the_o east_n semicircle_n of_o the_o horizon_n see_v how_o many_o hour_n the_o index_n pass_v over_o in_o the_o houre-circle_n for_o so_o many_o hour_n long_o be_v the_o night_n as_o for_o example_n suppose_v the_o sun_n to_o be_v as_o before_o in_o the_o 10._o degree_n of_o taurus_n bring_v the_o same_o degree_n to_o the_o east_n part_n of_o the_o horizon_n and_o the_o point_n of_o the_o index_n to_o the_o meridian_n then_o turn_v about_o the_o sphere_n till_o the_o same_o degree_n come_v to_o the_o west_n part_n of_o the_o horizon_n you_o shall_v find_v that_o in_o the_o mean_a time_n the_o point_n of_o the_o index_n shall_v pass_v over_o 14._o hour_n and_o 24._o minute_n which_o be_v the_o length_n of_o the_o day_n likewise_o if_o you_o bring_v the_o same_o 10._o degr_n of_o taurus_n to_o the_o west_n part_n of_o the_o horizon_n and_o the_o index_n to_o the_o meridian_n and_o turn_v about_o the_o sphere_n till_o that_o degree_n come_v to_o the_o east_n semicircle_n of_o the_o horizon_n the_o number_n of_o hour_n that_o the_o index_n run_v over_o in_o the_o mean_a time_n upon_o the_o hour_n circle_n shall_v be_v find_v to_o be_v 9_o degree_n and_o 36._o minute_n prop._n xi_o to_o know_v the_o meridian_n altitude_n or_o the_o height_n of_o the_o sun_n at_o noon_n for_o any_o time_n and_o place_n set_v the_o sphere_n to_o the_o latitude_n of_o the_o place_n where_o you_o desire_v to_o know_v the_o sun_n height_n at_o noon_n bring_v the_o place_n of_o the_o sun_n be_v find_v as_o before_o by_o the_o 2._o prop._n to_o the_o meridian_n then_o see_v how_o many_o degree_n of_o the_o meridian_n be_v contain_v between_o the_o horizon_n and_o the_o place_n of_o the_o sun_n for_o so_o much_o be_v the_o height_n of_o the_o sun_n at_o noon_n in_o like_a sort_n it_o may_v be_v know_v how_o much_o the_o sun_n be_v under_o the_o horizon_n at_o midnight_n after_o this_o manner_n bring_v the_o place_n of_o the_o sun_n in_o the_o zodiac_n to_o the_o meridian_n under_o the_o 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degree_n and_o a_o half_a at_o london_n prop._n xii_o to_o know_v how_o high_a the_o sun_n be_v above_o the_o horizon_n at_o any_o time_n of_o the_o day_n bring_v the_o place_n of_o the_o sun_n find_v by_o the_o 2._o prop._n to_o the_o meridian_n set_v the_o hour_n index_n to_o 12._o a_o clock_n upon_o the_o hour_n circle_n turn_v the_o sphere_n about_o till_o the_o index_n come_v to_o the_o hour_n at_o which_o you_o desire_v to_o know_v the_o height_n of_o the_o sun_n above_o the_o horizon_n take_v the_o distance_n of_o the_o place_n of_o the_o sun_n from_o the_o horizon_n with_o a_o large_a pair_n of_o compass_n then_o set_v both_o foot_n of_o the_o compass_n in_o the_o ecliptic_a and_o look_v how_o many_o degree_n be_v contain_v between_o they_o for_o so_o much_o be_v the_o height_n of_o the_o sun_n thus_o may_v you_o find_v by_o the_o sphere_n that_o when_o the_o sun_n be_v in_o the_o ten_o degree_n of_o taurus_n his_o height_n at_o 10._o of_o the_o clock_n in_o the_o forenoon_n the_o sphere_n be_v due_o rectify_v by_o the_o first_o proposition_n shall_v be_v about_o 45._o degree_n and_o a_o half_a at_o london_n prop._n xiii_o to_o find_v the_o hour_n of_o the_o day_n by_o the_o height_n of_o the_o sun_n etc._n etc._n set_v the_o pole_n arctic_a of_o the_o sphere_n to_o his_o elevation_n for_o that_o place_n where_o you_o desire_v to_o know_v the_o hour_n of_o the_o day_n bring_v the_o place_n of_o the_o sun_n in_o the_o zodiac_n to_o the_o meridian_n and_o the_o hour_n index_n to_o 12._o a_o clock_n of_o the_o hour_n circle_n take_v so_o many_o degree_n of_o the_o ecliptic_a between_o the_o foot_n of_o your_o compass_n as_o the_o height_n of_o the_o sun_n amount_v unto_o then_o set_v one_o foot_n of_o your_o compass_n in_o the_o place_n of_o the_o sun_n and_o turn_v the_o sphere_n about_o eastward_n if_o it_o be_v in_o the_o forenoon_n or_o westward_n if_o in_o the_o afternoon_n till_o you_o can_v but_o only_o touch_v the_o horizon_n with_o the_o other_o foot_n of_o your_o compass_n for_o then_o the_o index_n point_v out_o the_o hour_n of_o the_o day_n in_o the_o hour_n circle_n as_o suppose_v you_o observe_v the_o height_n of_o the_o sun_n be_v in_o the_o 10._o degr_n of_o taurus_n and_o find_v he_o to_o be_v 30._o degree_n high_a in_o the_o forenoon_n you_o shall_v find_v follow_v the_o direction_n prescribe_v in_o this_o proposition_n that_o it_o shall_v then_o be_v about_o 8._o of_o the_o clock_n in_o the_o morning_n prop._n xiiii_o to_o find_v the_o amplitude_n or_o breadth_n of_o the_o sun_n rise_v or_o set_v etc._n etc._n the_o pole_n of_o the_o sphere_n be_v set_v to_o his_o elevation_n and_o the_o place_n of_o the_o sun_n to_o the_o east_n semicircle_n of_o the_o horizon_n see_v how_o many_o degree_n of_o the_o horizon_n be_v contain_v between_o the_o place_n of_o the_o sun_n and_o the_o true_a east_n point_n for_o so_o you_o shall_v have_v the_o breadth_n of_o the_o sun_n rise_n thus_o the_o sun_n be_v in_o the_o 10._o degree_n of_o taurus_n you_o shall_v find_v by_o the_o sphere_n that_o for_o the_o latitude_n of_o london_n he_o rise_v about_o 23._o degr_n and_o a_o half_a northwards_o from_o the_o true_a east_n point_n and_o that_o he_o set_v as_o many_o degree_n towards_o the_o north_n from_o the_o true_a west_n point_n prop._n xv._n to_o find_v the_o place_n of_o the_o sun_n etc._n etc._n the_o quarter_n of_o the_o year_n be_v know_v bring_v the_o quarter_n of_o the_o ecliptic_a that_o be_v answerable_a thereto_o under_o the_o meridian_n and_o turn_v the_o sphere_n to_o or_o fro_o till_o there_o be_v so_o many_o degree_n and_o minute_n of_o the_o meridian_n contain_v between_o the_o ecliptic_a and_o the_o equator_fw-la as_o the_o declination_n come_v to_o then_o look_v what_o degree_n of_o the_o ecliptic_a be_v under_o the_o meridian_n for_o that_o be_v the_o place_n of_o the_o sun_n as_o suppose_v the_o declination_n of_o the_o sun_n in_o some_o day_n of_o the_o springtime_n of_o the_o year_n be_v find_v to_o be_v 14._o degr_n 51._o min._n turn_v therefore_o the_o sphere_n to_o and_o fro_o till_o some_o part_n of_o the_o spring_n quarter_n of_o the_o ecliptic_a come_v right_a under_o that_o degree_n and_o minute_n of_o declination_n in_o the_o meridian_n you_o may_v find_v that_o the_o sun_n be_v then_o in_o the_o ten_o degree_n of_o taurus_n prop._n xvi_o to_o find_v what_o day_n of_o the_o month_n it_o be_v etc._n etc._n the_o place_n of_o the_o sun_n be_v find_v by_o his_o declination_n as_o be_v already_o show_v seek_v the_o place_n of_o the_o sun_n in_o the_o horizon_n of_o the_o sphere_n and_o look_v what_o day_n be_v answerable_a thereto_o for_o that_o be_v the_o day_n of_o the_o month_n which_o be_v seek_v for_o as_o the_o place_n of_o the_o sun_n be_v find_v by_o his_o declination_n as_o be_v show_v in_o the_o former_a proposition_n to_o be_v in_o the_o 10._o degree_n of_o taurus_n the_o day_n of_o the_o month_n shall_v thus_o be_v find_v to_o be_v the_o 21._o of_o april_n prop._n xvii_o the_o day_n of_o the_o month_n be_v know_v to_o find_v at_o what_o time_n the_o day_n break_v find_v the_o place_n of_o the_o sun_n by_o the_o 2._o prop._n and_o bring_v it_o to_o the_o meridian_n then_o bring_v the_o hour_n index_n to_o 12._o a_o clock_n upon_o the_o hour_n circle_n find_v out_o also_o the_o point_n of_o the_o ecliptic_a that_o be_v right_o over_o against_o the_o place_n of_o the_o sun_n then_o take_v between_o the_o foot_n of_o your_o compass_n 17._o degree_n of_o the_o ecliptic_a and_o set_v one_o foot_n of_o the_o compass_n in_o the_o point_n opposite_a to_o the_o place_n of_o
gemini_fw-la and_o that_o eclipse_n which_o shall_v be_v the_o next_o year_n after_o near_a the_o same_o intersection_n the_o 19_o of_o november_n in_o the_o morning_n shall_v be_v about_o the_o 6._o degree_n and_o 40._o minute_n of_o gemini_fw-la etc._n etc._n all_o this_o remove_n of_o the_o eclipse_n backward_o come_v to_o pass_v by_o reason_n of_o the_o motion_n of_o this_o orb_n carry_v the_o dragon_n head_n and_o tail_n contrary_a to_o the_o course_n and_o order_n of_o the_o sign_n this_o orb_n continue_v always_o right_a under_o tail_n and_o even_o with_o the_o orb_n of_o the_o sphere_n of_o the_o sun_n which_o abide_v always_o in_o all_o part_n just_a under_o the_o ecliptic_a line_n and_o have_v his_o centre_n agree_v and_o all_o one_o with_o the_o centre_n of_o the_o world_n and_o of_o the_o ecliptic_n and_o therefore_o the_o pole_n and_o axtree_n about_o which_o this_o orb_n be_v turn_v agree_v just_o with_o the_o axtree_n of_o the_o ecliptic_a the_o rest_n of_o the_o orb_n of_o the_o moon_n orb_n that_o be_v contain_v within_o this_o have_v all_o their_o plain_n agree_v in_o one_o and_o lie_v even_o one_o with_o another_o but_o the_o one_o half_a of_o all_o their_o plain_n arise_v above_o the_o plain_n of_o the_o former_a orb_n and_o of_o the_o ecliptic_a towards_o the_o north_n pole_n of_o the_o zodiac_n and_o the_o other_o half_o descend_v beneath_o the_o plain_n of_o the_o ecliptic_n towards_o the_o south_n pole_n even_o as_o the_o one_o half_a of_o the_o zodiac_n arise_v above_o the_o equinoctial_a circle_n towards_o the_o north_n and_o the_o other_o half_o descend_v towards_o the_o south_n and_o as_o the_o angle_n of_o intersection_n or_o obliquity_n of_o the_o ecliptic_n with_o the_o equinoctial_a circle_n be_v 23._o degr_n and_o a_o half_a or_o little_o more_o so_o the_o angle_n of_o intersection_n or_o obliquity_n of_o the_o plain_n of_o these_o orb_n of_o the_o moon_n from_o the_o plain_a of_o the_o ecliptic_a and_o of_o the_o former_a orb_n carry_v the_o dragon_n head_n and_o tail_n be_v 5._o degree_n or_o according_a to_o tigâ—â—_n brahe_n his_o observation_n 5._o degr_n and_o a_o quarter_n almost_o sometime_o and_o sometime_o less_o than_o 5._o degr_n that_o point_n or_o intersection_n of_o these_o orb_n with_o the_o former_a from_o which_o they_o begin_v to_o arise_v about_o the_o plain_n of_o the_o ecliptic_n towards_o the_o north_n proceed_v east-ward_n be_v call_v the_o dragon_n head_n and_o be_v signify_v by_o this_o character_n ☊_o and_o the_o other_o point_n or_o intersection_n diametral_o opposite_a unto_o this_o be_v call_v the_o dragon_n tail_n which_o be_v also_o signify_v by_o the_o former_a character_n turn_v up_o side_n down_o after_o this_o manner_n ☋_o the_o two_o point_n of_o these_o orb_n that_o be_v further_a distant_a from_o the_o plain_a of_o the_o 〈◊〉_d be_v call_v the_o bound_n or_o limit_n of_o the_o moon_n latitude_n and_o they_o be_v 90._o deg_n from_o the_o dragon_n head_n and_o tail_n and_o 5._o deg_n and_o a_o quarter_n almost_o from_o the_o plain_n of_o the_o ecliptic_a according_a to_o the_o obliquity_n or_o great_a declination_n of_o the_o plain_n of_o these_o orb_n from_o the_o plain_n of_o the_o ecliptic_n of_o these_o two_o point_n that_o which_o be_v in_o the_o north_n side_n of_o the_o ecliptic_n be_v call_v the_o north_n limit_n or_o bind_v of_o the_o moon_n latitude_n and_o contrariwise_o the_o other_o point_n opposite_a to_o this_o on_o the_o south_n side_n of_o the_o ecliptic_a be_v call_v the_o south_n limit_v of_o the_o moon_n latitude_n and_o when_o the_o moon_n come_v to_o either_o of_o these_o two_o point_n she_o have_v her_o great_a latitude_n chap._n x._o of_o the_o orb_n carry_v the_o moon_n apogaeum_n and_o perigaeum_n next_o within_o the_o orb_n carry_v the_o dragon_n head_n and_o tail_n be_v contain_v the_o orb_n call_v deferens_fw-la apogaeum_n lunae_fw-la which_o be_v the_o point_n wherein_o the_o moon_n be_v further_a distant_a from_o the_o 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colour_n in_o this_o sphere_n be_v move_v equal_o about_o the_o centre_n of_o the_o same_o orb_n from_o the_o west_n towards_o the_o east_n finish_v his_o motion_n under_o the_o zodiac_n in_o the_o space_n of_o 27._o day_n and_o 8._o hour_n almost_o and_o with_o this_o motion_n it_o carry_v about_o the_o moon_n epicycle_n equal_o under_o the_o zodiac_n therefore_o the_o motion_n of_o this_o orb_n about_o his_o own_o centre_n must_v needs_o be_v unequal_a that_o be_v to_o say_v swift_a in_o those_o part_n that_o be_v about_o the_o apogaeum_n and_o slow_a in_o the_o low_a part_n about_o the_o perigaeum_n because_o that_o great_a arch_n of_o the_o eccentrick_a do_v answer_n to_o equal_a arch_n of_o the_o zodiac_n about_o the_o apogaeum_n then_o about_o the_o perigaeum_n of_o the_o eccentrick_a the_o axtree_n about_o which_o this_o orb_n be_v move_v be_v always_o in_o all_o place_n equidistant_a from_o the_o axtree_n of_o the_o orb_n carry_v the_o apogaeum_n of_o the_o moon_n and_o the_o pole_n of_o the_o axtree_n of_o the_o moon_n eccentrick_a be_v fasten_v in_o the_o orb_n carry_v the_o moon_n apogaeum_n equidistant_o from_o the_o pole_n of_o the_o same_o orb_n therefore_o these_o pole_n together_o with_o the_o whole_a axtree_n of_o the_o eccentrick_a be_v carry_v and_o equal_o move_v about_o the_o pole_n and_o axtree_n of_o the_o orb_n carry_v the_o apogaeum_n from_o the_o east_n towards_o the_o west_n with_o this_o motion_n therefore_o the_o pole_n and_o centre_n of_o the_o eccentrick_a describe_v certain_a little_a circle_n of_o equal_a bigness_n about_o the_o pole_n and_o centre_n of_o the_o orb_n carry_v the_o apogaeum_n from_o the_o east_n westward_n and_o therefore_o also_o the_o apogaeum_n of_o the_o eccentrick_a be_v move_v about_o equal_o under_o the_o ecliptic_n contrary_a to_o the_o
the_o description_n and_o use_n of_o the_o sphere_n divide_v into_o three_o principal_a part_n whereof_o the_o first_o intreat_v especial_o of_o the_o circle_n of_o the_o uppermost_a movable_a sphere_n and_o of_o the_o manifold_a use_n of_o every_o one_o of_o they_o several_o the_o second_o show_v the_o plentiful_a use_n of_o the_o uppermost_a sphere_n and_o of_o the_o circle_n thereof_o joint_o the_o three_o contain_v the_o description_n of_o the_o orb_n whereof_o the_o sphere_n of_o the_o sun_n and_o moon_n have_v be_v suppose_v to_o be_v make_v with_o their_o motion_n and_o use_v by_o edward_n wright_n the_o content_n of_o each_o part_n be_v more_o particular_o set_v down_o in_o the_o table_n london_n print_v by_o b._n a._n and_o t._n faucet_n for_o john_n tap_n and_o be_v to_o be_v sell_v at_o his_o shop_n at_o s._n magnus_n corner_n 1627._o a_o table_n of_o the_o content_n of_o this_o book_n the_o first_o part._n of_o the_o circle_n of_o the_o uppermost_a sphere_n and_o their_o several_a use_n the_o definition_n and_o division_n of_o this_o sphere_n chap._n 1._o the_o description_n of_o the_o horizon_n chap._n 2._o the_o use_n of_o the_o horizon_n chap._n 3._o the_o description_n of_o the_o meridian_n chap._n 4._o the_o use_n of_o the_o meridian_n chap._n 5._o the_o description_n of_o the_o houre-circle_n and_o pole_n of_o this_o sphere_n chap._n 6._o of_o the_o equinoctial_a circle_n and_o why_o it_o be_v so_o call_v and_o how_o divide_v together_o with_o his_o manifold_a use_n chap._n 7._o the_o description_n of_o the_o zodiac_n of_o this_o sphere_n chap._n 8._o the_o use_n of_o the_o zodiac_n chap._n 9_o the_o description_n of_o the_o two_o colour_n together_o with_o the_o use_v common_a to_o they_o both_o chap._n 10._o the_o use_n of_o the_o equinoctial_a colour_n chap._n 11._o the_o use_n of_o the_o solstitial_a colour_n chap._n 12._o the_o description_n of_o the_o two_o tropicke_n chap._n 13._o the_o use_n of_o the_o tropicke_n chap._n 14._o the_o polar_a circle_n chap._n 15._o use_v of_o the_o polar_a circle_n chap._n 16._o of_o the_o zone_n chap._n 17._o the_o difference_n of_o shadow_n that_o the_o sun_n make_v in_o these_o zone_n chap._n 18._o the_o second_o part._n of_o the_o use_n of_o the_o uppermost_a sphere_n and_o of_o the_o circle_n thereof_o joint_o to_o rectify_v the_o sphere_n that_o be_v to_o set_v the_o sphere_n to_o the_o latitude_n of_o that_o place_n for_o which_o you_o will_v use_v it_o prop._n 1._o to_o know_v the_o place_n of_o the_o sun_n by_o this_o sphere_n prop._n 2._o to_o know_v the_o declination_n of_o the_o sun_n or_o of_o any_o point_n of_o the_o ecliptic_a prop._n 3._o to_o know_v the_o right_a ascension_n of_o the_o sun_n or_o any_o point_n of_o the_o zodiac_n prop._n 4._o to_o know_v the_o oblique_a ascension_n of_o the_o sun_n or_o of_o any_o star_n or_o point_n in_o the_o zodiac_n prop._n 5._o to_o find_v the_o difference_n of_o ascension_n prop._n 6._o to_o find_v at_o what_o time_n the_o sun_n rise_v or_o set_v prop._n 7._o to_o find_v the_o length_n of_o the_o artificial_a day_n or_o night_n prop._n 8._o to_o know_v the_o time_n of_o the_o sun_n rise_v or_o sun_n set_v prop._n 9_o to_o find_v the_o length_n of_o the_o artificial_a day_n or_o night_n otherwise_o by_o the_o sphere_n prop._n 10._o to_o know_v the_o meridian_n altitude_n of_o the_o sun_n at_o any_o place_n who_o latitude_n be_v know_v prop._n 11._o to_o know_v how_o high_a the_o sun_n be_v about_o the_o horizon_n at_o any_o time_n of_o the_o day_n prop._n 12._o to_o find_v the_o hour_n of_o the_o day_n by_o the_o height_n of_o the_o sun_n the_o place_n of_o the_o sun_n and_o height_n of_o the_o pole_n be_v give_v prop._n 13._o to_o find_v the_o breadth_n of_o the_o sun_n rise_v or_o set_v that_o be_v how_o far_o he_o rise_v or_o set_v from_o the_o point_n of_o true_a east_n or_o west_n at_o any_o time_n prop._n 14._o to_o find_v the_o place_n of_o the_o sun_n his_o declination_n and_o the_o quarter_n of_o the_o year_n be_v know_v prop._n 15._o to_o find_v what_o day_n of_o the_o month_n it_o be_v by_o knowledge_n of_o the_o sun_n declination_n prop._n 16._o the_o day_n of_o the_o month_n be_v know_v to_o find_v at_o what_o time_n the_o day_n break_v prop._n 17._o to_o find_v how_o long_o the_o twilight_n continue_v prop._n 18._o to_o find_v how_o much_o the_o declination_n of_o the_o sun_n must_v alter_v at_o any_o time_n of_o the_o year_n to_o make_v the_o day_n one_o hour_n long_o or_o short_a prop._n 19_o to_o find_v how_o many_o day_n it_o be_v ere_o the_o day_n lengthen_v or_o shorten_v a_o hour_n prop._n 20._o to_o make_v a_o horizontal_a dial_n by_o the_o sphere_n prop._n 21._o how_o to_o make_v a_o direct_a mural_a dial_n by_o the_o sphere_n prop._n 22._o to_o make_v any_o direct_a incline_n or_o direct_a recline_a dial_n by_o the_o sphere_n prop._n 23._o to_o know_v at_o what_o time_n the_o moon_n or_o any_o other_o of_o the_o planet_n or_o fix_v star_n that_o be_v within_o the_o breadth_n of_o the_o zodiac_n rise_v or_o set_v or_o come_v to_o the_o meridian_n as_o also_o with_o what_o degree_n of_o the_o ecliptic_n they_o rise_v set_v or_o mid_n heaven_n together_o with_o their_o declination_n and_o their_o right_n and_o oblique_a ascension_n and_o descension_n and_o their_o amplitude_n or_o bredth_n of_o rise_v or_o set_v prop._n 24._o to_o know_v how_o long_o the_o moon_n or_o any_o of_o the_o planet_n or_o fix_a star_n do_v shine_v or_o continue_v above_o the_o horizon_n prop._n 25._o to_o find_v which_o of_o the_o planet_n of_o fix_a star_n that_o be_v within_o the_o compass_n of_o the_o zodiac_n be_v above_o or_o under_o the_o horizon_n at_o any_o time_n of_o the_o day_n or_o night_n prop._n 26._o to_o find_v in_o what_o time_n any_o sign_n or_o part_n of_o the_o ecliptic_a rise_v or_o set_v prop._n 27._o to_o find_v the_o hour_n of_o the_o night_n by_o any_o of_o the_o planet_n or_o fix_v star_n in_o the_o zodiac_n that_o appear_v above_o the_o horizon_n prop._n 28._o to_o know_v at_o any_o time_n of_o the_o year_n what_o star_n in_o the_o zodiac_n arise_v or_o set_v cosmical_o achronycal_o or_o heliacal_o prop._n 29._o the_o meridian_n line_n of_o the_o use_n of_o the_o sphere_n and_o globe_n pars_fw-la 1._o the_o description_n of_o the_o sphere_n and_o globe_n divide_v into_o three_o principal_a part_n whereof_o this_o first_o intreat_v special_o of_o the_o circle_n of_o the_o uppermost_a movable_a sphere_n and_o of_o their_o peculiar_a use_n chap._n i._n the_o definition_n and_o division_n of_o the_o sphere_n this_o sphere_n be_v nothing_o else_o but_o a_o representation_n of_o the_o celestial_a orb_n and_o circle_n that_o have_v be_v imagine_v for_o the_o easy_a understanding_n express_v and_o count_v of_o the_o motion_n and_o appaâ—ences_n either_o common_a to_o the_o whole_a heaven_n or_o proper_a to_o the_o sun_n and_o moon_n the_o circle_n of_o this_o sphere_n be_v either_o inmoveable_a as_o the_o two_o great_a and_o utmost_a circle_n the_o horizon_n and_o meridian_n whereto_o be_v adjoin_v the_o little_a hour_n circle_n that_o be_v fix_v to_o the_o meridian_n or_o else_o movable_a as_o all_o the_o rest_n contain_v within_o these_o chap._n ii_o the_o description_n of_o the_o horizon_n the_o great_a and_o utmost_a circle_n of_o the_o sphere_n that_o lie_v level_a on_o all_o side_n from_o the_o ground_n be_v call_v the_o horizon_n which_o be_v divide_v into_o 7._o limb_n or_o border_n the_o first_o and_o utmost_a of_o they_o contain_v the_o 32._o point_n of_o the_o compass_n or_o the_o wind_n as_o they_o be_v at_o this_o day_n divide_v and_o use_v by_o seaman_n with_o their_o latin_a name_n adjoin_v unto_o they_o the_o second_o limb_n contain_v the_o name_n and_o division_n of_o the_o 12._o wind_n as_o they_o be_v wont_a to_o be_v divide_v in_o old_a time_n the_o three_o be_v divide_v into_o the_o month_n and_o day_n of_o the_o new_a calendar_n first_o establish_v by_o pope_n gregory_n the_o xiii_o and_o now_o use_v in_o many_o place_n beyond_o the_o sea_n in_o the_o four_o limb_n be_v set_v down_o the_o month_n and_o day_n of_o the_o ordinary_a calendar_n use_v in_o england_n next_o within_o this_o be_v place_v the_o 12._o sign_n and_o degree_n of_o the_o zodiac_n that_o so_o the_o place_n of_o the_o sun_n may_v be_v present_o know_v for_o any_o day_n of_o the_o year_n give_v or_o contrariwise_o that_o the_o day_n of_o the_o month_n may_v be_v ready_o find_v by_o the_o place_n of_o the_o sun_n after_o this_o follow_v the_o six_o limb_n contain_v the_o 32._o wind_n or_o point_n of_o the_o compass_n with_o letter_n represent_v the_o name_n now_o in_o use_n
that_o degree_n and_o the_o equinoctial_a to_o be_v 14._o degree_n and_o about_o 51._o minute_n prop._n four_o to_o know_v the_o right_a ascension_n of_o the_o sun_n etc._n etc._n bring_v that_o point_n as_o before_o to_o the_o meridian_n and_o see_v then_o how_o many_o degree_n and_o minute_n of_o the_o equinoctial_a be_v contain_v between_o the_o beginning_n of_o aries_n and_o the_o meridian_n for_o that_o be_v the_o right_a ascension_n of_o that_o point_n so_o you_o shall_v find_v the_o right_a ascension_n of_o the_o 10._o degr_n of_o taurus_n to_o be_v 37._o degr_n 35._o min._n for_o if_o you_o bring_v that_o degree_n of_o taurus_n to_o the_o meridian_n you_o shall_v find_v so_o many_o degree_n and_o min._n between_o the_o begin_n of_o aries_n and_o the_o meridian_n prop._n v._o to_o know_v the_o oblique_a ascension_n of_o the_o sun_n etc._n etc._n set_v the_o sphere_n to_o the_o elevation_n of_o the_o place_n for_o which_o you_o desire_v to_o know_v the_o oblique_a ascension_n then_o bring_v the_o sun_n star_n or_o point_n who_o oblique_a ascension_n you_o will_v know_v unto_o the_o east_n semicircle_n of_o the_o horizon_n and_o look_v how_o many_o degree_n and_o minute_n of_o the_o equinoctial_a circle_n be_v contain_v between_o the_o east_n point_n of_o the_o horizon_n and_o the_o beginning_n of_o aries_n for_o so_o much_o be_v the_o oblique_a ascension_n desire_v as_o for_o example_n if_o you_o see_v the_o sphere_n to_o the_o latitude_n of_o london_n 51._o degr_n 32._o min._n and_o then_o bring_v the_o 10._o degree_n of_o taurus_n to_o the_o east_n part_n of_o the_o horizon_n you_o shall_v find_v about_o 19_o degree_n and_o a_o half_a of_o the_o equinoctial_a at_o the_o same_o east_n part_n of_o the_o horizon_n which_o be_v the_o oblique_a ascension_n of_o that_o degree_n of_o taurus_n for_o the_o latitude_n of_o the_o city_n of_o london_n prop._n vi_o to_o find_v the_o difference_n of_o ascension_n compare_v the_o right_a and_o oblique_a ascension_n of_o the_o sun_n or_o of_o any_o point_n of_o the_o zodiac_n together_o and_o subtract_v the_o less_o from_o the_o great_a for_o the_o remainder_n shall_v be_v the_o difference_n of_o ascension_n as_o for_o example_n the_o right_a ascension_n of_o the_o 10._o degree_n of_o taurus_n be_v find_v by_o the_o 4._o propo._n to_o be_v 37._o degree_n 35._o min._n and_o the_o oblique_a ascension_n of_o the_o same_o degree_n at_o london_n by_o the_o 5._o prop._n 19_o degree_n 30._o min._n by_o subtraction_n of_o the_o less_o out_o of_o the_o great_a the_o difference_n shall_v be_v find_v to_o be_v 18._o degr_n and_o 5._o minute_n which_o be_v the_o difference_n of_o ascension_n seek_v for_o prop._n vii_o to_o find_v at_o what_o time_n the_o sun_n rise_v or_o set_v reduce_v the_o difference_n of_o ascension_n into_o hour_n and_o minute_n take_v for_o every_o 15_o degree_n 1._o hour_n and_o for_o every_o one_o degree_n that_o remain_v 4._o minute_n and_o for_o every_o minute_n of_o a_o degree_n 4_o second_n for_o these_o hour_n minute_n and_o second_n be_v add_v to_o 6._o hour_n if_o the_o sun_n be_v in_o any_o of_o the_o south_n sign_n or_o subtract_v if_o he_o be_v in_o the_o north_n sign_n show_v the_o time_n of_o the_o sunrising_n and_o contrariwise_o the_o same_o hour_n and_o minute_n subtract_v from_o six_o hour_n when_o the_o sun_n be_v in_o the_o south_n sign_n or_o add_v when_o he_o be_v in_o the_o north_n sign_n show_v the_o the_o time_n of_o the_o sunne-setting_a as_o for_o example_n the_o sun_n be_v in_o the_o 10._o degree_n of_o taurus_n which_o happen_v about_o the_o 20._o or_o 21._o day_n of_o april_n i_o will_v know_v at_o what_o hour_n and_o minute_n the_o sun_n rise_v and_o set_v at_o london_n have_v therefore_o find_v by_o the_o former_a proposition_n the_o difference_n of_o ascension_n to_o be_v 18._o degr_n and_o 5._o minute_n i_o take_v for_o 15._o degree_n thereof_o one_o hour_n and_o for_o the_o three_o degr_n remain_v 12._o minute_n of_o a_o hour_n and_o for_o the_o 5._o minute_n 20._o second_n of_o a_o hour_n which_o hour_n minute_n and_o second_n be_v subtract_v out_o of_o 6._o hour_n because_o the_o sun_n be_v in_o a_o north_n sign_n there_o remain_v the_o time_n of_o the_o sun_n rise_v at_o 4._o a_o clock_n 47._o minute_n 40._o second_n and_o add_v the_o same_o hour_n min._n and_o second_o to_o 6._o hour_n you_o have_v the_o time_n of_o the_o sunsetting_a that_o day_n at_o 7._o a_o clock_n 12._o min._n and_o 20._o second_n prop._n viii_o to_o find_v the_o length_n of_o the_o artificial_a day_n or_o night_n the_o artificial_a day_n be_v the_o time_n contain_v between_o the_o sunrising_n and_o the_o sunsetting_a and_o the_o artificial_a night_n be_v the_o time_n between_o sunne-setting_a and_o sunrising_n the_o length_n of_o both_o these_o be_v find_v after_o this_o manner_n have_v find_v the_o difference_n of_o ascension_n and_o reduce_v it_o into_o hour_n and_o minute_n as_o in_o the_o former_a proposition_n double_v thâ—se_a hour_n and_o minute_n and_o add_v they_o to_o 12._o hour_n if_o the_o sun_n be_v in_o the_o north_n sign_n or_o subtract_v they_o from_o 12._o hour_n if_o the_o sun_n be_v in_o the_o south_n sign_n for_o so_o shall_v you_o have_v the_o length_n of_o the_o day_n but_o contrariwise_o subtract_v the_o same_o hour_n and_o minute_n be_v double_v from_o 12._o hour_n the_o sun_n be_v in_o the_o north_n sign_n and_o add_v they_o to_o 12._o hour_n when_o he_o be_v in_o the_o south-signe_n so_o have_v you_o the_o length_n of_o the_o night_n or_o else_o double_v the_o time_n of_o the_o sunsetting_a so_o have_v you_o the_o length_n of_o the_o day_n and_o double_v the_o time_n of_o the_o sunrising_n so_o have_v you_o the_o length_n of_o the_o right_n as_o the_o time_n of_o the_o sunrising_n be_v find_v by_o the_o former_a proposition_n to_o be_v 4_o hour_n 48._o minute_n after_o mignight_n at_o london_n the_o sun_n be_v in_o the_o 10._o degr_n of_o taurus_n by_o double_v the_o time_n of_o the_o sunrising_n the_o length_n of_o the_o night_n shall_v be_v find_v to_o be_v 9_o hour_n and_o 36._o minute_n and_o double_v the_o time_n of_o the_o sunset_n that_o be_v 7._o hour_n and_o 12._o minute_n you_o have_v the_o length_n of_o the_o day_n 14._o hour_n and_o 24._o minute_n prop._n ix_o to_o know_v the_o time_n of_o the_o sun_n rise_v and_o sun_n set_v the_o place_n of_o the_o sun_n be_v find_v by_o the_o 2._o proposition_n bring_v the_o same_o to_o the_o meridian_n and_o withal_o set_v the_o point_n of_o the_o index_n of_o the_o hour_n circle_n to_o the_o 12._o hour_n in_o the_o same_o circle_n then_o bring_v the_o place_n of_o the_o sun_n to_o the_o horizon_n eastward_n and_o the_o point_n of_o the_o hour_n index_n shall_v show_v you_o in_o the_o hour_n circle_n the_o time_n of_o the_o sunrising_n but_o if_o you_o bring_v the_o place_n of_o the_o sun_n to_o the_o horizon_n westward_n the_o point_n of_o the_o index_n will_v show_v in_o the_o hour_n circle_v the_o time_n of_o the_o sunsetting_a as_o for_o example_n the_o sun_n be_v in_o the_o 10._o degree_n of_o taurus_n bring_v the_o same_o degree_n to_o the_o meridian_n and_o bring_v the_o point_n of_o the_o hour_n index_n also_o to_o the_o meridian_n then_o the_o sphere_n be_v set_v to_o the_o latitude_n of_o london_n bring_v the_o same_o 10._o degree_n of_o taurus_n to_o the_o east_n part_n of_o the_o horizon_n for_o then_o the_o hour_n index_n will_v show_v you_o in_o the_o hour_n circle_n that_o the_o sun_n rise_v at_o 4._o of_o the_o clock_n and_o 48._o minute_n and_o bring_v the_o same_o degree_n to_o the_o west_n semicircle_n of_o the_o horizon_n the_o same_o index_n will_v show_v the_o time_n of_o the_o sunsetting_a to_o be_v 7._o hour_n and_o 12._o min._n after_o noon_n prop._n x._o to_o find_v the_o length_n of_o the_o artificial_a day_n or_o night_n bring_v the_o place_n of_o the_o sun_n be_v find_v as_o before_o to_o the_o east_n semicircle_n of_o the_o horizon_n set_v the_o hour_n index_n 12._o a_o clock_n in_o the_o hour_n circle_n turn_v about_o the_o sphere_n from_o the_o east_n westward_n till_o the_o place_n of_o the_o sun_n come_v to_o the_o horizon_n and_o mark_v how_o many_o hour_n the_o index_n have_v run_v over_o upon_o the_o hour_n circle_n in_o the_o mean_a time_n for_o so_o much_o be_v the_o length_n of_o the_o day_n and_o to_o find_v the_o length_n of_o the_o night_n bring_v the_o place_n of_o the_o sun_n to_o the_o west_n semicircle_n of_o the_o horizon_n and_o set_v the_o index_n to_o 12._o a_o clock_n as_o before_o then_o turn_v forward_o the_o sphere_n from_o east_n westward_o till_o the_o place_n of_o the_o sun_n come_v to_o
the_o sun_n turn_v the_o sphere_n westward_n till_o you_o can_v but_o only_o touch_v the_o horizon_n with_o the_o other_o foot_n for_o then_o the_o index_n show_v in_o the_o hour_n circle_n at_o what_o time_n the_o day_n break_v so_o the_o 21._o of_o april_n the_o sun_n be_v in_o the_o 10_o degr_n of_o taurus_n you_o shall_v find_v that_o the_o day_n break_v about_o half_a a_o hour_n past_o 2._o of_o the_o clock_n in_o the_o morning_n prop._n xviii_o to_o find_v how_o long_o the_o twilight_n continue_v find_v out_o by_o the_o former_a prop._n at_o what_o time_n the_o day_n break_v and_o learn_v also_o at_o what_o time_n the_o sun_n rise_v by_o the_o 7._o or_o 9_o prop._n then_o subtract_v the_o lesser_a from_o the_o great_a and_o there_o shall_v remain_v the_o length_n of_o the_o twilight_n or_o else_o thus_o have_v bring_v the_o point_n that_o be_v opposite_a to_o the_o place_n of_o the_o sun_n to_o be_v 17._o degree_n above_o the_o horizon_n westward_n in_o such_o sort_n as_o be_v show_v in_o the_o former_a proposition_n and_o keep_v the_o sphere_n in_o that_o position_n bring_v about_o the_o point_n of_o the_o hour_n index_n unto_o 12._o a_o clock_n upon_o the_o hour_n circle_n then_o tune_v the_o sphere_n westward_n until_o the_o degree_n or_o point_n of_o the_o ecliptic_a that_o be_v opposite_a to_o the_o place_n of_o the_o sun_n come_v to_o the_o horizon_n and_o see_v how_o many_o hour_n the_o point_n of_o the_o index_n have_v run_v over_o in_o the_o mean_a time_n upon_o the_o hour_n circle_n for_o so_o many_o hour_n continue_v the_o twilight_n by_o either_o of_o these_o way_n the_o sun_n be_v in_o the_o 10._o degr_n of_o taurus_n you_o shall_v find_v that_o the_o twilight_n that_o be_v the_o time_n from_o the_o break_n of_o the_o day_n till_o sun-rise_n be_v about_o 2._o hour_n and_o 20._o minute_n prop._n xix_o to_o find_v how_o much_o the_o declination_n of_o the_o sun_n must_v alter_v at_o any_o time_n of_o the_o year_n to_o make_v the_o day_n a_o hour_n long_o or_o short_a bring_v the_o place_n of_o the_o sun_n find_v by_o the_o second_o prop._n to_o the_o east_n semicircle_n of_o the_o horizon_n and_o mark_v what_o degree_n or_o point_n of_o the_o horizon_n it_o fall_v upon_o bring_v one_o of_o the_o colour_n to_o the_o same_o degree_n or_o point_n and_o there_o make_v a_o prick_n in_o that_o colour_n and_o hold_v the_o sphere_n immovable_a mark_v withal_o what_o degree_n of_o the_o equinoctial_a or_o of_o either_o of_o the_o tropicke_n be_v then_o at_o the_o horizon_n then_o turn_v the_o sphere_n 7._o degree_n and_o a_o half_a forward_o towards_o the_o west_n if_o the_o day_n shorten_v but_o contrariwise_o if_o the_o day_n lengthen_v and_o hold_v the_o sphere_n there_o immovable_a make_v another_o prick_n in_o the_o colour_n at_o the_o horizon_n for_o the_o distance_n of_o these_o two_o prick_v in_o the_o colour_n take_v with_o the_o compass_n and_o bring_v to_o the_o ecliptic_a or_o equinoctial_a show_v how_o much_o the_o sun_n declination_n must_v alter_v to_o make_v the_o day_n a_o hour_n long_o if_o the_o day_n increase_n or_o short_a if_o they_o decrease_v after_o this_o manner_n you_o shall_v find_v that_o the_o sun_n be_v in_o the_o 10._o degree_n of_o taurus_n his_o declination_n must_v increase_v about_o 5._o degree_n or_o little_o more_o to_o make_v the_o day_n a_o hour_n long_o but_o when_o the_o sun_n be_v in_o the_o 20._o degree_n of_o pisces_fw-la his_o declination_n or_o rather_o his_o meridian_n altitude_n must_v increase_v about_o 6._o degree_n to_o make_v the_o day_n a_o hour_n long_o and_o when_o he_o be_v in_o the_o begin_n of_o capricorn_n his_o declination_n decrease_v scarce_o 5._o degree_n to_o make_v the_o day_n a_o hour_n long_o prop._n xx._n to_o find_v how_o many_o day_n it_o be_v ere_o the_o day_n lengthen_v or_o shorten_v a_o hour_n bring_v the_o foresay_a prick_v make_v in_o the_o colour_n by_o the_o former_a proposition_n unto_o the_o meridian_n and_o there_o make_v two_o mark_n just_o answerable_a unto_o those_o prick_v in_o the_o colour_n turn_v about_o the_o sphere_n till_o the_o ecliptic_a line_n come_v just_a under_o one_o of_o those_o mark_n and_o there_o make_v a_o prick_n in_o the_o ecliptic_a then_o again_o turn_v the_o sphere_n till_o the_o ecliptic_a come_v just_a under_o the_o other_o mark_v make_v in_o the_o meridian_n and_o there_o make_v another_o prick_n in_o the_o ecliptic_a but_o here_o it_o be_v to_o be_v note_v that_o whereas_o the_o ecliptic_a may_v be_v bring_v under_o that_o mark_n whether_o way_n soever_o you_o turn_v the_o sphere_n it_o must_v i_o say_v be_v note_v that_o the_o sphere_n must_v be_v turn_v that_o way_n which_o may_v soon_o bring_v the_o ecliptic_a under_o that_o mark_n last_o find_v out_o among_o the_o sign_n and_o degree_n describe_v upon_o the_o horizon_n the_o like_a arch_n to_o this_o that_o be_v contain_v between_o these_o prick_v in_o the_o ecliptic_a for_o the_o number_n of_o day_n answerable_a to_o this_o arch_n in_o the_o horizon_n be_v the_o time_n wherein_o the_o day_n grow_v a_o hour_n long_o or_o short_a thus_o shall_v you_o find_v that_o when_o the_o sun_n be_v in_o the_o begin_n of_o aries_n it_o will_v be_v about_o 18._o day_n after_o ere_o the_o day_n be_v one_o hour_n long_o but_o when_o the_o sun_n be_v in_o the_o begin_n of_o capricorn_n you_o shall_v find_v that_o it_o will_v be_v almost_o twice_o so_o much_o that_o be_v near_o 34._o day_n before_o the_o day_n will_v be_v a_o hour_n long_o hereby_o therefore_o the_o error_n of_o they_o manifest_o appear_v which_o think_v that_o in_o every_o 15._o day_n the_o day_n be_v lengthen_v or_o shorten_v a_o hour_n whereas_o indeed_o the_o lengthen_v or_o shorten_v of_o the_o day_n keep_v no_o such_o rule_n for_o when_o the_o sun_n be_v about_o the_o equinoctial_a point_n the_o day_n lenghthen_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 they_o grow_v long_o or_o short_a very_o slow_o prop._n xxi_o to_o make_v a_o horizontall_a dial_n set_v the_o sphere_n to_o the_o elevation_n of_o the_o place_n for_o which_o you_o will_v make_v the_o dial_n turn_v about_o the_o sphere_n till_o the_o solstitial_a colour_n be_v 15._o degree_n measure_v in_o the_o equinoctial_a from_o the_o meridian_n and_o where_o the_o colour_n cross_v the_o horizon_n there_o make_v a_o prick_n then_o turn_v the_o colour_n yet_o 15._o degr_n further_o that_o be_v 30._o degree_n from_o the_o meridian_n and_o where_o the_o colour_n cross_v the_o horizon_n there_o make_v a_o other_o prick_n again_o turn_v the_o colour_n forward_o yet_o 15._o deg_n more_o that_o be_v 45._o degree_n from_o the_o meridian_n and_o at_o the_o common_a meeting_n of_o the_o colour_n and_o horizon_n make_v the_o three_o prick_n in_o the_o horizon_n and_o so_o proceed_v with_o the_o rest_n till_o you_o have_v make_v so_o many_o prick_n on_o that_o side_n of_o the_o horizon_n as_o there_o be_v hour_n in_o halse_a the_o long_a day_n then_o look_v how_o many_o degree_n the_o first_o second_o three_o four_o prick_v etc._n etc._n be_v from_o the_o meridian_n for_o so_o many_o degree_n must_v the_o hour_n line_n of_o 11._o a_o clock_n and_o one_o a_o clock_n of_o 10._o and_o 2_o of_o 9_o and_o 3._o of_o 8._o and_o 4._o etc._n etc._n be_v from_o the_o 12._o a_o clock_n line_n in_o the_o horizontall_a dial_n after_o this_o manner_n in_o a_o horizontall_a dial_n make_v for_o the_o latitude_n of_o london_n which_o be_v 51._o degr_n and_o 32._o minute_n you_o shall_v find_v the_o distance_n of_o all_o the_o rest_n of_o the_o houre-line_n from_o the_o 12._o a_o clock_n line_n as_o follow_v betwixt_o twelve_o and_o 11._o and_o twelve_o and_o 1._o be_v conceyn_v 12._o degree_n almost_o between_o 12._o and_o 10._o and_o 12._o and_o 2._o there_o be_v contain_v 14._o degr_n and_o a_o half_a between_o 12._o and_o 9_o and_o 12._o and_o 3._o 38._o degr_n between_o 12._o and_o 8._o and_o 12._o and_o 4._o 53._o degr_n between_o 12._o and_o 7._o and_o 12._o and_o 5._o 70._o degree_n and_o a_o half_a between_o 12._o and_o 6._o both_o before_o and_o after_o noon_n 90._o degr_n the_o other_o hour_n space_n before_o 6._o in_o the_o morning_n and_o after_o 6._o in_o the_o evening_n be_v equal_a to_o the_o hour_n space_n after_o six_o in_o the_o morning_n and_o before_o 6._o in_o the_o afternoon_n prop._n xxii_o how_o to_o make_v a_o direct_a mural_a dial_n set_v the_o pole_n arctic_a of_o the_o sphere_n so_o much_o under_o the_o horizon_n as_o be_v the_o compliment_n of_o the_o pole_n elevation_n the_o horizon_n therefore_o be_v thus_o set_v as_o it_o be_v to_o the_o zenith_n of_o the_o sphere_n and_o
27._o day_n of_o may_n it_o our_o latitude_n of_o london_n the_o bull_n eye_n rise_v cosmical_o and_o the_o star_n in_o serpentarius_n his_o right_a foot_n set_v cosmical_o you_o may_v see_v also_o that_o the_o same_o day_n the_o star_n in_o the_o bull_n south_n horn_n set_v achronycal_o and_o the_o northermost_a star_n in_o serpentarius_n his_o right_a foot_n rise_v achronycal_o and_o last_o you_o may_v find_v that_o about_o the_o same_o time_n the_o pleiade_n and_o the_o star_n in_o the_o bull_n north_n home_o rise_v heliacal_o and_o that_o the_o same_o star_n also_o and_o the_o former_a twin_n foot_n set_v heliacal_o prop._n xxx_o to_o find_v the_o four_o principal_a or_o cardinal_a point_n of_o heaven_n as_o the_o astrologian_n call_v they_o at_o any_o time_n these_o four_o cardinal_n point_n be_v nothing_o else_o but_o four_o point_n of_o the_o ecliptic_a whereof_o one_o be_v at_o the_o east_n part_n of_o the_o horizon_n ascend_v and_o be_v therefore_o call_v the_o ascendent_n another_o be_v at_o the_o upper_a part_n of_o the_o meridian_n above_o the_o horizon_n and_o be_v call_v the_o midst_n of_o heaven_n and_o the_o hart_n of_o heaven_n the_o three_o be_v at_o the_o west_n part_n of_o the_o horizon_n descend_v and_o may_v be_v therefore_o call_v the_o descendent_a the_o four_o point_n be_v that_o which_o be_v at_o the_o nether_a part_n of_o the_o meridian_n under_o the_o horizon_n which_o four_o point_n be_v the_o beginning_n of_o the_o first_o ten_o seven_o and_o four_o house_n therefore_o to_o find_v these_o point_n at_o any_o time_n by_o the_o sphere_n bring_v the_o place_n of_o the_o sun_n be_v find_v for_o that_o time_n by_o the_o 2._o proposition_n to_o the_o meridian_n and_o the_o index_n to_o 12._o a_o clock_n then_o turn_v the_o sphere_n till_o the_o index_n come_v to_o that_o hour_n at_o which_o you_o desire_v to_o know_v those_o four_o point_n and_o there_o hold_v the_o sphere_n that_o it_o move_v not_o and_o look_v withal_o what_o point_v of_o the_o ecliptic_a be_v at_o the_o east_n and_o west_n semicircle_n of_o the_o horizon_n and_o at_o the_o upper_a and_o nether_a part_n of_o the_o meridian_n for_o those_o be_v the_o four_o principal_a or_o cardinal_n point_v you_o seek_v for_o take_v for_o example_n the_o time_n of_o the_o sun_n entrance_n into_o aries_n this_o present_a year_n 1600._o which_o be_v upon_o the_o ten_o day_n of_o march_n about_o eight_o of_o the_o clock_n in_o the_o morning_n or_o little_o after_o with_o we_o here_o at_o london_n have_v therefore_o bring_v the_o beginning_n of_o aries_n together_o with_o the_o hour_n index_n to_o the_o meridian_n and_o then_o turn_v back_o the_o whole_a sphere_n till_o the_o index_n come_v to_o 8._o of_o the_o clock_n upon_o the_o hour_n circle_n you_o shall_v find_v the_o ascendent_n at_o that_o time_n to_o be_v the_o 27._o degree_n of_o taurus_n the_o midst_n or_o hart_n of_o heaven_n the_o 27._o of_o capricorn_n the_o descendent_a the_o 27._o deg_n of_o scorpio_n and_o the_o low_a part_n of_o heaven_n the_o 27._o degree_n of_o cancer_n prop._n xxxi_o to_o find_v out_o the_o breadth_n of_o any_o climate_n etc._n etc._n lift_v up_o or_o put_v down_o the_o pole_n of_o the_o sphere_n till_o you_o find_v that_o there_o be_v 7._o deg_n and_o a_o half_a of_o the_o tropic_a of_o cancer_n more_o or_o less_o above_o the_o horizon_n than_o there_o be_v before_o and_o mark_v with_o all_o how_o much_o the_o pole_n of_o the_o sphere_n be_v raise_v or_o let_v fall_v in_o the_o mean_a time_n more_o than_o it_o be_v before_o for_o so_o much_o be_v the_o breadth_n of_o that_o climate_n as_o far_o example_n have_v set_v the_o sphere_n to_o our_o latitude_n of_o london_n of_o 51._o deg_n and_o a_o half_a with_o the_o point_n of_o your_o compass_n hold_v and_o guide_v some_o point_n of_o the_o tropic_a of_o cancer_n right_n under_o the_o horizon_n then_o lift_v up_o the_o pole_n till_o you_o find_v 7._o degree_n and_o a_o half_n more_o above_o the_o horizon_n than_o be_v before_o you_o shall_v find_v the_o pole_n elevate_v about_o 2._o degr_n and_o a_o half_n more_o than_o it_o be_v before_o likewise_o if_o you_o put_v down_o the_o pole_n till_o there_o be_v 7._o degree_n and_o a_o half_a of_o the_o tropic_n of_o cancer_n few_o above_o the_o horizon_n than_o be_v before_o you_o shall_v find_v the_o elevation_n of_o the_o pole_n to_o be_v about_o 3._o degree_n less_o than_o before_o prop._n xxxii_o the_o reason_n of_o the_o inequality_n of_o natural_a day_n etc._n etc._n the_o reason_n hereof_o be_v show_v partly_o by_o the_o inequality_n of_o the_o difference_n of_o right_a ascension_n answerable_a to_o equal_a arck_n of_o the_o zodiac_n and_o partly_o by_o the_o unequal_a apparent_a motion_n of_o the_o sun_n for_o the_o first_o the_o difference_n of_o right_a ascension_n answerable_a to_o the_o part_n of_o the_o ecliptic_a about_o the_o tropical_a point_n of_o cancer_n and_o capricorn_n be_v much_o great_a than_o about_o the_o equinoctial_a point_n of_o aries_n and_o libra_n in_o so_o much_o that_o whereas_o the_o difference_n of_o right_a ascension_n answerable_a to_o one_o sign_n or_o 30._o degree_n take_v about_o those_o tropical_a point_n be_v more_o than_o 32._o degree_n and_o a_o half_a about_o the_o equinoctial_a point_n it_o be_v little_o more_o than_o 27._o degree_n and_o a_o half_a as_o it_o may_v appear_v by_o the_o sphere_n so_o as_o you_o may_v hereby_o gather_v that_o the_o difference_n of_o ascension_n answerable_a to_o one_o degree_n which_o about_o the_o begin_n of_o capricorn_n be_v one_o degree_n and_o about_o 6._o minute_n about_o the_o begin_n of_o aries_n or_o libra_n be_v only_o 55_o minute_n second_o the_o apparent_a motion_n of_o the_o sun_n be_v much_o swift_a about_o his_o parigâ—â—â—_n in_o the_o sign_n of_o capricorn_n then_o about_o his_o apogaeum_n in_o cancer_n or_o in_o other_o part_n of_o the_o zodiac_n so_o that_o whereas_o the_o sun_n be_v in_o capricorn_n move_v 61._o minute_n and_o something_o more_o in_o a_o day_n in_o aries_n or_o libra_n he_o move_v but_o 59_o min._n or_o very_o little_a more_o in_o the_o same_o time_n therefore_o see_v the_o natural_a day_n be_v nothing_o else_o but_o the_o time_n wherein_o the_o sun_n move_v from_o the_o meridian_n about_o till_o it_o return_v again_o to_o the_o same_o part_n of_o the_o meridian_n it_o must_v needs_o be_v that_o always_o in_o one_o natural_a day_n there_o be_v make_v one_o whole_a revolution_n of_o the_o equinoctial_a circle_n and_o so_o much_o more_o as_o be_v the_o difference_n of_o right_a ascension_n answerable_a to_o the_o apparent_a motion_n of_o the_o sun_n in_o the_o mean_a time_n which_o difference_n of_o ascension_n because_o they_o be_v unequal_a for_o the_o two_o cause_n before_o allege_v the_o natural_a day_n must_v needs_o also_o be_v unequal_a the_o motion_n of_o the_o equinoctial_a circle_n about_o his_o own_o centre_n be_v as_o it_o have_v be_v always_o suppose_v to_o be_v equal_a that_o be_v move_v always_o a_o equal_a space_n in_o equal_a time_n which_o by_o this_o example_n may_v most_o plain_o appear_v the_o sun_n be_v in_o capricorn_n move_v 61._o minute_n in_o a_o natural_a day_n difference_n of_o ascension_n agreeable_a thereto_o be_v 67._o minute_n or_o something_o more_o therefore_o at_o that_o time_n in_o the_o space_n of_o one_o natural_a day_n the_o equinoctial_a circle_n must_v make_v one_o full_a revolution_n and_o 67._o minute_n more_o but_o when_o the_o sun_n be_v in_o aries_n move_v only_o 59_o minute_n in_o a_o day_n and_o the_o difference_n of_o right_a ascension_n answerable_a thereto_o scarce_o 54._o minute_n more_o than_o one_o revolution_n of_o the_o equinoctial_a circle_n there_o shall_v pass_v only_o 54._o minute_n more_o in_o a_o natural_a day_n so_o as_o here_o the_o equinoctial_a circle_n move_v not_o about_o so_o much_o in_o one_o day_n as_o before_o by_o 13._o minute_n see_v then_o that_o 15._o degr_n or_o little_o more_o of_o the_o equinoctial_a circle_n do_v pass_v the_o meridian_n in_o every_o hour_n and_o consequent_o one_o degree_n of_o the_o equinoctial_a pass_v the_o meridian_n in_o 4._o minute_n of_o a_o hour_n and_o one_o minute_n of_o a_o degree_n in_o 4._o second_n of_o a_o hour_n therefore_o 13._o minute_n of_o the_o equinoctial_a shall_v pass_v the_o meridian_n in_o 52._o second_n that_o be_v almost_o in_o one_o minute_n of_o a_o hour_n whereby_o it_o manifest_o appear_v that_o the_o natural_a day_n that_o be_v to_o say_v the_o space_n of_o 24._o hour_n which_o be_v the_o time_n wherein_o the_o sun_n move_v from_o the_o noonestead_n to_o the_o same_o noonestead_n again_o be_v in_o our_o age_n great_a almost_o by_o one_o minute_n of_o a_o hour_n when_o the_o sun_n be_v in_o capricorn_n then_o
when_o he_o be_v in_o aries_n or_o libra_n prop._n xxxiii_o to_o find_v by_o the_o sphere_n how_o much_o the_o natural_a day_n be_v long_o at_o one_o time_n of_o the_o year_n then_o at_o another_o for_o this_o purpose_n it_o will_v be_v best_a to_o take_v a_o good_a number_n of_o day_n together_o as_o for_o example_n take_v the_o whole_a month_n of_o december_n and_o the_o whole_a month_n of_o march_n both_o which_o month_n consist_v of_o the_o same_o number_n of_o 31._o natural_a day_n find_v the_o place_n of_o the_o sun_n for_o the_o beginning_n and_o end_v of_o both_o month_n which_o you_o may_v find_v by_o the_o second_o proposition_n to_o be_v for_o the_o begin_n of_o march_n this_o present_a year_n 1600._o about_o 20._o degree_n and_o 13._o minute_n of_o pisces_fw-la and_o for_o the_o end_n about_o 20._o degr_n 48._o minute_n of_o aries_n also_o for_o the_o begin_n of_o december_n the_o same_o year_n 18._o degr_n 46._o minute_n of_o sâ—gitarie_a and_o for_o the_o end_n 20._o degree_n 24._o minute_n of_o capricorn_n then_o seek_v out_o the_o right_a ascension_n of_o the_o same_o place_n of_o the_o sun_n for_o the_o beginning_n and_o end_n of_o both_o those_o month_n by_o the_o four_o proposition_n and_o the_o difference_n of_o ascension_n answerable_a to_o the_o motion_n of_o the_o sun_n in_o each_o month_n by_o the_o six_o proposition_n which_o you_o may_v find_v by_o the_o sphere_n to_o be_v about_o 33._o degree_n 24_o minute_n for_o december_n and_o 28._o degree_n 39_o minute_n for_o march._n last_o find_v out_o the_o difference_n of_o these_o difference_n of_o ascension_n by_o substract_v the_o lesser_a out_o of_o the_o great_a which_o in_o this_o example_n be_v 4._o degree_n 45._o minute_n which_o resolve_v into_o minute_n of_o a_o hour_n by_o take_v for_o every_o degree_n 4._o minute_n of_o a_o hour_n and_o for_o every_o 15._o minute_n of_o a_o degree_n one_o minute_n of_o a_o hour_n shall_v amount_v to_o 19_o minute_n of_o a_o hour_n that_o be_v a_o quarter_n of_o a_o hour_n and_o 4._o minute_n and_o so_o much_o be_v the_o month_n of_o december_n long_a than_o the_o month_n of_o march_n notwithstanding_o both_o of_o they_o consist_v of_o the_o same_o number_n of_o 31._o natural_a day_n the_o three_o part._n of_o the_o orb_n whereof_o the_o sphere_n of_o the_o sun_n and_o moon_n have_v be_v imagine_v to_o be_v make_v and_o of_o their_o motion_n and_o use_v chap._n i._o of_o the_o orb_n whereof_o the_o sphere_n of_o the_o sun_n be_v make_v within_o the_o sphere_n or_o orb_n contain_v all_o the_o circle_n that_o we_o have_v hitherto_o speak_v of_o and_o represent_v unto_o we_o the_o primum_fw-la mobile_a that_o be_v the_o first_o and_o high_a movable_a heaven_n that_o have_v be_v imagine_v by_o the_o astronomer_n to_o show_v the_o reason_n of_o that_o daily_a motion_n which_o appear_v to_o be_v in_o all_o the_o heaven_n and_o of_o all_o the_o apparence_n that_o follow_v thereupon_o be_v include_v the_o sphere_n and_o orb_n of_o the_o sun_n and_o moon_n the_o sphere_n of_o the_o sun_n contain_v three_o orb_n the_o uppermost_a of_o they_o which_o in_o this_o sphere_n be_v signify_v by_o the_o yellow_a circle_n that_o come_v next_o within_o the_o compass_n of_o the_o zodiac_n be_v call_v deferens_fw-la apogaeum_fw-la solis_fw-la that_o be_v the_o orb_n which_o carry_v about_o that_o point_n wherein_o the_o sun_n be_v further_a distant_a from_o the_o earth_n next_o within_o this_o orb_n be_v place_v the_o eccentrick_a carry_v about_o the_o body_n of_o the_o sun_n which_o in_o this_o sphere_n be_v represent_v by_o the_o green_a colour_a circle_n that_o come_v next_o under_o the_o deferens_fw-la apogaeum_fw-la again_o within_o this_o eccentrick_a be_v include_v the_o three_o orb_n of_o the_o sphere_n of_o the_o sun_n call_v deferens_fw-la perigaeum_n solis_fw-la that_o be_v the_o orb_n carry_v about_o that_o point_n wherein_o the_o sun_n be_v near_a to_o the_o earth_n this_o be_v the_o nethermost_a of_o the_o three_o orb_n of_o the_o sun_n and_o in_o this_o sphere_n be_v represent_v unto_o you_o by_o the_o yellow_a colour_a circle_n next_o under_o the_o sun_n eccentricke_a chap._n ii_o of_o the_o uppermost_a and_o nethermost_a orb_n of_o the_o sphere_n of_o the_o sun_n more_o particular_o in_o the_o uppermost_a and_o nethermost_a of_o these_o three_o orb_n there_o be_v 4._o point_n especial_o to_o be_v consider_v that_o be_v the_o point_n where_o they_o be_v narrow_a and_o where_o they_o be_v broad_a and_o where_o they_o be_v of_o a_o mean_a breadth_n betwixt_o the_o narrow_a and_o broad_a for_o at_o the_o narrow_a part_n of_o the_o uppermost_a orb_n where_o you_o may_v see_v write_v aux_fw-fr solis_fw-la and_o the_o broad_a part_n of_o the_o nethermost_a orb_n be_v the_o place_n of_o the_o sun_n apogaeum_n so_o that_o whensoever_o the_o sun_n come_v there_o he_o be_v further_a distant_a from_o the_o earth_n as_o you_o may_v easy_o try_v if_o with_o a_o pair_n of_o compass_n or_o otherwise_o you_o 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distance_n and_o at_o those_o part_n of_o this_o orb_n which_o be_v in_o the_o midst_n between_o the_o former_a the_o sun_n have_v a_o mean_a distance_n from_o the_o earth_n a_o mean_a i_o say_v between_o the_o least_o and_o great_a distance_n the_o very_a point_n wherein_o this_o mean_a or_o middle_a distance_n happen_v be_v show_v by_o the_o point_n that_o be_v just_a in_o the_o midst_n between_o the_o short_a line_n ab_fw-la and_o ik_fw-mi which_o be_v draw_v overthwart_o on_o either_o side_n of_o this_o orb_n these_o point_n be_v call_v longitudines_fw-la media_fw-la that_o be_v the_o mean_a distance_n of_o the_o sun_n because_o the_o sun_n come_v to_o these_o point_n have_v a_o mean_a distance_n between_o the_o least_o and_o the_o great_a about_o these_o point_n also_o the_o true_a motion_n of_o the_o sun_n be_v as_o it_o be_v in_o a_o mean_a between_o the_o slow_a which_o happen_v the_o sun_n be_v about_o the_o apogaeum_n and_o the_o swift_a which_o happen_v about_o his_o 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call_v the_o houre-circle_n which_o be_v divide_v into_o 24._o equal_a part_n signify_v and_o represent_v unto_o we_o so_o many_o equal_a hour_n whereof_o both_o the_o 〈◊〉_d hour_n be_v fix_v just_a upon_o the_o meridian_n becausâ—â—â—hen_o the_o sun_n come_v to_o the_o meridian_n it_o be_v just_a twelve_o a_o clock_n the_o upper_a xii_o serve_v for_o the_o day_n and_o the_o other_o xii_o beneath_o serve_v for_o the_o night_n the_o index_n or_o the_o painter_n in_o form_n of_o a_o arrow_n fasten_v upon_o the_o pin_n that_o come_v through_o the_o midst_n and_o centre_n of_o this_o circle_n be_v make_v to_o show_v and_o point_n out_o the_o say_a hour_n as_o need_n shall_v requite_v in_o the_o use_n of_o the_o sphere_n the_o use_n of_o this_o hour_n circle_n shall_v be_v show_v hereafter_o when_o we_o shall_v speak_v of_o the_o common_a use_n of_o many_o circle_n of_o the_o sphere_n together_o and_o these_o two_o circle_n that_o be_v the_o meridian_n and_o horizon_n be_v call_v 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alone_o be_v perpendicular_a to_o the_o 〈…〉_z world_n about_o which_o the_o sphere_n be_v equal_o turn_v be_v divide_v into_o two_o halt_v by_o every_o horizon_n in_o the_o same_o point_n 2._o it_o be_v the_o measure_n of_o time_n because_o it_o measure_v the_o quantity_n of_o the_o artificial_a and_o natural_a day_n of_o which_o month_n and_o year_n be_v make_v it_o measure_v also_o the_o quantity_n of_o hour_n and_o of_o other_o time_n which_o the_o sun_n make_v go_v under_o the_o zodiac_n and_o therefore_o the_o degree_n of_o the_o equinoctial_a be_v call_v tempora_fw-la that_o be_v time_n 3._o it_o show_v the_o two_o equinoctial_a point_n in_o the_o ecliptic_a cut_v the_o ecliptic_a in_o two_o place_n which_o be_v the_o beginning_n of_o aries_n and_o libra_n and_o the_o sun_n when_o he_o come_v to_o those_o two_o point_n be_v equal_o distant_a from_o both_o pole_n of_o the_o world_n and_o make_v equality_n of_o day_n and_o night_n in_o all_o place_n which_o happen_v in_o our_o time_n about_o the_o 10._o or_o 11._o day_n of_o march_n and_o the_o 13._o or_o 14._o of_o september_n 4._o the_o irregularity_n of_o the_o zodiac_n and_o of_o all_o the_o sign_n and_o degree_n thereof_o be_v measure_v by_o this_o circle_n for_o see_v the_o most_o part_n of_o the_o apparence_n of_o the_o first_o motion_n be_v refer_v to_o the_o zodiac_n which_o be_v not_o turn_v about_o his_o own_o pole_n but_o about_o the_o pole_n of_o the_o sphere_n and_o therefore_o must_v needs_o be_v unequal_o turn_v about_o it_o be_v needful_a that_o this_o inequality_n shall_v be_v rule_v and_o measure_v by_o some_o other_o equal_a motion_n 5._o it_o devide_v the_o sphere_n into_o two_o half_n which_o they_o call_v hemisphaere_n that_o be_v into_o the_o north_n half_a or_o hemisphere_n wherein_o be_v the_o north_n pole_n and_o into_o the_o south_n hemisphere_n wherein_o be_v the_o south_n pole_n 6._o so_o it_o devide_v the_o zodiac_n into_o the_o north_n half_a and_o the_o south_n half_a or_o into_o the_o north_n sign_n and_o the_o south_n sign_n 7._o from_o this_o circle_n be_v number_v the_o declination_n of_o the_o star_n and_o of_o the_o degree_n and_o part_n of_o the_o ecliptic_a and_o of_o any_o other_o point_n of_o heaven_n 8._o and_o in_o this_o circle_n be_v count_v the_o right_a ascension_n of_o the_o same_o degree_n and_o star_n etc._n etc._n for_o the_o right_a ascension_n of_o any_o star_n or_o point_n of_o the_o heaven_n be_v nothing_o else_o but_o the_o arch_n of_o the_o equinoctial_a circle_n contain_v between_o the_o beginning_n of_o aries_n and_o the_o meridian_n the_o same_o star_n or_o point_n be_v first_o bring_v under_o the_o meridian_n 9_o in_o the_o equinoctial_a be_v count_v the_o ascentionall_a difference_n and_o the_o oblique_a ascension_n and_o descension_n of_o any_o point_n of_o heaven_n and_o from_o the_o same_o circle_n be_v reckon_v the_o distance_n of_o the_o sun_n rise_v from_o the_o true_a east_n point_n for_o the_o oblique_a ascension_n or_o descension_n be_v nothing_o else_o but_o the_o arch_n of_o the_o equinoctial_a contain_v between_o the_o beginning_n of_o aries_n and_o that_o point_n of_o the_o equinoctial_a eastward_n which_o arise_v or_o set_v together_o with_o the_o star_n or_o point_n that_o be_v give_v in_o a_o oblique_a sphere_n and_o the_o difference_n ascentionall_a or_o descentionall_a be_v nought_o else_o but_o the_o arch_n of_o the_o equator_fw-la whereby_o the_o right_a and_o oblique_a ascension_n or_o descension_n of_o a_o star_n or_o any_o other_o point_n in_o heaven_n do_v differ_v each_o from_o other_o the_o distance_n of_o the_o sun_n rise_v from_o the_o true_a east_n point_n which_o in_o latin_a be_v call_v amplitudo_fw-la ortiva_fw-la be_v the_o arch_n of_o the_o horizon_n contain_v between_o the_o equinoctial_a and_o the_o parallel_n of_o the_o sun_n or_o his_o centre_n when_o he_o rise_v 10._o in_o geography_n we_o count_v the_o longitude_n of_o place_n in_o this_o circle_n and_o from_o it_o we_o reckon_v the_o latitude_n in_o the_o globe_n of_o the_o earth_n and_o in_o map_n and_o sea_n chart_n for_o the_o longitude_n of_o a_o place_n be_v nothing_o else_o but_o the_o arch_n of_o the_o equinoctial_a circle_n contain_v between_o two_o meridian_n whereof_o one_o go_v by_o the_o canary_n land_n and_o the_o other_o by_o the_o place_n that_o be_v give_v and_o the_o latitude_n of_o a_o place_n be_v the_o arch_n of_o a_o meridian_n contain_v between_o the_o equinoctial_a and_o the_o zenith_n of_o the_o place_n that_o be_v give_v 11._o in_o dial_v this_o circle_n be_v of_o especial_a use_n for_o by_o mean_n of_o it_o the_o space_n of_o the_o hour_n be_v divide_v in_o all_o kind_n of_o dial_n horizontall_a erect_v direct_a decline_a incline_v recline_a etc._n etc._n 12._o in_o astrology_n the_o twelve_o house_n be_v set_v out_o by_o the_o equal_a division_n of_o this_o circle_n into_o twelve_o part_n according_a to_o the_o way_n devise_v by_o regiomontanus_n which_o way_n be_v common_o call_v rational_a or_o reasonable_a and_o this_o circle_n govern_v the_o direction_n whereby_o thing_n to_o come_v be_v artificial_o foretold_v chap._n viii_o the_o description_n of_o the_o zodiac_n the_o great_a broad_a circle_n that_o compass_v about_o the_o sphere_n oblique_o come_v near_o the_o pole_n of_o the_o sphere_n in_o one_o place_n then_o in_o another_o be_v call_v the_o zodiac_n round_o about_o through_o the_o midst_n of_o this_o circle_n be_v draw_v the_o circumference_n common_o call_v the_o ecliptic_a line_n divide_v the_o whole_a sphere_n and_o the_o whole_a breadth_n of_o the_o zodiac_n throughout_o into_o two_o equal_a part_n in_o this_o sphere_n there_o be_v represent_v unto_o we_o two_o ecliptic_a line_n the_o one_o may_v be_v call_v the_o middle_n or_o fix_v ecliptic_a which_o keep_v always_o the_o
more_o year_n it_o return_v again_o into_o aries_n the_o revolution_n of_o one_o trigon_n contain_v almost_o 200._o year_n after_o which_o time_n the_o same_o great_a conjunction_n remove_v into_o the_o next_o trigon_n chap._n ix_o the_o use_n of_o the_o zodiac_n 1._o the_o zodiac_n be_v the_o measure_n of_o the_o second_o motion_n as_o the_o equinoctial_a be_v the_o measure_n of_o the_o first_o motion_n 2._o for_o in_o this_o circle_n we_o reckon_v the_o longitude_n and_o from_o it_o we_o count_v the_o latitude_n of_o all_o the_o star_n for_o the_o longitude_n of_o a_o star_n be_v nothing_o else_o but_o the_o arch_n of_o the_o ecliptck_n contain_v between_o the_o beginning_n of_o aries_n and_o the_o circle_n of_o the_o star_n latitude_n and_o the_o latitude_n be_v the_o arch_n of_o a_o great_a circle_n draw_v by_o the_o pole_n of_o the_o ecliptic_a contain_v between_o the_o star_n and_o the_o ecliptic_a 3._o according_a to_o this_o circle_n the_o whole_a heaven_n yea_o the_o whole_a world_n be_v divide_v into_o twelve_o sign_n whereof_o it_o come_v that_o because_o of_o this_o circle_n aswell_o the_o fix_a as_o the_o wander_a star_n which_o we_o call_v planet_n yea_o and_o those_o star_n also_o that_o appear_v of_o a_o sudden_a as_o blaze_a star_n or_o comet_n and_o other_o meteor_n be_v say_v to_o be_v in_o this_o or_o that_o sign_n and_o that_o three_o manner_n of_o way_n first_o to_o be_v in_o a_o sign_n be_v to_o be_v under_o some_o one_o of_o the_o 12._o part_n of_o the_o ecliptic_a thus_o the_o star_n which_o be_v under_o the_o ecliptic_a but_o especial_o the_o sun_n which_o run_v always_o under_o it_o be_v say_v to_o be_v in_o the_o sign_n second_o because_o the_o zodiac_n have_v latitude_n those_o star_n be_v say_v to_o be_v in_o a_o sign_n which_o although_o they_o be_v beside_o the_o ecliptic_a yet_o be_v under_o the_o zodiac_n and_o so_o any_o of_o the_o other_o planet_n which_o for_o the_o most_o part_n wander_v beside_o the_o ecliptic_a may_v be_v say_v to_o be_v in_o some_o sign_n three_o if_o we_o understand_v six_o great_a circle_n to_o be_v draw_v by_o the_o beginning_n of_o the_o twelve_o sign_n and_o by_o the_o pole_n of_o the_o ecliptic_a by_o these_o circle_v the_o whole_a heaven_n or_o rather_o the_o whole_a world_n be_v divide_v into_o twelve_o part_n which_o with_o a_o general_a name_n be_v call_v sign_n thus_o all_o the_o star_n aswell_o fix_v as_o planet_n and_o comet_n which_o be_v without_o the_o zodiac_n in_o any_o of_o these_o part_n may_v be_v say_v to_o be_v in_o some_o sign_n 4._o in_o this_o circle_n be_v note_v the_o degree_n of_o the_o sign_n with_o which_o the_o star_n do_v rise_v and_o set_v as_o well_o in_o a_o right_a as_o in_o a_o oblique_a sphere_n for_o because_o this_o circle_n be_v the_o chief_a all_o celestial_a appearance_n or_o at_o least_o the_o most_o part_n of_o they_o be_v refer_v unto_o it_o and_o not_o unto_o the_o equinoctial_a but_o the_o equinoctial_a measure_v the_o time_n of_o their_o rise_n and_o setting_n 5._o the_o obliquity_n of_o the_o ecliptic_a be_v the_o cause_n of_o the_o inequality_n aswell_o of_o natural_a day_n in_o both_o sphere_n as_o of_o artificial_a day_n in_o a_o oblique_a sphere_n for_o see_v it_o be_v move_v unequal_o because_o it_o be_v move_v upon_o other_o pole_n than_o his_o own_o the_o sun_n which_o be_v the_o author_n and_o maker_n of_o time_n move_v under_o it_o must_v needs_o make_v unequal_a day_n 6._o the_o chief_a time_n be_v define_v by_o this_o circle_n as_o the_o time_n of_o a_o year_n by_o the_o motion_n of_o the_o sun_n the_o time_n of_o a_o month_n by_o the_o motion_n of_o the_o moon_n through_o the_o whole_a compass_n of_o this_o circle_n also_o the_o four_o quarter_n of_o the_o year_n spring_n summer_n autumn_n and_o winter_n whereto_o may_v be_v add_v plato_n his_o great_a year_n which_o be_v the_o time_n wherein_o the_o fix_a star_n make_v one_o revolution_n about_o the_o axtree_n and_o pole_n of_o the_o zodiac_n if_o god_n will_v have_v the_o world_n to_o last_v so_o long_o 7._o the_o ecliptic_a line_n show_v the_o place_n and_o time_n of_o the_o eclipse_n for_o the_o sun_n and_o moon_n be_v eclipse_v only_o under_o it_o or_o near_o unto_o it_o 8._o as_o the_o description_n of_o the_o tropic_n depend_v on_o the_o obliquity_n of_o the_o ecliptic_a so_o the_o polar_n circle_n be_v describe_v by_o the_o pole_n thereof_o 9_o hereof_o it_o come_v that_o by_o reason_n of_o the_o same_o obliquity_n the_o zone_n and_o climate_n be_v set_v forth_o and_o bound_v 10._o this_o circle_n be_v of_o especial_a use_n in_o astrology_n for_o it_o distinguish_v the_o point_n of_o the_o 12._o house_n and_o in_o it_o the_o aspect_n and_o configuration_n of_o the_o planet_n be_v observe_v the_o chief_a judgement_n aswell_o in_o cast_v figure_n as_o in_o revolution_n and_o direction_n be_v take_v from_o this_o circle_n chap._n x._o the_o description_n of_o the_o two_o colour_n the_o two_o circle_n cross_v each_o other_o at_o right_a angle_n in_o the_o pole_n of_o the_o sphere_n be_v call_v the_o colour_n whereof_o the_o one_o that_o pass_v by_o the_o common_a meeting_n of_o the_o ecliptic_a and_o equinoctial_a be_v call_v colurus_n aequinoctiorum_fw-la that_o be_v the_o equinoctial_a colour_n or_o the_o colour_n of_o equal_a day_n and_o night_n the_o other_o pass_v by_o the_o pole_n of_o the_o ecliptic_a and_o the_o solstitial_a point_n be_v call_v colurus_n solstitiorum_fw-la the_o solstitial_a colour_n or_o colour_n of_o the_o sunne-standing_n use_v common_a to_o both_o colour_n 1._o by_o mean_n of_o these_o two_o colour_n all_o the_o movable_a circle_n of_o the_o material_a sphere_n be_v frame_v together_o that_o so_o they_o may_v be_v turn_v about_o like_v as_o the_o whole_a heaven_n be_v move_v 2._o the_o pole_n be_v fasten_v in_o the_o common_a meeting_n of_o these_o two_o circle_n and_o the_o pole_n be_v also_o show_v by_o the_o same_o common_a meeting_n 3._o they_o show_v the_o four_o principal_a point_n of_o the_o ecliptic_a that_o be_v the_o two_o equinoctial_a and_o the_o two_o solstitial_a point_n 4._o these_o circle_n show_v those_o point_n of_o the_o ecliptic_a wherein_o the_o sun_n be_v either_o equal_o distant_a from_o both_o pole_n of_o the_o sphere_n or_o come_v near_a to_o either_o of_o they_o in_o which_o point_v the_o sun_n make_v the_o day_n long_a or_o short_a or_o of_o a_o mean_a length_n between_o both_o these_o in_o a_o oblique_a sphere_n 5._o they_o divide_v the_o ecliptic_a into_o four_o quarter_n in_o which_o the_o sun_n make_v four_o quarter_n of_o the_o year_n the_o spring_n the_o summer_n autumn_n and_o winter_n 6._o they_o divide_v the_o ecliptic_a and_o equinoctial_a into_o such_o four_o quarter_n as_o in_o a_o right_a sphere_n do_v rise_v together_o in_o equal_a time_n chap._n xi_o use_v of_o the_o equinoctial_a colour_n 1._o the_o section_n of_o this_o circle_n with_o the_o ecliptic_a show_v the_o equinoctial_a point_n wherein_o the_o equinoctial_a and_o the_o ecliptic_a do_v divide_v and_o cross_v each_o other_o in_o which_o point_v the_o sun_n make_v equality_n of_o day_n and_o night_n throughout_o the_o whole_a world_n whereof_o this_o circle_n be_v also_o call_v colurus_n aequinoctiorum_fw-la that_o be_v the_o colour_n of_o equal_a day_n and_o night_n or_o the_o equinoctial_a colour_n 2._o it_o devide_v the_o ecliptic_a into_o the_o north_n and_o south_n half_n 3._o it_o devide_v the_o sign_n wherein_o the_o sun_n make_v the_o day_n long_o than_o the_o night_n from_o those_o sign_n wherein_o the_o day_n be_v make_v short_a than_o the_o night_n 4._o it_o show_v which_o half_n of_o the_o ecliptic_a and_o equator_fw-la do_v arise_v together_o in_o equal_a time_n in_o a_o oblique_a sphere_n 5._o it_o show_v the_o two_o high_a sunne-standing_n in_o a_o right_a sphere_n in_o the_o time_n of_o which_o sunne-standing_n the_o sun_n pass_v by_o the_o zenith_n chap._n xii_o use_v of_o the_o solstitial_a colour_n 1._o the_o common_a meeting_n of_o this_o circle_n with_o the_o ecliptic_a show_v the_o solstitial_a or_o tropical_a point_n in_o which_o point_v the_o sun_n seem_v to_o stand_v and_o then_o return_v back_o again_o for_o which_o cause_n this_o circle_n be_v call_v the_o colour_n of_o the_o sun-standing_n these_o point_n be_v call_v tropical_a which_o be_v as_o much_o to_o say_v as_o turne-point_n or_o point_n of_o return_n because_o that_o when_o the_o sun_n go_v always_o under_o the_o ecliptic_a come_v to_o these_o point_n which_o be_v further_a distant_a from_o the_o equinoctial_a circle_n it_o return_v again_o towards_o the_o same_o circle_n but_o they_o be_v call_v solstitial_a or_o sun-ding_a point_n because_o that_o while_o the_o sun_n be_v about_o those_o
point_n the_o difference_n of_o the_o sun_n return_v be_v for_o certain_a day_n insensible_a hereof_o the_o sun_n be_v say_v to_o make_v his_o station_n or_o to_o stand_v when_o he_o come_v to_o either_o of_o those_o point_n they_o that_o dwell_v without_o the_o tropicke_n have_v two_o sunne-standing_n that_o be_v the_o summer_n sun-standing_a or_o high_a sun-standing_a when_o the_o sun_n in_o summer_n time_n be_v at_o the_o high_a and_o next_o unto_o our_o zenith_n be_v in_o the_o begin_n of_o cancer_n and_o the_o winterly_a or_o low_a sun-standing_a when_o the_o sun_n in_o winter_n time_n be_v low_a in_o the_o meridian_n and_o further_a from_o our_o zenith_n but_o they_o that_o dwell_v within_o the_o tropic_n by_o a_o certain_a similitude_n take_v from_o our_o sun-standing_n wherein_o the_o sun_n be_v either_o high_a or_o low_a be_v say_v to_o have_v four_o sun-standing_n that_o be_v two_o high_a sun-standing_n when_o the_o sun_n pass_v by_o their_o zenith_n the_o high_a point_n in_o the_o heaven_n which_o happen_v twice_o every_o year_n in_o two_o place_n equal_o distant_a from_o the_o beginning_n of_o cancer_n and_o capricorn_n and_o two_o low_a sun-standing_n when_o the_o sun_n be_v in_o the_o begin_n of_o cancer_n and_o capricorn_n 2._o in_o this_o circle_n by_o the_o arch_n contain_v between_o the_o equator_fw-la and_o ecliptic_a we_o measure_v the_o great_a declination_n of_o the_o sun_n or_o obliquity_n of_o the_o ecliptic_a which_o in_o ptolomee_n time_n be_v 23._o degree_n 51._o minute_n and_o one_o three_o part_n of_o a_o minute_n but_o ever_o since_o that_o time_n it_o have_v be_v find_v by_o observation_n to_o decrease_v so_o as_o in_o this_o our_o age_n it_o be_v no_o more_o than_o 23._o degree_n and_o one_o half_a or_o little_o more_o notwithstanding_o copernicus_n think_v that_o the_o great_a obliquity_n be_v 23._o degree_n 28._o minute_n 3._o it_o show_v the_o place_n of_o the_o ecliptic_a in_o which_o the_o sun_n come_v near_o to_o our_o zenith_n make_v the_o artificial_a day_n long_a or_o go_v further_a from_o the_o same_o point_n make_v the_o same_o short_a 4._o it_o devide_v the_o zodiac_n into_o two_o half_n the_o one_o ascend_v and_o the_o other_o descend_v 5._o hereby_o also_o the_o sign_n be_v distinguish_v which_o do_v rise_v right_o and_o which_o rise_v oblique_o in_o a_o oblique_a sphere_n for_o the_o descend_v half_n rise_v right_o and_o the_o ascend_a half_n rise_v oblique_o 6._o so_o the_o point_n of_o the_o ecliptic_a be_v show_v by_o this_o circle_n wherein_o the_o great_a difference_n of_o right_n and_o oblique_a ascension_n happen_v it_o distinguish_v those_o sign_n in_o which_o when_o the_o sun_n move_v the_o artificial_a day_n be_v increase_v and_o the_o night_n decrease_v from_o those_o sign_n wherein_o the_o day_n be_v diminish_v and_o the_o night_n increase_n 7._o in_o this_o circle_n be_v the_o bredth_n of_o the_o zone_n bound_v for_o the_o obliquity_n of_o the_o ecliptic_a double_v show_v the_o breadth_n of_o the_o torrid_a or_o burn_a zone_n the_o distance_n of_o the_o pole_n of_o the_o ecliptic_a and_o of_o the_o pole_n of_o the_o equator_fw-la show_v the_o breadth_n of_o the_o cold_a or_o freeze_a zone_n and_o the_o other_o two_o arch_n remain_v show_v the_o bredth_n of_o the_o temperate_a zone_n chap._n xiii_o the_o description_n of_o the_o two_o tropicke_n the_o two_o small_a circle_n equidistant_a in_o all_o place_n from_o the_o equinoctial_a and_o come_v under_o these_o solstitial_a point_n of_o the_o ecliptic_a on_o both_o side_n be_v call_v the_o tropic_n that_o be_v circle_n of_o return_n and_o they_o be_v so_o call_v because_o that_o when_o the_o sun_n come_v to_o they_o it_o begin_v to_o return_v back_o again_o towards_o the_o equinoctial_a circle_n or_o else_o they_o may_v be_v so_o call_v because_o they_o be_v describe_v by_o the_o turn_n about_o of_o the_o tropical_a point_n of_o cancer_n and_o capricorn_n they_o be_v also_o call_v solstitial_a circle_n that_o be_v circle_n of_o the_o sun-standing_n because_o that_o by_o reason_n of_o the_o insensible_a alteration_n of_o the_o declination_n of_o the_o ecliptic_a for_o some_o space_n both_o before_o and_o after_o the_o tropical_a point_n the_o sun_n in_o respect_n of_o his_o meridian_n altitude_n or_o in_o respect_n of_o the_o motion_n he_o have_v towards_o the_o north_n or_o south_n by_o reason_n of_o the_o obliquity_n of_o the_o ecliptic_a seem_v to_o stand_v as_o it_o be_v for_o certain_a day_n in_o those_o place_n there_o be_v two_o tropic_n the_o tropic_a of_o cancer_n and_o the_o tropic_n of_o capricorn_n the_o tropic_n of_o cancer_n touch_v the_o ecliptic_a in_o the_o begin_n of_o cancer_n which_o be_v the_o most_o northerly_a point_n of_o the_o ecliptic_a or_o it_o be_v the_o tropic_a describe_v in_o the_o first_o movable_a sphere_n by_o the_o summer_n solstitial_a point_n this_o circle_n be_v call_v the_o tropic_a of_o cancer_n because_o it_o touch_v the_o ecliptic_a in_o the_o begin_n of_o cancer_n it_o be_v also_o call_v the_o summer_n tropic_n and_o the_o tropic_a of_o the_o summer_n sun-standing_a because_o that_o when_o the_o sun_n come_v to_o it_o the_o summer_n begin_v it_o be_v call_v the_o north_n tropic_n because_o it_o be_v in_o the_o north_n part_n of_o the_o world_n and_o the_o circle_n of_o the_o high_a sunne-standing_a because_o the_o sun_n come_v to_o it_o be_v high_a in_o the_o meridian_n and_o next_o unto_o our_o zenith_n which_o dwell_v in_o the_o north_n part_n of_o the_o world_n without_o the_o tropic_n the_o tropic_a of_o capricorn_n be_v the_o tropic_a which_o touch_v the_o ecliptic_a in_o the_o first_o point_n of_o capricorn_n it_o be_v call_v the_o tropic_a of_o capricorn_n because_o it_o touch_v the_o ecliptic_a in_o the_o begin_n of_o capricorn_n it_o be_v call_v the_o winter_n tropic_n and_o tropic_a of_o the_o winter_n sun-standing_a because_o the_o sun_n come_v to_o it_o in_o winter_n it_o be_v also_o call_v the_o circle_n of_o the_o low_a sunne-standing_a because_o that_o when_o the_o sun_n come_v to_o this_o tropic_n it_o be_v further_a distant_a from_o our_o zenith_n and_o have_v his_o low_a height_n in_o the_o meridian_n chap._n xiiii_o use_v of_o the_o tropicke_n 1._o the_o tropic_n show_v the_o tropical_a or_o solstitial_a point_n of_o the_o ecliptic_a that_o be_v the_o point_n wherein_o the_o sun_n seem_v to_o stand_v and_o begin_v to_o return_v back_o again_o 2._o they_o bind_v out_o the_o great_a declination_n of_o the_o sun_n which_o in_o our_o time_n be_v about_o 23._o degree_n and_o a_o half_a 3._o therefore_o they_o do_v also_o bind_v out_o the_o obliquity_n of_o the_o ecliptic_a for_o they_o be_v the_o bound_n of_o the_o sun_n way_n beyond_o which_o the_o sun_n go_v not_o at_o any_o time_n 4._o the_o sun_n come_v to_o either_o of_o these_o circle_n be_v either_o near_a or_o further_a distant_a from_o our_o vertical_a point_n 5._o in_o a_o oblique_a sphere_n they_o measure_v out_o the_o short_a and_o long_a artificial_a day_n and_o night_n 6._o the_o tropic_n aswell_o in_o heaven_n as_o in_o earth_n contain_v betwixt_o they_o the_o torrid_a zone_n and_o separate_v it_o from_o the_o temperate_a chap._n xv._n the_o polar_a circle_n the_o two_o small_a circle_n that_o be_v next_o about_o the_o pole_n of_o the_o sphere_n be_v call_v the_o polar_n circle_n they_o be_v draw_v by_o the_o pole_n of_o the_o ecliptic_a and_o be_v every_o where_o equidistant_a from_o the_o equinoctial_a and_o from_o the_o pole_n of_o the_o sphere_n they_o be_v call_v polar_n circle_n either_o because_o they_o be_v near_o the_o pole_n of_o the_o sphere_n or_o else_o because_o they_o be_v describe_v by_o the_o motion_n of_o the_o pole_n of_o the_o ecliptic_a and_o therefore_o there_o be_v two_o polar_n circle_n that_o be_v so_o many_o as_o there_o be_v pole_n of_o the_o ecliptic_a the_o polar_a circle_n arctic_a and_o the_o polar_a antarctic_a the_o arctic_a polar_n circle_n be_v that_o which_o pass_v by_o the_o north_n pole_n of_o the_o ecliptic_a or_o which_o be_v describe_v by_o the_o north_n pole_n of_o the_o ecliptic_a be_v carry_v about_o with_o the_o motion_n of_o the_o first_o movable_a sphere_n the_o antarctic_a polar_n circle_n be_v that_o which_o go_v by_o the_o south_n pole_n of_o the_o ecliptic_a be_v describe_v with_o the_o first_o motion_n by_o the_o antarctic_a pole_n of_o the_o ecliptic_a the_o distance_n of_o these_o polar_n circle_n from_o the_o pole_n of_o the_o sphere_n be_v equal_a to_o the_o distance_n of_o the_o tropick_n from_o the_o equinoctial_a which_o in_o our_o time_n be_v about_o 23._o degr_n and_o a_o half_a for_o so_o much_o as_o be_v the_o obliquity_n of_o the_o zodiac_n whereto_o the_o distance_n of_o the_o tropic_n from_o the_o equinoctial_a be_v always_o equal_a so_o
great_a star_n call_v the_o bull_n eye_n who_o place_n in_o longitude_n be_v about_o the_o 4._o degr_n of_o taurus_n and_o his_o latitude_n about_o 5._o degree_n and_o a_o half_a southwards_o follow_v therefore_o the_o direction_n prescribe_v in_o this_o proposition_n you_o shall_v find_v that_o upon_o the_o first_o day_n of_o april_n this_o present_a year_n 1600._o the_o same_o star_n rise_v here_o at_o london_n about_o half_a a_o hour_n past_o 7._o of_o the_o clock_n in_o the_o morning_n and_o set_v about_o a_o quarter_n of_o a_o hour_n past_o 10._o at_o night_n and_o come_v to_o the_o meridian_n about_o 3._o a_o clock_n afternoon_n also_o you_o shall_v find_v that_o it_o rise_v with_o the_o 15._o degree_n of_o gemini_fw-la and_o set_v with_o the_o last_o degr_n of_o taurus_n and_o come_v to_o the_o meridian_n or_o mid_v heaven_n with_o the_o 5._o deg_n of_o gemini_fw-la three_o you_o shall_v find_v his_o declination_n to_o be_v about_o 15._o deg_n and_o 2._o three_o part_n his_o right_a ascension_n 63._o degr_n and_o a_o quarter_n his_o oblique_a ascension_n 43._o degr_n and_o his_o oblique_a descension_n about_o 84._o deg_n and_o a_o half_a and_o last_o his_o amplitude_n of_o breadth_n of_o rise_v or_o let_v about_o 25._o degr_n and_o a_o half_a from_o the_o true_a east_n and_o west_n point_v towards_o the_o north._n prop._n xxv_o to_o know_v how_o long_o the_o moon_n or_o any_o of_o the_o planet_n of_o fix_a star_n do_v shine_v or_o continue_v above_o the_o horizon_n the_o sphere_n bring_v set_v up_o the_o latitude_n of_o the_o place_n and_o the_o place_n of_o the_o moon_n planet_n or_o fix_a star_n be_v find_v and_o mark_v in_o the_o zodiac_n hoth_v in_o longitude_n and_o latitude_n as_o in_o the_o 〈◊〉_d prop._n bring_v the_o place_n of_o the_o moon_n planet_n or_o star_n 〈◊〉_d east_n semicircle_n of_o the_o horizon_n and_o the_o index_n of_o hour_n to_o 12._o a_o clock_n then_o 〈◊〉_d about_o the_o sphere_n westward_n till_o the_o same_o place_n of_o the_o moon_n or_o 〈◊〉_d the_o same_o planet_n or_o star_n come_v to_o the_o west_n semicircle_n of_o the_o horizon_n and_o mark_v 〈◊〉_d how_o many_o hour_n the_o index_n run_v over_o in_o the_o mean_a time_n upon_o the_o hour_n circle_n for_o so_o many_o hour_n continue_v the_o moon_n planet_n or_o star_n above_o the_o horizon_n thus_o shall_v you_o find_v that_o the_o foresay_a 〈…〉_z the_o bull_n eye_n 〈…〉_z the_o horizon_n at_o london_n about_o 14._o 〈…〉_z and_o 3._o quarter_n prop._n xxvi_o to_o find_v which_o of_o the_o planet_n or_o fix_a star_n be_v above_o or_o under_o the_o horizon_n at_o any_o time_n etc._n etc._n the_o place_n of_o the_o plantes_n or_o fix_v star_n be_v mark_v in_o the_o zodiac_n of_o the_o sphere_n as_o in_o the_o former_a proposition_n and_o the_o place_n of_o the_o sun_n bring_v to_o the_o meridian_n and_o then_o the_o index_n to_o 12._o 〈…〉_z sphere_n 〈◊〉_d the_o index_n 〈◊〉_d to_o that_o hour_n upon_o the_o hour_n 〈◊〉_d at_o which_o you_o desire_v to_o know_v what_o planet_n be_v above_o or_o under_o the_o horizon_n and_o then_o hold_v still_o the_o sphere_n and_o mark_v what_o planet_n or_o star_n be_v above_o or_o under_o the_o horizon_n in_o the_o sphere_n for_o the_o same_o planet_n or_o star_n be_v above_o or_o under_o the_o horizon_n in_o the_o heaven_n as_o for_o example_n the_o 1._o of_o april_n 1600_o at_o 9_o of_o the_o clock_n at_o night_n you_o may_v by_o the_o proposition_n find_v that_o the_o most_o part_n of_o the_o fix_a star_n that_o be_v in_o the_o constestation_n of_o taurus_n gemini_fw-la cancer_n leo_n virgo_fw-la and_o libra_n together_o with_o the_o three_o superior_a planet_n 〈◊〉_d â—upiter_n &_o mars_n be_v at_o 〈…〉_z to_o be_v see_v above_o the_o horizon_n and_o that_o the_o rest_n of_o the_o planet_n and_o fix_a star_n that_o be_v within_o the_o compass_n of_o the_o zodiac_n be_v under_o the_o horizon_n and_o can_v then_o be_v see_v prop._n xxvii_o to_o find_v in_o what_o time_n any_o sign_n or_o part_n of_o the_o ecliptic_a rise_v or_o set_v bring_v the_o beginning_n of_o the_o sign_n or_o part_n of_o the_o ecliptic_a to_o the_o east_n semicircle_n of_o the_o horizon_n if_o you_o will_v know_v in_o how_o long_a time_n it_o rise_v or_o to_o the_o west_n part_n of_o the_o horizon_n if_o you_o will_v know_v in_o what_o time_n it_o set_v then_o set_v the_o index_n to_o 12._o a_o clock_n and_o turn_v forward_o the_o sphere_n till_o the_o whole_a sign_n or_o part_n of_o the_o zodiac_n be_v rise_v or_o set_v for_o then_o the_o index_n show_v upon_o the_o hour_n circle_n in_o how_o long_a time_n that_o sign_n or_o part_n of_o the_o zodiac_n rise_v or_o set_v thus_o you_o may_v find_v for_o example_n that_o the_o whole_a sign_n of_o aries_n here_o at_o london_n rise_v in_o one_o hour_n or_o somewhat_o less_o and_o set_v in_o two_o hour_n and_o three_o quarter_n or_o something_o more_o and_o that_o the_o whole_a quarter_n of_o the_o zodiac_n from_o the_o begin_n of_o aries_n to_o the_o begin_n of_o cancer_n rise_v in_o less_o than_o four_o hour_n but_o set_v in_o more_o than_o 8._o hour_n prop._n xxviii_o to_o find_v the_o hour_n of_o the_o night_n by_o any_o of_o the_o planet_n or_o fix_a star_n in_o the_o zodiac_n etc._n etc._n the_o place_n that_o be_v to_o say_v the_o longitude_n &_o latitude_n of_o any_o planet_n or_o fix_a star_n in_o the_o zodiac_n that_o be_v above_o the_o horizon_n be_v first_o find_v and_o mark_v in_o the_o zodiac_n of_o the_o sphere_n bring_v the_o place_n of_o the_o sun_n find_v by_o the_o 2._o proposition_n to_o the_o meridian_n and_o the_o index_n to_o 12._o a_o clock_n upon_o the_o hour_n circle_n then_o have_v find_v the_o height_n of_o the_o star_n or_o planet_n by_o observation_n and_o the_o sphere_n also_o be_v set_v to_o the_o latitude_n of_o the_o place_n of_o observation_n take_v between_o the_o foot_n of_o your_o compass_n so_o many_o degree_n of_o the_o ecliptic_a or_o equinoctial_a as_o the_o height_n of_o the_o planet_n or_o star_n observe_v come_v to_o and_o set_v one_o foot_n of_o your_o compass_n in_o the_o place_n of_o the_o planet_n or_o fix_a star_n that_o you_o observe_v in_o the_o zodiac_n turn_v the_o sphere_n forward_o or_o backward_o till_o you_o can_v but_o only_o touch_v the_o horizon_n with_o the_o other_o foot_n for_o then_o the_o index_n in_o the_o hour_n circle_n shall_v show_v you_o the_o hour_n of_o the_o night_n suppose_v for_o example_n i_o shall_v observe_v the_o height_n of_o the_o foresay_a bull_n eye_n and_o shall_v find_v the_o same_o to_o be_v 29._o degree_n the_o first_o day_n of_o march_n at_o evening_n find_v therefore_o the_o place_n of_o that_o star_n in_o the_o zodiac_n of_o the_o sphere_n and_o bring_v it_o with_o help_n of_o the_o compass_n to_o the_o height_n observe_v have_v first_o set_v the_o place_n the_o sun_n and_o houre-index_n both_o together_o to_o the_o meridian_n the_o index_n of_o the_o hour_n will_v show_v that_o when_o that_o star_n have_v that_o height_n of_o 29._o degree_n it_o be_v about_o 9_o of_o the_o clock_n at_o night_n prop._n xxix_o to_o know_v at_o any_o time_n of_o the_o year_n what_o star_n in_o the_o zodiac_n arise_v or_o set_v cosmical_o achronical_o or_o heliacal_o such_o star_n as_o rise_v together_o with_o the_o sun_n be_v say_v to_o rise_v cosmical_o and_o such_o star_n as_o set_v when_o the_o sun_n rise_v be_v say_v to_o set_v cosmical_o but_o those_o star_n which_o set_v together_o with_o the_o sun_n set_v achronycal_o and_o those_o star_n that_o rise_v when_o the_o sun_n set_v be_v say_v to_o rise_v achronical_o last_o those_o star_n that_o rise_v a_o little_a before_o the_o sun_n rise_v heliacal_o and_o those_o that_o set_v a_o little_a after_o the_o sun_n set_v heliacal_o all_o which_o may_v thus_o be_v find_v bring_v the_o place_n of_o the_o sun_n to_o the_o east_n semicircle_n of_o the_o horizon_n for_o the_o star_n that_o be_v then_o a_o little_a above_o the_o horizon_n rise_v heliacal_o but_o those_o that_o be_v in_o the_o horizon_n in_o the_o east_n rise_v cosmical_o and_o they_o that_o be_v in_o the_o west_n semicircle_n of_o the_o horizon_n set_v cosmical_o but_o bring_v the_o place_n of_o the_o sun_n to_o the_o west_n semicircle_n of_o the_o horizon_n for_o those_o star_n as_o be_v at_o the_o west_n part_n of_o the_o horizon_n at_o the_o same_o time_n set_v achronycal_o but_o those_o that_o be_v then_o in_o the_o east_n semicircle_n of_o the_o horizon_n rise_v achronycal_o and_o they_o which_o be_v a_o little_a above_o the_o west_n semicircle_n of_o the_o horizon_n set_v heliacal_o thus_o you_o may_v know_v that_o upon_o the_o 26._o or_o
uttermost_a edge_n of_o this_o orb_n at_o the_o perigaeum_n and_o turn_v the_o other_o foot_n towards_o the_o centre_n of_o the_o sphere_n so_o much_o as_o this_o foot_n of_o the_o compass_n be_v from_o the_o inner_a edge_n of_o the_o deferens_fw-la paerigaeum_fw-la so_o much_o be_v the_o sun_n further_o distant_a from_o the_o earth_n at_o that_o time_n then_o when_o he_o be_v in_o his_o paerigaeum_fw-la chap._n four_o of_o the_o situation_n and_o motion_n of_o the_o uppermost_a and_o nethermost_a orb_n of_o the_o sun_n the_o uppermost_a and_o nethermost_o of_o these_o three_o orb_n call_v deferens_fw-la apogaeum_n &_o perigaeum_n solis_fw-la do_v always_o answer_v each_o to_o other_o in_o such_o sort_n that_o the_o broad_a part_n of_o the_o one_o be_v always_o against_o the_o narrow_a part_n of_o the_o other_o and_o therefore_o both_o of_o they_o be_v move_v thgether_o with_o one_o motion_n about_o the_o axtree_n and_o pole_n of_o the_o ecliptic_a make_v one_o revolution_n under_o the_o zodiac_n in_o the_o space_n of_o 17000._o year_n almost_o for_o in_o ptolemee_n his_o time_n that_o be_v about_o the_o year_n of_o our_o lord_n 134._o the_o place_n of_o the_o sun_n apogaeum_n be_v about_o the_o midst_n of_o the_o 6._o deg_n of_o gemini_fw-la as_o it_o may_v appear_v by_o the_o 4._o chapter_n of_o the_o 3._o book_n of_o his_o almage_a but_o in_o our_o time_n we_o find_v that_o it_o can_v exceed_v the_o 7._o degr_n of_o cancer_n although_o after_o the_o account_n of_o copernicus_n and_o of_o the_o prutenicke_n table_n it_o shall_v be_v in_o the_o 9_o degr_n of_o cancer_n so_o as_o if_o the_o rest_n of_o the_o motion_n of_o the_o sun_n apogaeum_n that_o be_v to_o come_v hereafter_o be_v proportionable_a to_o that_o be_v past_a the_o whole_a revolution_n thereof_o shall_v be_v finish_v in_o 1699._o year_n under_o the_o zodiac_n for_o in_o 1463._o year_n betwixt_o ptolemee_n his_o time_n and_o we_o it_o have_v move_v about_o 31._o degn_n therefore_o it_o shall_v 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