equinoctial_a point_n by_o its_o mutual_a section_n with_o the_o ecliptic_a in_o which_o point_n when_o the_o sun_n be_v exist_v there_o be_v a_o universal_a equinox_n over_o the_o whole_a earth_n 2._o it_o be_v divide_v the_o ecliptic_a into_o two_o half_n the_o one_o call_v the_o north_n part_n the_o other_o the_o south_n part_n 3._o it_o distinguish_v the_o sign_n in_o which_o when_o the_o sun_n be_v exist_v the_o day_n be_v long_o than_o the_o night_n from_o those_o sign_n in_o which_o when_o the_o sun_n be_v exist_v the_o night_n be_v long_o than_o the_o day_n the_o proper_a uses_n of_o the_o solstice_n colour_n be_v 1._o it_o demonstrat_n to_o we_o the_o two_o solstice_n point_n in_o which_o when_o the_o sun_n be_v exist_v he_o be_v either_o near_a to_o our_o zenith_n or_o further_a remove_v from_o it_o 2._o upon_o this_o colour_n we_o reckon_v the_o sun_n great_a declination_n or_o the_o great_a obliquity_n of_o the_o ecliptic_a which_o be_v find_v to_o be_v this_o day_n twenty_o three_o degree_n and_o thirty_o minute_n 3._o it_o divide_v the_o zodiac_n into_o two_o half_n the_o one_o call_v ascend_v the_o other_o descend_v 4._o it_o distinguish_v the_o sign_n in_o which_o when_o the_o sun_n be_v exist_v the_o day_n become_v long_o and_o the_o night_n become_v short_a from_o those_o sign_n in_o which_o when_o the_o sun_n be_v exist_v the_o night_n become_v long_o and_o the_o day_n become_v short_a 5._o in_o this_o circle_n be_v the_o two_o pole_n of_o the_o ecliptic_a as_o many_o degree_n distant_a from_o the_o pole_n of_o the_o world_n as_o the_o great_a obliquity_n of_o the_o ecliptic_a contain_v 6._o upon_o this_o colour_n the_o latitude_n of_o the_o zone_n be_v determine_v for_o between_o the_o tropic_n be_v contain_v the_o breadth_n of_o the_o torrid_a zone_n between_o the_o tropic_n and_o the_o near_a polar_a circle_n be_v contain_v the_o two_o temperate_a zone_n and_o the_o other_o two_o remain_a arch_n of_o this_o circle_n contain_v the_o breadth_n of_o the_o two_o frigid_a or_o cold_a zone_n chap._n v._o of_o the_o horizon_n the_o horizon_n be_v one_o of_o the_o great_a circle_n of_o the_o sphere_n immovable_a and_o equal_o distant_a from_o the_o vertical_a point_n it_o be_v call_v immovable_a that_o it_o may_v be_v difference_v from_o the_o rest_n of_o the_o movable_a circle_n but_o especial_o first_o from_o their_o equinoctial_a who_o live_v under_o the_o pole_n second_o from_o their_o ecliptic_a who_o zenith_n be_v place_v in_o the_o polar_a circle_n for_o their_o ecliptic_a every_o day_n be_v twice_o unite_a with_o their_o horizon_n but_o without_o delay_n three_o from_o their_o circle_n of_o declination_n or_o their_o colour_n who_o live_v under_o the_o line_n for_o there_o the_o forementioned_a circle_n and_o the_o horizon_n be_v twice_o by_o every_o revolution_n of_o the_o sphere_n unite_v but_o the_o circle_n of_o declination_n follow_v the_o motion_n of_o the_o primum_fw-la mobile_n but_o the_o horizon_n stand_v immovable_a the_o horizon_n be_v say_v indeed_o to_o be_v immovable_a but_o not_o unchangeable_a for_o there_o be_v as_o many_o orison_n as_o there_o be_v vertical_a point_n and_o while_o we_o change_v our_o vertical_a point_n of_o necessity_n we_o change_v our_o horizon_n also_o two_o way_n be_v the_o horizon_n divide_v first_o in_o relation_n to_o the_o equinoctial_a which_o be_v call_v a_o right_a horizon_n a_o oblique_a horizon_n and_o a_o parallel_n horizon_n the_o right_a horizon_n be_v so_o call_v because_o it_o cut_v the_o equinoctial_a at_o right_a angle_n it_o be_v call_v oblique_a because_o it_o cut_v the_o equinoctial_a at_o oblique_a angle_n and_o it_o be_v call_v a_o parallel_n horizon_n when_o it_o lie_v parallel_v to_o the_o plain_a of_o the_o equinoctial_a or_o rather_o when_o it_o be_v unite_v with_o the_o equinoctial_a and_o according_a to_o this_o relation_n it_o have_v to_o the_o equinoctial_a the_o sphere_n itself_o have_v obtain_v the_o same_o division_n second_o the_o horizon_n be_v either_o rational_a or_o sensible_a the_o rational_a horizon_n be_v defiâ—…ed_v above_o and_o be_v understand_v to_o divide_v the_o whole_a world_n or_o sphere_n of_o the_o world_n into_o two_o equal_a part_n the_o first_o whereof_o be_v call_v the_o uppermost_a hemisphere_n the_o second_o the_o nethermost_a hemisphere_n it_o be_v call_v rational_a because_o though_o we_o can_v see_v the_o whole_a world_n or_o the_o exact_a half_a of_o it_o yet_o reason_n tell_v we_o by_o the_o rise_n and_o set_v of_o the_o sun_n moon_n and_o star_n that_o the_o inferior_a part_n of_o the_o world_n be_v equal_a to_o the_o superior_a part_n the_o sensible_a horizon_n be_v nothing_o else_o but_o so_o much_o of_o the_o earth_n as_o a_o man_n by_o turn_v his_o eye_n once_o do_v behold_v round_o about_o he_o the_o use_v of_o the_o horizon_n be_v these_o first_o it_o divide_v that_o part_n of_o the_o heaven_n which_o be_v see_v from_o the_o other_o which_o be_v not_o see_v the_o superior_a part_n from_o the_o inferior_a part_n 2._o through_o the_o pole_n of_o the_o horizon_n the_o meridian_n ought_v to_o pass_v therefore_o the_o description_n of_o the_o meridian_n depend_v from_o the_o horizon_n 3._o by_o the_o situation_n of_o the_o horizon_n we_o know_v whether_o it_o be_v a_o right_a sphere_n oblique_a sphere_n or_o a_o parallel_n sphere_n 4._o in_o the_o horizon_n the_o rise_n or_o set_v of_o the_o star_n be_v observe_v 5._o the_o horizon_n show_v what_o degree_n of_o the_o ecliptic_a what_o part_n also_o of_o the_o equinoctial_a or_o what_o degree_n with_o any_o give_a point_n of_o the_o heaven_n rise_v or_o set_v 6._o it_o bound_v and_o terminat_n the_o ascensional_a difference_n 7._o upon_o the_o horizon_n be_v number_v the_o rise_n or_o set_v amplitude_n of_o any_o point_n in_o the_o heaven_n 8._o it_o demonstrat_n and_o show_v the_o cause_n and_o reason_n of_o the_o equality_n of_o day_n and_o night_n in_o a_o right_a sphere_n and_o of_o the_o unequality_n of_o the_o same_o in_o a_o oblique_a sphere_n for_o the_o horizon_n in_o a_o right_a sphere_n cut_v all_o the_o circle_n of_o the_o natural_a day_n equal_o but_o unequal_o in_o a_o oblique_a sphere_n 9_o from_o the_o horizon_n we_o number_v the_o morning-twilight_n for_o when_o the_o sun_n â—…s_v distant_a in_o some_o vertical_a circle_n 18_o or_o 19_o degreee_n from_o the_o horizon_n so_o that_o â—…rom_o that_o moment_n he_o approach_v near_o â—…nd_v near_o unto_o it_o then_o begin_v the_o morning-twilight_n but_o the_o evening-twilight_n end_v when_o the_o sun_n after_o his_o setâ—…ing_n come_v to_o that_o 18_o or_o 19_o degree_n â—…oresaid_a for_o than_o do_v the_o light_n turn_v â—…nto_o darkness_n 10._o from_o the_o horizon_n we_o number_v the_o elevation_n of_o the_o pole_n â—…nd_v equinoctial_a 11._o from_o the_o horiâ—…on_n be_v number_v various_a and_o divers_a â—…inds_n of_o hour_n as_o the_o italic_a and_o jewish_a nocturnal_a hour_n from_o the_o west_n part_n of_o the_o horizon_n but_o the_o babylonish_n hour_n â—…nd_v the_o jewish_a unequal_a diurnal_a hour_n â—…rom_o the_o east_n part_n chap._n vi_o of_o the_o meridian_n the_o meridian_n be_v one_o of_o the_o great_a circle_n in_o the_o sphere_n pass_v through_o the_o pole_n of_o the_o world_n and_o the_o pole_n of_o the_o horizon_n by_o the_o word_n through_o the_o pole_n of_o the_o horizon_n it_o be_v distinguish_v from_o the_o horary_a circle_n of_o which_o none_o but_o itself_o pass_v through_o the_o pole_n of_o the_o horizon_n it_o have_v acquire_v divers_a and_o sundry_a name_n by_o reason_n of_o its_o manifold_a use_n by_o astrologer_n which_o be_v not_o fit_a to_o repeat_v now_o what_o be_v say_v above_o concern_v the_o colour_n and_o circle_n of_o declination_n to_o wit_n that_o they_o be_v in_o number_n equal_a to_o the_o vertical_a point_n the_o same_o may_v be_v say_v of_o the_o meridian_n for_o as_o many_o of_o they_o may_v be_v imagine_v as_o there_o be_v vertical_a point_n which_o be_v infinite_a provide_v a_o man_n travel_n from_o east_n to_o west_n for_o if_o a_o man_n go_v from_o north_n to_o south_n or_o from_o south_n to_o north_n he_o travel_v round_o about_o the_o world_n without_o variation_n of_o his_o meridian_n the_o brazen_a meridian_n in_o the_o celestial_a or_o terrestrial_a globe_n supply_v the_o office_n of_o they_o all_o which_o be_v innumerable_a but_o in_o geographical_a table_n and_o map_n geographer_n use_v to_o extend_v one_o meridian_n through_o two_o and_o two_o opposite_a degree_n of_o the_o equinoctial_a for_o find_v out_o the_o more_o easy_o the_o latitude_n of_o place_n of_o all_o these_o meridian_n there_n be_v a_o common_a beginning_n seâ—…led_v in_o the_o fortunate_a or_o canary_n island_n because_o the_o ancient_a geographer_n deem_v those_o island_n to_o be_v the_o westmost_a part_n of_o the_o world_n and_o therefore_o they_o
fix_v their_o first_o march-stone_n there_o whence_o they_o begin_v to_o reckon_v but_o the_o late_a geographer_n have_v remove_v this_o march-stone_n 10_o degree_n more_o westerly_a and_o have_v make_v the_o common_a beginning_n of_o the_o meridian_n to_o pass_v through_o one_o of_o the_o island_n call_v osore_n whence_o they_o begin_v to_o reckon_v from_o west_n to_o east_n imitaâ—…ing_v the_o order_n of_o the_o 12_o sign_n the_o use_n of_o the_o meridian_n be_v these_o 1._o it_o distinguish_v the_o eastern_a part_n of_o the_o world_n from_o the_o western_a part_n the_o anterior_a part_n from_o the_o posterior_n part_n 2._o it_o let_v we_o know_v the_o south_n part_n of_o the_o world_n and_o the_o north_n part_n for_o when_o the_o sun_n be_v in_o the_o meridian_n â—…en_o be_v midday_n and_o when_o the_o sun_n be_v in_o the_o northern_a part_n of_o the_o meridian_n then_o be_v midnight_n 3._o it_o divide_v the_o nocturnal_a and_o diurnal_a time_n into_o two_o half_n that_o be_v when_o the_o sun_n be_v come_v to_o the_o meridian_n in_o our_o hemisphere_n as_o much_o of_o the_o day_n be_v past_a as_o what_o be_v to_o come_v and_o when_o the_o sun_n be_v come_v to_o the_o northern_a part_n of_o the_o meridian_n as_o much_o of_o the_o night_n be_v past_a as_o what_o be_v to_o come_v 4._o the_o meridian_n supply_v in_o every_o oblique_a sphere_n the_o place_n of_o the_o right_a horizon_n therefore_o as_o the_o star_n do_v ascend_v above_o the_o right_a horizon_n so_o they_o pass_v over_o the_o meridian_n and_o those_o â—…ransitions_n be_v call_v the_o right_a ascension_n of_o the_o middle_a heaven_n 5._o from_o the_o meridian_n astronomer_n begin_v their_o time._n 6._o in_o the_o meridian_n we_o find_v out_o the_o zenith_n therefore_o when_o the_o star_n come_v to_o it_o they_o be_v either_o high_a above_o the_o horizon_n and_o be_v say_v by_o astrologer_n to_o culminate_v or_o they_o be_v in_o the_o low_a and_o opposite_a part_n of_o it_o which_o be_v the_o nadir_n 7._o in_o the_o meridian_n we_o find_v out_o the_o distance_n between_o the_o tropic_n and_o the_o whole_a obliquity_n of_o the_o ecliptic_a 8._o upon_o the_o meridian_n we_o number_v the_o latitude_n of_o place_n upon_o the_o earth_n and_o likewise_o the_o elevation_n of_o the_o pole_n and_o equinoctial_a the_o elevation_n of_o the_o pole_n be_v define_v a_o arch_n of_o the_o meridian_n measure_v between_o the_o horizon_n and_o the_o apparent_a pole_n of_o the_o world_n which_o may_v be_v find_v out_o after_o the_o follow_a manner_n observe_v the_o great_a and_o least_o altitude_n of_o any_o of_o the_o star_n which_o do_v not_o set_v subtract_v the_o least_o altitude_n from_o the_o great_a and_o divide_v the_o difference_n this_o difference_n be_v subtract_v from_o the_o great_a elevation_n or_o add_v to_o the_o least_o give_v the_o true_a height_n of_o the_o pole._n december_n 17._o 1669_o i_o observe_v with_o a_o large_a quadrant_n half_o 9_o a_o clock_n at_o night_n the_o foremost_a guard-star_n when_o it_o be_v in_o the_o meridian_n and_o low_a to_o have_v 41_o degree_n 22_o have_v of_o altitude_n and_o on_o january_n 7._o 1670_o at_o 7_o a_o clock_n in_o the_o morning_n i_o find_v it_o when_o it_o be_v in_o the_o meridian_n and_o high_o to_o have_v 70_o degree_n 27_o minute_n i_o subtract_v 41_o degree_n 22_o have_v from_o 70_o degree_n 27_o have_v and_o the_o difference_n be_v 29_o degree_n 5_o minute_n divide_v this_o and_o you_o have_v 14_o degree_n 32_o have_v and_o 30_o second_o this_o be_v add_v to_o 41_o degree_n 22_o have_v give_v you_o 55_o degree_n 54_o have_v 30_o second_o or_o subtract_v 14_o degree_n 32_o have_v and_o 30_o second_o from_o 70_o degree_n 27_o have_v and_o there_o remain_v 55_o degree_n 54_o have_v and_o 30_o second_o for_o our_o height_n of_o the_o pole_n at_o edinburgh_n 9_o the_o meridian_n do_v terminate_v and_o bind_v the_o longitude_n of_o place_n as_o well_o in_o the_o terrestrial_a globe_n as_o in_o the_o map_n and_o card_n project_v in_o plano_n 10._o the_o meridian_n do_v terminate_v and_o bind_v the_o breadth_n and_o latitude_n of_o the_o zone_n and_o also_o of_o the_o climate_n 11._o we_o find_v out_o in_o the_o meridian_n the_o antipode_n the_o anteci_n and_o perieci_n chap._n vii_o of_o the_o tropic_n the_o tropic_n be_v lesser_a movable_a circle_n of_o the_o sphere_n describe_v from_o the_o solsticial_a point_n by_o the_o moâ—…ion_n of_o the_o primum_fw-la mobile_n they_o be_v call_v lesser_a because_o there_o be_v in_o the_o sphere_n great_a circle_n than_o they_o be_v they_o be_v call_v movable_a that_o they_o may_v be_v distinguish_v chief_o from_o the_o paralâ—…els_n of_o their_o horizon_n call_v almicanâ—…ars_n who_o live_v under_o the_o pole_n and_o â—…rom_o the_o ancient_a polar_n of_o those_o who_o â—…ive_v under_o the_o polar_n with_o who_o the_o tropic_n be_v equal_a to_o those_o circle_n which_o comprehend_v the_o star_n which_o never_o come_v above_o the_o horizon_n nor_o ever_o go_v under_o it_o they_o be_v two_o in_o number_n to_o wit_n the_o tropic_a of_o cancer_n and_o the_o tropic_a of_o capricorn_n the_o tropic_a of_o cancer_n be_v a_o lesser_a movable_a circle_n describe_v from_o the_o summer-solstitial-point_n of_o the_o ecliptic_a by_o the_o motion_n of_o the_o primum_fw-la mobile_n the_o tropic_a of_o capricorn_n be_v lesser_a movable_a circle_n describe_v froâ—…_n the_o winter-solstitial-point_n of_o the_o ecliptic_a by_o the_o motion_n of_o the_o primum_fw-la mobile_n the_o use_n of_o the_o tropic_n be_v these_o 1._o they_o demonstrate_v to_o we_o in_o the_o ecliptic_a the_o two_o tropical_a or_o solstic_a point_n to_o wit_n the_o beginning_n of_o cancer_n and_o the_o beginning_n of_o capricorn_n 2._o they_o terminate_v and_o bound_v the_o sun_n great_a declination_n and_o consequent_o the_o great_a obliquity_n of_o the_o ecliptic_a 3._o when_o the_o sun_n come_v to_o either_o of_o thâ—…_n two_o tropic_n he_o be_v either_o near_a tâ—…_n our_o vertical-point_n or_o further_a remove_v from_o it_o 4._o in_o a_o oblique_a sphere_n they_o lie_v parallel_n to_o the_o long_a and_o shortesâ—…_n day_n 5._o between_o the_o tropic_n iâ—…_n comprehend_v the_o torrid_a zone_n as_o well_o in_o the_o heaven_n as_o in_o the_o earth_n and_o by_o the_o same_o tropic_n the_o torrid_a zone_n be_v divide_v from_o the_o temperate_a zone_n chap._n viii_o of_o the_o polar_n the_o polar_n be_v lesser_a circle_n of_o the_o sphere_n movable_a describe_v from_o the_o pole_n of_o the_o ecliptic_a by_o the_o motion_n of_o the_o primum_fw-la mobile_n for_o this_o cause_n they_o be_v call_v the_o polar_a circle_n they_o be_v two_o in_o number_n the_o polar_a arctic_a and_o the_o polar_a antarctic_a the_o polar_a arctic_a be_v a_o lesser_a circle_n of_o the_o sphere_n movable_a describe_v from_o the_o north_n pole_n of_o the_o ecliptic_a by_o the_o motion_n of_o the_o primum_fw-la mobile_n the_o polar_a antarctic_a be_v a_o lesser_a circle_n of_o the_o sphere_n movable_a describe_v from_o the_o south_n pole_n of_o the_o ecliptic_a by_o the_o motion_n of_o the_o primum_fw-la mobile_n they_o let_v we_o see_v first_o the_o pole_n of_o the_o zodiac_n and_o they_o measure_v their_o distance_n from_o the_o pole_n of_o the_o world._n 2._o they_o bind_v the_o temperate_a zone_n and_o separat_n they_o from_o the_o cold_a zone_n which_o be_v bound_v and_o enclose_v by_o their_o circumference_n it_o be_v to_o be_v observe_v that_o the_o ancient_a astronomer_n proclus_n cleomedes_n and_o the_o rest_n have_v not_o the_o same_o description_n of_o the_o polar_n which_o we_o have_v for_o the_o ancient_n do_v not_o describe_v they_o as_o pass_v through_o the_o pole_n of_o the_o ecliptic_a but_o through_o the_o common_a section_n of_o the_o meridian_n and_o horizon_n equidistant_a to_o the_o equinoctial_a and_o therefore_o so_o much_o be_v their_o distance_n from_o the_o pole_n of_o the_o world_n aâ—…_n the_o height_n of_o the_o pole_n be_v above_o the_o horizon_n and_o by_o this_o mean_n where_o there_o be_v no_o elevation_n of_o the_o pole_n as_o in_o a_o right_a sphere_n there_o be_v no_o polar_n but_o from_o thence_o they_o be_v more_o and_o more_o gradual_o augment_v and_o enlarge_v according_a to_o the_o increment_n of_o the_o pole_n elevation_n the_o use_n of_o the_o polar_n according_a to_o the_o ancient_n be_v these_o 1._o they_o comprehend_v the_o arch_n of_o the_o elevation_n of_o the_o pole._n 2._o of_o all_o the_o parallel_n of_o the_o equinoctial_a which_o be_v always_o see_v above_o the_o horizon_n they_o be_v the_o great_a and_o of_o all_o the_o parallel_n of_o the_o equinoctial_a which_o lie_v hide_v under_o the_o horizon_n they_o be_v the_o great_a also_o but_o contraâ—…iwise_o of_o all_o the_o parallel_n of_o the_o equinoctial_a which_o arise_v and_o set_v in_o twenty_o four_o hour_n they_o be_v the_o
least_o therefore_o 3_o the_o foresay_a polar_n comprehend_v within_o their_o compass_n and_o circle_n â—…he_v whole_a star_n and_o point_n of_o heaven_n which_o be_v always_o in_o sight_n and_o do_v not_o â—…et_o hence_o there_o arise_v a_o threefold_a â—…istinction_n of_o the_o star_n 1._o there_o be_v â—…ome_v which_o have_v a_o perpetual_a day_n and_o â—…ever_o set_v or_o fall_v under_o the_o horizon_n to_o â—…it_v those_o which_o be_v comprehend_v within_o the_o circle_n of_o the_o polar_a arctic_a 2._o there_o be_v other_o which_o have_v a_o perpetual_a night_n which_o never_o rise_v or_o come_v â—…p_n above_o the_o horizon_n to_o wit_v all_o those_o which_o be_v include_v within_o the_o circle_n of_o â—…he_n polar_a antarctic_a there_o be_v 3._o other_o which_o both_o rise_n and_o set_v in_o four_o â—…nd_v twenty_o hour_n to_o wit_v those_o which_o â—…ither_o on_o this_o side_n or_o that_o side_n of_o the_o equinoctial_a tend_v towards_o and_o come_v near_a to_o the_o foresay_a polar_n chap._n ix_o concern_v other_o circle_n of_o the_o sphere_n both_o great_a and_o lesser_a which_o can_v be_v convenient_o draw_v upon_o it_o beside_o the_o circle_n of_o the_o sphere_n hitherto_o explain_v there_o be_v yet_o innumerable_a more_o both_o of_o the_o great_a and_o lesser_a sort_n which_o astronomer_n have_v excogitated_a for_o attain_v a_o more_o perfect_a knowledge_n of_o the_o heavenly_a motion_n 1._o there_o be_v of_o the_o great_a sort_n vertical_n which_o pass_v through_o every_o point_n oâ—_n the_o horizon_n cut_v one_o another_o there_o which_o by_o the_o arabian_n be_v call_v azimuth_n 2._o there_o be_v the_o horary_a circle_n which_o divide_v the_o heaven_n into_o four_o and_o twenty_o part_n which_o be_v oâ—_n three_o sort_n for_o either_o they_o have_v the_o beginning_n in_o the_o meridian_n and_o paâ—â—_n through_o the_o pole_n of_o the_o world_n or_o the_o have_v their_o beginning_n in_o the_o east_n oâ—_n west-part_n of_o the_o horizon_n by_o whicâ—_n mean_v they_o touch_v light_o the_o two_o circle_n lie_v parallel_n to_o the_o equinoctial_a of_o which_o one_o be_v the_o great_a of_o all_o which_o be_v always_o see_v above_o the_o horizon_n the_o other_o the_o great_a of_o all_o which_o be_v not_o see_v above_o the_o horizon_n or_o last_o they_o have_v their_o beginning_n in_o the_o horizon_n but_o neither_o go_v through_o the_o pole_n of_o the_o world_n nor_o go_v near_o to_o the_o foresay_a parallel_n but_o divide_v all_o the_o segment_n of_o the_o parallel_n which_o be_v above_o or_o below_o the_o horizon_n into_o twelve_o equal_a part_n 3._o there_o be_v circle_n of_o declination_n which_o pass_v through_o the_o pole_n of_o the_o world_n and_o every_o point_n of_o the_o equinoctial_a there_o be_v 4._o circle_n of_o latitude_n which_o pass_v through_o the_o pole_n of_o the_o ecliptic_a and_o every_o one_o of_o his_o degree_n the_o lesser_a circle_n be_v infinite_a also_o for_o there_o be_v no_o great_a circle_n which_o have_v not_o his_o own_o parallel_n as_o first_o the_o horizon_n which_o have_v circle_n of_o altitude_n call_v by_o the_o arabian_n almicanthar_n the_o equinoctial_a have_v its_o own_o parallel_n to_o wit_n describe_v by_o the_o primum_fw-la mobile_n from_o all_o and_o whatsoever_o point_n be_v in_o the_o heaven_n so_o have_v the_o zodiac_n his_o parallel_n describe_v about_o the_o pole_n of_o the_o ecliptic_a which_o parallel_n every_o star_n or_o point_n of_o the_o heaven_n according_a to_o the_o proper_a motion_n of_o the_o eight_o sphere_n do_v describe_v and_o many_o more_o be_v there_o invent_v by_o astronomer_n for_o astronomical_a use_n chap._n x._o of_o the_o zone_n to_o the_o doctrine_n of_o the_o sphere_n be_v common_o annex_v the_o geographical_a tractat_fw-la of_o the_o zone_n the_o zone_n therefore_o be_v nothing_o else_o but_o as_o much_o bound_n of_o the_o heaven_n or_o of_o the_o earth_n as_o be_v comprehend_v between_o both_o the_o tropic_n or_o between_o either_o of_o the_o two_o tropic_n and_o the_o next_o polar_a or_o between_o either_o of_o the_o two_o polar_n and_o the_o neighbour_a pole._n therefore_o the_o zone_n be_v either_o celestial_a or_o terrestrial_a the_o celestial_a zone_n be_v bound_v by_o themselves_o and_o their_o own_o circle_n in_o the_o heaven_n the_o terrestrial_a zone_n lie_v direct_o under_o the_o same_o place_n of_o the_o heaven_n they_o be_v five_o in_o number_n one_o torrid_a two_o temperate_a and_o two_o frigid_a the_o torrid_a zone_n be_v that_o space_n of_o the_o heaven_n or_o the_o earth_n comprehend_v between_o the_o two_o tropic_n this_o be_v divide_v into_o two_o part_n of_o which_o one_o be_v call_v the_o northern_a the_o other_o the_o southern_a part_n it_o be_v call_v torrid_a because_o here_o the_o ray_n of_o the_o sun_n be_v more_o perpendicular_a and_o so_o hot_a that_o the_o inhabitant_n be_v in_o a_o manner_n scorch_v and_o burn_v up_o with_o heat_n the_o temperate_a zone_n be_v that_o space_n of_o the_o heaven_n or_o of_o the_o earth_n comprehend_v between_o either_o of_o the_o two_o tropic_n and_o the_o neighbour_a polar_n and_o that_o which_o be_v include_v between_o the_o tropic_a of_o cancer_n and_o the_o polar_a arctic_a be_v call_v the_o temperate_a northern_a zone_n wherein_o be_v contain_v all_o europe_n almost_o and_o a_o great_a part_n of_o asia_n and_o also_o a_o part_n of_o america_n but_o that_o which_o be_v include_v between_o the_o tropic_a of_o capricorn_n and_o the_o antarctic_a polar_a be_v call_v the_o southern_a temperate_a zone_n this_o contain_v more_o sea_n and_o less_o land_n they_o be_v call_v temperate_a because_o the_o ray_n of_o the_o sun_n be_v more_o oblique_a there_o be_v not_o such_o a_o reflection_n of_o heat_n but_o offer_v a_o most_o commodious_a dwelling_n to_o the_o inhabitant_n the_o frigid_a zone_n be_v that_o space_n of_o the_o heaven_n and_o of_o the_o earth_n comprehend_v between_o either_o of_o the_o polar_n and_o the_o neighbour_a pole_n of_o the_o world._n and_o that_o bound_n which_o be_v include_v between_o the_o polar_a arctic_a and_o the_o north_n pole_n be_v call_v the_o northern_a frigid_a zone_n and_o that_o bound_n which_o be_v include_v between_o the_o polar_a antarctic_a and_o the_o south_n pole_n be_v call_v the_o southern_a frigid_a zone_n they_o be_v call_v frigid_a because_o the_o ray_n of_o the_o sun_n be_v most_o oblique_a and_o be_v absent_a almost_o half_a a_o year_n so_o that_o all_o thing_n become_v rigid_a and_o stiff_a with_o frost_n ice_n and_o snow_n in_o this_o zone_n lie_v island_n and_o greenland_n but_o in_o the_o southern_a cold_a zone_n the_o part_n be_v unknown_a to_o we_o the_o inhabitant_n of_o the_o five_o zone_n have_v obtain_v divers_a name_n for_o those_o who_o inhabit_v the_o torrid_a zone_n be_v call_v amphiscii_n as_o have_v a_o shadow_n on_o both_o side_n i_o say_v on_o both_o side_n in_o respect_n of_o the_o vertical_a point_n for_o the_o sun_n with_o they_o be_v sometime_o on_o this_o side_n and_o sometime_o on_o that_o side_n of_o their_o vertical_a point_n sometime_o the_o shadow_n of_o their_o dial_n be_v project_v from_o south_n to_o north_n and_o sometime_o from_o north_n to_o south_n when_o he_o be_v in_o the_o meridian_n the_o inhabitant_n of_o the_o temperate_a zone_n be_v call_v heteroscii_n as_o have_v but_o one_o shadow_n for_o at_o 12_o a_o clock_n in_o the_o day_n the_o shadow_n be_v either_o casten_z towards_o the_o north_n as_o with_o we_o or_o towards_o the_o south_n as_o with_o those_o who_o dwell_v in_o the_o southern_a temperate_a zone_n but_o those_o who_o live_v in_o the_o frigid_a zone_n be_v call_v periscii_n as_o have_v a_o shadow_n which_o go_v round_o about_o they_o because_o they_o have_v the_o sun_n for_o several_a month_n of_o the_o year_n above_o their_o horizon_n and_o the_o heaven_n there_o like_o a_o millstone_n be_v whirl_v about_o so_o that_o the_o sun_n and_o star_n describe_v parallel_n to_o the_o horizon_n and_o therefore_o in_o four_o and_o twenty_o hour_n he_o run_v about_o without_o rise_v and_o set_v and_o project_n his_o shadow_n into_o a_o orb_n or_o circle_n there_o be_v likewise_o the_o antipode_n anteci_n and_o perieci_n antipode_n be_v those_o who_o have_v the_o same_o meridian_n but_o dwell_v in_o point_n of_o it_o diametraliter_fw-la opposite_a and_o be_v under_o opposite_a parallel_n to_o wit_n in_o a_o oblique_a sphere_n of_o which_o the_o one_o be_v southern_a the_o other_o northern_a these_o follow_a phenomena_n be_v proper_a to_o they_o 1._o though_o they_o have_v the_o same_o rational_a horizon_n yet_o behold_v the_o opposite_a face_n all_o thing_n fall_v out_o to_o they_o contrariwise_o for_o when_o we_o have_v day_n and_o midday_n our_o antipode_n have_v night_n and_o midnight_n when_o we_o have_v summer_n they_o have_v winter_n when_o the_o sun_n rise_v to_o we_o he_o set_v to_o they_o we_o have_v
which_o set_v with_o the_o sun._n subtract_v the_o lesser_a from_o the_o great_a and_o half_a the_o difference_n be_v the_o ascensional_a difference_n which_o add_v to_o six_o hour_n in_o the_o summer_n half_a year_n but_o subtract_v therefrom_o in_o the_o winter_n half_a year_n give_v half_o the_o diurnal_a arch_n who_o double_a be_v the_o whole_a diurnal_a arch_n and_o the_o compliment_n of_o the_o diurnal_a arch_n to_o 24_o hour_n be_v the_o nocturnal_a arch._n for_o example_n the_o ten_o day_n of_o april_n 1687_o the_o oblique_a ascension_n of_o the_o sun_n be_v in_o the_o first_o degree_n of_o taurus_n be_v 10_o deg_n 21._o m._n the_o oblique_a descension_n be_v 45_o deg_n 27_o m._n who_o difference_n be_v 35_o deg_n 6._o m._n who_o half_a be_v 17_o deg_n 33_o m._n the_o ascensional_a difference_n which_o be_v add_v to_o 90_o deg_n or_o 6_o hour_n be_v 107_o deg_n 33_o m._n which_o make_v 7_o hour_n 10_o m._n fere_n for_o the_o time_n of_o the_o sun_n set_v which_o be_v always_o half_a the_o diurnal_a arch._n therefore_o the_o diurnal_a arch_n be_v 14_o hour_n 20_o m._n which_o take_v from_o 24_o hour_n there_o remain_v 9_o hour_n 40_o m._n for_o the_o nocturnal_a arch_n require_v note_v that_o the_o ascensional_a difference_n add_v to_o the_o oblique_a ascension_n in_o the_o summer_n half_a year_n but_o subtract_v from_o it_o in_o the_o winter_n half_a year_n give_v the_o right_a ascension_n of_o the_o sun_n or_o any_o of_o the_o star_n what_o be_v say_v of_o the_o day_n in_o respect_n of_o the_o sun_n may_v be_v most_o commodious_o apply_v to_o the_o star_n for_o the_o day_n of_o a_o star_n be_v right_o call_v the_o space_n of_o time_n wherein_o it_o be_v above_o the_o horizon_n and_o the_o night_n of_o a_o star_n the_o space_n of_o time_n wherein_o it_o be_v below_o the_o horizon_n concern_v the_o day_n of_o the_o fix_a star_n let_v the_o follow_a theorem_n be_v observe_v 1._o in_o a_o right_a sphere_n the_o star_n have_v a_o perpetual_a equinox_n 2._o but_o in_o a_o oblique_a sphere_n the_o fix_a star_n who_o north_n declination_n be_v great_a than_o the_o compliment_n of_o the_o altitude_n of_o the_o pole_n be_v say_v to_o have_v a_o eternal_a day_n but_o those_o star_n who_o south_n declination_n exceed_v the_o compliment_n of_o the_o altitude_n of_o the_o pole_n be_v say_v to_o have_v a_o eternal_a night_n the_o intermediate_v star_n have_v the_o course_n of_o rise_v and_o set_v 3._o in_o a_o parallel_n sphere_n the_o fix_a star_n be_v say_v to_o have_v eternal_a day_n and_o eternal_a night_n day_n civil_a be_v call_v the_o space_n of_o time_n of_o one_o revolution_n of_o the_o equinoctial_a which_o according_a to_o every_o nation_n or_o country_n be_v divers_a way_n begin_v and_o make_v use_v of_o for_o as_o there_o be_v various_a and_o divers_a nation_n in_o the_o world_n so_o each_o one_o have_v a_o different_a way_n of_o begin_v their_o hour_n for_o the_o jew_n by_o divine_a institution_n begin_v their_o day_n from_o the_o set_n of_o the_o sun_n which_o custom_n the_o italian_n do_v observe_v the_o babylonian_n begin_v their_o day_n from_o sun_n rise_v who_o practice_n the_o norinberger_n the_o people_n call_v the_o umbri_n and_o the_o egyptian_n do_v imitate_v the_o arabian_n as_o the_o astronomer_n begin_v their_o day_n from_o the_o meridian_n the_o roman_n from_o midnight_n the_o german_n the_o frenche_n and_o spainards_n begin_v their_o day_n from_o the_o meridian_n and_o midnight_n for_o their_o clock_n and_o watch_n be_v so_o contrive_v that_o they_o return_v from_o one_o a_o clock_n in_o the_o nighttime_n to_o twelve_o a_o clock_n in_o the_o daytime_n and_o from_o one_o a_o clock_n in_o the_o daytime_n to_o twelve_o a_o clock_n at_o nighttime_n their_o day_n be_v divide_v as_o the_o astronomical_a day_n into_o one_o artificial_a day_n and_o likewise_o into_o forenoon_n and_o afternoon_n and_o because_o hour_n be_v part_n of_o the_o day_n therefore_o we_o must_v speak_v a_o little_a of_o they_o the_o hour_n be_v the_o twenty_o and_o four_o part_n of_o the_o natural_a day_n or_o the_o space_n of_o time_n wherein_o the_o twenty_o and_o four_o part_n of_o the_o equinoctial_a or_o 15_o degree_n thereof_o rise_v above_o the_o horizon_n but_o this_o definition_n be_v not_o sufficient_a because_o it_o do_v not_o agree_v to_o all_o hour_n for_o every_o twelve_o part_n of_o every_o day_n and_o every_o night_n whatsoever_o be_v call_v by_o the_o jew_n and_o the_o ancient_n a_o hour_n but_o 15_o degree_n of_o the_o equinoctial_a do_v not_o always_o ascend_v above_o the_o horizon_n every_o one_o of_o these_o hour_n but_o sometime_o more_o and_o sometime_o few_o as_o will_v appear_v afterward_o therefore_o a_o hour_n may_v rather_o be_v define_v thus_o a_o certain_a part_n of_o the_o artificial_a day_n and_o night_n make_v use_v of_o by_o divers_a nation_n after_o a_o divers_a manner_n that_o it_o may_v be_v know_v general_o what_o the_o hour_n be_v for_o in_o effect_n that_o definition_n agree_v only_o to_o to_o those_o hour_n which_o be_v call_v horâ—…_n aequales_fw-la equal_a hour_n the_o hour_n then_o which_o be_v call_v unequal_a aught_o to_o be_v define_v thus_o the_o twelve_o part_n of_o every_o artificial_a day_n and_o night_n therefore_o according_a to_o the_o divers_a season_n of_o the_o year_n the_o hour_n be_v sometime_o short_a and_o sometime_o long_o in_o summer_n long_o and_o in_o winter_n short_a as_o be_v thâ—…_n jewish_a hour_n for_o they_o divide_v both_o the_o day_n and_o the_o night_n into_o twelve_o part_n both_o in_o summer_n and_o in_o winter_n call_v the_o rise_n of_o the_o sun_n the_o beginning_n of_o the_o first_o hour_n and_o consequent_o nine_o their_o three_o hour_n twelve_o their_o six_o hour_n three_o a_o clock_n in_o the_o afternoon_n their_o nine_o hour_n and_o the_o set_n of_o the_o sun_n the_o end_n of_o their_o twelve_o hour_n by_o which_o mean_n their_o hour_n must_v be_v far_o long_o in_o summer_n than_o in_o winter_n the_o equal_a hour_n be_v of_o three_o sort_n for_o some_o take_v their_o beginning_n from_o the_o set_n of_o the_o sun_n as_o the_o italian_a hour_n other_o take_v their_o beginning_n from_o the_o rise_n of_o the_o sun_n as_o be_v the_o babylonish_n hour_n and_o the_o hour_n of_o the_o city_n of_o norimberg_n who_o from_o the_o rise_n of_o the_o sun_n begin_v the_o number_n of_o the_o hour_n of_o the_o day_n the_o circle_n of_o which_o hour_n do_v light_o touch_v the_o great_a parallel_n of_o all_o which_o do_v appear_v above_o the_o horizon_n and_o of_o all_o which_o do_v not_o appear_v last_o other_o do_v take_v their_o beginning_n from_o the_o meridian_n which_o astronomer_n make_v use_v of_o and_o these_o nation_n which_o either_o take_v their_o beginning_n of_o hour_n from_o the_o superior_a part_n of_o the_o same_o circle_n or_o from_o the_o inferior_a part_n chap._n xiii_o concern_v year_n as_o hour_n make_v up_o day_n so_o day_n make_v up_o year_n therefore_o we_o must_v speak_v somewhat_o of_o year_n the_o year_n than_o be_v twofold_a astronomical_a and_o political_n the_o astronomical_a year_n be_v the_o space_n of_o time_n wherein_o the_o sun_n return_v either_o to_o the_o same_o point_n of_o the_o ecliptic_a or_o to_o the_o same_o fix_a star._n and_o this_o be_v twofold_a the_o tropical_a year_n call_v annus_fw-la vertens_fw-la or_o the_o syderial_a year_n annus_fw-la vertens_fw-la be_v a_o space_n of_o time_n wherein_o the_o sun_n leave_v some_o point_n of_o the_o ecliptic_a return_v again_o to_o the_o same_o point_n the_o quantity_n of_o this_o year_n be_v changeable_a for_o sometime_o it_o be_v more_o and_o sometime_o it_o be_v less_o between_o these_o two_o extreme_n the_o middle_a year_n contain_v 365_o day_n hour_n 5_o m._n 49_o sec._n 15._o three_o 46._o but_o the_o true_a or_o apparent_a year_n be_v sometime_o 365_o day_n hour_n 5_o min._n 56._o sec._n 53_o three_o 1._o sometime_o it_o be_v 365_o day_n hour_n 5_o min._n 42_o sec._n 28_o three_o 27._o the_o syderial_a year_n be_v a_o space_n of_o time_n wherein_o the_o sun_n under_o the_o starry_a sky_n return_v to_o the_o same_o fix_a star._n the_o quantity_n of_o this_o year_n be_v 365_o day_n hour_n 6_o min._n 6_o sec._n 39_o it_o be_v always_o equal_a to_o itself_o and_o therefore_o the_o measure_n of_o the_o year_n call_v annus_fw-la vertens_fw-la the_o beginning_n of_o this_o annus_fw-la vertens_fw-la be_v take_v from_o the_o vernal_a equinox_n but_o the_o begin_n of_o the_o syderial_a year_n from_o the_o first_o star_n of_o aries_n the_o political_a year_n be_v a_o annual_a space_n of_o time_n which_o be_v either_o accommodate_v to_o the_o course_n of_o the_o sun_n or_o the_o moon_n or_o to_o both_o according_a to_o the_o common_a reckon_n of_o several_a country_n
and_o two_o winter_n but_o unequal_a as_o appear_v from_o the_o various_a situation_n of_o the_o parallel_n 9_o the_o long_a day_n be_v not_o when_o the_o sun_n be_v in_o the_o high_a solstice_n but_o in_o the_o tropic_a of_o cancer_n 10._o there_o be_v five_o different_a shadow_n as_o we_o observe_v in_o the_o first_o position_n 11._o the_o end_n or_o extremity_n of_o the_o gnomon_n by_o its_o shadow_n when_o the_o sun_n be_v out_o of_o the_o equinoctial_a describe_v as_o in_o the_o first_o position_n the_o figure_n call_v hyperbole_n but_o the_o opposite_a side_n be_v not_o equal_a as_o there_o but_o unequal_a 12._o in_o any_o part_n of_o this_o position_n where_o the_o elevation_n of_o the_o pole_n be_v less_o than_o the_o declination_n of_o the_o sun_n the_o shadow_n of_o a_o style_n perpendicular_o erect_v upon_o a_o plain_a may_v have_v a_o natural_a visible_a retrocession_n in_o the_o matter_n of_o ahaz_n his_o dial_n the_o retrogradation_n of_o the_o shadow_n be_v miraculous_a because_o it_o be_v do_v without_o and_o not_o within_o the_o tropic_n neither_o be_v it_o possible_a in_o nature_n it_o can_v happen_v but_o where_o the_o elevation_n of_o the_o pole_n be_v less_o than_o the_o sun_n declination_n which_o be_v only_o within_o the_o tropic_n but_o the_o foresay_a dial_n be_v place_v far_o without_o to_o wit_n under_o the_o latitude_n of_o 35_o degree_n chap._n xvii_o of_o the_o phenomena_n of_o the_o three_o position_n 1._o all_o the_o star_n which_o be_v comprehend_v within_o the_o north_n polar_a remain_v always_o above_o the_o horizon_n neither_o do_v they_o ever_o set_v unless_o it_o be_v by_o a_o general_a set_a heliace_n and_o contrariwise_o all_o the_o star_n which_o be_v comprehend_v within_o the_o south_n polar_a have_v a_o perpetual_a night_n therefore_o the_o polar_n according_a to_o the_o ancient_n be_v now_o equal_a to_o our_o polar_n 2._o the_o long_a artificial_a day_n be_v when_o the_o sun_n pass_v over_o our_o zenith_n the_o short_a when_o the_o sun_n be_v far_a in_o the_o meridian_n remove_v from_o it_o 3._o once_o a_o year_n only_o be_v the_o sun_n vertical_a to_o wit_n when_o he_o be_v in_o the_o begin_n of_o cancer_n 4._o the_o sun_n in_o the_o meridian_n never_o descend_v from_o the_o zenith_n towards_o the_o north_n but_o return_v from_o the_o tropic_a of_o cancer_n he_o be_v always_o in_o the_o south_n 5._o there_o be_v here_o but_o two_o solstice_n one_o high_a another_o low_a the_o high_a when_o the_o sun_n be_v in_o the_o tropic_a of_o cancer_n the_o low_a when_o the_o sun_n be_v in_o the_o tropic_a of_o capricorn_n 6._o the_o day_n be_v long_a when_o the_o sun_n be_v in_o the_o tropic_a of_o cancer_n it_o be_v short_a when_o the_o sun_n be_v in_o the_o tropic_a of_o capricorn_n 7._o there_o be_v one_o summer_n when_o the_o sun_n be_v in_o the_o zenith_n and_o one_o winter_n when_o he_o be_v in_o the_o winter_n solstice_n 8._o they_o have_v four_o different_a shadow_n one_o perpendicular_a one_o oriental_a one_o occidental_a and_o one_o meridional_a here_o begin_v the_o heteroscii_n for_o the_o meridional_a shadow_n begin_v there_o to_o decay_v that_o be_v the_o shadow_n project_v towards_o the_o south_n 9_o the_o extremity_n or_o end_n of_o their_o gnomon_n upon_o their_o dial_n describe_v also_o the_o figure_n call_v hyperbole_n the_o side_n opposite_a be_v unequal_a chap._n xviii_o of_o the_o phenomena_n of_o the_o four_o position_n as_o the_o arctic_a and_o antarctic_a of_o the_o ancient_n be_v great_a than_o our_o polar_n so_o there_o be_v more_o star_n in_o this_o position_n of_o the_o sphere_n see_v perpetual_o and_o more_o perpetual_o lurk_v under_o the_o horizon_n than_o in_o the_o last_o position_n 2._o the_o unequality_n of_o day_n and_o night_n be_v also_o augment_v the_o artificial_a day_n be_v at_o the_o long_a when_o the_o sun_n come_v near_a to_o our_o zenith_n and_o at_o the_o short_a when_o he_o be_v further_a remove_v from_o it_o and_o as_o the_o short_a artificial_a day_n can_v be_v less_o than_o 13_o hour_n and_o a_o half_a so_o the_o long_a day_n can_v be_v 24_o hour_n this_o least_o artificial_a day_n be_v true_o the_o long_a day_n our_o vertical_a point_n come_v near_o to_o the_o tropic_a it_o be_v call_v the_o least_o artificial_a day_n because_o it_o be_v the_o short_a of_o all_o the_o long_a day_n which_o can_v arise_v from_o the_o variation_n of_o the_o vertical_a point_n between_o the_o tropic_a and_o the_o polar_a and_o therefore_o itis_fw-la not_o call_v minimum_n the_o least_o in_o respect_n of_o the_o rest_n of_o the_o day_n of_o the_o same_o elevation_n of_o the_o pole_n but_o in_o respect_n of_o the_o rest_n of_o the_o long_a day_n which_o may_v be_v find_v between_o the_o tropic_a and_o polar_a the_o long_a day_n in_o this_o four_o position_n of_o the_o sphere_n the_o zenith_n come_v near_o to_o our_o tropic_n can_v be_v less_o than_o 13_o hour_n and_o a_o half_a as_o the_o long_a day_n can_v contain_v 24_o hour_n for_o this_o come_v to_o pass_v when_o the_o zenith_n be_v in_o the_o polar_a therefore_o we_o must_v read_v as_o the_o short_a artificial_a long_a day_n can_v be_v less_o than_o 13_o hour_n and_o a_o half_a etc._n etc._n 3._o the_o sun_n can_v never_o come_v to_o their_o zenith_n neither_o can_v he_o ever_o touch_v light_o stringere_fw-la their_o horizon_n when_o he_o be_v in_o the_o meridian_n 4._o there_o be_v two_o solstice_n one_o when_o the_o sun_n be_v in_o cancer_n and_o high_a another_o low_a when_o he_o be_v in_o the_o tropic_a of_o capricorn_n 5._o there_o be_v one_o summer_n and_o one_o winter_n 6._o there_o be_v only_o three_o different_a shadow_n one_o oriental_a the_o second_o occidental_a and_o the_o three_o northern_a 7._o the_o extremity_n or_o end_n of_o their_o gnomon_n fix_v upon_o the_o ground_n perpendicular_o describe_v as_o yet_o hyperbole_n chap._n xix_o of_o the_o phenomena_n of_o the_o five_o position_n all_o the_o star_n who_o distance_n from_o the_o equinoctial_a be_v great_a than_o the_o obliquity_n of_o the_o ecliptic_a either_o do_v not_o set_v under_o the_o horizon_n if_o they_o be_v northern_a star_n and_o do_v not_o rise_v above_o the_o horizon_n if_o they_o be_v southern_a star_n therefore_o the_o arctic_a and_o antarctic_a of_o the_o ancient_n be_v equal_a to_o the_o tropic_n 2._o the_o long_a day_n contain_v 24_o hour_n and_o then_o there_o be_v no_o night_n and_o contrariwise_o the_o long_a night_n consist_v of_o twenty_o and_o four_o hour_n and_o the_o artificial_a short_a day_n be_v nothing_o 3._o the_o sun_n every_o year_n touch_v light_o the_o border_n of_o the_o horizon_n twice_o without_o rise_v and_o set_v namely_o when_o he_o be_v in_o the_o tropic_n 4._o the_o sun_n at_o twelve_o a_o clock_n in_o the_o day_n be_v always_o south_n nevertheless_o when_o he_o be_v in_o the_o tropic_a of_o cancer_n the_o half_a of_o his_o body_n may_v be_v see_v in_o the_o north_n at_o 12_o a_o clock_n at_o night_n 5._o there_o be_v here_o two_o solstice_n one_o high_a in_o cancer_n the_o other_o low_o in_o capricorn_n but_o according_a to_o the_o similitude_n of_o solstice_n which_o be_v in_o other_o zone_n we_o may_v say_v there_o be_v three_o solstice_n there_o one_o high_a in_o cancer_n when_o the_o sun_n be_v high_a in_o the_o meridian_n to_o wit_n 47_o degree_n above_o the_o horizon_n which_o be_v the_o distance_n of_o the_o tropic_n there_o be_v two_o low_a of_o which_o one_o be_v in_o the_o same_o tropic_a of_o cancer_n towards_o the_o north_n when_o he_o touch_v light_o the_o border_n of_o the_o horizon_n the_o other_o in_o the_o tropic_a of_o capricorn_n where_o he_o also_o light_o touch_v the_o border_n of_o the_o horizon_n 6._o there_o be_v one_o summer_n and_o one_o winter_n 7._o there_o be_v four_o different_a shadow_n one_o eastern_a one_o western_a one_o northern_a and_o one_o southern_a though_o this_o happen_v but_o once_o a_o year_n the_o sun_n shine_v with_o the_o half_a only_o of_o his_o ray_n which_o make_v the_o light_n more_o obscure_a and_o dark_a than_o when_o he_o shine_v with_o his_o full_a ray_n here_o begin_v the_o heteroscii_n 8._o the_o extremity_n or_o end_n of_o the_o gnomon_n describe_v the_o figure_n call_v parabola_fw-la upon_o the_o horizontal_n dial_n but_o a_o hyperbole_n so_o soon_o as_o the_o sun_n be_v go_v from_o the_o equinoctial_a whereas_o on_o all_o other_o plain_n he_o describe_v always_o straight_o and_o right_a line_n chap._n xx._n of_o the_o phenomena_n of_o the_o six_o position_n there_o be_v very_o few_o star_n which_o can_v rise_v or_o set_v to_o wit_n those_o only_a who_o declination_n be_v less_o than_o the_o distance_n of_o the_o tropic_n because_o the_o arctic_a and_o antarctic_a circle_n comprehend_v within_o they_o the_o star_n which_o
the_o oblique_a and_o right_a circle_n of_o the_o sphere_n it_o be_v call_v by_o divers_a name_n for_o sometime_o it_o be_v call_v the_o equator_fw-la sometime_o the_o equinoctial_a and_o sometime_o the_o middle_a and_o great_a of_o the_o parallel_n the_o use_v and_o office_n of_o the_o equinoctial_a be_v these_o 1._o it_o measure_v the_o first_o motion_n for_o this_o circle_n of_o all_o the_o circle_n of_o the_o sphere_n under_o any_o position_n whatsoever_o move_v equal_o and_o therefore_o it_o ought_v to_o be_v also_o the_o measure_n of_o time_n it_o be_v most_o fit_a for_o determine_v the_o quantity_n of_o the_o artificial_a and_o natural_a day_n for_o this_o cause_n it_o be_v that_o the_o degree_n of_o the_o equinoctial_a be_v call_v by_o some_o tempora_fw-la time_n 2._o it_o point_v forth_o to_o we_o in_o the_o ecliptic_a the_o two_o equinoctial_a point_n those_o point_n in_o which_o the_o equinoctial_a and_o ecliptic_a cut_v one_o another_o in_o the_o begin_n of_o aries_n and_o libra_n for_o when_o the_o sun_n come_v to_o these_o point_n the_o day_n and_o the_o night_n be_v of_o equal_a length_n over_o all_o the_o earth_n which_o fall_v out_o on_o the_o 10_o or_o 11_o of_o march_n and_o on_o the_o 13_o or_o 14_o of_o september_n 3._o that_o which_o be_v anomolous_a and_o irregular_a in_o the_o oblique_a motion_n of_o the_o zodiac_n be_v reduce_v to_o a_o sure_a rule_n by_o the_o help_n of_o the_o equinoctial_a 4._o it_o divide_v the_o sphere_n into_o two_o equal_a part_n the_o one_o call_v the_o north_n part_n in_o which_o be_v the_o pole_n name_v polus_n septentrionalis_n boreus_n or_o articus_n the_o other_o call_v the_o south_n part_n in_o which_o be_v the_o pole_n name_v polus_n australis_fw-la meridionalis_fw-la or_o antarticus_n 5._o by_o this_o mean_n it_o divide_v the_o zodiac_n into_o six_o sign_n call_v northern_a sign_n and_o into_o other_o six_o call_v southern_a sign_n 6._o from_o the_o equinoctial_a be_v number_v the_o declination_n of_o all_o and_o whatsoever_o point_v in_o heaven_n as_o well_o south_n as_o north._n the_o declination_n of_o any_o point_n or_o star_n be_v a_o arch_n of_o a_o circle_n of_o declination_n measure_v between_o the_o equinoctial_a and_o the_o say_a point_n or_o centre_n of_o the_o say_v star._n circle_n of_o declination_n be_v of_o the_o great_a circle_n in_o the_o sphere_n movable_a pass_v through_o the_o pole_n of_o the_o world_n and_o any_o point_n give_v 7._o upon_o the_o equinoctial_a we_o reckon_v the_o right_a ascension_n of_o any_o or_o whatsoever_o point_n in_o heaven_n right_o ascension_n be_v nothing_o else_o but_o a_o arch_n of_o the_o equinoctial_a measure_v between_o the_o first_o point_n of_o aries_n and_o that_o circle_n of_o declination_n which_o pass_v through_o the_o point_n give_v 8._o upon_o the_o same_o equinoctial_a we_o measure_v the_o oblique_a ascension_n and_o descension_n of_o any_o point_n in_o heaven_n whatsoever_o oblique_a ascension_n be_v a_o arch_n of_o the_o equinoctial_a measure_v between_o the_o first_o point_n of_o aries_n and_o that_o point_v of_o the_o equinoctial_a which_o rise_v in_o the_o same_o moment_n of_o time_n with_o the_o point_n give_v oblique_a descension_n be_v a_o arch_n of_o the_o equinoctial_a measure_v between_o the_o point_n foresay_a and_o that_o point_v of_o the_o equinoctial_a which_o set_v in_o the_o same_o moment_n of_o time_n with_o the_o point_n give_v 9_o upon_o the_o equinoctial_a we_o count_v and_o reckon_v the_o ascensional_a difference_n which_o be_v nothing_o else_o but_o a_o arch_n of_o the_o equinoctial_a by_o which_o right_a ascension_n differ_v from_o oblique_a 10._o upon_o the_o equinoctial_a we_o measure_v the_o rise_n and_o set_v amplitude_n this_o rise_n and_o set_v amplitude_n be_v nothing_o else_o but_o a_o arch_n of_o the_o horizon_n measure_v between_o the_o rise_n or_o set_v of_o the_o equinoctial_a and_o the_o rise_n or_o set_v of_o any_o star_n or_o point_v give_v 11._o upon_o the_o equinoctial_a we_o number_v the_o longitude_n of_o place_n and_o upon_o the_o same_o we_o reckon_v the_o latitude_n of_o place_n the_o longitude_n of_o a_o place_n be_v a_o arch_n of_o the_o equinoctial_a measure_v between_o the_o first_o meridian_n and_o the_o meridian_n of_o the_o place_n the_o latitude_n of_o a_o place_n be_v a_o arch_n of_o the_o meridian_n measure_v between_o the_o equinoctial_a and_o zenith_n of_o the_o place_n 12._o the_o equinoctial_a be_v most_o useful_a for_o make_v of_o sun-dials_n for_o there_o must_v be_v as_o many_o hour_n upon_o the_o plain_a as_o there_o be_v 15_o degree_n in_o the_o equinoctial_a four_o and_o twenty_o time_n number_v chap._n iii_o of_o the_o zodiac_n the_o zodiac_n be_v one_o of_o the_o great_a circle_n of_o the_o sphere_n movable_a under_o which_o the_o planet_n perpetual_o haunt_v the_o first_o and_o second_o difference_n be_v add_v as_o in_o the_o definition_n of_o the_o equinoctial_a the_o three_o which_o be_v in_o these_o word_n under_o which_o the_o planet_n perpetual_o haunt_v do_v distinguish_v the_o zodiac_n from_o all_o other_o circle_n for_o it_o may_v come_v to_o pass_v that_o this_o or_o that_o planet_n by_o his_o proper_a motion_n may_v be_v under_o the_o meridian_n may_v be_v under_o some_o horary_a circle_n may_v touch_v light_o the_o horizon_n but_o that_o be_v not_o always_o nor_o do_v they_o always_o abide_v in_o the_o same_o situation_n but_o their_o stay_n be_v perpetual_a under_o the_o zodiac_n and_o because_o the_o planet_n wander_v in_o the_o heaven_n viâ_fw-la obliquâ_fw-la therefore_o this_o circle_n be_v make_v oblique_a and_o see_v in_o this_o obliquity_n they_o make_v digression_n from_o this_o side_n to_o that_o side_n and_o from_o that_o to_o this_o therefore_o astronomer_n have_v grant_v to_o this_o circle_n latitude_n whereby_o also_o it_o may_v be_v difference_v from_o all_o other_o circle_n none_o of_o which_o ever_o claim_v latitude_n the_o zodiac_n be_v divide_v first_o in_o relation_n to_o its_o latitude_n into_o north_n latitude_n and_o south_n latitude_n north_n latitude_n be_v that_o half_a part_n of_o the_o zodiac_n which_o from_o the_o ecliptic_a the_o middle_a line_n of_o it_o decline_v towards_o the_o north._n south_n latitude_n be_v opposite_a to_o this_o each_o one_o of_o they_o contain_v eight_o degree_n whereof_o the_o equinoctial_a contain_v 360._o the_o ecliptic_a or_o middle_a line_n of_o the_o zodiac_n be_v one_o of_o the_o great_a circle_n of_o the_o sphere_n movable_a under_o which_o the_o sun_n from_o west_n to_o east_n move_v perpetual_o this_o line_n as_o likewise_o the_o zodiac_n be_v divide_v according_a to_o longitude_n into_o twelve_o part_n which_o be_v call_v in_o greek_a 〈◊〉_d every_o one_o of_o these_o twelve_o be_v subdivide_v into_o 30_o part_n so_o that_o the_o whole_a zodiac_n contain_v 360_o degree_n these_o twelve_o division_n be_v call_v aries_n taurus_n gemini_fw-la cancer_n leo_n virgo_fw-la libra_n scorpius_n sagittarius_fw-la capâ—…s_fw-la aquarius_n pisces_fw-la but_o see_v there_o be_v four_o cardinal_n point_n two_o of_o the_o equinoctial_a and_o two_o solstice_n point_n it_o have_v please_v astronomeâ—…_n to_o make_v the_o beginning_n of_o their_o reckon_n from_o the_o vernal_a equinoctial_a point_n because_o the_o sun_n be_v there_o he_o not_o only_o begin_v the_o spring_n but_o open_v the_o earth_n and_o give_v life_n to_o all_o vegetable_n and_o thing_n which_o grow_v which_o can_v be_v do_v either_o in_o any_o of_o the_o solstice_n or_o when_o he_o be_v in_o the_o autumnal_a equinoctial_a point_n next_o the_o distinction_n of_o the_o sign_n be_v manifold_a for_o some_o of_o they_o be_v call_v northern_a sign_n and_o other_o be_v call_v southern_a the_o northern_a decline_v from_o the_o equinoctial_a towards_o the_o north_n which_o be_v aries_n taurus_n gemini_fw-la cancer_n leo_n virgo_fw-la the_o southern_a decline_n from_o the_o equinoctial_a towards_o the_o south_n which_o be_v 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cardinal_n middle_n or_o fix_v or_o common_a or_o
and_o nation_n this_o political_a year_n be_v manifold_a for_o it_o be_v either_o julian_n which_o contain_v 365_o day_n hour_n 6_o which_o six_o hour_n if_o they_o be_v reckon_v every_o year_n will_v make_v confusion_n therefore_o the_o master_n of_o astronomy_n have_v appoint_v they_o shall_v be_v omit_v till_o the_o four_o year_n and_o then_o four_o time_n six_o make_v 24_o which_o make_v up_o a_o full_a and_o complete_a day_n which_o be_v inter_v call_v that_o be_v interlace_v or_o put_v between_o as_o in_o leap_v year_n there_o be_v a_o day_n put_v between_o the_o 28_o of_o february_n and_o the_o first_o of_o march_n the_o year_n be_v call_v annus_fw-la intercalaris_fw-la or_o bissextile_a year_n it_o be_v to_o be_v advert_v that_o the_o cause_n of_o correct_v the_o julian_n calendar_n by_o pope_n gregory_n the_o 13_o in_o the_o year_n 1582_o be_v the_o unjust_a quantity_n of_o it_o for_o by_o this_o it_o come_v to_o pass_v that_o after_o some_o age_n the_o four_o cardinal_n point_n do_v anticipate_v and_o prevent_v their_o seat_n and_o so_o at_o length_n the_o four_o season_n of_o the_o year_n may_v be_v interchange_v from_o this_o it_o be_v evident_a this_o day_n that_o according_a to_o these_o time_n the_o equinoctial_a and_o the_o ingress_n of_o the_o sun_n into_o the_o 12_o sign_n have_v anticipate_v almost_o 13_o degree_n that_o be_v the_o entering_z of_o the_o sun_n into_o aries_n taurus_n etc._n etc._n fall_v out_o soon_o by_o 13_o degree_n than_o to_o the_o roman_n which_o come_v to_o pass_v because_o more_o than_o what_o be_v just_a be_v give_v to_o the_o space_n of_o the_o year_n for_o there_o be_v give_v to_o the_o year_n by_o the_o correction_n of_o julius_n cesar_n 365_o day_n and_o six_o hour_n for_o which_o hour_n every_o four_o year_n one_o day_n be_v add_v and_o so_o the_o common_a julian_n year_n contain_v 365_o day_n but_o the_o bissextile_a 366._o but_o see_v the_o solar_a year_n in_o which_o the_o sun_n run_v through_o the_o whole_a 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these_o year_n be_v divers_a also_o for_o the_o ancient_a roman_n begin_v their_o year_n from_o march_n the_o late_a roman_n from_o the_o midst_n of_o winter_n call_v bruma_n the_o jew_n by_o divine_a institution_n begin_v their_o year_n from_o the_o new_a moon_n which_o be_v next_o after_o to_o the_o vernal_a equinox_n that_o we_o this_o day_n begin_v our_o year_n from_o the_o first_o of_o january_n it_o be_v for_o this_o because_o we_o follow_v the_o custom_n of_o the_o late_a roman_n begin_v their_o year_n from_o the_o midst_n of_o winter_n which_o be_v near_a to_o the_o first_o of_o january_n by_o little_a and_o little_a the_o winter_n solstice_n do_v prevent_v and_o anticipat_v its_o seat_n and_o place_n the_o egyptian_a year_n have_v not_o a_o sure_a beginning_n by_o reason_n that_o six_o hour_n be_v omit_v hence_o be_v it_o that_o every_o four_o year_n it_o anticipat_v one_o day_n and_o therefore_o within_o 365_o year_n four_o time_n number_v or_o 1460_o julian_n year_n the_o 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aries_n and_o libra_n where_o he_o describe_v a_o straight_a and_o right_a line_n chap._n xvi_o of_o the_o phenomena_n of_o the_o second_o position_n 1._o some_o northern_a star_n tarry_v always_o above_o our_o horizon_n have_v eternal_a day_n and_o contrariwise_o there_o be_v some_o about_o the_o south_n pole_n which_o never_o come_v above_o the_o horizon_n but_o have_v eternal_a night_n 2._o the_o arctic_a and_o antarctic_a circle_n according_a to_o the_o ancient_n be_v not_o as_o yet_o equal_a to_o our_o polar_n 3._o the_o artificial_a day_n be_v not_o equal_a to_o its_o own_o night_n two_o day_n only_o except_v when_o the_o sun_n be_v in_o the_o equinoctial_a point_n at_o which_o time_n there_o be_v through_o the_o whole_a world_n a_o equinox_n 4._o the_o long_a day_n there_o do_v not_o exceed_v thirteen_o hour_n and_o a_o half_a 5._o the_o sun_n be_v to_o they_o twice_o vertical_a every_o year_n to_o wit_n when_o he_o come_v to_o those_o degree_n of_o the_o ecliptic_a who_o declination_n be_v equal_a to_o the_o latitude_n of_o the_o place_n for_o he_o describe_v then_o a_o parallel_n through_o the_o zenith_n 6._o the_o sun_n in_o the_o meridian_n go_v further_a towards_o the_o south_n than_o towards_o the_o north._n note_v that_o we_o be_v now_o speak_v and_o in_o the_o follow_a discourse_n of_o those_o seven_o position_n which_o be_v in_o the_o northern_a sphere_n 7._o there_o be_v here_o four_o solstice_n two_o high_a and_o two_o low_a the_o two_o high_a fall_n out_o when_o the_o sun_n be_v in_o that_o parallel_n which_o pass_v through_o the_o zenith_n the_o two_o low_a be_v when_o the_o sun_n be_v in_o the_o tropic_n yet_o that_o which_o fall_v out_o in_o the_o tropic_a of_o capricorn_n be_v low_a than_o that_o which_o fall_v out_o in_o the_o tropic_a of_o cancer_n 8._o they_o have_v two_o summer_n
grow_a of_o the_o tide_n above_o the_o stagnant_a mercury_n raise_v it_o high_o and_o high_a in_o the_o glass_n so_o the_o ascend_n of_o the_o vapour_n loadn_v the_o atmosphere_n more_o and_o more_o and_o consequent_o it_o press_v with_o more_o weight_n upon_o the_o mercury_n in_o the_o cistern_n and_o as_o the_o vapour_n be_v turn_v into_o rain_n and_o the_o mercury_n fall_v down_o so_o by_o the_o ebb_a of_o the_o water_n the_o three_o inch_n of_o mercury_n fall_v down_o within_o the_o weatherglass_n it_o may_v be_v inquire_v how_o far_o do_v these_o vapour_n ascend_v i_o answer_v that_o philospher_n distinguish_v the_o air_n into_o three_o region_n the_o first_o second_o and_o three_o but_o both_o philospher_n and_o astronomer_n do_v vary_v exceed_o in_o determine_v the_o height_n of_o any_o of_o they_o i_o shall_v not_o curious_o inquire_v but_o shall_v speak_v a_o little_a to_o what_o concern_v the_o present_a purpose_n it_o be_v probable_a that_o these_o thin_a and_o light_a vapour_n which_o flow_v out_o of_o the_o earth_n and_o water_n go_v many_o mile_n above_o the_o cloud_n where_o there_o be_v neither_o wind_n nor_o rain_n for_o the_o pressure_n of_o the_o air_n be_v powerful_a many_o mile_n up_o must_v carry_v the_o vapour_n so_o far_o up_o but_o to_o determine_v particular_o it_o be_v not_o possible_a only_o in_o general_n they_o ascend_v very_o far_o now_o it_o be_v evident_a that_o the_o atmosphere_n be_v compose_v and_o consist_v of_o such_o vapour_n be_v call_v sphaera_fw-la halituum_fw-la which_o no_o doubt_n be_v of_o a_o considerable_a thickness_n and_o hight_v these_o vapour_n when_o they_o be_v once_o past_o the_o inferior_a region_n of_o the_o air_n which_o will_v not_o exceed_v a_o english_a mile_n and_o a_o half_a go_v up_o quick_o and_o be_v receive_v by_o the_o atmosphere_n where_o they_o accresce_fw-it to_o a_o considerable_a height_n perhaps_o 40_o or_o 50_o mile_n above_o the_o cloud_n where_o by_o some_o extrinsic_a cause_n as_o extremity_n of_o cold_a they_o fall_v down_o from_o the_o atmosphere_n first_o as_o mist_n or_o dew_n till_o they_o come_v to_o the_o low_a region_n where_o in_o a_o very_a short_a time_n they_o cover_v the_o whole_a heaven_n though_o never_o so_o clear_a before_o how_o many_o time_n before_o rain_n will_v this_o be_v see_v beside_o there_o be_v above_o the_o atmosphere_n that_o which_o astronomer_n call_v the_o diluculum_fw-la and_o the_o crepusculum_fw-la that_o be_v both_o the_o dawn_v of_o the_o day_n and_o the_o twilight_n in_o the_o evening_n the_o one_o beginning_n about_o two_o hour_n before_o the_o sun_n rise_v and_o the_o other_o end_v about_o two_o hour_n after_o the_o sun_n be_v go_v down_o for_o if_o that_o crepusculum_fw-la be_v not_o there_o we_o shall_v have_v no_o light_n until_o the_o body_n of_o the_o sun_n be_v above_o the_o horizon_n and_o shall_v have_v no_o light_n after_o the_o body_n of_o the_o sun_n be_v set_v this_o sphere_n be_v unalterable_a and_o without_o accresce_fw-it or_o decrease_n but_o the_o atmosphere_n be_v not_o so_o by_o reason_n of_o the_o vapour_n come_v to_o it_o and_o decrease_v again_o next_o the_o refraction_n which_o make_v the_o sun_n or_o star_n to_o appear_v above_o the_o horizon_n high_o than_o real_o it_o be_v be_v cause_v by_o the_o atmosphere_n it_o be_v observe_v by_o shepherd_n that_o if_o the_o sun_n appear_v soon_o above_o the_o horizon_n than_o ordinary_a the_o day_n follow_v shall_v be_v rainy_n they_o see_v indeed_o the_o image_n of_o the_o sun_n a_o little_a before_o he_o rise_v which_o be_v cause_v by_o the_o refraction_n or_o thick_a medium_fw-la of_o the_o vapour_n which_o lie_v about_o the_o horizon_n for_o example_n let_v a_o man_n so_o fix_v his_o eye_n upon_o a_o wide_a vessel_n with_o a_o open_a mouth_n with_o a_o piece_n of_o money_n in_o the_o bottom_n he_o shall_v not_o see_v it_o till_o the_o vessel_n be_v fill_v with_o water_n for_o water_n be_v a_o thick_a medium_fw-la raise_v the_o image_n 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