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
place_n of_o the_o sun_n apply_v the_o same_o to_o the_o meridian_n and_o reckon_v thereon_o how_o many_o degree_n the_o sun_n be_v distante_n from_o the_o aequator_fw-la for_o somany_n will_v the_o degree_n be_v to_o the_o sun_n declination_n for_o the_o day_n assign_v for_o the_o declination_n of_o the_o sun_n or_o of_o any_o other_o star_n be_v nothing_o else_o but_o the_o distance_n of_o the_o same_o from_o the_o aequator_fw-la reckon_v on_o the_o meridian_n but_o the_o sun_n declination_n may_v be_v much_o more_o exact_o find_v out_o of_o those_o table_n which_o mariner_n use_v in_o which_o the_o meridian_n altitude_n or_o declination_n of_o the_o sun_n for_o every_o day_n in_o the_o year_n and_o the_o quantity_n of_o it_o be_v express_v one_o thing_n i_o shall_v give_v you_o notice_n of_o by_o the_o way_n and_o that_o be_v that_o you_o make_v use_v of_o those_o that_o be_v late_a make_v as_o never_o as_o you_o can_v for_o all_o of_o they_o after_o some_o certain_a space_n of_o time_n will_v have_v their_o error_n and_o i_o give_v this_o advertisement_n the_o rather_o for_o that_o i_o have_v see_v some_o that_o have_v some_o of_o these_o table_n that_o be_v very_o ancient_a and_o write_v out_o with_o great_a care_n and_o diligence_n which_o notwithstanding_o will_v differ_v from_o the_o late_a table_n and_o indeed_o from_o the_o truth_n itself_o often_o time_n at_o least_o 10._o m._n and_o sometime_o more_o yet_o will_v they_o always_o use_v they_o very_o constant_o and_o with_o a_o kind_n of_o religion_n but_o these_o man_n take_v a_o great_a deal_n of_o pain_n and_o care_n to_o bring_v upon_o themselves_o no_o small_a error_n pont_n you_o also_o find_v out_o the_o sun_n great_a declination_n by_o his_o great_a and_o least_o altitude_n both_o in_o summer_n and_o winter_n by_o substract_v the_o least_o out_o of_o the_o great_a for_o than_o half_a that_o which_o remain_v will_v be_v the_o declination_n you_o seek_v for_o so_o regiomontanus_n at_o vienna_n find_v the_o meridian_n altitude_n of_o the_o sun_n at_o the_o summer_n solstice_n to_o be_v 65._o gr_n 30._o m._n and_o the_o least_o altitude_n of_o it_o on_o the_o winter_n solstice_n to_o be_v 18._o gr_n 30._o m._n when_o therefore_o he_o have_v deduct_v the_o least_o number_n 18._o gr_n 30._o m._n out_o of_o 65._o gr_n 30._o m._n be_v find_v the_o remainder_n to_o be_v 47._o gr_n 0._o m._n the_o half_a of_o which_o be_v the_o sun_n great_a declination_n namely_o 23._o gr_n 30._o m._n which_o be_v the_o number_n of_o degree_n now_o common_o receive_v notwithstanding_o it_o have_v be_v since_o observe_v by_o some_o in_o our_o time_n to_o be_v somewhat_o less_o now_o to_o know_v the_o longitude_n of_o the_o sun_n for_o any_o time_n that_o be_v to_o say_v in_o what_o degree_n of_o the_o zodiaque_fw-la he_o be_v you_o must_v do_v thus_o seek_v in_o the_o limb_n of_o the_o horizon_n for_o the_o day_n of_o the_o month_n for_o which_o you_o will_v know_v the_o longitude_n of_o the_o sun_n which_o find_v you_o shall_v see_v over_o against_o it_o among_o the_o sign_n of_o the_o zodiaque_fw-la describe_v also_o upon_o the_o horizon_n the_o degree_n of_o the_o sign_n that_o exact_o answer_v to_o it_o and_o which_o be_v the_o place_n of_o the_o sun_n for_o that_o day_n and_o month_n but_o if_o it_o be_v leap_v year_n you_o must_v remember_v after_o the_o 28_o of_o february_n to_o add_v one_o day_n more_o still_a as_o you_o go_v as_o if_o you_o shall_v look_v for_o the_o place_n of_o the_o sun_n on_o the_o 13_o march_v you_o must_v take_v that_o degree_n which_o be_v set_v for_o the_o 14_o of_o march_n which_o be_v the_o 3_o gr_n of_o v._n chap._n vi_o how_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 other_o star_n observe_v the_o meridian_n altitude_n of_o the_o sun_n with_o the_o cross_a staff_n quadrant_n or_o other_o like_a instrument_n &_o have_v also_o find_v the_o place_n of_o the_o sun_n in_o the_o ecliptic_a apply_v the_o same_o to_o the_o meridian_n and_o so_o move_v the_o meridian_n up_o and_o down_o through_o the_o notch_n it_o stand_v in_o until_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 the_o sun_n altititude_n be_v and_o the_o globe_n stand_v in_o this_o position_n the_o elevation_n of_o either_o of_o the_o pole_n will_v show_v the_o latitude_n of_o the_o place_n wherein_o you_o be_v a_o example_n whereof_o may_v be_v this_o on_o the_o 12_o of_o june_n according_a to_o the_o old_a julian_n account_n the_o sun_n be_v in_o the_o first_o degree_n of_o cancer_n and_o have_v his_o great_a declination_n 23â—…_n degree_n and_o on_o the_o same_o day_n suppose_v the_o meridian_n altitude_n of_o the_o sun_n to_o be_v 50._o degree_n we_o inquire_v therefore_o now_o what_o be_v the_o latitude_n of_o the_o place_n where_o this_o observation_n be_v make_v and_o this_o we_o find_v out_o after_o this_o manner_n we_o apply_v the_o first_o degree_n of_o cancer_n to_o the_o meridian_n which_o wâ—…_n move_v up_o and_o down_o till_o the_o same_o degree_n be_v elevate_v above_o the_o horizon_n 50_o degree_n which_o be_v the_o meridian_n altitude_n of_o the_o sun_n observe_v now_o in_o this_o position_n of_o the_o globe_n we_o find_v the_o north_n pole_n to_o be_v elevate_v 63_o gr_n and_o a_o half_a so_o that_o we_o conclude_v this_o to_o be_v the_o latitude_n of_o the_o place_n where_o our_o observation_n be_v make_v the_o like_a way_n of_o proceed_v do_v mariner_n also_o use_v for_o the_o find_v out_o of_o the_o latitude_n of_o place_n by_o the_o meridian_n altitude_n of_o the_o sun_n and_o their_o table_n of_o declination_n but_o i_o shall_v not_o here_o speak_v any_o further_a of_o this_o as_o well_o for_o that_o the_o explication_n hereof_o do_v not_o so_o proper_o concern_v our_o present_a intention_n as_o also_o because_o it_o be_v so_o well_o know_v to_o every_o body_n as_o that_o the_o handle_n of_o it_o in_o this_o place_n will_v be_v needless_a and_o superfluous_a the_o like_a effect_n may_v bewrought_a in_o observe_v the_o meridian_n altitude_n of_o any_o other_o star_n express_v in_o the_o globe_n for_o if_o you_o set_v your_o globe_n so_o as_o that_o the_o star_n you_o mean_v to_o observe_v be_v so_o much_o elevate_v above_o the_o horizon_n as_o the_o meridian_n altitude_n of_o it_o be_v observe_v to_o be_v the_o elevation_n of_o the_o pole_n above_o the_o horizon_n will_v show_v the_o latitude_n of_o the_o place_n but_o here_o i_o shall_v advise_v that_o the_o latitude_n of_o place_n be_v rather_o inquire_v after_o by_o the_o meridian_n altitude_n of_o the_o sun_n then_o of_o the_o fix_a star_n because_o the_o declination_n as_o we_o have_v already_o show_v be_v very_o much_o change_v unless_o they_o be_v restore_v to_o their_o proper_a place_n by_o late_a observation_n some_o there_o be_v that_o undertake_v to_o perform_v the_o same_o not_o only_o by_o the_o meridian_n altitude_n of_o the_o sun_n or_o star_n but_o also_o by_o observe_v it_o at_o two_o several_a time_n and_o know_v the_o space_n of_o time_n or_o horizontall_a distance_n betwixt_o the_o two_o observation_n but_o the_o practice_n hereof_o be_v prolix_a and_o doubtful_a beside_o that_o by_o reason_n of_o the_o multitude_n of_o observation_n that_o must_v be_v make_v it_o be_v also_o subject_a to_o many_o error_n and_o difficulty_n notwithstanding_o the_o easy_a way_n of_o proceed_v that_o i_o know_v in_o this_o kind_n be_v this_o that_o follow_v to_o find_v out_o the_o latitude_n of_o any_o place_n by_o know_v the_o place_n of_o the_o sun_n or_o other_o star_n and_o observe_v the_o altitude_n of_o it_o two_o several_a time_n with_o the_o space_n of_o time_n betwixt_o the_o two_o observation_n first_o have_v take_v with_o your_o compass_n the_o compliment_n of_o the_o altitude_n of_o your_o first_o observation_n now_o the_o compliment_n of_o the_o altitude_n be_v nothing_o else_o but_o the_o difference_n of_o degree_n by_o which_o the_o altitude_n be_v find_v to_o be_v less_o than_o 90_o degree_n you_o must_v set_v one_o of_o the_o feeâ—…_n of_o your_o compass_n in_o that_o degree_n of_o the_o ecliptic_a that_o the_o sun_n be_v in_o at_o that_o time_n and_o with_o the_o other_o describe_v a_o circle_n upon_o the_o superficies_n of_o the_o globe_n tend_v somewhat_o towards_o the_o west_n if_o the_o observation_n be_v take_v before_o noon_n but_o towards_o the_o east_n if_o ibe_v make_v in_o the_o afternoon_n then_o have_v make_v your_o second_o observation_n and_o observe_v the_o space_n of_o time_n betwixt_o it_o and_o the_o former_a apply_v the_o place_n of_o the_o sun_n to_o the_o meridian_n turn_v the_o globe_n towards_o the_o east_n
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 rise_n in_o a_o right_a sphere_n be_v these_o 1._o the_o whole_a quadrant_n or_o quarter_n of_o the_o zodiaque_fw-la and_o equinoctial_a rise_n and_o set_v in_o a_o equal_a space_n of_o time_n 2._o but_o the_o the_o part_n of_o the_o quadrant_n rise_v and_o set_v unequal_o 3._o those_o sign_n that_o be_v equal_o distant_a from_o any_o of_o those_o point_n have_v also_o equal_a ascension_n as_o gemini_fw-la and_o cancer_n 4._o the_o ascension_n of_o a_o sign_n be_v always_o equal_a to_o the_o descension_n of_o the_o same_o 5._o four_o sign_n only_o rise_v right_o namely_o gemini_fw-la cancer_n sagittarius_fw-la and_o capricornus_fw-la and_o all_o the_o rest_n oblique_o rule_n for_o the_o astronomical_a rise_n in_o a_o oblique_a sphere_n in_o a_o oblique_a sphere_n the_o two_o half_n that_o begin_v at_o the_o two_o equinoctial_a point_n do_v rise_v together_o 2._o the_o part_n of_o these_o half_n do_v rise_v unequal_o 3._o those_o sign_n that_o rise_v right_o descend_v oblique_o and_o 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
thus_o first_o set_v your_o globe_n to_o the_o latitude_n of_o your_o place_n then_o have_v find_v the_o place_n of_o of_o the_o sun_n for_o the_o time_n assign_v apply_v the_o same_o to_o the_o meridian_n and_o withal_o you_o must_v set_v the_o point_n of_o the_o houre-index_n at_o the_o figure_n twelve_o in_o the_o houre-circle_n and_o have_v thus_o do_v you_o must_v turn_v about_o the_o globe_n towards_o the_o east_n part_n till_o the_o place_n of_o the_o sun_n touch_v the_o horizon_n which_o do_v you_o shall_v have_v the_o amplitude_n of_o the_o sun_n rise_v also_o in_o the_o aequator_fw-la which_o you_o mustr_n eckon_v as_o we_o have_v say_v from_o the_o east_n point_n or_o place_n of_o intersection_n betwixt_o the_o aequator_fw-la and_o horizon_n and_o then_o if_o you_o but_o turn_v the_o globe_n about_o to_o the_o west_n side_n of_o the_o horizon_n you_o shall_v in_o like_a manner_n have_v the_o hour_n of_o his_o set_n and_o occidental_a amplitude_n and_o if_o at_o the_o same_o time_n and_o for_o the_o same_o latitude_n of_o place_n you_o desire_v to_o know_v the_o hour_n and_o amplitude_n of_o rise_v and_o set_v or_o the_o great_a elevation_n of_o any_o other_o star_n express_v in_o the_o globe_n you_o must_v turn_v about_o the_o globe_n the_o index_n remane_v still_o in_o the_o same_o position_n and_o situation_n of_o the_o index_n as_o before_o till_o the_o say_a star_n come_v to_o the_o horizon_n either_o on_o the_o east_n or_o west_n and_o so_o shall_v you_o plain_o have_v the_o hour_n and_o latitude_n that_o the_o star_n rise_v or_o seat_v in_o in_o like_a manner_n as_o you_o have_v in_o the_o sun_n and_o then_o if_o you_o apply_v the_o same_o to_o the_o meridian_n you_o shall_v also_o have_v the_o meridian_n altitude_n of_o the_o same_o star_n a_o example_n of_o the_o amplitude_n of_o the_o sun_n rise_v and_o set_v may_v be_v this_o when_o the_o sun_n enter_v in_o to_o taurus_n which_o in_o our_o time_n happenâ—…_n about_o the_o eleven_o of_o april_n according_a to_o the_o julian_n account_n i_o desire_v to_o know_v the_o hour_n and_o amplitude_n of_o the_o sun_n rise_v for_o the_o northernlatitude_n fifty_o one_o degree_n now_o to_o find_v out_o this_o i_o set_v my_o globe_n so_o that_o the_o north_n pole_n be_v elevate_v above_o the_o horizon_n fifty_o one_o degree_n then_o i_o apply_v the_o first_o degree_n of_o taurus_n to_o the_o meridian_n and_o the_o hour-index_n to_o the_o twelve_o hour_n in_o the_o hour-circle_n which_o do_v i_o turn_v about_o the_o globe_n towards_o the_o east_n till_o that_o the_o first_o degree_n of_o taurus_n touch_v the_o horizon_n and_o then_o i_o find_v that_o this_o point_n touch_v the_o horizon_n about_o the_o twenty_o five_o degree_n northward_o from_o the_o east_n point_n therefore_o i_o conclude_v that_o to_o be_v the_o amplitude_n of_o the_o sun_n for_o that_o day_n in_o the_o mean_a time_n the_o index_n strike_v upon_o half_a a_o hour_n after_o four_o which_o i_o take_v to_o be_v the_o â—…me_n of_o the_o sun_n rise_n chap._n x._o of_o the_o threefold_a rise_n and_o set_v of_o star_n beside_o the_o ordinary_a emersion_n and_o depression_n of_o the_o star_n in_o regard_n of_o the_o horizon_n by_o reason_n of_o the_o circumvolution_n of_o the_o heaven_n there_o be_v also_o observe_v a_o threefold_a rise_n &_o set_v of_o the_o star_n the_o first_o of_o these_o be_v call_v in_o latin_a ortus_fw-la matutinus_fw-la sive_fw-la cosmicus_fw-la the_o morning_n or_o cosmical_a rise_n the_o second_o vespertinus_fw-la sive_fw-la achronicus_fw-la the_o evening_n or_o acronical_a and_o the_o last_o heliachus_fw-la vel_fw-la solaris_fw-la heliacall_a or_o solar_a the_o cosmical_a or_o morning_n rise_v of_o a_o star_n be_v when_o as_o it_o rise_v above_o the_o horizon_n together_o with_o the_o sun_n and_o the_o cosmical_a or_o morning_n set_v of_o a_o star_n be_v when_o it_o set_v at_o the_o opposite_a part_n of_o heaven_n whâ—…n_o the_o sun_n rise_v the_o acronychal_a or_o evening_n rise_v of_o a_o star_n be_v when_o it_o rise_v on_o the_o opposite_a part_n when_o the_o sun_n set_v and_o the_o acronychall_n set_v of_o a_o star_n be_v when_o it_o set_v at_o the_o same_o time_n with_o the_o sun_n the_o heliacall_a rise_n of_o a_o star_n which_o you_o may_v proper_o call_v the_o emersion_n of_o it_o be_v when_o a_o star_n that_o be_v bid_v before_o by_o the_o sun_n beam_n begin_v now_o to_o have_v recover_v itself_o out_o of_o the_o same_o and_o to_o appear_v and_o so_o likewise_o the_o set_n of_o such_o a_o star_n which_o mav_v also_o fit_o be_v call_v the_o occultation_n of_o the_o same_o be_v when_o the_o sun_n by_o his_o own_o proper_a motion_n overtake_v any_o star_n so_o that_o by_o reason_n of_o the_o brightness_n of_o his_o beam_n it_o can_v no_o more_o be_v see_v pont_n concern_v the_o rise_n and_o set_v of_o the_o star_n which_o be_v consider_v in_o respect_n of_o the_o horizon_n and_o aequator_fw-la have_v be_v speak_v already_o in_o the_o seven_o chapter_n where_o we_o also_o show_v that_o that_o kind_a of_o rise_v and_o set_v of_o the_o star_n be_v call_v astronomical_a but_o in_o this_o place_n the_o rise_n of_o the_o star_n be_v consider_v in_o relation_n only_o to_o the_o horizon_n and_o sun_n aspect_n but_o not_o of_o the_o aequator_fw-la and_o therefore_o it_o be_v also_o common_o call_v the_o poëtioall_n rise_v and_o set_v of_o the_o star_n now_o as_o touch_v the_o last_o of_o these_o kind_n many_o author_n be_v of_o opinion_n that_o the_o fix_a star_n of_o the_o first_o magnitude_n do_v begin_v to_o show_v themselves_o after_o their_o emersion_n out_o of_o the_o sunbeam_n when_o as_o they_o be_v yet_o in_o the_o upper_a hemisphere_n and_o the_o sun_n be_v go_v down_o twelve_o degree_n under_o the_o horizon_n but_o these_o of_o the_o second_o magnitude_n require_v that_o the_o sun_n be_v depress_v 13_o gr_n and_o those_o of_o the_o three_o require_v fourteen_o and_o of_o the_o four_o fifteen_o of_o the_o five_o sixteen_o of_o the_o six_o seventeen_o and_o the_o cloudy_a and_o obscure_a star_n require_v eighteen_o degree_n of_o the_o sun_n depression_n but_o ptolemy_n have_v determine_v nothing_o at_o all_o in_o this_o case_n and_o withal_o very_o right_o give_v this_o admonishment_n and_o lib._n 8._o cap_n ult_n almag_n that_o be_v a_o very_a hard_a matter_n to_o set_v down_o any_o determination_n thereof_o for_o as_o he_o there_o well_o note_v by_o reason_n of_o the_o unequal_a disposition_n of_o the_o air_n this_o distance_n also_o of_o the_o sun_n for_o the_o occultation_n and_o emersion_n of_o the_o star_n must_v needs_o be_v unequal_a and_o one_o thing_n more_o we_o have_v to_o increase_v our_o suspicion_n of_o the_o incertainâ—…y_n of_o this_o receive_a opinion_n and_o that_o be_v that_o vitellio_n require_v nineteen_o degree_n of_o the_o sun_n depression_n under_o the_o horizon_n before_o the_o evening_n twilight_n be_v end_v now_o that_o the_o obscure_a and_o cloudy_a star_n shall_v appear_v ever_o before_o the_o twilight_n be_v down_o i_o shall_v very_o hardly_o be_v persuade_v to_o believe_v notwithstanding_o however_o the_o truth_n of_o the_o matter_n be_v we_o will_v follow_v the_o common_a opinion_n now_o therefore_o if_o you_o desire_v to_o know_v at_o what_o time_n of_o the_o year_n any_o star_n rise_v or_o 〈◊〉_d in_o the_o morning_n or_o the_o evening_n in_o any_o climate_n whatsoever_o you_o may_v find_v it_o out_o thus_o 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 then_o apply_v the_o star_n you_o inquire_v after_o to_o the_o eastern_a part_n of_o the_o horizon_n and_o you_o shall_v have_v that_o degree_n of_o the_o ecliptic_a with_o which_o the_o say_a star_n rise_v cosmical_o and_o set_v acronychally_n and_o on_o the_o opposite_a side_n on_o the_o west_n the_o horizon_n will_v show_v the_o degree_n of_o the_o ecliptic_a wih_o which_o the_o same_o star_n rise_v acronychally_n and_o set_v cosmical_o for_o the_o cosmical_a rise_n and_o achronicall_a set_n and_o so_o likewise_o the_o acronycall_a rise_n and_o cosmical_a set_n of_o a_o star_n be_v all_o one_o according_a to_o those_o old_a verse_n cosmicè_fw-la deseendit_fw-la signum_fw-la quòd_fw-la acronychè_fw-fr surgit_fw-la chronychè_fw-fr descendit_fw-la signum_fw-la quod_fw-la cosmici_fw-la surgit_fw-la but_o these_o thing_n be_v to_o be_v explain_v more_o full_o for_o a_o star_n do_v not_o always_o rise_v and_o set_v with_o the_o same_o degree_n of_o the_o ecliptic_a for_o the_o southern_a star_n do_v anticipate_v the_o degree_n with_o which_o they_o rise_v at_o their_o set_n but_o the_o northern_a star_n come_v after_o it_o that_o be_v if_o the_o elevation_n be_v of_o the_o arctic_a â—…ole_n otherwise_o it_o be_v quite_o contrary_a if_o the_o south_n pole_n be_v elevate_v now_o
both_o after_o the_o set_n and_o before_o the_o rise_n of_o the_o sun_n of_o which_o the_o first_o be_v call_v the_o evening_n twilight_n and_o the_o other_o the_o morning_n now_o the_o beginning_n of_o the_o one_o and_o the_o end_n of_o the_o other_o be_v perceive_v at_o the_o same_o equal_a space_n of_o time_n from_o the_o rise_n and_o set_v of_o the_o sun_n notwithstanding_o the_o continuance_n of_o each_o of_o they_o be_v sometime_o great_a and_o sometime_o less_o for_o in_o summer_n the_o twilight_n be_v much_o long_o then_o in_o the_o winter_n the_o measure_n of_o they_o they_o common_o make_v to_o be_v whenas_o the_o sun_n be_v depress_v 18_o degree_n under_o the_o horizon_n but_o as_o p._n nonius_n right_o observe_v there_o can_v be_v any_o certain_a measure_n or_o term_n assign_v they_o by_o reason_n of_o the_o various_a disposition_n of_o the_o air_n and_o the_o elevation_n of_o the_o vapour_n that_o be_v exhale_v out_o of_o the_o earth_n which_o the_o same_o author_n say_v he_o find_v to_o be_v also_o diverse_a sometime_o high_o and_o sometime_o low_o vitelio_n and_o alhazenus_n before_o he_o will_v have_v it_o to_o be_v when_o the_o sun_n be_v depress_v under_o the_o horizon_n nineteen_o degree_n but_o how_o ever_o the_o truth_n be_v we_o shall_v follow_v the_o common_a rceived_a opinion_n herein_o now_o therefore_o if_o you_o desire_v to_o know_v upon_o these_o ground_n here_o lay_v down_o at_o what_o hour_n the_o twilight_n begin_v and_o end_v at_o any_o time_n or_o latitude_n of_o place_n you_o must_v do_v thus_o first_o set_v your_o globe_n to_o the_o latitude_n of_o that_o place_n and_o apply_v that_o degree_n of_o the_o ecliptic_a wherein_o the_o sun_n be_v at_o that_o time_n to_o the_o meridian_n and_o withal_o direct_v the_o point_n of_o the_o index_n to_o twelve_o in_o the_o hour-circle_n then_o mark_v the_o degree_n of_o the_o ecliptic_a that_o be_v direct_o opposite_a to_o the_o place_n of_o the_o sun_n turn_v about_o your_o globe_n till_o such_o time_n as_o the_o opposite_a degree_n of_o the_o sun_n be_v elevate_v eighteen_o gr_n above_o the_o horizon_n towards_o the_o west_n part_n of_o it_o and_o forthwith_o the_o index_n will_v show_v in_o the_o houre-circle_n the_o beginning_n of_o the_o morning_n twilight_n and_o if_o you_o turn_v about_o your_o globe_n in_o like_a manner_n to_o the_o east_n you_o shall_v also_o have_v the_o hour_n when_o the_o evening_n twilight_n end_v pont_n our_o northern_a region_n have_v their_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d or_o twilight_n of_o above_o a_o hour_n long_o but_o those_o country_n where_o the_o tropicke_n be_v very_o far_o beneath_o their_o horizon_n have_v in_o a_o manner_n no_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d no_o twilight_n or_o break_v of_o day_n and_o therefore_o those_o that_o inhabit_v near_o the_o aequator_fw-la have_v not_o the_o beginning_n nor_o late_a part_n of_o the_o night_n enlighten_v at_o all_o neither_o be_v there_o any_o appearance_n of_o light_n before_o the_o sun_n be_v rise_v whereas_o on_o the_o contrary_a side_n those_o that_o have_v the_o tropic_n very_o near_o their_o horizon_n must_v necessary_o have_v twilight_n almost_o all_o the_o night_n long_o in_o summer_n and_o therefore_o when_o the_o roman_n come_v into_o britain_n and_o perceive_v that_o at_o the_o summer_n sostice_n their_o night_n be_v light_a almost_o all_o the_o night_n long_o they_o do_v not_o ac_fw-la ount_n this_o twilight_n to_o be_v night_n but_o say_v minimâ_fw-la nocte_fw-la contentos_fw-la britannos_fw-la that_o the_o britain_n be_v content_v with_o a_o very_a short_a night_n now_o this_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d as_o it_o be_v define_v by_o joseph_n scaliger_n upon_o manilius_n be_v nothing_o else_o but_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d a_o kind_n of_o antiperistasis_n or_o circumstipation_n as_o we_o may_v call_v it_o of_o the_o light_n which_o can_v be_v none_o at_o all_o in_o those_o place_n where_o the_o tropic_n and_o horizon_n be_v far_o distant_a for_o this_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d as_o scaliger_n in_o that_o place_n accurate_o observe_v be_v only_o find_v under_o those_o sign_n which_o be_v near_o the_o solsticiall_a point_n as_o gemini_fw-la and_o cancer_n and_o that_o in_o those_o country_n too_o where_o the_o night_n be_v somewhat_o large_a than_o it_o be_v under_o the_o pole_n of_o the_o ecliptic_a as_o for_o example_n to_o use_v scaliger_n own_o word_n those_o that_o have_v not_o the_o tropic_n for_o their_o arctic_a circle_n nor_o where_o it_o touch_v the_o north_n point_n of_o the_o horizou_fw-mi with_o they_o the_o night_n be_v so_o long_o dark_a as_o while_o the_o tropic_n come_v to_o strike_v upon_o the_o north_n point_n of_o the_o horizon_n as_o we_o know_v it_o happen_v a_o scotland_n where_o our_o country_n man_n that_o be_v soldier_n there_o can_v see_v to_o play_v at_o dice_n all_o night_n long_o without_o any_o candle_n about_o the_o time_n that_o the_o day_n be_v at_o the_o long_a now_o the_o tropic_a be_v distant_a from_o the_o horzizon_n at_o edenburge_n 9_o gr_n 17._o m._n or_o thereabouts_o and_o therefore_o so_o much_o be_v the_o distance_n betwixt_o the_o sun_n and_o their_o horizon_n at_o midnight_n in_o the_o summer_n solstice_n so_o that_o necessary_o the_o rest_n of_o the_o night_n must_v be_v twilight_n and_o of_o 6._o hour_n 23._o minute_n which_o be_v the_o length_n of_o their_o night_n not_o above_o 37_o m._n which_o be_v not_o much_o above_o half_a a_o hour_n be_v quite_o dark_a and_o all_o the_o rest_n of_o the_o night_n be_v light_a whence_o you_o may_v perceive_v the_o reason_n of_o the_o long_a continuance_n of_o the_o day_n in_o those_o region_n that_o have_v the_o tropic_n near_o border_v on_o their_o horizon_n and_o therefore_o the_o roman_n be_v not_o well_o acquaint_v with_o this_o antiperistasis_n of_o the_o light_n think_v that_o in_o those_o part_n they_o have_v have_v scarce_o any_o night_n at_o all_o and_o hence_o it_o necessary_o follow_v that_o by_o how_o much_o the_o tropic_n be_v more_o remote_a from_o the_o horizon_n by_o so_o much_o be_v the_o night_n less_o enlighten_v and_o those_o that_o inhabit_v near_o the_o equinoctial_a be_v so_o far_o from_o have_v their_o day_n extend_v far_o either_o before_o the_o sun_n rise_v or_o after_o it_o set_v as_o that_o with_o they_o there_o be_v no_o appearance_n of_o light_n at_o all_o before_o the_o sun_n be_v up_o and_o there_o be_v scarce_o any_o twilight_n or_o dawn_n of_o the_o day_n at_o all_o in_o those_o region_n that_o lie_v within_o ten_o degree_n of_o the_o equinoctial_a for_o which_o there_o can_v bâ—…_n no_o other_o reason_n give_v but_o only_o the_o distance_n betwixt_o the_o tropic_n and_o their_o horizon_n and_o if_o they_o have_v no_o twilight_n in_o the_o summer_n how_o much_o less_o will_v there_o be_v any_o when_o the_o sun_n be_v in_o the_o other_o tropic_n so_o that_o we_o have_v no_o reason_n to_o give_v any_o credit_n to_o alosiyus_fw-la cadamustus_fw-la who_o when_o he_o have_v occasion_n to_o write_v of_o this_o argument_n give_v this_o to_o be_v the_o reason_n of_o it_o because_o there_o be_v no_o mountain_n there_o to_o hinder_v but_o that_o the_o sun_n may_v be_v see_v at_o the_o instant_n of_o his_o rise_n but_o this_o be_v a_o ridiculous_a reason_n and_o not_o worthy_a a_o consutation_n thus_o scaliger_n chap._n xii_o how_o to_o find_v the_o length_n of_o the_o artificial_a day_n or_o night_n or_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 for_o any_o latitude_n of_o place_n and_o time_n assign_v as_o also_o to_o find_v the_o same_o of_o any_o other_o star_n the_o day_n we_o have_v already_o show_v to_o to_o be_v twofold_a either_o natural_a or_o artificial_a the_o natural_a day_n be_v define_v by_o the_o whole_a revolution_n of_o the_o aequator_fw-la with_o that_o portion_n also_o of_o the_o same_o that_o answer_v to_o such_o a_o arch_n of_o the_o ecliptic_a which_o the_o sun_n pass_v over_o in_o one_o day_n now_o the_o whole_a revolution_n of_o the_o aequator_fw-la beside_o that_o portion_n which_o answer_v to_o the_o sun_n proper_a motion_n be_v divide_v into_o twenty_o four_o equal_a part_n which_o they_o call_v equal_a hour_n because_o they_o be_v all_o of_o equal_a length_n fifteen_o degree_n of_o the_o aequator_fw-la rise_v and_o as_o many_o set_n every_o hour_n space_n now_o the_o beginning_n of_o this_o day_n be_v diverse_a according_a to_o the_o diversity_n of_o country_n some_o beginning_n iâ—…_n at_o sunset_n as_o the_o athenian_n and_o jew_n soâ—…e_v at_o midnight_n as_o the_o egyptian_n and_o roman_n other_o at_o sunrising_n as_o the_o chaldean_n or_o at_o noon_n as_o the_o umbrian_n and_o common_o our_o astronomer_n do_v at_o this_o day_n this_o be_v
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 and_o direct_v the_o houre-index_n to_o the_o number_n of_o 12._o in_o the_o circle_n and_o then_o turn_v about_o the_o globe_n till_o that_o the_o place_n of_o the_o sun_n touch_v the_o horizon_n at_o the_o eastern_a part_n the_o index_n will_v show_v the_o hour_n in_o the_o circle_n of_o the_o rise_n of_o the_o sun_n and_o if_o you_o but_o turn_v it_o about_o again_o to_o the_o west_n you_o shall_v in_o like_a manner_n have_v the_o hour_n of_o his_o set_n and_o so_o by_o this_o mean_n find_v out_o the_o length_n of_o the_o artificial_a day_n now_o if_o you_o multiply_v the_o number_n of_o the_o hour_n by_o 15._o for_o so_o many_o degree_n as_o we_o have_v already_o often_o say_v be_v allow_v to_o one_o equal_a equinoctial_a hour_n you_o shall_v present_o have_v the_o number_n of_o degree_n of_o the_o sun_n parallel_n that_o appear_v above_o the_o horizon_n which_o if_o you_o subtract_v out_o of_o 360._o the_o remainder_n will_v be_v the_o quantity_n of_o that_o part_n of_o the_o 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
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
on_o every_o side_n â—…quidistant_n from_o the_o horzion_n be_v common_o â—…ailed_v zenith_n but_o the_o arabian_n name_v it_o seâ—…th_v but_o the_o former_a corrupt_a name_n have_v yet_o â—…revailed_v so_o that_o it_o be_v always_o use_v among_o wriâ—…ers_n general_o and_o that_o point_n which_o be_v oppoâ—…ite_a to_o it_o in_o the_o low_a hemisphere_n the_o arabiansâ—…all_a â—…all_z nathire_n but_o it_o be_v common_o write_v nadir_n these_o two_o point_n be_v call_v also_o the_o pole_n of_o the_o horizon_n furtheremore_n upon_o the_o superficies_n of_o the_o hoâ—…izon_n in_o a_o material_a globe_n there_o be_v describe_v first_o the_o twelve_o sign_n of_o the_o zodiaque_fw-la and_o â—…ach_v of_o these_o be_v again_o divide_v into_o twenty_o lesser_a portion_n so_o that_o the_o whole_a horizon_n be_v divide_v â—…nto_o 360._o part_n which_o they_o also_o call_v degree_n and_o if_o every_o degree_n be_v diuâ—…ded_v into_o sixty_o part_n â—…lso_o each_o of_o they_o be_v call_v a_o scruple_n or_o minute_n and_o so_o by_o the_o like_a subdivision_n of_o minutâ—…â—…nto_n fixty_n part_n will_v arise_v second_o and_o of_o these_o three_o and_o likewise_o four_o hâ—…_n and_o fifths_o etc._n etc._n by_o the_o like_a partition_n still_o of_o each_o into_o â—…xty_a part_n pont_n in_o the_o midst_n among_o these_o sign_n be_v there_o describe_v certain_a character_n to_o denote_v the_o particular_a planet_n to_o who_o dominion_n each_o sigâ—…_n do_v appertain_v next_o to_o this_o there_o be_v another_o section_n wherein_o be_v set_v down_o the_o several_a dayâ—…_n of_o every_o week_n after_o that_o follow_v the_o number_n of_o the_o day_n of_o every_o month_n throughout_o thâ—…_n whole_a year_n beside_o this_o number_n of_o the_o dayâ—…s_n each_o of_o they_o have_v in_o their_o several_a order_n some_o one_o of_o these_o three_o letter_n affix_v k._n n._n i._n signify_v the_o kalend_n nones_n and_o ides_n which_o term_n the_o ancient_a roman_n use_v in_o their_o account_n to_o signâ—…_n fie_o the_o day_n of_o every_o month_n for_o they_o do_v 〈◊〉_d reckon_v as_o we_o do_v now_o from_o the_o first_o day_n of_o every_o month_n to_o the_o 30._o or_o 31._o of_o the_o same_o but_o their_o account_n be_v according_a to_o the_o kalende_n noneâ—…_n and_o ides_n so_o that_o the_o first_o of_o each_o month_n wâ—…_n the_o kalend_n and_o the_o rest_n of_o the_o day_n of_o the_o same_o month_n be_v not_o reckon_v forward_o but_o after_o a_o retrograde_a manner_n as_o for_o example_n the_o last_o day_n of_o december_n with_o we_o be_v the_o 31._o they_o call_v the_o second_o of_o the_o kalend_n or_o january_n and_o the_o 30._o of_o the_o same_o month_n the_o three_o of_o the_o kalend_n of_o january_n thus_o reckon_v backward_o till_o they_o come_v to_o the_o ides_n which_o be_v the_o fourteen_o of_o december_n and_o the_o nineteen_o of_o the_o kalend_n of_o january_n the_o like_a order_n they_o observe_v in_o the_o ides_n and_o nones_n also_o now_o what_o month_n have_v more_o or_o few_o kalend_n or_o nones_n may_v be_v find_v upon_o the_o horizon_n as_o we_o have_v say_v and_o as_o may_v be_v gather_v also_o out_o of_o these_o old_a verse_n majus_n sex_n nonas_fw-la october_n julius_n &_o mars_n quatuor_fw-la at_o reliqui_fw-la tenet_n idus_fw-la quilibet_fw-la octo_fw-la ind_n dies_fw-la reliquos_fw-la dic_fw-la omnes_fw-la esse_fw-la calendas_fw-la there_o be_v also_o describe_v upon_o the_o horizon_n the_o roman_a calendar_n and_o that_o three_o several_a way_n â—…o_o wit_n the_o ancient_a way_n which_o be_v still_o in_o use_n â—…ith_v we_o here_o in_o england_n and_o the_o new_a way_n apâ—…ointed_v by_o pope_n gregory_n 13._o wherein_o the_o eâ—…uinoxes_n &_o solstice_n be_v restore_v to_o the_o same_o â—…laces_n wherein_o they_o be_v at_o the_o time_n of_o the_o ceâ—…ebration_n of_o the_o council_n of_o nice_a and_o in_o the_o â—…hird_n the_o say_v equinoctial_a and_o solsticial_a point_n â—…re_v restore_v to_o the_o place_n that_o they_o be_v in_o at_o â—…he_a time_n of_o our_o saviour_n christ_n nativity_n the_o â—…onths_n in_o the_o calendar_n be_v divide_v into_o day_n â—…nd_a week_n to_o which_o be_v annex_v as_o their_o peâ—…uliar_a character_n the_o seven_o first_o letter_n of_o the_o latin_a alphabet_n which_o manner_n of_o design_v â—…he_a day_n of_o the_o month_n be_v first_o bring_v in_o by_o dionysius_n exigum_n a_o roman_a abbot_n after_o the_o council_n of_o niee_n the_o innermost_a border_n of_o the_o horizon_n be_v divide_v into_o 32._o part_n according_a to_o the_o number_n â—…f_o the_o wind_n which_o be_v observe_v by_o our_o modeâ—…ne_n sea-fareing_a man_n in_o their_o navigation_n by_o â—…hich_v also_o they_o be_v wont_n to_o design_n forth_o the_o â—…uarters_n of_o the_o heaven_n &_o the_o coast_n of_o counâ—…ries_n for_o the_o ancient_n observe_v but_o four_o â—…inds_n only_o to_o which_o be_v after_o add_v four_o â—…ore_o but_o after_o age_n not_o content_a with_o this_o â—…umber_n increase_v it_o to_o twelve_o and_o at_o â—…ength_n they_o bring_v it_o to_o twenty_o four_o as_o 〈◊〉_d be_v note_n and_o now_o these_o latertime_n haâ—…e_v â—…ade_v they_o up_o thirty_o two_o the_o name_n whereoâ—…_n â—…oth_v in_o english_a and_o latin_a be_v set_v down_o in_o the_o â—…he_a horizon_n of_o material_a globe_n pont_n the_o true_a horizon_n be_v either_o rational_a or_o sensible_a the_o rational_a or_o intelligible_a horizoâ—…_n divide_v the_o the_o sphere_n into_o two_o equal_a part_n exact_o and_o these_o be_v call_v the_o upper_a and_o the_o low_a hemisphaere_n the_o sensible_a or_o apparent_a horizon_n be_v sâ—…_n call_v because_o it_o only_o seem_v to_o divide_v the_o heaven_n into_o two_o equal_a part_n or_o hemisphaere_n whereas_o indeed_o it_o do_v not_o divide_v it_o so_o exact_o but_o only_o seem_v so_o to_o do_v the_o rational_a horizon_n be_v also_o call_v the_o artificial_a because_o that_o it_o be_v bring_v in_o for_o the_o use_n of_o astronomy_n the_o use_n of_o the_o horizon_n be_v manifold_a first_o it_o divide_v the_o heaven_n into_o two_o hemisphaere_n second_o it_o show_v what_o star_n never_o set_v and_o so_o what_o never_o rise_v from_o under_o the_o earth_n and_o so_o likewise_o what_o star_n do_v both_o rise_v and_o set_v three_o it_o show_v the_o cause_n of_o the_o equality_n and_o in_o equality_n of_o the_o artificial_a day_n and_o night_n four_o it_o conduee_v to_o the_o find_v out_o of_o the_o latitude_n of_o any_o place_n five_o it_o be_v the_o cause_n of_o the_o rectitude_n and_o obliquity_n of_o the_o sphere_n whereof_o we_o have_v occasion_n to_o speak_v more_o large_o hereafter_o there_o be_v also_o let_v into_o this_o horizon_n two_o notch_n opposite_a one_o to_o the_o other_o a_o circle_n of_o brass_n make_v right_a angle_n with_o the_o say_a horizon_n and_o place_v so_o that_o it_o may_v be_v move_v at_o pleasure_n up_o and_o down_o by_o those_o notch_n aâ—…_n need_n shall_v require_v this_o circle_n be_v call_v the_o meridian_n because_o that_o one_o side_n of_o it_o which_o be_v merinian_n in_o like_a manner_n divide_v in_o 360._o degree_n supply_v the_o office_n of_o the_o true_a meridian_n now_o the_o meridian_n be_v one_o of_o the_o great_a circle_n pass_v through_o the_o pole_n of_o the_o world_n and_o also_o of_o the_o horizon_n to_o which_o when_o the_o sun_n in_o his_o daily_a revolution_n be_v arrive_v in_o the_o upper_a hemisphere_n it_o be_v midday_n and_o when_o it_o touch_v the_o same_o in_o the_o low_a hemisphere_n it_o be_v midnight_n at_o that_o place_n who_o meridian_n it_o be_v these_o two_o circle_n the_o horizon_n and_o meridian_n be_v various_a and_o mutable_a in_o the_o heaven_n and_o earth_n according_a as_o the_o place_n be_v change_v but_o in_o the_o material_a globe_n they_o be_v make_v fix_v and_o constant_a and_o the_o earth_n be_v make_v movable_a that_o so_o the_o meridian_n may_v be_v apply_v to_o the_o vertical_a point_n of_o any_o place_n pont_n the_o usâ—…s_n of_o the_o meridian_n be_v these_o especial_o first_o it_o determine_v the_o paint_v of_o midday_n and_o midnight_n whence_o the_o astronomer_n begin_v the_o day_n always_o from_o the_o circle_n second_o in_o the_o meridian_n be_v observe_v the_o zenith_n or_o uâ—…rticall_a point_n of_o place_n whence_o afterward_o the_o distance_n of_o star_n and_o parallel_n circle_n be_v gather_v three_o the_o longitude_n and_o latitude_n of_o place_n be_v take_v from_o hence_o four_o it_o show_v the_o great_a elevation_n of_o the_o sun_n and_o other_o star_n which_o elevation_n be_v call_v their_o meridian_n altitude_n five_o by_o the_o meridional_a eleudtion_n of_o the_o sun_n when_o he_o be_v in_o the_o equinoctial_a point_n may_v be_v find_v out_o the_o elevation_n of_o the_o pole_n and_o habitude_n or_o position_n of_o the_o sphere_n for_o the_o quarter_n of_o a_o circle_n be_v 90._o degree_n if_o then_o we_o subtract_v the_o merâ—…dionall_a altitude_n of_o
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 very_a centre_n of_o the_o houre-circle_n and_o this_o pin_n be_v call_v in_o latin_a index_n horarius_fw-la and_o be_v so_o make_v as_o that_o it_o turn_v about_o and_o point_v to_o every_o of_o the_o 24._o section_n in_o the_o houre-circle_n according_a as_o the_o globe_n itself_o be_v move_v about_o so_o that_o you_o may_v place_v the_o point_n of_o it_o to_o what_o hour_n you_o please_v pont_n the_o use_n of_o this_o houre-circle_n and_o index_n be_v to_o denote_v the_o hour_n of_o the_o rise_n and_o set_v of_o the_o sun_n and_o other_o star_n which_o must_v be_v practise_v after_o this_o manner_n first_o you_o must_v set_v the_o globe_n to_o your_o elevation_n or_o pole_n and_o then_o apply_v the_o degree_n of_o the_o sign_n in_o which_o the_o sun_n at_o the_o time_n be_v to_o the_o meridian_n and_o the_o index_n to_o the_o twelve_o hour_n which_o be_v uppermost_a and_o so_o have_v thus_o do_v you_o must_v turn_v the_o globe_n about_o till_o the_o degree_n wherein_o the_o sun_n 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
ancient_a greek_n who_o first_o of_o all_o observe_v the_o place_n and_o situation_n of_o the_o fix_a star_n and_o express_v the_o same_o by_o asterism_n and_o constellation_n the_o first_o star_n of_o aries_n be_v then_o a_o very_a small_a space_n distant_a from_o the_o very_a intersection_n for_o in_o thales_n milesius_n his_o time_n it_o be_v two_o degree_n before_o the_o intersection_n in_o the_o time_n of_o meton_n the_o athenian_a it_o be_v in_o the_o very_a intersection_n in_o timocharis_n his_o time_n it_o come_v two_o degree_n after_o the_o intersection_n and_o so_o by_o reason_n of_o its_o vicinity_n the_o ancient_n assign_v the_o first_o part_n of_o the_o zodiac_n to_o aries_n the_o second_o to_o tauruâ—…_n and_o so_o the_o rest_n in_o their_o order_n as_o it_o be_v observe_v by_o succeed_a age_n even_o to_o this_o very_a day_n pont_n thales_n milesius_n be_v the_o first_o that_o calculate_v the_o time_n of_o the_o aequinoxe_n and_o eclipse_n and_o he_o flourish_v about_o the_o year_n of_o the_o creation_n 3370._o which_o be_v about_o 634._o year_n before_o christ_n meton_n live_v about_o 431_o year_n before_o christ_n in_o the_o year_n of_o the_o creation_n 3517._o he_o be_v the_o son_n of_o 〈◊〉_d and_o be_v a_o man_n of_o excellent_a knowledge_n in_o astronomy_n he_o also_o first_o invent_v the_o moon_n circle_n of_o 19_o year_n who_o first_o new_a moon_n fall_v upon_o the_o 13_o day_n of_o the_o month_n scriophorion_n which_o be_v the_o same_o with_o our_o 16_o of_o june_n be_v on_o a_o friday_n with_fw-mi dâ—…dorum_fw-la siculum_n censorinus_n write_v of_o he_o thus_o praeterea_fw-la sunt_fw-la etc._n etc._n there_o be_v say_v he_o beside_o many_o other_o great_a year_n as_o the_o metonicall_a year_n which_o meton_n the_o athenian_a invent_v and_o consist_v of_o 19_o common_a year_n etc._n etc._n timochares_n be_v by_o nation_n a_o alexandrian_a and_o he_o live_v 300_o year_n before_o christ._n under_o this_o circle_n the_o sun_n and_o the_o rest_n of_o the_o planeâ—…s_v finish_v their_o several_a course_n and_o period_n in_o their_o several_a manner_n and_o time_n the_o sun_n keep_v his_o course_n in_o the_o mide_v of_o the_o zodiaque_fw-la and_o therewiâ—…h_n describe_v the_o ecliptic_a circle_n but_o the_o rest_n hâ—…ve_v all_o of_o they_o their_o latitude_n and_o deviation_n â—…rom_o the_o sun_n course_n or_o ecliptic_a by_o reaso_n of_o which_o their_o digression_n and_o extravagation_n the_o ancient_n assign_v the_o zodiaque_fw-la 12._o degree_n of_o latitude_n but_o our_o moderen_a astronomer_n by_o reason_n of_o the_o evagation_n of_o mars_n and_o venus_n have_v add_v on_o each_o side_n two_o degree_n more_o so_o that_o the_o whole_a latitude_n of_o the_o zodiaque_fw-la be_v confine_v within_o 16._o degree_n but_o the_o ecliptic_a only_o be_v describe_v on_o the_o globe_n and_o be_v divide_v in_o like_a manner_n as_o the_o other_o circle_n into_o 360._o degree_n pont_n the_o whole_a latitude_n of_o the_o zodiaquâ—…_n be_v divide_v into_o two_o part_n by_o the_o ecliptic_a which_o be_v the_o circle_n or_o circumference_n under_o which_o the_o sun_n steer_v his_o course_n continual_o whence_o it_o be_v call_v in_o latin_a via_fw-la solis_fw-la &_o orbita_fw-la solis_fw-la the_o sunâ—…_n high_a way_n and_o in_o gâ—…eek_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d a_o circle_n divide_v the_o zodiac_n in_o the_o midst_n and_o it_o be_v call_v the_o ecliptic_a because_o the_o eclipse_n of_o the_o sun_n and_o moon_n never_o haeppen_v but_o when_o they_o be_v either_o in_o conjunction_n or_o opposition_n under_o this_o line_n or_o very_o near_o the_o same_o the_o sun_n run_v through_o this_o circle_n in_o his_o yearly_a motion_n finish_v every_o day_n in_o the_o year_n almost_o a_o degree_n by_o his_o mean_a motion_n that_o be_v 59_o minute_n 8._o second_n and_o in_o this_o space_n he_o twice_o croâ—…seth_v the_o aequator_fw-la in_o two_o point_n equal_o distant_a from_o each_o other_o so_o that_o when_o he_o pass_v over_o the_o aequator_fw-la at_o the_o beginning_n of_o aries_n and_o libra_n the_o day_n and_o night_n be_v then_o of_o equal_a length_n and_o so_o likewise_o when_o the_o sun_n be_v now_o at_o the_o far_a distance_n from_o the_o aequator_fw-la and_o be_v get_v to_o the_o begin_n of_o cancer_n or_o capricorn_n he_o than_o cause_v the_o winter_n and_o summer_n so_o isticeâ—…_n i_o be_o not_o ignorant_a that_o vitruvius_n pliny_n thcoâ—…_n alexandrinus_n censorinus_n and_o columolla_o be_v of_o another_o opinion_n but_o they_o be_v upon_o another_o ground_n when_o as_o they_o say_v that_o the_o aequinox_n be_v when_o as_o the_o sun_n pass_v through_o the_o eight_o degree_n of_o aries_n and_o libra_n and_o then_o it_o be_v the_o midst_n of_o summer_n and_o winter_n when_o the_o sun_n enter_v into_o the_o same_o degree_n of_o cancer_n end_n capricorn_n but_o all_o these_o author_n define_v the_o solstice_n by_o the_o return_v of_o the_o shadow_n of_o dial_n which_o shadow_n can_v be_v perceive_v to_o return_v back_o again_o as_o theon_n say_v till_o the_o sun_n be_v enter_v into_o the_o eight_o degree_n of_o libra_n and_o aâ—…ies_n pont_n the_o office_n and_o use_n of_o the_o zodiac_n be_v fiâ—…st_a in_o that_o it_o be_v a_o rule_n or_o measure_n of_o the_o proper_a motion_n of_o the_o planet_n second_o by_o the_o help_n of_o the_o zodiac_n the_o true_a place_n of_o all_o the_o star_n be_v sound_a beside_o it_o may_v be_v know_v in_o what_o sign_n any_o fix_a star_n or_o planet_n may_v be_v say_v to_o be_v three_o it_o show_v the_o latitude_n of_o the_o planet_n and_o fix_a star_n four_o all_o eclipse_n happen_v when_o the_o sun_n and_o moon_n be_v under_o the_o ecliptic_a five_o the_o obliquity_n of_o the_o ecliptic_a be_v the_o cause_n of_o the_o inequality_n of_o the_o artificial_a day_n and_o night_n the_o space_n wherein_o the_o sun_n be_v finish_v his_o course_n through_o the_o zodiac_n be_v define_v â—…o_o be_v a_o year_n which_o consist_v of_o 365._o day_n and_o almost_o 6._o hour_n but_o they_o that_o think_v to_o find_v the_o exact_a measure_n of_o this_o period_n will_v find_v themselves_o frustrate_a for_o it_o be_v finish_v in_o a_o unequal_a time_n it_o have_v be_v always_o a_o controversy_n very_o much_o agitate_a among_o the_o ancienâ—…_n astronomer_n and_o not_o yet_o determine_v philolaus_n a_o pythagoraean_a determine_v it_o to_o be_v 365._o dâ—…yes_n but_o all_o the_o rest_n have_v add_v something_o more_o to_o this_o number_n harpalus_n will_v have_v it_o to_o be_v 369._o day_n and_o a_o half_a democritus_n 365._o day_n and_o a_o quarter_n add_v beside_o the_o 164_o part_n of_o a_o day_n oenopides_n will_v have_v it_o to_o be_v 365._o day_n and_o almost_o 9_o hour_n meton_n the_o athenian_a determine_v it_o to_o be_v 365._o day_n 6._o hour_n and_o almost_o 19_o minute_n after_o he_o calipius_fw-la reduce_v it_o to_o 365._o day_n and_o 6._o hour_n which_o account_n of_o his_o be_v follow_v by_o aristarchus_n of_o samos_n and_o 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
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
the_o same_o latitude_n of_o forty_o one_o gr_n where_o eleven_o german_a mile_n and_o nineteen_o minute_n answer_v to_o a_o degree_n of_o that_o parallel_n but_o these_o place_n differ_v in_o longitude_n which_o at_o naples_n be_v 39_o gr_n 30_o m_o but_o at_o troy_n 55._o gr_n 50._o m._n naw_o the_o difference_n betwixt_o they_o be_v 16_o gr_n 20._o m._n which_o be_v as_o much_o as_o 184._o german_n mile_n and_o fifty_o scruple_n the_o just_a distance_n betwixt_o these_o two_o place_n a_o table_n of_o miles_n answer_v to_o a_o degree_n in_o each_o several_a latitude_n miles_n degree_n german_n scrup._n english_a scrup._n 1_o 41_o 59_o 59_o 59_o 2_o 14_o 59_o 59_o 58_o 3_o 14_o 58_o 59_o 51_o 4_o 14_o 58_o 59_o 51_o 5_o 14_o 56_o 59_o 46_o 6_o 14_o 55_o 59_o 40_o 7_o 14_o 53_o 59_o 33_o 8_o 14_o 51_o 59_o 25_o 9_o 14_o 48_o 59_o 16_o 10_o 14_o 16_o 19_o 5_o 11_o 14_o 43_o 58_o 54_o 12_o 14_o 40_o 58_o 41_o 13_o 14_o 37_o 58_o 8_o 14_o 14_o 33_o 58_o 13_o 15_o 14_o 29_o 57_o 57_o 16_o 14_o 25_o 57_o 41_o 17_o 14_o 21_o 57_o 23_o 18_o 14_o 16_o 57_o 4_o 19_o 14_o 11_o 56_o 44_o 20_o 14_o 6_o 56_o 23_o 21_o 14_o 0_o 56_o 1_o 22_o 14_o 54_o 55_o 38_o 23_o 13_o 48_o 55_o 14_o 24_o 13_o 42_o 54_o 49_o 25_o 13_o 36_o 54_o 23_o 26_o 13_o 29_o 54_o 56_o 27_o 13_o 22_o 53_o 28_o 28_o 13_o â—…5_n 52_o 59_o 29_o 13_o 〈◊〉_d 52_o 29_o 30_o 1â—…_n â—…9_n 51_o 18_o 31_o 1â—…_n â—…2_n 51_o 26_o 3_o 12_o 43_o 50_o 53_o 33_o 12_o 35_o 50_o 19_o 3â—…_n 1â—…_n 2â—…_n 49_o 45_o 3â—…_n 1â—…_n 17_o 49_o 9_o 36_o 12_o 3â—…_n â—…8_n 32_o 3â—…_n 11_o 59_o 47_o 55_o 38_o 11_o 49_o 47_o 1â—…_n 39_o 11_o 39_o 46_o 38_o 40_o 11_o 29_o 45_o 5â—…_n 41_o â—…1_n 19_o 45_o 1â—…_n 42_o 11_o 9_o 44_o 35_o 41_o 10_o 5_o 43_o 53_o 44_o 10_o 47_o 43_o 10_o 45_o 10_o 36_o 42_o 26_o 4â—…_n 10_o â—…5_n 41_o 41_o 47_o 10_o 14_o 40_o 55_o 48_o 10_o 2_o 40_o 9_o 49_o 9_o 50_o 39_o 22_o 50_o 9_o 38_o 38_o 34_o 51_o 9_o 36_o 37_o 46_o 52_o 9_o 14_o 36_o 56_o 53_o 9_o 2_o 36_o 7_o 54_o 8_o 49_o 35_o 16_o 55_o 8_o 36_o 34_o 25_o 56_o 8_o 23_o 3â—…_n 33_o 57_o 8_o 10_o 32_o 41_o 58_o 〈◊〉_d 57_o 31_o 48_o 59_o 7_o 43_o 3â—…_n 54_o 60_o 7_o 30_o 30_o 0_o 61_o 7_o 16_o 29_o 5_o 6â—…_n 〈◊〉_d 2_o 28_o 10_o 6â—…_n 6_o 48_o 27_o â—…4_n 64_o 6_o 34_o 2â—…_n â—…8_n 65_o 6_o â—…0_n 2â—…_n 21_o 6â—…_n 5_o 6_o 24_o 24_o 6â—…_n 5_o 52_o 23_o 27_o 68_o 〈◊〉_d 37_o 2â—…_n 29_o 6â—…_n 5_o 23_o 21_o â—…0_n 70_o 5_o 8_o 20_o 31_o 71_o 4_o 53_o 19_o â—…2_n 72_o 4_o 38_o 18_o 32_o 73_o 4_o 23_o 17_o 33_o 74_o 4_o 8_o 16_o 32_o 75_o 3_o â—…3_n 15_o 32_o 76_o 3_o 38_o 14_o 31_o 77_o 3_o 22_o 13_o 30_o 78_o 3_o 7_o 12_o 28_o 79_o 2_o 52_o 11_o 27_o 80_o 2_o 36_o 10_o 25_o 81_o 2_o â—…1_n 9_o 23_o 82_o 2_o 5_o 8_o 21_o 83_o 1_o 50_o 7_o 19_o 84_o 1_o 34_o 6_o 16_o 85_o 1_o 18_o 5_o 14_o 86_o 1_o 3_o 4_o 11_o 87_o 0_o 47_o 31_o 8_o 88_o 0_o 31_o 2_o 5_o 89_o 0_o 10_o 1_o 3_o 90_o 0_o 0_o 0_o 0_o the_o longitude_n or_o latitude_n of_o any_o place_n or_o city_n be_v know_v either_o by_o observation_n as_o have_v already_o be_v show_v or_o else_o out_o of_o some_o geographical_a table_n the_o situation_n os_fw-la the_o same_o in_o the_o globe_n may_v also_o be_v find_v out_o by_o this_o same_o mean_n you_o must_v first_o reckon_v the_o longitude_n of_o your_o place_n among_o the_o circle_n of_o longitude_n which_o be_v describe_v upon_o the_o globe_n beginning_n at_o that_o which_o be_v draw_v through_o the_o fortunate_a island_n and_o observe_v the_o circle_n where_o you_o end_v your_o reckon_n then_o if_o the_o latitude_n of_o your_o place_n be_v northern_a you_o must_v reckon_v that_o also_o among_o the_o parallel_n towards_o the_o arctic_a pole_n begnine_v from_o the_o aequator_fw-la but_o if_o it_o have_v southern_a latitude_n you_o must_v then_o proceed_v in_o like_a manner_n but_o reckon_v towards_o the_o antarctique_a and_o the_o intersection_n or_o point_n where_o these_o two_o circle_n cut_v each_o other_o sheweth_z the_o situation_n of_o your_o place_n but_o if_o these_o circle_n of_o longâ—…ude_n be_v express_v in_o your_o globe_n then_o must_v you_o place_v that_o degree_n of_o the_o equinoctial_a that_o answer_v to_o the_o longitude_n of_o your_o place_n under_o the_o meridian_n and_o so_o reckon_v the_o latitude_n of_o your_o place_n among_o the_o degree_n of_o the_o meridian_n towards_o either_o pole_n and_o you_o have_v the_o situation_n of_o the_o place_n you_o look_v after_o a_o table_n of_o longitude_n and_o latitude_n of_o some_o certain_a city_n of_o note_n  _fw-fr longit._n latti_n alexandria_n 60_o 30_o 13._o 42._o amsterdam_n â—…1_n 43_o â—…2_n 30._o antwâ—…rp_a 20._o 16._o 51._o â—…8_n athens_n 52._o 45_o â—…7_n 15_o brussels_n 20._o 4â—…_n 51._o 0_o bremen_n 35._o 16_o 53._o 40_o bamberg_n 28._o 10._o 4â—…_n 56._o bâ—…sell_n 24._o 22._o 4â—…_n 〈◊〉_d bononia_n 32._o 5_o 43._o 54._o constantin_n 56._o 0_o 42._o 5_o cassell_n 26._o 36._o 51._o 43._o colen_n 33._o 20._o 51_o 0_o corinth_n 31._o 15._o 3â—…_n 5â—…_n dâ—…sden_n 38._o 5_o 51._o 6_o dover_n 28._o 10._o 51._o 0_o dâ—…ntzik_n 39_o 2_o 5â—…_n 〈◊〉_d dublin_n 16._o 40_o 53._o 10._o erfâ—…d_n 28._o 40._o 51._o 10_o estinga_fw-mi 26._o 36_o 48._o 39_o francford_n ad_fw-la mâ—…n_n 25._o 38_o 50._o 12._o jerâ—…acia_n â—…2_n 1â—…_n 44._o 23_o genâ—…a_o 〈◊〉_d 〈◊〉_d 13._o 50._o gant_n 19_o 8_o 51._o 24_o graeningen_n 22._o 54._o 53._o 16_o heidelberg_n 25._o 38._o 49._o 35_o jena_n 29._o 2_o 51._o 8_o lubâ—…k_n 28._o â—…0_n 54._o 48_o leiden_fw-mi 20._o 47._o 52._o 10_o regius_n mos_fw-la 46._o 45_o 54._o 21_o boruss_n  _fw-fr  _fw-fr london_n 25._o 〈◊〉_d 51._o 3â—…_n marpurg_n 25._o 16._o 5â—…_n 0_o milan_n 38._o 20_o 45._o 〈◊〉_d norimberg_n 20._o 20_o 49._o 24_o naples_n 30_o 10._o 41_o 0_o orleans_n 15_o 3â—…_n 47._o 16_o oxford_n 24._o 0_o 52._o 0_o prage_n 32._o 0._o â—…0_n 6_o paris_n 29_o 25._o 48_o 30_o ratisbane_n 29._o 50._o 4â—…_n 56_o rostock_n 30._o 14_o 54._o 36_o spier_n 35._o 29._o 49._o 20_o â—…ubing_v 20._o 23._o 48._o 38_o â—…ienna_n 34_o 36._o 47_o 44_o â—…orke_n 23._o 30._o 54._o 30_o chap._n iv._o to_o find_v the_o altitude_n of_o the_o sun_n or_o other_o star_n the_o altitude_n of_o the_o sun_n or_o other_o star_n be_v the_o distance_n of_o the_o same_o reckon_v in_o a_o great_a circle_n pass_v the_o zenith_n of_o any_o place_n and_o the_o body_n of_o the_o sun_n or_o star_n now_o that_o the_o manner_n of_o observe_v the_o same_o be_v to_o be_v perform_v either_o by_o the_o cross_a staff_n quadrant_n or_o other_o like_a instrument_n be_v a_o thing_n so_o well_o know_v as_o that_o it_o be_v vain_a to_o report_v it_o gemma_fw-la frisius_n teach_v a_o way_n how_o to_o observe_v the_o altitude_n of_o the_o sun_n by_o a_o spherical_a gnomon_n but_o this_o way_n of_o proceed_v be_v not_o so_o well_o like_v as_o be_v subject_a to_o many_o difficulty_n and_o error_n as_o whosoever_o prove_v it_o shall_v easy_o find_v chap._n v._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 have_v first_o learn_v the_o day_n of_o the_o month_n you_o must_v look_v for_o the_o same_o in_o the_o calendar_n describe_v in_o the_o horizon_n of_o your_o globe_n over_o against_o which_o in_o the_o same_o horizon_n you_o shall_v find_v the_o sign_n of_o the_o zodiaque_fw-la and_o the_o degree_n of_o the_o same_o that_o the_o sun_n be_v in_o at_o that_o time_n but_o if_o it_o be_v leap-yeare_n then_o for_o the_o next_o day_n after_o the_o 28_o of_o february_n you_o must_v take_v that_o degree_n of_o the_o sign_n which_o be_v a_o scribe_v to_o the_o day_n follw_v it_o as_o for_o example_n if_o you_o desire_v to_o know_v what_o degree_n of_o the_o zodiac_n the_o sun_n be_v in_o 29_o of_o february_n you_o must_v take_v that_o degree_n which_o be_v assign_v for_o the_o first_o of_o march_n and_o for_o the_o first_o of_o march_n take_v the_o degree_n of_o the_o second_o and_o so_o forward_o yet_o i_o shall_v rather_o counsel_v if_o the_o piace_n of_o the_o sun_n be_v accurate_o to_o be_v know_v that_o you_o will_v have_v recourse_n to_o some_o ephemride_n where_o you_o may_v have_v the_o place_n of_o the_o sun_n exact_o calculate_v for_o every_o day_n of_o the_o year_n neither_o indeed_o can_v the_o practice_n by_o the_o globe_n in_o this_o case_n be_v so_o accurate_a as_o often_o time_n it_o be_v require_v to_o be_v now_o when_o you_o have_v find_v the_o
until_o that_o so_o many_o degree_n of_o the_o aequator_fw-la have_v pass_v by_o the_o meridian_n aâ—…answer_n to_o the_o space_n of_o time_n that_o pass_v betwixt_o your_o observation_n allow_v for_o every_o hour_n fifteen_o degree_n in_o the_o aequator_fw-la and_o mark_v the_o place_n in_o the_o parallel_n of_o the_o sun_n declination_n that_o the_o meridian_n cross_v after_o this_o turn_n about_o of_o the_o globe_n and_o then_o set_v he_o foot_n of_o your_o compass_n in_o the_o very_a intersection_n describe_v a_o arch_n of_o a_o circle_n with_o the_o other_o foot_n of_o the_o compass_n extend_v to_o the_o compliment_n of_o the_o second_o observation_n which_o arch_n must_v cut_v the_o former_a circle_n and_o the_o common_a intersection_n of_o these_o two_o circle_n will_v show_v the_o vertical_a point_n of_o the_o place_n wherein_o you_o be_v so_o that_o have_v reckon_v the_o distance_n of_o it_o from_o the_o aequator_fw-la you_o shall_v present_o have_v the_o latitude_n of_o the_o same_o the_o same_o may_v be_v effect_v if_o you_o take_v any_o star_n and_o work_v by_o it_o after_o the_o same_o manner_n or_o it_o you_o describe_v two_o circle_n mutual_o cross_v each_o other_o to_o the_o compliment_n of_o any_o two_o star_n pont_n the_o meridian_n altitude_n of_o the_o sun_n be_v find_v by_o the_o help_n of_o of_o the_o meridian_n circle_n it_o will_v be_v very_o easy_a to_o find_v out_o the_o latitude_n of_o the_o place_n or_o elevation_n of_o the_o pole_n in_o any_o region_n whatsoever_o for_o see_v the_o zenith_n or_o vertex_fw-la of_o every_o place_n be_v distant_a aquarter_n of_o a_o circle_n that_o be_v 90._o degree_n from_o the_o horizon_n if_o then_o the_o sun_n be_v in_o either_o of_o the_o equinoctial_a point_n the_o meridian_n altitude_n be_v substract_v from_o 90_o degree_n the_o remainder_n will_v be_v the_o distance_n betwixt_o the_o zenith_n of_o the_o place_n and_o the_o equinoctial_a circle_n which_o will_v be_v the_o latitude_n of_o the_o same_o place_n and_o the_o reason_n also_o of_o this_o deduction_n be_v manifest_a because_o that_o the_o equinoctial_a altitude_n of_o the_o sun_n be_v nothing_o else_o but_o the_o elevation_n of_o the_o aequator_fw-la the_o compliment_n whereof_o be_v always_o equali_fw-la to_o the_o elevation_n of_o the_o pole_n but_o this_o will_v appear_v more_o plain_a by_o a_o example_n which_o shall_v be_v thus_o the_o equinoctial_a altitude_n of_o the_o sun_n at_o rome_n be_v 40._o degree_n which_o be_v substract_v from_o 90_o gr_n the_o remainder_n which_o be_v 42._o gr_n be_v the_o elevation_n of_o the_o pole_n and_o the_o latitude_n of_o rome_n so_o likewise_o here_o at_o london_n in_o the_o meridian_n altitude_n of_o the_o sun_n when_o he_o be_v in_o the_o equinoctial_a be_v find_v to_o be_v 38_o degree_n and_o a_o half_a which_o be_v deduct_v out_o of_o 90_o gr_n which_o be_v the_o quadrant_n of_o a_o circle_n there_o wâ—…ll_v remain_v 15½_n gr_n which_o be_v the_o latitude_n of_o london_n and_o the_o elevation_n of_o the_o pole_n the_o same_o also_o may_v be_v do_v by_o observe_v any_o one_o of_o the_o fix_a sarre_n which_o be_v be_v so_o near_o the_o pole_n as_o that_o it_o never_o set_v in_o that_o country_n who_o latitude_n you_o seek_v for_o you_o must_v observe_v both_o the_o great_a and_o least_o altitude_n of_o the_o same_o star_n both_o which_o will_v happen_v in_o the_o meridian_n the_o least_o of_o they_o 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 to_o the_o great_a and_o so_o divide_v the_o whole_a into_o two_o part_n the_o half_a will_v be_v the_o altitude_n of_o the_o pole_n as_o have_v be_v show_v before_o chap._n vii_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 assign_v the_o ascension_n of_o the_o sun_n or_o star_n be_v the_o degree_n of_o the_o aequator_fw-la that_o rise_v with_o the_o same_o above_o the_o horizon_n and_o the_o descension_n of_o of_o it_o be_v the_o degree_n of_o the_o aequator_fw-la that_o go_v under_o the_o horizon_n with_o the_o same_o both_o these_o be_v either_o right_n or_o oblique_a the_o right_a ascension_n or_o descension_n be_v the_o degree_n of_o the_o aequator_fw-la that_o ascend_v or_o descend_v with_o the_o sun_n or_o other_o star_n in_o a_o right_a sphere_n and_o the_o oblique_a be_v the_o degree_n that_o ascend_v or_o descend_v with_o the_o same_o in_o a_o oblique_a the_o form_n of_o these_o be_v simple_a and_o of_o one_o kind_n only_o because_o there_o can_v be_v but_o one_o position_n of_o a_o right_a sphere_n but_o the_o late_a be_v various_a and_o manifold_a according_a to_o the_o diverse_a inclination_n of_o the_o same_o now_o if_o you_o desire_v to_o know_v the_o right_a ascension_n or_o descension_n of_o any_o star_n for_o any_o time_n and_o place_n assign_v apply_v the_o same_o star_n to_o the_o meridian_n of_o your_o globe_n and_o that_o degree_n of_o the_o aequator_fw-la that_o the_o meridian_n cross_v at_o that_o situation_n of_o the_o globe_n will_v show_v the_o right_a ascension_n and_o descension_n of_o the_o same_o and_o also_o divide_v each_o hemisphere_n in_o the_o midst_n at_o the_o same_o time_n with_o it_o and_o if_o you_o will_v know_v the_o oblique_a ascension_n or_o descension_n of_o any_o star_n you_o must_v first_o set_v the_o globe_n to_o the_o latitude_n of_o the_o place_n and_o then_o place_v the_o star_n at_o the_o eastern_a part_n of_o the_o horizon_n and_o the_o horizon_n will_v show_v in_o the_o aequator_fw-la the_o degree_n of_o oblique_a ascension_n and_o if_o you_o turn_v it_o about_o to_o the_o well_o side_n of_o the_o horizon_n the_o same_o will_v also_o show_v in_o the_o aequator_fw-la the_o oblique_a descension_n of_o that_o star_n in_o like_a manner_n you_o may_v find_v out_o the_o oblique_a ascension_n of_o the_o sunâ—…_n or_o any_o degree_n of_o the_o ecliptic_a have_v first_o find_v ou_fw-fr in_o the_o manner_n we_o have_v former_o show_v the_o place_n of_o the_o sun_n and_o hence_o also_o may_v be_v find_v the_o difference_n of_o the_o right_n and_o oblique_a ascension_n whence_o arise_v the_o diverse_a length_n of_o day_n as_o for_o example_n the_o sun_n enter_v into_o capricorn_n on_o the_o eleven_o day_n of_o december_n according_a to_o the_o old_a account_n i_o will_v now_o therefore_o know_v the_o right_n and_o oblique_a ascension_n of_o this_o degree_n of_o the_o ecliptic_a for_o the_o latitude_n of_o fifty_o two_o degree_n first_o therefore_o i_o apply_v the_o first_o degree_n of_o capricorn_n to_o the_o meridian_n where_o i_o find_v the_o same_o to_o cut_v the_o aequator_fw-la at_o 270._o gr_n which_o be_v the_o degree_n of_o the_o right_a ascension_n but_o if_o you_o set_v the_o globe_n to_o the_o latitude_n of_o fifty_o two_o degree_n and_o apply_v the_o same_o degree_n of_o capricorn_n to_o the_o horizon_n you_o shall_v find_v the_o 303_o gr_n 50._o m._n to_o rise_v with_o the_o same_o so_o that_o the_o difference_n of_o the_o right_a ascension_n 270._o and_o the_o oblique_a 303._o gr_n 50._o m._n will_v be_v find_v to_o be_v 33._o gr_n 50._o minute_n pont_n this_o ascension_n and_o descension_n be_v also_o call_v the_o astro_fw-la nomicall_a rising_z and_o set_v of_o the_o star_n and_o that_o inrespect_n of_o the_o arch_n and_o part_n of_o the_o ecl_n ptick_a or_o star_n either_o above_o or_o beneath_o the_o horizon_n now_o a_o arch_n of_o the_o ecliptic_a or_o zodiac_n be_v tobe_n understand_v two_o manner_n of_o way_n namely_o continue_v or_o discrete_a a_o continue_a arch_n be_v when_o it_o be_v reckon_v in_o the_o aequator_fw-la in_o a_o continue_a series_n from_o the_o begin_n of_o aries_n and_o so_o forward_o into_o the_o consequent_a sign_n a_o discrete_a arch_n be_v so_o call_v because_o it_o be_v not_o reckon_v from_o the_o first_o degree_n of_o aries_n but_o from_o any_o other_o point_n in_o the_o aequator_fw-la as_o if_o you_o shall_v say_v a_o arch_n from_o the_o 14._o gr_n of_o gemini_fw-la to_o the_o 14._o gr_n of_o taurus_n beside_o this_o right_a ascension_n be_v call_v also_o the_o great_a ascension_n because_o that_o in_o it_o a_o great_a arch_n of_o the_o aequator_fw-la rise_v above_o the_o horizon_n then_o of_o the_o zodiac_n &_o it_o be_v call_v right_o because_o that_o in_o this_o the_o angle_n which_o be_v make_v by_o the_o horizon_n and_o ecliptic_a be_v near_a to_o a_o right_a angle_n then_o that_o that_o be_v make_v by_o any_o other_o part_n of_o the_o ecliptic_a with_o the_o same_o and_o that_o be_v say_v to_o be_v a_o great_a arch_n or_o portion_n of_o the_o aequator_fw-la which_o be_v more_o than_o 30._o degree_n in_o the_o ascension_n or_o descension_n and_o that_o be_v call_v a_o
have_v find_v the_o degree_n of_o the_o ecliptic_a with_o which_o the_o star_n you_o inquire_v after_o do_v rise_v and_o set_v if_o you_o seek_v for_o the_o same_o degree_n of_o the_o sign_n in_o the_o horizon_n of_o your_o globe_n you_o shall_v present_o have_v the_o month_n and_o day_n express_v wherein_o the_o sun_n come_v to_o the_o same_o degree_n and_o sign_n and_o as_o for_o the_o heliacall_a rise_n and_o set_v of_o a_o star_n you_o may_v find_v it_o thus_o have_v set_v your_o globe_n to_o the_o latitude_n of_o your_o place_n you_o must_v turn_v about_o the_o star_n propose_v to_o the_o west_n side_n of_o the_o horizon_n and_o withal_o on_o the_o opposite_a east_n part_n observe_v what_o degree_n of_o the_o ecliptic_a be_v elevate_v above_o the_o horizon_n 12_o 13_o 14._o or_o any_o other_o number_n of_o degree_n that_o the_o magnitude_n of_o your_o star_n shall_v require_v for_o distance_n from_o the_o sun_n and_o when_o the_o sun_n shall_v be_v in_o the_o opposite_a degree_n to_o this_o than_o that_o star_n will_v set_v heliacal_o that_o be_v to_o say_v it_o will_v be_v quite_o take_v out_o of_o our_o sight_n by_o the_o brightness_n of_o the_o sun_n beam_n now_o if_o on_o the_o other_o side_n you_o apply_v the_o same_o star_n to_o the_o east_n and_o find_v out_o the_o opposite_a degree_n in_o the_o ecliptic_a on_o the_o west_n part_n that_o be_v the_o same_o number_n of_o degree_n above_o the_o horizon_n when_o the_o sun_n come_v to_o this_o place_n the_o same_o star_n will_v rise_v heliacal_o or_o recover_v itself_o out_o of_o the_o sun_n beam_n and_o so_o if_o you_o but_o find_v the_o same_o degree_n of_o the_o ecliptic_a among_o the_o sign_n on_o the_o horizon_n of_o your_o globe_n you_o have_v the_o month_n and_o the_o day_n when_o the_o sun_n will_v be_v in_o those_o degree_n and_o the_o same_o also_o be_v the_o time_n of_o the_o emersion_n and_o occultation_n of_o the_o star_n you_o inquire_v after_o but_o we_o will_v here_o propose_v a_o example_n of_o the_o occultation_n of_o some_o fix_a star_n of_o the_o first_o magnitude_n which_o do_v the_o emersion_n of_o the_o same_o be_v also_o find_v by_o the_o contrary_a way_n of_o work_v and_o the_o star_n we_o propose_v shall_v be_v that_o bright_a star_n in_o the_o mouth_n of_o the_o great_a dog_n which_o be_v call_v sirius_n who_o occultation_n we_o desire_v to_o know_v for_o the_o latitude_n of_o 51._o gr_n northward_o now_o this_o star_n be_v of_o the_o first_o magnitude_n begin_v to_o be_v hide_v whenas_o it_o touch_v the_o horizon_n in_o the_o upper_a hemisphere_n and_o the_o sun_n be_v at_o the_o same_o time_n depress_v under_o the_o horizon_n but_o 12._o degree_n if_o therefore_o you_o apply_v this_o star_n to_o the_o west_n part_n of_o the_o horizon_n have_v first_o set_v your_o globe_n to_o the_o latitude_n of_o 51_o degree_n and_o on_o the_o opposite_a east_n side_n observe_v what_o degree_n of_o the_o ecclipticke_a be_v just_a 12_o degree_n above_o the_o horizon_n now_o this_o degree_n be_v very_o near_o the_o 11._o gr_n of_o scorpius_n when_o the_o sun_n shall_v come_v to_o the_o opposite_a degree_n in_o the_o ecliptic_a which_o be_v the_o 11._o of_o taurus_n that_o star_n will_v set_v heliacal_o and_o be_v hide_v by_o the_o sunbeam_n but_o the_o sun_n come_v to_o this_o degree_n of_o taurus_n about_o the_o 22._o of_o april_n therefore_o we_o conclude_v that_o the_o dog_n star_n set_v heliacal_o about_o that_o time_n and_o if_o you_o work_v in_o the_o same_o manner_n apply_v the_o star_n to_o the_o east_n part_n of_o the_o horizon_n you_o shall_v have_v the_o time_n of_o itâ—…_n heliacal_a rise_n or_o emersion_n out_o oâ—…_n the_o sun_n beâ—…_n nâ—…t_v unlike_o this_o be_v the_o manner_n of_o proceed_v alâ—…o_o in_o find_v the_o bâ—…ginning_n and_o end_v of_o the_o twilight_n of_o which_o we_o shall_v speak_v in_o the_o next_o chapter_n pont_n the_o use_n and_o benefit_n of_o this_o discourse_n concern_v these_o kind_n of_o rise_v and_o set_v of_o the_o star_n be_v principal_o see_v in_o read_v of_o the_o ancient_a author_n and_o poet_n especial_o those_o that_o have_v write_v of_o husbandry_n and_o the_o several_a season_n of_o the_o year_n for_o so_o virgil._n lib._n 1._o georg._n make_v mention_n of_o the_o cosmical_a rise_n of_o the_o star_n in_o these_o verse_n candidus_n auratis_fw-la aperit_fw-la cum_fw-la cornibus_fw-la annum_fw-la taurus_n &_o adverso_fw-la cadens_fw-la canis_fw-la occidit_fw-la astro_fw-la which_o be_v thus_o english_v by_o t._n may._n when_o with_o his_o golden_a horn_n bright_a taurus_n open_v the_o year_n and_o downward_o the_o cross_a dog-star_n stoopeâ—…_n in_o which_o place_n he_o mean_v to_o intimate_v the_o month_n of_o april_n when_o as_o the_o snnne_n be_v in_o the_o sign_n tâ—…us_a and_o rise_v with_o it_o and_o we_o have_v a_o example_n also_o of_o the_o cosmical_a set_n in_o the_o same_o place_n where_o he_o say_v at_o si_fw-la triticeam_fw-la in_o messem_fw-la robustaque_fw-la farra_fw-la exercebiâ—…_n humum_fw-la solisque_fw-la instabis_fw-la aristis_fw-la an_fw-mi â—…ibi_fw-la eoae_fw-la atlantâ—…des_fw-la abscondantur_fw-la gnoâ—…áque_fw-la arden_n decâ—…dat_fw-la stella_fw-la coronâ—…_n debâ—…ta_fw-la quamâ—…ulcis_fw-la commiâ—…tas_fw-la sâ—…ina_fw-la quamque_fw-la invitae_fw-la properes_fw-la anni_fw-la spem_fw-la credere_fw-la terrae_fw-la mult_fw-la 〈…〉_z pere_fw-fr sed_fw-la illos_fw-la expectata_fw-la 〈◊〉_d vanis_fw-la 〈◊〉_d venis_fw-la thus_o render_v by_o t._n may._n but_o if_o thou_o plough_v to_o sow_v more_o solid_a grain_n a_o wheat_n or_o barley_n harvest_n to_o obtain_v first_o let_v the_o morning_n pleiades_n be_v set_v and_o ariadne_n shine_a coronet_n ere_o thou_o commit_v thy_o seed_n to_o ground_n and_o there_o dare_v trust_v the_o hope_n of_o all_o the_o follow_a year_n some_o that_o before_o the_o fall_n of_o the_o pleyade_n begin_v to_o sow_v deceive_v in_o the_o increase_n have_v reap_v wild_a oat_n for_o wheat_n etc._n etc._n where_o he_o will_v have_v they_o to_o expect_v their_o sow_a time_n till_o that_o the_o altaâ—â—ide_n that_o be_v the_o pleyade_n ere_fw-we seven_o star_n be_v hide_v in_o the_o east_n that_o be_v in_o the_o morning_n by_o the_o approach_n of_o the_o sun_n which_o be_v also_o call_v occaâ—us_a cosmicus_n at_o which_o time_n also_o the_o bright_a star_n in_o the_o northern_a crown_n set_v in_o the_o evening_n with_o the_o sun_n or_o heliacal_o and_o so_o the_o poet_n by_o a_o twofold_a kind_n of_o set_v of_o the_o star_n describe_v the_o 28._o and_o 29._o of_o october_n a_o example_n of_o the_o achronycall_a rise_n you_o have_v in_o ovid._n lib._n 1_o de_fw-fr ponto_n eleg._n 9_o where_o he_o decribe_v the_o tediousness_n of_o his_o exile_n from_o the_o autumnal_a or_o vespertine_n rise_v of_o the_o pleyade_n in_o word_n ut_fw-la careo_fw-la vobis_fw-la sythicas_fw-la detrusus_fw-la in_o oras_fw-la quatuor_fw-la autumnos_fw-la plëâ—as_fw-la orta_fw-la facit_fw-la in_o english_a thus_o since_o of_o your_o joyful_a sight_n cold_a scythia_n i_o deprive_v the_o rise_a pleiades_n four_o autumn_n have_v revive_v and_o he_o also_o mention_v the_o achronicall_a set_n lib._n 2._o fast_o where_o speak_v of_o the_o three_o of_o february_n he_o do_v it_o by_o this_o periphrasis_n quem_fw-la modo_fw-la celatum_fw-la stellis_fw-la delphina_fw-la videbas_fw-la be_v fugiet_fw-la visus_fw-la noâ—…te_fw-la sequente_fw-la tuos_fw-la that_o be_v to_o say_v the_o dolphin_n erst_o with_o star_n you_o see_v bedight_v the_o next_o night_n vanish_v out_o of_o your_o sight_n a_o example_n of_o the_o heliacall_a rise_n in_o february_n you_o have_v in_o the_o same_o author_n in_o these_o word_n tertia_fw-la nox_fw-la veniet_fw-la custodem_fw-la protinus_fw-la ursae_fw-la aspicies_fw-la geminos_fw-la exeruisse_fw-la pedes_fw-la which_o may_v be_v english_v thus_o when_o now_o the_o three_o night_n come_v you_o shall_v perceive_v arctophylax_n will_v both_o his_o foot_n up_o heave_v and_o for_o the_o heliacall_a set_n you_o have_v a_o instance_n above_o out_o of_o virgil._n georg._n 1._o et_fw-la adverso_fw-la cadens_fw-la canis_fw-la occidit_fw-la astro_fw-la in_o which_o place_n the_o poet_n speak_v of_o sow_v millet_n and_o bean_n in_o the_o spring_n time_n to_o these_o we_o may_v also_o add_v these_o several_a kind_n of_o poetical_a rise_n and_o set_v of_o star_n express_v cosmicus_fw-la est_fw-la ortus_fw-la cum_fw-la sol_fw-la emergere_fw-la quaerit_fw-la ipsius_fw-la oppositum_fw-la lapsus_fw-la ad_fw-la ima_fw-la gerit_fw-la chronicus_n est_fw-la lapsus_fw-la cum_fw-la sol_fw-la in_o vespere_fw-la tabet_fw-la ipsius_fw-la oppositum_fw-la chronicus_n ortus_fw-la habet_fw-la heliacus_fw-la signo_fw-la datur_fw-la ortus_fw-la sole_a remoto_fw-la illius_fw-la occasum_fw-la proximitate_fw-la noto_fw-la chap._n xi_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 time_n and_o latitude_n of_o place_n the_o twilight_n be_v define_v to_o be_v a_o kind_n of_o imperfect_a light_n betwixt_o the_o day_n and_o the_o night_n
and_o that_o the_o sphere_n of_o the_o fix_a star_n be_v go_v back_o into_o the_o saccee_a part_n and_o he_o do_v not_o perswadâ—…_n himself_o only_o to_o this_o but_o even_o ptolemy_n also_o and_o ptolemy_n all_o that_o come_v after_o he_o so_o great_a be_v the_o power_n of_o prejudicate_v authority_n and_o he_o also_o rectify_v the_o globe_n and_o make_v the_o tail_n of_o the_o little_a bear_n to_o be_v distant_a from_o the_o pole_n twelve_o gr_n twenty_o four_o min._n choose_v rather_o to_o believe_v it_o to_o be_v so_o then_o to_o consult_v with_o the_o star_n to_o see_v whether_o it_o be_v so_o indeed_o or_o no._n which_o thing_n i_o can_v sufficient_o wonder_v at_o in_o he_o see_v that_o not_o only_o in_o his_o time_n but_o also_o two_o hunare_v and_o eighteen_o year_n before_o he_o the_o tail_n of_o the_o lesser_a bear_n be_v no_o far_o from_o the_o pole_n of_o the_o world_n than_o it_o be_v at_o this_o day_n as_o eudoxus_n observe_v which_o i_o have_v most_o plain_o demonstrate_v in_o my_o book_n of_o the_o praecession_n of_o the_o equinoctial_a poinâ—…_n beside_o eratosthenes_n also_o who_o write_v one_o hundred_o twenty_o eight_o year_n after_o fudoxus_fw-la affirm_v the_o same_o of_o the_o same_o star_n and_o so_o do_v those_o that_o write_v in_o augustus_n his_o time_n if_o therefore_o two_o hundred_o and_o eighteen_o year_n before_o hipparchus_n time_n that_o star_n be_v where_o it_o be_v now_o how_o then_o can_v that_o position_n of_o hipparchus_n stand_v who_o place_v it_o 12._o gr_n 24_o min._n of_o the_o pole_n of_o the_o world_n for_o if_o the_o sphere_n of_o the_o fix_a star_n lay_v more_o backward_o into_o the_o succeed_a part_n as_o he_o will_v have_v it_o and_o that_o in_o his_o time_n the_o tail_n of_o the_o cynosure_n be_v 12._o gr_n 24._o min._n distant_a from_o the_o pole_n it_o necessary_o follow_v that_o in_o eudoxus_n time_n it_o must_v have_v be_v far_o distant_a from_o the_o pole_n by_o 13._o or_o 14._o gr_n for_o this_o be_v the_o proportion_n of_o degree_n require_v for_o that_o motion_n but_o it_o be_v then_o no_o far_o distant_a than_o it_o be_v at_o this_o day_n and_o therefore_o hipparchus_n have_v abuse_v both_o himself_o and_o all_o that_o have_v come_v after_o he_o and_o indeed_o i_o myself_o have_v make_v a_o collection_n out_o of_o he_o of_o all_o the_o rise_n and_o setting_n of_o the_o star_n which_o no_o man_n shall_v ever_o be_v able_a to_o understand_v except_o he_o first_o make_v such_o a_o globe_n wherein_o the_o tail_n of_o the_o cynosure_n shall_v be_v 12._o gr_n 24._o min._n distant_a from_o the_o pole_n which_o thing_n when_o i_o impart_v to_o that_o great_a astronomer_n tycho_n brahe_n he_o be_v amuse_v and_o wonder_v very_o much_o at_o the_o novelty_n and_o strangeness_n of_o the_o thing_n and_o indeed_o not_o without_o cause_n for_o i_o do_v not_o speak_v a_o word_n to_o he_o of_o the_o construction_n of_o hipparchus_n his_o globe_n and_o the_o distance_n of_o the_o cynosure_n from_o the_o pole_n of_o it_o and_o therefore_o we_o plain_o see_v that_o for_o as_o much_o as_o this_o star_n keep_v the_o same_o distance_n from_o the_o pole_n at_o this_o day_n that_o it_o do_v 1967._o year_n since_o there_o be_v no_o motion_n at_o all_o of_o the_o eight_o sphere_n into_o the_o succeed_v part_n but_o of_o the_o equinoctial_a point_n into_o the_o precedent_n for_o of_o the_o motion_n there_o be_v no_o doubt_n at_o all_o to_o be_v make_v for_o at_o this_o time_n the_o aequinoxe_n fall_v before_o the_o first_o star_n in_o aries_n above_o 28._o gr_n which_o notwithstanding_o in_o eudoxus_n his_o time_n happen_v at_o the_o very_a star_n but_o now_o whether_o the_o star_n have_v leave_v the_o sun_n behind_o it_o or_o the_o sun_n the_o star_n be_v the_o principal_a matter_n in_o question_n for_o it_o must_v be_v that_o one_o of_o they_o must_v stand_v still_o and_o the_o other_o move_v but_o we_o have_v already_o show_v that_o the_o star_n be_v immovable_a and_o therefore_o the_o sun_n and_o equinoctial_a point_n be_v movable_a and_o indeed_o they_o have_v manifest_o go_v forward_o since_o eudox_n time_n 28._o degree_n this_o copernicus_n that_o great_a scholar_n and_o second_o ptolemy_n of_o our_o age_n perceive_v when_o he_o speak_v these_o word_n vos_fw-fr putatis_fw-la etc._n etc._n you_o think_v say_v he_o that_o the_o eight_o sphere_n move_v into_o the_o consequent_a part_n but_o consider_v whether_o the_o equinoctial_a point_n do_v not_o rather_o move_v forward_o whence_o it_o appear_v that_o this_o never_o suffioient_o commend_v man_n conclude_v that_o there_o be_v a_o praecession_n of_o the_o equinoctial_a point_n and_o not_o a_o motion_n of_o the_o eight_o sphere_n into_o the_o subsâ—…quent_a paert_n for_o one_o of_o these_o be_v grant_v the_o other_o must_v necessary_o be_v take_v away_o for_o if_o the_o eight_o sphere_n do_v not_o move_v backward_o the_o equinoctial_a point_n must_v necessary_o move_v forward_o and_o therefore_o herein_o copernicus_n conjecture_v aright_o but_o he_o omit_v the_o chief_a matter_n of_o all_o either_o because_o perhaps_o he_o perceive_v it_o not_o or_o else_o despair_v of_o ever_o be_v able_a to_o demonstrate_v it_o for_o see_v that_o the_o equinoctial_a point_n be_v movable_a it_o must_v needs_o follow_v that_o a_o great_a circle_n describe_v by_o the_o same_o must_v be_v movable_a also_o by_o the_o twenty_o sphaeric_a element_n and_o if_o the_o circle_n be_v movable_a the_o pole_n must_v also_o be_v movable_a and_o therefore_o the_o pole_n of_o the_o equinoctial_a be_v not_o the_o same_o with_o the_o pole_n of_o the_o world_n for_o this_o be_v immovable_a but_o the_o other_o movable_n for_o so_o consequent_o all_o the_o great_a circle_n pass_v through_o these_o pole_n which_o be_v the_o meridian_n be_v also_o movable_a so_o that_o sunne-dialls_a and_o all_o sciotericall_a instrument_n that_o be_v place_v upon_o a_o meridian_n line_n after_o some_o certain_a term_n of_o year_n must_v necessary_o be_v defective_a because_o the_o line_n itself_o be_v remove_v from_o its_o former_a situation_n of_o which_o variableness_n we_o have_v obse_o ve_v notable_a argument_n in_o monument_n of_o antiquity_n these_o thing_n it_o do_v concern_v copernicus_n either_o to_o have_v see_v or_o demonstrate_v who_o be_v the_o first_o man_n that_o ever_o reject_v that_o fabulous_a and_o ridiculousmotionof_o the_o eight_o sphere_n and_o withal_o propose_v this_o opinion_n of_o the_o praecession_n of_o the_o equinoctial_a point_n who_o have_v he_o but_o see_v see_v those_o thing_n which_o we_o have_v observe_v historical_o out_o of_o the_o write_n of_o the_o ancient_a astronomer_n so_o great_a be_v the_o ingenuity_n of_o the_o man_n that_o he_o will_v have_v instant_o consent_v and_o demonstrate_v the_o matter_n mathematical_o which_o certain_o be_v no_o hard_a matter_n to_o do_v for_o be_v there_o any_o man_n so_o void_a of_o all_o reason_n and_o judgement_n as_o have_v grant_v the_o equinoctial_a point_n to_o be_v movable_a to_o deny_v that_o a_o great_a circle_n describe_v by_o the_o same_o must_v necessary_o be_v movable_a also_o and_o if_o so_o that_o the_o pole_n be_v also_o movable_a and_o again_o this_o 〈◊〉_d grant_v that_o the_o meridian_n be_v so_o too_o he_o that_o shall_v deny_v this_o i_o can_v see_v what_o it_o have_v profit_v bim_n to_o have_v study_v the_o mathematics_n but_o you_o will_v object_v that_o the_o meridian_n be_v not_o change_v because_o they_o pass_v through_o the_o pole_n of_o the_o world_n which_o be_v immutable_a but_o than_o you_o have_v forget_v our_o hypothesis_n which_o be_v that_o the_o pole_n of_o the_o equinoctial_a be_v not_o the_o same_o with_o the_o pole_n of_o the_o world_n for_o these_o be_v immutable_a but_o those_o other_o mutable_a and_o therefore_o we_o see_v the_o necessity_n of_o this_o argument_n and_o withal_o that_o these_o thing_n be_v so_o we_o be_v yet_o very_o far_o to_o seek_v in_o many_o thing_n necessary_a for_o the_o situation_n and_o construction_n of_o the_o sphere_n for_o by_o this_o reckon_n it_o follow_v necessary_o that_o the_o equinoctial_a circle_n shall_v not_o be_v describe_v direct_o parallel_n to_o the_o pole_n of_o the_o world_n and_o many_o other_o thing_n of_o this_o nature_n which_o may_v hence_o be_v conclude_v i_o may_v willing_o omit_v because_o i_o speak_v to_o a_o mathematician_n who_o may_v better_o teach_v in_o these_o thing_n wherefore_o i_o think_v i_o may_v bold_o say_v that_o none_o can_v be_v so_o impudent_a as_o to_o deny_v these_o thing_n which_o be_v so_o manifest_a as_o that_o we_o can_v prove_v they_o not_o only_o historical_o but_o also_o apodictical_o by_o certain_a demonstration_n and_o it_o behoove_v you_o to_o see_v and_o examine_v more_o narrow_o whatsoever_o have_v be_v write_v by_o mathematician_n concern_v this_o