ecliptic_a which_o be_v so_o under_o the_o circle_n shall_v be_v call_v the_o place_n of_o that_o star_n and_o the_o star_n be_v say_v to_o be_v under_o that_o sign_n of_o who_o the_o aforesaid_a point_n be_v a_o part_n the_o longitude_n may_v also_o be_v take_v if_o you_o do_v but_o fix_v the_o quadrant_n of_o altitude_n in_o the_o pole_n of_o the_o ecliptic_a and_o stir_v not_o at_o all_o the_o meridian_n circle_n propositio_fw-la 39_o to_o find_v the_o latitude_n of_o any_o star_n the_o latitude_n of_o a_o star_n be_v the_o portion_n of_o the_o circle_n that_o pass_v from_o the_o pole_n of_o the_o ecliptic_a line_n by_o the_o centre_n of_o any_o star_n which_o be_v enclose_v betwixt_o the_o ecliptic_a line_n and_o the_o centre_n of_o the_o star_n and_o be_v find_v thus_o your_o circle_n stand_v in_o the_o pole_n of_o the_o zodiac_n as_o before_o turn_v the_o star_n under_o the_o say_a circle_n for_o then_o the_o portion_n of_o that_o circle_n betwixt_o the_o star_n and_o the_o ecliptic_a be_v his_o latitude_n and_o this_o latitude_n be_v northern_a when_o the_o star_n be_v north_n from_o the_o ecliptic_a and_o southern_a of_o contrary_n propositio_fw-la 40._o to_o find_v what_o star_n be_v above_o ground_n at_o any_o time_n of_o the_o day_n or_o night_n if_o you_o will_v know_v it_o in_o the_o day_n time_n when_o the_o sun_n shine_v then_o take_v the_o height_n of_o the_o sun_n by_o the_o 2._o proposition_n afterward_o find_v his_o place_n by_o the_o 5._o proposition_n last_o by_o help_n of_o the_o quadrant_n of_o altitude_n set_v the_o sun_n at_o his_o own_o height_n &_o coast_n and_o then_o all_o the_o star_n above_o the_o horizon_n do_v appear_v in_o the_o globe_n now_o if_o it_o be_v in_o the_o night_n and_o the_o star_n appear_v then_o take_v the_o height_n of_o some_o know_a star_n and_o place_v the_o same_o star_n at_o his_o due_a height_n in_o the_o globe_n so_o shall_v you_o see_v the_o same_o propositio_fw-la 41._o to_o do_v the_o same_o without_o sun_n or_o appearance_n of_o any_o star_n you_o must_v know_v what_o it_o be_v of_o the_o clock_n at_o that_o time_n when_o you_o will_v work_v this_o conclusion_n then_o rectify_v the_o index_n by_o the_o 14._o proposition_n last_o turn_v the_o globe_n till_o the_o index_n come_v on_o the_o same_o hour_n as_o be_v give_v by_o the_o clock_n for_o then_o the_o star_n appear_v as_o they_o shall_v propositio_fw-la 42._o to_o find_v what_o star_n will_v pass_v direct_o over_o our_o head_n in_o the_o motion_n of_o the_o heaven_n after_o that_o the_o quadrant_n of_o altitude_n be_v fix_v in_o his_o due_a place_n as_o be_v speak_v of_o before_o so_o that_o he_o now_o do_v show_v the_o zenith_n or_o vertical_a point_n then_o move_v about_o the_o globe_n and_o mark_v what_o star_n pass_v under_o the_o zenith_n in_o this_o motion_n for_o those_o be_v such_o as_o go_v by_o our_o head_n &_o be_v call_v sometime_o culminant_a star_n sometime_o vertical_a star_n and_o have_v their_o chief_a use_n in_o astrology_n propositio_fw-la 43._o to_o know_v with_o what_o degree_n of_o the_o ecliptic_a any_o star_n rise_v come_v to_o the_o meridian_n or_o set_v move_v the_o globe_n till_o the_o star_n who_o you_o propose_v ascend_v above_o the_o horizon_n and_o then_o mark_v the_o degree_n of_o the_o ecliptic_a that_o rise_v with_o he_o again_o move_v he_o to_o the_o meridian_n and_o mark_v the_o degree_n of_o the_o ecliptic_a so_o do_v by_o he_o in_o the_o west_n side_n of_o the_o horizon_n and_o you_o shall_v have_v your_o intent_n propositio_fw-la 44._o to_o know_v the_o hour_n of_o any_o star_n rise_v rectify_v the_o index_n by_o the_o 14._o proposition_n then_o turn_v the_o globe_n till_o the_o say_a star_n who_o time_n of_o rise_v you_o desire_v touch_v the_o east_n side_n of_o the_o horizon_n for_o then_o the_o index_n give_v his_o time_n of_o rise_v and_o if_o you_o turn_v he_o to_o the_o meridian_n the_o index_n will_v show_v his_o time_n of_o come_v the_o there_o or_o if_o you_o turn_v he_o to_o the_o west_n side_n of_o the_o horizon_n the_o index_n show_v his_o set_n propositio_fw-la 45._o to_o find_v in_o how_o long_a time_n any_o whole_a sign_n arise_v rectify_v the_o index_n by_o the_o fowerteenth_fw-mi proposition_n then_o put_v the_o beginning_n of_o the_o sign_n who_o time_n of_o rise_v you_o seek_v to_o the_o east_n part_n of_o the_o horizon_n and_o mark_v what_o the_o index_n stand_v on_o then_o again_o put_v the_o last_o degree_n of_o the_o say_a sign_n to_o the_o horizon_n and_o see_v what_o the_o index_n show_v for_o the_o difference_n of_o the_o two_o time_n by_o the_o index_n be_v the_o time_n in_o which_o that_o sign_n rise_v propositio_fw-la 46._o to_o find_v in_o what_o coast_n any_o star_n be_v and_o how_o many_o degree_n from_o the_o meridian_n find_v the_o star_n above_o ground_n by_o the_o 40._o proposition_n then_o the_o globe_n be_v fix_v put_v the_o quadrant_n of_o altitude_n to_o any_o state_n then_o shall_v the_o foot_n of_o the_o quadrant_n show_v in_o the_o horizon_n how_o far_o the_o same_o star_n be_v from_o east_n west_n north_n or_o south_n but_o if_o you_o first_o rectify_v your_o index_n by_o the_o 14._o proposition_n and_o then_o find_v the_o star_n above_o by_o the_o 40._o proposition_n again_o at_o the_o same_o time_n mark_v where_o the_o index_n stand_v last_o put_v any_o star_n under_o the_o meridian_n and_o again_o note_v the_o stand_n of_o the_o index_n the_o difference_n of_o those_o two_o time_n show_v by_o the_o index_n be_v the_o distance_n of_o that_o star_n from_o the_o meridian_n in_o the_o time_n of_o your_o observation_n propositio_fw-la 47._o to_o find_v what_o star_n rise_v or_o set_v any_o day_n cosmical_o achronical_o or_o helical_o such_o star_n as_o be_v near_o to_o the_o sun_n in_o any_o day_n and_o ascend_v above_o the_o horizon_n a_o little_a before_o the_o appearance_n of_o the_o same_o be_v say_v to_o rise_v helical_o and_o such_o star_n as_o set_v very_o little_a after_o the_o 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question_n and_o be_v thus_o know_v if_o you_o seek_v they_o in_o the_o day_n the_o sun_n shine_v then_o find_v the_o star_n above_o ground_n by_o the_o 40._o proposition_n and_o with_o all_o mark_n the_o degree_n of_o the_o ecliptic_a in_o the_o east_n so_o likewise_o in_o the_o south_n west_n and_o north_n for_o those_o be_v then_o the_o cardinal_n point_v again_o if_o it_o be_v in_o the_o night_n then_o find_v the_o star_n above_o by_o the_o same_o 40._o proposition_n and_o the_o point_n shall_v likewise_o appear_v last_o if_o nether_a the_o sun_n shine_v or_o star_n then_o know_v the_o hour_n by_o the_o clock_n and_o afterward_o find_v the_o star_n
above_o ground_n at_o the_o say_a hour_n by_o the_o 41._o proposition_n so_o shall_v the_o point_n be_v give_v as_o before_o propositio_fw-la 50._o to_o find_v the_o bigness_n of_o the_o angle_n make_v betwixt_o the_o meridian_n circle_n and_o any_o circle_n of_o position_n circle_n of_o position_n be_v all_o such_o as_o be_v draw_v from_o the_o north_n point_n of_o any_o horizon_n by_o the_o centre_n of_o any_o star_n and_o so_o to_o go_v to_o the_o south_n point_n of_o the_o same_o horizon_n to_o return_v to_o the_o north_n again_o and_o every_o one_o of_o these_o circle_n do_v make_v some_o with_o the_o meridian_n and_o the_o say_a angle_n have_v his_o bigness_n show_v by_o a_o portion_n of_o the_o fix_a vertical_a so_o that_o to_o find_v the_o bigness_n of_o the_o angle_n make_v betwixt_o the_o meridian_n and_o any_o circle_n of_o position_n be_v to_o find_v the_o portion_n of_o the_o fix_a vertical_a enclose_v betwixt_o the_o meridian_n and_o the_o say_a circle_n of_o position_n 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enclose_v in_o each_o space_n &_o to_o do_v it_o we_o thus_o proceed_v first_o find_v out_o the_o four_o cardinal_n point_n by_o the_o 49._o proposition_n for_o those_o be_v the_o beginning_n of_o 4._o howsen_z of_o the_o twelve_o the_o cardinal_n point_n under_o the_o meridian_n above_o ground_n be_v the_o begin_n of_o the_o ten_o house_n this_o do_v fix_v the_o globe_n then_o reckon_v from_o the_o degree_n of_o the_o aequator_fw-la be_v then_o under_o the_o meridian_n 30._o degree_n towards_o the_o east_n point_n &_o raise_v up_o your_o brass_n half_a circle_n to_o stand_v on_o the_o point_n of_o the_o aequator_fw-la on_o which_o you_o leave_v for_o look_v then_o what_o degree_n of_o the_o ecliptic_a be_v cut_v then_o by_o the_o brass_n half_a circle_n the_o same_o be_v the_o end_n of_o the_o ten_o house_n and_o beginning_n of_o the_o eleven_o again_o yet_o reckon_v 30._o degree_n more_o in_o the_o aequator_fw-la towards_o the_o east_n and_o put_v the_o brass_n half_a circle_n to_o 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proposition_n then_o subduce_v the_o less_o from_o the_o great_a for_o the_o remain_v be_v the_o difference_n of_o ascension_n propositio_fw-la 10._o to_o find_v the_o length_n of_o the_o artificial_a day_n in_o any_o region_n or_o country_n find_v out_o the_o difference_n of_o ascension_n of_o the_o place_n of_o the_o sun_n by_o the_o 9_o proposition_n and_o double_a the_o same_o then_o convert_n be_v all_o into_o hour_n and_o part_n of_o hour_n allow_v for_o one_o hour_n 15._o degree_n and_o for_o a_o half_a 7._o degree_n 30._o minute_n etc._n etc._n this_o time_n which_o come_v of_o the_o difference_n of_o ascension_n add_v to_o 12._o hour_n if_o the_o place_n of_o the_o sun_n be_v any_o degree_n betwixt_o aries_n and_o libra_n or_o subduct_v it_o from_o 12._o if_o he_o be_v betwixt_o libra_n and_o aries_n for_o the_o number_n make_v or_o leave_v be_v the_o length_n of_o the_o day_n as_o the_o sun_n be_v in_o the_o first_o of_o tanrus_n his_o difference_n of_o ascension_n be_v 15._o degree_n 6._o minute_n this_o double_a and_o convert_v into_o time_n make_v 2._o hour_n and_o 12._o aequinoctial_a minute_n and_o because_o tanrus_n be_v a_o northern_a sign_n you_o must_v add_v this_o difference_n to_o 12._o hour_n so_o do_v you_o make_v 14._o hour_n and_o 12._o aequinoctial_a minute_n for_o the_o length_n of_o that_o whole_a day_n propositio_fw-la 11._o to_o find_v the_o hour_n of_o the_o sun_n rise_v or_o of_o his_o set_n know_v the_o length_n of_o the_o artificial_a day_n by_o the_o 10._o proposition_n and_o take_v half_a of_o the_o same_o day_n for_o that_o show_v the_o hour_n of_o sun_n set_v but_o if_o you_o reckon_v so_o much_o from_o noon_n forward_o it_o give_v sun_n rise_v as_o the_o sun_n be_v in_o the_o first_o of_o taurus_n the_o day_n be_v 14._o hour_n and_o 12._o minute_n the_o half_a be_v 7._o hour_n and_o 6._o minute_n i_o say_v then_o the_o sun_n set_v after_o 7._o of_o the_o clock_n 6._o minute_n again_o thus_o much_o take_v from_o noon_n forward_o 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