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horizon_n that_o the_o sun_n in_o the_o equatoure_n place_v by_o rise_v and_o set_v pass_v do_v part_n and_o divide_v either_o half_a circle_n into_o equal_a quarter_n and_o with_o these_o point_n do_v the_o pole_n of_o the_o meridian_n join_v and_o either_o quarter_n do_v the_o other_o two_o as_o the_o rise_n and_o set_v divide_v into_o two_o unequal_a ark_n for_o of_o the_o twoe_o northerly_a quarter_n the_o same_o which_o tend_v and_o look_v unto_o the_o east_n be_v the_o solsticial_a rise_n and_o the_o other_o the_o solsticiall_a set_n but_o of_o the_o twoe_o southerly_a the_o easterly_a do_v the_o winter_n rise_v divide_v and_o the_o westerly_a do_v the_o winter_n set_v part_n but_o by_o what_o space_n these_o rise_n and_o setting_n may_v differ_v and_o be_v distant_a from_o the_o former_a middle_n in_o every_o horizon_n and_o in_o the_o largeness_n of_o rise_v do_v ptolemy_n instruct_v in_o that_o elevation_n of_o 40._o degree_n and_o fifteen_o scruple_n of_o the_o shadow_n 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declare_v which_o star_n be_v of_o continual_a appearance_n and_o which_o continual_o hide_v under_o the_o horizon_n which_o do_v set_v and_o which_o do_v arise_v above_o the_o horizon_n so_o that_o it_o appear_v that_o the_o star_n consist_v in_o a_o triple_a defference_n as_o that_o certain_a do_v arise_v and_o set_v certain_a never_o appear_v above_o the_o horizone_n and_o certain_a continue_v and_o be_v always_o above_o the_o horizon_n 3_o the_o horizon_n therefore_o be_v cause_v of_o the_o habitude_n as_o well_o of_o the_o right_n as_o the_o thwart_a sphere_n 4_o the_o rising_z and_o set_v of_o the_o star_n be_v apply_v unto_o the_o horizon_n by_o which_o setting_n and_o rise_n the_o description_n of_o time_n be_v change_v and_o it_o also_o declare_v the_o degree_n of_o the_o zodiac_n with_o the_o which_o each_o star_n rise_v and_o set_v 5_o the_o horizone_n show_v the_o rise_n and_o set_v of_o the_o sign_n of_o the_o zodiac_n the_o exaltation_n or_o elevation_n of_o the_o pole_n and_o the_o equatoure_n the_o latitude_n of_o place_n to_o the_o largeness_n of_o rise_v which_o be_v the_o ark_n of_o the_o horizon_n to_o the_o star_n or_o point_n of_o the_o ecclipticke_a and_o equatour_n arise_v together_o include_v with_o the_o beginning_n of_o the_o twelve_o house_n of_o heaven_n 6_o by_o the_o office_n of_o the_o horizone_n at_o any_o time_n we_o may_v learn_v and_o know_v the_o quantity_n of_o the_o artificial_a day_n and_o night_n and_o likewise_o procure_v or_o show_v the_o just_a cause_n of_o the_o inequality_n of_o the_o artificial_a day_n it_o do_v also_o declare_v the_o rise_n and_o set_v of_o the_o sun_n for_o as_o the_o horizon_n according_a to_o the_o elevation_n or_o depression_n of_o the_o pole_n be_v vary_v even_o so_o be_v the_o verticiall_a day_n in_o themselves_o cause_v unequal_a yea_o in_o those_o point_n of_o the_o zodiac_n 7_o by_o the_o benefit_n of_o the_o horizon_n the_o sun_n shine_v we_o attain_v and_o come_v each_o day_n unto_o the_o knowledge_n of_o the_o unequal_a hour_n of_o the_o day_n 8_o it_o show_v to_o we_o the_o elongation_n of_o the_o star_n from_o the_o rise_n and_o set_v which_o the_o astronomer_n call_v the_o largeness_n of_o the_o rise_n and_o set_v or_o the_o zenith_n of_o the_o rise_n and_o set_v 9_o by_o this_o circle_n we_o learn_v how_o much_o the_o rise_n aswell_o of_o the_o star_n as_o the_o other_o point_n of_o heaven_n be_v distant_a from_o the_o true_a and_o the_o equinoctial_a rise_n that_o be_v in_o the_o same_o be_v the_o latitude_n of_o the_o star_n account_v from_o the_o equinoctial_a and_o also_o their_o rise_n and_o setting_n 10_o it_o manife_v the_o degree_n of_o the_o zodiac_n with_o the_o which_o the_o purpose_a star_n rise_v and_o set_v 11_o it_o iudicate_v the_o star_n or_o the_o celestial_a image_n that_o be_v continual_o in_o sight_n or_o always_o hide_v 12_o it_o make_v manifest_v the_o rise_n and_o setting_n of_o the_o sign_n of_o the_o zodiac_n it_o do_v likewise_o make_v 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meridian_n either_o have_v or_o may_v have_v the_o same_o altitude_n from_o the_o horizon_n as_o to_o the_o eye_n be_v offer_v in_o this_o figure_n follow_v where_o a_o b_o d_o c._n be_v the_o meridian_n b_o e_z c._n the_o great_a half_n of_o the_o parallel_n of_o the_o horizon_n f_o g._n the_o least_o b._n the_o north_n and_o c._n the_o south_n a._n the_o point_n of_o the_o top_n o._n or_o q._n the_o place_n of_o the_o star_n give_v by_o which_o a_o o_o k._n or_o a_o q_o n_z the_o vertical_a circle_n pass_v and_o the_o like_a do_v the_o parallel_n p_o l_o k._n the_o ark_n k_o o._n or_o n_o q._n be_v affirm_v to_o be_v the_o altitude_n or_o elevation_n of_o the_o star_n from_o the_o horizon_n that_o end_v at_o the_o parallel_n p_o o_o l_o r._n and_o p_o o._n be_v the_o distance_n of_o the_o star_n from_o the_o noonestead_n a_o p_o d_o c._n now_o when_o the_o star_n by_o the_o motion_n of_o the_o principal_a be_v draw_v unto_o the_o point_n q._n in_o which_o when_o the_o same_o shall_v be_v it_o will_v be_v equal_o distant_a from_o the_o meridian_n circle_n wherefore_o through_o the_o equal_a distance_n of_o the_o parallel_n of_o which_o they_o be_v name_v shall_v the_o ark_n o_o k._n be_v equal_a to_o the_o ark_n n_o q._n of_o this_o proceed_v and_o be_v cause_v that_o in_o the_o hour_n equidistant_a from_o the_o noonestead_n as_o be_v the_o seven_o hour_n before_o noon_n and_o the_o fifte_a hour_n after_o noon_n likewise_o the_o eight_o and_o the_o four_o the_o nine_o and_o the_o third_o the_o ten_o and_o second_o and_o so_o of_o the_o rest_n the_o sun_n obtain_v equal_a elevation_n above_o the_o horizon_n this_o much_o avail_v in_o the_o composition_n or_o make_v of_o dial_n and_o give_v great_a light_n and_o brevity_n to_o the_o same_o practice_n as_o may_v appear_v elsewhere_o but_o the_o vertical_a circle_n in_o the_o solyde_a sphere_n and_o globe_n by_o one_o quarter_n of_o the_o circle_n depend_v of_o the_o vertical_a point_n unto_o the_o horizon_n divide_v into_o 90._o degree_n be_v declare_v the_o hour_n circle_n in_o that_o the_o whole_a work_n of_o dialle_n depend_v upon_o the_o knowledge_n of_o the_o hour_n circle_n it_o be_v therefore_o requisite_a and_o necessary_a to_o entreat_v full_o of_o the_o circle_n distinguisher_n of_o the_o hour_n or_o at_o the_o least_o utter_v a_o brief_a instruction_n of_o this_o first_o you_o shall_v understande_v that_o the_o equatoure_n only_o which_o as_o afore_o teach_v the_o sun_n be_v either_o in_o the_o begin_n of_o aries_n or_o libra_n be_v regular_o move_v aswell_o in_o the_o right_n as_o thwart_v horizone_n and_o thereof_o be_v always_o the_o one_o half_a above_o the_o horizon_n &_o the_o other_o half_o hide_v under_o the_o horizon_n through_o this_o his_o equal_a motion_n or_o regular_fw-la motion_n be_v it_o judge_v worthy_a and_o laudable_a see_v by_o it_o the_o equal_a hour_n as_o well_o by_o day_n as_o night_n be_v attain_v and_o have_v and_o this_o conceive_v that_o there_o be_v 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noon_n and_o the_o other_o half_n of_o it_o the_o line_n of_o the_o sixth_o hour_n at_o after_o noon_n by_o which_o imagination_n firm_o conceive_v may_v a_o man_n imagine_v between_o the_o half_a horizontall_a circle_n and_o the_o half_a meridian_n circle_n to_o be_v other_o five_o half_a circle_n firm_a and_o immovable_a which_o be_v not_o move_v but_o as_o the_o vertical_a point_n be_v move_v be_v distant_a each_o from_o other_o by_o a_o equal_a distance_n as_o by_o 15._o degree_n of_o the_o equatour_n the_o first_o after_o the_o horizon_n be_v apply_v to_o the_o seven_o hour_n &_o so_o forth_o of_o the_o rest_n and_o in_o like_a manner_n between_o the_o meridian_n half_a circle_n and_o the_o occidental_a horizone_fw-fr be_v other_o five_o circle_n understand_v according_a to_o the_o fourmer_n division_n and_o that_o which_o follow_v the_o meridian_n shall_v be_v apply_v to_o the_o first_o hour_n that_o which_o next_o follow_v to_o the_o second_o hour_n and_o so_o forth_o of_o the_o other_o beside_o imagine_v the_o sun_n to_o ascend_v from_o the_o horizon_n and_o when_o he_o shall_v be_v come_v unto_o the_o first_o half_a circle_n from_o the_o horizon_n then_o shall_v he_o shed_v a_o shadow_n further_a westward_o and_o be_v draw_v up_o unto_o the_o second_o shall_v make_v a_o short_a shadow_n and_o the_o shadow_n shall_v always_o until_o the_o sun_n be_v come_v unto_o the_o half_a noonestéede_o circle_n where_o he_o shed_v or_o send_v a_o shadow_n plum_n down_o right_a to_o the_o earth_n but_o descend_v from_o the_o noonstéede_o unto_o the_o west_n the_o sun_n cause_v then_o the_o like_a shadow_n contrary_a further_o conceive_v that_o the_o exetrée_n of_o the_o world_n in_o who_o pole_n as_o be_v afore_o teach_v all_o the_o hour_n circle_n meet_v together_o in_o one_o do_v perform_v &_o express_v the_o same_o which_o the_o foresay_a circle_n teach_v as_o by_o the_o sun_n dial_n the_o like_a be_v ready_o understand_v and_o know_v the_o circle_n devide_v the_o 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especial_o the_o ancient_a which_o be_v campanus_n a_o singular_a mathematician_n and_o astronmer_n divide_v the_o house_n by_o the_o five_o circle_n of_o heaven_n meeting_n anâ—_n join_v at_o the_o pole_n of_o the_o world_n from_o which_o they_o divide_v the_o whole_a heaven_n together_o with_o the_o meridiane_n into_o twelve_o equal_a house_n but_o for_o a_o better_a and_o ready_a instruction_n they_o form_v and_o draw_v they_o in_o this_o manner_n after_o the_o four_o principal_a quarter_n or_o angle_n of_o heaven_n be_v draw_v and_o that_o the_o right_a ascension_n of_o the_o middle_n of_o heaven_n be_v have_v then_o be_v the_o part_n of_o the_o zodiac_n diligent_o consider_v that_o occupy_v as_o well_o the_o easterly_a as_o the_o westerly_a horizone_n and_o then_o be_v the_o right_a ascension_n seek_v of_o those_o part_n which_o be_v do_v the_o constitution_n and_o make_n of_o the_o two_o house_n in_o the_o easterly_a part_n of_o heaven_n be_v the_o right_a ascension_n of_o the_o 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the_o day_n in_o the_o right_a sphere_n and_o of_o the_o unequalnesse_n in_o the_o thwart_a or_o bow_v sphere_n and_o where_o the_o day_n space_n be_v increase_v and_o lengthen_v there_o the_o night_n space_n be_v lessen_v and_o decrease_v and_o be_v otherwise_o they_o show_v the_o contrary_n in_o the_o second_o the_o parallel_n which_o the_o verticial_a point_n form_n when_o they_o express_v the_o bound_n of_o the_o latitude_n of_o place_n then_o be_v they_o stand_v under_o by_o which_o their_o longitude_n or_o distance_n from_o the_o west_n be_v account_v in_o the_o three_o the_o parallel_n which_o either_o the_o planet_n or_o the_o fix_a star_n describe_v refer_v unto_o the_o equatour_n do_v express_v the_o bound_n of_o their_o drawing_n or_o motion_n from_o the_o equatour_n the_o other_o or_o rest_n which_o apply_v unto_o the_o ecclipticke_a describe_v do_v show_v the_o bound_n of_o the_o latitude_n and_o that_o for_o how_o long_a time_n they_o tarry_v above_o the_o earth_n or_o otherwise_o hide_v within_o the_o earth_n and_o under_o the_o horizone_n do_v either_o show_n in_o the_o four_o the_o great_a and_o chief_a utility_n of_o the_o parallel_n be_v that_o which_o on_o the_o habitable_a earth_n the_o practisioner_n sever_v by_o such_o distance_n as_o by_o how_o much_o y_fw-mi e_fw-es great_a artificial_a day_n be_v by_o a_o quarter_n of_o a_o hour_n long_o increase_v and_o extend_v for_o they_o distinguish_v the_o habitable_a earth_n and_o that_o by_o observation_n into_o certain_a necessary_a space_n and_o do_v iudicate_v the_o regular_a increasing_n of_o the_o day_n and_o what_o be_v common_a to_o each_o dwell_n under_o those_o parallel_n in_o much_o as_o the_o quantity_n the_o increasing_n and_o deminishing_n of_o the_o day_n and_o night_n the_o rise_n and_o setting_n of_o the_o star_n the_o noonstéede_o shadow_n and_o the_o nature_n of_o the_o winter_n and_o summer_n but_o those_o which_o be_v contrary_a as_o that_o there_o be_v a_o difference_n &_o diversity_n of_o the_o dwell_a place_n be_v under_o diverse_a parallel_n they_o indeed_o be_v necessary_a unto_o the_o distribution_n and_o description_n of_o the_o climate_n although_o the_o number_n of_o these_o circle_n be_v so_o infinite_a as_o be_v the_o infinite_a variety_n of_o the_o star_n and_o vertical_a point_n yet_o be_v there_o four_o usual_o rehearse_v in_o these_o element_n or_o introduction_n that_o be_v especial_o note_v and_o describe_v by_o peculiar_a name_n and_o for_o the_o same_o cause_n as_o seem_v to_o i_o in_o that_o they_o divide_v the_o whole_a globe_n of_o heaven_n and_o earth_n into_o five_o zone_n and_o these_o apply_v unto_o the_o plain_a or_o flat_a of_o the_o equatour_n the_o tropic_n of_o cancer_n or_o summer_n tropic_n the_o tropic_n of_o capricorn_n or_o winter_n tropic_n the_o arctic_a or_o northerly_a pole_n the_o antarctic_a or_o southerly_a pole_n which_o circle_n be_v call_v the_o tropicke_n the_o sun_n according_a to_o the_o former_a word_n through_o the_o motion_n of_o the_o first_o mover_n be_v in_o 24_o hour_n draw_v once_o about_o and_o for_o that_o he_o be_v carry_v in_o the_o thwart_a circle_n and_o in_o the_o same_o by_o his_o proper_a motion_n change_v daily_o unto_o other_o place_n of_o the_o zodiac_n it_o must_v needs_o ensue_v that_o he_o describe_v in_o each_o day_n a_o new_a parallel_n and_o those_o do_v the_o sun_n repeat_v in_o the_o part_n of_o the_o zodiac_n which_o be_v equidistant_a from_o the_o solsticiall_a point_n in_o such_o wise_a that_o they_o be_v in_o the_o whole_a 182._o circle_n and_o these_o do_v they_o call_v the_o circle_n of_o the_o natural_a day_n of_o which_o the_o uttermost_a and_o further_a that_o include_v the_o sun_n way_n be_v name_v the_o tropic_n which_o be_v in_o english_a the_o sun_n bound_n in_o that_o the_o sun_n never_o pass_v they_o neither_o towards_o the_o north_n nor_o towards_o the_o south_n but_o after_o his_o touch_v of_o each_o he_o return_v again_o the_o one_o of_o these_o call_v the_o tropic_n of_o cancer_n and_o the_o other_o the_o tropic_n of_o capricorn_n why_o these_o be_v call_v the_o tropicke_n they_o be_v name_v the_o tropic_n of_o the_o greek_a word_n tropikoi_fw-fr which_o be_v in_o english_a the_o turn_n again_o in_o that_o when_o the_o sun_n be_v digress_v from_o the_o equatoure_n and_o come_v unto_o those_o he_o turn_v back_o again_o also_o the_o tropic_n circle_n touch_v the_o zodiac_n at_o the_o beginning_n of_o cancer_n and_o capricorn_n of_o which_o the_o one_o be_v call_v the_o tropic_n of_o cancer_n and_o the_o other_o of_o capricorn_n the_o one_o be_v northerly_a and_o the_o other_o southerly_a and_o as_o to_o our_o dwell_n the_o one_o be_v call_v the_o summer_n circle_n and_o the_o other_o the_o winter_n so_o that_o when_o the_o sun_n touch_v any_o of_o these_o he_o turn_v again_o and_o be_v carry_v towards_o the_o other_o as_o by_o this_o example_n further_o appear_v where_o all_o that_o season_n and_o time_n from_o the_o twelve_o day_n of_o december_n unto_o the_o eleven_o day_n of_o june_n a_o man_n may_v perceive_v the_o sun_n every_o day_n arise_v high_a and_o high_o and_o when_o he_o be_v at_o the_o high_a over_o our_o head_n that_o day_n do_v he_o by_o his_o course_n describe_v the_o summer_n tropic_n from_o which_o again_o turn_v the_o sun_n every_o day_n after_o draw_v low_a and_o low_a from_o our_o vertical_a point_n until_o he_o be_v come_v again_o unto_o the_o low_a in_o which_o twelve_o day_n of_o december_n not_o go_v any_o further_a towards_o the_o south_n but_o be_v come_v unto_o the_o begin_n of_o capricorn_n he_o describe_v the_o winter_n tropic_n the_o tropic_n of_o cancer_n be_v a_o lesser_a circle_n which_o the_o sun_n describe_v at_o the_o enter_v into_o the_o beginning_n thereof_o and_o be_v draw_v by_o the_o daily_a motion_n who_o plain_a or_o flat_o pass_v not_o by_o the_o centre_n of_o the_o earth_n and_o it_o be_v one_o of_o the_o natural_a circle_n which_o be_v outermost_a describe_v of_o the_o sun_n towards_o the_o north_n and_o draw_v by_o the_o begin_n of_o cancer_n and_o it_o have_v also_o his_o name_n of_o the_o stand_n in_o that_o the_o same_o be_v the_o bind_v of_o the_o sun_n journey_n or_o course_n towards_o the_o north_n and_o the_o nigh_a come_v unto_o we_o unto_o which_o be_v bring_v he_o turn_v back_o and_o direct_v his_o course_n into_o the_o south_n of_o which_o that_o place_n be_v call_v trope_n it_o be_v continual_o distant_a from_o the_o equatour_n by_o the_o quantity_n of_o the_o sun_n great_a declination_n which_o at_o this_o day_n be_v of_o 23._o degree_n 28._o minute_n and_o two_o fift_n almost_o and_o it_o enclose_v also_o the_o sun_n way_n and_o do_v beside_o with_o the_o other_o 3._o parallel_n divide_v the_o zone_n of_o heaven_n and_o earth_n further_o this_o be_v name_v the_o circle_n of_o the_o summer_n solstice_n by_o the_o same_o reason_n in_o that_o it_o be_v draw_v by_o the_o point_n of_o the_o summer_n solstice_n and_o the_o northerly_a tropic_n in_o that_o it_o be_v the_o northerly_a part_n of_o the_o world_n and_o the_o summer_n circle_n for_o that_o the_o sun_n in_o the_o summer_n fall_v into_o this_o circle_n also_o this_o circle_n in_o all_o the_o northerly_a tract_n be_v on_o this_o wise_a that_o the_o great_a part_n or_o portion_n be_v above_o the_o horizone_n and_o the_o lesser_a part_n as_o to_o we_o under_o the_o horizon_n so_o that_o the_o sun_n run_v in_o that_o circle_n cause_v the_o long_a day_n of_o summer_n and_o while_o the_o sun_n describe_v these_o circle_n the_o day_n be_v long_o than_o the_o night_n for_o the_o long_a day_n increase_v from_o minute_n to_o minute_n from_o hour_n to_o hour_n and_o from_o the_o latitude_n of_o one_o degree_n unto_o the_o latitude_n of_o 66._o degree_n and_o 30._o minute_n in_o which_o the_o day_n artificial_a be_v of_o 24._o hour_n and_o be_v thereof_o call_v a_o whole_a day_n for_o in_o the_o latitude_n follow_v and_o beyond_o he_o increase_v into_o many_o whole_a day_n a_o like_a definition_n have_v proelus_fw-la where_o he_o write_v that_o the_o summer_n tropic_n be_v the_o further_a circle_n northward_o that_o the_o sun_n describe_v into_o which_o when_o the_o sun_n be_v come_v he_o than_o make_v his_o summer_n turn_v and_o cause_v also_o at_o that_o time_n the_o long_a day_n and_o short_a night_n of_o the_o year_n from_o which_o turn_v back_o he_o go_v again_o towards_o the_o contrary_a coast_n of_o the_o world_n so_o that_o of_o the_o same_o proclus_n it_o be_v call_v a_o tropic_n which_o be_v in_o english_a a_o return_a circle_n for_o it_o be_v evident_a to_o all_o man_n that_o after_o the_o sun_n begin_v to_o turn_v he_o may_v in_o short_a time_n after_o or_o at_o the_o least_o within_o 5._o day_n
through_o the_o difficulty_n of_o measure_v and_o this_o whole_a compass_n be_v not_o only_o mean_v of_o the_o earth_n but_o of_o the_o earth_n and_o water_n joint_o together_o both_o which_o be_v say_v to_o make_v one_o sphere_n also_o eratostenes_n gather_v the_o compass_n of_o all_o the_o earthly_a orb_n by_o the_o proportion_n of_o the_o particular_a or_o the_o degree_n of_o the_o celestial_a circle_n unto_o the_o like_a space_n on_o earth_n for_o he_o affirm_v that_o to_o one_o degree_n of_o the_o celestial_a equatour_n answer_v 700._o furlong_n or_o 15._o german_a mile_n but_o ptolemy_n attribute_v to_o a_o degree_n 500_o furlong_n which_o be_v thus_o to_o be_v understand_v that_o a_o circle_n be_v imagine_v on_o earth_n direct_o under_o the_o equinoctial_a or_o merydian_a line_n devide_v the_o earth_n into_o twoe_o half_n and_o that_o this_o circle_n be_v likewise_o divide_v into_o 360._o part_n or_o degree_n as_o the_o celestial_a circle_n be_v and_o each_o of_o these_o part_n do_v like_a unto_o the_o celestial_a part_n contain_v 700._o furlonge_v or_o 15._o german_a mile_n this_o now_o be_v try_v and_o find_v what_o the_o whole_a sum_n either_o of_o the_o furlong_n or_o mile_n of_o the_o whole_a cyrcumference_n of_o the_o earth_n which_o contain_v 360._o part_n or_o degree_n you_o shall_v easy_o find_v and_o know_v the_o same_o by_o this_o manner_n multiply_v the_o whole_a compass_n of_o the_o earth_n that_o be_v the_o 368._o degree_n by_o the_o 700._o furlong_n or_o fifteen_o german_a mile_n and_o the_o whole_a compass_n shall_v either_o appear_v to_o be_v 252000._o furlong_n or_o 5400._o german_a mile_n this_o whole_a compass_n of_o the_o earth_n divide_v by_o 22._o and_o the_o number_n come_v thereof_o shall_v be_v the_o 22._o part_n of_o the_o compass_n of_o it_o that_o be_v 11454_o 12_o 22._o furlong_n or_o 254_o â—0_n 22._o german_a mile_n and_o abate_v this_o 22._o part_n from_o the_o whole_a sum_n of_o the_o circumference_n and_o the_o number_n in_o furlong_n shall_v remain_v and_o be_v 240545_o 10_o 22._o and_o in_o german_a mile_n 5154_o 1â—_n 22._o and_o if_o any_o of_o these_o sum_n be_v divide_v a_o part_n by_o 3._o it_o shall_v be_v find_v in_o furlong_n to_o be_v 80181._o a_o half_a and_o a_o three_o part_n or_o 3_o 2._o 10_o 66._o and_o in_o german_a mile_n 1718_o 4_o 22._o that_o be_v the_o dyameter_n of_o the_o earth_n aswell_o in_o the_o furlonge_v as_o german_a mile_n and_o archimedes_n by_o sundry_a labour_n and_o witty_a invention_n and_o by_o geometrical_a practice_n have_v find_v that_o the_o like_a proportion_n be_v of_o the_o circumference_n of_o the_o whole_a circle_n un_fw-fr to_o the_o diameter_n of_o the_o same_o as_o be_v 22._o unto_o 7._o that_o be_v the_o diameter_n thrice_o with_o a_o seven_o part_n and_o a_o half_a but_o whensoever_o any_o man_n will_v by_o the_o cyrcumference_n of_o the_o circle_n gather_v and_o find_v his_o diameter_n work_v the_o number_n thus_o as_o this_o example_n teach_v first_o set_v down_o 22._o at_o the_o left_a hand_n towards_o the_o right_a hand_n 7._o and_o the_o cyrcumference_n between_o those_o two_o number_n 22._o 5400._o 7._o after_o multiply_v the_o first_o by_o the_o second_o that_o be_v 7._o by_o 5400._o the_o number_n increase_v which_o be_v 47800._o divide_v by_o the_o third_o that_o be_v 22._o and_o you_o shall_v find_v in_o the_o quotient_a 1718_o 4_o 22._o german_a mile_n or_o thus_o in_o furlong_n the_o number_n be_v set_v down_o alike_o 22._o 252000._o 7._o then_o multiply_v the_o first_o by_o the_o second_o as_o 7._o by_o 25200._o and_o the_o increase_n shall_v be_v 1764000._o after_o the_o increase_v number_n divide_v by_o the_o three_o as_o by_o 22._o and_o the_o diameter_n shall_v be_v 80181_o 18_o 22._o if_o any_o covet_v to_o find_v the_o upper_a face_n of_o the_o earth_n by_o the_o dyameter_n and_o cyrcumference_n know_v work_v one_o into_o the_o other_o and_o you_o shall_v have_v that_o you_o seek_v but_o if_o you_o desire_v to_o know_v the_o thickness_n of_o the_o earth_n then_o join_v the_o superficial_a solydenes_n of_o the_o sphere_n unto_o the_o sixth_o part_n of_o the_o diameter_n and_o you_o shall_v obtain_v your_o desire_n the_o second_o part_n of_o the_o spherical_a element_n of_o the_o celestial_a circle_n with_o the_o use_n of_o the_o same_o circle_n what_o be_v the_o sum_n of_o this_o second_o part._n whereas_o in_o the_o first_o part_n be_v only_o teh_a rudiment_n of_o the_o sphere_n handle_v and_o teach_v which_o be_v also_o write_v and_o contain_v in_o diverse_a phycite_n book_n as_o of_o the_o world_n and_o the_o many_o part_n thereof_o that_o be_v of_o the_o ethereal_a and_o elementary_a region_n and_o also_o of_o the_o part_n motion_n and_o formeâ—_n of_o â—he_n etherial_a region_n as_o heaven_n and_o the_o forâ—â—â—e_n 〈◊〉_d and_o quantity_n of_o the_o earth_n here_o in_o this_o second_o part_n shall_v full_o be_v â—etâ—â—â—_n thâ—_n and_o large_o handle_v the_o manifold_a use_n of_o the_o circle_n of_o which_o the_o material_a sphere_n be_v frame_v and_o make_v further_o this_o second_o part_n be_v divide_v into_o three_o part_n the_o first_o teach_v the_o division_n of_o the_o circle_n in_o that_o the_o ancient_a astronomer_n for_o a_o plain_a instruction_n divided_a heaven_n into_o sundry_a circle_n and_o of_o these_o some_o in_o great_a and_o other_o some_o in_o lesser_a circle_n in_o the_o second_o part_n be_v the_o definition_n description_n and_o utility_n of_o all_o the_o circle_n teach_v in_o the_o three_o and_o last_o part_n be_v the_o place_n of_o the_o zone_n learned_o describe_v and_o the_o utility_n of_o they_o so_o that_o this_o second_o part_n do_v especial_o entreat_v of_o the_o circle_n see_v the_o principal_a point_n of_o the_o sphere_n be_v of_o the_o celestial_a appearance_n which_o by_o reason_n of_o the_o celestial_a circle_n or_o of_o the_o first_o mover_n be_v cause_v as_o may_v appear_v of_o the_o ascension_n and_o descension_n of_o the_o sign_n 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great_a circle_n consist_v in_o the_o middle_n of_o the_o zodiac_n and_o devide_v it_o into_o twoe_o equal_a compass_n define_v to_o be_v eight_o degree_n in_o breadth_n on_o either_o side_n which_o the_o sun_n make_v by_o a_o yearly_a motion_n go_v thwart_o in_o one_o continual_a way_n be_v divide_v by_o the_o four_o principal_a point_n as_o the_o two_o equinoctial_o and_o the_o solstice_n into_o four_o quarter_n for_o as_o the_o whole_a zodiac_n even_o so_o the_o eccliptick_a to_o the_o equatour_n rest_v as_o it_o be_v in_o two_o only_a point_n but_o in_o the_o rest_n of_o the_o circle_n it_o bend_v â—â—om_o either_o point_n towards_o the_o opposite_a pole_n of_o the_o world_n decline_v by_o the_o one_o half_a circle_n into_o the_o north_n and_o by_o the_o other_o half_n into_o the_o south_n the_o point_n that_o touch_v be_v the_o equinoctial_a as_o we_o have_v above_o write_v but_o the_o other_o two_o further_a distant_a from_o the_o equatoure_n which_o be_v as_o mark_n or_o bound_n for_o the_o sun_n departure_n that_o when_o he_o come_v to_o the_o one_o he_o be_v carry_v no_o further_o but_o stay_v there_o and_o from_o thence_o draw_v unto_o the_o contrary_n bind_v through_o which_o turn_v back_o of_o the_o sun_n they_o be_v name_v the_o tropicke_n of_o the_o greek_n and_o of_o the_o latin_n the_o solsticiall_a point_n not_o for_o that_o the_o sun_n be_v carry_v unto_o they_o stay_v and_o remain_v any_o space_n but_o never_o rest_v nor_o leave_v of_o his_o course_n see_v within_o certain_a day_n the_o meridiane_a or_o noon_n shadow_n be_v vary_v the_o day_n &_o night_n space_n either_o lengthen_v and_o increase_v or_o decrease_v and_o shorten_v notable_o as_o the_o like_a be_v yearly_a see_v of_o these_o that_o which_o in_o the_o northerly_a half_a circle_n be_v further_a distant_a from_o the_o equatoure_n name_v the_o point_n of_o the_o summer_n solstice_n the_o other_o stand_v or_o be_v right_o against_o that_o the_o point_n of_o the_o winter_n solstice_n these_o point_n change_v their_o place_n two_o manner_n of_o way_n as_o well_o according_a to_o length_n of_o the_o zodiac_n by_o creep_v further_o in_o the_o before_o go_v as_o in_o go_v to_o and_o come_v short_a unto_o the_o equatoure_n first_o that_o the_o equinoctial_a point_n do_v over_o go_v the_o place_n of_o the_o fix_a star_n against_o the_o order_n and_o course_n of_o the_o sign_n and_o therefore_o do_v the_o day_n of_o the_o solstice_n begin_v and_o go_v before_o for_o the_o summer_n solstice_n about_o the_o begin_n of_o olimpias_n the_o first_o day_n of_o july_n which_o begin_v the_o year_n with_o the_o greek_n at_o the_o morning_n rise_v of_o that_o constellation_n syrius_n be_v notable_o know_v to_o many_o but_o in_o the_o year_n of_o christ_n birth_n it_o happen_v in_o the_o 24._o day_n of_o june_n and_o in_o the_o year_n 1570._o it_o happen_v in_o the_o 12._o day_n of_o june_n about_o 11._o of_o the_o clock_n before_o noon_n the_o winter_n solstice_n in_o the_o first_o 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same_o to_o be_v of_o 23._o degree_n 52._o minute_n and_o 20._o second_n and_o ptolemy_n note_v that_o he_o find_v it_o to_o be_v just_a much_o mahomates_n aratensir_fw-fr which_o be_v after_o ptolemy_n 749._o year_n find_v this_o declination_n to_o be_v of_o 23._o degree_n and_o 35._o minute_n arzahell_n the_o spaniard_n that_o be_v 190._o year_n after_o albategnius_n find_v it_o to_o be_v of_o 23._o degree_n and_o 34._o minute_n prophatius_fw-la judius_fw-la which_o be_v 230._o year_n after_o arzahell_n find_v this_o declination_n to_o be_v of_o 23._o degree_n and_o â—2_n minute_n dominicus_n maria_n be_v in_o the_o year_n of_o christ_n 1491._o find_v this_o declination_n to_o be_v of_o 23._o degree_n and_o 29._o minute_n vueruerus_n be_v
of_o the_o zodiac_n and_o the_o other_o by_o the_o section_n of_o the_o zodiac_n and_o equatoure_n that_o which_o pass_v by_o the_o pole_n of_o the_o equatour_n and_o zodiac_n do_v divide_v in_o two_o part_n each_o half_a circle_n as_o well_o of_o the_o equatour_n as_o the_o zodiac_n therefore_o the_o one_o condition_n of_o the_o colour_n go_v by_o the_o solsticiall_a point_n of_o the_o zodiac_n which_o be_v the_o beginning_n of_o cancer_n and_o capricorn_n and_o the_o further_a point_n from_o the_o equatour_n whereof_o it_o be_v name_v the_o solsticiall_a colour_n the_o other_o be_v name_v the_o equinoctial_a colour_n see_v it_o enter_v by_o the_o say_v equinoctial_a section_n which_o be_v the_o beginning_n of_o aries_n and_o libra_n that_o be_v the_o equinoctial_a point_n so_o that_o these_o colour_n divide_v aswell_o the_o equinoctial_a as_o the_o zodiac_n into_o four_o quarter_n in_o that_o they_o go_v by_o the_o four_o principal_a point_n of_o they_o the_o colour_n general_o be_v call_v all_o the_o great_a circle_n draw_v by_o the_o pole_n of_o the_o world_n which_o take_v their_o name_n thereof_o insomuch_o as_o they_o never_o be_v discern_v or_o see_v whole_a in_o the_o turn_n about_o of_o the_o world_n as_o the_o other_o circle_n but_o unperfect_a and_o lack_v for_o both_o the_o ark_n right_a against_o one_o another_o about_o the_o pole_n in_o the_o thwart_a sphere_n be_v not_o see_v both_o at_o once_o for_o they_o be_v either_o continual_o in_o sight_n to_o we_o and_o never_o draw_v away_o or_o hide_v like_o unto_o those_o which_o be_v near_o to_o the_o elevate_v pole_n or_o else_o they_o never_o appear_v in_o sight_n to_o we_o but_o be_v continual_o hide_v from_o we_o as_o those_o which_o be_v the_o opposite_n but_o the_o reach_a of_o the_o colour_n fasten_v in_o the_o two_o circle_n extend_v and_o pass_v by_o the_o four_o principal_a point_n of_o the_o ecclipticke_a as_o the_o equinoctial_o and_o solsticials_n which_o touch_v one_o another_o in_o the_o pole_n of_o the_o world_n do_v in_o their_o cyrcumference_n make_v right_a angle_n and_o part_v the_o zodiac_n and_o equatoure_n into_o four_o equal_a quarter_n the_o colour_n of_o the_o equinoctial_o rest_v in_o the_o equinoctial_a point_n the_o other_o contain_v the_o solstiticiall_a point_n be_v call_v the_o colour_n of_o the_o solstice_n the_o colour_n of_o the_o equinoctial_o be_v a_o great_a circle_n movable_a and_o every_o where_o alike_o draw_v by_o the_o pole_n of_o the_o world_n or_o equatour_n and_o the_o equinoctial_a point_n as_o the_o beginning_n of_o aries_n and_o libra_n make_v with_o the_o equatour_n right_o spherical_a angle_n with_o the_o zodiac_n thwart_o angle_n for_o oftentimes_o the_o great_a circle_n by_o a_o mutual_a touch_v together_o do_v make_v right_a angle_n in_o the_o sphere_n as_o they_o cut_v in_o two_o part_n or_o into_o equal_a half_a circle_n and_o by_o the_o pole_n one_o another_o and_o contrariwaise_v when_o they_o cut_v one_o another_o by_o the_o pole_n then_o do_v they_o form_v and_o make_v right_a angle_n with_o their_o cyrcumference_n and_o part_v one_o the_o other_o into_o equal_a part_n as_o write_v theodosius_n in_o his_o first_o book_n de_fw-fr sphera_fw-la and_o in_o propositi_fw-la 18._o 19_o 20._o and_o 21._o or_o thus_o the_o colour_n of_o the_o equinoctial_o which_o be_v name_v the_o equinoctial_a colour_n be_v a_o great_a circle_n pass_v by_o the_o pole_n of_o the_o world_n and_o the_o first_o point_n of_o aries_n &_o libra_n where_o the_o two_o equinoctial_a point_n be_v say_v to_o be_v in_o that_o the_o sun_n cause_v a_o like_a day_n and_o night_n in_o every_o place_n or_o for_o that_o these_o point_n be_v in_o the_o equator_fw-la whereof_o it_o be_v call_v the_o colour_n distinguish_v the_o equinoctial_o so_o that_o the_o two_o colour_n cross_v one_o another_o on_o the_o pole_n of_o the_o world_n at_o right_a spericall_a angle_n it_o be_v call_v the_o colour_n of_o the_o equinoctial_o for_o that_o it_o pass_v by_o the_o equinoctial_a point_n as_o by_o the_o beginning_n of_o aries_n &_o libra_n which_o they_o call_v the_o equinoctial_a point_n for_o that_o when_o the_o sun_n happen_v into_o either_o of_o they_o the_o day_n and_o night_n be_v of_o equal_a length_n throughout_o the_o earth_n which_o come_v to_o pass_v twice_o in_o the_o year_n as_o in_o the_o spring_n and_o harvest_n whereof_o the_o one_o be_v call_v the_o equinoctial_a spring_n and_o at_o this_o day_n be_v about_o the_o eleven_o of_o march_n which_o be_v the_o day_n before_o gregory_n the_o other_o the_o harvest_n spring_n and_o happen_v in_o our_o time_n the_o 14._o of_o september_n that_o be_v three_o day_n afore_o lambert_n whereof_o arise_v this_o ancient_a verse_n lampert_n gregori_n nox_fw-la est_fw-la aequata_fw-la diei_fw-la the_o colour_n of_o the_o solstice_n be_v a_o great_a circle_n movable_a and_o every_o where_o alike_o draw_v by_o the_o solsticiall_a point_n or_o the_o beginning_n of_o cancer_n &_o capricornus_fw-la and_o the_o pole_n of_o the_o zodiac_n and_o equatoure_n make_v right_o spherical_a angle_n with_o both_o for_o of_o both_o be_v the_o pole_n comprehend_v and_o according_a to_o theodosius_n propo_fw-it lib._n 2._o de_fw-fr spera_n that_o by_o any_o twoe_o circle_n cross_v one_o the_o other_o when_o a_o third_o devide_v the_o part_n of_o both_o equal_o and_o in_o two_o part_n the_o same_o be_v the_o great_a circle_n and_o pass_v by_o the_o pole_n of_o both_o but_o that_o which_o pass_v by_o the_o pole_n of_o the_o other_o circle_n do_v part_v it_o in_o two_o part_n and_o at_o right_a angle_n here_o may_v be_v demand_v why_o the_o other_o twoe_o be_v call_v the_o solsticiall_a point_n see_v the_o sun_n stay_v no_o where_o which_o be_v thus_o answer_v that_o the_o sun_n digress_v from_o either_o equinoctial_a point_n by_o his_o proper_a motion_n do_v daily_o depart_v from_o the_o equinoctial_a circle_n till_o he_o come_v unto_o the_o solstitial_a point_n where_o he_o be_v further_a distant_a from_o the_o equatoure_n but_o immediate_o after_o he_o begin_v to_o return_v and_o come_v again_o unto_o the_o equatour_n till_o he_o come_v unto_o the_o other_o equinoctial_a point_n so_o that_o the_o point_n of_o the_o sun_n further_a distance_n which_o be_v the_o begin_n of_o cancer_n or_o capricornus_fw-la and_o of_o the_o same_o call_v the_o solstice_n in_o that_o the_o sun_n stay_v there_o that_o be_v cease_v from_o his_o further_a go_v or_o departure_n and_o begin_v again_o to_o come_v to_o the_o equatoure_n for_o the_o sun_n after_o his_o come_n unto_o that_o point_n depart_v and_o come_v again_o to_o the_o equatour_n so_o that_o the_o end_n the_o departure_n and_o beginning_n of_o his_o come_n be_v the_o solstice_n therefore_o not_o for_o that_o the_o sun_n stay_v there_o be_v they_o call_v the_o solstice_n although_o about_o those_o point_n of_o the_o go_n and_o come_v of_o the_o sun_n it_o be_v so_o small_a that_o for_o four_o sire_n or_o more_o day_n after_o he_o seem_v in_o judgement_n as_o it_o be_v to_o stay_v in_o one_o declination_n and_o therefore_o for_o that_o cause_n may_v be_v name_v the_o solstitial_o these_o of_o sundry_a as_o of_o campanus_n be_v also_o call_v tropic_n point_n through_o the_o sun_n return_v and_o these_o may_v be_v call_v uerticiall_a or_o cardinal_a circle_n see_v they_o go_v by_o those_o top_n of_o the_o world_n and_o express_v or_o show_v the_o four_o quarter_n of_o the_o zodiac_n moreover_o see_v certain_a part_n of_o these_o circle_n be_v near_o the_o pole_n be_v hide_v and_o the_o other_o right_n against_o they_o nothing_o at_o all_o discern_v at_o any_o time_n therefore_o be_v it_o that_o they_o be_v call_v in_o greek_a kolouroi_n which_o be_v in_o english_a maim_v and_o unperfect_a as_o proclus_n diadochus_n mocrobius_fw-la and_o capella_n write_v but_o this_o agree_v not_o in_o the_o right_a horizont_n see_v there_o be_v no_o part_n of_o heaven_n which_o do_v always_o remain_v there_o hide_v but_o in_o the_o description_n of_o the_o astrolobie_n how_o large_a soever_o the_o same_o be_v yet_o only_o these_o circle_n appear_v continual_o unperfect_a yet_o further_o the_o colour_n of_o the_o solstice_n or_o the_o circle_n distinguish_v the_o solstice_n which_o also_o be_v call_v the_o solstitial_a circle_n be_v a_o great_a circle_n draw_v and_o pass_v by_o the_o pole_n of_o the_o world_n and_o zodiac_n and_o the_o great_a declination_n of_o the_o same_o and_o by_o the_o beginning_n of_o cancer_n and_o capricornus_fw-la it_o be_v call_v the_o colour_n of_o the_o solstice_n in_o that_o it_o pass_v by_o the_o solsticiall_a point_n as_o by_o the_o beginning_n of_o cancer_n and_o capricornus_fw-la which_o be_v name_v the_o solsticiall_a point_n for_o that_o in_o they_o the_o solstice_n be_v cause_v that_o be_v the_o sun_n come_v unto_o
those_o point_n depart_v not_o further_o from_o the_o equinoctial_a but_o come_v again_o unto_o the_o equinoctial_a which_o be_v cause_v twice_o in_o the_o year_n as_o in_o summer_n and_o winter_n whereof_o the_o one_o be_v call_v the_o summer_n solstice_n which_o in_o our_o time_n happen_v the_o 12._o of_o june_n or_o thereabouts_o be_v the_o next_o day_n after_o s._n barnaby_n the_o apostle_n where_o the_o long_a day_n be_v hold_v to_o be_v the_o other_o the_o winter_n solstice_n which_o in_o our_o time_n happen_v about_o the_o 11._o or_o 12._o day_n of_o december_n be_v a_o day_n or_o two_o before_o lucy_n where_o the_o day_n be_v account_v short_a whereof_o be_v this_o ancient_a verse_n extant_a vitus_n est_fw-fr lucia_n daunt_v tibi_fw-la solstitia_fw-la bina_fw-la of_o the_o former_a also_o ensue_v that_o there_o be_v certain_a fix_a and_o movable_a colour_n for_o there_o be_v a_o fix_a colour_n of_o the_o equiâ—octiale_fw-la which_o pass_v by_o the_o pole_n of_o the_o world_n and_o section_n of_o the_o equatoure_n and_o ecclipticke_a of_o the_o first_o mover_n the_o fix_a colour_n of_o the_o solstice_n do_v cut_v this_o at_o right_a angle_n in_o the_o pole_n of_o the_o world_n and_o pass_v by_o the_o middle_n of_o the_o sun_n great_a declination_n see_v neither_o the_o equinoctial_o nor_o solstice_n be_v cause_v according_a to_o the_o true_a meaning_n of_o the_o astronomer_n as_o afore_o may_v appear_v both_o in_o these_o point_n aswell_o as_o in_o other_o therefore_o a_o man_n must_v conceive_v that_o the_o colour_n be_v movable_a of_o which_o the_o one_o go_v by_o the_o true_a equinoctial_a that_o be_v by_o the_o section_n of_o the_o sun_n way_n and_o equatour_n and_o by_o the_o pole_n of_o the_o world_n and_o the_o other_o of_o the_o solstice_n pass_v by_o the_o sun_n great_a declination_n these_o hitherto_o write_v may_v more_o plain_a appear_v by_o this_o demonstration_n here_o follow_v in_o this_o figure_n be_v the_o circle_n and_o part_n of_o the_o circle_n note_v with_o their_o name_n in_o which_o the_o letter_n f._n express_v the_o true_a and_o movable_a equinoctial_a the_o letter_n e._n be_v a_o note_n of_o the_o fix_a equinoctial_a the_o letter_n d._n point_v out_o the_o head_n of_o aries_n of_o the_o eight_o sphere_n the_o letter_n c._n the_o centre_n of_o the_o eight_o sphere_n the_o letter_n a._n of_o the_o nine_o and_o ten_o sphere_n the_o letter_n k._n n._n represent_v the_o sun_n great_a declination_n true_o the_o letter_n r._n m._n the_o sun_n middle_a declination_n great_a how_o much_o the_o equinoctial_o be_v distant_a one_o from_o another_o the_o former_a large_a instruction_n of_o the_o equinoctial_o may_v easy_o show_v at_o any_o time_n unto_o which_o a_o man_n must_v always_o resort_v the_o sun_n great_a declination_n be_v the_o ark_n of_o the_o colour_n of_o the_o solstice_n contain_v between_o the_o equatoure_n and_o either_o tropic_n this_o of_o sundry_a practisioner_n be_v diverse_o note_v for_o ptolemy_n find_v the_o same_o in_o his_o time_n to_o be_v of_o 23._o degree_n 51._o minute_n and_o 20._o second_n of_o which_o the_o whole_a circle_n be_v note_v to_o be_v 360._o degree_n but_o after_o alnieon_n of_o 23._o degree_n and_o 33._o minute_n but_o the_o late_a practisioner_n have_v find_v the_o same_o to_o be_v 23._o degree_n and_o 30._o minute_n purbachius_n have_v find_v the_o same_o to_o be_v of_o 23._o and_o 21._o minute_n which_o variation_n of_o the_o sun_n great_a declination_n be_v through_o the_o come_n and_o go_v of_o the_o eight_o sphere_n which_o be_v name_v the_o tremble_a motion_n but_o this_o be_v demonstrate_v and_o teach_v more_o at_o large_a in_o the_o theorick_n if_o any_o desire_n to_o observe_v the_o sun_n great_a declination_n let_v he_o take_v the_o altitude_n of_o the_o sun_n about_o the_o winter_n solstice_n in_o the_o short_a day_n at_o noon_n which_o altitude_n be_v keep_v a_o part_n work_v the_o like_a the_o sun_n be_v about_o the_o summer_n solstice_n 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elevation_n of_o thâ—_n pole_n if_o the_o sun_n be_v carry_v in_o the_o southerly_a sign_n then_o work_v contrary_a for_o that_o which_o remain_v shall_v be_v the_o sun_n particular_a declination_n as_o by_o a_o like_a example_n use_v this_o the_o sun_n be_v imagine_v to_o be_v elevate_v above_o the_o horizont_n 63._o degree_n 21._o minute_n and_o 4._o second_n the_o elevation_n of_o the_o pole_n be_v 41._o degree_n and_o 30._o minute_n and_o the_o compliment_n of_o the_o same_o altitude_n of_o the_o pole_n to_o be_v 48._o degree_n and_o 30._o minute_n with_o the_o which_o subtract_v the_o sun_n altitude_n at_o noon_n and_o the_o remaurer_n shall_v be_v the_o sun_n declination_n which_o be_v 14._o degree_n 51._o minute_n &_o 4._o second_n be_v the_o distance_n of_o the_o sun_n from_o the_o begin_n of_o aries_n abate_v for_o the_o sun_n run_v in_o the_o northerly_a sign_n at_o the_o time_n of_o the_o observation_n before_o the_o summer_n solstice_n what_o the_o office_n or_o utility_n 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measure_v and_o number_v in_o that_o the_o sun_n great_a declination_n be_v the_o ark_n of_o the_o colour_n of_o the_o colsticis_fw-la enclose_v between_o the_o beginning_n of_o cancer_n and_o the_o equatour_n which_o arcke_n be_v either_o increase_v or_o diminish_v according_a to_o the_o wind_a in_o and_o out_o of_o the_o ecliptic_n unto_o the_o equatour_n as_o be_v afore_o mention_v 6._o they_o serve_v to_o distinguish_v the_o equinectiall_a the_o zodiac_n and_o all_o heaven_n into_o four_o equal_a part_n the_o use_n of_o which_o matter_n shall_v appear_v in_o the_o place_n of_o the_o ascension_n of_o the_o sign_n 7_o each_o colour_n beside_o have_v his_o private_a office_n or_o utility_n as_o the_o colour_n of_o the_o solstice_n which_o have_v four_o office_n the_o first_o demonstrate_v the_o solsticiall_a point_n the_o second_o contain_v and_o measure_v the_o sun_n great_a declination_n the_o three_o that_o it_o stay_v up_o the_o pole_n of_o the_o zodiac_n and_o show_v their_o distance_n from_o the_o pole_n of_o world_n the_o four_o that_o it_o devide_v the_o zodiac_n into_o two_o half_n as_o into_o the_o ascend_a and_o descend_v also_o the_o same_o in_o the_o thwart_a sphere_n do_v separate_v the_o sign_n right_o arise_v from_o the_o sign_n thwart_o rise_v 8_o the_o colour_n of_o the_o equinoctial_o have_v twoe_o office_n the_o first_o that_o it_o demonstrate_v the_o equinoctial_a point_n the_o second_o that_o it_o devide_v the_o zodiac_n into_o two_o half_n as_o into_o the_o northerly_a and_o southerly_a half_n 9_o to_o conclude_v the_o colour_n of_o the_o solstice_n do_v often_o supply_v and_o be_v use_v in_o the_o stead_n of_o the_o meridiane_a when_o as_o in_o every_o daily_a revolution_n of_o the_o first_o mover_n it_o do_v twice_o enter_v into_o the_o place_n of_o the_o meridiane_n or_o be_v twice_o join_v in_o
the_o plain_a of_o the_o same_o the_o description_n name_n and_o office_n of_o the_o meridiane_a circle_n and_o horizont_a the_o four_o great_a circle_n which_o we_o have_v already_o describe_v that_o with_o the_o motion_n of_o the_o sphere_n be_v draw_v about_o and_o every_o where_o be_v alike_o which_o the_o other_o twoe_o circle_n be_v contrary_a as_o the_o meridiane_n and_o horizont_n that_o be_v not_o turn_v in_o the_o draw_v about_o of_o the_o sphere_n but_o remain_v as_o immovable_a and_o fix_v neither_o be_v they_o alike_o in_o all_o place_n but_o be_v continual_o change_v stand_v or_o place_v on_o the_o earth_n in_o that_o all_o place_n have_v their_o proper_a meridians_fw-la and_o horizont_v for_o both_o by_o a_o mutual_a touch_v and_o join_v together_o do_v make_v right_a angle_n and_o they_o continual_o divide_v the_o whole_a heaven_n into_o four_o equal_a part_n and_o make_v the_o four_o angle_n and_o quarter_n of_o heaven_n unto_o which_o by_o a_o continual_a turn_n about_o of_o heaven_n both_o the_o one_o and_o the_o other_o star_n as_o it_o be_v by_o a_o orderly_a succession_n draw_v work_n and_o send_v forth_o their_o virtue_n more_o effectuous_a and_o excercise_n their_o quality_n in_o the_o element_n then_o in_o any_o other_o place_n especial_o the_o sun_n be_v draw_v unto_o those_o bond_n for_o he_o both_o begin_v and_o end_v the_o day_n and_o night_n and_o distinguish_v they_o equal_o as_o it_o be_v in_o the_o middle_a parcel_n of_o time_n the_o sun_n also_o come_v unto_o the_o meridian_n do_v then_o more_o heat_n dry_v up_o and_o consume_v vapour_n the_o meridiane_a of_o any_o place_n be_v a_o great_a circle_n which_o go_v or_o reach_v by_o the_o pole_n of_o the_o world_n and_o height_n of_o any_o place_n and_o for_o that_o it_o pass_v by_o the_o pole_n of_o the_o equatour_n parallel_n and_o the_o horizont_n through_o the_o same_o do_v it_o make_v right_a angle_n with_o they_o and_o of_o this_o it_o devide_v all_o the_o ark_n of_o the_o parallel_n as_o well_o in_o sight_n as_o not_o in_o sight_n into_o two_o equal_a half_n this_o circle_n have_v sundry_a name_n for_o varro_n name_v it_o the_o meridian_n or_o midday_n circle_n of_o the_o noonestéed_n in_o that_o when_o the_o sun_n be_v in_o the_o meridian_n or_o any_o other_o star_n above_o the_o earth_n then_o have_v it_o perform_v half_o the_o day_n ark_n and_o be_v then_o at_o the_o bind_v of_o the_o noon_n time_n but_o the_o other_o half_n of_o the_o night_n be_v cause_v at_o the_o instant_a point_n of_o midnight_n the_o half_a then_o reach_v from_o east_n and_o west_n so_o that_o of_o the_o same_o this_o circle_n of_o all_o writer_n in_o this_o science_n name_v the_o meridiane_n but_o of_o ptolemy_n the_o circle_n of_o midday_n and_o middle_a heaven_n by_o the_o same_o reason_n the_o astrologian_n call_v this_o circle_n the_o royal_a cusp_n the_o regal_a quarter_n the_o beginning_n of_o the_o ten_o house_n and_o the_o middle_n of_o heaven_n in_o that_o this_o place_n be_v principal_a and_o of_o worthy_a dignity_n than_o the_o other_o quarter_n of_o which_o shall_v further_o be_v write_v in_o his_o proper_a place_n further_o it_o behove_v by_o the_o addition_n 31._o primi_fw-la theodosij_n that_o the_o equatâ—ure_n and_o horizont_a in_o the_o contrary_a manner_n to_o pass_v by_o the_o pole_n of_o the_o meridian_n &_o of_o the_o same_o that_o those_o pole_n be_v none_o otherwise_o place_v than_o in_o the_o common_a section_n of_o the_o equatour_n and_o horizont_n by_o which_o section_n &_o by_o those_o pole_n of_o the_o horizont_n be_v a_o certain_a third_o circle_n great_a draw_v which_o johannes_n a_o regio_n monte_fw-fr name_v the_o verticial_a circle_n so_o that_o by_o the_o foresay_a corolary_n or_o addition_n ensue_v that_o of_o these_o three_o circle_n of_o each_o exetrée_n and_o pole_n be_v they_o in_o that_o common_a section_n of_o the_o other_o two_o circle_n like_o as_o of_o the_o equinoctial_a and_o two_o colour_n by_o right_n may_v be_v conclude_v so_o that_o a_o triple_a division_n be_v cause_v by_o the_o three_o circle_n which_o appear_v on_o this_o wise_a that_o as_o the_o meridian_n tend_v by_o our_o top_n and_o height_n from_o the_o south_n into_o the_o north_n even_o so_o by_o the_o same_o top_n it_o behove_v the_o other_o circle_n to_o be_v draw_v and_o pass_v from_o the_o east_n into_o the_o west_n that_o both_o cut_v one_o the_o other_o at_o right_a angle_n shall_v express_v the_o four_o foresay_a quarter_n of_o the_o world_n as_o the_o horizont_n distinguish_v the_o upper_a half_a sphere_n from_o the_o nether_a and_o the_o meridiane_n from_o the_o east_n to_o the_o west_n even_o so_o it_o fall_v out_o that_o the_o third_o circle_n as_o that_o verticiall_a shall_v separate_v the_o northerly_a from_o the_o southerly_a half_a sphere_n to_o these_o while_o any_o stand_v upright_o towards_o the_o welt_n on_o such_o manner_n that_o you_o â—_o middle_n of_o his_o body_n be_v in_o the_o common_a centre_n of_o three_o circle_n then_o do_v the_o horizont_n divide_v his_o upper_a half_n from_o the_o nether_a and_o the_o meridiane_a the_o fore_a part_n from_o the_o hinder_a and_o the_o vertical_a circle_n the_o right_a part_n from_o the_o left_a the_o three_o common_a section_n of_o these_o circle_n be_v their_o exe-trée_n as_o be_v afore_o write_v do_v indicate_v or_o show_v the_o four_o principal_a point_n of_o heaven_n which_o be_v the_o fix_v pole_n of_o the_o circle_n place_v in_o the_o section_n of_o the_o cyrcumference_n as_o the_o high_a or_o low_a point_n which_o be_v the_o pole_n of_o the_o horizont_a the_o point_n also_o most_o easterly_a and_o westerly_a which_o be_v the_o pole_n of_o the_o meridiane_a to_o conclude_v the_o point_n most_o northerly_a and_o southerly_a which_o be_v the_o pole_n of_o the_o verticiall_a circle_n those_o people_n that_o seem_v to_o have_v their_o foot_n against_o we_o in_o respect_n of_o the_o roundness_n of_o the_o earth_n that_o they_o dwell_v as_o it_o be_v under_o we_o have_v alike_o horizont_a agreeable_a to_o we_o alike_o meridian_n and_o alike_o verticial_a circle_n but_o of_o these_o two_o the_o half_a circle_n which_o be_v extant_a to_o we_o be_v hide_v or_o as_o it_o be_v under_o they_o contrariwise_o those_o which_o be_v hide_v to_o we_o be_v to_o they_o extaunt_a the_o point_n also_o high_v to_o we_o be_v low_a to_o they_o contrariwise_o the_o low_a to_o we_o be_v high_a to_o they_o the_o figure_n afore_o place_v do_v plain_a express_v that_o afore_o teach_v where_o the_o letter_n a._n b._n c._n d._n represent_v the_o meridiane_a the_o letter_n b._n e._n d._n f._n the_o horizont_a the_o letter_n f._n a._n e._n c._n the_o vertical_a circle_n the_o letter_n g._n the_o centre_n of_o the_o circle_n and_o world_n the_o letter_n a._n c._n the_o exetrée_n of_o the_o horizont_n the_o letter_n b._n d._n the_o exetrée_n of_o the_o verticiall_a circle_n the_o letter_n e._n f._n the_o exetrée_n of_o the_o meridian_n to_o conclude_v the_o point_n that_o to_o we_o be_v most_o easterly_a be_v to_o they_o most_o westerly_a et_fw-la è_fw-la contrario_fw-la for_o the_o point_n most_o northerly_a and_o southerly_a do_v not_o change_v the_o surname_n except_o you_o listen_v to_o change_v or_o alter_v the_o name_n like_v as_o of_o the_o pole_n of_o the_o world_n for_o that_o which_o be_v to_o we_o apparent_a be_v to_o they_o hide_v and_o contrariwise_o to_o we_o hide_v to_o they_o manifest_v here_o may_v be_v demand_v whether_o that_o point_n of_o heaven_n most_o northerly_a be_v not_o the_o northerly_a pole_n of_o the_o world_n and_o that_o point_v most_o southerly_a the_o southerly_a pole_n of_o the_o world_n to_o which_o be_v thus_o answer_v that_o if_o regard_v be_v have_v unto_o the_o equatoure_n and_o right_a horizont_n which_o pass_v by_o the_o pole_n of_o the_o world_n and_o have_v the_o equatour_n for_o the_o verticiall_a or_o in_o steed_n of_o the_o verticiall_a circle_n but_o we_o which_o have_v not_o the_o pole_n of_o the_o world_n in_o the_o horizont_n in_o who_o cyrcumference_n these_o four_o principal_a point_n of_o the_o east_n west_n north_n and_o south_n be_v accustom_v to_o be_v note_v be_v force_v to_o call_v that_o northerly_a section_n of_o the_o meridiane_a and_o horizont_a the_o most_o northerly_a point_n and_o that_o section_n right_a against_o the_o most_o southerly_a point_n for_o in_o every_o place_n there_o be_v two_o section_n which_o the_o meridiane_n and_o verticiall_a circle_n do_v make_v with_o the_o horizont_n which_o be_v two_o right_a section_n in_o the_o plain_a of_o that_o horizont_n cut_v at_o right_n angle_v one_o a_o other_o in_o the_o centre_n that_o express_a and_o show_v those_o four_o quarter_n of_o the_o world_n from_o which_o the_o principal_a wind_n blow_v as_o east_n west_n
be_v the_o ark_n of_o the_o meridian_n from_o the_o horizont_n unto_o the_o pole_n raise_v on_o high_a from_o the_o plain_a of_o the_o horizont_n the_o latitude_n of_o a_o place_n be_v the_o ark_n of_o the_o same_o meridian_n place_v between_o the_o equinoctial_a and_o verticiall_a point_n to_o conclude_v the_o latitude_n of_o a_o place_n and_o elevation_n of_o the_o pole_n do_v not_o differ_v in_o the_o magnitude_n or_o largeness_n but_o in_o stand_v only_o by_o the_o former_a figure_n appear_v that_o the_o ark_n of_o the_o longitude_n of_o place_n or_o city_n know_v be_v forthwith_o offer_v at_o the_o first_o sight_n as_o the_o ark_n e._n p._n or_o p._n o._n or_o o._n n._n etc._n etc._n and_o see_v the_o equatour_n be_v in_o compass_n about_o 360._o degree_n do_v whole_o ascend_v in_o 24._o hour_n above_o the_o horizont_n regular_o of_o this_o it_o come_v to_o pass_v while_o in_o each_o hour_n 15._o degree_n of_o the_o equatour_n do_v ascend_v that_o through_o the_o longitude_n of_o city_n it_o be_v easy_o know_v the_o hourly_a distance_n of_o one_o place_n unto_o a_o other_o see_v the_o sun_n come_v late_a to_o the_o meridian_n to_o they_o which_o be_v near_a to_o the_o east_n then_o to_o they_o in_o the_o west_n whereof_o if_o a_o city_n shall_v be_v situate_v in_o l._n and_o a_o other_o in_o k._n the_o ark_n l._n k._n shall_v be_v of_o 30._o degree_n then_o shall_v the_o sun_n come_v soon_o unto_o the_o easterly_a meridian_n k._n by_o two_o hour_n then_o unto_o the_o westerly_a but_o if_o one_o city_n shall_v be_v in_o p._n and_o the_o other_o in_o z._n then_o in_o latitude_n only_o shall_v they_o differ_v and_o shall_v be_v under_o one_o meridian_n which_o be_v declare_v in_o the_o last_o part_n of_o the_o description_n of_o the_o meridian_n what_o the_o office_n and_o utility_n of_o the_o meridiane_a be_v 1_o the_o utility_n and_o use_n of_o this_o circle_n be_v many_o of_o which_o the_o first_o be_v that_o it_o distinguish_v the_o day_n and_o night_n into_o 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thwartnesse_n of_o the_o horizont_n which_o cause_v the_o variety_n &_o notable_a difference_n of_o the_o inclination_n of_o the_o zodiac_n unto_o the_o horizont_n of_o the_o angle_n and_o largeness_n of_o the_o rise_n but_o they_o begin_v to_o account_v from_o noon_n or_o midnight_n the_o sun_n then_o occupy_v the_o meridian_n through_o the_o sun_n which_o congruence_n all_o the_o meridiane_n have_v with_o the_o right_a horizont_n and_o that_o a_o lesser_a variety_n of_o the_o inclination_n of_o the_o zodiac_n happen_v unto_o the_o meridiane_fw-la and_o angle_n which_o it_o make_v with_o the_o meridiane_n also_o in_o this_o circle_n be_v the_o zenith_n or_o direct_a point_n note_v from_o which_o the_o distance_n of_o the_o star_n and_o parallel_v circle_n be_v gather_v 4_o in_o the_o meridiane_n as_o in_o the_o subject_n the_o distance_n of_o the_o star_n from_o the_o equatoure_n the_o latitude_n of_o place_n and_o the_o elevation_n of_o the_o pole_n be_v account_v for_o the_o 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from_o the_o further_a point_n of_o the_o ecclipticke_a unto_o the_o equatour_n by_o which_o it_o appear_v that_o so_o much_o be_v the_o distance_n of_o the_o pole_n of_o the_o ecclipticke_a from_o the_o pole_n of_o the_o world_n as_o be_v the_o sun_n great_a declination_n be_v 23._o degree_n and_o 28._o minute_n and_o two_o fifte_n almost_o or_o thus_o that_o the_o pole_n of_o the_o zodiac_n be_v far_o distant_a from_o the_o pole_n of_o the_o world_n as_o be_v the_o great_a declination_n of_o the_o sun_n from_o the_o equinoctial_a circle_n and_o by_o the_o equidistance_n also_o on_o each_o side_n of_o the_o arctic_a circle_n from_o the_o pole_n of_o the_o world_n that_o that_o part_n of_o the_o colour_n comprehend_v between_o the_o first_o point_n of_o cancer_n and_o the_o arctic_a circle_n be_v almost_o double_a so_o much_o unto_o the_o great_a declination_n of_o the_o sun_n and_o if_o cyrcumspect_o you_o consider_v the_o manner_n of_o the_o motion_n you_o shall_v ready_o perceive_v that_o those_o circle_n which_o ever_o more_o be_v of_o like_a largeness_n increase_n and_o decrease_v together_o with_o the_o twoe_o tropic_n circle_n according_a to_o the_o increase_n or_o decrease_v of_o the_o sun_n declination_n as_o appear_v by_o the_o letter_n n._n in_o the_o foresay_a figure_n that_o represent_v the_o northerly_a pole_n of_o the_o ecclipticke_a or_o zodiac_n move_v from_o the_o letter_n n._n into_o o._n by_o the_o motion_n of_o the_o first_o mover_n and_o return_v again_o into_o the_o point_n n_o shall_v be_v move_v the_o circle_n describe_v n_o o._n be_v distant_a from_o the_o northerly_a pole_n a._n much_o as_n be_v the_o sun_n great_a declination_n h_o g._n as_o hereafter_o by_o demonstration_n shall_v plain_o appear_v and_o this_o circle_n name_v the_o arctic_a in_o that_o it_o be_v describe_v by_o the_o arctic_a of_o the_o zodiac_n the_o like_a be_v describe_v from_o the_o point_n r._n be_v the_o pole_n antarcticke_a by_o the_o motion_n from_o r._n unto_o 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the_o pole_n of_o the_o world_n unto_o the_o equinoctial_a and_o that_o other_o be_v that_o which_o be_v from_o the_o pole_n of_o the_o zodiac_n unto_o the_o zodiac_n or_o ecclipticke_a and_o of_o this_o i_o thus_o reason_n that_o when_o the_o equal_n be_v deduct_v or_o abate_v from_o the_o equal_n the_o remainder_n shall_v be_v equal_a therefore_o be_v the_o foresay_a quarter_n equal_a in_o that_o they_o be_v in_o the_o same_o circle_n and_o that_o from_o either_o be_v the_o equal_a or_o common_a ark_n deduct_v that_o be_v the_o same_o which_o be_v contain_v between_o the_o equinoctial_a and_o the_o pole_n of_o the_o zodiac_n which_o ark_n do_v contain_v 66._o degree_n and_o 31._o minute_n almost_o so_o that_o the_o ark_n rest_v or_o remain_v of_o these_o quarter_n be_v equal_a that_o be_v the_o distance_n of_o the_o pole_n of_o the_o zodiac_n and_o the_o equinoctial_a be_v equal_a to_o the_o sun_n great_a declination_n for_o if_o 66._o degree_n and_o 31._o minute_n be_v deduct_v 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solsticiall_a tropic_n after_o the_o greek_n be_v to_o define_v the_o long_a summer_n day_n and_o the_o winter_n tropic_n to_o determine_v the_o short_a winter_n day_n and_o long_a night_n for_o proclus_n to_o find_v the_o long_a day_n do_v divide_v the_o summer_n solstice_n into_o 8._o equal_a part_n of_o which_o so_o divide_v he_o affirm_v three_o part_n to_o be_v continual_o hide_v under_o the_o horizon_n and_o five_o above_o the_o truth_n of_o which_o be_v know_v if_o the_o sphere_n be_v rectify_v for_o the_o latitude_n of_o 41._o degree_n where_o by_o this_o division_n the_o long_a day_n contain_v 15_o hour_n and_o the_o night_n but_o 9_o hour_n 2_o many_n and_o notable_a office_n do_v the_o tropic_n circle_n offer_v as_o well_o unto_o the_o composition_n of_o dialle_n as_o unto_o the_o prepare_v many_o other_o instrument_n in_o astronomy_n 3_o they_o declare_v the_o place_n of_o the_o ecclipticke_a in_o which_o the_o sun_n solstice_n be_v cause_v whereof_o the_o long_a or_o 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the_o earth_n albategnius_n affirm_v the_o star_n of_o mercury_n to_o be_v least_o of_o all_o the_o star_n and_o suppose_v or_o account_v he_o to_o be_v as_o one_o part_n of_o 19000._o part_n of_o the_o earth_n the_o high_a ascension_n of_o mercury_n sphere_n be_v from_o the_o earth_n after_o albategnius_n distant_a 166._o semidiametres_fw-fr but_o the_o low_a point_n in_o the_o same_o orb_n be_v 56._o semidiametres_fw-fr distant_a from_o the_o earth_n the_o moon_n be_v low_a of_o all_o the_o planet_n do_v compass_n about_o the_o whole_a zodiac_n in_o 27._o day_n 7._o hour_n 43._o minute_n and_o 7._o second_n she_o be_v lesser_a than_o the_o earth_n after_o the_o judgement_n of_o ptolemy_n by_o three_o hundred_o nine_o time_n and_o a_o unity_n more_o than_o eight_o part_n for_o the_o triple_a proportion_n of_o the_o diametre_fw-la of_o the_o earth_n unto_o the_o moon_n by_o devide_v above_o the_o five_o part_n be_v even_o the_o like_a as_o 27._o unto_o 5._o but_o lesser_a she_o be_v 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