the_o pole_n that_o the_o long_a day_n of_o one_o place_n exceed_v the_o long_a day_n of_o the_o vicine_fw-la place_n which_o be_v more_o nigh_o the_o aequator_fw-la every_o where_n equal_a in_o excess_n or_o that_o the_o long_a day_n equal_o may_v increase_v pole_n of_o parallel_n between_o the_o aequator_fw-la and_o the_o pole_n these_o parallel_n shall_v not_o equal_o be_v distant_a one_o from_o another_o viz_o every_o vicine_fw-la couple_n but_o these_o which_o be_v more_o remote_a from_o the_o aequator_fw-la shall_v have_v a_o less_o distance_n than_o those_o more_o near_o the_o aequator_fw-la the_o truth_n of_o this_o proposition_n be_v show_v from_o the_o precedent_n for_o if_o these_o parallel_n shall_v be_v equal_o distant_a from_o one_o another_o viz._n every_o two_o vicine_fw-la the_o quantity_n of_o the_o long_a day_n in_o these_o parallel_n will_v not_o augment_v by_o a_o equal_a increase_n as_o we_o have_v here_o show_v and_o it_o be_v now_o lay_v down_o that_o the_o 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shall_v be_v equal_a or_o of_o equal_a day_n except_o some_o day_n viz._n five_o in_o which_o the_o summer_n and_o four_o in_o which_o the_o spring_n of_o the_o northern_a place_n exceed_v the_o autumn_n and_o the_o winter_n but_o in_o the_o southern_a place_n it_o be_v otherwise_o for_o autumn_n and_o winter_n exceed_v the_o spring_n and_o summer_n which_o as_o we_o have_v show_v before_o proceed_v from_o the_o excentricity_n of_o the_o sun_n 2._o in_o place_n lie_v under_o the_o aequator_fw-la there_o be_v two_o summer_n as_o also_o other_o season_n but_o hoth_v short_a as_o also_o both_o the_o spring_n viz._n each_o summer_n and_o each_o spring_n have_v only_o 32_o day_n which_o be_v 64_o day_n but_o the_o autumn_n and_o winter_n be_v long_o viz._n 55_o day_n which_o be_v 110_o day_n 3._o in_o the_o place_n of_o the_o torrid_a zone_n by_o how_o much_o the_o less_o they_o be_v remote_a from_o the_o aequator_fw-la by_o so_o much_o the_o more_o they_o have_v the_o long_a summer_n the_o 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libra_n to_o the_o first_o of_o aries_n be_v consider_v it_o will_v again_o be_v manifest_a that_o they_o be_v very_o little_o depress_v below_o the_o horizon_n and_o so_o we_o have_v show_v the_o second_o member_n or_o part_n of_o this_o proposition_n last_o let_v the_o pole_n be_v elevate_v for_o the_o latitude_n of_o any_o place_n situate_v in_o the_o temperate_a zone_n and_o the_o depression_n of_o the_o parallel_n beneath_o the_o horizon_n again_o be_v consider_v the_o three_o part_n of_o this_o proposition_n will_v be_v prove_v proposition_n vii_o a_o place_n be_v give_v in_o the_o globe_n and_o the_o day_n of_o the_o year_n to_o find_v the_o longitude_n of_o the_o crepusculum_fw-la or_o twilight_n in_o the_o place_n give_v at_o the_o day_n give_v that_o time_n be_v
find_v at_o the_o day_n take_v and_o note_v in_o the_o ecliptic_a of_o the_o globe_n then_o let_v the_o pole_n be_v elevate_v for_o the_o latitude_n of_o the_o earth_n of_o the_o one_o place_n take_v and_o let_v the_o longitude_n of_o the_o day_n and_o the_o night_n or_o the_o stay_n of_o the_o sun_n above_o or_o beneath_o the_o horizon_n in_o that_o place_n at_o the_o assume_v day_n be_v find_v by_o the_o six_o proposition_n of_o this_o chap._n then_o let_v the_o pole_n be_v elevate_v for_o the_o latitude_n of_o the_o other_o place_n and_o let_v the_o longitude_n of_o the_o day_n and_o night_n or_o stay_v of_o the_o sun_n above_o or_o beneath_o the_o horizon_n be_v find_v at_o the_o same_o assume_v day_n let_v this_o longitude_n so_o find_v be_v compare_v with_o the_o other_o and_o the_o truth_n of_o this_o proposition_n will_v be_v manifest_a so_o that_o the_o place_n more_o remote_a have_v all_o the_o day_n of_o one_o half_a year_n long_o than_o the_o place_n more_o nigh_o on_o the_o contrary_a it_o will_v have_v all_o the_o day_n of_o the_o other_o half_a year_n short_a corollary_n what_o have_v be_v show_v of_o all_o the_o day_n of_o the_o year_n except_o the_o aequinoctial_o the_o same_o be_v also_o of_o force_n in_o the_o quantity_n of_o the_o long_a and_o short_a day_n and_o in_o this_o it_o be_v most_o observe_v and_o note_v because_o here_o be_v the_o great_a difference_n between_o the_o longitude_n of_o the_o night_n and_o day_n not_o so_o great_a in_o other_o day_n of_o the_o year_n therefore_o of_o the_o two_o place_n that_o which_o be_v more_o remote_a from_o the_o aequator_fw-la or_o more_o near_o to_o the_o pole_n have_v the_o long_a day_n great_a than_o the_o place_n more_fw-mi vicine_fw-la to_o the_o aequator_fw-la and_o the_o short_a day_n lesser_a proposition_n viii_o all_o place_n of_o the_o earth_n situate_v in_o one_o of_o the_o same_o parallel_n have_v all_o the_o day_n of_o the_o year_n equal_a and_o therefore_o the_o same_o quantity_n 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arch_n in_o these_o denote_v the_o stay_n of_o the_o sun_n above_o the_o horizon_n of_o the_o place_n then_o let_v the_o second_o place_n be_v bring_v to_o the_o meridian_n or_o vertex_fw-la that_o the_o wooden_a horizon_n may_v be_v the_o horizon_n of_o it_o and_o let_v the_o arch_n of_o the_o tropic_a above_o the_o horizon_n again_o be_v mark_v which_o if_o it_o be_v compare_v with_o the_o former_a we_o shall_v find_v that_o they_o be_v equal_a the_o same_o may_v be_v show_v also_o by_o hour_n on_o the_o horary_a circle_n therefore_o the_o sun_n remain_v a_o equal_a time_n above_o the_o orison_n of_o those_o place_n and_o therefore_o the_o day_n shall_v be_v equal_a as_o also_o the_o night_n definition_n from_o these_o aforesaid_a proposition_n the_o original_a of_o the_o division_n of_o the_o earth_n into_o climate_n be_v easy_o to_o be_v understand_v climate_n observation_n concern_v a_o climate_n for_o a_o climate_n be_v say_v to_o be_v one_o part_n of_o the_o earth_n of_o those_o part_n into_o which_o the_o superficies_n situate_v between_o the_o aequator_fw-la and_o the_o pole_n be_v so_o cut_v by_o draw_v parallel_n that_o the_o long_a day_n in_o the_o parallel_n more_o remote_a from_o the_o aequator_fw-la exceed_v the_o long_a day_n of_o the_o parallel_n more_o near_o the_o equator_fw-la in_o a_o certain_a part_n of_o a_o hour_n or_o number_n of_o hour_n viz._n half_a a_o hour_n in_o place_n situate_v even_o to_o the_o arctic_a circle_n in_o other_o place_n a_o whole_a hour_n or_o some_o hour_n and_o day_n the_o begin_n of_o a_o climate_n be_v call_v a_o parallel_n with_o which_o the_o climate_n begin_v and_o be_v more_o nigh_o the_o aequator_fw-la the_o end_n of_o a_o climate_n be_v call_v a_o parallel_n terminate_n the_o climate_n the_o middle_n of_o a_o climate_n be_v call_v a_o parallel_n draw_v almost_o through_o the_o middle_a superficies_n of_o a_o climate_n so_o that_o in_o that_o the_o long_a day_n exceed_v the_o long_a day_n of_o the_o begin_n of_o a_o climate_n by_o a_o quarter_n of_o a_o hour_n or_o a_o half_a difference_n wherein_o the_o long_a day_n of_o the_o end_n of_o a_o climate_n exceed_v the_o long_a day_n of_o the_o begin_n of_o a_o climate_n a_o parallel_n space_n be_v say_v to_o be_v that_o which_o the_o middle_a parallel_n of_o a_o climate_n comprehend_v with_o the_o begin_n or_o end_n of_o a_o climate_n proposition_n ix_o if_o more_o place_n of_o the_o earth_n be_v take_v from_o the_o aequator_fw-la towards_o the_o pole_n who_o distance_n from_o the_o aequator_fw-la equal_o augment_v from_o one_o degree_n to_o 10_o 20_o 30_o 40_o degree_n the_o long_a day_n in_o these_o place_n shall_v not_o be_v equal_o great_a or_o not_o equal_o augment_v but_o they_o shall_v more_o augment_v in_o place_n more_o remote_a and_o where_o the_o place_n be_v more_o near_o to_o the_o pole_n pole_n touch_v the_o length_n of_o day_n of_o place_n take_v from_o the_o aequator_fw-la towards_o the_o pole_n to_o show_v the_o verity_n of_o this_o proposition_n by_o the_o globe_n let_v place_n be_v take_v remote_a from_o the_o aequator_fw-la towards_o the_o pole_n by_o a_o equal_a increase_n of_o distance_n viz._n for_o conveniency_n parallel_n of_o 10_o 20_o 30_o 40_o 50_o 60_o degree_n of_o latitude_n for_o these_o parallel_n in_o the_o globe_n let_v the_o pole_n be_v elevate_v to_o the_o latitude_n of_o 10_o degree_n and_o the_o first_o degree_n of_o cancer_n be_v bring_v to_o the_o oriental_a horizon_n and_o that_o be_v note_v let_v the_o point_n of_o the_o tropic_n be_v also_o note_v which_o then_o be_v in_o the_o occidental_a horizon_n for_o the_o arch_n of_o the_o tropic_a then_o be_v above_o the_o horizon_n show_v the_o stay_n of_o the_o sun_n above_o the_o horizon_n of_o the_o place_n 10_o degree_n of_o latitude_n the_o hour_n of_o this_o his_o stay_n may_v also_o be_v know_v by_o the_o index_n and_o horary_a circle_n then_o let_v the_o pole_n be_v elevate_v according_a to_o the_o latitude_n of_o the_o second_o place_n 20_o degree_n and_o the_o first_o degree_n of_o cancer_n be_v again_o bring_v to_o the_o oriental_a horizon_n let_v the_o point_n of_o the_o tropic_n be_v note_v in_o the_o occidental_a for_o the_o arch_n above_o the_o horizon_n will_v again_o note_v the_o stay_n which_o also_o may_v be_v know_v by_o the_o index_n and_o the_o circle_n in_o the_o hour_n the_o same_o may_v be_v use_v with_o place_n who_o latitude_n be_v 40_o 50_o 60_o 70_o degree_n and_o the_o like_a which_o be_v do_v let_v the_o diurual_a hour_n of_o the_o sun_n stay_v above_o the_o the_o horizon_n or_o the_o arch_n of_o the_o tropic_n be_v compare_v and_o it_o will_v be_v manifest_a that_o the_o quantity_n of_o the_o long_a day_n do_v much_o more_o increase_n in_o place_n more_o remote_a than_o in_o the_o place_n more_o adjacent_a to_o the_o aequator_fw-la and_o therefore_o the_o increase_n of_o the_o long_a day_n do_v more_o augment_v than_o the_o increase_n of_o the_o distance_n of_o the_o place_n from_o the_o aequator_fw-la note_v what_o have_v be_v say_v and_o show_v concern_v the_o long_a day_n that_o be_v true_a of_o all_o the_o day_n of_o one_o half_a of_o the_o year_n and_o be_v demonstrate_v after_o the_o same_o manner_n if_o instead_o of_o the_o tropic_a of_o cancer_n the_o parallel_n of_o the_o place_n be_v take_v and_o therefore_o although_o general_n must_v be_v deliver_v general_o yet_o because_o the_o doctrine_n of_o climate_n especial_o require_v the_o explication_n of_o the_o increase_n of_o the_o long_a day_n therefore_o we_o do_v not_o observe_v in_o this_o doctrine_n that_o law_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d proposition_n x._o if_o so_o many_o place_n or_o parallel_n be_v so_o take_v between_o the_o aequator_fw-la and_o
above_o almost_o make_v up_o and_o moderate_v they_o to_o wit_n in_o the_o region_n of_o the_o northern_a temperate_a zone_n it_o be_v spring_n and_o summer_n the_o sun_n go_v from_o aries_n by_o cancer_n to_o libra_n because_o than_o he_o be_v more_o near_o they_o then_o the_o sun_n go_v from_o libra_n through_o capricorn_n to_o aries_n it_o be_v autumn_n and_o winter_n but_o in_o the_o southern_a temperate_a zone_n the_o matter_n be_v contrary_a neither_o can_v those_o other_o cause_n altogether_o disable_v the_o force_n of_o this_o first_o and_o induce_v a_o new_a course_n of_o the_o season_n and_o be_v able_a to_o alter_v the_o time_n as_o in_o the_o torrid_a zone_n 2._o yet_o those_o season_n of_o divers_a place_n vary_v so_o that_o in_o one_o place_n there_o may_v be_v more_o heat_n or_o cold_a or_o rain_v than_o in_o another_o although_o the_o place_n lie_v in_o the_o same_o climate_n but_o yet_o they_o cause_v not_o the_o winter_n to_o be_v change_v into_o summer_n or_o 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rain_n but_o from_o the_o heat_n and_o cold_a now_o in_o the_o coast_n of_o persia_n and_o ormus_n there_o be_v so_o great_a heat_n without_o rain_n in_o the_o summer_n by_o reason_n of_o the_o vicinity_n of_o the_o sun_n rhat_o both_o the_o man_n and_o their_o wife_n lie_v in_o cistern_n full_a of_o water_n the_o like_a heat_n be_v in_o arabia_n barbary_n the_o region_n of_o africa_n on_o the_o mediterranean_a sea_n be_v call_v the_o coast_n of_o barbary_n throughout_o all_o barbary_n the_o middle_a of_o october_n be_v past_a shower_n and_o cold_n begin_v to_o increase_v and_o in_o december_n and_o january_n the_o cold_a be_v perceive_v more_o intense_a and_o that_o only_a in_o the_o morning_n and_o withal_o so_o remiss_a that_o the_o fire_n be_v not_o desire_v february_n take_v away_o the_o great_a part_n of_o the_o cold_a from_o the_o winter_n but_o yet_o it_o be_v so_o inconstant_a that_o sometime_o 5_o or_o 6_o time_n in_o one_o day_n the_o air_n change_v in_o the_o month_n of_o march_n the_o north_n and_o west_n wind_n blow_v violent_o and_o cause_v whole_a tree_n to_o be_v vest_v with_o blossom_n april_n give_v form_n almost_o to_o all_o fruit_n so_o that_o the_o entrance_n of_o may_n and_o the_o end_n of_o april_n be_v wont_v natural_o to_o produce_v cherry_n in_o the_o middle_n of_o may_v they_o gather_v fig_n and_o in_o the_o middle_n of_o june_n in_o some_o place_n be_v ripe_a grape_n barbary_n of_o the_o season_n of_o the_o year_n of_o barbary_n the_o fig_n or_o autumn_n be_v gather_v in_o august_n and_o there_o be_v no_o great_a plenty_n of_o fig_n and_o pear_n than_o in_o september_n there_o be_v not_o so_o great_a intempery_n of_o the_o year_n in_o those_o place_n but_o that_o the_o three_o month_n of_o the_o spring_n be_v always_o temperate_a the_o entrance_n of_o the_o spring_n that_o be_v the_o terrestrial_a not_o the_o celestial_a be_v as_o they_o reckon_v on_o the_o 15_o of_o february_n and_o the_o end_n the_o 18_o of_o may_n in_o all_o which_o time_n the_o air_n be_v most_o grateful_a to_o they_o if_o from_o the_o 25_o of_o april_n to_o the_o 5_o of_o may_v they_o have_v no_o rain_n they_o esteem_v the_o same_o as_o ominous_a they_o count_v their_o summer_n even_o to_o the_o 16_o of_o august_n at_o which_o time_n they_o have_v a_o very_a hot_a and_o serene_a air._n their_o autumn_n from_o the_o 17_o of_o august_n to_o the_o 16_o of_o november_n and_o they_o have_v that_o for_o two_o month_n to_o wit_n august_n and_o september_n yet_o not_o great_a that_o which_o be_v include_v between_o the_o 15_o of_o august_n and_o the_o 15_o of_o september_n be_v wont_a to_o be_v term_v by_o the_o ancient_n the_o furnace_n of_o the_o whole_a year_n and_o that_o because_o it_o produce_v fig_n pear_n and_o that_o kind_a of_o fruit_n to_o maturity_n from_o the_o 15_o of_o november_n they_o reckon_v their_o winter_n which_o they_o extend_v to_o the_o 14_o of_o february_n at_o the_o entrance_n of_o this_o they_o begin_v to_o till_o their_o land_n which_o be_v the_o plain_a but_o the_o mountainous_a in_o the_o month_n of_o october_n the_o african_n have_v a_o certain_a persuasion_n that_o the_o year_n have_v 40_o very_a hot_a day_n and_o on_o the_o other_o side_n so_o many_o cold_a arabian_n the_o opinion_n of_o the_o arabian_n day_n which_o they_o say_v begin_v from_o the_o 12_o of_o december_n they_o begin_v the_o aequinox_n on_o the_o 16_o of_o march_n and_o on_o the_o 16_o of_o september_n their_o solstice_n on_o the_o 16_o of_o june_n and_o the_o 16_o of_o december_n the_o end_n of_o their_o autumn_n all_o their_o winter_n and_o a_o good_a part_n of_o their_o spring_n be_v full_a of_o violent_a wind_n accompanied_z with_o hail_o lightning_n and_o dreadful_a thunder_n neither_o be_v there_o want_v in_o many_o place_n of_o barbary_n a_o abundance_n of_o snow_n in_o mount_n atlas_n 7_o degree_n distant_a from_o the_o tropic_a of_o cancer_n they_o divide_v the_o year_n only_o into_o two_o part_n for_o from_o october_n even_o to_o april_n they_o have_v a_o continual_a winter_n and_o from_o april_n again_o to_o october_n they_o have_v summer_n in_o this_o there_o be_v no_o day_n in_o which_o the_o mountain_n top_n glitter_v with_o snow_n numidia_n the_o season_n of_o numidia_n in_o numidia_n the_o part_n of_o the_o year_n swift_o pass_v away_o for_o in_o may_v they_o reap_v their_o corn_n in_o october_n they_o gather_v their_o date_n but_o from_o the_o middle_n of_o september_n to_o january_n a_o violent_a frost_n continue_v october_n abstain_v from_o rains_n all_o hope_n of_o sow_v be_v take_v from_o the_o husbandman_n the_o same_o happen_v if_o that_o april_n produce_v not_o pluvial_a water_n leo_fw-la astricanus_fw-la remember_v many_o mountain_n of_o snow_n in_o africa_n not_o far_o from_o the_o tropic_a of_o cancer_n china_n of_o china_n the_o north_n part_n of_o china_n although_o no_o more_o remote_a from_o the_o aequator_fw-la than_o italy_n yet_o it_o have_v a_o cold_a more_o sharp_a for_o great_a river_n and_o lake_n be_v congeal_v up_o with_o frost_n the_o cause_n of_o which_o be_v not_o yet_o sufficient_o know_v except_o we_o shall_v refer_v it_o to_o the_o snowy_a mountain_n of_o tartary_n not_o far_o remote_a to_o the_o avoid_n of_o which_o cold_a they_o abound_v with_o the_o skin_n of_o fox_n and_o scythilian_a rat_n england_n new_a england_n new_a england_n although_o it_o lie_v in_o 42_o degree_n of_o north_n latitude_n and_o therefore_o no_o more_o remove_v from_o the_o aequator_fw-la than_o italy_n yet_o in_o the_o month_n of_o june_n when_o sir_n francis_n drake_n be_v there_o the_o air_n be_v so_o vehement_a cold_n that_o he_o be_v compel_v to_o sail_v back_o to_o the_o south_n for_o the_o mountain_n be_v then_o cover_v with_o snow_n the_o cause_n be_v the_o frigid_a temperature_n of_o the_o earth_n be_v stony_n egypt_n the_o season_n of_o egypt_n in_o egypt_n which_o be_v bound_v with_o the_o tropic_a of_o cancer_n the_o spring_n and_o temperate_a season_n 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depart_v from_o the_o meridian_n for_o that_o be_v equal_a to_o the_o latitude_n of_o the_o place_n proposition_n x._o the_o place_n of_o the_o earth_n situate_v under_o the_o aequator_fw-la have_v no_o latitude_n or_o elevation_n of_o the_o pole_n but_o both_o the_o pole_n lie_v in_o their_o horizon_n latitude_n the_o place_n under_o the_o aequator_fw-la have_v not_o latitude_n the_o place_n under_o the_o pole_n have_v the_o latitude_n of_o 90_o degree_n viz._n the_o pole_n in_o the_o vertex_fw-la and_o the_o aequator_fw-la in_o the_o horizon_n the_o place_n between_o the_o pole_n and_o the_o aequator_fw-la have_v a_o less_o latitude_n than_o ninety_o degree_n the_o truth_n of_o this_o proposition_n be_v evident_a therefore_o it_o need_v no_o explication_n proposition_n xi_o if_o we_o be_v either_o on_o the_o sea_n or_o land_n and_o know_v not_o the_o place_n where_o we_o be_v let_v the_o latitude_n be_v find_v to_o exhibit_v that_o parallel_n in_o the_o globe_n that_o we_o may_v be_v certain_a that_o we_o be_v in_o one_o point_n of_o it_o this_o be_v do_v after_o the_o same_o manner_n that_o we_o have_v show_v in_o the_o six_o proposition_n viz._n a_o parallel_n must_v be_v describe_v at_o the_o give_v or_o observe_v latitude_n and_o this_o be_v the_o parallel_n demand_v the_o same_o be_v also_o easy_a in_o map_n chap._n xxiv_o of_o the_o division_n of_o the_o earth_n into_o zone_n and_o the_o celestial_a appearance_n in_o the_o divers_a zone_n proposition_n i._o from_o the_o proper_a or_o annual_a motion_n of_o the_o sun_n there_o arise_v a_o certain_a division_n of_o the_o superficies_n of_o the_o earth_n into_o five_o part_n or_o zone_n scheme_n the_o division_n of_o the_o earth_n into_o 5_o zone_n see_v scheme_n see_v that_o the_o sun_n do_v not_o always_o continue_v in_o the_o aequator_fw-la but_o decline_v from_o it_o describe_v by_o his_o motion_n a_o path_n which_o cut_v the_o aequator_fw-la so_o that_o his_o great_a declination_n be_v in_o 23½_n degree_n 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temperate_a and_o 2._o frigid_a zone_n torrid_a zone_n the_o torrid_a zone_n be_v that_o part_n of_o the_o earth_n which_o lie_v between_o the_o tropic_n of_o cancer_n and_o capricorn_n zone_n temperate_a zone_n the_o temperate_a zone_n which_o lie_v between_o one_o of_o the_o tropic_n and_o the_o adjacent_a polary_a circle_n the_o northern_o temperate_a zone_n be_v that_o which_o lie_v between_o the_o tropic_a of_o cancer_n and_o the_o arctic_a circle_n the_o southern_o temperate_a zone_n be_v that_o which_o lie_v between_o the_o tropic_a of_o capricorn_n and_o the_o antarctic_a circle_n zone_n frigid_a zone_n the_o frigid_a or_o cold_a zone_n be_v those_o part_n of_o the_o earth_n which_o lie_v about_o the_o pole_n even_o to_o the_o polary_a circle_n and_o they_o be_v as_o well_o northern_o as_o southern_o cold_a circle_n proposition_n ii_o in_o the_o place_n according_a to_o their_o latitude_n in_o what_o zone_n they_o be_v in_o those_o place_n of_o the_o earth_n who_o latitude_n be_v less_o than_o 23_o degree_n and_o 30_o minute_n they_o lie_v in_o the_o torrid_a zone_n those_o who_o latitude_n be_v 23_o degree_n and_o 30_o minute_n they_o lie_v in_o the_o tropic_n viz._n in_o the_o extremity_n of_o the_o torrid_a zone_n those_o who_o latitude_n be_v great_a than_o 23_o degree_n and_o 30_o minute_n and_o less_o than_o 66_o degree_n and_o 30_o minute_n they_o lie_v in_o the_o temperate_a zone_n those_o who_o latitude_n be_v 66_o degree_n and_o 30_o minute_n they_o lie_v in_o the_o polary_a circle_n viz._n in_o the_o term_n of_o the_o temperate_a zone_n those_o who_o latitude_n be_v great_a than_o 66_o degree_n and_o 30_o minute_n they_o lie_v in_o the_o frigid_a zone_n these_o be_v manifest_a from_o the_o definition_n of_o the_o tropical_a and_o polary_a circle_n which_o we_o have_v treat_v of_o in_o the_o 23th_o chapter_n proposition_n iii_o the_o aequator_fw-la of_o the_o earth_n pass_v through_o these_o place_n through_o place_n which_o the_o aequator_fw-la pass_v through_o through_o the_o island_n of_o st._n thomas_n in_o the_o great_a bay_n of_o africa_n which_o be_v call_v the_o aethiopian_a ocean_n through_o aethiopia_n through_o the_o indian_a ocean_n through_o the_o middle_n of_o sumatra_n through_o the_o chersonesus_n of_o malacca_n and_o other_o island_n in_o the_o indian_a ocean_n through_o the_o moluccas_n themselves_o and_o the_o pacifick_n ocean_n through_o the_o entrance_n of_o the_o province_n of_o peruana_n by_o the_o lake_n parima_fw-la through_o the_o atlantic_a ocean_n even_o to_o the_o island_n of_o st._n thomas_n the_o aequator_fw-la divide_v the_o torrid_a zone_n into_o two_o equal_a part_n so_o that_o they_o may_v deserve_o be_v term_v two_o torrid_a zone_n one_o northern_a and_o the_o other_o southern_a these_o place_n lie_v in_o the_o torrid_a zone_n zone_n place_n which_o lie_v in_o the_o torrid_a zone_n the_o great_a part_n of_o africa_n the_o indian_a ocean_n abyssine_n part_n of_o arabia_n cambaja_n india_n the_o isle_n of_o the_o indian_a sea_n java_n ceilan_n peruvia_n mexico_n great_a part_n of_o the_o atlantic_a ocean_n the_o island_n of_o st._n helena_n brazil_n new_a guinee_n through_o place_n which_o the_o tropic_a of_o cancer_n pass_v through_o the_o tropic_a of_o cancer_n pass_v through_o these_o place_n viz._n through_o the_o confine_n of_o lybia_n and_o other_o place_n in_o the_o inland_a africa_n through_o syena_n in_o aethiopia_n thence_o pass_v the_o red_a sea_n beyond_o the_o mountain_n sinai_n and_o mecca_n the_o birth-place_n of_o mahomet_n it_o pass_v through_o arabia_n felix_n hence_o it_o enter_v the_o indian_a ocean_n and_o touch_v the_o border_n of_o persia_n and_o pass_v over_o cambaja_n india_n and_o the_o border_n of_o china_n until_o it_o come_v into_o the_o pacifick_n sea_n which_o be_v pass_v over_o it_o fall_v in_o with_o california_n into_o the_o kingdom_n of_o mexico_n and_o again_o enter_v into_o the_o atlantic_a ocean_n pass_v the_o gulf_n of_o mexico_n it_o sweep_v the_o coast_n of_o the_o isle_n of_o cuba_n and_o thence_o return_v to_o the_o occidental_a shore_n of_o africa_n through_o place_n which_o the_o tropic_a of_o capricorn_n pass_v through_o the_o tropic_a of_o capricorn_n pass_v through_o very_a few_o place_n of_o the_o earth_n its_o great_a part_n lie_v in_o the_o sea_n the_o place_n through_o which_o it_o pass_v be_v through_o the_o tongue_n of_o africa_n through_o monomotapa_n madagascar_n the_o indian_a ocean_n new_a guinee_n the_o pacifick_n ocean_n peru_n brazil_n and_o through_o the_o atlantic_a ocean_n zone_n place_n situate_a in_o the_o northern_a and_o southern_a temperate_a zone_n many_o place_n in_o the_o earth_n lie_v in_o the_o northern_a temperate_a zone_n and_o those_o almost_o all_o know_v and_o inhabit_v viz._n all_o europe_n all_o asia_n except_o part_n of_o india_n malacca_n and_o the_o isle_n of_o the_o indian_a ocean_n great_a part_n of_o america_n septentrionalis_n and_o part_n of_o the_o atlantic_a and_o pacifick_n ocean_n in_o the_o southern_a temperate_a zone_n few_o place_n lie_v and_o those_o not_o full_o know_v with_o a_o large_a portion_n of_o the_o sea_n viz._n part_n of_o the_o prominent_a part_n of_o africa_n monomotapa_n a_o great_a part_n of_o terra_fw-la magellanica_fw-la part_n of_o brazil_n chili_n the_o strait_n of_o magellan_n and_o a_o great_a part_n of_o the_o atlantic_a indian_a and_o pacifick_n ocean_n through_o place_n which_o the_o arctic_a and_o antarctic_a polary_n circle_n pass_v through_o the_o arctic_a polary_n circle_n pass_v almost_o through_o the_o middle_n of_o izland_n through_o the_o upper_a norway_n the_o north_n sea_n lapland_n the_o bay_n of_o russia_n samojeda_n tartary_n america_n septentrionalis_n and_o groenland_n the_o antarctic_a polary_n circle_n pass_v through_o terra_fw-la magellanica_fw-la of_o which_o we_o have_v little_a or_o no_o knowledge_n at_o this_o day_n zone_n place_n which_o lie_v in_o the_o cold_a northern_a and_o southern_a
or_o heaven_n which_o the_o meridian_n line_n be_v find_v be_v easy_a to_o do_v by_o the_o mariner_n compass_n or_o the_o magnetic_a needle_n the_o globe_n be_v thus_o place_v at_o every_o moment_n of_o the_o day_n when_o the_o sun_n shine_v on_o the_o globe_n may_v be_v see_v the_o part_n of_o the_o earth_n illuminate_v and_o the_o part_n not_o illuminate_v those_o place_n which_o lie_v in_o the_o middle_a semicircle_n of_o the_o part_n illuminate_v be_v those_o which_o will_v have_v the_o meridies_n at_o that_o moment_n of_o time_n to_o those_o which_o be_v seat_v in_o the_o oriental_a semicircle_n divide_v the_o illuminate_v part_n from_o the_o part_n not_o illuminate_v the_o sun_n set_v but_o to_o those_o which_o be_v in_o the_o occidental_a semicircle_n separate_v the_o illuminate_v part_n from_o the_o part_n not_o illuminate_v the_o sun_n rise_v to_o find_v out_o the_o place_n of_o the_o sun_n in_o the_o ecliptic_a let_v the_o needle_n or_o spherical_a gromon_n be_v move_v 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in_o which_o the_o globe_n be_v so_o place_v or_o hang_v let_v that_o place_n be_v bring_v to_o the_o meridian_n to_o which_o the_o sun_n be_v vertical_a the_o index_n to_o the_o 12_o hour_n of_o the_o horary_a circle_n and_o let_v the_o globe_n be_v turn_v round_o until_o our_o place_n or_o that_o in_o which_o the_o globe_n be_v seat_v do_v come_v to_o the_o meridian_n the_o index_n will_v show_v the_o hour_n but_o because_o the_o globe_n can_v be_v turn_v round_o when_o it_o be_v affix_v by_o the_o iron_n style_n to_o the_o horizontal_n plain_a therefore_o it_o will_v be_v convenient_a that_o the_o quadrant_n be_v tie_v to_o the_o pole_n or_o part_n of_o the_o circle_n of_o the_o periphery_n 113_o â—_o â—_o for_o here_o the_o arch_n be_v bring_v to_o the_o place_n of_o the_o needle_n will_v show_v the_o declination_n of_o the_o sun_n from_o the_o aequator_fw-la whence_o the_o place_n of_o the_o sun_n and_o the_o day_n of_o the_o year_n shall_v be_v find_v the_o same_o arch_n will_v show_v the_o degree_n in_o the_o aequator_fw-la from_o whence_o if_o that_o the_o degree_n be_v number_v to_o the_o brazen_a meridian_n and_o these_o degree_n be_v change_v into_o hour_n or_o part_n of_o hour_n hour_n fifteen_o degree_n make_v a_o hour_n you_o shall_v have_v the_o hour_n of_o the_o place_n if_o so_o be_v that_o the_o sun_n be_v between_o the_o occident_n and_o the_o brazen_a meridian_n that_o be_v of_o our_o place_n but_o if_o that_o it_o be_v between_o the_o east_n and_o our_o meridian_n the_o hour_n find_v out_o must_v be_v subtract_v from_o 12_o and_o the_o remain_a number_n will_v show_v the_o hour_n from_o midnight_n if_o that_o such_o a_o brazen_a arch_n be_v adjoin_v to_o the_o pole_n of_o the_o globe_n as_o i_o have_v describe_v 113_o ½_n degree_n it_o may_v be_v bore_v through_o from_o the_o end_n even_o to_o 47_o degree_n that_o be_v from_o the_o departure_n of_o the_o sun_n from_o the_o aequator_fw-la and_o a_o turn_a plate_n be_v insert_v in_o it_o which_o 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meridian_n be_v take_v in_o the_o globe_n for_o these_o do_v reckon_v all_o the_o same_o hour_n and_o that_o at_o once_o then_o let_v a_o parallel_n be_v describe_v for_o any_o assume_v day_n and_o it_o will_v be_v manifest_a that_o any_o point_n of_o this_o parallel_n be_v far_a distant_a from_o the_o more_o remote_a place_n than_o from_o the_o place_n more_o near_o the_o sun_n therefore_o be_v above_o the_o point_n of_o this_o parallel_n will_v be_v far_a distant_a from_o the_o vertex_fw-la of_o the_o remote_a place_n than_o from_o the_o vertex_fw-la of_o those_o that_o be_v near_o and_o therefore_o he_o shall_v be_v less_o elevate_v over_o the_o horizon_n of_o those_o place_n than_o of_o these_o proposition_n iv_o by_o how_o much_o the_o place_n of_o the_o earth_n be_v more_o remote_a from_o the_o aequator_fw-la or_o more_o near_o the_o pole_n by_o so_o much_o the_o more_o the_o part_n of_o the_o horizon_n be_v distant_a in_o which_o the_o sun_n rise_v on_o the_o day_n of_o the_o solstice_n and_o the_o day_n of_o the_o winter_n as_o also_o those_o in_o which_o he_o set_v the_o same_o be_v true_a concern_v the_o moon_n and_o all_o the_o planet_n take_v what_o place_n you_o please_v of_o a_o diverse_a distance_n from_o the_o aequator_fw-la and_o let_v the_o pole_n be_v elevate_v for_o the_o latitude_n of_o every_o one_o of_o they_o and_o let_v the_o point_n be_v note_v in_o the_o horizon_n in_o which_o the_o tropic_n of_o capricorn_n and_o cancer_n cut_v it_o a_o comparison_n be_v make_v the_o truth_n of_o the_o proposition_n will_v appear_v this_o be_v also_o show_v the_o same_o way_n by_o how_o much_o the_o place_n be_v more_o remote_a from_o the_o aequator_fw-la by_o so_o much_o the_o more_o the_o sun_n in_o his_o aequinoctial_a rise_n be_v distant_a in_o the_o east_n on_o every_o day_n of_o the_o year_n the_o astronomer_n term_v it_o the_o rise_a amplitude_n proposition_n v._o star_n place_v between_o the_o parallel_n of_o any_o place_n lie_v without_o the_o aequator_fw-la and_o the_o pole_n be_v less_o elevate_v above_o the_o horizon_n of_o the_o place_n between_o this_o parallel_n and_o the_o other_o pole_n of_o those_o situate_v there_o than_o above_o the_o horizon_n of_o the_o place_n situate_v between_o this_o parallel_n and_o the_o near_a pole_n etc._n of_o the_o elevation_n of_o star_n etc._n etc._n the_o parallel_n of_o any_o star_n may_v be_v design_v on_o the_o terrestrial_a globe_n or_o a_o point_n only_o note_v for_o a_o star_n and_o any_o place_n more_o remote_a from_o the_o pole_n be_v assume_v design_v the_o parallel_n of_o the_o place_n then_o take_v another_o place_n situate_v towards_o the_o other_o pole_n the_o stay_n of_o the_o star_n above_o the_o horizon_n of_o both_o place_n may_v be_v find_v and_o the_o truth_n of_o the_o proposition_n will_v be_v manifest_a proposition_n vi_o in_o place_n situate_a in_o and_o near_o the_o aequator_fw-la the_o sun_n and_o star_n direct_o ascend_v above_o the_o horizon_n even_o to_o the_o meridian_n and_o so_o descend_v again_o but_o in_o place_n situate_v above_o the_o aequator_fw-la they_o oblique_o ascend_v and_o descend_v and_o so_o much_o the_o more_o oblique_o by_o how_o much_o the_o place_n be_v more_o remote_a from_o the_o aequator_fw-la star_n of_o the_o ascension_n and_o descension_n of_o the_o sun_n and_o star_n let_v any_o parallel_n of_o the_o sun_n be_v describe_v on_o the_o globe_n such_o as_o some_o already_o be_v delineate_v on_o the_o globe_n viz._n the_o aequator_fw-la the_o tropic_n and_o some_o intermedial_a one_o then_o let_v the_o pole_n be_v place_v in_o the_o very_a horizon_n that_o it_o may_v be_v the_o horizon_n of_o the_o place_n of_o the_o aequator_fw-la and_o it_o will_v be_v evident_a that_o the_o point_n of_o the_o
parallel_n direct_o ascend_v from_o the_o horizon_n to_o the_o meridian_n then_o let_v the_o pole_n be_v elevate_v for_o the_o latitude_n of_o any_o other_o place_n and_o it_o will_v appear_v that_o the_o parallel_n be_v so_o much_o the_o more_o oblique_a to_o the_o horizon_n by_o how_o much_o the_o more_o the_o pole_n be_v elevate_v that_o be_v by_o the_o wooden_a horizon_n become_v the_o horizon_n of_o the_o place_n more_o remote_a from_o the_o aequator_fw-la or_o near_o to_o the_o pole_n proposition_n vii_o by_o how_o much_o the_o place_n be_v more_o remote_a from_o the_o aequator_fw-la by_o so_o much_o the_o more_o the_o sign_n of_o the_o zodiac_n and_o the_o other_o constellation_n require_v the_o great_a time_n to_o arise_v and_o set_v and_o they_o pass_v through_o the_o meridian_n of_o all_o place_n at_o a_o equal_a time_n let_v two_o place_n be_v take_v on_o the_o globe_n unequal_o distant_a from_o the_o aequator_fw-la and_o let_v the_o pole_n be_v elevate_v and_o observe_v separately_z for_o each_o of_o they_o how_o much_o time_n any_o sign_n of_o the_o zodiac_n require_v to_o ascend_v above_o the_o horizon_n viz._n the_o entrance_n of_o the_o sign_n be_v bring_v to_o the_o oriental_a horizon_n let_v the_o index_n be_v place_v at_o the_o 12_o hour_n and_o the_o globe_n be_v turn_v round_o until_o the_o whole_a sign_n be_v rise_v the_o index_n will_v show_v the_o hour_n elapse_v in_o the_o space_n whilst_o the_o sign_n arise_v for_o by_o the_o comparison_n of_o the_o time_n the_o truth_n of_o the_o proposition_n will_v be_v manifest_a proposition_n viii_o the_o day_n of_o the_o year_n be_v give_v to_o find_v or_o show_v on_o the_o globe_n those_o place_n in_o which_o the_o sun_n arise_v in_o any_o give_a quarter_n globe_n to_o find_v the_o rise_n of_o the_o sun_n in_o any_o quarter_n by_o the_o globe_n this_o problem_n and_o those_o that_o follow_v shall_v be_v propound_v and_o resolve_v concern_v the_o earth_n itself_o if_o that_o we_o will_v act_v according_a to_o art_n for_o these_o affection_n belong_v unto_o it_o but_o they_o be_v propound_v concern_v the_o globe_n because_o here_o it_o represent_v the_o earth_n although_o another_o method_n must_v be_v use_v in_o the_o earth_n or_o another_o construction_n which_o although_o it_o can_v only_o be_v comprehend_v by_o the_o mind_n be_v sufficient_a that_o it_o may_v hinder_v in_o the_o practice_n by_o reason_n of_o the_o obstacle_n this_o be_v the_o same_o with_o that_o problem_n the_o day_n and_o the_o quarter_n be_v give_v in_o which_o the_o rise_n of_o the_o sun_n be_v observe_v to_o find_v the_o latitude_n of_o that_o place_n or_o its_o parallel_n in_o any_o point_n of_o which_o it_o be_v manifest_a that_o we_o be_v place_v 11._o see_v chap._n 23._o proposit_n 11._o the_o solution_n of_o which_o we_o have_v deliver_v in_o the_o 23_o chapter_n proposition_n 11._o proposition_n ix_o the_o day_n and_o the_o hour_n or_o part_n of_o the_o hour_n be_v give_v to_o show_v the_o place_n on_o the_o globe_n to_o which_o the_o sun_n be_v then_o vertical_a first_o let_v the_o place_n of_o the_o sun_n from_o the_o give_v day_n be_v find_v be_v note_v on_o the_o ecliptic_a of_o the_o globe_n and_o that_o be_v bring_v to_o the_o meridian_n let_v a_o mark_n be_v make_v with_o a_o chalk_n on_o the_o supereminent_a point_n then_o let_v those_o place_n be_v find_v in_o who_o meridian_n the_o sun_n be_v at_o the_o give_v moment_n of_o time_n and_o let_v they_o be_v bring_v to_o the_o brazen_a meridian_n these_o be_v do_v that_o place_n which_o be_v subject_a to_o the_o note_a point_n of_o the_o meridian_n be_v the_o place_n which_o be_v demand_v viz._n that_o to_o which_o the_o sun_n be_v vertical_a at_o the_o give_v moment_n of_o time_n proposition_n x._o note_v further_o note_v the_o day_n and_o the_o hour_n be_v give_v to_o show_v all_o the_o place_n on_o the_o globe_n from_o who_o vertex_fw-la the_o sun_n be_v distant_a the_o give_v degree_n at_o that_o hour_n but_o the_o give_v degree_n must_v not_o exceed_v a_o hundred_o and_o eighty_o or_o the_o day_n and_o the_o hour_n be_v give_v to_o show_v on_o the_o globe_n those_o place_n above_o who_o horizon_n the_o sun_n have_v the_o give_v altitude_n or_o the_o give_v depression_n beneath_o it_o but_o the_o altitude_n give_v must_v not_o exceed_v 90_o degree_n as_o likewise_o the_o depression_n let_v the_o place_n be_v find_v on_o the_o globe_n to_o which_o the_o sun_n be_v vertical_a at_o the_o hour_n give_v and_o let_v this_o be_v bring_v to_o the_o meridian_n and_o let_v the_o quadrant_n be_v affix_v to_o the_o imminent_a point_n of_o the_o meridian_n let_v the_o degree_n of_o distance_n from_o the_o vertex_fw-la give_fw-mi be_v note_v and_o the_o quadrant_n be_v turn_v round_o the_o globe_n remain_v immovable_a all_o the_o place_n of_o the_o earth_n through_o which_o the_o note_a degree_n of_o the_o quadrant_n pass_v be_v those_o from_o who_o the_o sun_n have_v the_o give_v distance_n or_o above_o who_o horizon_n the_o sun_n have_v the_o give_v altitude_n proposition_n xi_o at_o the_o give_v hour_n of_o the_o day_n to_o show_v on_o the_o globe_n all_o plain_n unto_o which_o the_o sun_n rise_v and_o set_v and_o to_o which_o he_o be_v fix_v at_o the_o meridian_n and_o all_o that_o be_v illuminate_v and_o not_o illuminate_v day_n further_o concern_v the_o rise_n and_o set_v of_o the_o sun_n find_v out_o by_o the_o globe_n at_o any_o day_n or_o hour_n of_o the_o day_n let_v the_o place_n be_v find_v in_o the_o globe_n to_o which_o the_o sun_n at_o the_o time_n give_v be_v vertical_a and_o let_v the_o place_n be_v bring_v to_o the_o meridian_n and_o the_o pole_n elevate_v for_o the_o latitude_n of_o that_o place_n or_o let_v that_o place_n be_v place_v in_o the_o vertex_fw-la of_o the_o horizon_n so_o all_o those_o place_n which_o be_v discover_v under_o the_o semicircle_n of_o the_o meridian_n above_o the_o horizon_n shall_v have_v the_o meridies_n but_o those_o place_n which_o be_v behold_v in_o the_o oriental_a semicircle_n of_o the_o horizon_n be_v those_o to_o which_o the_o sun_n than_o set_v but_o to_o those_o which_o lie_v in_o the_o occidental_a semicircle_n of_o the_o horizon_n the_o sun_n rise_v at_o the_o give_v time_n and_o all_o the_o place_n which_o be_v above_o the_o horizon_n be_v illuminate_v by_o the_o sun_n on_o the_o contrary_a all_o the_o place_n situate_v beneath_o the_o same_o then_o want_v the_o presence_n of_o the_o sun_n note_v that_o the_o problem_n must_v be_v understand_v of_o the_o rise_n and_o set_v of_o the_o body_n of_o the_o centre_n of_o the_o sun_n for_o the_o body_n of_o the_o sun_n illustrate_v part_n of_o the_o earth_n somewhat_o big_a than_o the_o hemisphere_n which_o how_o big_a it_o be_v shall_v be_v discover_v in_o the_o follow_a proposition_n therefore_o we_o may_v show_v the_o place_n to_o which_o the_o sun_n rise_v or_o set_v when_o we_o have_v noon_n or_o midnight_n and_o contrariwise_o those_o in_o which_o he_o set_v when_o he_o arise_v to_o we_o who_o then_o have_v midnight_n or_o midday_n proposition_n xii_o the_o semidiameter_n of_o the_o sun_n and_o earth_n be_v give_v and_o the_o distance_n of_o the_o sun_n from_o the_o earth_n be_v know_v to_o find_v out_o the_o part_n of_o the_o earth_n which_o the_o sun_n illuminate_v scheme_n see_v scheme_n let_v the_o semidiameter_n of_o the_o earth_n be_v a_o b_o a_o c_o a_o the_o centre_n a_o b_o c_o d_o e_o the_o great_a circle_n of_o the_o earth_n s_n the_o centre_n of_o the_o sun_n s_o l_o s_o o_o the_o semidiameter_n of_o the_o sun_n l_o b_o o_o c_o the_o ray_n touch_v the_o globe_n of_o the_o sun_n and_o earth_n for_o these_o distinguish_v the_o part_n illuminate_v from_o the_o part_n not_o illuminate_v therefore_o the_o arch_n b_o d_o c_o represent_v the_o part_n of_o the_o superficies_n of_o the_o earth_n illuminate_v and_o the_o arch_n blc_n the_o part_n not_o illuminate_v let_v the_o tangent_n lb_n o_o c_o be_v extend_v until_o they_o concur_v in_o r_n and_z b_o n_n parallel_v to_o a_o s_n therefore_o in_o the_o triangle_n b_o n_o l_o let_v n_n l_o be_v give_v the_o excess_n s_o l_o above_o a_o b_o and_z b_o n_z of_o equal_a distance_n to_o a_o s_n the_o angle_n b_o n_o l_o be_v direct_a because_o that_o b_o l_o touch_v the_o circle_n wherefore_o in_o the_o triangle_n b_o l_o n_o let_v the_o angle_n n_o b_o l_o be_v find_v according_a to_o this_o proposition_n that_o as_o b_o n_n be_v to_o n_n l_o so_fw-mi be_v the_o whole_a sign_n to_o the_o tangent_fw-la of_o the_o angle_n n_o b_o l._n moreover_n the_o two_o angle_n l_o n_n b_o n_o b_o l_o be_v together_o equal_a to_o one_o straight_o or_o 90_o
be_v find_v in_o the_o hemisphere_n only_o except_o the_o horizon_n of_o the_o pole_n which_o be_v the_o very_a aequator_fw-la so_o we_o shall_v have_v three_o or_o four_o chief_a point_n through_o which_o the_o horizon_n ought_v to_o pass_v to_o find_v out_o the_o other_o point_n there_o be_v no_o more_o commodious_a way_n than_o by_o the_o benefit_n of_o the_o globe_n viz._n let_v the_o pole_n be_v elevate_v for_o the_o latitude_n of_o the_o place_n assume_v then_o in_o every_o parallel_n let_v one_o point_v be_v choose_v through_o which_o the_o first_o meridian_n pass_v and_o let_v that_o be_v bring_v to_o the_o meridian_n which_o do_v let_v the_o degree_n under_o the_o meridian_n be_v note_v and_o so_o you_o must_v do_v in_o every_o parallel_n these_o be_v note_v let_v so_o many_o degree_n be_v reckon_v on_o both_o side_n from_o every_o parallel_n from_o the_o meridian_n of_o the_o place_n give_v in_o the_o map_n on_o the_o aequator_fw-la viz._n for_o 10_o 20_o 30_o and_o so_o on_o and_o where_o the_o meridian_n cut_n the_o convenient_a parallel_n they_o shall_v be_v the_o point_v demand_v to_o wit_n through_o which_o the_o horizon_n be_v to_o be_v draw_v and_o the_o situation_n of_o the_o other_o place_n may_v be_v examine_v in_o some_o measure_n at_o that_o by_o this_o method_n the_o whole_a superficies_n of_o the_o earth_n may_v almost_o be_v represent_v on_o one_o table_n if_o that_o either_o of_o the_o pole_n viz._n the_o antarctick_a be_v assume_v for_o the_o eye_n if_o a_o table_n or_o glass_n plain_o be_v take_v of_o any_o parallel_n near_o the_o pole_n for_o instance_n the_o plain_a of_o the_o arctic_a pole_n and_o the_o antarctick_a circle_n on_o one_o plain_a neither_o do_v any_o thing_n else_o remain_v to_o be_v do_v or_o add_v to_o the_o former_a construction_n but_o that_o the_o meridian_n line_n shall_v be_v protract_v and_o the_o parallel_n draw_v from_o the_o other_o part_n of_o the_o aequator_fw-la then_o let_v the_o whole_a ecliptic_a be_v draw_v and_o if_o you_o please_v let_v the_o horizon_n be_v complete_v but_o see_v that_o the_o part_n and_o degree_n situate_v beyond_o the_o aequator_fw-la towards_o the_o antarctick_a pole_n by_o this_o mode_n will_v become_v far_o great_a than_o the_o part_n about_o and_o in_o the_o aequator_fw-la which_o be_v contrary_a to_o the_o truth_n of_o the_o matter_n therefore_o it_o be_v better_a to_o make_v the_o projecture_n on_o two_o hemisphere_n that_o one_o may_v show_v the_o arctic_a orb_n the_o other_o the_o antarctick_a table_n describe_v according_a to_o this_o method_n be_v very_o few_o to_o general_a map_n of_o right_a line_n two_o other_o map_n very_o small_a describe_v in_o this_o method_n be_v wont_a to_o be_v add_v whereof_o one_o exhibit_v the_o region_n about_o the_o arctic_a pole_n the_o other_o those_o about_o the_o antarctick_a which_o the_o reader_n may_v look_v upon_o for_o the_o better_a understanding_n of_o what_o have_v be_v say_v but_o these_o be_v better_o learn_v from_o practice_n than_o from_o precept_n the_o second_o mode_n the_o eye_n be_v place_v in_o the_o plain_a of_o the_o aequator_fw-la scheme_n the_o second_o mode_n see_v scheme_n the_o precede_a mode_n of_o describe_v of_o geographical_a map_n do_v neither_o fit_o show_v the_o magnitude_n and_o situation_n of_o place_n neither_o be_v commodious_a to_o describe_v the_o hemisphere_n intercept_v between_o the_o two_o pole_n and_o to_o represent_v all_o the_o place_n lie_v in_o the_o same_o meridian_n moreover_o it_o seem_v to_o be_v repugnant_a to_o our_o conception_n that_o the_o pole_n of_o the_o earth_n shall_v fall_v into_o the_o centre_n and_o therefore_o those_o describe_v table_n afford_v a_o more_o difficult_a imagination_n therefore_o another_o method_n have_v be_v find_v which_o be_v somewhat_o more_o hard_a than_o the_o former_a but_o more_o apt_o represent_v the_o place_n of_o the_o earth_n and_o remove_v the_o pole_n from_o the_o aequator_fw-la for_o the_o conceive_n of_o this_o method_n we_o must_v understand_v the_o superficies_n of_o the_o earth_n to_o be_v cut_v into_o two_o hemisphere_n from_o the_o whole_a periphery_n of_o the_o meridian_n and_o in_o two_o table_n we_o exhibit_v those_o hemisphere_n one_o in_o one_o the_o other_o in_o the_o gther_o the_o eye_n be_v place_v in_o the_o point_n of_o the_o aequator_fw-la which_o be_v remove_v 90_o degree_n from_o the_o first_o meridian_n the_o table_n or_o glass_n in_o which_o this_o representation_n ought_v to_o be_v make_v be_v assume_v the_o place_n of_o the_o first_o meridian_n and_o hemisphere_n which_o lie_v beneath_o that_o plain_a in_o respect_n of_o the_o eye_n be_v take_v to_o represent_v it_o on_o the_o plain_a in_o this_o form_n of_o projecture_n the_o semicircle_n of_o the_o aequator_fw-la become_v a_o right_a line_n and_o that_o meridian_n which_o be_v distant_a from_o the_o first_o 90_o degree_n unto_o which_o the_o eye_n be_v conceive_v eminent_a will_v also_o become_v the_o right_a line_n all_o the_o other_o meridian_n and_o all_o the_o parallel_n of_o the_o aequator_fw-la become_v the_o arch_n of_o the_o circle_n because_o their_o cones_n be_v cut_v from_o the_o plain_a of_o the_o table_n by_o a_o subcontrary_a section_n the_o explication_n of_o which_o must_v be_v demand_v from_o the_o conical_a doctrine_n and_o may_v better_o be_v show_v than_o express_v but_o the_o ecliptic_a become_v a_o portion_n of_o the_o eclipse_n for_o the_o cause_n allege_v in_o the_o former_a method_n explain_v the_o description_n mathematical_o explain_v this_o description_n be_v thus_o make_v the_o point_n e_o be_v take_v for_o the_o centre_n in_o the_o table_n a_o great_a or_o small_a periphery_n of_o the_o circle_n be_v describe_v a_o b_o c_o d_o as_o we_o desire_v to_o have_v the_o table_n great_a or_o small_a this_o represent_v the_o first_o meridian_n and_o its_o opposite_a viz._n the_o diameter_n b_o d_o be_v draw_v there_o arise_v two_o semiperiphery_n whereof_o one_o b_o a_o d_o be_v the_o first_o meridian_n the_o other_o b_o c_o d_o be_v the_o opposite_a or_o of_o longitude_n 180._o this_o diameter_n b_o d_o represent_v the_o meridian_n 90_o degree_n distant_a from_o the_o first_o and_o his_o point_n d_o be_v one_o pole_n viz._n the_o arctic_a but_o the_o point_n d_o be_v the_o pole_n antarctick_a the_o diameter_n a_o c_o to_z b_o d_o be_v the_o perpendicular_a line_n of_o the_o aequator_fw-la let_v these_o quadrant_n a_o b_o b_o c_o c_o d_o d_o a_o be_v divide_v every_o one_o into_o 90_o degree_n moreover_o we_o must_v do_v thus_o for_o the_o representation_n of_o the_o meridian_n and_o parallel_n or_o for_o the_o find_v out_o the_o arch_n of_o the_o meridian_n and_o parallel_n first_o the_o line_n of_o the_o aequator_fw-la a_o c_o must_v be_v divide_v into_o its_o degree_n to_o wit_n 180_o because_o it_o only_o show_v half_o the_o aequator_fw-la or_o a_o e_o e_o c_o into_o 90_o after_o this_o mode_n from_o the_o point_n d_o let_v the_o semiperiphery_n right_a line_n a_o b_o c_o be_v draw_v to_o every_o degree_n or_o which_o be_v as_o well_o let_v the_o rule_n be_v apply_v to_o the_o point_n d_o and_o to_o every_o degree_n of_o the_o semiperiphery_n a_o b_o c_o these_o line_n shall_v cut_v the_o line_n of_o the_o aequator_fw-la into_o 180_o part_n which_o shall_v represent_v the_o degree_n which_o be_v the_o degree_n of_o longitude_n and_o therefore_o the_o number_n 1_o 2_o 3_o 4_o and_o the_o like_a must_v be_v ascribe_v begin_v from_o the_o first_o meridian_n d_o a_o b._n through_o every_o one_o of_o these_o point_n 1_o 2_o 3_o and_o both_o the_o pole_n b_o d_o the_o arch_n of_o the_o circle_n must_v be_v describe_v which_o shall_v represent_v the_o meridian_n but_o how_o the_o periphery_n must_v be_v describe_v through_o these_o three_o give_v point_n for_o example_n b_o d_o or_o b_o 2_o d_o and_o the_o like_a be_v teach_v by_o geometry_n viz._n you_o must_v find_v the_o centre_n for_o every_o periphery_a to_o be_v describe_v which_o centre_n be_v place_v in_o the_o very_a line_n of_o the_o aequator_fw-la as_o be_v the_o centre_n e_o of_o the_o meridian_n d_o a_o b._n those_o point_n be_v find_v according_a to_o euclid_n method_n proposition_n 1_o lib._n 3._o if_o the_o line_n b_o 1_o b_o 2_o b_o 3_o 1._o see_v euclid_n lib._n 3._o proposition_n 1._o etc._n etc._n be_v double_o cut_v by_o the_o perpendicular_a line_n this_o be_v most_o easy_a by_o the_o application_n of_o the_o rule_n where_o these_o perpendicular_a line_n fall_v into_o the_o protract_a line_n e_o c_o of_o the_o aequator_fw-la if_o there_o be_v need_n there_o be_v the_o centre_n for_o the_o describe_v of_o the_o arch_n b_o 1_o d_o b_o 2_o d_o etc._n etc._n but_o the_o centre_n of_o the_o arch_n b_o 91_o d_o b_o 92_o d_o b_o 93_o d_o etc._n etc._n
two_o kind_n of_o situation_n the_o quarter_n of_o the_o second_o place_n be_v not_o vary_v at_o the_o intermedial_a place_n for_o example_n let_v amsterdam_n be_v take_v for_o the_o first_o place_n from_o whence_o the_o voyage_n be_v to_o be_v begin_v and_o fernambuck_n in_o brasilia_n for_o the_o second_o or_o unto_o which_o the_o voyage_n be_v appoint_v let_v amsterdam_n therefore_o be_v bring_v to_o the_o brass_n meridian_n and_o let_v the_o pole_n be_v elevate_v for_o the_o latitude_n of_o the_o same_o for_o so_o the_o wooden_a horizon_n represent_v the_o horizon_n of_o the_o place_n let_v the_o quadrant_n be_v affix_v to_o the_o vertex_fw-la and_o let_v it_o be_v apply_v to_o fernambuck_n it_o will_v show_v the_o quarter_n in_o the_o horizon_n in_o which_o fernambuck_n lie_v from_o amsterdam_n and_o the_o arch_n interject_v between_o these_o two_o place_n exhibit_v on_o the_o globe_n the_o intermedial_a point_n it_o must_v therefore_o be_v show_v that_o the_o quarter_n in_o which_o fernambuck_n lie_v from_o every_o one_o of_o these_o point_n be_v not_o the_o same_o but_o all_o divers_a or_o that_o from_o every_o one_o of_o those_o intermedial_a place_n fernambuck_n do_v not_o lie_v towards_o one_o and_o the_o same_o quarter_n for_o the_o understanding_n of_o this_o we_o must_v repeat_v from_o the_o precede_a doctrine_n that_o the_o angle_n with_o the_o meridian_n of_o this_o assume_v place_n make_v with_o the_o vertical_a pass_v through_o the_o other_o place_n sheweth_z the_o quarter_n of_o another_o place_n from_o some_o one_o place_n assume_v or_o the_o arch_n of_o the_o horizon_n intercept_v between_o the_o meridian_n and_o this_o vertical_a as_o the_o angle_n show_v the_o quarter_n of_o fernambuck_n from_o amsterdam_n which_o the_o quadrant_n with_o the_o brass_n meridian_n make_v which_o be_v of_o amsterdam_n itself_o therefore_o to_o prove_v the_o truth_n of_o this_o proposition_n let_v what_o point_v you_o please_v be_v take_v between_o amsterdam_n and_o fernambuck_n in_o the_o arch_a subject_n to_o the_o quadrant_n and_o let_v the_o meridian_n pass_v through_o by_o they_o be_v conceive_v it_o be_v best_a to_o take_v those_o point_n through_o which_o on_o the_o globe_n the_o meridian_n pass_n or_o the_o circle_n of_o longitude_n because_o therefore_o the_o quadrant_n pass_v through_o every_o one_o of_o these_o place_n and_o fernambuck_n itself_o it_o will_v represent_v the_o vertical_a of_o every_o place_n in_o which_o fernambuck_n lie_v from_o they_o therefore_o the_o angle_n which_o it_o make_v with_o the_o meridian_n of_o each_o place_n be_v the_o angle_n of_o position_n and_o show_v the_o quarter_n in_o which_o or_o towards_o which_o fernambuck_n lie_v from_o every_o intermedial_a place_n now_o these_o angle_n be_v unequal_a and_o of_o a_o different_a magnitude_n therefore_o the_o quarter_n also_o towards_o which_o fernambuck_n lie_v from_o those_o place_n be_v divers_a now_o that_o these_o angles_n be_v unequal_a be_v manifest_a from_o the_o very_a sight_n or_o more_o evident_a if_o that_o by_o any_o interval_n of_o the_o compass_n you_o draw_v a_o arch_n from_o each_o point_n and_o measure_v these_o arch_n intercept_v between_o each_o meridian_n and_o the_o vertical_a or_o if_o that_o we_o have_v ready_a by_o itself_o a_o crooked_a portion_n which_o may_v be_v fit_v to_o the_o superficies_n of_o the_o globe_n or_o if_o that_o the_o place_n themselves_o be_v bring_v to_o the_o brazen_a meridian_n and_o the_o pole_n be_v elevate_v for_o their_o latitude_n let_v the_o quadrant_n be_v apply_v to_o the_o vertex_fw-la and_o to_o fernambuck_n and_o in_o that_o situation_n let_v the_o degree_n of_o the_o arch_n of_o the_o horizon_n be_v reckon_v defective_a straight_o line_v and_o sea_n map_n be_v defective_a corollary_n therefore_o the_o straight_o line_v and_o sea_n map_n be_v very_o defective_a which_o do_v so_o represent_v the_o place_n that_o if_o that_o any_o two_o place_n be_v take_v at_o one_o of_o which_o the_o situation_n or_o quarter_n of_o the_o other_o be_v examine_v this_o other_o do_v seem_v to_o be_v in_o one_o and_o the_o same_o quarter_n from_o the_o intermedial_a place_n which_o yet_o be_v false_a the_o cause_n of_o the_o fault_n be_v that_o they_o exhibit_v the_o meridian_n parallel_n which_o yet_o do_v meet_v in_o the_o pole_n but_o seaman_n regard_v not_o this_o fault_n so_o that_o they_o do_v but_o relate_v the_o course_n or_o quarter_n which_o they_o ought_v to_o have_v observe_v in_o sail_v from_o one_o place_n to_o another_o proposition_n iv_o if_o a_o voyage_n be_v to_o be_v make_v or_o that_o a_o ship_n be_v to_o sail_n from_o one_o place_n to_o another_o which_o two_o place_n be_v not_o in_o one_o meridian_n or_o both_o of_o they_o in_o the_o aequator_fw-la by_o a_o most_o short_a cut_v or_o by_o this_o mean_n that_o it_o may_v never_o recede_v from_o the_o interpose_a arch_n of_o the_o vertical_a in_o such_o a_o voyage_n the_o quarter_n be_v change_v every_o moment_n or_o the_o quarter_n become_v another_o and_o another_o into_o which_o the_o voyage_n be_v to_o be_v take_v or_o the_o ship_n be_v to_o be_v sail_v this_o proposition_n be_v manifest_a from_o the_o forego_n 3._o see_v prop._n 3._o for_o let_v the_o voyage_n be_v take_v from_o amsterdam_n to_o fernambuck_n by_o the_o near_a way_n that_o be_v through_o the_o arch_n of_o the_o quadrant_n affix_v at_o amsterdam_n and_o pass_v through_o by_o fernambuck_n because_o therefore_o every_o where_n in_o the_o whole_a voyage_n or_o in_o every_o point_n the_o voyage_n be_v direct_v towards_o fernambuck_n and_o it_o be_v show_v in_o the_o precedent_a proposition_n that_o the_o quarter_n be_v divers_a towards_o which_o from_o those_o middle_n point_v fernambuck_n lie_v therefore_o it_o be_v manifest_a that_o the_o quarter_n become_v another_o and_o another_o in_o every_o moment_n and_o in_o each_o point_n into_o which_o the_o ship_n be_v to_o sail_n or_o to_o be_v sail_v that_o it_o may_v respect_n fernambuck_n but_o if_o that_o the_o place_n be_v situate_v in_o one_o meridian_n or_o if_o that_o both_o be_v in_o the_o aequator_fw-la the_o case_n be_v otherwise_o for_o in_o they_o the_o same_o quarter_n of_o the_o voyage_n of_o the_o north_n or_o south_n remain_v in_o these_o the_o cardinal_n quarter_n of_o the_o east_n or_o west_n proposition_n v._o a_o voyage_n can_v be_v so_o undertake_v or_o a_o ship_n so_o direct_v that_o it_o may_v tend_v in_o each_o moment_n to_o other_o and_o other_o quarter_n but_o for_o some_o time_n at_o the_o least_o whilst_o it_o be_v move_v it_o tend_v to_o one_o and_o the_o same_o quarter_n in_o appearance_n therefore_o whilst_o we_o be_v to_o sail_v from_o one_o place_n to_o another_o such_o a_o way_n or_o line_n of_o a_o way_n be_v most_o convenient_a who_o every_o two_o near_a point_n be_v situate_v in_o one_o and_o the_o same_o quarter_n in_o show_n although_o that_o this_o way_n be_v not_o the_o short_a another_o a_o ship_n in_o a_o moment_n can_v move_v from_o one_o quarter_n to_o another_o a_o ship_n can_v tend_v from_o one_o quarter_n to_o another_o in_o a_o moment_n of_o time_n but_o whilst_o that_o it_o be_v move_v for_o some_o time_n at_o the_o least_o it_o tend_v to_o it_o moreover_o it_o can_v by_o no_o mean_n be_v do_v that_o the_o seaman_n shall_v know_v the_o quarter_n unto_o which_o the_o ship_n shall_v be_v sail_v if_o that_o another_o quarter_n be_v so_o often_o to_o be_v assume_v therefore_o it_o be_v evident_a that_o that_o passage_n between_o two_o place_n be_v most_o commodious_a for_o navigation_n who_o every_o two_o vicine_fw-la point_n be_v situate_v in_o one_o and_o the_o same_o quarter_n so_o that_o the_o ship_n may_v be_v continual_o direct_v unto_o one_o quarter_n and_o to_o come_v by_o such_o a_o direction_n to_o the_o place_n appoint_v this_o be_v suppose_v let_v we_o inquire_v what_o way_n be_v thence_o for_o the_o motion_n of_o the_o ship_n which_o way_n indeed_o if_o that_o the_o place_n be_v situate_v in_o one_o meridian_n shall_v be_v part_n of_o the_o meridian_n itself_o if_o in_o the_o aequator_fw-la that_o way_n shall_v be_v a_o portion_n of_o the_o aequator_fw-la itself_o if_o in_o one_o parallel_n it_o shall_v be_v a_o part_n of_o this_o parallel_n if_o in_o any_o other_o circle_n beside_o these_o that_o way_n shall_v be_v another_o line_n not_o that_o circle_n as_o we_o shall_v show_v in_o the_o follow_a proposition_n proposition_n vi_o if_o that_o a_o voyage_n be_v appoint_v or_o that_o a_o ship_n be_v direct_v to_o the_o north_n or_o south_n quarter_n that_o be_v if_o that_o the_o place_n from_o whence_o and_o the_o place_n unto_o which_o be_v in_o one_o meridian_n the_o line_n of_o the_o motion_n of_o the_o ship_n itself_o shall_v be_v a_o part_n of_o the_o meridian_n it_o be_v prove_v from_o the_o first_o proposition_n of_o