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the_o end_n that_o by_o mean_n of_o the_o same_o the_o doctrine_n of_o the_o true_a motion_n of_o the_o celestial_a body_n may_v the_o more_o easy_o be_v apprehend_v and_o what_o be_v say_v of_o the_o aequator_fw-la zodiaque_fw-la axe_n and_o the_o other_o circle_n be_v also_o to_o be_v understand_v of_o the_o other_o orb_n themselves_o and_o their_o hypothesis_n for_o as_o concern_v the_o objection_n make_v long_o since_o by_o rhoeticus_fw-la and_o late_o by_o peter_n ramus_n lib._n 2._o schol._n math._n touch_v the_o facility_n the_o ancient_a egyptians_n have_v in_o search_n ing_z out_o the_o course_n of_o the_o star_n i_o think_v it_o not_o amiss_o to_o let_v you_o see_v what_o the_o noble_a tycho_n opinion_n be_v herein_o and_o what_o answer_n he_o once_o upon_o occasion_n give_v ramus_n himself_o propose_v the_o same_o unto_o he_o as_o we_o find_v it_o relate_v by_o himself_o in_o his_o book_n of_o astronomical_a epistle_n pag._n 60._o and_o thus_o it_o be_v quod_fw-la celeberrimus_fw-la ille_fw-la noltri_fw-la aevi_fw-la philosophus_fw-la petus_n ramus_n etc._n etc._n where_o as_o that_o famous_a philosopher_n of_o our_o time_n peter_n ramus_n be_v of_o opinion_n that_o the_o science_n of_o astronomy_n may_v be_v frame_v by_o some_o certain_a logical_a way_n of_o computation_n with_o hypothesis_n this_o be_v nothing_o else_o but_o a_o mere_a groundless_a conjecture_n which_o conâ—…eit_n of_o he_o he_o propose_v indeed_o to_o i_o about_o sixteen_o â—…eares_n since_o when_o as_o we_o be_v together_o at_o auâ—…purge_n wish_v i_o withal_o that_o when_o as_o i_o have_v â—…nce_o reduce_v the_o course_n of_o the_o star_n into_o some_o â—…xact_a order_n by_o the_o hypothesis_n now_o in_o use_n i_o â—…ould_v then_o try_v what_o may_v be_v do_v without_o they_o and_o that_o this_o may_v possible_o be_v effect_v he_o bring_v this_o for_o his_o reason_n because_o that_o he_o have_v read_v that_o the_o egyptians_n have_v ancient_o a_o most_o easy_a and_o 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to_o show_v the_o measure_n of_o the_o apparent_a motion_n of_o the_o heavenly_a body_n by_o circle_n and_o other_o figure_n which_o be_v again_o resolve_v into_o number_n by_o arithmetic_n without_o which_o whosoever_o shall_v think_v to_o attain_v to_o the_o knowledge_n of_o the_o motion_n of_o the_o star_n he_o may_v be_v say_v to_o invoke_v fortune_n as_o the_o proverb_n be_v and_o dream_n of_o some_o strange_a incorporeal_a and_o more_o than_o seraphical_a way_n above_o the_o reach_n of_o humane_a capacity_n beside_o the_o body_n of_o the_o globe_n itself_o and_o those_o â—…hings_n which_o we_o have_v say_v to_o be_v thereon_o inscribe_v there_o be_v also_o annex_v a_o certain_a frame_n with_o necessary_a instrument_n thereto_o belong_v which_o we_o shall_v declare_v in_o order_n the_o fabric_n of_o his_o frame_n be_v thus_o first_o of_o all_o there_o be_v a_o base_a or_o foot_n to_o rest_v upon_o on_o which_o there_o be_v raise_v perpendicular_o six_o c_o pillar_n b_o or_o a_o column_n of_o equal_a length_n and_o distance_n upon_o the_o top_n of_o which_o there_o be_v fasten_v to_o a_o level_n and_o parallel_v to_o the_o base_a a_o round_a plate_n or_o circle_n of_o wood_n of_o a_o sufficient_a breadth_n and_o thickness_n which_o they_o call_v the_o horizon_n because_o that_o the_o uppermost_a superficies_n thereof_o horizon_n perform_v the_o office_n of_o the_o true_a horizon_n for_o it_o be_v so_o place_v that_o it_o divide_v the_o whole_a globe_n â—…nto_o two_o equal_a part_n whereof_o that_o which_o 〈◊〉_d uppermost_o represent_v unto_o we_o the_o visible_a â—…emisphaere_n and_o the_o other_o that_o which_o be_v hide_v â—…omus_fw-la so_o likewise_o that_o circle_n which_o diviâ—…es_v that_o part_n of_o the_o world_n which_o we_o â—…ee_v from_o â—…hat_o other_o which_o we_o see_v not_o be_v call_v the_o horiâ—…on_n and_o that_o point_n which_o be_v direct_o over_o our_o â—…eads_n in_o our_o hemisphere_n and_o be_v
the_o sun_n in_o the_o equinoctial_a from_o 90._o degree_n the_o remainder_n show_v the_o elevation_n of_o the_o pole_n as_o for_o example_n the_o elevation_n of_o the_o sun_n at_o noon_n when_o it_o be_v in_o the_o aequinoxe_n be_v about_o 38._o degree_n with_o we_o here_o at_o london_n which_o be_v deduct_v out_o of_o 90._o there_o remain_v 52._o which_o be_v the_o elevation_n of_o the_o pole_n with_o we_o so_o at_o rome_n the_o equinoctial_a altitude_n of_o the_o sun_n be_v about_o 48._o degree_n which_o be_v substract_v from_o 90_o degree_n which_o be_v a_o quadrant_n there_o remain_v 42._o for_o the_o elevation_n of_o the_o pole_n in_o two_o opposite_a point_n of_o this_o meridian_n be_v fasten_v the_o two_o end_n of_o aâ—…_n iron_n pin_n pass_v through_o the_o body_n of_o the_o globe_n and_o its_o centre_n axis_n one_o of_o which_o end_n be_v call_v the_o arctic_a oâ—…_n north_n pole_n of_o the_o world_n and_o the_o other_o the_o antarctick_a or_o south_n pole_n and_o the_o pin_n itself_o be_v call_v the_o axis_n for_o the_o axis_n of_o the_o world_n be_v the_o diameter_n about_o which_o it_o be_v turn_v and_o the_o extreme_a end_n of_o the_o axis_n be_v call_v the_o pole_n to_o either_o of_o these_o pole_n when_o need_n shall_v require_v there_o be_v a_o certain_a brass_n circle_n or_o ring_n of_o a_o reasonable_a strong_a make_n to_o be_v fasten_v which_o circle_n be_v divide_v into_o 24._o equal_a part_n according_a to_o the_o number_n of_o the_o hour_n of_o the_o day_n &_o night_n and_o it_o be_v therefore_o call_v the_o houre-circle_n and_o this_o circle_n be_v to_o be_v apply_v to_o either_o of_o the_o pole_n houre-circle_n in_o such_o sort_n as_o that_o the_o section_n where_o 12._o be_v describe_v â—…ay_o precise_o agree_v with_o the_o point_n of_o mid_a day_n and_o midnight_n in_o the_o superficies_n of_o the_o tâ—…ue_a meridian_n there_o be_v also_o another_o little_a pin_n or_o stile_n to_o be_v fasten_v to_o the_o end_n of_o the_o axis_n in_o the_o 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be_v come_v to_o the_o eastern_a side_n of_o the_o horizon_n which_o do_v the_o index_n will_v point_v out_o the_o hour_n of_o his_o rise_n and_o if_o you_o turn_v it_o about_o to_o the_o west_n side_n you_o shall_v in_o like_a manner_n have_v the_o hour_n of_o his_o set_n there_o be_v also_o belong_v to_o the_o meridian_n a_o quadrant_n of_o altitude_n be_v make_v of_o a_o long_a thin_a plate_n of_o steel_n or_o brass_n and_o fashion_v crooked_a so_o that_o it_o may_v be_v apply_v to_o the_o convexs_n superficies_n of_o the_o globe_n and_o have_v the_o four_o part_n of_o the_o circle_n in_o length_n and_o this_o quadrant_n be_v make_v in_o such_o a_o sort_n as_o that_o altitude_n it_o may_v be_v fasten_v on_o the_o meridian_n and_o so_o be_v apply_v to_o the_o zenith_n of_o any_o place_n whatsoever_o be_v divide_v from_o one_o end_n to_o the_o other_o into_o 90._o equal_a part_n or_o degree_n there_o be_v beside_o at_o the_o foot_n of_o the_o globe_n a_o mariner_n compass_n place_v which_o serve_v to_o show_v how_o to_o place_v the_o globe_n right_o according_a to_o the_o four_o wind_n or_o quarter_n of_o the_o world_n chap_n ii_o of_o the_o circle_n which_o be_v describe_v upon_o the_o superficies_n of_o thâ—…_n globe_n and_o now_o in_o the_o next_o place_n we_o will_v show_v whâ—…_n circle_n be_v describe_v upon_o the_o globe_n itself_o and_o first_o of_o all_o there_o be_v dâ—…awn_v a_o circle_n in_o a_o equal_a distance_n from_o both_o the_o pole_n that_o be_v 90._o degree_n which_o be_v call_v the_o equinoctial_a or_o aequator_fw-la aequator_fw-la because_o that_o when_o the_o suâ—…_n be_v in_o this_o circle_n day_n and_o night_n be_v of_o equal_a length_n in_o all_o place_n by_o the_o râ—…volution_n of_o this_o circle_n be_v defend_v a_o natural_a day_n which_o the_o greek_n call_v 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d for_o a_o day_n be_v 〈◊〉_d natural_a and_o artificial_a a_o natural_a day_n be_v define_v to_o be_v the_o space_n of_o time_n wherâ—…_n in_o the_o whole_a aequator_fw-la artificial_a make_v a_o full_a revolution_n and_o this_o be_v do_v in_o 24._o hour_n a_o artificâ—…all_a day_n be_v the_o space_n wherein_o the_o sun_n be_v passiâ—…g_v through_o our_o upper_a hemisphere_n to_o which_o be_v oppose_v the_o artificial_a night_n while_o thâ—…_n sun_n be_v carry_v about_o in_o the_o low_a hemisphere_n so_o that_o a_o artificial_a day_n and_o night_n be_v comprehenâ—…ed_v within_o a_o natural_a day_n the_o part_n of_o a_o dav_fw-mi be_v call_v hour_n which_o be_v either_o equal_a or_o unequal_a a_o equal_a hour_n be_v the_o 24._o part_n of_o a_o natural_a day_n in_o which_o unâ—…quall_a space_n 15._o dâ—…grees_n of_o the_o aequator_fw-la do_v always_o rise_v and_o as_o mâ—…ny_n be_v depreâ—…ied_v on_o the_o opposite_a part_n a_o unequal_a hour_n be_v the_o 12._o part_n of_o a_o artificial_a day_n betwâ—…xt_v the_o â—…ime_n of_o the_o sun_n rise_v and_o set_v again_o thâ—…se_a hour_n be_v again_o divide_v into_o minute_n now_o a_o minute_n be_v the_o 60._o part_n of_o a_o hour_n in_o which_o space_n of_o time_n a_o quarter_n of_o a_o degree_n in_o the_o aequator_fw-la that_o be_v 15._o minute_n do_v â—…ise_a and_o aâ—…_n many_o set_v pont_n the_o use_n of_o the_o aequâ—…tor_n consist_v chief_o in_o these_o thing_n first_o it_o show_v the_o time_n of_o the_o aequinox_n which_o be_v always_o when_o the_o sun_n faly_n upon_o the_o equinoctial_a circle_n and_o this_o be_v when_o as_o the_o sun_n enter_v into_o the_o first_o degree_n of_o aries_n and_o libra_n according_a to_o that_o of_o manilâ—…us_n libra_n ariesque_fw-la parem_fw-la reddunt_fw-la noctemque_fw-la diemque_fw-la in_o english_a thus_o the_o sun_n in_o libra_n and_o aries_n place_v each_o year_n the_o day_n and_o night_n be_v equal_a every_o where_o second_o â—…he_v aequator_fw-la divide_v the_o heaven_n into_o two_o equal_a part_n or_o hemisphaere_n whereof_o one_o be_v call_v the_o septeutrionall_a or_o northern_a hemisphere_n the_o other_o the_o meridional_a or_o southern_a three_o it_o show_v the_o ascension_n and_o descension_n of_o the_o part_n of_o the_o zodiac_n whence_o the_o length_n of_o the_o artificial_a day_n and_o night_n for_o any_o position_n of_o sphere_n may_v be_v know_v fouâ—…thly_a 〈◊〉_d show_v what_o star_n and_o part_n of_o the_o ecliptic_a have_v any_o declination_n the_o aequator_fw-la be_v cross_v or_o cut_v in_o two_o opposite_a point_n by_o a_o oblique_a circle_n which_o be_v call_v the_o zodiac_n the_o obliquity_n of_o this_o circle_n be_v say_v to_o have_v be_v first_o observe_v by_o anaximander_n milesius_n in_o the_o 58._o olympiad_n as_o pliny_n write_v in_o hiâ—…_n lib._n 2._o cap._n 8_o who_o also_o in_o the_o same_o place_n affiâ—…mes_v that_o it_o be_v first_o divide_v into_o 12_o part_n which_o they_o call_v sign_n by_o cleostretus_fw-la tenedius_n in_o like_a manner_n as_o we_o see_v it_o at_o this_o day_n each_o of_o these_o sign_n be_v again_o subdivide_v into_o 30._o part_n so_o that_o the_o whole_a zodiac_n be_v divide_v in_o all_o into_o 360._o part_n like_v as_o the_o orhe_a circle_n be_v the_o first_o twelve_o part_n whereof_o beginning_n at_o the_o vernal_a intersection_n when_o the_o aequator_fw-la and_o zodiack_n cross_v each_o other_o it_o assign_v to_o aries_n the_o second_o to_o taurus_n etc._n etc._n reckon_n from_o west_n to_o east_n but_o here_o a_o young_a beginner_n in_o astronomy_n may_v just_o doubt_v what_o be_v the_o reason_n that_o the_o first_o 30._o degree_n or_o 12_o part_n of_o the_o zodiac_n be_v attribute_v to_o aries_n whereas_o the_o first_o star_n of_o aries_n fall_v short_a of_o the_o intersection_n of_o the_o equinoctial_a and_o zodiac_n no_o less_o than_o 27._o degree_n the_o reason_n of_o this_o be_v because_o that_o in_o the_o time_n of_o the_o
manifest_a error_n in_o that_o he_o affirm_v that_o the_o first_o star_n of_o aries_n at_o the_o time_n of_o our_o saviour_n naâ—…ivity_n be_v in_o the_o very_a vernal_a intersection_n especial_o contend_v to_o prove_v it_o as_o he_o do_v out_o of_o ptolemy_n observation_n out_o of_o which_o it_o plain_o appear_v that_o it_o be_v behind_o it_o no_o less_o than_o 5._o degree_n in_o like_a manner_n the_o place_n of_o the_o solstice_n be_v also_o change_v as_o be_v always_o equal_o distant_a from_o the_o equinoctial_a point_n this_o mâ—…tion_n be_v finish_v upon_o the_o pole_n of_o the_o ecliptic_a as_o be_v agree_v upon_o both_o by_o hipparchus_n and_o ptolemy_n and_o all_o the_o rest_n that_o have_v come_v after_o they_o which_o be_v the_o reaso_n that_o the_o fix_a star_n have_v always_o keep_v the_o same_o latitude_n though_o they_o have_v change_v their_o declination_n for_o confirmation_n whereof_o many_o testimony_n may_v be_v bring_v out_o of_o ptolemy_n lib_n 7._o cap._n 3_o almag_n i_o will_v only_o all_o dg_n one_o more_z not_o able_a than_o the_o râ—…st_n out_o of_o petolomies_n georgr_n lib._n 1._o cap._n 7._o the_o star_n which_o we_o call_v the_o polar_a star_n and_o be_v the_o last_o in_o the_o tail_n of_o the_o bear_n be_v certain_o know_v in_o our_o time_n to_o be_v scarce_o three_o degree_n distant_a from_o the_o pole_n which_o very_a star_n in_o hipparchus_n his_o time_n be_v above_o 12._o degree_n distant_a from_o the_o pole_n as_o merinus_n in_o ptolemy_n affirm_v i_o will_v produce_v the_o whole_a passage_n which_o be_v thus_o in_o the_o torrid_a zone_n say_v he_o the_o whole_a zodiac_n pass_v over_o it_o and_o therefore_o the_o shadow_n be_v cast_v both_o way_n and_o all_o starrr_n there_o be_v see_v to_o rise_v and_o set_v only_o the_o little_a bear_n begin_v to_o appear_v above_o the_o horixon_n in_o those_o place_n that_o be_v 5_o 0_o furlong_n northward_o from_o ocele_n for_o the_o parallel_n that_o pass_v through_o ocele_n 〈◊〉_d distant_a from_o the_o aequator_fw-la 11._o gra_fw-mi â…–_n and_o hipparchus_n affirm_v that_o the_o star_n in_o the_o end_n of_o the_o little_a bear_n tail_n which_o be_v the_o most_o southward_o of_o that_o constellation_n be_v distant_a from_o the_o pole_n 12._o degree_n â…–_n this_o excellent_a testimony_n of_o he_o the_o interpreter_n have_v in_o their_o translate_n the_o place_n most_o strange_o corrupt_v aâ—…_n both_o johannes_n wernerus_n and_o after_o he_o peter_n nonius_n have_v observe_v set_v down_o in_o stead_n of_o 500_o quinque_fw-la mille_fw-la 5000_o and_o for_o australissimam_fw-la the_o most_o southern_a borealissimam_fw-la the_o most_o northerly_a be_v lead_v into_o this_o error_n perhaps_o because_o that_o this_o star_n be_v indeed_o in_o our_o time_n the_o most_o northern_a but_o if_o these_o testimony_n of_o marinus_n and_o ptolemy_n in_o this_o point_n be_v substract_v strabo_n in_o his_o lib._n 2._o geogr._n shall_v acquit_v they_o of_o this_o crime_n and_o he_o write_v thus_o it_o be_v affirm_v by_o hipparchus_n say_v he_o that_o those_o that_o inhabit_v under_o the_o parallel_n that_o run_v through_o the_o country_n call_v cinnamomifera_n which_o be_v distant_a from_o meroe_n southward_o 3000._o furlong_n and_o from_o the_o equinoctial_a 8800._o be_v situate_v almost_o in_o the_o midst_n betwixt_o the_o aequator_fw-la and_o the_o summer_n tropic_n which_o pass_v through_o syene_n which_o be_v distant_a from_o meroe_n 5000._o furlong_n and_o these_o that_o dwell_v here_o be_v the_o first_o that_o have_v the_o constellation_n of_o the_o little_a bear_n enclose_v within_o their_o arctic_a circle_n so_o that_o it_o never_o set_v with_o they_o for_o the_o bright_a star_n that_o be_v see_v in_o the_o end_n of_o the_o tail_n which_o be_v also_o the_o most_o southward_o of_o all_o be_v so_o place_v in_o the_o very_a cirele_n itself_o that_o it_o do_v touch_v the_o horizon_n this_o be_v the_o testimony_n of_o strabo_n which_o be_v the_o very_a same_o that_o ptolemy_n and_o merinus_n affirm_v save_v that_o both_o in_o this_o place_n and_o elsewhere_o he_o always_o assign_v 700._o furlong_n in_o the_o earth_n to_o a_o degree_n in_o the_o heaven_n according_a to_o the_o doctrine_n of_o eratosthenes_n whereas_o both_o marinus_n and_o ptolemy_n allow_v but_o 500_o only_a os_fw-la which_o we_o shall_v speak_v more_o hereafter_o let_v we_o now_o come_v to_o the_o lesser_a circle_n which_o be_v describe_v in_o the_o globe_n and_o these_o be_v all_o parallel_n to_o the_o aequator_fw-la as_o first_o of_o all_o the_o tropicke_n which_o be_v circle_n draw_v through_o the_o point_n of_o the_o great_a declination_n of_o the_o ecliptic_a on_o each_o side_n of_o the_o aequator_fw-la of_o which_o that_o which_o look_v towards_o the_o north_n tropic_a pole_n be_v call_v the_o tropic_n of_o cancer_n and_o the_o other_o border_v on_o the_o south_n the_o tropic_n of_o capricorn_n for_o the_o sun_n in_o his_o yearly_a motion_n through_o the_o ecliptic_a arrive_v at_o these_o point_n as_o his_o utmost_a bound_n râ—…turneth_v again_o towards_o the_o aequator_fw-la this_o retrocession_n be_v call_v by_o the_o greek_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d and_o the_o parallel_n circle_n draw_v through_o the_o same_o point_n be_v likewise_o call_v tropicke_n pont_n the_o use_n of_o those_o tropicke_n be_v first_o to_o show_v when_o the_o sun_n in_o a_o oblique_a sphere_n be_v near_o the_o vertical_a point_n of_o any_o place_n and_o so_o likewise_o when_o the_o far_a off_o second_o they_o show_v when_o the_o sun_n in_o his_o diurnal_a motion_n make_v the_o long_a or_o short_a day_n in_o the_o year_n three_o they_o be_v as_o it_o be_v the_o limit_n and_o bound_n wherein_o the_o sun_n finish_v his_o yearly_a course_n four_o they_o distinguish_v the_o torrid_a zone_n in_o the_o heaven_n from_o the_o two_o temperate_a zone_n the_o distance_n of_o the_o tropic_n from_o the_o aequator_fw-la be_v diverse_o alter_v as_o it_o may_v plain_o appear_v by_o compare_v the_o observation_n of_o late_a time_n with_o those_o of_o the_o ancient_n for_o not_o to_o speak_v any_o thing_n of_o strabo_n proclus_n and_o leontius_n mechanicus_fw-la who_o all_o assign_v the_o distance_n of_o either_o tropic_n from_o the_o aequator_fw-la to_o be_v 24._o degreeâ—…_n for_o these_o seem_v to_o have_v handle_v the_o matterbut_n careless_o we_o may_v observe_v the_o same_o from_o the_o more_o accurate_a observation_n of_o the_o great_a artist_n for_o ptolemy_n find_v the_o distance_n of_o either_o tropic_n to_o be_v 23._o gr_n 51._o min._n and_o â…“_n just_a as_o great_a aâ—…_n eratosthenes_n and_o hipparchus_n have_v find_v it_o before_o he_o and_o therefore_o he_o conceive_v it_o to_o be_v immutable_a machomethes_n aratensis_fw-la observe_v this_o distan_n to_o be_v 23._o degree_n 35._o minute_n right_o as_o almamon_n king_n of_o arabia_n have_v do_v before_o he_o arzâ—…l_v the_o spaniard_n find_v it_o to_o be_v in_o his_o time_n 23._o degee_n 34._o minute_n almehon_n the_o son_n of_o albumasar_n 23_o degree_n 33._o minute_n and_o half_o a_o minute_n prophatius_fw-la a_o jew_n 23._o degree_n 32._o minute_n purbachius_n and_o regiomontanus_n 25._o degree_n 28._o minute_n johan_n wernerus_n 23_o degree_n and_o 28._o minute_n and_o a_o half_a and_o copernicus_n find_v it_o in_o his_o time_n to_o be_v just_a as_o much_o pont_n this_o distance_n of_o the_o tropicke_n from_o the_o aequator_fw-la be_v cause_v by_o the_o sun_n great_a declination_n as_o the_o astronomer_n call_v it_o which_o great_a declination_n of_o the_o sun_n have_v be_v at_o divers_a time_n find_v to_o be_v variable_a for_o begin_n as_o sar_n backward_o as_o possible_o we_o can_v and_o so_o drive_v it_o down_o by_o the_o olympiad_n and_o the_o year_n of_o christ_n even_o to_o these_o present_a time_n according_a to_o tychoes_n calculation_n we_o find_v it_o to_o be_v thus_o both_o in_o the_o degree_n and_o minute_n as_o be_v here_o express_v in_o this_o ensue_a table_n  _fw-fr gr_fw-fr m._n 11._o  _fw-fr aratus_n 24._o 0._o 0._o olympiad_n hipparchus_n 23._o 51½_n 124._o eratosthenes_n  _fw-fr 127._o ptolomaeus_n 23._o 51._o 20_o a_o christi_fw-la 140._o albategnius_n 23._o 35._o 0._o 749._o arzahel_n 23._o 34._o 0._o 1070._o almeon_n 23._o 33_o ½_o 1140._o prophatius_fw-la judaeus_n 23._o 32._o 0._o 1300._o purbachius_n 23._o 29._o 30._o 1458._o regiomontanus_n 23._o 30._o 0._o 1490._o copernicus_n 23._o 38_o 30._o 1500._o tycho_n brahe_n 23._o 31._o ½_o 1592._o to_o which_o we_o may_v add_v these_o word_n out_o of_o tychoe_n 1._o book_n of_o new_a star_n which_o appear_v an._n 1572._o p._n 101._o where_o he_o say_v that_o by_o certain_a observation_n it_o have_v be_v find_v that_o both_o the_o sun_n great_a declination_n as_o also_o the_o other_o intermediat_a by_o the_o same_o reason_n be_v alter_v as_o it_o be_v testify_v by_o the_o whole_a current_n of_o the_o most_o skilful_a artist_n
in_o a_o continual_a succession_n of_o time_n so_o that_o ptolemy_n time_n &_o some_o certain_a year_n before_o he_o it_o be_v find_v to_o be_v 23._o gr_n 51._o ½_o but_o it_o do_v not_o appear_v by_o any_o certain_a testimony_n to_o have_v be_v ever_o great_a whence_o may_v be_v collect_v that_o aratus_n who_o we_o have_v set_v in_o the_o first_o place_n who_o assign_v 24._o gr_n speak_v with_o the_o large_a and_o as_o it_o be_v at_o random_n and_o as_o our_o learned_a author_n have_v also_o observe_v of_o strabo_n proclus_n and_o leontius_n mechanicus_fw-la not_o so_o accurate_o as_o he_o shall_v have_v there_o be_v also_o two_o other_o lesser_a circle_n describe_v in_o a_o equal_a distance_n from_o the_o pole_n to_o that_o of_o the_o tropicke_n from_o the_o aequator_fw-la which_o circle_n take_v their_o denomination_n from_o the_o pole_n on_o which_o they_o border_n so_o that_o one_o of_o circle_n they_o be_v call_v the_o arctic_a or_o north_n circle_n and_o and_o the_o oppsite_a circle_n the_o antarctick_a or_o southern_a in_o these_o circle_v the_o pole_n of_o the_o ecliptic_a be_v fix_v the_o solsticiall_a colour_n cross_v they_o in_o the_o same_o place_n strabo_n proclus_n cleomedes_n all_o greek_a author_n and_o some_o of_o the_o latin_n also_o assign_v no_o certain_a distance_n to_o these_o circle_n from_o the_o pole_n but_o make_v they_o various_a and_o mutable_a according_a to_o the_o diversity_n of_o elevation_n of_o the_o pole_n or_o diverse_a position_n of_o the_o sphere_n so_o that_o one_o of_o they_o must_v be_v conceive_v to_o be_v describe_v round_o about_o that_o pole_n which_o be_v elevate_v and_o to_o touch_v the_o very_a horizon_n and_o be_v therefore_o the_o great_a of_o all_o the_o parallel_n that_o be_v always_o in_o sight_n and_o the_o other_o must_v be_v imagine_v as_o draw_v in_o a_o equal_a distance_n from_o the_o opposite_a pole_n and_o this_o be_v the_o great_a of_o those_o parallel_n that_o be_v always_o hide_v pont_n the_o arctique_a and_o antarctique_a circle_n do_v show_v 1._o the_o pole_n of_o the_o zodiaque_fw-la and_o their_o distance_n from_o the_o pole_n of_o the_o world_n 2._o they_o do_v distinguish_v the_o frigid_a zone_n from_o the_o temperate_a and_o with_o the_o tropique_n and_o aequator_fw-la they_o help_v to_o divide_v the_o whole_a heaven_n into_o five_o part_n or_o region_n which_o they_o call_v zone_n beside_o these_o circle_n express_v in_o the_o globe_n there_o be_v also_o some_o certain_a other_o circle_n in_o familiar_a use_n with_o the_o practical_a astronomer_n which_o they_o call_v vertical_a circle_n these_o be_v circle_n great_a circle_n draw_v from_o the_o vertical_a point_n through_o the_o horizon_n in_o what_o number_n you_o please_v and_o they_o be_v call_v by_o the_o arabian_n azimuth_n which_o appellation_n be_v also_o in_o common_a use_n among_o our_o ordinary_a astronomer_n the_o office_n of_o these_o circle_n be_v supply_v by_o the_o help_n of_o a_o quadrant_n of_o altitude_n which_o be_v a_o thin_a plate_n of_o brass_n divide_v into_o 90._o degree_n this_o quadrant_n must_v be_v apply_v to_o the_o vetrex_n of_o any_o place_n when_o you_o desire_v to_o use_v it_o so_o that_o the_o low_a end_n of_o it_o note_v with_o the_o number_n of_o 90._o may_v just_o touch_v the_o horizon_n in_o every_o place_n this_o quadrant_n be_v make_v movable_a that_o so_o it_o may_v be_v fasten_v to_o the_o vertical_a point_n of_o any_o place_n pont_n concern_v the_o moveableness_n or_o mutability_n of_o the_o arctique_a and_o antarctique_a circle_n joseph_n scaliger_n report_v himself_o to_o be_v the_o first_o that_o observe_v it_o out_o of_o the_o ancient_a greek_a author_n as_o you_o may_v see_v in_o his_o commentary_n upon_o manilius_n revise_v and_o publish_v by_o himself_o a_o little_a before_o his_o death_n neither_o do_v he_o think_v that_o any_o ancient_a latin_a author_n within_o 400._o year_n after_o those_o greek_a writer_n nor_o scarce_o any_o before_o sacrobosco_n time_n can_v be_v find_v to_o have_v determine_v they_o to_o be_v immovable_a but_o because_o there_o be_v many_o excellent_a thing_n to_o be_v meet_v withal_o in_o that_o pssage_n of_o he_o and_o that_o he_o set_v down_o the_o same_o by_o way_n of_o demonstration_n i_o have_v think_v it_o not_o impertinent_a see_v our_o author_n have_v give_v a_o touch_n at_o it_o to_o set_v down_o scaliger_n opinâ—…n_n in_o his_o own_o word_n as_o you_o have_v they_o upon_o those_o verse_n of_o monilius_fw-la lib._n 1._o astron._n circulus_fw-la ad_fw-la borean_a fulgentem_fw-la sustinet_fw-la arcton_n sexque_fw-la fugit_fw-la folidas_fw-la a_o coeli_fw-la vertice_fw-la part_n he_o proceed_v after_o this_o manner_n describantur_fw-la circuli_fw-la aequinoctiali_fw-la paralleli_fw-la xc_o etc._n etc._n let_v there_o be_v describe_v say_v he_o 90._o parallel_v circle_n to_o the_o equinoctial_a and_o these_o will_v be_v the_o same_o that_o gaminus_fw-la call_v 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d always_o appear_v now_o among_o all_o those_o that_o which_o touch_v the_o horizon_n in_o the_o point_n of_o intersection_n of_o the_o horizon_n and_o meridian_n will_v be_v 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d the_o great_a of_o those_o that_o always_o appear_v and_o so_o conseqvent_o the_o arctique_a circle_n of_o that_o place_n now_o because_o the_o orison_n be_v movable_a the_o arctique_a circle_n must_v also_o be_v movable_a so_o in_o the_o climate_n wherein_o cnidus_n lie_v the_o elevation_n of_o the_o pole_n be_v thirty_o six_o degree_n eudoxus_fw-la determine_v the_o arctic_a circle_n also_o to_o be_v so_o many_o degree_n from_o the_o pole_n in_o like_a manner_n in_o another_o climate_n it_o will_v be_v diverse_a according_a to_o the_o diversity_n of_o the_o elevation_n of_o the_o pole_n thus_o hipparchus_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d at_o athens_n say_v he_o the_o great_a of_o the_o circle_n always_o appear_v be_v distant_a from_o the_o pole_n thirty_o seven_o degree_n but_o that_o in_o rhodes_n thirie_n six_o degree_n and_o look_v how_o great_a the_o altitude_n of_o the_o place_n be_v the_o same_o must_v the_o distance_n necessary_o be_v betwixi_fw-la the_o pole_n and_o that_o point_n by_o which_o the_o arctic_a circle_n be_v describe_v and_o therefore_o the_o ancient_a greek_n always_o define_v the_o arctique_a circle_n to_o be_v 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d sive_fw-la 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d the_o most_o northern_a point_n that_o their_o horizon_n or_o place_n of_o habitation_n have_v so_o that_o the_o arctic_a circle_n be_v nothing_o else_o but_o the_o point_n of_o their_o habitation_n which_o touch_v the_o horizon_n for_o in_o describe_v they_o have_v both_o one_o common_a point_n only_o in_o this_o they_o differ_v that_o the_o centre_n of_o the_o arctique_a circle_n be_v the_o pole_n of_o the_o world_n but_o the_o centre_n of_o the_o horizon_n be_v the_o vertical_a circle_n or_o zenith_n of_o the_o place_n as_o for_o example_n a._n f._n d._n e._n be_v the_o horizon_n a._n g_o c._n h._n the_o arctic_a circle_n a._n d._n the_o meridian_n a._n the_o point_n of_o intersection_n of_o the_o horizon_n with_o the_o meridian_n in_o which_o place_n also_o the_o arctic_a and_o horizon_n in_o describe_v do_v mutual_o touch_v each_o other_o b._n the_o pole_n c._n the_o zenith_n of_o the_o place_n i._o the_o opposite_a point_n of_o the_o diameter_n of_o the_o actique_fw-la circle_n now_o if_o the_o elevation_n of_o the_o pole_n be_v full_a 45._o degree_n as_o it_o be_v at_o vienna_n in_o francâ—…_n than_o the_o point_n i._o will_v be_v the_o same_o with_o c_o that_o be_v to_o say_v the_o opposite_a part_n of_o the_o arctique_a cirâ—…le_n will_v touch_v the_o zenith_n of_o the_o place_n ent_n if_o the_o elevation_n of_o the_o pole_n be_v less_o than_o 45°_n degree_n the_o zenith_n will_v then_o fall_v without_o the_o circle_n but_o if_o it_o be_v great_a it_o will_v fall_v within_o sâ—…_n that_o by_o this_o mean_v it_o will_v come_v to_o pass_v that_o the_o near_o we_o be_v to_o the_o aequator_fw-la the_o lesser_a these_o circle_n will_v be_v and_o contrariwise_o the_o far_o we_o live_v off_o the_o aequator_fw-la the_o great_a they_o be_v but_o under_o the_o equinoctial_a itself_o that_o be_v in_o a_o right_a position_n of_o sphere_n there_o be_v no_o arctic_a circle_n at_o all_o pytheas_n write_v that_o those_o that_o inhabit_v thule_n now_o call_v iseland_n have_v a_o tropic_a for_o their_o arctique_a circle_n whether_o therefore_o this_o circle_n fall_v within_o or_o without_o the_o tropic_n the_o distance_n of_o it_o from_o the_o poiâ—…t_n l._n will_v be_v as_o great_a as_o be_v the_o difference_n betwixt_o the_o elevation_n of_o the_o pole_n and_o the_o elevation_n of_o the_o equinoctial_a above_o the_o horizon_n of_o the_o place_n as_o for_o example_n the_o elevation_n of_o the_o pole_n at_o rome_n be_v 41._o degree_n therefore_o the_o equinoctial_a be_v
time_n see_v that_o it_o be_v always_o divide_v into_o 12._o intoâ—…4_n â—…4_z equal_a part_n which_o be_v therefore_o call_v equal_a hour_n because_o they_o be_v always_o of_o equal_a length_n fifteen_o degree_n of_o the_o aequator_fw-la rise_v &_o set_v every_o hour_n for_o the_o whole_a aequator_fw-la be_v divide_v into_o 24._o part_n there_o be_v contain_v in_o the_o revolution_n of_o it_o 15._o part_n of_o time_n which_o be_v the_o measure_n of_o a_o hour_n so_o that_o a_o equal_a hour_n be_v the_o 24_o part_n of_o the_o while_o equinoctial_a circle_n in_o the_o latitude_n of_o 49._o degree_n the_o long_a day_n contain_v 16_o hour_n now_o therefore_o when_o it_o be_v 10_o of_o the_o clock_n before_o noon_n or_o the_o six_o hour_n after_o sunrising_n on_o this_o day_n 〈◊〉_d to_o know_v what_o unequal_a hour_n of_o the_o day_n it_o be_v i_o therefore_o dispose_v my_o proportional_a term_n thus_o 16_o give_v 6_o therefore_o 12._o which_o be_v the_o number_n of_o equal_a hour_n in_o every_o day_n or_o nigh_o give_v 4._o and_o and_o a_o half_a and_o if_o we_o desire_v to_o know_v how_o many_o degree_n of_o the_o aequator_fw-la do_v answer_n to_o one_o unequal_a hour_n we_o may_v do_v it_o thus_o namely_o by_o divide_v the_o whole_a number_n of_o degree_n of_o the_o 〈◊〉_d 〈◊〉_d arch_n by_o 12._o as_o if_o the_o artificial_a day_n 〈◊〉_d 〈◊〉_d equal_a hour_n in_o length_n than_o the_o arch_n of_o the_o diurnal_a parallel_n will_v be_v 240_o degree_n which_o if_o we_o divide_v by_o 12_o the_o quotient_a which_o 〈◊〉_d will_v show_v the_o number_n of_o degree_n in_o the_o aequator_fw-la that_o answer_n to_o one_o unequal_a â—…ou_fw-mi 〈◊〉_d like_o method_n also_o be_v to_o be_v observe_v in_o find_v out_o the_o length_n of_o the_o unequal_a hour_n of_o the_o night_n chap._n fourteen_o to_o find_v out_o the_o longitude_n latitude_n and_o declination_n of_o any_o fix_a star_n as_o it_o be_v express_v in_o the_o globe_n the_o longitude_n of_o a_o star_n be_v a_o arch_n of_o ecliptic_a intercept_v betwixt_o two_o of_o the_o great_a circle_n which_o be_v draw_v through_o the_o pole_n of_o the_o ecliptic_a the_o one_o of_o which_o pass_v through_o the_o intersection_n of_o the_o aequator_fw-la and_o ecliptic_a and_o the_o other_o through_o the_o centre_n of_o the_o star_n the_o latitude_n of_o a_o star_n be_v the_o distance_n of_o it_o from_o the_o eccliptick_a which_o be_v also_o to_o be_v reckon_v in_o that_o circle_n which_o pass_v through_o the_o centre_n thereof_o now_o if_o you_o desire_v to_o find_v out_o either_o of_o these_o you_o must_v take_v the_o quadrant_n of_o altitude_n or_o any_o other_o quadrant_n of_o a_o circle_n that_o be_v but_o exact_o divide_v into_o 90_o part_n and_o lay_v one_o end_n of_o it_o on_o either_o pole_n of_o the_o ecliptic_a either_o northern_a or_o southern_a as_o the_o latitude_n of_o the_o star_n shall_v require_v then_o let_v it_o pass_v through_o the_o centre_n of_o the_o star_n to_o the_o very_a ecliptic_a and_o there_o the_o other_o end_n will_v show_v the_o degree_n of_o longitude_n of_o the_o same_o which_o you_o must_v reckon_v from_o the_o begin_n of_o aries_n and_o so_o that_o portion_n of_o the_o quadrant_n that_o be_v contain_v betwixt_o the_o star_n itself_o and_o the_o ecliptic_a will_v also_o show_v the_o latitude_n of_o the_o star_n pont_n the_o manner_n how_o to_o find_v the_o longitude_n and_o latitude_n of_o star_n may_v be_v show_v by_o this_o example_n first_o let_v we_o propose_v the_o head_n of_o medusa_n which_o be_v find_v in_o the_o table_n to_o be_v in_o the_o twenty_o one_o gr_n 8._o and_o it_o have_v in_o northern_a latitude_n twenty_o three_o degree_n now_o therefore_o in_o the_o superficies_n of_o the_o globe_n we_o must_v look_v for_o the_o sign_n 8._o and_o reckon_v 21._o gr_n from_o the_o begin_n of_o the_o same_o on_o the_o ecliptic_a and_o the_o circle_n that_o shall_v be_v draw_v from_o the_o pole_n of_o the_o ecliptic_a through_o this_o degree_n shall_v be_v 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of_o which_o be_v northern_a i_o apply_v the_o end_n of_o the_o quadrant_n to_o the_o north_n pole_n of_o the_o zodiac_n otherwise_o have_v it_o be_v southern_a it_o must_v have_v be_v fit_v to_o the_o southern_a pole_n which_o doâ—…e_n i_o seek_v in_o the_o ecliptic_o for_o the_o 21_o gr_n of_o taurus_n which_o be_v the_o logitude_n of_o the_o star_n and_o have_v find_v it_o i_o lay_v the_o other_o end_n of_o my_o quadrant_n over_o it_o for_o by_o this_o mean_v the_o quadrant_n shall_v supply_v the_o office_n of_o the_o circle_n of_o longitude_n of_o medusa_n head_n 〈◊〉_d therefore_o if_o i_o reckon_v 23_o degree_n on_o the_o say_a quadrant_n begin_v from_o the_o ecliptic_a i_o shall_v have_v the_o true_a situation_n of_o this_o star_n in_o the_o globe_n in_o like_a manner_n may_v we_o find_v by_o a_o globe_n that_o have_v the_o star_n describe_v on_o it_o the_o longitude_n and_o latitude_n of_o any_o star_n in_o the_o heaven_n for_o if_o we_o fit_v the_o quadrant_n to_o the_o northern_a pole_n of_o the_o zodiaque_fw-la if_o the_o star_n have_v northern_a latitude_n and_o then_o let_v it_o pass_v through_o the_o centre_n of_o any_o star_n the_o degree_n of_o the_o ecliptic_a that_o the_o other_o end_n of_o it_o shall_v point_v out_o will_v be_v the_o longitude_n of_o the_o say_a star_n and_o the_o degree_n that_o be_v contain_v betwixt_o the_o ecliptic_a and_o the_o star_n will_v show_v you_o the_o latitude_n of_o the_o same_o a_o for_o example_n if_o the_o quadrant_n be_v first_o apply_v to_o the_o northern_a pole_n of_o the_o zodiaque_fw-la be_v afterward_o lay_v along_o over_o the_o the_o bright_a star_n in_o the_o crown_n the_o other_o end_n of_o it_o will_v fall_v on_o the_o 6._o gr_n m._n which_o be_v the_o longitude_n of_o this_o star_n and_o then_o if_o you_o reckon_v the_o number_n of_o degree_n betwixt_o the_o ecliptic_a and_o the_o same_o star_n you_o shall_v find_v they_o to_o be_v 44½_n which_o be_v the_o northern_a latitude_n of_o the_o same_o the_o declination_n of_o a_o star_n be_v the_o distance_n of_o it_o from_o the_o aequator_fw-la which_o distance_n must_v be_v reckon_v on_o a_o great_a circle_n pass_v through_o the_o pole_n of_o the_o aequator_fw-la and_o therefore_o if_o you_o but_o apply_v any_o star_n to_o the_o meridian_n you_o shall_v present_o have_v the_o declination_n of_o it_o if_o you_o account_v the_o degree_n and_o minute_n of_o the_o meridian_n if_o there_o be_v any_o that_o be_v contain_v betwixt_o the_o centre_n of_o the_o star_n and_o the_o aequator_fw-la pont_n the_o declination_n of_o star_n as_o also_o their_o right_a ascension_n may_v be_v know_v by_o the_o globe_n in_o this_o manner_n the_o star_n propose_v must_v be_v apply_v to_o the_o meridian_n and_o forthwith_o the_o same_o meridian_n will_v discover_v among_o the_o degree_n of_o the_o aequator_fw-la the_o right_a ascension_n of_o the_o same_o and_o it_o will_v also_o give_v you_o the_o declination_n if_o you_o reckon_v upon_o it_o the_o number_n of_o degree_n that_o be_v comprehend_v betwixt_o the_o equinoctial_a and_o the_o star_n propose_v and_o for_o a_o example_n of_o this_o let_v we_o propose_v the_o great_a dog_n who_o right_a ascension_n and_o declination_n we_o desire_v to_o know_v first_o therefore_o we_o set_v the_o star_n itself_o direct_o under_o the_o meridian_n and_o find_v the_o meridian_n to_o cut_v the_o equinoctial_a at_o 97._o gr_n 15._o min._n and_o this_o be_v the_o right_a ascension_n of_o this_o star_n and_o then_o reckon_v the_o number_n of_o the_o degree_n comprehend_v betwixt_o it_o and_o the_o equinoctial_a southward_n we_o find_v they_o to_o be_v 16_o degree_n which_o we_o conclude_v to_o be_v the_o southern_a latitude_n of_o the_o star_n the_o same_o also_o may_v be_v demonstrate_v