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same_o time_n as_o the_o sun_n the_o last_o be_v the_o moon_n make_v one_o perfect_a revolution_n from_o west_n towards_o east_n in_o 27._o day_n 7._o hour_n 43′_n 7″_n yet_o all_o these_o be_v carry_v by_o violence_n of_o the_o first_o movable_a from_o east_n to_o west_n as_o be_v before_o say_v of_o the_o circle_n of_o the_o sphere_n of_o heaven_n and_o of_o their_o name_n and_o how_o they_o be_v make_v astronomer_n to_o the_o end_n they_o may_v show_v the_o motion_n of_o heaven_n and_o the_o strange_a and_o wonderful_a conclusion_n of_o the_o celestial_a body_n have_v imagine_v certain_a circle_n in_o the_o body_n of_o the_o first_o sphere_n or_o first_o mooveable_a and_o principal_o ten_o whereof_o some_o be_v great_a circle_n of_o the_o sphere_n so_o call_v because_o the_o centre_n of_o these_o circle_n be_v also_o the_o centre_n of_o heaven_n &_o every_o such_o circle_n divide_v the_o whole_a sphere_n into_o two_o equal_a part_n of_o this_o sort_n be_v six_o the_o aequinoctial_a 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circle_n or_o line_n for_o that_o that_o when_o the_o sun_n and_o moon_n be_v both_o under_o this_o line_n in_o a_o diameter_n then_o the_o moon_n be_v eclipse_v under_o this_o circle_n the_o sun_n move_v daily_o without_o decline_v any_o way_n the_o quantity_n of_o one_o degree_n very_o near_o in_o each_o day_n the_o rest_n of_o the_o planet_n be_v find_v some_o time_n on_o one_o side_n the_o ecliptic_a &_o some_o time_n on_o the_o other_o this_o zodiac_n take_v his_o name_n of_o a_o greek_a word_n signify_v a_o live_a creature_n or_o as_o the_o latens_fw-la will_n be_v call_v signifer_fw-la for_o that_o that_o it_o bear_v the_o 12._o sign_n the_o axe_n of_o the_o zodiac_n and_o the_o ecliptic_a be_v all_o one_o be_v a_o line_n diverse_a from_o the_o axe_n of_o the_o world_n and_o the_o pole_n be_v two_o point_n always_o so_o much_o distant_a from_o the_o pole_n of_o the_o world_n as_o the_o great_a declination_n of_o the_o ecliptic_a come_v unto_o a_o colour_n do_v general_o signify_v any_o circle_n pass_v by_o the_o pole_n of_o the_o world_n and_o have_v his_o name_n of_o his_o unperfect_a show_v himself_o in_o the_o motion_n of_o heaven_n but_o now_o by_o the_o name_n of_o colour_n we_o understand_v two_o great_a circle_n the_o one_o go_v from_o the_o pole_n of_o the_o world_n by_o the_o point_n where_o the_o aequinoctial_a and_o zodiac_n cut_v themselves_o which_o be_v call_v the_o aequinoctial_a point_n and_o be_v call_v the_o aequinoctial_a colour_n the_o other_o pass_v from_o the_o pole_n of_o the_o world_n by_o those_o point_n of_o the_o ecliptic_a which_z swerve_v most_o of_o all_o other_o from_o the_o aequinoctial_a line_n which_o point_n be_v call_v the_o solsticiall_a point_n and_o this_o be_v call_v the_o solsticial_a colour_n and_o here_o be_v you_o to_o know_v that_o these_o four_o great_a circle_n which_o we_o have_v define_v be_v still_o the_o same_o through_o the_o whole_a world_n and_o be_v say_v to_o be_v movable_a circle_n for_o so_o much_o as_o in_o the_o motion_n of_o heaven_n they_o be_v also_o move_v of_o which_o some_o be_v movable_a perfect_o as_o the_o aequinoctial_a and_o zodiac_n for_o they_o in_o the_o go_n about_o of_o heaven_n do_v ascend_v by_o little_a and_o little_a till_o the_o whole_a circle_n have_v go_v our_o the_o horizon_n some_o unperfect_o movable_a as_o the_o two_o colour_n which_o never_o show_v the_o whole_a circle_n in_o any_o crooked_a sphere_n the_o other_o two_o great_a circle_n which_o follow_v be_v call_v fix_v for_o that_o they_o never_o move_v by_o the_o motion_n of_o heaven_n but_o they_o be_v changeable_a in_o every_o region_n the_o horizon_n be_v a_o great_a circle_n divide_v the_o half_a of_o the_o heaven_n which_o we_o see_v from_o the_o half_n which_o we_o see_v not_o and_o be_v call_v in_o latin_a finitor_n because_o it_o end_v our_o sight_n the_o horizon_n make_v four_o principal_a point_n east_n west_n north_n and_o south_n his_o axe_n be_v a_o line_n imagine_v to_o fall_v from_o the_o point_n of_o heaven_n which_o be_v direct_o over_o our_o head_n where_o we_o be_v down_o to_o the_o ground_n like_o a_o plum_n line_n and_o his_o pole_n be_v the_o end_n of_o that_o line_n call_v the_o vertical_a point_n and_o point_v opposite_a to_o the_o vertical_a the_o meridian_n be_v also_o a_o great_a circle_n pass_v from_o the_o pole_n of_o the_o world_n by_o our_o vertical_a point_n cut_v the_o horizon_n in_o the_o north_n and_o south_n point_v his_o axe_n be_v a_o line_n go_v from_o the_o east_n point_n of_o the_o horizon_n to_o the_o west_n and_o his_o pole_n be_v the_o same_o point_n and_o these_o two_o circle_n do_v always_o change_v &_o be_v diverse_a in_o every_o region_n for_o so_o much_o as_o the_o vertical_a point_n of_o every_o region_n be_v diverse_a by_o the_o which_o the_o meridian_n of_o necessity_n must_v pass_v and_o be_v the_o pole_n also_o of_o the_o horizon_n of_o the_o lesser_a circle_n of_o the_o sphere_n and_o their_o name_n and_o of_o their_o make_n the_o less_o circle_n of_o the_o sphere_n in_o number_n be_v four_o the_o tropic_n of_o cancer_n the_o tropic_n of_o capricorn_n and_o the_o two_o articke_n the_o tropic_n of_o cancer_n be_v a_o less_o circle_n of_o the_o sphere_n which_o be_v equal_o distant_a from_o the_o aequinoctial_a lie_v betwixt_o the_o aequinoctial_a and_o the_o north_n pole_n and_o touch_v the_o ecliptic_a in_o the_o begin_n of_o cancer_n this_o circle_n be_v describe_v by_o the_o body_n of_o the_o sun_n in_o the_o long_a day_n of_o summer_n at_o which_o time_n the_o sun_n be_v enter_v the_o solstitial_a point_n or_o beginning_n of_o cancer_n &_o be_v call_v the_o tropic_a of_o a_o greek_a word_n which_o signify_v a_o return_v because_o the_o sun_n be_v bring_v to_o this_o point_n fall_v in_o his_o noon_n height_n and_o return_v again_o the_o tropic_n of_o capricorn_n be_v a_o like_a circle_n betwixt_o the_o aequator_fw-la &_o the_o south_n pole_n and_o be_v describe_v by_o the_o sun_n in_o the_o short_a day_n of_o winter_n at_o which_o time_n the_o sun_n be_v in_o the_o beginning_n of_o capricorn_n whereof_o it_o be_v call_v the_o tropic_a of_o capricorn_n the_o arctic_a circle_n be_v a_o less_o circle_n of_o the_o sphere_n describe_v by_o the_o northern_a pole_n of_o the_o ecliptic_a proclus_n say_v it_o be_v describe_v by_o the_o foremost_a foot_n of_o the_o great_a bear_n and_o thereof_o take_v his_o name_n the_o antarctic_a be_v a_o like_a circle_n describe_v by_o the_o south_n pole_n of_o the_o ecliptic_a &_o be_v call_v antarctic_a of_o the_o greek_a word_n which_o signify_v opposition_n because_o it_o be_v opposite_a to_o the_o other_o of_o the_o use_n of_o the_o circle_n of_o the_o sphere_n or_o globle_a the_o most_o
his_o index_n stand_v on_o the_o hour_n which_o be_v know_v before_o then_o fix_v the_o globe_n for_o remove_v last_o turn_v your_o quadrant_n of_o altitude_n to_o the_o ecliptic_a line_n and_o look_v what_o degree_n of_o the_o ecliptic_a agree_v in_o your_o quadrant_n with_o the_o height_n that_o be_v before_o know_v and_o that_o be_v the_o place_n of_o the_o sun_n on_o that_o day_n propositio_fw-la 20._o the_o hour_n and_o place_n of_o the_o sun_n be_v give_v to_o find_v how_o far_o the_o sun_n be_v go_v from_o the_o true_a east_n point_n the_o place_n of_o the_o sun_n be_v give_v by_o supposition_n 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 index_n show_v the_o hour_n give_v this_o be_v do_v fix_v the_o globe_n that_o he_o move_v not_o away_o and_o set_v the_o edge_n of_o the_o quadrant_n of_o altitude_n to_o the_o place_n of_o the_o sun_n and_o withal_o mark_v how_o many_o degree_n of_o the_o horizon_n be_v enclose_v betwixt_o the_o true_a east_n point_n and_o the_o edge_n of_o the_o quadrant_n at_o such_o time_n as_o he_o stand_v on_o the_o place_n of_o the_o sun_n for_o so_o much_o be_v he_o distant_a in_o the_o horizon_n from_o true_a east_n propositio_fw-la 21._o the_o distance_n of_o the_o sun_n be_v give_v from_o true_a east_n together_o with_o his_o height_n at_o the_o same_o time_n and_o the_o height_n of_o the_o pole_n for_o the_o same_o region_n to_o find_v the_o true_a place_n of_o the_o sun_n at_o any_o time_n to_o the_o end_n we_o make_v not_o unnecessary_a repetition_n of_o the_o first_o principle_n know_v this_o that_o in_o all_o the_o proposition_n follow_v we_o always_o suppose_v before_o the_o work_n the_o globe_n right_o rectify_v as_o be_v specify_v in_o the_o beginning_n for_o the_o performance_n therefore_o of_o this_o practice_n first_o consider_v diligent_o in_o what_o quarter_n of_o the_o year_n you_o be_v in_o that_o be_v whether_o it_o be_v betwixt_o the_o equinoctial_a of_o march_n and_o height_n of_o summer_n or_o betwixt_o height_n of_o summer_n and_o aequinoctial_a of_o september_n likewise_o whether_o betwixt_o aequinoctial_a of_o september_n and_o dept_z of_o winter_n or_o betwixt_o dept_z of_o winter_n and_o equinoctial_a of_o march._n for_o then_o set_v the_o edge_n of_o the_o quadrant_a of_o altitude_n at_o the_o true_a distance_n of_o the_o sun_n from_o the_o east_n and_o turn_v the_o globe_n till_o that_o quarter_n of_o the_o ecliptic_a come_v under_o he_o which_o serve_v for_o the_o quarter_n of_o the_o year_n in_o which_o you_o be_v and_o see_v what_o degree_n of_o that_o part_n of_o the_o ecliptic_a agree_v with_o the_o height_n propose_v for_o that_o be_v the_o place_n of_o the_o sun_n at_o that_o time_n note_v therefore_o here_o that_o to_o the_o spring_n which_o be_v from_o the_o equinoctial_a of_o march_n till_o the_o height_n of_o summer_n answer_v the_o part_n of_o the_o zodiac_n from_o aries_n to_o cancer_n to_o summer_n which_o be_v from_o the_o height_n till_o the_o equinoctial_a of_o september_n answer_v the_o part_n from_o cancer_n to_o libra_n the_o autumn_n be_v guide_v by_o the_o quarter_n from_o libra_n to_o capricorn_n and_o winter_n by_o the_o sign_n from_o capricorn_n to_o aries_n propositio_fw-la 22._o the_o distance_n of_o the_o sun_n be_v give_v from_o true_a east_n and_o the_o place_n of_o the_o same_o to_o find_v the_o height_n of_o the_o sun_n which_o he_o have_v at_o the_o same_o time_n place_v the_o quadrant_a of_o altitude_n at_o the_o true_a distance_n from_o east_n so_o shall_v he_o cut_v the_o place_n of_o the_o sun_n by_o the_o 21._o proposition_n and_o therefore_o the_o portion_n of_o the_o quadrant_n betwixt_o the_o place_n of_o the_o sun_n and_o the_o horizon_n be_v his_o height_n propositio_fw-la 23._o the_o distance_n of_o the_o sun_n from_o true_a east_n be_v give_v and_o his_o place_n to_o find_v the_o hour_n of_o the_o day_n first_o have_v his_o place_n rectify_v your_o index_n by_o the_o 14._o proposition_n again_o set_v the_o quadrant_n of_o altitude_n in_o the_o distance_n from_o true_a east_n reduce_v the_o place_n of_o the_o sun_n till_o he_o fall_v in_o the_o edge_n of_o the_o quadrant_n for_o then_o the_o index_n do_v show_v the_o hour_n propositio_fw-la 24._o the_o distance_n of_o the_o sun_n be_v give_v from_o true_a east_n and_o his_o height_n to_o find_v the_o time_n of_o his_o rise_n the_o distance_n be_v give_v find_v his_o place_n by_o the_o 21_o proposition_n and_o then_o rectify_v the_o index_n by_o the_o 14_o proposition_n last_o put_v the_o place_n of_o the_o sun_n to_o the_o east_n side_n of_o the_o horizon_n for_o then_o the_o index_n will_v show_v the_o sun_n rise_v propositio_fw-la 25._o the_o distance_n of_o the_o sun_n be_v give_v from_o true_a east_n and_o his_o height_n to_o find_v his_o declination_n the_o distance_n be_v give_v his_o place_n be_v find_v by_o the_o 21._o proposition_n &_o his_o place_n be_v know_v give_v his_o declination_n by_o the_o 6._o proposition_n so_o may_v we_o likewise_o by_o the_o say_a distance_n find_v his_o place_n find_v his_o right_n or_o crooked_a ascension_n or_o difference_n of_o ascension_n and_o length_n of_o artificial_a day_n propositio_fw-la 26._o the_o declination_n of_o the_o sun_n be_v know_v to_o find_v the_o place_n of_o the_o sun_n consider_v first_o diligent_o in_o what_o quarter_n of_o the_o year_n you_o be_v in_o as_o be_v express_v before_o then_o take_v that_o quarter_n of_o the_o ecliptic_a which_o answer_v to_o your_o quarter_n of_o the_o year_n and_o move_v it_o still_o under_o the_o meridian_n of_o your_o globe_n till_o you_o find_v no_o more_o of_o the_o meridian_n enclose_v betwixt_o the_o aequator_fw-la and_o ecliptic_a than_o the_o declination_n that_o be_v give_v come_v unto_o for_o then_o look_v what_o degree_n of_o the_o ecliptic_a be_v under_o the_o meridian_n that_o be_v the_o place_n of_o the_o sun_n as_o the_o declination_n of_o the_o sun_n in_o the_o quarter_n of_o the_o year_n betwixt_o the_o aequinoctial_a of_o march_n and_o height_n of_o summer_n be_v give_v to_o be_v 11._o degree_n 50._o minute_n and_o to_o this_o quarter_n of_o the_o year_n answer_v the_o quarter_n of_o the_o ecliptic_a from_o aries_n to_o cancer_n therefore_o move_v the_o say_a quarter_n under_o the_o meridian_n i_o find_v the_o first_o of_o taurus_n to_o answer_v to_o this_o declination_n and_o therefore_o that_o be_v the_o place_n of_o the_o sun_n propositio_fw-la 27._o the_o declination_n of_o the_o sun_n be_v know_v to_o find_v the_o day_n of_o the_o month_n by_o the_o declination_n give_v find_v the_o place_n of_o the_o sun_n by_o the_o 26._o proposition_n they_o take_v the_o say_a place_n in_o the_o horizon_n of_o your_o globe_n for_o look_v what_o day_n answer_v against_o it_o that_o be_v the_o day_n of_o the_o month_n propositio_fw-la 28._o the_o day_n of_o the_o month_n be_v know_v to_o find_v the_o length_n of_o the_o planetary_a hour_n the_o artificial_a day_n be_v from_o sun_n rise_v to_o sun_n set_v and_o the_o 12._o part_n of_o this_o day_n whether_o it_o be_v long_o or_o short_a than_o a_o hour_n by_o the_o clock_n be_v the_o planetary_a hour_n and_o may_v thus_o be_v know_v the_o day_n be_v giâ—en_o find_v the_o length_n of_o that_o day_n by_o the_o 10._o proposition_n and_o divide_v all_o by_o 12._o the_o quotient_n be_v the_o length_n of_o a_o planetary_a or_o artificial_a hour_n of_o that_o day_n as_o the_o day_n be_v 15._o hour_n by_o the_o clock_n i_o divide_v it_o by_o 12._o the_o quotient_n be_v one_o hour_n and_o a_o quarter_n and_o so_o much_o be_v a_o planetary_a hour_n of_o that_o day_n propositio_fw-la 29._o the_o day_n of_o the_o month_n be_v give_v to_o find_v the_o dawn_n of_o the_o day_n by_o the_o day_n know_v find_v the_o place_n of_o the_o sun_n by_o the_o 5._o proposition_n and_o then_o rectify_v your_o index_n by_o the_o 14._o proposition_n again_o take_v the_o degree_n of_o the_o ecliptic_a 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