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archimedes_n of_o syracuse_n and_o according_a to_o this_o determination_n of_o they_o julius_n caesar_n define_v the_o measure_n of_o his_o civil_a year_n have_v first_o consult_v as_o the_o report_n go_v which_o one_o sosigines_n a_o peripatetic_a and_o a_o great_a mathematician_n but_o all_o these_o â—…xcept_v philolaus_n who_o come_v short_a of_o the_o just_a measure_n assign_v too_o much_o to_o the_o quantity_n of_o a_o year_n for_o that_o it_o be_v somewhat_o less_o than_o 365._o day_n 6._o hour_n be_v a_o truth_n confirm_v by_o the_o most_o accurate_a observation_n of_o all_o time_n and_o the_o skilful_a artist_n in_o astronomical_a affair_n but_o how_o much_o this_o space_n exceed_v the_o just_a quantity_n of_o a_o year_n be_v not_o so_o easy_a a_o matter_n to_o determine_v hipparchus_n and_o after_o he_o ptolemy_n will_v have_v the_o 300._o part_n of_o a_o day_n substract_v from_o this_o measure_n for_o jacobus_n christmannus_n be_v mistake_v when_o he_o affirm_v that_o a_o tropical_a 〈◊〉_d according_a to_o the_o opinion_n of_o hipparchus_n and_o ptolemy_n do_v consist_v of_o 365._o day_n and_o the_o 300_o part_n of_o a_o day_n for_o they_o do_v not_o say_v so_o but_o that_o the_o just_a quantity_n of_o a_o year_n be_v 365._o day_n and_o 6._o hour_n abate_v the_o 300._o part_n of_o a_o day_n as_o may_v be_v plain_o gather_v out_o of_o ptolemy_n almage_a lib._n 3._o cap._n 2._o and_o aâ—…_n christmannus_n himself_o have_v else_o where_o right_o observe_v now_o ptolemy_n will_v have_v this_o to_o be_v the_o just_a quantity_n of_o a_o year_n perpetual_o and_o immutable_o neither_o will_v he_o be_v persuade_v to_o the_o contrary_a notwithstanding_o the_o observatiâ—…s_n of_o hipparchus_n concâ—…ning_v the_o inequality_n of_o the_o sun_n periodiacall_a revolution_n but_o yet_o the_o observation_n of_o succeed_a time_n compare_v with_o those_o of_o hipparchus_n
accident_n common_a with_o our_o perioeci_n for_o we_o both_o inhabit_v the_o same_o temperate_a zone_n and_o have_v summer_n winter_n increase_n and_o decrease_v of_o day_n and_o night_n at_o the_o same_o time_n only_o this_o difference_n be_v betwixt_o we_o that_o when_o it_o be_v noon_n with_o we_o it_o be_v midnight_n with_o they_o those_o author_n that_o have_v add_v this_o differnce_n also_o that_o when_o the_o sun_n rise_v with_o we_o it_o set_v with_o those_o that_o be_v our_o perioecij_fw-la have_v betray_v their_o own_o ignorance_n for_o if_o this_o be_v so_o it_o will_v then_o follow_v that_o when_o the_o day_n be_v long_a with_o we_o it_o shall_v be_v at_o the_o short_a with_o they_o but_o this_o be_v most_o false_a they_o have_v commit_v the_o like_a error_n concern_v our_o antoeci_n also_o when_o as_o they_o will_v have_v the_o sun_n to_o rise_v with_o we_o and_o they_o at_o the_o same_o time_n the_o ground_n of_o which_o their_o error_n perhaps_o may_v be_v in_o that_o 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a_o mount_n to_o 38._o in_o the_o meridian_n of_o a_o material_a globe_n there_o be_v describe_v nine_o climate_n differ_v from_o each_o other_o by_o the_o quantity_n of_o half_a a_o hour_n after_o these_o there_o be_v other_z also_o set_v according_a to_o the_o difference_n of_o a_o whole_a hour_n and_o last_o of_o all_o those_o that_o differ_v in_o whole_a monthâ—…_n be_v continue_v to_o the_o very_a pole_n each_o of_o they_o express_v in_o their_o several_a latitude_n the_o distance_n of_o all_o both_o climate_n and_o parrallelâ—…_n together_o with_o their_o latitude_n from_o the_o aequator_fw-la and_o difference_n of_o the_o quantity_n of_o the_o long_a day_n be_v here_o full_o express_v it_o this_o table_n follow_v ampihscij_fw-la climate_n parallel_n the_o long_a summer_n day_n hour_n scr._n latitude_n and_o elevation_n of_o pole_n hour_n scr._n the_o breadth_n of_o the_o climate_n deg._n scrup._n 0_o 0_o 12_o 0_o 0_o 0_o 4_o 18_o 1_o 12_o 15_o 4_o 18_o 1_o 〈◊〉_d 12_o 30_o 8_o 34_o 8_o 25_o 〈◊〉_d 12_o 45_o 1â—…_n 43_o 2_o 4_o 13_o 0_o 16_o 43_o 7_o 50_o 5_o 13_o 15_o 20_o 33_o 3_o 6_o 13_o 30_o 23_o 10_o 7_o 3_o 7_o 13_o 45_o 27_o 36_o heteroscij_fw-la 4_o 8_o 14_o 0_o 30_o 47_o 6_o 9_o 〈◊〉_d 14_o 15_o 33_o 45_o 5_o 10_o 14_o 30_o 30_o 30_o 5_o 17_o 11_o 14_o 45_o 39_o 2_o 6_o 12_o 15_o 0_o 41_o 22_o 4_o 30_o 13_o 15_o 15_o 43_o 32_o 7_o 14_o 15_o 30_o 45_o 29_o 3_o 48_o 15_o 15_o 45_o 47_o 20_o heteroscij_fw-la climate_n parallel_n the_o long_a summer_n day_n hour_n scr._n latitude_n and_o elevation_n of_o the_o pole_n degr._fw-la scr_n the_o breadth_n of_o the_o climate_n degr._fw-la scr._n 8_o 16_o 16_o â—…0_n 49_o 1_o 3_o 13_o 17_o 16_o 15_o 50_o 33_o 9_o 18_o 16_o 30_o 51_o 58_o 2_o 44_o 19_o 16_o 45_o 53_o 1â—…_n 10_o 20_o 17_o 0_o 54_o 29_o 2_o 17_o 21_o 17_o 15_o 55_o 34_o 11_o 22_o 17_o 30_o 56_o 37_o 2_o 0_o 23_o 17_o 45_o 57_o 34_o 12_o 24_o 18_o 0_o 58_o 26_o 1_o 40_o 25_o 18_o 15_o 59_o 14_o 13_o 26_o 18_o 30_o 59_o 5â—…_n 1_o 26_o 27_o 18_o 45_o 60_o 40_o 14_o 28_o 19_o 0_o 61_o 18_o 1_o 13_o 29_o 19_o 15_o 61_o 53_o 15_o 30_o 19_o 30_o 62_o 25_o 1_o 1_o 31_o 19_o 45_o 62_o 54_o 16_o 32_o 20_o 0_o 63_o 22_o 0_o 52_o 33_o 20_o 15_o 63_o 46_o 17_o 34_o 20_o 30_o 64_o 〈◊〉_d 0_o 46_o 35_o 20_o 45_o 64_o 3â—…_n 18_o 36_o 21_o 0_o 69_o 49_o 0_o 36_o 37_o 21_o 15_o 65_o 6_o 19_o 38_o 21_o 30_o 65_o 21_o 0_o 29_o 39_o 21_o 45_o 65_o 35_o 20_o 40_o 22_o 0_o 65_o 47_o 0_o 22_o 41_o 22_o 1â—…_n 65_o 57_o 21_o 42_o 22_o 30_o 66_o 6_o 0_o 17_o 43_o 22_o 45_o 66_o 14_o 22_o 44_o 23_o 0_o 66_o 20_o 0_o 11_o 45_o 23_o 15_o 66_o 25_o 23_o 46_o 23_o 30_o 66_o â—…8_n 0_o 5_o 47_o 23_o 45_o 66_o â—…0_n 24_o 48_o 24_o 0_o 66_o 31_o 0_o 0_o  _fw-fr  _fw-fr month_n periscij_fw-la here_o the_o climate_n begin_v to_o be_v accounâ—…_n t_v by_o month_n from_o 66_o gr_n 3â—…_n 〈◊〉_d where_o the_o day_n be_v 24_o hour_n lonâ—…_n to_o the_o pole_n itself_o whoâ—…e_v it_o be_v 6._o month_n in_o length_n 1_o 67_o 15_o 2_o 69_o 30_o 3_o 73_o 20_o 4_o 78_o 20_o 5_o 84_o 0_o 6_o 90_o 0_o the_o second_o part_n chap._n i._o of_o such_o thing_n as_o be_v proper_a to_o the_o celestial_a globe_n and_o first_o of_o the_o planet_n hitherto_o have_v our_o discourse_n be_v concern_v those_o thing_n which_o be_v common_a to_o both_o globe_n we_o will_v now_o descend_v to_o speak_v of_o those_o that_o proper_o belong_v to_o each_o of_o they_o in_o particular_a and_o first_o of_o those_o thing_n that_o only_o concern_v the_o celestial_a globe_n as_o namely_o the_o star_n with_o their_o several_a configuration_n the_o whole_a number_n of_o star_n have_v be_v divide_v by_o the_o ancient_a astronomer_n who_o first_o apply_v themselves_o to_o the_o diligent_a observe_v of_o the_o same_o into_o two_o kind_n the_o first_o be_v of_o the_o planet_n or_o wander_a star_n the_o other_o of_o the_o fix_a the_o first_o of_o which_o they_o therefore_o call_v planet_n or_o wanderer_n because_o they_o observe_v no_o constant_a distance_n or_o situation_n 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not_o a_o thing_n suitable_a to_o our_o present_a purpose_n i_o shall_v not_o proceed_v any_o further_a in_o the_o explanation_n of_o the_o same_o the_o artificial_a day_n be_v define_v to_o be_v that_o space_n of_o time_n that_o the_o sun_n be_v in_o our_o upper_a hemisphere_n to_o which_o be_v oppose_v the_o artificial_a night_n while_o the_o sun_n remain_v in_o the_o low_a hemisphere_n the_o artificial_a day_n as_o also_o the_o night_n be_v divide_v each_o of_o they_o into_o 1â—…_n part_n which_o they_o call_v unequal_a hour_n because_o that_o according_a to_o the_o different_a season_n of_o the_o year_n they_o be_v great_a or_o less_o and_o be_v never_o always_o of_o the_o same_o length_n the_o length_n of_o the_o artificial_a day_n be_v thus_o sound_a out_o the_o globe_n be_v set_v to_o the_o latitude_n of_o the_o place_n you_o must_v find_v out_o the_o degree_n of_o the_o ecliptic_a that_o the_o sun_n iâ—…_n in_o at_o that_o time_n and_o apply_v the_o same_o to_o the_o meridian_n 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same_o parallel_n that_o always_o be_v hide_v under_o the_o horizon_n or_o else_o you_o may_v proceed_v the_o contrary_a way_n and_o first_o find_v out_o the_o quantity_n of_o the_o diurnal_a arch_n and_o afterward_o by_o the_o same_o you_o may_v gather_v the_o number_n of_o the_o hour_n also_o for_o the_o globe_n be_v set_v to_o the_o latitude_n of_o the_o place_n and_o the_o degree_n of_o the_o ecliptic_a that_o the_o sun_n be_v in_o be_v know_v you_o may_v find_v out_o in_o the_o manner_n now_o set_v down_o the_o difference_n of_o the_o right_n and_o oblique_a ascension_n of_o the_o same_o degree_n of_o the_o ecliptic_a for_o the_o latitude_n of_o that_o place_n for_o this_o difference_n will_v be_v the_o half_a of_o that_o wherein_o the_o artificial_a day_n for_o that_o time_n and_o place_n be_v either_o deficient_a or_o exceed_v the_o length_n of_o our_o equinoctial_a day_n and_o therefore_o you_o must_v add_v it_o when_o the_o day_n be_v long_o than_o the_o night_n which_o be_v from_o the_o 11_o of_o march_n to_o the_o 12_o of_o september_n but_o subtract_v all_o other_o time_n of_o the_o year_n when_o as_o the_o night_n be_v long_o than_o the_o day_n as_o for_o example_n on_o the_o 12_o day_n of_o june_n according_a to_o the_o old_a account_n the_o sun_n enter_v into_o cancer_n the_o right_a ascension_n of_o which_o degree_n of_o the_o ecliptic_a be_v 90._o degree_n but_o if_o in_o the_o latitude_n of_o 52_o gr_n the_o first_o degree_n of_o cancer_n be_v apply_v to_o the_o horizon_n we_o shall_v find_v the_o oblique_a ascension_n of_o it_o to_o be_v fifty_o six_o gr_n and_o about_o ten_o m_o so_o that_o the_o difference_n betwixt_o they_o be_v 33._o gr_n 5â—…_n m_o which_o if_o you_o add_v to_o nintie_a gr_n the_o half_a of_o the_o equinoctial_a day_n the_o length_n of_o the_o artificial_a day_n will_v then_o be_v 123._o gr_n fifty_o m._n and_o the_o whole_a diurnal_a arch_n 247._o gr_n 40._o m._n which_o if_o you_o divide_v by_o fifteen_o the_o quotient_n will_v be_v sixteen_o and_o almost_o a_o half_a which_o be_v the_o number_n of_o hour_n in_o the_o artificial_a day_n on_o the_o twelve_o of_o june_n for_o the_o latitude_n of_o fifty_o two_o degree_n and_o by_o this_o mean_n may_v you_o also_o find_v out_o the_o quantity_n of_o the_o long_a or_o short_a or_o any_o other_o intermediate_v day_n together_o with_o the_o increase_n and_o decrease_v of_o the_o same_o for_o any_o time_n or_o latitude_n of_o place_n cleomedes_n will_v have_v the_o quantity_n of_o the_o day_n to_o increase_v and_o diminish_v after_o this_o manner_n that_o the_o month_n immediate_o before_o and_o also_o after_o the_o aequinox_n the_o day_n shall_v increase_v and_o decrease_v the_o four_o part_n of_o the_o whole_a difference_n betwixt_o the_o length_n of_o the_o long_a and_o the_o short_a day_n of_o the_o whole_a year_n and_o the_o second_o month_n they_o shall_v differ_v a_o six_o part_n and_o the_o three_o a_o twelve_o part_n that_o be_v if_o the_o whole_a difference_n betwixt_o the_o long_a and_o the_o short_a day_n be_v six_o hour_n so_o that_o the_o month_n go_v immediate_o before_o and_o after_o the_o aequinoxe_n the_o day_n increase_n and_o decrease_v a_o hour_n and_o a_o half_a that_o be_v to_o say_v the_o four_o 〈◊〉_d part_n of_o 6._o hour_n the_o second_o month_n a_o whole_a hour_n and_o the_o three_o month_n half_a a_o hour_n but_o suppose_v we_o this_o to_o be_v exact_o agreeable_a to_o some_o certain_a determinate_a latitude_n yet_o it_o be_v not_o general_o so_o in_o all_o place_n for_o according_a to_o the_o diverse_a inclination_n of_o the_o sphere_n the_o day_n also_o be_v observe_v to_o increase_v and_o decrease_v diverse_o for_o see_v that_o the_o parallel_n in_o every_o several_a latitude_n be_v cut_v by_o the_o aequator_fw-la in_o a_o different_a manner_n it_o must_v needs_o follow_v that_o the_o proportion_n of_o the_o increase_n and_o decrease_v of_o the_o day_n must_v be_v also_o different_a i_o shall_v not_o here_o need_v to_o set_v down_o the_o manner_n how_o to_o find_v the_o apparent_a arch_n of_o the_o parallel_n of_o any_o star_n see_v that_o it_o be_v find_v out_o in_o the_o same_o manner_n as_o the_o diurnal_a arch_n of_o the_o sun_n parallel_n be_v chap._n xiii_o how_o to_o find_v out_o the_o hour_n of_o the_o day_n and_o night_n both_o equal_a and_o unequal_a for_o any_o tâ—…me_n and_o latitude_n of_o place_n if_o you_o desire_v to_o find_v out_o the_o equal_a hour_n of_o the_o day_n first_o set_v your_o globe_n to_o the_o latitude_n of_o the_o place_n you_o be_v in_o and_o also_o observe_v the_o latitude_n of_o the_o sun_n which_o do_v apply_v the_o place_n of_o the_o sun_n to_o the_o meridian_n and_o set_v the_o index_n to_o the_o twelve_o hour_n in_o the_o circle_n and_o then_o turn_v about_o the_o globe_n either_o to_o the_o east_n or_o west_n as_o your_o observation_n shall_v require_v until_o that_o the_o place_n of_o the_o sun_n be_v elevate_v so_o many_o degree_n above_o the_o horizon_n as_o shall_v agree_v with_o your_o observation_n as_o have_v be_v already_o show_v in_o declare_v how_o to_o find_v the_o azimuth_n and_o the_o globe_n stand_v in_o this_o situation_n the_o index_n will_v point_v out_o in_o the_o hour-circle_n the_o hour_n of_o the_o day_n wherein_o your_o observation_n be_v make_v after_o the_o same_o manner_n also_o you_o may_v find_v the_o hour_n of_o the_o night_n by_o observe_v the_o altitude_n of_o any_o know_a star_n that_o be_v express_v in_o the_o globe_n for_o the_o index_n must_v stand_v â—…il_n as_o it_o do_v before_o when_o it_o be_v fit_v to_o the_o place_n of_o the_o sun_n and_o the_o globe_n must_v be_v turn_v about_o till_o the_o star_n be_v observe_v to_o have_v the_o same_o elevation_n above_o the_o horizon_n of_o the_o globe_n as_o it_o have_v in_o the_o heaven_n and_o then_o the_o index_n will_v show_v the_o hour_n of_o the_o night_n now_o the_o manner_n how_o to_o find_v out_o the_o unequal_a hour_n of_o the_o day_n be_v this_o first_o you_o be_v to_o find_v out_o as_o we_o have_v already_o show_v the_o quantity_n or_o number_n of_o the_o hour_n of_o the_o artificial_a day_n and_o also_o the_o equal_a hour_n of_o the_o same_o whence_o by_o the_o rule_n of_o proportion_n you_o may_v also_o come_v to_o the_o knowledge_n of_o the_o unequal_a hour_n pont_n the_o unequal_a hour_n do_v answer_v to_o the_o artificial_a day_n which_o as_o you_o have_v hear_v before_o be_v define_v to_o be_v the_o space_n of_o time_n that_o the_o sun_n remain_v in_o the_o upp_a hemisphoere_n to_o which_o be_v oppose_v the_o artificial_a night_n comprehend_v all_o that_o time_n while_o the_o sun_n be_v hide_v from_o we_o which_o space_n of_o
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 call_v the_o the_o circle_n of_o longitude_n of_o the_o head_n of_o medusa_n after_o this_o reckon_v the_o latitude_n of_o the_o star_n also_o in_o the_o same_o circle_n among_o the_o parallel_n of_o latitude_n begin_v from_o the_o ecliptic_a and_o so_o forward_o towards_o the_o arctic_a pole_n because_o the_o latitude_n of_o it_o be_v northern_a until_o you_o have_v account_v 23._o gr_n which_o be_v the_o number_n of_o the_o degree_n of_o latitude_n and_o show_v the_o place_n of_o that_o star_n now_o because_o that_o all_o the_o circle_n of_o longitude_n and_o latitude_n neither_o be_v nor_o indeed_o can_v convenient_o be_v express_v on_o the_o globe_n therefore_o the_o quadrant_n of_o altitude_n be_v to_o serve_v in_o stead_n of_o the_o same_o for_o the_o find_v out_o of_o the_o longitude_n and_o situation_n of_o the_o star_n that_o be_v set_v in_o the_o globe_n and_o that_o after_o this_o manner_n let_v we_o take_v our_o former_a example_n of_o medusa_n be_v head_n the_o latitude_n 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
with_o the_o change_n of_o their_o declination_n what_o the_o arctic_a and_o antarctick_a circle_n be_v of_o the_o vertical_a circle_n and_o quadrant_n of_o altitude_n chap._n 3._o of_o the_o three_o position_n of_o sphere_n right_o parallel_n and_o oblique_a with_o their_o several_a affection_n chap._n 4._o of_o the_o zone_n and_o their_o number_n the_o vain_a opinion_n of_o the_o ancient_n concern_v the_o temperature_n of_o the_o zone_n be_v reject_v both_o by_o the_o testemony_n of_o some_o of_o the_o ancient_n themselves_o as_o also_o by_o the_o experience_n of_o late_a time_n chap._n 5._o of_o the_o amphiscij_fw-la periscij_fw-la and_o heteroscij_fw-la chap._n 6._o of_o the_o perioeci_n antoeci_n and_o antipode_n compare_v to_o each_o other_o chap._n 7._o of_o climate_n and_o parallel_n the_o second_o part_n chap._n 1._o of_o such_o thing_n as_o be_v proper_a to_o the_o celestial_a globe_n as_o namely_o of_o the_o star_n and_o first_o of_o the_o planet_n or_o wander_a star_n chap._n 2._o of_o the_o fix_a star_n and_o their_o constellation_n chap_n 3._o of_o the_o constellation_n of_o the_o northern_a hemisphere_n chap._n 4._o the_o sign_n of_o the_o zodiac_n and_o first_o of_o the_o northern_a chap._n 5._o the_o constellation_n of_o the_o southern_a hemisphere_n and_o first_o of_o those_o in_o the_o zodiac_n chap._n 6._o of_o the_o rest_n of_o the_o constellation_n of_o the_o southern_a hemisphere_n chap._n 7._o of_o the_o other_o star_n which_o be_v not_o express_v in_o globe_n why_o the_o star_n appear_v sometime_o in_o great_a number_n then_o at_o other_o time_n and_o sometime_o great_a and_o at_o other_o time_n less_o with_o the_o confutation_n of_o some_o vain_a opinion_n concern_v the_o same_o the_o idle_a relation_n of_o americus_n vespasius_n cardan_n and_o partcis_n concern_v the_o extraordinary_a greatness_n of_o the_o star_n about_o the_o south_n pole_n be_v refute_v out_o of_o the_o author_n own_o experience_n the_o three_o part_n chap._n 1._o the_o geographical_a description_n of_o the_o terrestrial_a globe_n with_o the_o part_n of_o the_o world_n that_o be_v yet_o know_v the_o error_n of_o ptolemy_n concern_v the_o southern_a bound_n of_o africa_n and_o asia_n as_o also_o of_o the_o northern_a limit_n of_o europe_n be_v condemn_v out_o of_o the_o write_n of_o the_o ancient_n and_o various_a experience_n of_o late_a writer_n chap._n 2._o of_o the_o compass_n of_o the_o earth_n and_o the_o measure_n of_o a_o degree_n with_o divers_a opinion_n concern_v the_o same_o of_o the_o greek_n as_o namely_o eratosthenes_n hipparchus_n posidonius_n cleomedes_n and_o ptolemy_n as_o also_o of_o the_o arabian_n jtalian_o german_n english_a and_o spanish_n posidonius_n and_o eratosthenes_n be_v confute_v out_o of_o their_o own_o observation_n and_o proposition_n ptolemy_n opinion_n be_v prefer_v before_o the_o rest_n and_o he_o free_v from_o the_o calumny_n of_o maurolycus_n who_o be_v also_o tax_v in_o that_o without_o cause_n favour_v posidonius_n he_o unjust_o condemn_v ptolemy_n the_o four_o part_n chap._n 1._o how_o to_o find_v out_o the_o longitude_n latitude_n distance_n and_o angle_n of_o position_n or_o situation_n of_o any_o place_n express_v in_o the_o terrestrial_a globe_n chap._n 2._o of_o the_o latitude_n of_o any_o place_n chap._n 3._o how_o to_o find_v the_o distance_n and_o angle_n of_o position_n of_o any_o two_o place_n chap._n 4._o to_o find_v the_o altitude_n of_o the_o sun_n or_o star_n chap._n 5._o to_o find_v the_o place_n and_o declination_n of_o the_o sun_n for_o any_o day_n give_v chap._n 6._o to_o find_v the_o latitude_n of_o any_o place_n by_o observe_v the_o meridian_n altitude_n of_o the_o sun_n or_o star_n chap._n 7._o how_o to_o find_v the_o right_n and_o oblique_a ascension_n of_o the_o sun_n and_o star_n for_o any_o latitude_n of_o place_n and_o time_n chap._n 8._o how_o to_o find_v the_o horizontall_a difference_n betwixt_o the_o meridian_n and_o the_o vertical_a circle_n of_o the_o sun_n or_o any_o other_o star_n which_o they_o call_v the_o azimuth_n for_o any_o time_n or_o place_n assign_v chap._n 9_o to_o find_v the_o hour_n of_o the_o day_n as_o also_o the_o amplitude_n of_o rise_v and_o set_v of_o the_o sun_n and_o star_n at_o any_o time_n and_o latitude_n of_o place_n chap._n 10._o of_o the_o threefold_a rise_n and_o set_v of_o star_n chap._n 11._o how_o to_o find_v the_o beginning_n and_o end_n of_o the_o twilight_n for_o any_o latitude_n of_o place_n and_o time_n chap._n 12._o to_o find_v for_o any_o latitude_n of_o place_n and_o time_n the_o length_n of_o the_o artificial_a day_n or_o night_n or_o the_o quantity_n of_o the_o sun_n parallel_n that_o remain_v above_o the_o horizon_n and_o that_o be_v hide_v beneath_o it_o and_o to_o perform_v the_o same_o by_o any_o other_o star_n chap._n 13_o to_o find_v the_o hour_n of_o the_o day_n and_o night_n both_o equal_a and_o unequal_a for_o any_o time_n &_o latitude_n of_o place_n chap._n 14._o to_o find_v the_o longitude_n latitude_n and_o declination_n of_o the_o fix_a star_n as_o they_o be_v express_v in_o the_o globe_n chap._n 15._o to_o find_v the_o declination_n of_o the_o needle_n from_o the_o true_a meridian_n which_o they_o common_o call_v the_o variation_n of_o the_o compass_n for_o any_o latitude_n assign_v where_o the_o error_n of_o those_o be_v discover_v who_o assign_v to_o the_o magnetical_a needle_n a_o certain_a meridian_n and_o fix_a poâ—…nt_n which_o it_o always_o respect_n and_o that_o affirm_v this_o change_n of_o variation_n to_o be_v regular_a all_o which_o vain_a conjecture_n of_o they_o and_o ungrounded_a hypothesis_n be_v refute_v both_o by_o more_o certain_a observation_n of_o other_o as_o also_o of_o the_o author_n himself_o chap._n 16._o how_o to_o make_v a_o sun_n dial_n by_o the_o help_n of_o the_o globe_n for_o any_o latitude_n of_o place_n the_o five_o and_o last_o part_n of_o the_o rumbe_n that_o be_v describe_v upon_o the_o terrestrial_a globe_n wherein_o their_o nature_n original_a and_o use_v in_o navigation_n be_v declare_v the_o preface_n there_o be_v two_o kind_n of_o instrument_n by_o which_o artificer_n have_v conceive_v that_o the_o figure_n of_o this_o so_o beautiful_a and_o various_a fabric_n of_o the_o whole_a universe_n may_v most_o apt_o be_v express_v and_o as_o it_o be_v at_o once_o present_v to_o the_o view_n the_o one_o exhibit_v this_o idea_n in_o a_o round_a solid_a be_v call_v a_o globe_n or_o sphere_n the_o other_o express_v the_o same_o in_o a_o plain_a they_o term_v a_o planisphaere_n or_o map_n both_o of_o which_o have_v be_v long_o since_o invent_v by_o the_o ancient_n have_v yet_o even_o to_o our_o time_n in_o a_o continue_a succession_n receive_v still_o more_o ripeness_n and_o perfection_n the_o sphere_n or_o globe_n and_o the_o use_n thereof_o be_v report_v by_o diodorus_n siculus_n to_o have_v be_v first_o find_v out_o by_o atlas_n of_o libya_n whence_o afterward_o spring_v the_o fable_n of_o his_o bear_n up_o the_o heaven_n with_o his_o shoulder_n other_o attribute_v the_o invention_n of_o the_o same_o to_o thales_n and_o it_o be_v afterward_o bring_v to_o perfection_n by_o crates_n of_o who_o strabo_n make_v mention_v archimedes_n and_o proclus_n but_o most_o of_o all_o by_o ptolemy_n according_a to_o who_o rule_n and_o observation_n especial_o succeed_a time_n compose_v their_o globe_n as_o leontius_n mechanicus_fw-la affirm_v and_o now_o there_o have_v be_v much_o perfection_n add_v to_o the_o same_o in_o these_o our_o late_a time_n by_o the_o industry_n and_o diligence_n gemma_fw-la frisius_n and_o gerardus_n mercator_n as_o it_o may_v appear_v by_o those_o globe_n that_o be_v set_v forth_o at_o london_n anno_fw-la 1593._o so_o that_o now_o there_o seem_v not_o to_o be_v any_o thing_n that_o may_v be_v add_v to_o they_o the_o planisphaere_n indeed_o be_v a_o fine_a invention_n and_o have_v in_o it_o wonderful_a variety_n of_o workmâ—…nship_n if_o so_o be_v that_o the_o composition_n of_o it_o be_v right_o deduce_v out_o of_o geometrical_a and_o opticall_a principle_n and_o it_o want_v not_o its_o great_a delightfullnesse_n and_o beauty_n also_o but_o yet_o that_o other_o be_v tbe_n more_o ancient_a have_v also_o the_o priority_n in_o nature_n and_o be_v of_o the_o most_o convenient_a form_n and_o therefore_o more_o apt_o accommodate_v for_o the_o understanding_n and_o fancy_n not_o to_o speak_v any_o thing_n of_o the_o beauty_n and_o gracefulness_n of_o it_o for_o it_o represent_v the_o thing_n themselves_o in_o proper_a genuive_v figur_n for_o as_o concern_v the_o figure_n of_o the_o heaven_n whether_o it_o be_v round_o be_v scarce_o e-eve_a question_v by_o any_o so_o likewise_o touch_v the_o figure_n of_o the_o earth_n notwithstanding_o many_o and_o sundry_a opinion_n have_v be_v broach_v among_o the_o ancient_a philosopher_n some_o of_o they_o contend_v for_o a_o plain_a other_o a_o hollow_a other_o
a_o cubic_n all_o and_o some_o a_o pyramidal_a form_n yet_o this_o opinion_n of_o its_o roundness_n with_o great_a consent_n of_o reason_n at_o length_n prevail_v the_o rest_n be_v all_o explode_a now_o we_o affirm_v it_o to_o be_v round_o yet_o so_o as_o that_o we_o also_o admit_v of_o its_o inequality_n by_o reason_n of_o those_o so_o great_a eminence_n of_o hill_n and_o depression_n of_o valley_n eratosthenes_n as_o he_o be_v cite_v by_o strabo_n in_o his_o first_o book_n say_v that_o the_o fashion_n of_o the_o earth_n be_v like_a that_o of_o a_o globe_n not_o so_o exact_o round_a as_o a_o artificial_a globe_n be_v but_o that_o it_o have_v certain_a inequality_n the_o earth_n can_v be_v say_v to_o be_v of_o a_o exact_a orbicular_a form_n by_o reason_n of_o somany_a high_a hill_n and_o low_a plain_n as_o pliny_n right_o observe_v and_o strabo_n also_o in_o his_o first_o book_n of_o his_o geography_n say_v that_o the_o earth_n and_o the_o water_n together_o make_v up_o one_o spherical_a body_n not_o of_o so_o exact_a a_o form_n as_o that_o of_o the_o heaven_n although_o not_o much_o unlike_o it_o this_o assertion_n of_o the_o roundness_n of_o the_o earth_n with_o the_o intervening_a sea_n be_v confirm_v also_o by_o these_o reason_n for_o first_o that_o it_o be_v round_o from_o east_n to_o west_n be_v prove_v by_o the_o sun_n moon_n and_o the_o other_o star_n which_o be_v see_v to_o rise_v and_o set_v first_o with_o those_o that_o inhabit_v more_o eastward_o and_o afterward_o with_o they_o that_o be_v far_a west_n the_o sun_n rise_v with_o the_o persian_n that_o dwell_v in_o the_o eastern_a part_n four_o hour_n soonner_o than_o it_o do_v with_o those_o that_o dwell_v in_o spain_n more_o westward_o as_o cleomedes_n affirm_v the_o same_o be_v also_o prove_v by_o the_o observe_n of_o eclipse_n especial_o those_o of_o the_o moon_n which_o although_o they_o happen_v at_o the_o same_o time_n be_v not_o yet_o observe_v in_o all_o place_n at_o the_o same_o hour_n of_o the_o day_n or_o night_n but_o the_o hour_n of_o their_o appear_v be_v late_a with_o they_o that_o inhabit_v eastward_o than_o it_o be_v with_o the_o more_o western_a people_n a_o eclipse_n of_o the_o moon_n which_o ptolemy_n report_v lib._n 1_o geogr._n cap._n 4._o to_o have_v be_v see_v in_o arbela_n a_o town_n in_o assyria_n at_o the_o five_o hour_n of_o the_o night_n the_o same_o be_v observe_v at_o carthage_n at_o the_o second_o hour_n in_o like_a manner_n a_o eclipse_n of_o the_o sun_n which_o be_v observe_v in_o campania_n to_o be_v betwixt_o 7._o and_o 8._o of_o the_o clock_n be_v see_v by_o coâ—…bulo_n a_o captain_n in_o armenia_n betwixt_o 10â—…_n and_o 11._o as_o it_o be_v relate_v by_o pliny_n now_o that_o it_o be_v also_o of_o a_o spherical_a figure_n from_o north_n to_o south_n may_v be_v clear_o demonstrate_v by_o the_o rise_n setting_n elevation_n and_o depression_n of_o the_o star_n and_o pole_n the_o bright_a star_n that_o shine_v so_o resplendent_o in_o the_o upper_a part_n of_o the_o stern_a of_o the_o ship_n argo_n and_o be_v call_v by_o the_o greeek_v 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d be_v scarce_o to_o be_v see_v at_o all_o in_o rhodes_n unless_o it_o be_v from_o some_o eminent_a high_a place_n yet_o the_o same_o be_v see_v very_o plain_o in_o alexandria_n as_o be_v elevate_v above_o the_o horizon_n about_o the_o four_o part_n of_o a_o sign_n as_o proclus_n affirm_v in_o the_o end_n of_o his_o book_n de_fw-fr sphaera_fw-la for_o i_o read_v it_o conspicuè_fw-fr cernitur_fw-la not_o as_o it_o be_v common_o prorsus_fw-la non_fw-la cernitur_fw-la notwith_v anding_n that_o both_o the_o greek_a text_n and_o also_o the_o latin_a translation_n be_v against_o it_o another_o argument_n may_v be_v take_v from_o the_o figure_n of_o the_o shadow_n in_o the_o eclipse_n of_o the_o moon_n cause_v by_o the_o interposition_n of_o the_o earth_n opacous_a body_n which_o shadow_n be_v spherical_a can_v proceed_v from_o any_o other_o than_o a_o round_a globous_a body_n as_o it_o be_v demonstrate_v unto_o we_o out_o of_o opticall_a principle_n but_o this_o one_o reason_n be_v beyond_o all_o exception_n that_o those_o that_o make_v towards_o the_o land_n at_o the_o sea_n shall_v first_o of_o all_o descry_v the_o top_n of_o the_o hill_n only_o aâ—…d_v afterward_o as_o they_o draw_v near_o to_o shore_n they_o see_v the_o low_a part_n of_o the_o same_o by_o little_a and_o little_a which_o can_v proceed_v from_o any_o other_o cause_n than_o the_o gibbosity_n of_o the_o earth_n superficies_n as_o for_o those_o other_o opinion_n of_o the_o hollow_a cubicall_a pyramidal_a and_o plain_a figure_n of_o the_o earth_n you_o have_v they_o all_o large_o examine_v both_o in_o theon_n ptolemy_n interpreter_n cleomedes_n and_o almost_o in_o all_o our_o ordinary_a author_n of_o the_o sphere_n together_o with_o the_o reason_n why_o they_o be_v reject_v yet_o that_o old_a conceit_n of_o the_o plainness_n of_o the_o earth_n superficies_n be_v again_o now_o at_o last_o tanquam_fw-la crambe_n recocta_fw-la set_v forth_o in_o a_o new_a dress_n and_o thrust_v upon_o we_o by_o franciscus_n patricius_n who_o by_o some_o few_o eold_a argument_n and_o misunderstand_v experiment_n endeavour_n to_o confirm_v his_o own_o and_o consequent_o to_o overthrow_v that_o other_o receive_v opinion_n of_o the_o spherical_a figure_n of_o the_o earth_n i_o shall_v only_o light_o touch_v at_o his_o chief_a argument_n my_o present_a purpose_n and_o intention_n suffer_v mce_n not_o to_o insist_v long_o on_o the_o confutation_n of_o they_o and_o fâ—…rst_v of_o all_o the_o great_a beight_n of_o hill_n and_o the_o depression_n of_o valley_n so_o much_o disagree_v from_o the_o evenness_n of_o the_o plain_a part_n of_o the_o earth_n scem_fw-la to_o make_v very_o much_o against_o the_o roundness_n of_o the_o earth_n who_o can_v hear_v with_o patience_n say_v he_o that_o those_o huge_a high_a mountain_n of_o norway_n or_o the_o mountain_n slotus_fw-la which_o lie_v under_o the_o pole_n and_o be_v the_o high_a in_o the_o world_n shall_v yet_o be_v think_v to_o have_v the_o same_o superficies_n with_o â—…he_n sealy_v beneath_o it_o this_o therefore_o be_v the_o chief_a reason_n that_o mâ—…y_v seem_v to_o overthrow_v the_o opinion_n of_o the_o earth_n and_o sea_n make_v up_o one_o spherical_a body_n let_v we_o examine_v it_o a_o little_a more_o near_o and_o consider_v how_o great_a this_o inequality_n may_v be_v that_o seem_v to_o make_v so_o much_o against_o the_o evennessc_n of_o this_o yerrestitall_a globe_n many_o strange_a and_o almost_o incredible_a thing_n be_v report_v by_o aristotle_n mela_n pliny_n and_o solinuâ—…_n of_o the_o unusual_a height_n of_o athoâ—…_n a_o hill_n in_o macedonia_n and_o of_o casius_n in_o syria_n as_o also_o of_o another_o of_o the_o same_o name_n in_o arabia_n and_o of_o the_o monntaine_n caucasus_n and_o among_o the_o rest_n one_o of_o the_o most_o miraculous_a thing_n which_o they_o have_v observe_v of_o the_o mountain_n athos_n be_v that_o whereas_o it_o be_v situate_a in_o macedony_n it_o cast_v a_o shadow_n into_o the_o market_n place_n at_o myrrhina_n a_o town_n in_o the_o island_n lemnos_n from_o whence_o athos_n be_v distant_a 86._o mile_n but_o for_o as_o much_o as_o athos_n lie_v westward_o from_o lemnos_n as_o may_v appear_v out_o of_o ptolemy_n table_n no_o marvel_n that_o it_o cast_v so_o large_a a_o shadow_n see_v that_o we_o may_v observe_v by_o daily_a experience_n that_o as_o well_o when_o the_o sunrise_v as_o when_o it_o set_v the_o shadow_n be_v always_o extraordinary_a long_o but_o that_o which_o pliny_n and_o solinus_n report_n of_o the_o same_o mountain_n i_o shall_v rather_o account_v among_o the_o rest_n of_o their_o fabulous_a story_n where_o as_o they_o affirm_v it_o to_o be_v so_o high_a that_o it_o be_v think_v to_o be_v above_o that_o region_n of_o the_o air_n whence_o the_o rain_n be_v wont_a to_o fall_v and_o this_o opinion_n say_v they_o be_v first_o ground_v upon_o a_o report_n that_o there_o go_v that_o the_o ash_n which_o be_v leave_v upon_o the_o altar_n on_o the_o top_n of_o this_o hill_n be_v never_o wash_v away_o but_o be_v find_v remain_v in_o heap_n upon_o the_o same_o to_o this_o may_v be_v add_v another_o testimony_n out_o of_o the_o excerpt_n of_o the_o seven_o book_n of_o strabo_n where_o it_o be_v say_v that_o those_o that_o inhabit_v the_o top_n of_o this_o mountain_n do_v see_v the_o sun_n three_o hour_n soon_o than_o those_o that_o live_v near_o the_o sea_n side_n the_o height_n of_o the_o mountâ—…in_n caucasus_n be_v in_o like_a manner_n celebrate_v by_o arisâ—…otle_n the_o top_n whereof_o be_v enlighten_v by_o the_o sun_n bâ—…ames_n the_o three_o part_n of_o the_o night_n both_o morning_n and_o evening_n no_o less_o fabulous_a be_v that_o which_o be_v report_v
and_o ptolemy_n doâ—…_n evince_n the_o contrary_n the_o indian_n and_o jew_n subtract_v the_o 110._o part_n of_o a_o day_n albategnius_n the_o 600._o part_n the_o persian_n the_o 115._o part_n according_a to_o who_o account_n messahalah_n and_o albumasar_n write_v the_o table_n of_o the_o mean_a motion_n of_o the_o sun_n azaphius_fw-la avarius_fw-la and_o arzachel_n affirm_v that_o the_o quantity_n assign_v be_v too_o mcch_n by_o the_o 126._o part_n of_o a_o day_n alphonsus_n abate_v the_o 122._o part_n of_o a_o day_n some_o other_o the_o 128._o and_o some_o the_o 130._o part_n of_o a_o day_n those_o that_o be_v late_o employ_v in_o the_o restitution_n of_o the_o roman_a calendar_n will_v have_v almost_o the_o 133._o part_n of_o 1._o day_n to_o be_v substract_v which_o they_o conceive_v in_o 400._o year_n will_v come_v to_o three_o whole_a day_n but_o copernicus_n observe_v that_o this_o quantity_n fall_v short_a by_o the_o 115._o part_n of_o a_o day_n most_o true_a therefore_o be_v that_o conclusion_n of_o censorinus_n that_o a_o year_n consist_v of_o 365._o day_n and_o i_o know_v not_o what_o certain_a portion_n not_o yet_o discover_v by_o astrologer_n by_o these_o divers_a opinion_n here_o allege_v be_v manifest_o discover_v the_o error_n of_o dion_n which_o be_v indeed_o a_o very_a ridiculous_a one_o for_o he_o have_v a_o conceit_n that_o in_o the_o space_n of_o 1461._o julian_n year_n there_o will_v be_v want_v a_o whole_a day_n for_o the_o just_a measure_n of_o a_o year_n which_o he_o will_v have_v to_o be_v intercale_v and_o so_o the_o civil_a julian_n year_n will_v accurate_o agree_v with_o the_o revolution_n of_o the_o sun_n and_o galen_n also_o the_o prince_n of_o physician_n be_v gross_o deceive_v when_o he_o think_v that_o the_o year_n consist_v of_o 365_o day_n 6._o hour_n and_o beside_o almost_o the_o 100_o part_n of_o a_o day_n so_o that_o at_o every_o hundred_o year_n end_n there_o must_v be_v a_o new_a intercalation_n of_o a_o whole_a day_n now_o 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notwithstanding_o he_o be_v a_o great_a mathematician_n in_o that_o above_o 100_o year_n after_o hipparchus_n in_o institute_v the_o julian_n calendar_n he_o assign_v the_o equinoxâ—…_n to_o be_v on_o the_o 25._o of_o march_n or_o the_o eight_o oâ—…_n thâ—…_n kalend_n of_o april_n which_o be_v the_o place_n it_o ought_v to_o have_v have_v almost_o 400._o year_n before_o his_o time_n this_o error_n of_o sosigenes_n be_v derive_v to_o succeed_a age_n also_o in_o so_o much_o that_o in_o gallen_n time_n which_o be_v almost_o 200._o year_n after_o julius_n caesar_n the_o aequinox_n be_v wont_a to_o be_v place_v on_o the_o 24._o day_n of_o march_n and_o september_n as_o theodorus_n gaza_n report_v in_o the_o year_n of_o our_o saviour_n incarnation_n it_o happen_v on_o the_o 10._o of_o the_o kalendâ—…_n of_o april_n or_o the_o 23_o of_o march._n and_o 140._o year_n after_o ptolemy_n observe_v it_o to_o fall_v on_o the_o 11._o of_o the_o kalend_n and_o in_o the_o time_n of_o the_o council_n of_o nice_a about_o the_o year_n of_o our_o lord_n 328._o it_o be_v find_v to_o be_v on_o the_o 21._o of_o march_n or_o the_o 12._o of_o the_o calends_o of_o april_n in_o the_o year_n 831._o thebit_fw-la ben_n chorah_n observe_v the_o vernal_a aequinoxe_n to_o fall_v on_o the_o 17._o day_n of_o march_n in_o alfraganus_n his_o time_n it_o come_v to_o the_o 16._o of_o march_n arzachel_n a_o spaniard_n in_o the_o year_n 1090._o observe_v to_o fall_v on_o the_o ides_n of_o march_n that_o be_v the_o 15._o day_n in_o the_o year_n 1316._o it_o be_v observe_v to_o be_v on_o the_o 13._o day_n of_o march._n and_o in_o in_o our_o time_n it_o be_v come_v to_o â—…he_v 11._o and_o 10._o of_o the_o same_o month_n so_o that_o in_o â—…he_a space_n of_o 1020._o yeaâ—…s_n or_o thereabouts_o the_o equinoctial_a point_n be_v get_v forward_o no_o less_o than_o 14._o day_n the_o time_n of_o the_o solstice_n also_o about_o 388._o year_n before_o christ_n be_v observe_v by_o meton_n and_o euctemon_n to_o fall_v â—…pon_o the_o 18._o dav_v of_o june_n as_o joseph_n scaliger_n and_o jacobus_n christmannus_n have_v observe_v but_o the_o same_o in_o our_o time_n be_v find_v to_o be_v on_o the_o 12._o of_o the_o same_o month_n the_o ecliptic_a and_o aequator_fw-la be_v cross_v by_o two_o great_a circle_n also_o which_o be_v call_v colour_n both_o which_o be_v draw_v through_o the_o pole_n oâ—…_n colour_n the_o world_n and_o cut_v the_o aequator_fw-la at_o â—…ght_a angle_n the_o one_o of_o they_o pass_v through_o the_o point_n of_o both_o the_o intersection_n and_o be_v call_v the_o equinoctial_a colour_n the_o other_o pass_v through_o the_o point_n of_o the_o great_a distance_n of_o the_o zodiac_n from_o the_o aequator_fw-la be_v therefore_o call_v the_o solsticiall_a colour_n pont_n the_o office_n of_o the_o colour_n in_o general_n be_v first_o to_o show_v the_o four_o principal_a point_n of_o the_o zodiac_n in_o which_o by_o reason_n of_o the_o motion_n of_o the_o sun_n there_o be_v cause_v the_o great_a change_n of_o the_o season_n of_o the_o year_n of_o which_o point_n two_o be_v in_o the_o aequator_fw-la at_o aries_n and_o libra_n determine_v the_o place_n of_o the_o aequinoctial_a colour_n and_o capricorn_n which_o constitute_v the_o solsticiall_a colour_n second_o to_o distinguish_v the_o aequator_fw-la zodiac_n and_o the_o whole_a sphere_n of_o the_o heaven_n into_o four_o equal_a part_n the_o use_n of_o which_o be_v principal_o see_v in_o examine_v the_o ascension_n of_o the_o sign_n these_o colour_n differ_v from_o each_o other_o in_o that_o the_o solsticiall_a colour_n pass_v through_o the_o pole_n of_o the_o world_n and_o also_o of_o the_o zodiac_n but_o the_o equinoctial_a colour_n pass_v through_o the_o pole_n of_o the_o world_n only_o now_o that_o both_o the_o colour_n as_o also_o the_o equinoctial_a point_n have_v leave_v the_o place_n where_o they_o be_v ancient_o sound_a to_o be_v in_o the_o heaven_n be_v a_o matter_n agree_v upon_o by_o all_o those_o that_o have_v apply_v themselves_o to_o the_o observation_n of_o the_o celestial_a motion_n only_o the_o doubt_n be_v whether_o fix_a star_n have_v go_v forward_o unto_o the_o proceed_n sign_n as_o ptolemy_n will_v have_v it_o or_o else_o whether_o the_o equinoctial_a and_o solsticiall_a point_n have_v go_v backward_o to_o the_o subsequent_a sign_n according_a to_o the_o series_n of_o the_o zodiac_n as_o copernicus_n opinion_n be_v pont_n what_o the_o opinion_n of_o joseph_n scaliger_n be_v concern_v the_o procession_n of_o aequinoctial_a point_n thus_o diverse_o think_v on_o by_o ptolemy_n and_o copernicus_n you_o have_v express_v in_o a_o epistle_n of_o his_o â—…o_n isaac_n casaubon_n there_o have_v be_v not_o long_o before_o a_o disputation_n hold_v concern_v some_o certain_a mathematical_a question_n at_o the_o entreaty_n of_o some_o of_o the_o chief_a of_o the_o state_n of_o the_o low_a country_n among_o which_o number_n scaliger_n be_v choose_v also_o as_o a_o arbitrator_n which_o epistle_n of_o he_o be_v afterward_o print_v among_o some_o other_o of_o his_o epistle_n at_o paris_n what_o the_o illustrious_a tycho_n also_o think_v concern_v this_o point_n you_o have_v in_o his_o progymâ—…asmata_fw-la instaur_n astron._n p._n 255._o but_o i_o will_v first_o set_v down_o scaliger_n opinion_n and_o afterward_o add_v tychoe_n and_o some_o other_o also_o scaliger_n speak_v thus_o alterae_fw-la literaetuae_fw-la etc._n etc._n i_o receive_v say_v he_o â—…eur_n second_o letter_n the_o next_o day_n aster_n your_o former_a in_o which_o you_o make_v mention_n of_o one_o that_o undertake_v â—…o_o discourse_n of_o the_o magnetical_a direction_n of_o the_o needle_n many_o indeed_o have_v endeavour_v in_o this_o matter_n and_o doc_fw-fr daily_a endeavour_n be_v thereto_o encourage_v by_o the_o reward_v propose_v by_o the_o illustrious_a state_n to_o who_o hand_n some_o have_v deliver_v
for_o whereas_o in_o his_o lib._n 6._o cap._n 22._o have_v discourse_v of_o the_o mâ—…gnitude_n of_o the_o isle_n taprobane_n which_o be_v now_o think_v to_o be_v sumatra_n and_o lie_v direct_o under_o the_o line_n out_o of_o eratosthenes_n and_o megasthenes_n he_o present_o add_v that_o beside_o the_o testimony_n of_o the_o ancient_n the_o roman_n have_v better_a knowledge_n of_o the_o same_o in_o the_o time_n of_o the_o emâ—…eror_n claudiuâ—…_n there_o be_v ambassador_n send_v from_o thence_o to_o rome_n who_o among_o other_o thing_n shall_v relate_v that_o with_o they_o gold_n &_o silver_n be_v in_o high_a account_n and_o that_o they_o have_v great_a wealth_n than_o the_o roman_n themselves_o but_o yet_o that_o the_o roman_n have_v great_a use_n of_o riches_n than_o they_o which_o word_n of_o pliny_n with_o many_o other_o there_o at_o large_a set_v down_o by_o he_o if_o they_o be_v but_o compare_v with_o what_o himself_o elsewhere_o write_v in_o his_o 2_o book_z chap._n 68_o he_o will_v be_v find_v manifest_o to_o contradict_v himself_o for_o dispute_v in_o this_o place_n and_o inquire_v how_o great_a a_o part_n of_o the_o earth_n be_v inhabit_v tres_n say_v he_o terrae_fw-la part_n abstulisse_fw-la nobis_fw-la coelum_fw-la etc._n etc._n three_o part_n of_o the_o world_n the_o heaveus_fw-la have_v rob_v we_o of_o to_o wit_n the_o torrid_a or_o middle_a zone_n â—…bat_n be_v whatsoever_o lie_v betwixt_o the_o two_o tropique_n and_o the_o two_o outmost_a or_o frigid_a zone_n that_o be_v to_o say_v whatever_o ground_n lie_v betwixt_o either_o pole_n and_o the_o arctique_a and_o antarctique_a circle_n according_a to_o that_o which_o the_o poet_n sing_v of_o old_a quarum_fw-la quae_fw-la media_fw-la est_fw-la non_fw-la est_fw-la habita_fw-la bilis_fw-la aestu_fw-la nix_n tegit_fw-la alta_fw-la duos_fw-la in_o english_a thus_o the_o midst_n of_o these_o be_v not_o inhabit_v through_o heat_n and_o two_o with_o snow_n be_v cover_v for_o this_o be_v that_o which_o pliny_n mean_v that_o those_o two_o outwardmost_a be_v not_o habitable_a by_o reason_n of_o extremity_n of_o â—…old_n nor_o the_o other_o through_o too_o violent_a heat_n but_o that_o which_o be_v more_o to_o be_v wonder_v at_o in_o so_o great_a a_o author_n who_o not_o withstand_v indifferent_o take_v up_o aswell_o the_o common_a popular_a fable_n as_o the_o extravagant_a fixion_n of_o the_o poet_n also_o be_v that_o which_o he_o very_o confident_o relate_v out_o of_o corlius_fw-la nepos_n how_o that_o one_o eudoxus_n take_v ship_n in_o the_o arabian_a gulf_n come_v as_o far_o as_o the_o gades_n two_o isle_n upon_o the_o confine_n of_o spain_n which_o voyage_n if_o we_o shall_v but_o thorough_o examine_v will_v be_v find_v to_o be_v as_o much_o 〈◊〉_d that_o all_o the_o fortugal_n and_o our_o countryman_n at_o this_o day_n perform_v in_o their_o sea_n voyage_n to_o the_o east_n indâ—…_n when_o as_o touch_v upon_o the_o cape_n of_o good_a hope_n they_o twice_o cross_v the_o line_n and_o pass_v through_o the_o whole_a torrid_a zone_n not_o to_o speak_v any_o thing_n of_o that_o which_o he_o write_v in_o his_o first_o book_n twenty_o three_o chapter_n namely_o that_o there_o be_v never_o a_o year_n that_o india_n do_v not_o suck_v out_o of_o the_o roman_a empire_n at_o the_o least_o 500000._o sesterce_n by_o send_v in_o such_o commodity_n as_o they_o sell_v to_o the_o roman_n for_o a_o hundred_o time_n as_o much_o as_o they_o be_v worth_a in_o india_n and_o that_o there_o be_v yearly_a traffic_n by_o ship_n through_o the_o red_a sea_n betwixt_o they_o and_o the_o roman_n who_o be_v sane_a for_o their_o safe_a passage_n to_o defend_v themselves_o from_o pirate_n by_o go_v provide_v with_o band_n of_o archer_n and_o here_o all_o that_o can_v be_v say_v in_o pliny_n defence_n be_v thaâ—…those_n thing_n which_o he_o relate_v in_o this_o second_o book_n be_v write_v by_o he_o long_o before_o the_o rest_n which_o followeh_n and_o that_o at_o that_o time_n these_o indian_a voyage_n be_v not_o so_o frequent_o undertake_v or_o the_o passage_n so_o well_o know_v unto_o the_o roman_n especial_o for_o that_o in_o the_o book_n follow_v as_o namely_o the_o six_o book_n 17._o and_o 23._o chapter_n he_o say_v that_o the_o whole_a course_n of_o the_o voyage_n from_o egypt_n into_o india_n begin_v but_o than_o first_o to_o be_v discover_v when_o as_o he_o be_v write_v the_o same_o and_o that_o seneca_n have_v not_o long_o before_o begin_v a_o description_n of_o india_n reckon_v up_o therein_o 60._o great_a river_n and_o 122._o nation_n to_o be_v contain_v within_o the_o same_o the_o principal_a cause_n of_o the_o habitablenesse_n and_o fortility_n of_o the_o part_n under_o the_o torrid_a zone_n iâ—…_n in_o that_o the_o sun_n shine_v upon_o they_o but_o 12._o hour_n so_o that_o the_o night_n be_v always_o as_o long_o as_o the_o day_n the_o coldness_n of_o the_o one_o do_v very_o much_o attemperate_a the_o excessive_a heat_n of_o the_o other_o in_o like_a manner_n that_o both_o the_o frigid_a zone_n be_v habitable_a be_v to_o be_v attribute_v to_o the_o sun_n which_o in_o his_o course_n through_o the_o six_o northern_a sign_n of_o the_o zodiaque_fw-la never_o set_v in_o six_o month_n space_n so_o those_o that_o live_v under_o 84_o degree_n of_o latitude_n so_o that_o by_o his_o continual_a preseneâ—…_n the_o extreme_a rigidity_n of_o the_o clime_n iâ—…_n mitigate_v and_o the_o cold_a by_o this_o mean_n dispel_v chap._n v._o of_o the_o amphiseij_fw-la hereroscij_fw-la and_o periscij_fw-la the_o inhabitant_n of_o these_o zone_n in_o respect_n of_o the_o diversity_n of_o their_o noonshadowe_v be_v divide_v into_o three_o kind_n amphisâ—…ij_fw-la heteroscij_fw-la and_o periscij_fw-la those_o that_o inhabit_v betwixt_o the_o two_o tropiquâ—…s_n be_v call_v amphiscij_fw-la because_o that_o their_o noon_n shadow_n be_v diverse_o cast_v sometime_o towards_o the_o south_n as_o when_o the_o sun_n be_v more_o northward_o than_o their_o vertical_a point_n and_o sometime_o towards_o the_o north_n as_o when_o the_o sun_n decline_v southwaâ—…_n from_o their_o zenith_n those_o that_o live_v betwixt_o the_o tropique_n and_o aâ—…ct_n que_fw-fr circle_n be_v call_v heteroscij_fw-la because_o the_o shadow_n at_o noon_n be_v cast_v only_o one_o way_n and_o that_o â—…ither_o north_n or_o south_n for_o the_o sun_n never_o come_v far_a north_n than_o our_o summer_n tropic_n nor_o more_o southward_o than_o the_o winter_n tropic_n so_o that_o those_o that_o inhabit_v northward_o of_o the_o summer_n tropic_n have_v their_o shadow_n cast_v always_o towards_o the_o north_n as_o in_o like_a manner_n those_o that_o dwell_v more_o southward_o than_o the_o winter_n tropic_n have_v their_o noon-shadow_n cast_v always_o coward_n the_o south_n those_o that_o inhabit_v betwixt_o the_o arctique_a or_o antarctique_a circle_n and_o the_o pole_n be_v call_v periscij_fw-la because_o that_o the_o gnomon_n do_v cast_v their_o shadow_n circular_o and_o the_o reason_n hereos_fw-la it_o for_o that_o the_o sun_n be_v carry_v round_o about_o above_o their_o horizon_n in_o his_o whole_a diurnal_a revolution_n pont_n the_o heterosciall_a zone_n be_v therefore_o two_o fold_v either_o northern_a or_o southern_a the_o northern_a be_v comprehend_v betwixt_o the_o tropic_n of_o cancer_n and_o the_o artik_a circle_n and_o â—…s_v call_v 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d septentrionalis_n because_o that_o in_o it_o the_o sun_n beam_n at_o noon_n be_v always_o cast_v to_o that_o part_n only_o that_o byoth_v towards_o the_o â—…ole_a arctic_n the_o southern_a hetorosciall_a zone_n contain_v all_o that_o space_n of_o ground_n that_o lie_v betwixt_o the_o tropic_n of_o capricorn_n and_o uâ—…e_v antarctique_a circle_n and_o it_o be_v callâ—…d_v 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d meridonalis_fw-la because_o the_o noon_n shadow_n be_v projeâ—…ed_v towards_o the_o south_n pole_n only_o the_o property_n of_o these_o several_a zone_n be_v these_o that_o follow_v first_o they_o that_o inhabit_v the_o midst_n of_o the_o torrid_a zone_n be_v in_o a_o right_a sphere_n for_o with_o they_o both_o the_o pole_n of_o the_o world_n lie_v in_o their_o horizon_n and_o their_o zenith_n or_o vertical_a point_n fall_v in_o the_o equinoctial_a circle_n so_o that_o their_o peculiar_a accident_n be_v these_o first_o all_z the_o sâ—…arres_n do_v rise_v and_o set_v in_o a_o equal_a space_n of_o time_n except_o the_o arctique_a and_o antarctique_a pole_n as_o we_o have_v demonstrate_v out_o of_o lerius_fw-la in_o our_o note_n upon_o the_o three_o chapter_n second_o they_o have_v a_o perpetual_a aequinoxe_n three_o they_o have_v the_o sun_n vertical_a unto_o they_o twice_o in_o a_o year_n namely_o when_o he_o enter_v into_o ♈_o and_o ♎_o four_o in_o the_o sun_n periodicall_a motion_n through_o the_o zodiaque_fw-la look_v how_o much_o he_o go_v southward_o from_o their_o zenith_n in_o his_o return_n he_o decline_v as_o far_o northward_o srom_o the_o same_o fiâ—…thly_o they_o have_v
star_n and_o fix_v not_o as_o if_o these_o be_v indeed_o fix_v in_o one_o certain_a place_n and_o altogether_o without_o motion_n and_o the_o other_o only_o movable_a and_o erratical_a but_o these_o appellation_n be_v only_o give_v then_o comparative_o in_o which_o sense_n also_o they_o be_v to_o be_v understand_v for_o see_v that_o the_o fix_a star_n be_v observe_v always_o to_o keep_v the_o same_o place_n in_o the_o eight_o sphere_n and_o the_o same_o distance_n srom_o each_o other_o notwithstanding_o that_o they_o be_v always_o in_o continual_a motion_n cause_v by_o the_o virtue_n of_o the_o first_o movable_a which_o carry_v they_o about_o in_o the_o space_n of_o twenty_o four_o hour_n but_o the_o planet_n beside_o this_o motion_n have_v a_o proper_a motion_n of_o their_o own_o so_o that_o they_o keep_v neither_o their_o the_o same_o distance_n from_o the_o fix_a star_n nor_o yet_o the_o same_o aspect_n to_o each_o other_o for_o these_o reason_n be_v the_o one_o call_v fix_v and_o the_o other_o planet_n for_o otherwise_o if_o the_o planet_n be_v consider_v several_o each_o one_o by_o himself_o there_o be_v nothing_o more_o certain_a than_o their_o periodicall_a motion_n so_o that_o tully_n allude_v hereto_o will_v have_v the_o planet_n to_o be_v call_v errantes_fw-la by_o antiphrasis_n quam_fw-la minimè_fw-la errantes_fw-la the_o planet_n exceed_v those_o two_o great_a light_n the_o sun_n and_o moon_n be_v five_o in_o number_n aâ—…_n which_o beside_o the_o diurnal_a motion_n by_o which_o they_o be_v carry_v about_o from_o east_n to_o west_n by_o the_o rapture_n of_o the_o first_o movable_a have_v also_o a_o free_a proper_a motion_n of_o their_o own_o which_o finish_v from_o west_n to_o east_n according_a to_o the_o succession_n of_o the_o sign_n upon_o the_o pole_n of_o the_o zodiaque_fw-la each_o of_o they_o in_o a_o several_a manner_n and_o space_n of_o time_n their_o order_n in_o the_o heaven_n and_o period_n of_o their_o motion_n be_v such_o as_o follow_v saturn_n call_v in_o greek_a 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d or_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d and_o by_o julius_n higinus_n stella_fw-la solis_fw-la the_o star_n of_o the_o sun_n be_v the_o high_a of_o all_o the_o planet_n and_o 〈◊〉_d about_o the_o great_a 〈◊〉_d but_o do_v not_o therefore_o appear_v to_o be_v the_o least_o of_o all_o the_o planet_n as_o pliny_n hence_o conjecture_v he_o finish_v his_o periodical_a course_n in_o twenty_o nine_o year_n five_o month_n fifteen_o day_n according_a to_o alfraganus_n jupiter_n in_o greek_a zeus_n and_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d move_v through_o the_o zodiaque_fw-la in_o the_o space_n of_o eleven_o year_n ten_o month_n and_o almost_o 16._o day_n mars_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d and_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d which_o be_v also_o cal-called_n by_o some_o hercules_n his_o star_n finish_v his_o course_n in_o two_o year_n sol_fw-it the_o sun_n in_o greek_a 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d perform_v his_o course_n in_o a_o year_n that_o be_v to_o say_v three_o hundred_o sixty_o five_o day_n and_o almost_o six_o hour_n venus_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d call_v by_o some_o june_n star_n by_o they_o isis_n and_o by_o other_o the_o mother_n of_o the_o god_n when_o it_o go_v before_o the_o sun_n it_o be_v call_v 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d the_o day_n star_n appear_v like_o another_o 〈◊〉_d sun_n and_o as_o it_o be_v matuâ—…g_v the_o day_n but_o when_o it_o follow_v the_o sun_n in_o the_o evening_n pâ—…otracting_v the_o light_n after_o the_o sun_n be_v â—…er_n and_o supply_v the_o place_n of_o the_o moon_n it_o be_v then_o call_v 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d the_o evening_n star_n the_o name_n of_o which_o star_n pythagoras_n samius_n 〈◊〉_d 〈◊〉_d first_o to_o have_v observe_v about_o the_o thiâ—…_n ie_fw-fr 2d._o olympiad_n as_o pliny_n relate_v lib._n 2._o cap._n 8._o it_o pâ—…meth_v its_o course_n in_o a_o year_n space_n or_o thereabouts_o and_o be_v never_o distanâ—…_n from_o the_o sun_n above_o forty_o six_o degree_n according_a to_o timaeus_n his_o computation_n notwithstance_v our_o late_a astronomer_n herein_o much_o more_o 〈◊〉_d than_o hâ—…_n allow_v it_o two_o whole_a sign_n or_o 60_o degree_n which_o be_v the_o utmost_a limit_n of_o its_o deviation_n from_o the_o sun_n mercury_n in_o greek_a 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d and_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d call_v by_o some_o apollo_n star_n 〈◊〉_d his_o course_n through_o the_o zodiaque_fw-la in_o a_o year_n also_o and_o according_a to_o the_o opinion_n of_o timeus_n and_o sosigenes_n 〈◊〉_d ever_o distant_a from_o the_o sun_n above_o 25._o gr_n or_o 〈◊〉_d our_o late_a writer_n will_v have_v it_o not_o above_o a_o whoâ—…e_n 〈◊〉_d or_o 30._o degree_n luna_fw-la 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d the_o moon_n be_v the_o low_a of_o all_o the_o planet_n and_o finish_v her_o course_n in_o twenty_o seven_o day_n and_o almost_o eight_o hour_n the_o various_a shape_n and_o appearance_n of_o which_o planet_n seem_v sometime_o to_o be_v â—…ned_v sometime_o equal_o divide_v into_o two_o half_n sometime_o finish_v like_o a_o imperfect_a circle_n and_o sometime_o in_o a_o respect_n circular_a 〈◊〉_d together_o with_o the_o other_o diversity_n of_o this_o star_n be_v first_o of_o all_o observe_v by_o endymion_n as_o it_o be_v relate_v by_o pliny_n whence_o spring_v that_o poëticall_a fiction_n of_o his_o be_v in_o love_n with_o the_o mâ—…on_n all_o theâ—…e_v planet_n be_v carry_v in_o orb_n which_o be_v eccentrical_a to_o the_o earth_n that_o be_v which_o have_v not_o the_o same_o centre_n with_o the_o earth_n the_o semidiameter_n of_o which_o orb_n compare_v to_o the_o semidiameter_n of_o the_o earth_n have_v this_o proportion_n as_o be_v here_o set_v down_o in_o this_o table_n of_o what_o part_n the_o â—…emidiameter_n of_o the_o earth_n i_o 1._o of_o tâ—…e_v same_o the_o 〈◊〉_d ter_z of_o the_o orb_n of_o luna_n 1_o 48._o 56_o m._n mercury_n 116._o 3_o m._n venus_n 641._o 45._o m_o sol_fw-la 1165._o 23._o m._n mars_n 5022._o 4._o m_o jupiter_n 11611._o 31._o m._n saturn_n 17225._o 16._o m_o the_o eccentricity_n of_o the_o orb_n compare_v to_o the_o orb_n themselves_o have_v this_o proportion_n of_o whatpart_n the_o semidiameter_n of_o the_o deferent_a be_v 60._o of_o the_o same_o the_o eccentricity_n of_o luna_fw-la 18_o 12._o 28._o m._n 30_o sec_fw-la maurolycus_n out_o of_o alphons_n mercury_n 2._o 0._o m._n venus_n 1._o 8._o m._n sol_fw-la 2._o 16._o m_o 6._o sec._n mars_n 6._o 0_o m._n jupiter_n 2._o 45_o m._n saturn_n 3._o 25_o m._n the_o eccentricity_n of_o some_o of_o the_o planet_n especial_o of_o the_o sun_n be_v find_v to_o have_v decrease_v and_o grow_v less_o since_o ptolomyesâ—…ime_n â—…ime_z for_o ptolemy_n set_v down_o the_o eccentricity_n of_o the_o moon_n to_o be_v 12._o gr_n 3â—…_n m._n but_o by_o alphonsus_n it_o be_v find_v to_o be_v but_o 13_o gr_n 28._o m._n and_o a_o half_a ptolemy_n assign_v eccentricity_n to_o venus_n 1_o gr_n 14._o m_o alphonsus_n 1._o gr_n 8._o m._n ptolemy_n find_v by_o his_o own_o observation_n and_o also_o by_o those_o that_o hipparchus_n have_v make_v that_o the_o eccentricity_n of_o the_o sun_n be_v 2_o gr_n 30._o m._n alphonsus_n observe_v it_o in_o his_o time_n to_o be_v but_o 2_o gr_n 16._o m._n and_o the_o 10_o part_n of_o a_o minute_n in_o the_o year_n of_o ouâ—…_n lord_n 1312_o it_o be_v find_v to_o be_v 2._o gr_n 2._o m._n 18._o sec._n copernicus_n find_v it_o to_o be_v less_o yet_o then_o that_o and_o to_o be_v but_o 1_o gr_n 56_o m_o 11._o sec._n so_o that_o without_o just_a cause_n do_v the_o illustrious_a julius_n scaliger_n think_v copernicus_n his_o write_n for_o this_o reason_n to_o deserve_v the_o sponge_n and_o the_o author_n himself_o the_o bastinado_n heâ—…ein_o deal_v more_o hardly_o with_o copernicus_n than_o he_o deserve_v pont_n beside_o the_o eccentricity_n of_o the_o planet_n it_o be_v worth_a our_o pain_n also_o to_o observe_v their_o magnitude_n and_o this_o consist_v especial_o in_o the_o knowledge_n of_o their_o diameter_n and_o what_o proportion_n they_o bear_v to_o each_o other_o for_o the_o diameter_n of_o a_o planet_n compare_v to_o the_o diameter_n of_o the_o earth_n be_v after_o this_o manner_z following_z the_o diameter_n of_o saturn_n compare_v â—…o_o the_o diameter_n of_o the_o earth_n be_v as_o 9_o 10_o 2_o jupiter_n 32_o 7_o mars_n 7_o 6_o sol_fw-la 11_o 2_o venus_n 3_o 10_o mercury_n 1_o 28_o luna_fw-la 5_o 17_o the_o diameter_n of_o the_o sun_n compare_v to_o the_o diameter_n of_o the_o moon_n bear_v the_o same_o proportion_n that_o be_v betwixt_o 187._o and_o 10._o and_o now_o that_o which_o be_v say_v may_v be_v demonstrate_v by_o a_o example_n let_v we_o suppose_v the_o diameter_n of_o the_o sun_n in_o proportion_n to_o the_o diameter_n of_o the_o earth_n to_o be_v
year_n 1598._o upon_o the_o eleven_o day_n of_o february_n at_o four_o of_o the_o clock_n and_o sixteen_o minute_n in_o the_o morning_n and_o that_o at_o regiomont_n a_o city_n in_o borussia_n who_o longitude_n or_o distance_n from_o the_o canary_n island_n be_v 41._o gr_n 16._o m._n for_o this_o longitude_n where_o these_o table_n calculate_v now_o i_o set_v myself_o to_o observe_v this_o same_o eclipse_n at_o marpurg_n and_o find_v it_o to_o happen_v at_o three_o of_o the_o clock_n and_o twelve_o minute_n on_o the_o same_o day_n of_o february_n now_o because_o the_o number_n of_o hour_n here_o be_v less_o it_o appear_v that_o marpurg_n be_v more_o westward_n than_o regiomont_n therefore_o i_o take_v away_o a_o less_o number_n from_o the_o great_a that_o be_v 3._o h._n 12._o m._n from_o 4._o h._n 16._o m._n and_o the_o remainder_n be_v 1_o h._n 4._o minute_n which_o show_v the_o difference_n of_o longitude_n in_o hour_n which_o make_v up_o sixteen_o degree_n therefore_o i_o again_o subtract_v these_o degree_n of_o difference_n from_o the_o longitude_n of_o regiomont_n as_o be_v more_o eastward_o than_o marpurge_n and_o so_o i_o find_v the_o latitude_n of_o marpurge_n from_o the_o canary_n island_n to_o be_v 25._o gr_n 16._o minute_n chap_n ii_o how_o to_o find_v the_o latitude_n of_o any_o place_n the_o latitude_n of_o a_o place_n be_v the_o distance_n of_o the_o zenith_n or_o the_o vertical_a point_n thereof_o from_o the_o aequator_fw-la now_o if_o you_o desire_v to_o find_v out_o the_o latitude_n of_o any_o place_n express_v in_o the_o globe_n you_o must_v apply_v the_o same_o to_o the_o meridian_n and_o reckon_v the_o number_n of_o the_o degree_n that_o it_o be_v distant_a from_o the_o aequator_fw-la for_o so_o much_o be_v the_o latitude_n of_o that_o place_n and_o this_o also_o you_o may_v observe_v that_o the_o latitude_n of_o every_o place_n be_v always_o equal_a to_o the_o elevation_n of_o the_o same_o place_n for_o look_v how_o many_o degree_n the_o vertical_a point_n of_o any_o place_n be_v distant_a from_o the_o aequator_fw-la just_o so_o many_o be_v the_o pole_n elevate_v above_o the_o horizon_n as_o you_o may_v prove_v by_o the_o globe_n if_o you_o so_o order_v it_o as_o that_o the_o zenith_n of_o the_o place_n be_v 90._o degree_n distant_a every_o way_n from_o the_o horizon_n pont_n see_v that_o the_o latitude_n of_o every_o place_n be_v always_o equal_a to_o the_o elevation_n of_o the_o pole_n it_o will_v not_o be_v amiss_o to_o show_v how_o the_o elevation_n of_o the_o pole_n or_o the_o latitude_n of_o any_o region_n may_v be_v find_v out_o by_o the_o observe_n of_o the_o same_o fix_a star_n in_o the_o heaven_n which_o be_v so_o near_o the_o pole_n aâ—…_n that_o it_o never_o set_v in_o that_o region_n which_o to_o do_v you_o must_v work_v thus_o you_o must_v observe_v both_o the_o least_o and_o also_o the_o great_a altitude_n of_o the_o sad_a star_n both_o which_o must_v necessary_o happen_v in_o the_o meridian_n the_o least_o whereof_o will_v be_v beneath_o the_o pole_n and_o the_o great_a above_o it_o which_o do_v you_o must_v add_v the_o least_o altitude_n of_o it_o to_o the_o great_a and_o so_o the_o half_a of_o the_o degree_n thus_o number_v together_o will_v be_v the_o latitude_n of_o the_o pole_n and_o latitude_n of_o that_o plaee_n a_o example_n whereof_o may_v be_v this_o the_o first_o star_n of_o the_o three_o in_o the_o tail_n of_o the_o great_a bear_n be_v in_o his_o least_o altitude_n observe_v at_o london_n to_o be_v about_o 11._o gr_n and_o the_o great_a altitude_n of_o the_o same_o when_o it_o be_v above_o the_o pole_n be_v find_v to_o be_v near_o upon_o 92._o degree_n both_o which_o number_n be_v add_v together_o do_v make_v up_o 103._o half_a of_o which_o sum_n namely_o 51â…“_n be_v the_o true_a elevation_n and_o latitude_n of_o london_n chap._n iii_o how_o to_o find_v the_o distance_n of_o two_o place_n and_o angle_v of_o position_n or_o situation_n if_o you_o set_v your_o globe_n in_o such_o sort_n as_o that_o the_o zenith_n of_o one_o of_o the_o place_n be_v 90._o gr_n distant_a every_o way_n from_o the_o horizon_n and_o then_o fasten_v the_o quadrant_n of_o altitude_n to_o the_o vertical_a point_n and_o so_o move_v it_o up_o and_o down_o until_o it_o pass_v through_o the_o vertex_fw-la of_o the_o other_o place_n the_o number_n of_o degree_n intercept_v in_o the_o quadrant_n betwixt_o the_o two_o place_n be_v resolve_v into_o furlong_n mile_n or_o league_n as_o you_o please_v will_v show_v the_o true_a distance_n of_o the_o place_n assign_v and_o the_o other_o end_n of_o the_o quadrant_n that_o touch_v upon_o the_o horizon_n will_v show_v on_o what_o wind_n or_o quarter_n of_o the_o world_n the_o one_o place_n be_v in_o respect_n of_o the_o other_o and_o what_o angle_n of_o position_n as_o they_o call_v it_o it_o have_v for_o the_o angle_n of_o position_n be_v that_o which_o be_v comprehend_v betwixt_o the_o meridian_n of_o any_o place_n and_o a_o great_a circle_n pass_v through_o the_o zenith_n of_o any_o two_o place_n assign_v and_o the_o quantity_n of_o it_o be_v to_o be_v number_v in_o the_o horizon_n as_o for_o example_n the_o longitude_n of_o london_n be_v twenty_o six_o degree_n and_o it_o have_v in_o northern_a latitude_n 51._o degree_n and_o a_o half_a now_o if_o it_o be_v demand_v what_o distance_n and_o angle_n of_o position_n it_o bear_v to_o saint_n michael_n island_n which_o be_v one_o of_o the_o azore_n we_o must_v proceed_v thus_o to_o find_v it_o first_o let_v the_o northern_a pole_n be_v elevate_v 51½_n degree_n which_o be_v the_o latitude_n of_o london_n then_o fasten_v the_o quadrant_n of_o altitude_n to_o the_o zenith_n of_o it_o that_o be_v to_o say_v fifty_o one_o degree_n and_o a_o half_a northward_o from_o the_o aequator_fw-la we_o must_v turn_v it_o about_o till_o it_o pass_v through_o saint_n michael_n island_n and_o we_o shall_v find_v the_o distance_n intercept_v betwixt_o these_o two_o place_n to_o be_v 11._o gr_n 40._o m._n or_o thereabouts_o which_o be_v 280_o of_o our_o league_n and_o if_o we_o observe_v in_o what_o part_n of_o the_o horizon_n the_o end_n of_o the_o quadrant_n 〈◊〉_d we_o shall_v find_v the_o angle_n of_o position_n â—…o_o shall_v near_o upon_o 50._o gr_n betwixt_o south-west_n and_o by-west_n and_o this_o be_v the_o situation_n of_o this_o 〈◊〉_d in_o respect_n of_o london_n pont_n the_o 〈◊〉_d of_o place_n â—…ring_v only_o in_o latitude_n may_v be_v find_v after_o this_o manner_n first_o you_o must_v subtract_v the_o lesser_a latitude_n from_o the_o great_a resolve_v a_o degree_n in_o minute_n if_o the_o substraction_n can_v be_v do_v otherwise_o convenient_o then_o multiply_v the_o degree_n by_o 15._o and_o divide_v the_o minute_n by_o 4._o and_o the_o sum_n produce_v will_v be_v the_o distance_n of_o those_o two_o place_n in_o common_a german_a mile_n one_o whereof_o contain_v four_o of_o our_o english_a mile_n as_o for_o example_n basile_n in_o germany_n and_o geneva_n have_v both_o the_o same_o longitude_n but_o differ_v in_o latitude_n which_o at_o basile_n be_v 47._o gr_n 30._o m._n and_o at_o geneva_n 45._o gr_n 45._o m._n therefore_o substract_v the_o lesser_a from_o the_o great_a the_o remainder_n will_v be_v 1._o gr_n 45._o m._n which_o be_v reduce_v into_o german_a mile_n will_v amount_v to_o 26._o and_o a_o quarter_n or_o a_o mile_n which_o be_v the_o distance_n of_o these_o two_o place_n assign_v now_o if_o the_o place_n propose_v be_v in_o diverse_a hemisphere_n than_o the_o degree_n and_o minute_n of_o latitude_n must_v first_o be_v add_v together_o and_o so_o the_o whole_a resolve_v into_o mile_n as_o former_o have_v be_v say_v as_o for_o example_n the_o cape_n of_o good_a hope_n in_o africa_n and_o constantinople_n be_v almost_o situate_a under_o the_o same_o meridian_n but_o in_o diverse_a hemisphaere_n now_o the_o elevation_n of_o the_o pole_n arctic_n at_o constantinople_n be_v 43._o gr_n or_o thereabouts_o and_o at_o the_o cape_n of_o good_a hope_n the_o antarctick_a pole_n be_v elovate_v above_o 35._o gr_n the_o whole_a sum_n therefore_o be_v 73._o degree_n that_o be_v to_o say_v 1170._o german_n mile_n the_o distance_n of_o place_n differ_v only_o in_o longitude_n be_v find_v thus_o first_o subtract_v the_o less_o number_n from_o the_o great_a then_o look_v in_o the_o table_n here_o under_o write_v how_o many_o mile_n answer_v to_o a_o degree_n 〈◊〉_d every_o parallel_n seek_v for_o the_o degree_n of_o latitude_n in_o the_o first_o column_n descend_v and_o the_o number_n of_o mile_n over_o against_o it_o then_o last_o let_v the_o difference_n of_o longitude_n be_v multiply_v into_o mile_n and_o minute_n and_o you_o have_v your_o desire_n as_o for_o example_n naples_n and_o ilium_n or_o troy_n be_v in_o
lesser_a arch_n which_o fall_v short_a of_o thirty_o degree_n in_o rise_v or_o set_v in_o a_o right_a sphere_n four_o sign_n only_o ascend_v right_o which_o be_v gemini_fw-la cancer_n sagittarius_fw-la and_o capricornus_fw-la all_o the_o rest_n ascend_v oblique_o in_o a_o oblique_a sphere_n six_o sign_n rise_v right_o and_o the_o other_o six_o oblique_o the_o right_a be_v these_o cancer_n leo_n virgo_fw-la libra_n scorpius_n sagittarius_fw-la and_o all_o the_o rest_n oblique_o oblique_a ascension_n be_v when_o a_o less_o arch_a or_o portion_n of_o the_o aequator_fw-la rise_v then_o of_o the_o zodiaque_fw-la or_o else_o that_o star_n may_v be_v say_v to_o rise_v oblique_o with_o who_o a_o less_o portion_n of_o the_o aequator_fw-la ascend_v above_o the_o horizon_n and_o so_o the_o oblique_a descension_n or_o set_v of_o a_o star_n be_v where_o a_o less_o portion_n of_o the_o aequator_fw-la descend_v with_o it_o as_o for_o example_n at_o rome_n with_o the_o arch_n of_o libra_n which_o contain_v 30._o gr_n in_o the_o zodiaque_fw-la there_o rise_v a_o arch_n of_o the_o equinoctial_a of_o 37_o gr_n so_o that_o this_o sign_n be_v say_v there_o to_o rise_v right_o because_o that_o a_o great_a arch_n of_o the_o aequator_fw-la ascend_v with_o it_o then_o of_o the_o zodiaque_fw-la but_o then_o at_o the_o same_o place_n with_o the_o arch_n of_o aries_n there_o arise_v only_o 17._o gr_n of_o the_o aequator_fw-la whence_o it_o follow_v that_o aries_n rise_v oblique_o at_o rome_n in_o our_o position_n of_o sphere_n also_o here_o at_o london_n which_o be_v oblique_a like_a as_o that_o at_o rome_n with_o libra_n there_o arise_v a_o arch_n of_o the_o aequinoctial_a concoutain_n about_o 41._o gr_n but_o with_o the_o arch_n of_o aries_n there_o arise_v not_o above_o 13_o degree_n therefore_o in_o our_o sphere_n libra_n ascend_v or_o rise_v right_o but_o aries_n oblique_o certain_a rule_n for_o the_o astronomical_a rise_n in_o a_o right_a sphere_n the_o rule_n of_o astronomical_a 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so_o contrary_o 4._o the_o ascension_n of_o any_o sign_n be_v equal_a to_o the_o descension_n of_o the_o same_o 5._o the_o ascensionall_a arch_n of_o the_o northern_a sign_n be_v less_o in_o a_o right_a sphere_n but_o in_o the_o southern_a sign_n they_o be_v great_a 6._o the_o ascension_n of_o opposite_a sign_n in_o a_o oblique_a sphere_n take_v together_o be_v equal_a to_o the_o ascension_n of_o the_o same_o in_o a_o right_a sphere_n 7._o those_o sign_n that_o be_v equidistant_a from_o either_o of_o the_o equinoctial_a point_n have_v equal_a ascension_n because_o they_o decline_v equal_o from_o the_o aequator_fw-la chap._n viii_o how_o to_o sinde_v out_o the_o horizontall_a difference_n betwixt_o the_o meridian_n and_o the_o vertical_a circle_n of_o the_o sun_n or_o any_o otheh_a star_n which_o they_o call_v the_o azimuth_n for_o any_o time_n or_o place_n assign_v have_v first_o observe_v the_o altitude_n of_o the_o sun_n or_o star_n that_o you_o desire_v to_o know_v set_v your_o globe_n to_o the_o latitude_n of_o the_o place_n you_o be_v in_o which_o do_v turn_v it_o about_o till_o the_o place_n of_o the_o sun_n or_o star_n which_o you_o have_v observe_v be_v elevate_v so_o much_o above_o the_o horizon_n as_o the_o altitude_n of_o the_o same_o you_o before_o observe_v now_o you_o shall_v find_v that_o you_o desire_v if_o you_o take_v the_o quadrant_n of_o altitude_n and_o fasten_v it_o to_o the_o vertical_a point_n of_o the_o place_n you_o be_v in_o and_o so_o move_v it_o together_o with_o the_o place_n of_o the_o sun_n or_o star_n up_o and_o down_o until_o it_o fall_v upon_o that_o which_o you_o have_v set_v down_o in_o your_o instrument_n at_o your_o observation_n now_o in_o this_o situation_n of_o the_o quadrant_n that_o end_n of_o it_o that_o touch_v the_o horizon_n will_v show_v the_o distance_n of_o the_o vertical_a circle_n in_o which_o you_o have_v observe_v the_o sun_n or_o star_n to_o be_v from_o the_o meridian_n as_o for_o example_n in_o the_o northern_a latitude_n of_o 51._o gr_n on_o the_o 11_o of_o march_n after_o the_o old_a account_n at_o what_o time_n the_o sun_n enter_v into_o art_n suppose_v the_o altitude_n of_o the_o sun_n before_o noon_n to_o be_v observe_v to_o be_v thâ—…rtiegr_n above_o the_o horizon_n and_o it_o be_v demand_v what_o be_v the_o azamuth_n or_o distance_n of_o the_o sun_n from_o the_o meridian_n first_o therefore_o have_v 〈◊〉_d the_o globe_n to_o the_o latitude_n of_o 51._o gr_n and_o fasten_v the_o quadrant_n of_o altitude_n to_o the_o zenith_n i_o turn_v the_o globe_n about_o till_o i_o find_v the_o first_o degree_n of_o aries_n to_o be_v 30_o gr_n above_o the_o horizon_n and_o then_o the_o quadrant_n of_o altitude_n be_v also_o apply_v to_o the_o same_o degree_n of_o aries_n will_v show_v upon_o the_o horizon_n the_o azimuth_n of_o the_o sun_n or_o distance_n of_o it_o from_o the_o meridian_n to_o be_v about_o forty_o five_o degree_n chap._n ix_o how_o to_o find_v the_o hour_n of_o the_o day_n as_o also_o the_o amplitude_n of_o rise_v and_o set_v of_o the_o sun_n and_o star_n for_o any_o time_n or_o latitude_n of_o place_n the_o sun_n we_o see_v do_v rise_v and_o set_v at_o several_a season_n of_o the_o year_n in_o diverse_a part_n of_o the_o horizon_n but_o among_o the_o rest_n it_o have_v three_o more_o notable_a place_n of_o rise_v and_o set_v the_o first_o whereof_o be_v in_o the_o aequator_fw-la and_o this_o be_v call_v his_o equinoctial_a rise_n and_o set_v the_o second_o be_v in_o the_o summer_n solstice_n when_o he_o be_v in_o the_o tropic_n of_o cancer_n and_o the_o three_o be_v in_o the_o winter_n solstice_n when_o he_o be_v in_o the_o tropic_n of_o capricorn_n now_o the_o equinoctial_a rise_n of_o the_o sun_n be_v one_o and_o the_o same_o in_o every_o climate_n for_o the_o aequator_fw-la always_o cut_v the_o horizon_n in_o the_o same_o point_n which_o be_v always_o just_a 90_o gr_n distant_a on_o each_o side_n from_o the_o meridian_n but_o the_o rest_n be_v variable_a and_o change_n according_a to_o the_o diverse_a inclination_n of_o the_o sphere_n and_o therefore_o the_o hour_n be_v unequal_a also_o pont_n and_o here_o you_o be_v to_o understand_v that_o the_o amplitude_n of_o the_o sun_n rise_v and_o set_v be_v a_o arch_n of_o the_o horizon_n intercept_v betwixt_o the_o aequator_fw-la and_o the_o place_n of_o the_o rise_n and_o set_v of_o the_o sun_n and_o it_o be_v either_o northern_a or_o southern_a the_o northern_a amplitude_n be_v when_o he_o set_v and_o rise_v on_o this_o side_n of_o the_o aequator_fw-la towards_o the_o north_n pole_n and_o the_o southern_a when_o he_o set_v or_o rise_v on_o the_o contrary_a side_n now_o when_o the_o sun_n be_v in_o the_o aequator_fw-la he_o have_v no_o amplitude_n at_o all_o but_o when_o he_o be_v in_o the_o solsticall_a point_n he_o have_v then_o the_o great_a amplitude_n of_o all_o of_o which_o that_o in_o the_o tropic_n of_o cancer_n be_v call_v the_o aestivall_n or_o summer_n solsticiall_a amplitude_n and_o the_o other_o the_o brumal_a or_o winter_n solsticiall_a amplitude_n and_o here_o it_o be_v to_o be_v note_v that_o in_o all_o place_n the_o ortive_a amplitude_n of_o any_o star_n be_v equal_a to_o the_o occidental_a amplitude_n of_o the_o same_o and_o likewise_o that_o two_o star_n be_v equal_o distant_a from_o the_o aequator_fw-la the_o one_o northward_o and_o the_o other_o southward_o or_o both_o of_o they_o northward_o or_o southward_o have_v equal_a amplitude_n of_o rise_v and_o set_v now_o if_o you_o desire_v to_o know_v the_o hour_n or_o distance_n of_o time_n betwixt_o the_o rise_n and_o set_v of_o the_o sun_n when_o he_o be_v in_o either_o of_o the_o solstice_n or_o in_o any_o other_o intermediate_v place_n and_o that_o for_o any_o time_n or_o latitude_n of_o place_n you_o shall_v work_v