_o termination_n of_o the_o sunshine_n about_o that_o pole_n it_o be_v always_o day_n till_o the_o sun_n decrease_v in_o declination_n for_o the_o sun_n go_v not_o below_o their_o horizon_n as_o you_o may_v see_v by_o turn_v the_o globe_n about_o upon_o its_o axis_n and_o a_o the_o opposite_a pole_n at_o the_o same_o distance_n the_o sunshine_n not_o reach_v thither_o it_o will_v be_v always_o night_n till_o the_o sun_n decrease_v in_o declination_n because_o the_o sun_n rise_v not_o above_o their_o horizon_n 7._o if_o you_o let_v the_o globe_n hang_v steady_a you_o may_v see_v on_o the_o east_n side_n of_o the_o globe_n in_o what_o place_n it_o grow_v night_n and_o on_o the_o west_n side_n the_o globe_n how_o by_o little_a and_o little_a the_o sun_n encroach_v upon_o it_o and_o therefore_o there_o make_v it_o day_n 8._o if_o you_o make_v of_o paper_n or_o parchment_n a_o narrow_a girdle_n to_o begird_v the_o globe_n just_a in_o the_o equinoctial_a and_o divide_v it_o into_o 24._o equal_a part_n to_o represent_v the_o 24._o hour_n of_o day_n and_o night_n and_o mark_v it_o in_o order_n with_o ay_o two_o iii_o etc._n etc._n to_o xii_o and_o then_o begin_v again_o with_o ay_o two_o iii_o etc._n etc._n to_o the_o other_o xii_o you_o may_v by_o place_v one_o of_o the_o xii_o s._n upon_o
the_o equinoctial_a under_o the_o meridian_n of_o your_o place_n have_v a_o continual_a sun-dyal_n of_o it_o and_o the_o hour_n of_o the_o day_n give_v on_o it_o at_o once_o in_o two_o place_n one_o by_o the_o part_a the_o enlighten_v hemisphere_n from_o the_o shadow_a on_o the_o eastern_a side_n the_o other_o by_o the_o part_a the_o enlighten_v hemisphere_n from_o the_o shadow_a on_o the_o western_a side_n the_o globe_n much_o more_o may_v be_v say_v on_o this_o problem_n but_o the_o ingenuous_a artist_n may_v of_o himself_o find_v out_o diversity_n of_o speculation_n therefore_o i_o forbear_v prob._n xlvi_o to_o know_v by_o the_o terrestrial_a globe_n in_o the_o zenith_n of_o what_o place_n of_o the_o earth_n the_o sun_n be_v this_o may_v be_v perform_v by_o the_o former_a problem_n in_o the_o day_n time_n if_o the_o sun_n shine_v but_o not_o else_o but_o to_o find_v it_o at_o all_o time_n do_v thus_o bring_v the_o place_n of_o your_o habitation_n to_o the_o meridian_n and_o the_o index_n of_o the_o hour-circle_n to_o 12_o then_o turn_v the_o globe_n eastward_n if_o afternoon_n or_o westward_n if_o before_o noon_n till_o the_o index_n of_o the_o hour-circle_n pass_v by_o so_o many_o hour_n from_o 12._o as_o your_o time_n give_v be_v either_o before_o or_o afternoon_n so_o shall_v the_o sun_n be_v in_o the_o zenith_n of_o that_o place_n where_o the_o meridian_n intersect_v the_o parallel_n of_o the_o sun_n declination_n for_o that_o day_n example_n may_v 10_o at_o ¾_n of_o a_o hour_n past_o 4._o a_o clock_n after_o noon_n i_o will_v know_v in_o what_o place_n of_o the_o earth_n the_o sun_n be_v in_o the_o zenith_n my_o habitation_n be_v london_n therefore_o i_o bring_v london_n to_o the_o meridian_n and_o the_o index_n of_o the_o hour-circle_n to_o 12._o and_o because_o it_o be_v after_o noon_n i_o turn_v the_o globe_n eastward_n till_o the_o index_n pass_v through_o 4_o hour_n and_o 3_o quarter_n or_o which_o be_v all_o one_o till_o 70_o degree_n 15_o minute_n of_o the_o equator_fw-la pass_v through_o the_o meridian_n then_o i_o find_v by_o prob._n 5._o the_o sun_n declination_n be_v 20._o degree_n 5._o minute_n which_o i_o find_v upon_o the_o meridian_n and_o in_o that_o place_n just_a under_o that_o degree_n and_o minute_n on_o the_o globe_n the_o sun_n be_v in_o the_o zenith_n which_o in_o this_o example_n be_v in_o the_o north_n east_n cape_n of_o hispaniola_n have_v thus_o find_v in_o what_o place_n of_o the_o earth_n the_o sun_n be_v in_o the_o zenith_n bring_v that_o place_n to_o the_o meridian_n and_o elevate_v its_o respective_a pole_n according_a to_o its_o respective_a elevation_n so_o shall_v all_o place_n cut_v by_o the_o horizon_n have_v the_o sun_n in_o their_o horizon_n those_o to_o the_o eastward_n shall_v have_v the_o sun_n set_v those_o to_o the_o westward_n shall_v have_v it_o rise_v in_o their_o horizon_n those_o at_o the_o intersection_n of_o the_o meridian_n and_o horizon_n under_o the_o elevate_v pole_n have_v the_o sun_n in_o their_o horizon_n at_o low_a but_o rise_v those_o at_o the_o intersection_n of_o the_o meridian_n and_o horizon_n under_o the_o depress_v pole_n have_v the_o sun_n in_o their_o horizon_n at_o high_a but_o set_v thus_o in_o those_o country_n that_o be_v above_o the_o horizon_n it_o be_v daylight_n and_o in_o those_o but_o 18_o degree_n below_o the_o horizon_n it_o be_v twilight_n but_o in_o those_o country_n further_a below_o the_o horizon_n it_o be_v at_o that_o time_n dark_a night_n and_o those_o country_n within_o the_o parallel_n of_o the_o same_o number_n of_o degree_n from_o the_o elevate_v pole_n that_o the_o sun_n declination_n be_v from_o the_o equinoctial_a have_v the_o sun_n always_o above_o the_o horizon_n till_o the_o sun_n have_v less_o respective_a declination_n than_o the_o elevate_v pole_n and_o those_o within_o the_o same_o parallel_n of_o the_o depress_v pole_n have_v the_o sun_n always_o below_o their_o horizon_n till_o the_o sun_n incline_v more_o towards_o the_o depress_v pole_n as_o you_o may_v see_v by_o turn_v about_o the_o globe_n for_o in_o this_o position_n that_o portion_n of_o the_o globe_n intercept_v between_o the_o elevate_v pole_n and_o the_o parallel_n circle_n of_o 20._o degree_n 5._o minute_n from_o the_o pole_n do_v not_o descend_v below_o the_o horizon_n neither_o do_v that_o portion_n of_o the_o globe_n intercept_v between_o the_o depress_v pole_n and_o the_o parallel_n circle_n within_o 20._o degree_n 5._o minute_n of_o that_o pole_n ascend_v above_o the_o horizon_n prob._n xlvii_o to_o find_v in_o what_o different_a place_n of_o the_o earth_n the_o sun_n have_v the_o same_o altitude_n at_o the_o same_o time_n found_a by_o the_o former_a problem_n in_o what_o place_n of_o the_o earth_n the_o sun_n be_v in_o the_o zenith_n and_o bring_v that_o place_n on_o the_o globe_n to_o the_o zenith_n and_o on_o the_o meridian_n there_o screw_v the_o quadrant_n of_o altitude_n and_o turn_v it_o about_o the_o horizon_n describe_v degree_n of_o almicantars_n thereby_o as_o by_o prob._n 23._o and_o all_o those_o country_n in_o any_o almicantar_n on_o the_o globe_n shall_v have_v the_o sun_n elevate_v the_o same_o number_n of_o degree_n above_o their_o horizon_n thus_o those_o country_n in_o the_o ten_o almicantar_n shall_v have_v the_o sun_n elevate_v 10._o degree_n above_o their_o horizon_n those_o in_o the_o 20_o the_o almicantar_n shall_v have_v the_o sun_n elevate_v 20_o degree_n above_o their_o horizon_n those_o in_o the_o 30_o the_o 30._o degree_n etc._n etc._n so_o that_o you_o may_v see_v when_o the_o sun_n be_v in_o the_o zenith_n of_o any_o place_n all_o the_o country_n or_o city_n in_o any_o almicantar_n have_v the_o sun_n in_o one_o height_n at_o the_o same_o time_n above_o their_o horizon_n but_o to_o find_v in_o what_o different_a place_n the_o sun_n have_v the_o same_o height_n at_o the_o same_o time_n as_o well_o before_o or_o after_o noon_n as_o at_o full_a noon_n and_o that_o in_o country_n that_o have_v great_a latitude_n than_o the_o sun_n great_a declination_n and_o therefore_o can_v have_v the_o sun_n in_o their_o zenith_n require_v another_o operation_n therefore_o elevate_v its_o respective_a pole_n according_a to_o your_o respective_a latitude_n and_o let_v the_o degree_n of_o the_o brazen_a meridian_n which_o be_v in_o the_o zenith_n represent_v your_o habitation_n and_o the_o degree_n of_o the_o ecliptic_a the_o sun_n be_v in_o represent_v the_o sun_n then_o bring_v the_o sun_n to_o the_o meridian_n and_o the_o index_n of_o the_o hour-circle_n to_o 12_o and_o turn_v the_o globe_n eastward_n if_o before_o noon_n or_o westward_n if_o after_o noon_n till_o the_o index_n point_n to_o the_o hour_n of_o the_o day_n then_o place_v the_o low_a end_n of_o the_o quadrant_n of_o altitude_n to_o the_o east_n point_n of_o the_o horizon_n and_o move_v the_o upper_a end_n by_o slide_v the_o nut_n over_o the_o meridian_n till_o the_o edge_n of_o the_o quadrant_n touch_v the_o place_n of_o the_o sun_n then_o see_v at_o what_o degree_n of_o the_o meridian_n the_o upper_a end_n of_o the_o quadrant_n of_o altitude_n touch_v the_o meridian_n and_o subtract_v that_o number_n of_o degree_n from_o the_o latitude_n of_o your_o place_n and_o count_v the_o number_n of_o remain_a degree_n on_o the_o meridian_n on_o the_o contrary_a side_n the_o degree_n of_o the_o meridian_n where_o the_o upper_a end_n of_o the_o quadrant_n of_o altitude_n touch_v the_o meridian_n and_o where_o that_o number_n of_o degree_n end_n on_o the_o meridian_n in_o that_o latitude_n and_o your_o habitation_n longitude_n have_v the_o sun_n the_o same_o height_n at_o the_o same_o time_n example_n may_v 10._o at_o 53._o minute_n past_o 8._o a_o clock_n in_o the_o morning_n i_o will_v know_v in_o what_o place_n the_o sun_n shall_v have_v the_o same_o altitude_n it_o shall_v have_v at_o london_n london_n latitude_n find_v by_o prob._n 1._o be_v 51½_n degree_n northwards_o and_o because_o the_o elevation_n of_o the_o pole_n be_v equal_a to_o the_o latitude_n of_o the_o place_n as_o be_v show_v prob._n 15._o therefore_o i_o elevate_v the_o north_n pole_n 51½_n degree_n so_o shall_v 51½_n degree_n on_o the_o meridian_n be_v in_o the_o zenith_n this_o 51½_n degree_n on_o the_o meridian_n represent_v london_n the_o sun_n place_v find_v by_o prob._n 3._o be_v ♉_o 29._o therefore_o i_o bring_v ♉_o 29_o to_o the_o meridian_n and_o the_o hour_n index_n to_o 12._o on_o the_o hour_n circle_n then_o i_o turn_v the_o globe_n eastward_n because_o it_o be_v before_o noon_n till_o the_o index_n point_n at_o 8._o hour_n 53_o minute_n on_o the_o hour-circle_n and_o place_v the_o low_a end_n of_o the_o quadrant_n of_o altitude_n to_o the_o east_n point_n in_o the_o horizon_n and_o slide_v the_o upper_a end_n either_o north_n or_o southwards_o
thereof_o mark_v it_o well_o first_o with_o your_o compass_n observe_v diligent_o upon_o which_o point_n thereof_o it_o lie_v and_o second_o you_o must_v there_o take_v the_o height_n of_o the_o sun_n or_o of_o the_o polestar_n as_o you_o be_v teach_v prob._n 13._o of_o the_o second_o book_n that_o you_o may_v know_v in_o what_o point_n your_o ship_n be_v and_o that_o point_v you_o must_v call_v the_o first_o point_n which_o be_v so_o do_v your_o ship_n may_v sail_v on_o her_o course_n all_o that_o day_n till_o the_o day_n follow_v without_o lose_v her_o way_n and_o the_o next_o day_n mark_v the_o land_n again_o and_o see_v upon_o what_o point_v it_o lie_v and_o then_o take_v your_o height_n and_o with_o it_o cast_v your_o point_n of_o traverse_n once_o again_o and_o that_o you_o may_v call_v your_o second_o point_n then_o take_v a_o pair_n of_o compass_n and_o place_v one_o foot_n upon_o the_o first_o point_n and_o the_o other_o upon_o the_o rhumb_n towards_o which_o the_o land_n do_v bear_n when_o you_o cast_v your_o first_o point_n set_v also_o one_o foot_n of_o another_o pair_n of_o compass_n in_o the_o second_o point_n and_o the_o other_o foot_n upon_o the_o rhumb_n upon_o which_o the_o land_n lie_v when_o you_o cast_v your_o second_o point_n and_o these_o two_o compass_n thus_o open_v you_o must_v move_v by_o their_o rhumb_n till_o those_o two_o foot_n of_o both_o compass_n do_v meet_v together_o which_o be_v move_v from_o the_o foresay_a two_o point_n and_o where_o they_o do_v so_o meet_v together_o there_o may_v you_o say_v be_v the_o land_n which_o you_o discover_v which_o land_n you_o may_v point_v out_o with_o the_o in_o let_n and_o outlet_n or_o cape_n and_o other_o sign_n which_o you_o see_v thereupon_o and_o by_o the_o graduation_n you_o may_v see_v the_o latitude_n thereof_o that_o thereby_o you_o may_v find_v it_o if_o a_o any_o time_n after_o you_o go_v to_o seek_v for_o it_o prob._n xviii_o see_v two_o know_a point_n or_o cape_n of_o land_n as_o you_o sail_v 〈◊〉_d long_o how_o to_o know_v the_o distance_n of_o your_o ship_n from_o they_o pitch_n one_o foot_n of_o one_o pair_n of_o compass_n upon_o one_o of_o the_o two_o foresay_a cape_n and_o the_o other_o foot_n upon_o the_o rhumâ—_n which_o in_o this_o compass_n point_v towards_o that_o cape_n 〈◊〉_d in_o like_a manner_n shall_v you_o do_v with_o another_o pair_n of_o compass_n place_v one_o foot_n thereof_o upon_o the_o other_o know_v cape_n 〈◊〉_d the_o other_o foot_n upon_o the_o rhumb_n which_o stretch_v towards_o 〈◊〉_d say_v second_o cape_n and_o move_v the_o two_o compass_n so_o open_v by_o these_o two_o rhumb_n off_o from_o the_o land_n the_o very_a same_o point_n where_o the_o two_o foot_n which_o come_v from_o the_o two_o cape_n do_v meet_v you_o may_v affirm_v to_o be_v the_o very_a point_n where_o your_o ship_n be_v and_o then_o measure_v by_o the_o degree_n of_o the_o equinoctial_a you_o may_v see_v what_o distance_n there_o be_v from_o the_o say_a point_n to_o either_o of_o the_o foresay_a cape_n or_o to_o any_o other_o place_n which_o you_o think_v good_a for_o it_o be_v a_o very_a easy_a matter_n if_o you_o know_v the_o point_n where_o your_o ship_n be_v prob._n xix_o of_o tide_n and_o how_o by_o help_n of_o the_o globe_n you_o may_v in_o general_a judge_n of_o they_o divide_v the_o equinoctial_a into_o 30_o equal_a part_n as_o be_v direct_v in_o prob._n 54._o of_o the_o last_o book_n these_o 30._o equal_a part_n represent_v the_o 30._o day_n of_o the_o moon_n age._n then_o on_o the_o north_n and_o south_n point_n of_o the_o compass_n in_o the_o outmost_a verge_n of_o the_o horizon_n write_v with_o red_a ink_n 12._o from_o the_o north_n eastward_o viz._n at_o the_o point_n north_n and_o by_o east_n write_v 11_o ¼_n at_o the_o next_o point_n to_o that_o the_o same_o way_n viz._n north_n north_n east_n write_v 10_o ½_o at_o the_o next_o viz._n north_n east_n and_o by_o north_n write_v 9_o ¾_n and_o so_o forward_o to_o every_o point_n of_o the_o compass_n rebate_n of_o the_o last_o hour_n ¾_n till_o you_o come_v to_o 12._o in_o the_o south_n where_o you_o must_v begin_v again_o to_o mark_v that_o semicircle_n also_o in_o the_o same_o order_n you_o do_v the_o last_o in_o this_o circle_n be_v then_o represent_v the_o point_n of_o the_o compass_n the_o sun_n and_o moon_n pass_v by_o every_o day_n and_o the_o figure_n annex_v represent_v the_o twice_o 12._o hour_n of_o day_n and_o night_n have_v thus_o prepare_v your_o globe_n and_o horizon_n you_o may_v by_o have_v the_o moon_n age_n and_o the_o point_n of_o the_o compass_n on_o which_o the_o moon_n make_v full_a sea_n at_o any_o place_n give_v find_v at_o what_o hour_n of_o day_n or_o night_n it_o shall_v be_v high_a tide_n in_o the_o same_o place_n thus_o it_o be_v a_o know_a rule_n that_o a_o north_n and_o south_n moon_n make_v high_a water_n at_o margarate_a therefore_o bring_v the_o first_o point_n of_o ♈_o to_o the_o north_n or_o south_n point_n in_o the_o horizon_n and_o elevate_v the_o north_n pole_n into_o the_o zenith_n then_o count_v in_o the_o equinoctial_a the_o day_n of_o the_o moon_n age_n number_v in_o red_a figure_n and_o the_o hour_n and_o minute_n write_v in_o red_a figure_n annex_v to_o the_o name_n of_o the_o wind_n that_o stand_v against_o the_o moon_n age_n shall_v be_v the_o hour_n of_o high_a tide_n on_o that_o day_n or_o night_n at_o margarate_n the_o end_n of_o the_o three_o book_n the_o four_o book_n show_v the_o practical_a use_n of_o the_o globe_n apply_v they_o to_o the_o solution_n of_o astrological_a problem_n preface_n the_o practice_n of_o astrology_n be_v ground_v upon_o a_o twofold_a doctrine_n the_o first_o for_o erect_v a_o figure_n of_o heaven_n place_v the_o planet_n in_o it_o find_v what_o aspect_n they_o bear_v each_o other_o and_o in_o what_o place_n they_o be_v constitute_v etc._n etc._n and_o this_o we_o call_v the_o astronomical_a part_n of_o astrology_n the_o second_o be_v how_o to_o judge_v of_o the_o event_n of_o thing_n by_o the_o figure_n erect_v and_o this_o be_v indeed_o the_o only_a astrological_a part_n the_o first_o of_o these_o i_o shall_v brief_o handle_v because_o what_o therein_o be_v propose_v may_v be_v perform_v by_o the_o globe_n both_o with_o speed_n ease_n delight_n and_o demonstration_n the_o second_o i_o shall_v not_o meddle_v with_o but_o refer_v you_o to_o the_o whole_a volume_n already_o write_v upon_o that_o subject_a prob._n i._n to_o erect_v a_o figure_n of_o the_o 12_o house_n of_o heaven_n before_o you_o erect_v a_o figure_n of_o the_o 12_o house_n of_o heaven_n it_o will_v be_v requisite_a you_o place_v the_o planet_n ☊_o and_o ☋_o according_a to_o their_o longitude_n and_o latitude_n upon_o the_o globe_n as_o be_v direct_v in_o prob._n 55._o of_o the_o second_o book_n for_o then_o as_o you_o divide_v the_o house_n of_o your_o figure_n by_o the_o circle_n of_o position_n you_o may_v by_o inspection_n behold_v in_o what_o house_n the_o planet_n be_v situate_v and_o also_o see_v what_o fix_a star_n they_o be_v apply_v to_o or_o separate_v from_o but_o to_o the_o matter_n there_o be_v disagreement_n between_o the_o ancient_n and_o modern_a astrologer_n about_o erect_v a_o figure_n of_o heaven_n m_o r_o palmer_n in_o his_o book_n of_o spherical_a problem_n chap._n 48._o mention_n four_o several_a way_n and_o the_o author_n that_o use_v they_o whereof_o one_o of_o they_o be_v call_v the_o rational_a way_n use_v by_o râ—giomontanus_n and_o now_o general_o practise_v by_o all_o the_o astrologer_n of_o this_o age._n this_o way_n the_o face_n of_o heaven_n be_v divide_v into_o twelve_o part_n which_o be_v call_v the_o twelve_o house_n of_o heaven_n number_v from_o the_o ascendent_n or_o angle_n at_o east_n downward_o with_o 1_o 2_o 3_o &c_n &c_n as_o in_o the_o follow_a figure_n in_o a_o direct_a sphere_n viz._n under_o the_o equator_fw-la these_o twelve_o house_n be_v twelve_o equal_a part_n but_o in_o a_o oblique_a sphere_n they_o be_v unequal_a part_n and_o that_o more_o or_o less_o according_a to_o the_o quantity_n of_o the_o sphere_n obliquity_n these_o twelve_o house_n be_v divide_v by_o 12._o semicircle_n of_o position_n which_o be_v semicircle_n pass_v from_o the_o two_o intersection_n of_o the_o horizon_n and_o meridian_n through_o any_o star_n degree_n or_o point_n in_o the_o heaven_n the_o degree_n and_o minute_n of_o the_o ecliptic_a upon_o the_o cusp_n of_o these_o four_o house_n that_o be_v upon_o the_o begin_n of_o these_o house_n be_v find_v all_o at_o once_o only_o by_o bring_v the_o rise_a degree_n of_o the_o ecliptic_a to_o the_o horizon_n for_o the_o horizon_n represent_v the_o cusp_n of_o the_o ascendent_n and_o then_o shall_v
that_o shadow_n shall_v be_v a_o meridian_n liâ—e_z second_o on_o the_o backside_n the_o clinatory_n describe_v a_o circle_n and_o draw_v a_o line_n through_o the_o centre_n to_o both_o side_n the_o circumference_n across_o this_o line_n with_o a_o other_o line_n at_o râ—ght_a angle_n in_o the_o centre_n so_o shall_v the_o circle_n be_v divide_v into_o four_o equal_a part_n these_o four_o part_n you_o must_v maâ—k_v with_o east_n west_n north_n south_n and_o divide_v each_o of_o they_o into_o 90._o degree_n in_o the_o centre_n of_o this_o plain_n erect_v a_o straight_a wire_n prependicular_o when_o you_o will_v find_v a_o meridian_n line_n examine_v by_o the_o ten_o prob._n of_o the_o second_o book_n the_o amplitude_n of_o the_o sun_n rise_v or_o set_v from_o the_o east_n or_o west_n point_n and_o wait_v the_o just_a rise_n or_o set_v that_o day_n turn_v the_o instrument_n about_o till_o the_o shadow_n of_o the_o wire_n fall_v upon_o the_o same_o degree_n from_o the_o east_n or_o west_n the_o amplitude_n be_v of_o for_o then_o the_o north_n and_o south_n line_n in_o the_o instrument_n will_v be_v the_o same_o with_o the_o north_n and_o south_n line_n in_o heaven_n three_o by_o the_o sun_n azimuth_n find_v the_o azimuth_n of_o the_o sun_n by_o prob._n 22._o of_o the_o second_o book_n and_o at_o the_o same_o instant_n turn_v the_o instrument_n till_o the_o shadow_n of_o the_o wire_n fall_v upon_o the_o degree_n on_o the_o instrument_n opposite_a to_o the_o degree_n of_o the_o sun_n azimuth_n so_o shall_v the_o meridional_a line_n of_o the_o instrument_n agree_v with_o the_o meridional_a line_n in_o heaven_n you_o may_v the_o same_o way_n work_n by_o the_o azimuth_n of_o any_o star_n only_o whereas_o the_o shadow_n of_o the_o wire_n shall_v fall_v upon_o the_o opposite_a degree_n aforesaid_a now_o you_o must_v place_v a_o sight_n or_o perpendicular_a upon_o that_o opposite_a degree_n and_o turn_v the_o instrument_n about_o till_o the_o wire_n at_o the_o centre_n the_o sight_n in_o the_o opposite_a degree_n of_o the_o star_n azimuth_n and_o the_o star_n in_o heaven_n come_v into_o one_o straight_a line_n so_o shall_v the_o meridian_n line_n of_o the_o instrument_n agree_v with_o the_o meridional_a line_n in_o heaven_n four_o it_o may_v be_v find_v by_o any_o star_n observe_v in_o the_o meridian_n if_o two_o perpendicular_o be_v erect_v in_o the_o meridian_n line_n of_o your_o instrument_n for_o then_o by_o turn_v the_o instrument_n till_o the_o two_o perpendicular_o and_o the_o star_n come_v into_o a_o straight_a line_n the_o meridian_n line_n of_o your_o instrument_n will_v be_v the_o same_o with_o the_o meridian_n line_n in_o heaven_n see_v more_o way_n in_o mr._n palmer_n on_o the_o planisphear_n book_n 4._o chap._n 9_o if_o your_o plain_a either_o recline_v or_o incline_v apply_v one_o of_o the_o side_n of_o your_o clinatory_a parallel_n to_o one_o of_o the_o semidiameters_a of_o the_o quadrant_n to_o the_o plain_a in_o such_o sort_n that_o the_o plumb-line_n hang_v at_o liberty_n may_v fall_v upon_o the_o circumference_n of_o the_o quadrant_n for_o then_o the_o number_n of_o degree_n of_o the_o quadrant_n comprehend_v between_o the_o side_n of_o the_o quadrant_n parallel_n to_o the_o plain_a and_o the_o plumb-line_n shall_v be_v the_o number_n of_o degree_n of_o reclination_n if_o thâ—_n centre_n of_o the_o quadrant_n point_v upward_o or_o inclination_n if_o thâ—_n centre_n point_v downward_o if_o your_o recline_a or_o incline_v plain_a decline_v draw_v upon_o it_o a_o line_n parallel_n to_o the_o horizon_n which_o you_o may_v do_v by_o apply_v the_o backside_n of_o the_o clinatory_n and_o raise_v or_o depress_v the_o centre_n of_o the_o quadrant_n till_o the_o plumb-line_n hang_v just_a upon_o one_o of_o the_o semidiameters_a for_o than_o you_o may_v by_o the_o upper_a side_n of_o the_o clinatory_n draw_v a_o horizontal_n line_n if_o the_o plain_n incline_v or_o by_o the_o under_o side_n if_o it_o recline_v if_o it_o neither_o incline_v or_o recline_v you_o may_v drawâ—_n a_o horizontal_n line_n both_o by_o the_o upper_a and_o under_o side_n of_o the_o clinatory_n have_v draw_v the_o horizontal_n line_n apply_v the_o north_n 〈◊〉_d â—_o of_o the_o clinatory_n to_o it_o and_o if_o the_o north_n end_n of_o the_o needle_n 〈◊〉_d direct_o towards_o the_o plain_a it_o be_v then_o a_o south_n plain_a if_o the_o 〈◊〉_d point_n of_o the_o needle_n point_v direct_o from_o the_o plain_a it_o be_v a_o norâ—â—_n plain_a but_o if_o it_o point_v towards_o the_o east_n it_o be_v a_o east_n plain_a if_o towards_o the_o west_n a_o west_n plain_a if_o it_o do_v not_o point_v direct_o 〈◊〉_d east_n west_n north_n or_o south_n than_o so_o many_o degree_n as_o the_o 〈◊〉_d decline_v from_o any_o of_o these_o four_o point_n to_o any_o of_o the_o other_o of_o 〈◊〉_d four_o point_n so_o many_o degree_n be_v the_o declination_n of_o the_o plain_a 〈◊〉_d respect_n as_o aforesaid_a have_v to_o the_o variation_n of_o the_o compass_n or_o if_o you_o find_v the_o azimuth_n of_o the_o sun_n by_o its_o altitude_n observe_v just_a when_o its_o beam_n be_v come_v on_o or_o go_v off_o youâ—_n plain_a that_o azimuth_n shall_v be_v the_o azimuth_n of_o your_o plain_n or_o you_o may_v erect_v a_o wire_n perpendicular_o on_o your_o plain_n and_o wait_v till_o the_o shadow_n of_o that_o wire_n come_v to_o be_v perpendicular_a with_o the_o horizon_n which_o you_o may_v examine_v by_o apply_v a_o plumb-line_n to_o it_o for_o then_o the_o shadow_n of_o the_o plumb-line_n and_o the_o shadow_n of_o the_o perpendicular_a will_v be_v in_o one_o then_o take_v the_o altitude_n of_o the_o sun_n you_o may_v by_o prob._n 22._o of_o the_o second_o book_n find_v its_o azimuth_n and_o thereby_o know_v in_o what_o azimuth_n the_o plain_a of_o your_o dyal_n lie_v for_o the_o azimuth_n your_o plain_n lie_v in_o be_v distant_a from_o the_o azimuth_n of_o the_o sun_n just_a 90._o degree_n prob._n i._n how_o by_o one_o position_n of_o the_o globe_n to_o find_v the_o distance_n of_o the_o hour-line_n on_o all_o manner_n of_o plain_n you_o may_v have_v meridian_n line_n draw_v from_o pole_n to_o pole_n through_o every_o 15._o degree_n of_o the_o equinoctial_a to_o represent_v the_o horary_a motion_n of_o the_o sun_n both_o day_n and_o night_n and_o when_o the_o pole_n of_o the_o globe_n be_v elevate_v to_o the_o height_n of_o the_o pole_n in_o any_o place_n and_o one_o of_o these_o meridian_n line_n be_v bring_v to_o the_o brazen_a meridian_n all_o the_o rest_n of_o the_o meridian_n line_n shall_v cut_v any_o circle_n which_o you_o intend_v shall_v represent_v the_o plain_a of_o a_o dyal_n in_o the_o number_n of_o degree_n on_o the_o same_o circle_n that_o each_o respective_a hour-line_n be_v distant_a from_o the_o noon-line_n point_n in_o the_o same_o circle_n thus_o if_o you_o shall_v inquire_v the_o distance_n of_o the_o hour-line_n upon_o a_o horizontal_n plain_n in_o london_n latitude_n the_o pole_n of_o the_o globe_n 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the_o moon_n be_v always_o a_o part_n of_o a_o circle_n therefore_o the_o earth_n and_o water_n which_o be_v the_o body_n shadow_v must_v also_o be_v a_o circular_a or_o round_a body_n for_o if_o it_o be_v three_o square_a four_o square_a or_o any_o other_o form_n than_o will_v the_o shadow_n which_o it_o make_v in_o the_o moon_n be_v of_o the_o same_o fashion_n beside_o of_o all_o figure_n the_o sphere_n or_o globe_n be_v most_o perfect_a most_o capacious_a and_o most_o entire_a of_o itself_o without_o either_o joint_n or_o angle_n which_o form_n we_o may_v also_o perceive_v the_o sun_n moon_n and_o star_n to_o have_v and_o all_o other_o thing_n that_o be_v bound_v by_o themselves_o as_o drop_n of_o water_n and_o other_o liquid_a thing_n but_o there_o be_v another_o frequent_a argument_n against_o the_o globulus_n form_n of_o the_o earth_n and_o that_o be_v that_o it_o seem_v impossible_a that_o the_o earth_n shall_v be_v round_o and_o yet_o also_o inhabible_a in_o all_o place_n for_o 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town_n hill_n cape_n sea_n sand_n etc._n etc._n as_o also_o the_o rhumb_n meridian_n parallel_n and_o other_o line_n that_o serve_v to_o facilitate_v the_o demostration_n of_o all_o manner_n of_o question_n to_o be_v perform_v upon_o the_o same_o and_o this_o globe_n be_v call_v the_o terrestrial_a globe_n ii_o of_o the_o two_o pole_n every_o globe_n have_v two_o pole_n the_o one_o north_n the_o other_o south_n the_o north_n pole_n be_v in_o the_o north_n point_n of_o the_o globe_n the_o south_n pole_n in_o the_o south_n point_fw-fr iii_o of_o the_o axis_n from_o the_o centre_n of_o the_o globe_n both_o way_n proceed_v a_o line_n through_o both_o the_o pole_n and_o continue_v itself_o infinite_o which_o be_v call_v the_o axis_n of_o the_o world_n and_o be_v represent_v by_o the_o two_o wire_n in_o the_o pole_n of_o the_o globe_n upon_o these_o two_o wire_n the_o globe_n be_v turn_v round_o even_o as_o the_o heaven_n be_v imagine_v to_o move_v upon_o the_o axis_n of_o the_o world_n four_o of_o the_o brazen_a meridian_n every_o globe_n be_v hang_v by_o the_o axis_n at_o both_o the_o pole_n in_o a_o brazen_a meridian_n which_o be_v divide_v into_o 360_o degree_n or_o which_o be_v all_o one_o into_o 4_o ninety_n the_o first_o beginning_n at_o the_o north_n pole_n be_v continue_v from_o the_o left_a hand_n towards_o the_o right_a till_o the_o termination_n of_o 90_o degree_n and_o be_v mark_v with_o 10_o 20_o 30_o etc._n etc._n to_o 90._o from_o whence_o the_o degree_n be_v number_v with_o 80_o 70_o 60_o etc._n etc._n to_o 0._o which_o be_v in_o the_o south_n pole_n from_o whence_o again_o the_o degree_n be_v number_v with_o 80_o 70_o 60_o etc._n etc._n to_o 0_o and_o last_o from_o 0_o the_o degree_n be_v number_v with_o 10_o 20_o 30_o to_o 90._o which_o be_v again_o in_o the_o north_n pole_n this_o brazen_a meridian_n be_v of_o great_a use_n for_o by_o help_n of_o it_o you_o may_v find_v the_o latitude_n of_o all_o place_n the_o declination_n of_o all_o the_o star_n &c_n &c_n and_o rectify_v the_o globe_n to_o any_o latitude_n v._o of_o the_o horizon_n the_o horizon_n be_v a_o broad_a wooden_a circle_n encompass_v the_o globe_n have_v two_o notch_n in_o it_o the_o one_o in_o the_o north_n the_o other_o in_o the_o south_n point_n the_o notch_n be_v make_v just_o fit_a to_o contain_v the_o brazen_a meridian_n that_o the_o globe_n be_v hang_v in_o in_o the_o bottom_n or_o under_o plane_n of_o the_o horizon_n there_o stand_v up_o a_o rop_n or_o as_o it_o be_v call_v a_o bed_n in_o which_o there_o be_v also_o a_o notch_n into_o which_o notch_n the_o brazen_a meridian_n be_v also_o let_v so_o lo_o as_o that_o both_o it_o and_o the_o globe_n may_v be_v divide_v into_o two_o equal_a half_n by_o the_o upper_a plane_n of_o the_o wooden_a horizon_n these_o notch_n be_v as_o gauge_n to_o keep_v the_o globe_n from_o incline_v more_o to_o the_o one_o side_n of_o the_o wooden_a horizon_n than_o the_o other_o upon_o the_o upper_a plane_n of_o the_o horizon_n be_v 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in_o the_o north_n and_o six_o month_n night_n in_o the_o south_n and_o contrary_o from_o the_o 11_o of_o september_n to_o the_o 10_o of_o march_n the_o sun_n be_v then_o in_o the_o southerly_a sign_n and_o therefore_o on_o the_o south_n side_n the_o horizon_n there_o be_v six_o month_n day_n in_o the_o south_n and_o six_o month_n night_n in_o the_o north._n it_o be_v call_v a_o parallel_n sphere_n because_o the_o sun_n moon_n or_o star_n in_o a_o diurnal_a revolution_n of_o the_o heaven_n neither_o ascend_v high_a or_o descend_v low_a but_o always_o move_v parallel_n to_o the_o horizon_n the_o earth_n be_v thus_o posit_v under_o both_o the_o pole_n viz._n in_o 90_o degree_n of_o latitude_n as_o may_v be_v see_v by_o the_o globe_n if_o you_o turn_v the_o brazen_a meridian_n till_o either_o of_o the_o pole_n be_v elevate_v 90_o degree_n above_o the_o horizon_n as_o in_o this_o figure_n a_o oblique_a sphere_n have_v the_o axis_n of_o the_o world_n neither_o direct_v sphere_n nor_o 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oblique_o about_o the_o horizon_n the_o earth_n be_v thus_o oblique_o posit_v to_o all_o those_o nation_n that_o inhabit_v under_o any_o degree_n of_o latitude_n either_o north_n or_o southward_o between_o the_o equator_fw-la and_o either_o pole_n as_o may_v various_o be_v see_v by_o the_o globe_n when_o the_o axis_n lie_v not_o on_o the_o horizon_n nor_o the_o equator_fw-la be_v parallel_n to_o the_o horizon_n as_o in_o this_o follow_a figure_n moreover_o all_o place_n have_v their_o antipode_n peraeci_n and_o antaeâ—i_fw-la the_o antipode_n of_o any_o place_n be_v the_o opposite_a degree_n on_o the_o antipode_n globe_n as_o if_o a_o perpendicular_a be_v let_v fall_n from_o the_o place_n you_o stand_v on_o through_o the_o centre_n of_o the_o earth_n and_o continue_v till_o it_o pass_v quite_o through_o the_o superficies_n of_o the_o earth_n on_o the_o other_o side_n then_o in_o the_o point_n where_o the_o perpendicular_a cut_v the_o superficies_n of_o the_o earth_n on_o the_o other_o 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respect_n of_o warp_a and_o shrink_v i_o have_v have_v few_o globe_n come_v to_o mend_v that_o have_v not_o have_v either_o break_a orison_n or_o some_o other_o notorious_a fault_n occasion_v through_o the_o sleightness_n of_o the_o orison_n in_o the_o use_v the_o globe_n keep_v the_o east_n side_n of_o the_o horizon_n always_o towards_o you_o unless_o your_o proposition_n require_v the_o turn_n of_o it_o which_o east_n side_n you_o may_v know_v by_o the_o word_n east_n place_v on_o the_o outmost_a verge_n thereof_o for_o then_o have_v you_o the_o graduated_a side_n of_o the_o meridian_n always_o towards_o you_o the_o quadrant_n of_o altitude_n before_o you_o and_o the_o globe_n divide_v exact_o into_o two_o equal_a part_n so_o oft_o as_o i_o name_n to_o at_z of_o or_o under_o the_o meridian_n or_o horizon_n i_o mean_v the_o east_n side_n of_o the_o meridian_n and_o superficies_n of_o the_o horizon_n because_o the_o east_n side_n of_o the_o meridian_n pass_v through_o the_o north_n 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degree_n that_o be_v at_o the_o horizon_n or_o meridian_n will_v be_v move_v away_o and_o thereby_o the_o position_n of_o the_o globe_n alter_v to_o avoid_v which_o inconvenince_n you_o may_v make_v use_n of_o a_o quill_n thrust_v the_o feather_n end_n between_o the_o ball_n and_o the_o brazen_a meridian_n and_o so_o wedge_n it_o up_o without_o wrong_v the_o globe_n at_o all_o till_o your_o proposition_n be_v answer_v problem_n i._n to_o find_v the_o longitude_n and_o latitude_n of_o place_n on_o the_o terrestrial_a globe_n seek_v the_o place_n on_o the_o terrestrial_a globe_n who_o longitude_n and_o latitude_n you_o will_v know_v and_o bring_v that_o place_n to_o the_o brazen_a meridian_n and_o see_v how_o many_o degree_n of_o the_o equator_fw-la be_v cut_v by_o the_o meridian_n from_o the_o first_o general_a meridian_n which_o on_o my_o globe_n pass_v through_o gratiosa_fw-la one_o of_o the_o isle_n of_o the_o azore_n for_o that_o number_n of_o degree_n be_v the_o longitude_n of_o the_o place_n example_n i_o desire_v to_o know_v the_o longitude_n of_o london_n and_o close_o to_o the_o name_n london_n i_o find_v a_o small_a mark_n 0_o thus_o which_o small_a mark_n be_v in_o some_o globe_n and_o map_n adorn_v with_o the_o picture_n of_o a_o steeple_n etc._n etc._n therefore_o i_o do_v not_o bring_v the_o word_n london_n to_o the_o meridian_n but_o that_o small_a mark_n for_o that_o always_o represent_v the_o the_o town_n or_o city_n seek_v for_o and_o keep_v the_o globe_n steady_a in_o this_o position_n i_o examine_v how_o many_o degree_n of_o the_o equator_fw-la be_v contain_v between_o the_o brazen_a meridian_n and_o the_o first_o general_a meridian_n which_o i_o find_v to_o be_v 24._o deg_n 00._o min._n therefore_o i_o say_v the_o longitude_n of_o london_n be_v 24._o degree_n 00._o min._n for_o the_o latitude_n see_v on_o the_o brazen_a meridian_n how_o many_o degree_n be_v contain_v between_o the_o equator_fw-la and_o the_o mark_n for_o london_n which_o in_o this_o example_n be_v 51½_n therefore_o i_o say_v london_n have_v 51½_n degree_n north_n latitude_n problem_n ii_o the_o longitude_n and_o latitude_n be_v know_v to_o rectify_v the_o globe_n fit_a for_o use_v 1._o when_o you_o rectify_v the_o globe_n to_o any_o particular_a latitude_n you_o must_v move_v the_o brazen_a meridian_n through_o the_o notch_n of_o the_o horizon_n till_o the_o same_o number_n of_o degree_n account_v on_o the_o meridian_n from_o the_o pole_n about_o which_o the_o hour-circle_n be_v towards_o the_o north_n point_n in_o the_o horizon_n if_o in_o north_n latitude_n and_o towards_o the_o south_n if_o in_o south_n latitude_n come_v just_a to_o the_o edge_n of_o the_o horizon_n example_n by_o the_o former_a proposition_n i_o find_v the_o latitude_n of_o london_n to_o be_v 51½_n degree_n north_n latitude_n therefore_o i_o count_v 51½_n degree_n from_o the_o pole_n downward_o towards_o my_o right_a hand_n and_o turn_v the_o meridian_n through_o the_o notch_n of_o the_o horizon_n till_o those_o 51½_n degree_n come_v exact_o to_o the_o uppermost_a edge_n of_o the_o north_n point_n in_o the_o horizon_n and_o then_o be_v the_o meridian_n rectify_v to_o the_o latitude_n of_o london_n 2._o next_o rectify_v the_o quadrant_n of_o altitude_n after_o this_o manner_n screw_v the_o edge_n of_o the_o nut_n that_o be_v even_o with_o the_o graduated_a edge_n of_o the_o thin_a plate_n to_o 51½_n degree_n of_o the_o brazen_a meridian_n account_v from_o the_o equinoctial_a on_o the_o southern_a side_n the_o horizon_n which_o be_v just_a the_o zenith_n of_o london_n and_o then_o be_v your_o quadrant_n rectify_v 3._o bring_v the_o degree_n of_o the_o ecliptic_a the_o sun_n be_v in_o that_o day_n to_o the_o meridian_n which_o you_o shall_v learn_v to_o know_v by_o the_o next_o problem_n and_o then_o turn_v the_o index_n of_o the_o hour_n circle_n to_o the_o hour_n 12._o on_o the_o south_n side_n the_o hour_n circle_n and_o then_o be_v your_o hour_n circle_n also_o rectify_v fit_a to_o use_v for_o that_o day_n 4._o last_o if_o you_o will_v rectify_v the_o globe_n to_o correspond_v in_o all_o respect_n with_o the_o position_n and_o situation_n of_o the_o sphere_n you_o must_v set_v the_o four_o quarter_n of_o the_o horizon_n viz._n east_n west_n north_n and_o south_n agreeable_a with_o the_o four_o quarter_n of_o the_o world_n which_o you_o may_v do_v by_o the_o needle_n in_o the_o bottom_n of_o the_o horizon_n for_o you_o must_v turn_v the_o globe_n so_o long_o till_o the_o needle_n point_fw-fr just_a to_o the_o flower_n de_fw-fr luce_fw-fr next_o you_o must_v set_v the_o plain_a of_o the_o wooden_a horizon_n parallel_v to_o the_o horizon_n of_o the_o world_n which_o you_o may_v try_v by_o set_v a_o common_a level_n on_o the_o four_o quatre_n of_o the_o horizon_n and_o then_o posit_v the_o degree_n of_o the_o ecliptic_a the_o sun_n be_v in_o to_o the_o height_n above_o or_o depth_n below_o the_o horizon_n the_o sun_n have_v in_o heaven_n as_o by_o the_o 11_o problem_n your_o globe_n be_v make_v correspondent_a in_o all_o point_n with_o the_o frame_n of_o the_o sphere_n for_o that_o particular_a time_n and_o latitude_n problem_n iii_o to_o find_v the_o place_n of_o the_o sun_n in_o the_o ecliptic_a the_o day_n of_o the_o month_n be_v first_o know_v seek_v the_o day_n of_o the_o month_n in_o the_o circle_n of_o month_n upon_o the_o horizon_n and_o right_a against_o it_o in_o the_o circle_n of_o sign_n be_v the_o degree_n of_o the_o ecliptic_a the_o sun_n be_v in_o example_n imagine_v the_o day_n to_o be_v give_v be_v may_v 10._o therefore_o i_o seek_v on_o the_o horizon_n in_o the_o circle_n of_o month_n for_o may_v and_o find_v the_o month_n divide_v into_o so_o many_o part_n as_o there_o be_v day_n in_o the_o month_n which_o part_n be_v mark_v with_o arithmetical_a figure_n from_o the_o begin_n of_o the_o month_n to_o the_o end_n and_o denote_v the_o number_n of_o the_o day_n of_o the_o month_n that_o each_o division_n represent_v therefore_o among_o the_o division_n i_o seek_v for_o 10_o and_o direct_o against_o it_o in_o the_o circle_n of_o sign_n i_o find_v ♉_o 29._o degree_n therefore_o i_o say_v may_v 10._o the_o sun_n place_n be_v in_o 29._o degree_n of_o ♉_o but_o note_n that_o if_o it_o be_v leap_v year_n instead_o of_o the_o 10._o of_o may_v you_o must_v take_v the_o 11._o of_o may_n because_o february_n have_v in_o a_o leap_v year_n 29._o day_n the_o 29._o of_o february_n must_v be_v reckon_v for_o the_o first_o of_o march_n and_o the_o first_o of_o march_n for_o the_o second_o of_o march_n the_o second_o of_o march_n for_o the_o three_o of_o march_n and_o so_o throughout_o the_o year_n the_o leap_v year_n be_v cause_v by_o the_o six_o odd_a hour_n more_o than_o 365._o day_n that_o be_v assign_v to_o
magnitude_n 16._o degree_n of_o the_o six_o magnitude_n 17_o degree_n the_o nebulous_a one_o 18._o degree_n yet_o this_o rule_n be_v not_o so_o certain_a but_o that_o either_o clear_a or_o cloudy_a weather_n may_v alter_v it_o read_v more_o of_o this_o subject_n in_o m_o r_o palmer_n on_o the_o plamsphear_n book_n 4._o chap._n 20_o now_o to_o find_v the_o time_n that_o any_o star_n shall_v rise_v heliacal_o do_v thus_o rectify_v the_o globe_n and_o quadrant_n of_o altitude_n to_o your_o latitude_n then_o bring_v the_o give_v star_n to_o the_o east_n side_n the_o horizon_n and_o turn_v the_o quadrant_n of_o altitude_n into_o the_o west_n side_n and_o see_v what_o degree_n of_o the_o ecliptic_a be_v elevate_v so_o many_o degree_n above_o the_o horizon_n as_o the_o magnitude_n of_o the_o star_n you_o inquire_v after_o require_v according_a to_o the_o forego_n rule_n for_o the_o opposite_a degree_n of_o the_o ecliptic_a be_v the_o degree_n the_o sun_n shall_v be_v in_o when_o that_o star_n rise_v heliacal_o have_v the_o degree_n of_o the_o ecliptic_a the_o sun_n be_v in_o you_o may_v find_v the_o day_n of_o the_o month_n by_o the_o four_o problem_n example_n i_o will_v know_v when_o cor_n leonis_fw-la shall_v rise_v heliacal_o here_o at_o london_n therefore_o i_o rectify_v the_o globe_n and_o quadrant_n of_o altitude_n for_o london_n and_o bring_v cor_fw-la leonis_fw-la to_o the_o east_n side_n the_o horizon_n and_o turn_v the_o quadrant_n of_o altitude_n into_o the_o west_n and_o because_o cor_fw-la leonis_fw-la be_v a_o star_n of_o the_o first_o magnitude_n therefore_o i_o see_v what_o degree_n of_o the_o ecliptic_a be_v elevate_v in_o the_o west_n side_n the_o horizon_n 12._o degree_n on_o the_o quadrant_n of_o altitude_n and_o find_v ♓_o 9_o deg_n now_o the_o degree_n of_o the_o ecliptic_a opposite_a to_o ♓_o 9_o be_v 〈◊〉_d 9_o therefore_o i_o say_v when_o the_o sun_n come_v to_o 〈◊〉_d 9_o degree_n which_o by_o the_o four_o problem_n i_o find_v be_v august_n 23._o cor_fw-la leonis_fw-la shall_v rise_v heliacal_o for_o the_o heliacal_a set_v the_o globe_n etc._n etc._n rectify_v as_o before_o bring_v the_o star_n to_o the_o west_n side_n the_o horizon_n then_o see_v what_o degree_n of_o the_o ecliptic_a be_v elevate_v on_o the_o quadrant_n of_o altitude_n so_o many_o degree_n as_o the_o star_n magnitude_n require_v for_o when_o the_o sun_n come_v to_o the_o opposite_a degree_n of_o the_o ecliptic_a that_o star_n shall_v set_v heliacal_o example_n i_o will_v know_v when_o bilanx_fw-la a_o star_n in_o the_o beam_n of_o the_o scale_n will_v set_v heliacal_o here_o at_o london_n the_o globe_n and_o quadrant_n rectify_v i_o bring_v bilanx_fw-la to_o the_o west_n side_n the_o horizon_n and_o turn_v the_o quadrant_n of_o altitude_n into_o the_o east_n then_o i_o examine_v what_o degree_n of_o the_o ecliptic_a be_v elevate_v 13._o degree_n of_o the_o quadrant_n of_o altitude_n because_o bilanx_fw-la be_v a_o star_n of_o the_o second_o magnitude_n and_o find_v ♉_o 4½_n opposite_a to_o ♉_o 4½_n be_v 〈◊〉_d 4½_n therefore_o i_o say_v when_o the_o sun_n come_v to_o 〈◊〉_d 4½_n which_o by_o problem_n 4._o will_v be_v october_n 18_o bilanx_fw-la shall_v set_v heliacal_o prob._n xxxviii_o to_o find_v the_o diurnal_a and_o nocturnal_a arch_n of_o the_o sun_n or_o star_n in_o any_o give_a latitude_n the_o semi-diurnal_a arch_n be_v the_o number_n of_o degree_n of_o the_o equator_fw-la that_o pass_v through_o the_o meridian_n while_o the_o sun_n or_o any_o star_n be_v ascend_v above_o the_o east_n side_n the_o horizon_n to_o the_o meridian_n to_o know_v the_o number_n of_o degree_n it_o contain_v rectify_v the_o globe_n to_o the_o give_v latitude_n and_o bring_v the_o place_n of_o the_o sun_n or_o star_n to_o the_o east_n side_n the_o horizon_n and_o note_v what_o number_n of_o degree_n of_o the_o equinoctial_a be_v then_o cut_v by_o the_o meridian_n then_o remove_v the_o place_n of_o the_o sun_n or_o star_n to_o the_o meridian_n and_o see_v again_o what_o number_n of_o degree_n of_o the_o equinoctial_a be_v then_o cut_v by_o the_o meridian_n and_o subtract_v the_o former_a from_o the_o latter_a and_o the_o remainder_n shall_v be_v the_o number_n of_o degree_n of_o the_o sun_n or_o star_n semi-diurnal_a arch._n but_o note_v if_o the_o equinoctial_a point_n ♈_o pass_n through_o the_o meridian_n while_o the_o sun_n or_o star_n be_v turn_v from_o the_o east_n side_n the_o horizon_n to_o the_o meridian_n than_o you_o must_v subtract_v the_o number_n of_o degree_n of_o the_o equinoctial_a cut_n by_o the_o meridian_n when_o the_o sun_n or_o star_n be_v at_o the_o east_n side_n the_o horizon_n from_o 360._o degree_n and_o to_o the_o remainder_n ad_fw-la the_o number_n of_o degree_n of_o the_o equinoctial_a that_o come_v to_o the_o meridian_n with_o the_o place_n of_o the_o sun_n or_o star_n and_o the_o sum_n of_o they_o both_o be_v the_o number_n of_o degree_n of_o the_o sun_n or_o star_n semi-diurnal_a arch_n which_o be_v double_v be_v the_o number_n of_o degree_n of_o the_o whole_a diurnal_a arch_n and_o which_o be_v substract_v from_o 360_o give_v the_o nocturnal_a arch._n example_n of_o the_o sun_n have_v rectify_v the_o globe_n i_o will_v may_n 10._o know_v the_o diurnal_a arch_n of_o the_o sun_n his_o place_n find_v by_o prob._n 3._o be_v 8_o 29._o therefore_o i_o bring_v ♉_o 29._o to_o the_o fast_a side_n the_o horizon_n and_o find_v then_o at_o the_o meridian_n 299._o degree_n 30._o min._n of_o the_o equinoctial_a then_o i_o turn_v the_o place_n of_o the_o sun_n to_o the_o meridian_n and_o find_v 56._o deg_n 30._o min._n of_o the_o equinoctial_a come_v to_o the_o meridian_n with_o it_o here_o the_o equinoctial_a point_n ♈_o passes_z through_o the_o meridian_n while_o the_o sun_n move_v between_o the_o horizon_n and_o the_o meridian_n therefore_o as_o aforesaid_a i_o subtract_v the_o first_o number_n of_o degree_n and_o minute_n viz._n 299._o deg_n 30._o min._n from_o 360._o degree_n and_o there_o remain_v 60_o degr_n 30._o min._n for_o the_o number_n of_o degree_n and_o minute_n contain_v between_o the_o degree_n of_o the_o equinoctial_a at_o the_o meridian_n and_o the_o equinoctial_a point_n ♈_o and_o to_o this_o 60._o deg_n 30._o min._n i_o add_v the_o second_o number_n of_o degree_n and_o minute_n viz._n 56._o deg_n 30._o min._n the_o number_n of_o degree_n and_o minute_n between_o the_o point_n ♈_o and_o the_o deg_n of_o the_o equinoctial_a at_o the_o meridian_n and_o they_o make_v together_o 117._o degree_n for_o the_o sun_n semi_a diurnal_a arch_n by_o double_v of_o which_o you_o have_v 234._o degree_n for_o the_o sun_n diurnal_a arch_n and_o by_o substract_v 234._o the_o diurnal_a arch_n from_o 360._o you_o have_v 126._o degree_n for_o the_o sun_n nocturnal_a arch._n example_n for_o a_o star_n i_o take_v sirius_n a_o bright_a star_n in_o the_o great_a dog_n mouth_n the_o globe_n rectify_v as_o before_o i_o bring_v sirius_n to_o the_o east_n side_n the_o horizon_n and_o find_v then_o 29._o degree_n 30_o minute_n of_o the_o equinoctial_a at_o the_o meridian_n than_o i_o turn_v sirius_n to_o the_o meridian_n and_o find_v 97._o degree_n 38_o minute_n of_o the_o equinoctial_a come_v to_o the_o meridian_n with_o it_o therefore_o i_o subtract_v the_o first_o number_n viz._n 29._o degree_n 30._o minute_n from_o the_o second_o 97._o 38_o and_o the_o remain_v be_v 68_o degree_n 8_o minute_n for_o the_o semi-diurnal_a arch_n of_o sirâ—us_n his_o nocturnal_a arch_n you_o may_v find_v as_o before_o prob._n thirty-nine_o to_o find_v the_o azimuth_n and_o almicantar_n of_o any_o star_n this_o problem_n be_v like_o the_o 22_o and_o 23._o problem_n which_o show_v the_o find_v the_o azimuth_n and_o almicantar_n of_o the_o sun_n only_o whereas_o there_o you_o be_v direct_v to_o bring_v the_o degree_n of_o the_o sun_n to_o the_o quadrant_n of_o altitude_n you_o must_v now_o bring_v the_o star_n propose_v to_o the_o quadrant_n of_o altitude_n and_o by_o the_o direction_n in_o those_o problem_n the_o resolution_n will_v be_v find_v prob._n xl._o to_o find_v the_o hour_n of_o the_o night_n by_o observe_v two_o know_v star_n in_o one_o azimuth_n or_o almicantar_n rectify_v the_o globe_n quadrant_n and_o hour_n index_n then_o find_v the_o two_o know_a star_n on_o the_o globe_n and_o if_o the_o two_o star_n be_v in_o one_o azimuth_n turn_v about_o the_o globe_n and_o quadrant_n of_o altitude_n till_o you_o can_v fit_v the_o two_o star_n to_o lie_v under_o the_o graduated_a edge_n of_o the_o quadrant_n of_o altitude_n so_o shall_v the_o index_n of_o the_o hour-circle_n pâ—int_n at_o thâ—_n hour_n of_o the_o night_n if_o the_o two_o star_n be_v in_o one_o almicantar_n turn_v the_o globe_n forward_o or_o backward_o till_o the_o two_o star_n come_v to_o such_o a_o position_n that_o by_o move_v the_o
to_o every_o twelth_n degree_n of_o the_o equinoctial_a account_v from_o the_o equinoctial_a colour_n mark_v they_o with_o 1_o 2_o 3_o 4._o etc._n etc._n to_o 30_o which_o will_v end_v where_o you_o begin_v viz._n at_o the_o equinoctial_a colour_n again_o so_o shall_v the_o equinoctial_a be_v divide_v into_o 30_o equal_a part_n represent_v the_o 30_o day_n of_o the_o moon_n age_n these_o figure_n to_o distinguish_v they_o from_o the_o degree_n of_o the_o equator_fw-la be_v best_a be_v write_v with_o red_a ink._n when_o you_o will_v inquire_v the_o moon_n place_n elevate_v the_o north_n pole_n 90_o degree_n that_o be_v in_o the_o zenith_n so_o shall_v the_o equator_fw-la lie_v in_o the_o horizon_n then_o bring_v the_o equinoctial_a colour_n against_o the_o day_n of_o the_o month_n in_o the_o horizon_n so_o shall_v the_o moon_n age_n write_v in_o red_a figure_n stand_v against_o the_o sign_n and_o degree_n in_o the_o horizon_n that_o the_o moon_n be_v in_o at_o that_o time_n example_n september_n 28._o 1658._o i_o will_v know_v the_o moon_n place_n in_o the_o ecliptic_a she_o be_v then_o 12_o day_n old_a therefore_o i_o elevate_v the_o north_n pole_n 90_o degree_n above_o the_o horizon_n and_o turn_v the_o globe_n about_o till_o the_o equinoctial_a colour_n come_v to_o september_n 28._o in_o the_o circle_n of_o day_n on_o the_o horizon_n then_o look_v against_o what_o sign_n and_o degree_n of_o the_o ecliptic_a circle_n in_o the_o horizon_n the_o 12_o the_o division_n in_o red_a figure_n stand_v i_o find_v ♓_o 9_o which_o be_v the_o sign_n and_o degree_n the_o moon_n be_v in_o according_a to_o her_o mean_a motion_n this_o problem_n may_v be_v apply_v to_o many_o use_v for_o have_v the_o moon_n place_v you_o may_v find_v the_o time_n of_o her_o rise_n sothe_v set_v and_o shine_v &c._n &c._n by_o work_v with_o she_o as_o you_o be_v teach_v to_o work_v with_o the_o sun_n in_o several_a foregoing_a problem_n proper_a to_o each_o purpose_n prob._n lv._o have_v the_o longitude_n and_o latitude_n or_o right_a ascension_n and_o declination_n of_o any_o planet_n or_o comet_n to_o place_v it_o on_o the_o globe_n to_o correspond_v with_o its_o place_n in_o heaven_n planet_n and_o comet_n can_v be_v place_v on_o the_o globe_n so_o as_o their_o place_n will_v long_o retain_v correspondence_n with_o their_o place_n in_o heaven_n because_o as_o be_v say_v chap._n 44._o they_o have_v a_o continual_a motion_n from_o west_n to_o east_n upon_o the_o pole_n of_o the_o ecliptic_a yet_o nevertheless_a you_o may_v by_o have_v their_o longitude_n and_o latitude_n or_o right_a ascension_n and_o declination_n for_o any_o set_a time_n place_z a_o mark_n for_o they_o on_o the_o globe_n either_o with_o ink_n if_o your_o globe_n be_v varnish_v for_o than_o you_o may_v with_o a_o wet_a finger_n wipe_v it_o off_o again_o or_o with_o black-lead_a if_o it_o be_v not_o varnish_v and_o then_o you_o may_v rub_v it_o out_o again_o with_o a_o little_a white_a bread_n which_o mark_v for_o that_o time_n will_v as_o effectual_o serve_v you_o to_o work_v by_o as_o any_o of_o the_o fix_a star_n place_v on_o the_o globe_n will_v do_v therefore_o if_o the_o longitude_n and_o latitude_n of_o any_o planet_n or_o comet_n be_v give_v do_v thus_o elevate_v the_o north_n pole_n if_o the_o latitude_n give_v be_v north_n but_o if_o the_o latitude_n give_v be_v south_n elevate_v the_o south_n pole_n 66_o ½_o degree_n and_o place_v the_o pole_n of_o the_o ecliptic_a in_o the_o zenith_n and_o over_o it_o screw_v the_o quadrant_n of_o altitude_n so_o shall_v the_o ecliptick_o in_o the_o horizon_n and_o the_o quadrant_n of_o altitude_n be_v turn_v about_o the_o horizon_n shall_v pass_v through_o all_o the_o degree_n of_o longitude_n then_o find_v the_o point_n of_o give_v longitude_n in_o the_o ecliptic_a and_o bring_v it_o to_o the_o quadrant_n of_o altitude_n and_o hold_v it_o there_o then_o count_v upward_o on_o the_o quadrant_n of_o altitude_n the_o number_n of_o degree_n and_o minute_n of_o give_v latitude_n and_o at_o the_o point_n where_o the_o number_n end_v close_o to_o the_o quadrant_n of_o altitude_n make_v a_o small_a prick_n and_o that_o prick_n shall_v represent_v the_o planet_n or_o comet_n you_o be_v to_o place_n on_o the_o globe_n if_o it_o be_v the_o right_a ascension_n and_o declination_n of_o a_o planet_n or_o comet_n that_o be_v give_v you_o must_v find_v the_o degree_n and_o minute_n of_o right_a ascension_n on_o the_o equinoctial_a and_o bring_v it_o to_o the_o meridian_n and_o keep_v the_o globe_n there_o steady_a then_o find_v the_o degree_n and_o minute_n of_o declination_n on_o the_o meridian_n and_o under_o that_o degree_n and_o minute_n on_o the_o globe_n make_v a_o prick_n and_o that_o prick_n shall_v represent_v the_o planet_n or_o comet_n as_o aforesaid_a if_o it_o be_v ♄_o or_o ♃_o that_o this_o prick_n be_v to_o represent_v it_o may_v stand_v on_o the_o globe_n sometime_o a_o week_n or_o a_o fortnight_n without_o much_o difference_n from_o the_o planet_n place_n in_o heaven_n but_o if_o the_o prick_n be_v to_o represent_v the_o other_o planet_n you_o must_v in_o regard_n of_o their_o swift_a motion_n alter_v it_o very_o often_o especial_o for_o the_o moon_n for_o so_o swift_a be_v her_o motion_n that_o in_o every_o two_o hour_n she_o alter_v about_o a_o degree_n in_o longitude_n have_v thus_o place_v this_o mark_n on_o the_o globe_n you_o may_v find_v out_o the_o time_n of_o its_o several_a position_n and_o aspect_n if_o you_o work_v by_o it_o as_o you_o be_v direct_v to_o work_v by_o the_o sun_n in_o the_o several_a respective_a problem_n throughout_o this_o book_n the_o end_n of_o the_o second_o book_n the_o three_o book_n be_v the_o practical_a use_n of_o the_o globe_n apply_v to_o the_o solution_n of_o problem_n in_o the_o art_n of_o navigation_n preface_n because_o the_o art_n of_o navigation_n consist_v aswell_o in_o the_o knowledge_n of_o astronomical_a and_o geographical_a problem_n as_o in_o problem_n mere_o nautical_a therefore_o i_o must_v desire_v the_o artist_n to_o seek_v in_o the_o last_o book_n such_o problem_n as_o be_v only_o astronomical_a or_o geographical_a for_o my_o design_n be_v here_o to_o collect_v such_o problem_n as_o be_v only_o use_v in_o the_o art_n of_o navigation_n some_o few_o particular_n except_v as_o for_o find_v latitude_n longitude_n course_n distance_n etc._n etc._n which_o though_o they_o be_v handle_v in_o than_o book_n yet_o for_o their_o exceed_a utility_n in_o the_o art_n of_o navigation_n and_o for_o that_o what_o there_o be_v give_v can_v always_o be_v have_v to_o work_v by_o therefore_o in_o this_o book_n i_o have_v mention_v divers_a other_o observation_n which_o be_v make_v or_o have_v you_o may_v by_o the_o rule_v proper_a for_o each_o observation_n find_v what_o shall_v be_v propose_v prob._n i._n the_o sun_n amplitude_n and_o difference_n of_o ascension_n give_v to_o find_v the_o height_n of_o the_o pole_n and_o declination_n of_o the_o sun_n elevate_v the_o pole_n so_o many_o degree_n as_o the_o difference_n of_o the_o sun_n ascension_n be_v and_o screw_v the_o quadrant_n of_o altitude_n to_o the_o zenith_n and_o bring_v the_o first_o point_n of_o ♈_o to_o the_o meridian_n than_o number_n on_o the_o quadrant_n of_o altitude_n upward_o the_o compliment_n to_o 90._o of_o the_o sun_n amplitude_n and_o move_v the_o quadrant_n of_o altitude_n till_o that_o number_n of_o degree_n cut_v the_o equator_fw-la so_o shall_v the_o quadrant_n cut_v in_o the_o horizon_n the_o degree_n of_o the_o pole_n elevation_n and_o in_o the_o equator_fw-la the_o degree_n of_o the_o sun_n declination_n example_n the_o difference_n of_o ascension_n be_v 27._o degree_n 7._o minute_n therefore_o i_o elevate_v the_o pole_n 27._o degree_n 7._o minute_n above_o the_o horizon_n and_o screw_v the_o quadrant_n of_o altitude_n to_o 27._o degree_n 7._o minute_n which_o be_v in_o the_o zenith_n then_o i_o bring_v the_o first_o point_n of_o ♈_o to_o the_o meridian_n and_o number_n on_o the_o quadrant_n of_o altitude_n upward_o 56._o degree_n 40._o minute_n the_o compliment_n of_o the_o sun_n amplitude_n and_o bring_v that_o degree_n to_o the_o equator_fw-la then_o i_o see_v in_o what_o degree_n of_o the_o horizon_n the_o quadrant_n cut_v the_o horizon_n and_o find_v 51_o ½_o which_o be_v the_o elevation_n of_o the_o pole_n then_o look_v in_o what_o degree_n of_o the_o equator_fw-la the_o quadrant_n of_o altitude_n cut_v the_o equator_fw-la i_o find_v 20_o degree_n 5_o min._n which_o be_v the_o declination_n of_o the_o sun_n at_o the_o same_o time_n prob._n ii_o the_o sun_n declination_n and_o amplitude_n give_v to_o find_v the_o pole_n elevation_n elevate_v the_o pole_n so_o many_o degree_n as_o the_o compliment_n of_o the_o sun_n amplitude_n be_v and_o screw_v the_o quadrant_n of_o altitude_n
opposite_a to_o the_o degree_n of_o declination_n find_v before_o the_o meridian_n line_n on_o the_o globe_n as_o before_o shall_v cut_v the_o quadrant_n of_o altitude_n in_o the_o number_n of_o degree_n count_v downward_o that_o each_o hour-line_n be_v distant_a from_o the_o other_o side_n the_o noon-line_n and_o line_n draw_v from_o the_o centre_n of_o that_o circle_n through_o those_o degree_n shall_v be_v the_o hour-line_n of_o the_o other_o half_a of_o the_o day_n if_o your_o plane_n decline_v and_o also_o recline_v or_o incline_v you_o must_v use_v the_o gnomonical_a semicircle_n describe_v in_o prob._n 12_o which_o must_v be_v elevate_v on_o the_o quadrant_n of_o altitude_n when_o it_o be_v set_v to_o the_o declination_n as_o by_o the_o former_a rule_n according_a to_o the_o compliment_n of_o reclination_n or_o inclination_n but_o if_o your_o plane_n be_v direct_a and_o recline_v or_o incline_v it_o must_v be_v set_v to_o the_o meridian_n and_o the_o meridian_n on_o the_o 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