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sea_n and_o the_o like_a be_v in_o guzurat_n but_o for_o very_a many_o month_n when_o it_o begin_v to_o blow_v in_o congo_n and_o guzurat_n in_o september_n it_o continue_v even_o to_o march_n the_o anniversary_n wind_n of_o the_o grecian_n which_o they_o call_v ornithia_n or_o the_o bridge_n wind_n this_o they_o say_v blow_v after_o the_o vernal_a aequinox_n the_o sun_n ascend_v to_o the_o vertex_fw-la of_o the_o european_n proposition_n v._o why_o the_o etesian_a wind_n blow_v not_o in_o italy_n france_n germany_n persia_n and_o other_o region_n especial_o see_v that_o they_o be_v more_o near_o the_o northern_a mountain_n from_o whence_o we_o assert_v the_o etesian_a wind_n of_o the_o grecian_n congo_n and_o guzurat_n do_v arise_v and_o blow_v mountain_n the_o etesian_a wind_n blow_v not_o in_o all_o region_n though_o near_o the_o northern_a mountain_n the_o question_n be_v of_o no_o small_a moment_n and_o i_o wish_v that_o we_o have_v more_o accurate_a observation_n concern_v this_o 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to_o all_o place_n for_o although_o by_o accident_n it_o happen_v that_o it_o be_v not_o discern_v in_o all_o place_n viz._n because_o other_o wind_n blow_v more_o strong_a yet_o it_o be_v proper_a to_o some_o the_o cause_n be_v allege_v in_o the_o place_n cite_v 2._o on_o the_o coast_n of_o peru_n and_o part_n of_o chili_n and_o to_o the_o adjacent_a sea_n the_o south_n wind_n be_v almost_o perpetual_a and_o his_o collateral_a wind_n at_o the_o west_n it_o begin_v at_o the_o 46_o deg_fw-la of_o latitude_n and_o blow_v to_o panama_n the_o american_n isthmus_n and_o cause_v that_o in_o few_o day_n ship_n arrive_v from_o lima_n at_o panama_n lade_v with_o gold_n silver_n etc._n etc._n but_o it_o require_v many_o day_n sail_n from_o panama_n to_o lima._n but_o this_o wind_n blow_v not_o in_o the_o sea_n remote_a from_o the_o coast_n of_o peru_n it_o be_v difficult_a to_o render_v the_o cause_n of_o this_o wind_n by_o reason_n that_o the_o south_n land_n from_o whence_o it_o seem_v to_o blow_v be_v not_o yet_o know_v unto_o we_o yet_o i_o think_v it_o probable_a that_o because_o that_o mountain_n be_v find_v in_o it_o cover_v with_o perpetual_a snow_n therefore_o the_o wind_n be_v generate_v from_o a_o continual_a resolution_n of_o they_o but_o i_o will_v not_o infect_v the_o mind_n of_o the_o reader_n with_o these_o my_o suspicion_n or_o conjecture_n for_o peradventure_o the_o snow_n which_o be_v find_v all_o the_o year_n long_o in_o the_o high_a mountain_n at_o the_o strait_n of_o magellan_n be_v the_o cause_n of_o these_o wind_n but_o yet_o it_o may_v be_v object_v that_o those_o mountain_n lie_v from_o the_o south_n towards_o the_o west_n decline_v from_o the_o south_n wherefore_o we_o shall_v leave_v this_o to_o a_o more_o diligent_a inquisition_n or_o a_o more_o full_a knowledge_n of_o the_o south_n continent_n 3._o at_o the_o coast_n of_o the_o land_n of_o magellan_n or_o del_n fugo_n about_o the_o straight_a le_fw-fr mair_n continual_a or_o at_o least_o very_a frequent_a western_o wind_n do_v blow_n and_o that_o with_o that_o force_n that_o they_o make_v the_o tree_n to_o bend_v towards_o the_o east_n from_o their_o perpendicular_a rectitude_n neither_o be_v there_o any_o part_n of_o the_o earth_n in_o which_o those_o occidental_a wind_n so_o often_o blow_v but_o on_o the_o other_o part_n of_o the_o strait_n le_fw-fr mair_n at_o the_o coast_n of_o the_o south_n land_n the_o south_n wind_n blow_v i_o can_v render_v no_o other_o cause_n of_o those_o occidental_a wind_n but_o that_o i_o suppose_v they_o to_o be_v raise_v from_o snow_n and_o cloud_n in_o the_o south_n continent_n which_o extend_v itself_o from_o the_o side_n of_o that_o occidental_a streight_n from_o the_o south_n towards_o the_o north._n but_o these_o be_v doubtful_a and_o more_o diligent_o to_o be_v inquire_v after_o 4._o on_o the_o malabarian_a coast_n of_o india_n for_o almost_o the_o whole_a year_n the_o north_n and_o north-east_n wind_n blow_v the_o cause_n proceed_v from_o the_o resolution_n of_o the_o snow_n of_o the_o mountain_n of_o the_o asiatic_a sarmatia_n viz._n imaus_n or_o caucasus_n from_o the_o cloud_n on_o the_o other_o mountain_n of_o asia_n which_o be_v collect_v and_o press_v the_o subject_n air._n 5._o in_o the_o sea_n near_o to_o guinea_n the_o north_n west_n wind_n be_v frequent_a and_o in_o the_o remote_a sea_n the_o north_n east_n 6._o in_o the_o middle_a passage_n between_o japan_n and_o liampo_n a_o maritimate_a city_n of_o china_n even_o unto_o these_o be_v find_v occidental_a wind_n which_o blow_n in_o japan_n in_o november_n and_o december_n 7._o at_o the_o isle_n guotou_n not_o far_o from_o the_o isle_n do_v cavallos_n in_o the_o sea_n of_o china_n be_v a_o frequent_a south_n wind_n when_o that_o yet_o in_o the_o neighbour_a ocean_n a_o north_n wind_n be_v predominate_v proposition_n vii_o unto_o these_o periodical_a or_o state_a wind_n appertain_v those_o also_o that_o be_v term_v day_n wind_n which_o in_o some_o region_n and_o at_o a_o certain_a time_n of_o the_o year_n blow_v for_o some_o hour_n every_o day_n call_v of_o day_n wind_n so_o call_v now_o they_o be_v find_v to_o be_v twofold_a and_o that_o only_a in_o some_o maritimate_a place_n for_o some_o blow_n from_o mediterranean_a place_n to_o the_o shore_n towards_o the_o sea_n and_o other_o on_o the_o contrary_a from_o the_o sea_n to_o the_o shore_n 1._o on_o the_o malabarian_a coast_n in_o the_o summer_n season_n viz._n from_o september_n to_o april_n the_o terrestrial_a wind_n or_o terrinhos_n do_v blow_n from_o the_o twelve_o hour_n of_o the_o night_n to_o the_o twelve_o hour_n of_o the_o day_n now_o these_o wind_n be_v eastern_a wind_n but_o from_o the_o twelve_o hour_n of_o the_o day_n to_o the_o twelve_o hour_n of_o the_o night_n the_o sea_n wind_n or_o viraconus_n to_o wit_n the_o west_n wind_n blow_v but_o this_o be_v very_o weak_a so_o that_o by_o its_o assistance_n the_o ship_n can_v hardly_o arrive_v at_o the_o shoar_n i_o suppose_v the_o cause_n of_o those_o oriental_a wind_n from_o twelve_o at_o night_n to_o twelve_o in_o the_o day_n partly_o to_o be_v a_o general_a wind_n and_o partly_o cloud_n on_o the_o mountain_n gatis_n but_o the_o cause_n of_o the_o occidental_a wind_n that_o blow_n from_o twelve_o in_o the_o day_n to_o twelve_o at_o night_n be_v the_o resolution_n of_o thick_a cloud_n cause_v by_o the_o set_n of_o the_o sun_n which_o cloud_n before_o by_o the_o oriental_a wind_n be_v force_v towards_o the_o west_n out_o of_o those_o name_v month_n the_o north_n wind_n predominate_v also_o the_o east_n and_o north-east_n neither_o by_o reason_n of_o the_o often_o tempest_n be_v these_o terrestrial_a and_o marine_a wind_n discern_v 2._o in_o musulipatan_n a_o city_n on_o the_o coast_n of_o charomandel_n these_o terrinhos_n begin_v to_o blow_v
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 as_o well_o towards_o the_o north_n from_o the_o aequator_fw-la as_o towards_o the_o south_n in_o which_o declination_n he_o describe_v the_o tropic_n of_o cancer_n and_o capricorn_n thence_o it_o be_v that_o he_o be_v not_o perpetual_o vertical_a to_o the_o place_n lie_v under_o the_o aequator_fw-la neither_o do_v he_o always_o keep_v one_o distance_n from_o other_o place_n for_o sometime_o he_o be_v more_o nigh_o and_o sometime_o more_o remote_a from_o a_o certain_a place_n and_o various_o change_v heat_n cold_a rain_n and_o other_o condition_n of_o the_o season_n these_o which_o we_o have_v now_o speak_v of_o may_v be_v show_v as_o well_o on_o the_o globe_n as_o in_o map_n a_o zone_n be_v term_v a_o part_n of_o the_o earth_n include_v within_o the_o tropic_a and_o the_o polary_a circle_n what_o a_o zone_n what_o and_o because_o there_o be_v two_o tropic_n and_o two_o polary_a circle_n thence_o it_o come_v to_o pass_v that_o there_o be_v five_o zone_n viz._n 1._o torrid_a 2._o 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
parallel_n long_a day_n elevation_n of_o the_o pole_n the_o interval_n  _fw-fr  _fw-fr hour_n min._n deg_fw-la min._n  _fw-fr  _fw-fr the_o first_o the_o begin_n middle_a end_n &_o begin_n of_o the_o 2._o 12_o 0_o 0_o 0_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 12_o 15_o 4_o 15_o 0_o 1_o  _fw-fr  _fw-fr 12_o 30_o 8_o 25_o 8_o 25_o  _fw-fr  _fw-fr 12_o 45_o 12_o 30_o  _fw-fr  _fw-fr the_o second_o the_o middle_a the_o end_n 13_o 0_o 16_o 25_o 8_o  _fw-fr  _fw-fr  _fw-fr 13_o 15_o 20_o 15_o  _fw-fr  _fw-fr the_o three_o the_o middle_a the_o end_n 13_o 30_o 23_o 50_o 7_o 25_o  _fw-fr  _fw-fr 13_o 45_o 27_o 40_o  _fw-fr  _fw-fr the_o four_o the_o middle_a the_o end_n 14_o 0_o 30_o 20_o 6_o 30_o  _fw-fr  _fw-fr 14_o 15_o 33_o 40_o  _fw-fr  _fw-fr the_o five_o the_o middle_a the_o end_n 14_o 30_o 36_o 28_o 6_o 8_o  _fw-fr  _fw-fr 14_o 45_o 39_o 2_o  _fw-fr  _fw-fr the_o six_o the_o middle_a the_o end_n 15_o 0_o 41_o 22_o 4_o 52_o  _fw-fr  _fw-fr 15_o 15_o 43_o 32_o  _fw-fr  _fw-fr the_o seven_o the_o middle_a the_o end_n 15_o 30_o 45_o 29_o 4_o 7_o  _fw-fr  _fw-fr 15_o 45_o 47_o 20_o  _fw-fr  _fw-fr the_o eighth_z the_o middle_a the_o end_n 16_o 0_o 49_o 1_o 3_o 31_o  _fw-fr  _fw-fr 16_o 15_o 50_o 33_o  _fw-fr  _fw-fr the_o nine_o the_o middle_a the_o end_n 16_o 30_o 51_o 58_o 2_o 7_o  _fw-fr  _fw-fr 16_o 45_o 53_o 17_o  _fw-fr  _fw-fr the_o ten_o the_o middle_a the_o end_n 17_o 0_o 54_o 27_o 2_o 49_o  _fw-fr  _fw-fr 17_o 15_o 55_o 34_o  _fw-fr  _fw-fr the_o eleven_o the_o middle_a the_o end_n 17_o 30_o 56_o 37_o 2_o 10_o  _fw-fr  _fw-fr 17_o 45_o 57_o 32_o  _fw-fr  _fw-fr the_o twelve_o the_o middle_a the_o end_n 18_o 0_o 58_o 29_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 18_o 15_o 59_o 14_o  _fw-fr  _fw-fr the_o thirteen_o the_o middle_a the_o end_n 18_o 30_o 59_o 58_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 18_o 45_o 60_o 40_o  _fw-fr  _fw-fr the_o fourteen_o the_o middle_a the_o end_n 19_o 0_o 61_o 18_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 19_o 15_o 61_o 55_o  _fw-fr  _fw-fr the_o fifteen_o the_o middle_a the_o end_n 19_o 30_o 62_o 25_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 19_o 45_o 62_o 54_o  _fw-fr  _fw-fr the_o sixteenth_o the_o middle_a the_o end_n 20_o 0_o 63_o 22_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 20_o 15_o 64_o 40_o  _fw-fr  _fw-fr the_o seventeen_o the_o middle_a the_o end_n 20_o 30_o 64_o 6_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 20_o 45_o 64_o 30_o  _fw-fr  _fw-fr the_o eighteen_o the_o middle_a the_o end_n 21_o 0_o 65_o 49_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 21_o 15_o 65_o 6_o  _fw-fr  _fw-fr the_o nineteenth_o the_o middle_a the_o end_n 21_o 30_o 65_o 21_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 21_o 45_o 65_o 35_o  _fw-fr  _fw-fr the_o twenty_o the_o middle_a the_o end_n 22_o 0_o 65_o 47_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 22_o 15_o 66_o 57_o  _fw-fr  _fw-fr the_o 21_o the_o middle_a the_o end_n 22_o 30_o 66_o 6_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 22_o 45_o 66_o 14_o  _fw-fr  _fw-fr the_o 22d_o the_o middle_a the_o end_n 23_o 0_o 66_o 20_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 23_o 15_o 66_o 25_o  _fw-fr  _fw-fr the_o 23d_o the_o middle_a the_o end_n 23_o 30_o 66_o 28_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 23_o 45_o 66_o 30_o  _fw-fr  _fw-fr the_o 24_o the_o middle_a the_o end_n 24_o 0_o 66_o 31_o  _fw-fr  _fw-fr the_o climate_n be_v wont_a to_o be_v extend_v no_o further_o because_o that_o in_o the_o follow_a place_n the_o long_a day_n do_v not_o increase_v by_o hour_n but_o by_o whole_a day_n or_o diurnal_a revolution_n and_o it_o be_v lose_v labour_n to_o compute_v they_o notwithstanding_o the_o follow_a canon_n will_v show_v the_o elevation_n of_o the_o pole_n or_o latitude_n of_o the_o place_n where_o the_o long_a day_n increase_v by_o whole_a month_n month_n 1_o 2_o 3_o 4_o 5_o 6_o the_o latitude_n of_o the_o place_n deg_fw-la min._n deg_fw-la min._n deg_fw-la min._n deg_fw-la min._n deg_fw-la min._n deg_fw-la min._n  _fw-fr 67_o 20_o 69_o 30_o 73_o 20_o 78_o 20_o 84_o 0_o 90_o 0_o proposition_n fourteen_o to_o explain_v the_o method_n of_o other_o geographer_n in_o reckon_n of_o the_o climate_n and_o make_v the_o table_n of_o the_o climate_n geographer_n the_o division_n of_o the_o earth_n into_o climate_n by_o the_o ancient_a geographer_n the_o ancient_a geographer_n especial_o the_o grecian_n who_o suppose_v only_o a_o small_a portion_n of_o the_o earth_n to_o be_v inhabit_v because_o that_o as_o well_o the_o place_n northern_o as_o those_o of_o the_o torrid_a zone_n they_o deny_v as_o impossible_a to_o be_v inhabit_v therefore_o they_o divide_v only_o that_o portion_n of_o the_o earth_n which_o they_o know_v into_o climate_n and_o so_o only_o number_v seven_o climate_n from_o the_o aequator_fw-la towards_o the_o pole_n arctic_a and_o name_v they_o from_o some_o note_a place_n through_o which_o the_o parallel_n of_o the_o climate_n pass_v viz._n the_o first_o climate_n they_o call_v the_o climate_n through_o meroe_n which_o be_v a_o island_n and_o city_n in_o africa_n encompass_v by_o the_o nile_n the_o second_o through_o syene_n a_o city_n of_o egypt_n the_o three_o through_o alexandria_n in_o egypt_n the_o four_o through_o the_o island_n of_o rhodes_n the_o five_o through_o the_o hellespont_n other_o through_o rome_n the_o six_o through_o borysthenes_n a_o famous_a river_n of_o the_o european_a sarmatia_n the_o seven_o through_o the_o riphaean_a mountain_n of_o sarmatia_n the_o ancient_n number_v not_o the_o other_o climate_n from_o the_o other_o side_n of_o the_o aequator_fw-la towards_o the_o south_n because_o all_o those_o place_n be_v unknown_a to_o they_o and_o many_o thought_n that_o the_o sea_n possess_v all_o the_o superficies_n of_o the_o earth_n which_o see_v it_o seem_v somewhat_o improbable_a to_o the_o latter_a these_o also_o number_v the_o climate_n from_o the_o other_o side_n of_o the_o aequator_fw-la and_o they_o name_v they_o not_o from_o any_o note_a place_n for_o they_o have_v no_o knowledge_n of_o any_o but_o by_o the_o same_o appellation_n with_o those_o of_o the_o northern_a only_o prepose_v the_o preposition_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d as_o the_o climate_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d as_o if_o you_o shall_v say_v the_o climate_n opposite_a to_o the_o climate_n through_o meroe_n or_o syene_n etc._n etc._n ancient_n other_o climate_n add_v by_o the_o ancient_n but_o when_o through_o progress_n of_o time_n they_o discover_v many_o part_n of_o the_o earth_n lie_v towards_o the_o south_n pole_n to_o be_v inhabit_v many_o more_o climate_n be_v number_v and_o constitute_v some_o name_v the_o eight_o clime_n from_o the_o palus_n maeotis_n the_o nine_o from_o the_o baltic_a sea_n the_o ten_o the_o eleven_o and_o the_o rest_n from_o other_o place_n which_o denomination_n although_o not_o necessary_a for_o the_o construction_n of_o a_o table_n yet_o they_o may_v be_v add_v unto_o our_o table_n in_o those_o areae_fw-la where_o we_o have_v place_v the_o number_n of_o the_o climate_n for_o so_o the_o climate_n will_v stick_v close_o in_o our_o memory_n as_o also_o the_o place_n in_o every_o climate_n and_o we_o may_v be_v able_a to_o make_v a_o better_a comparison_n between_o the_o difference_n of_o cold_a and_o heat_n but_o this_o be_v better_a to_o leave_v to_o the_o industry_n of_o the_o reader_n and_o to_o those_o that_o be_v studious_a than_o to_o add_v it_o to_o it_o that_o so_o we_o may_v afford_v they_o a_o great_a occasion_n of_o contemplate_v the_o terrestrial_a globe_n and_o by_o this_o mean_n may_v more_o easy_o commit_v they_o to_o memory_n climate_n where_o the_o ancient_n begin_v the_o climate_n you_o must_v also_o take_v notice_n that_o the_o ancient_n do_v not_o begin_v the_o numeration_n of_o the_o climate_n from_o the_o aequator_fw-la itself_o as_o our_o table_n do_v but_o from_o the_o place_n or_o parallel_n where_o the_o long_a day_n consist_v of_o 12¾_n hour_n and_o therefore_o their_o first_o climate_n be_v the_o second_o in_o our_o table_n their_o second_o our_o three_o and_o so_o on_o for_o they_o suppose_v those_o place_n which_o we_o ascribe_v to_o the_o first_o climate_n can_v not_o possible_o be_v inhabit_v by_o man_n by_o reason_n of_o the_o excessive_a heat_n of_o the_o sun_n latitude_n the_o first_o climate_n of_o 9_o degree_n of_o latitude_n that_o therefore_o they_o judge_v it_o not_o meet_v to_o reckon_v those_o place_n but_o see_v that_o experience_n have_v demonstrate_v the_o contrary_a we_o will_v observe_v their_o mode_n of_o name_v and_o constitute_v of_o those_o climate_n ptolemy_n begin_v the_o first_o climate_n from_o the_o parallel_n where_o the_o long_a day_n be_v 12¼_n hour_n or_o where_o the_o latitude_n or_o distance_n from_o the_o aequator_fw-la be_v four_o degree_n 15_o minute_n the_o matter_n be_v of_o no_o
great_a concernment_n yet_o it_o be_v better_a to_o begin_v from_o the_o aequator_fw-la that_o all_o the_o place_n may_v lie_v in_o some_o climate_n proposition_n xv._o to_o show_v the_o use_n of_o the_o table_n of_o the_o climate_n 1._o the_o latitude_n of_o some_o place_n or_o elevation_n of_o the_o pole_n be_v give_v to_o know_v the_o quantity_n of_o the_o long_a day_n in_o that_o place_n and_o the_o climate_n in_o which_o it_o lie_v let_v the_o give_v elevation_n of_o the_o pole_n be_v seek_v in_o the_o table_n and_o on_o the_o opposite_a region_n we_o shall_v find_v both_o the_o quantity_n of_o the_o long_a day_n as_o also_o the_o climate_n and_o the_o parallel_n if_o that_o the_o give_v elevation_n can_v be_v find_v in_o the_o table_n then_o take_v that_o elevation_n which_o be_v less_o near_o or_o the_o like_a which_o be_v find_v in_o the_o table_n climate_n from_o the_o longitude_n of_o the_o long_a day_n of_o any_o place_n to_o know_v the_o latude_n of_o the_o place_n and_o the_o parallel_n and_o climate_n 2._o the_o longitude_n of_o the_o long_a day_n of_o any_o place_n be_v give_v which_o any_o person_n have_v observe_v or_o receive_v by_o relation_n to_o know_v from_o thence_o the_o latitude_n of_o that_o place_n the_o parallel_n and_o the_o climate_n in_o which_o that_o place_n lie_v enter_v the_o table_n with_o the_o latitude_n give_v and_o you_o shall_v see_v on_o the_o opposite_a region_n both_o the_o latitude_n and_o the_o place_n demand_v as_o also_o the_o climate_n and_o parallel_n 3._o a_o climate_n be_v give_v to_o determine_v the_o longitude_n of_o the_o long_a day_n and_o the_o elevation_n of_o the_o pole_n this_o be_v facile_a from_o the_o very_a sight_n of_o the_o table_n chap._n xxvi_o of_o the_o light_n heatt_z cold_a rains_n in_o the_o diverse_a part_n of_o the_o earth_n or_o zone_n and_o other_o property_n of_o the_o zone_n proposition_n i._o these_o cause_n be_v efficacious_a to_o generate_v and_o procure_v light_a heatt_z cold_a and_o rain_n with_o other_o meteor_n in_o the_o place_n of_o the_o earth_n and_o the_o vicine_fw-la air._n heat_n of_o the_o cause_n of_o heat_n 1._o the_o more_o or_o less_o or_o no_o obliquity_n of_o the_o ray_n of_o the_o sun_n come_v to_o or_o emit_v on_o any_o place_n for_o the_o ray_n fall_v perpendicular_a on_o any_o place_n cause_n great_a heat_n and_o the_o other_o ray_n slide_v oblique_o have_v for_o that_o very_a reason_n a_o less_o power_n of_o heat_n by_o how_o much_o the_o obliquity_n of_o they_o be_v the_o great_a that_o be_v by_o how_o much_o the_o more_o they_o decline_v from_o the_o perpendicular_a ray._n 2._o the_o diurnal_a stay_n of_o the_o sun_n above_o the_o horizon_n of_o the_o place_n for_o the_o same_o heat_n make_v more_o hot_a and_o change_v the_o air_n in_o a_o long_a time_n than_o in_o a_o short_a 3._o the_o depression_n of_o the_o sun_n beneath_o the_o horizon_n be_v more_o or_o less_o in_o the_o night_n season_n for_o this_o difference_n of_o depression_n cause_v that_o either_o more_o or_o less_o light_a be_v perceive_v in_o the_o air_n also_o more_o or_o less_o heat_n rain_n thick_a cloud_n hitherto_o belong_v the_o twilight_n 4._o the_o more_o or_o less_o elevation_n of_o the_o moon_n above_o the_o horizon_n the_o more_o or_o less_o depression_n of_o the_o same_o beneath_o the_o horizon_n the_o more_o or_o less_o diurnal_a stay_n of_o the_o same_o above_o the_o horizon_n the_o cause_n be_v the_o same_o with_o those_o allege_v in_o the_o three_o forego_v paragraph_n air._n the_o planet_n and_o fix_a star_n raise_v vapour_n etc._n etc._n in_o the_o air._n 5._o the_o same_o may_v be_v say_v of_o fix_a star_n especial_o of_o those_o more_o note_a one_o and_o of_o the_o five_o other_o planet_n saturn_n jupiter_n mars_n venus_n and_o mercury_n for_o they_o generate_v some_o light_n and_o heat_n in_o the_o air_n although_o it_o be_v but_o little_a and_o change_v the_o air_n divers_a way_n and_o raise_v vapour_n if_o that_o we_o may_v credit_v astronomer_n 6._o the_o propriety_n or_o species_n of_o the_o earth_n of_o every_o place_n for_o where_o the_o earth_n be_v more_o stony_a and_o rocky_a there_o for_o the_o most_o part_n it_o be_v more_o cold_a than_o where_o it_o be_v sulphureous_a and_o fat_a and_o here_o again_o it_o be_v more_o fertile_a where_o there_o be_v much_o sand_n and_o no_o river_n there_o be_v great_a heat_n lake_n fume_n and_o mist_n proceed_v from_o lake_n 7._o lake_n or_o the_o sea_n adjacent_a from_o thence_o also_o fume_n and_o mist_n be_v raise_v more_o moist_a and_o frequent_a in_o the_o air_n and_o the_o ray_n be_v less_o powerful_o reflect_v from_o the_o sea_n than_o from_o the_o earth_n 8._o the_o situation_n of_o place_n for_o the_o sun_n act_v otherwise_o on_o mountain_n and_o mountainous_a place_n than_o on_o valley_n and_o plain_n moreover_o mountain_n hinder_v the_o free_a access_n of_o the_o ray_n of_o the_o sun_n to_o the_o subject_a place_n for_o to_o they_o the_o vapour_n of_o the_o air_n be_v in_o some_o sort_n attract_v 20._o see_v chap._n 20._o whence_o the_o mountain_n change_v the_o season_n of_o the_o adjacent_a place_n as_o heatt_z rain_n and_o the_o like_a for_o these_o will_v be_v otherwise_o in_o the_o subject_a place_n if_o that_o the_o mountain_n be_v absent_a weather_n the_o wind_n cause_n difference_n in_o the_o weather_n 9_o the_o wind_n especial_o the_o general_a so_o the_o etesian_a wind_n temperate_a and_o allay_v the_o canicular_a heat_n a_o general_a wind_n in_o the_o torrid_a zone_n especial_o the_o subsolan_n wind_n in_o brasilia_n render_v the_o heat_n temperate_a when_o in_o africa_n which_o be_v occidental_a the_o heat_n be_v vehement_a because_o these_o place_n feel_v not_o so_o general_a a_o wind._n the_o northern_a wind_n be_v cold_a and_o dry_a the_o southern_a warm_a and_o moist_a in_o our_o place_n 10._o cloud_n rain_n and_o fog_n take_v away_o and_o diminish_v light_a and_o heat_n i_o suppose_v that_o there_o be_v not_o many_o cause_n of_o this_o variety_n in_o light_n and_o heat_n etc._n etc._n which_o be_v observe_v in_o divers_a place_n of_o the_o earth_n or_o also_o in_o the_o same_o place_n but_o yet_o in_o a_o different_a time_n or_o season_n proposition_n ii_o how_o be_v the_o season_n of_o the_o year_n spring_n summer_n autumn_n and_o winter_n to_o be_v define_v year_n the_o four_o season_n of_o the_o year_n although_o in_o science_n we_o ought_v not_o to_o contend_v and_o dispute_v concern_v definition_n yet_o because_o certain_a homonyme_n or_o likeness_n do_v here_o occur_v without_o the_o explication_n of_o which_o there_o will_v arise_v much_o confusion_n in_o the_o follow_a doctrine_n therefore_o i_o will_v so_o propose_v this_o question_n that_o you_o may_v the_o more_o cautious_o avoid_v this_o homonyme_n that_o they_o may_v not_o be_v deceive_v and_o entangle_v by_o the_o same_o the_o question_n comprehend_v two_o difficulty_n first_o whether_o these_o season_n ought_v to_o be_v define_v from_o the_o entrance_n of_o the_o sun_n and_o his_o stay_n in_o certain_a sing_v of_o the_o ecliptic_a and_o zodiac_n astrologer_n according_a to_o astronomer_n and_o astrologer_n for_o so_o astronomer_n and_o astrologer_n common_o do_v say_v that_o that_o be_v the_o spring_n whilst_o the_o sun_n move_v from_o the_o first_o degree_n of_o aries_n to_o the_o first_o of_o cancer_n that_o be_v summer_n whilst_o the_o sun_n move_v from_o the_o first_o of_o cancer_n to_o the_o first_o of_o libra_n that_o be_v autumn_n whilst_o the_o sun_n move_v from_o the_o first_o of_o libra_n to_o the_o first_o of_o capricorn_n and_o that_o be_v winter_n whilst_o the_o sun_n move_v from_o the_o first_o of_o capricorn_n to_o the_o first_o degree_n of_o aries_n now_o it_o be_v manifest_a that_o these_o definition_n be_v not_o general_a and_o agreeable_a to_o all_o place_n because_o they_o be_v only_o of_o force_n in_o the_o northern_a place_n situate_v from_o the_o aequator_fw-la towards_o the_o pole_n arctic_a and_o not_o in_o the_o southern_a so_o that_o for_o these_o definition_n the_o same_o person_n bring_v definition_n contrary_a to_o the_o former_a say_v that_o in_o these_o place_n the_o spring_n begin_v from_o the_o first_o degree_n of_o libra_n proceed_v unto_o the_o first_o of_o capricorn_n the_o summer_n from_o the_o first_o of_o capricorn_n to_o the_o first_o of_o aries_n the_o autumn_n from_o the_o first_o of_o aries_n to_o the_o first_o of_o cancer_n and_o the_o winter_n from_o the_o first_o of_o cancer_n to_o the_o first_o of_o libra_n but_o from_o thence_o it_o will_v follow_v that_o those_o season_n can_v possible_o be_v define_v which_o be_v false_a and_o general_n ought_v to_o be_v define_v by_o general_n second_o definition_n so_o make_v can_v have_v place_n in_o the_o place_n of_o the_o torrid_a zone_n
definition_n spring_n summer_n autumn_n and_o winter_n may_v be_v attribute_v to_o all_o place_n of_o the_o earth_n neither_o be_v it_o easy_a to_o find_v out_o any_o other_o mode_n of_o define_v they_o so_o that_o they_o may_v agree_v with_o all_o place_n now_o these_o definition_n be_v lay_v down_o let_v we_o come_v to_o the_o matter_n itself_o proposition_n iii_o the_o celestial_a summer_n of_o the_o place_n of_o the_o earth_n which_o lie_v between_o the_o tropic_a of_o cancer_n and_o the_o pole_n arctic_a begin_v with_o the_o entrance_n of_o the_o sun_n into_o the_o first_o degree_n of_o cancer_n viz._n the_o 21_o of_o june_n and_o end_n with_o the_o entrance_n of_o the_o sun_n into_o the_o first_o degree_n of_o libra_n viz._n the_o 21_o of_o september_n and_o that_o together_o at_o once_o in_o all_o those_o place_n so_o that_o autumn_n be_v in_o those_o place_n the_o sun_n go_v from_o the_o first_o of_o libra_n unto_o the_o first_o of_o capricorn_n the_o winter_n whilst_o the_o sun_n move_v from_o the_o first_o of_o capricorn_n to_o the_o first_o of_o aries_n the_o spring_n whilst_o the_o sun_n move_v from_o the_o first_o degree_n of_o aries_n unto_o the_o first_o of_o cancer_n year_n further_o concern_v the_o season_n of_o the_o year_n the_o truth_n of_o this_o proposition_n be_v easy_o show_v by_o the_o antecedent_n definition_n and_o may_v be_v demonstrate_v on_o the_o globe_n and_o in_o universal_a map_n for_o the_o sun_n come_v to_o the_o first_o degree_n of_o cancer_n have_v the_o least_o distance_n in_o the_o meridies_n from_o the_o vertex_n of_o every_o one_o of_o the_o place_n of_o the_o northern_a temperate_a and_o frigid_a zone_n after_o the_o same_o mode_n the_o sun_n in_o the_o first_o degree_n of_o libra_n have_v a_o moderate_a distance_n from_o those_o vertex_n in_o the_o first_o of_o capricorn_n a_o great_a in_o the_o first_o of_o aries_n a_o moderate_a and_o he_o ascend_v to_o a_o more_o great_a which_o be_v apparent_a both_o from_o the_o declination_n of_o the_o sun_n and_o from_o the_o globe_n and_o map_n therefore_o it_o be_v infer_v by_o the_o definition_n lay_v down_o before_o that_o the_o summer_n the_o winter_n and_o the_o spring_n of_o those_o place_n begin_z and_o end_v in_o those_o day_n we_o have_v speak_v of_o the_o summer_n of_o those_o place_n of_o the_o earth_n which_o lie_v between_o the_o tropic_a of_o capricorn_n and_o the_o antarctic_a pole_n or_o those_o of_o the_o southern_a zone_n temperate_a and_o frigid_a begin_v with_o the_o entrance_n of_o the_o sun_n into_o the_o first_o of_o capricorn_n viz._n 21_o of_o december_n and_o end_n with_o the_o entrance_n of_o the_o sun_n into_o the_o first_o of_o aries_n viz._n the_o 21_o of_o march._n the_o autumn_n of_o those_o place_n begin_v with_o the_o entrance_n of_o the_o sun_n into_o the_o first_o of_o aries_n and_o end_n with_o the_o entrance_n of_o the_o sun_n into_o the_o first_o of_o cancer_n viz._n the_o 21_o of_o june_n with_o this_o the_o winter_n of_o those_o place_n begin_v which_o end_v with_o the_o entrance_n of_o the_o sun_n into_o the_o first_o of_o libra_n viz._n 21_o of_o september_n and_o with_o this_o their_o spring_n begin_v and_o end_v with_o the_o entrance_n of_o the_o sun_n into_o the_o first_o of_o capricorn_n viz._n 21_o of_o december_n where_o the_o summer_n begin_v again_o these_o be_v show_v after_o the_o same_o mode_n by_o the_o definition_n deliver_v and_o by_o the_o globe_n or_o map_n by_o which_o we_o show_v the_o former_a because_o in_o the_o first_o degree_n of_o capricorn_n the_o sun_n have_v the_o least_o distance_n from_o the_o vertex_n of_o those_o place_n in_o the_o first_o of_o aries_n a_o moderate_a and_o descend_v to_o the_o less_o in_o the_o first_o of_o cancer_n the_o great_a in_o the_o first_o of_o libra_n a_o moderate_a and_o ascend_v to_o a_o great_a but_o the_o celestial_a summer_n spring_n autumn_n and_o winter_n of_o the_o place_n of_o the_o earth_n which_o lie_v in_o the_o torrid_a zone_n between_o the_o tropic_a of_o cancer_n and_o capricorn_n do_v not_o begin_v on_o one_o and_o the_o same_o day_n of_o the_o year_n but_o on_o divers_a day_n in_o every_o place_n of_o diverse_a parallel_n or_o of_o a_o diverse_a latitude_n of_o this_o zone_n now_o the_o place_n of_o the_o torrid_a zone_n be_v threefold_a viz._n the_o place_n of_o the_o aequator_fw-la the_o northern_a place_n of_o the_o torrid_a zone_n and_o the_o southern_a place_n of_o the_o torrid_a zone_n 1._o the_o place_n lie_v in_o the_o aequator_fw-la have_v this_o peculiar_a to_o they_o that_o they_o enjoy_v two_o summer_n two_o winter_n two_o spring_n season_n and_o two_o autumn_n and_o that_o in_o every_o year_n so_o that_o in_o half_a a_o year_n they_o have_v or_o aught_o to_o have_v those_o four_o season_n according_a to_o our_o definition_n and_o the_o celestial_a law_n they_o have_v again_o the_o same_o four_o season_n from_o the_o 21_o of_o september_n to_o the_o 21_o of_o march_n september_n half_n a_o year_n be_v from_o the_o 21_o of_o march_n to_o the_o 21_o of_o september_n viz._n one_o summer_n whilst_o the_o sun_n move_v from_o the_o first_o degree_n of_o aries_n to_o the_o second_o of_o taurus_n from_o the_o 21_o of_o march_n to_o the_o 22_o of_o april_n autumn_n whilst_o the_o sun_n move_v from_o the_o second_o degree_n of_o taurus_n to_o the_o first_o of_o cancer_n from_o the_o 22_o of_o april_n to_o the_o 21_o of_o june_n zodiac_n the_o motion_n of_o â—he_n sun_n in_o the_o 12_o sign_n of_o the_o zodiac_n winter_n whilst_o the_o sun_n move_v from_o the_o first_o degree_n of_o cancer_n to_o the_o second_o of_o leo_n from_o the_o 21_o of_o june_n to_o the_o 19_o of_o august_n the_o spring_n whilst_o the_o sun_n move_v from_o the_o 28_o degree_n of_o leo_n to_o the_o first_o of_o libra_n from_o the_o 19_o of_o august_n to_o the_o 21_o of_o september_n the_o other_o summer_n whilst_o the_o sun_n move_v from_o the_o first_o degree_n of_o libra_n to_o the_o second_o of_o 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again_o opposite_a four_o day_n of_o the_o year_n in_o two_o of_o which_o the_o sun_n shall_v obtain_v a_o middle_a distance_n from_o the_o place_n give_v if_o therefore_o the_o place_n give_v be_v north_n take_v two_o of_o those_o four_o day_n whereof_o one_o happen_v between_o the_o 21_o of_o december_n and_o the_o 21_o of_o march_n this_o shall_v be_v the_o entrance_n of_o the_o spring_n the_o other_o between_o the_o 21_o of_o september_n and_o the_o 21_o of_o december_n this_o shall_v be_v the_o entrance_n of_o autumn_n but_o if_o the_o place_n give_v be_v south_n from_o those_o four_o day_n you_o must_v take_v the_o day_n between_o the_o 21_o of_o june_n and_o the_o 21_o of_o september_n for_o the_o entrance_n of_o the_o spring_n and_o for_o the_o begin_n of_o autumn_n that_o which_o happen_v between_o the_o 21_o of_o march_n and_o the_o 21_o of_o june_n the_o beginning_n of_o winter_n shall_v be_v the_o 21_o of_o june_n if_o the_o place_n be_v south_n but_o if_o north_n the_o 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the_o air_n than_o it_o will_v do_v without_o this_o refraction_n we_o shall_v anon_o allege_v a_o example_n of_o the_o appearancy_n of_o the_o sun_n proceed_v from_o refraction_n 4._o the_o full_a moon_n and_o near_o the_o full_a remain_v above_o the_o horizon_n for_o many_o day_n when_o the_o sun_n be_v depress_v beneath_o it_o viz._n for_o so_o many_o more_o day_n by_o how_o much_o that_o place_n be_v more_o near_o the_o pole_n yet_o it_o be_v not_o so_o high_o elevate_v above_o the_o horizon_n as_o to_o cause_v any_o warmness_n but_o the_o full_a moon_n in_o those_o month_n in_o which_o the_o sun_n remain_v above_o the_o horizon_n in_o a_o whole_a revolution_n the_o full_a moon_n be_v never_o above_o the_o horizon_n horizon_n the_o planet_n not_o always_o the_o same_o above_o horizon_n 5._o the_o fix_a star_n be_v almost_o the_o same_o always_o above_o the_o horizon_n but_o not_o the_o planet_n for_o saturn_n remain_v 15_o year_n above_o the_o horizon_n of_o the_o place_n near_o 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plaga_fw-la seldom_o the_o east_n wind_n and_o least_o of_o all_o the_o west_n in_o the_o cold_a arctic_a plaga_fw-la the_o north_n wind_n rage_n in_o the_o antarctic_a the_o south_n 10._o cloud_n and_o rain_n frequent_o perplex_v these_o region_n from_o these_o cause_n it_o be_v not_o difficult_a to_o collect_v what_o the_o condition_n of_o the_o season_n in_o these_o region_n be_v for_o in_o the_o winter_n time_n when_o the_o sun_n rise_v not_o for_o whole_a day_n it_o can_v otherwise_o be_v but_o that_o for_o the_o most_o part_n thick_a cloud_n frost_n and_o cold_a must_v render_v the_o land_n uninhabitable_a they_o be_v not_o altogether_o deprive_v of_o light_n for_o that_o time_n for_o the_o moon_n be_v above_o the_o horizon_n for_o a_o long_a time_n give_v light_a and_o the_o twilight_n be_v daily_o afford_v from_o the_o sun_n to_o the_o vicine_fw-la horizon_n but_o the_o snow_n the_o stick_n close_o about_o the_o earth_n which_o can_v be_v discuss_v by_o the_o heat_n of_o the_o sun_n and_o therefore_o hinder_v the_o aspect_n of_o remote_a thing_n there_o be_v no_o fertility_n but_o all_o barren_a and_o uncultivated_a for_o that_o which_o some_o suppose_v by_o how_o much_o any_o region_n be_v near_a to_o the_o pole_n by_o so_o much_o less_o it_o feel_v the_o intenseness_n of_o the_o cold_a and_o the_o field_n be_v find_v more_o fertile_a seem_v not_o probable_a to_o i_o when_o neither_o in_o nova_n zembla_n which_o be_v distant_a 16_o degree_n from_o the_o pole_n nor_o in_o spitzbirga_n which_o be_v only_o 8_o degree_n distant_a such_o a_o constitution_n of_o the_o earth_n be_v find_v but_o a_o roughness_n and_o hardness_n and_o almost_o in_o the_o middle_n of_o summer_n snow_n or_o at_o least_o shower_n and_o very_o cold_a wind_n neither_o be_v their_o opinion_n help_v by_o one_o example_n observe_v by_o mariner_n in_o a_o certain_a region_n 9_o degree_n distant_a from_o the_o pole_n which_o most_o man_n suppose_v to_o be_v groenland_n for_o in_o this_o green_a grass_n be_v find_v and_o a_o air_n more_o warm_a than_o in_o nova_n zembla_n as_o be_v most_o certain_a the_o only_a animal_n peculiar_a to_o these_o northern_a region_n venison_n rhinoceros_n a_o kind_n of_o venison_n be_v the_o rhinoceros_n and_o this_o in_o the_o space_n of_o a_o month_n become_v exceed_o fat_a by_o feed_v on_o this_o grass_n nevertheless_o see_v that_o as_o yet_o not_o many_o region_n be_v hitherto_o find_v of_o this_o temperature_n in_o the_o frigid_a zone_n it_o be_v not_o expedient_a for_o we_o from_o this_o single_a example_n to_o make_v a_o general_a conjecture_n especial_o see_v that_o the_o cause_n of_o this_o peculiar_a constitution_n be_v manifest_a for_o that_o land_n be_v full_a of_o marsh_n and_o sedgey_a and_o the_o grass_n by_o which_o the_o rhinoceros_n or_o dear_a be_v tender_v so_o fat_a be_v not_o a_o kind_n of_o terrestrial_a grass_n but_o sedge_n and_o osier_n but_o other_o herb_n be_v not_o there_o find_v or_o any_o tree_n from_o whence_o we_o may_v gather_v that_o that_o land_n contain_v some_o fat_a and_o sulphureous_a substance_n which_o be_v mix_v which_o the_o water_n produce_v such_o a_o oil_n and_o fatten_v sedge_n but_o that_o the_o like_a earth_n be_v to_o be_v find_v in_o other_o part_n of_o the_o frigid_a zone_n have_v not_o as_o yet_o be_v observe_v but_o rather_o the_o contrary_n therefore_o in_o the_o winter_n in_o these_o place_n be_v little_a light_n but_o a_o incredible_a and_o great_a violence_n of_o cold_a snow_n shower_n and_o polary_a wind_n and_o this_o winter_n begin_v in_o the_o northern_a frigid_a zone_n when_o the_o sun_n first_o enter_v capricorn_n although_o also_o the_o autumn_n the_o sun_n go_v from_o the_o 1_o degree_n of_o libra_n to_o the_o 1_o of_o capricorn_n be_v little_o different_a from_o this_o violent_a winter_n the_o spring_n indeed_o be_v less_o infest_a with_o this_o violence_n of_o the_o air_n yet_o it_o be_v without_o snow_n shower_n and_o cold_a polary_a wind_n yet_o the_o increase_n of_o heat_n in_o the_o day_n or_o rather_o the_o decrease_n of_o cold_a be_v discover_v at_o that_o time_n viz._n the_o sun_n go_v from_o the_o 1_o degree_n of_o aries_n to_o the_o 1_o of_o cancer_n and_o in_o this_o vernal_a season_n or_o in_o the_o latter_a day_n of_o it_o the_o sun_n continue_v above_o the_o horizon_n in_o entire_a revolution_n and_o therefore_o then_o there_o be_v discover_v a_o moderate_a heat_n which_o yet_o be_v not_o of_o that_o force_n as_o to_o melt_v and_o dissolve_v the_o snow_n of_o all_o those_o place_n into_o water_n much_o less_o be_v it_o able_a to_o melt_v the_o ice_n whence_o mariner_n report_v that_o here_o be_v to_o be_v find_v snow_n and_o ice_n of_o a_o perpetual_a duration_n then_o the_o summer_n shall_v be_v from_o the_o go_n of_o the_o sun_n from_o the_o 1_o degree_n of_o cancer_n to_o the_o 1_o of_o libra_n in_o the_o first_o part_n of_o which_o the_o sun_n yet_o remain_v for_o whole_a day_n above_o the_o horizon_n and_o augment_v the_o heat_n by_o some_o accession_n so_o that_o june_n july_n and_o august_n be_v month_n of_o a_o tolerable_a air._n in_o some_o place_n among_o the_o mountain_n the_o heat_n of_o the_o sun_n be_v intense_a but_o the_o shower_n and_o cloud_n do_v much_o hinder_v this_o benignity_n of_o the_o sun_n and_o especial_o the_o most_o sharp_a northern_a wind_n unto_o which_o sometime_o snow_n be_v adjoin_v so_o that_o no_o fruit_n or_o corn_n can_v here_o arrive_v to_o any_o maturity_n except_o in_o some_o place_n near_o the_o arctic_a circle_n chap._n xxvii_o of_o the_o shadow_n which_o the_o body_n erect_v in_o the_o earth_n and_o illuminate_v by_o the_o sun_n do_v cast_v and_o of_o the_o division_n of_o the_o earth_n arise_v from_o thence_o see_v that_o the_o shadow_n in_o divers_a place_n of_o the_o earth_n which_o the_o illuminate_v body_n of_o the_o sun_n do_v cast_v be_v carry_v into_o divers_a place_n and_o fall_v on_o the_o sense_n have_v much_o variety_n hence_o it_o come_v to_o pass_v that_o man_n who_o be_v ignorant_a of_o this_o cause_n be_v strike_v with_o a_o admiration_n and_o in_o respect_n of_o the_o shadow_n of_o the_o earth_n divide_v the_o inhabitant_n of_o the_o earth_n as_o it_o be_v into_o three_o sort_n which_o division_n must_v be_v apply_v to_o the_o place_n of_o the_o earth_n or_o to_o its_o superficies_n so_o that_o they_o term_v some_o amphiscij_fw-la other_o heteroscij_fw-la and_o the_o rest_n periscij_fw-la the_o explication_n of_o which_o term_n see_v that_o they_o contain_v but_o small_a learning_n we_o shall_v say_v somewhat_o also_o concern_v shadow_n which_o although_o they_o do_v not_o pertain_v to_o geography_n yet_o by_o reason_n of_o their_o near_a affinity_n they_o may_v be_v propose_v in_o this_o chapter_n shadow_n of_o
that_o day_n let_v the_o place_n be_v find_v in_o which_o the_o sun_n become_v vertical_a on_o the_o day_n of_o the_o year_n give_v according_a to_o the_o 9th_o proposition_n in_o the_o 24_o chapter_n these_o shall_v be_v the_o place_n seek_v proposition_n viii_o a_o place_n of_o the_o frigid_a zone_n be_v give_v to_o find_v the_o day_n of_o the_o year_n in_o which_o the_o inhabitant_n of_o it_o be_v periscii_n let_v the_o day_n of_o the_o year_n be_v find_v in_o which_o the_o sun_n set_v not_o in_o the_o give_v place_n according_a to_o the_o 10_o proposition_n of_o the_o 24_o chapter_n they_o be_v the_o day_n seek_v proposition_n ix_o the_o day_n of_o the_o year_n be_v give_v to_o find_v out_o the_o place_n of_o the_o frigid_a zone_n the_o inhabitant_n of_o which_o be_v periscii_n that_o day_n so_o that_o this_o day_n be_v the_o first_o day_n let_v those_o place_n of_o the_o frigid_a zone_n be_v find_v in_o which_o the_o sun_n in_o the_o day_n give_v do_v not_o first_o begin_v to_o set_v they_o shall_v be_v the_o place_n seek_v for_o proposition_n x._o in_o place_n situate_v in_o the_o aequator_fw-la the_o meridian_n shadow_n fall_v half_o the_o year_n towards_o the_o north_n the_o other_o half_o towards_o the_o south_n and_o in_o the_o day_n of_o the_o equinox_n the_o inhabitant_n be_v amphiscii_n for_o because_o the_o sun_n in_o one_o half_a of_o the_o year_n recede_v from_o the_o aequator_fw-la towards_o the_o south_n the_o other_o half_o towards_o the_o north_n the_o shadow_n be_v carry_v to_o the_o quarter_n opposite_a to_o the_o quarter_n of_o the_o sun_n and_o thence_o it_o come_v to_o pass_v that_o in_o one_o half_a year_n the_o meridian_n shadow_n be_v carry_v to_o the_o north_n and_o the_o other_o half_a to_o the_o south_n proposition_n xi_o to_o place_v a_o plain_a above_o the_o horizontal_n plain_n of_o our_o place_n in_o which_o the_o erect_a style_n perpendicular_a may_v be_v the_o amphiscii_n for_o some_o day_n of_o the_o year_n on_o some_o day_n of_o the_o year_n the_o meridian_n shadow_n may_v be_v carry_v to_o the_o north_n on_o other_o to_o the_o south_n that_o be_v in_o which_o the_o meridian_n shadow_n may_v be_v so_o cast_v as_o in_o some_o give_a place_n of_o the_o torrid_a zone_n let_v the_o latitude_n of_o the_o place_n give_v of_o the_o torrid_a zone_n be_v take_v from_o the_o latitude_n of_o our_o place_n if_o the_o latitude_n be_v cognominal_a but_o if_o they_o be_v of_o a_o diverse_a species_n let_v both_o the_o latitude_n be_v add_v and_o the_o remain_a degree_n keep_v then_o in_o the_o horizontal_n plain_a the_o meridian_n line_n be_v find_v and_o also_o the_o line_n of_o the_o aequator_fw-la which_o be_v perpendicular_a to_o the_o meridian_n line_n let_v some_o plain_n be_v erect_v above_o the_o line_n of_o the_o aequator_fw-la that_o it_o may_v incline_v above_o the_o horizon_n so_o many_o degree_n as_o be_v keep_v before_o the_o style_n or_o pin_n erect_v in_o this_o plain_n shall_v cast_v such_o shadow_n as_o if_o they_o be_v erect_v in_o the_o place_n of_o the_o torrid_a zone_n proposition_n xii_o in_o the_o place_n seat_v in_o the_o aequator_fw-la the_o shadow_n of_o the_o style_n perpendicular_o erect_v in_o the_o whole_a day_n of_o the_o aequinox_n remain_v in_o one_o right_a line_n whether_o before_o noon_n â—t_z be_v continual_o cast_v into_o one_o quarter_n of_o the_o west_n or_o after_o noon_n into_o a_o quarter_n of_o the_o east_n now_o in_o the_o other_o day_n of_o the_o year_n the_o shadow_n be_v carry_v round_o into_o the_o semicircle_n aequator_fw-la of_o place_n seat_v without_o the_o aequator_fw-la in_o place_n situate_v without_o the_o aequator_fw-la in_o the_o torrid_a zone_n whilst_o the_o sun_n be_v move_v in_o part_n of_o the_o ecliptic_a which_o lie_v between_o the_o vertex_fw-la of_o any_o place_n and_o the_o vicine_fw-la tropic_n the_o shadow_n wander_v through_o the_o lesser_a part_n of_o the_o subject_a superficies_n in_o a_o semicircle_n in_o the_o place_n of_o the_o temperate_a zone_n whilst_o the_o sun_n be_v move_v in_o a_o more_o remote_a circle_n from_o those_o or_o the_o zodiac_n the_o shadow_n steal_v by_o the_o lesser_a superficies_n in_o a_o semicircle_n and_o the_o greaten_v whilst_o the_o sun_n run_v through_o the_o near_a semicircle_n of_o the_o zodiac_n in_o the_o day_n of_o the_o aequinox_n the_o shadow_n of_o a_o erect_a style_n be_v carry_v round_o in_o a_o semicircle_n in_o all_o the_o place_n of_o the_o earth_n except_o the_o aequator_fw-la and_o the_o pole_n these_o be_v all_o render_v perspicuous_a partly_o from_o the_o sight_n of_o the_o globe_n and_o partly_o from_o the_o declination_n of_o the_o diagram_n proposition_n xiii_o in_o the_o place_n of_o the_o torrid_a zone_n whilst_o the_o sun_n be_v in_o the_o arch_n of_o the_o ecliptic_a between_o the_o vicine_fw-la tropic_n and_o the_o parallel_n of_o the_o place_n in_o those_o day_n the_o shadow_n of_o the_o erect_a style_n twice_o return_v back_o and_o go_v over_o the_o line_n leave_v behind_o viz._n once_o before_o noon_n and_o once_o after_o noon_n the_o sun_n also_o in_o these_o day_n will_v seem_v to_o inflect_v his_o course_n zone_n of_o the_o shadow_n of_o the_o sun_n in_o the_o place_n of_o the_o torrid_a zone_n take_v any_o place_n of_o the_o torrid_a zone_n in_o the_o globe_n and_o let_v the_o pole_n be_v elevate_v according_a to_o his_o latitude_n and_o let_v the_o parallel_n of_o the_o place_n be_v describe_v which_o shall_v cut_v the_o ecliptic_a in_o two_o point_n i_o say_v that_o whilst_o the_o sun_n move_v in_o the_o intercept_a arch_n of_o the_o ecliptic_a between_o this_o parallel_n and_o the_o vicine_fw-la tropic_n in_o those_o day_n the_o sun_n will_v seem_v to_o be_v twice_o retrograde_a and_o go_v over_o the_o line_n leave_v behind_o let_v any_o of_o the_o point_n of_o that_o arch_n be_v take_v and_o let_v the_o parallel_n of_o the_o sun_n be_v describe_v viz._n which_o the_o sun_n be_v in_o that_o point_n describe_v by_o diurnal_a circumvolution_n for_o example_n take_v the_o first_o degree_n of_o cancer_n or_o capricorn_n and_o another_o of_o their_o tropic_n for_o so_o there_o will_v be_v no_o need_n of_o the_o description_n of_o a_o parallel_n until_o it_o come_v to_o the_o point_n in_o which_o the_o quadrant_n touch_v the_o parallel_n the_o sun_n be_v in_o this_o seat_n or_o in_o this_o quarter_n will_v seem_v to_o bend_v his_o course_n towards_o the_o vertex_fw-la of_o the_o place_n and_o the_o shadow_n shall_v begin_v to_o be_v retrograde_a from_o the_o line_n of_o the_o aequator_fw-la towards_o the_o meridian_n line_n after_o the_o same_o manner_n if_o that_o you_o apply_v the_o quadrant_n to_o the_o occidental_a part_n of_o the_o parallel_n you_o shall_v see_v in_o that_o point_n in_o which_o the_o quadrant_n touch_v the_o parallel_n that_o the_o sun_n go_v to_o the_o quarter_n he_o have_v leave_v and_o set_v in_o that_o quarter_n in_o which_o some_o hour_n before_o he_o be_v corollary_n therefore_o it_o be_v not_o against_o nature_n that_o the_o shadow_n shall_v go_v back_o on_o sun-dials_n but_o than_o it_o be_v miraculous_a if_o that_o it_o be_v do_v sudden_o in_o a_o note_a space_n also_o if_o it_o repeat_v the_o lineary_a hour_n viz._n if_o that_o the_o style_n be_v not_o perpendicular_a but_o parallel_n to_o the_o mundane_a axletree_n yea_o although_o it_o be_v perpendicular_a yet_o do_v not_o the_o line_n of_o the_o shadow_n itself_o show_v the_o hour_n but_o the_o line_n of_o the_o shadow_n of_o the_o axis_n of_o the_o world_n part_n of_o which_o be_v conceal_v in_o the_o mind_n on_o the_o dial_n if_o that_o it_o be_v want_v proposition_n fourteen_o a_o place_n be_v give_v in_o the_o torrid_a zone_n and_o one_o day_n of_o those_o in_o which_o the_o sun_n seem_v to_o bend_v his_o course_n and_o the_o shadow_n of_o the_o style_n seem_v to_o go_v back_o to_o find_v the_o quarter_n in_o which_o the_o sun_n then_o shall_v be_v and_o the_o hour_n when_o it_o shall_v be_v let_v the_o pole_n be_v elevate_v for_o the_o latitude_n of_o the_o place_n give_v and_o let_v the_o place_n of_o the_o sun_n be_v find_v at_o the_o give_v day_n and_o let_v it_o be_v note_v in_o the_o ecliptic_a and_o let_v the_o parallel_n be_v describe_v with_o chalk_n which_o the_o sun_n be_v in_o that_o point_n describe_v let_v the_o quadrant_n be_v apply_v to_o the_o vertex_fw-la and_o so_o turn_v about_o until_o it_o touch_v the_o describe_v parallel_n so_o the_o extremity_n of_o the_o quadrant_n in_o the_o horizon_n shall_v show_v the_o place_n seek_v for_o now_o that_o the_o hour_n may_v be_v find_v let_v that_o point_n of_o the_o parallel_n be_v note_v in_o which_o the_o contact_n be_v make_v let_v the_o index_n be_v place_v at_o the_o twelve_o
hour_n of_o the_o cycle_n and_o let_v the_o note_a point_n of_o the_o parallel_n be_v turn_v to_o the_o meridian_n the_o index_n will_v show_v how_o many_o hour_n before_o and_o how_o many_o hour_n after_o noon_n the_o regress_n begin_v proposition_n xv._o the_o longitude_n of_o the_o shadow_n decrease_v the_o altitude_n of_o the_o sun_n increase_v and_o on_o the_o contrary_a the_o altitude_n of_o the_o sun_n decrease_v the_o shadow_n increase_v increase_v they_o decrease_v from_o the_o east_n to_o the_o meridies_n and_o from_o the_o meridies_n to_o the_o set_n the_o shadow_n again_o increase_v for_o the_o sun_n be_v more_o near_o the_o vertex_fw-la of_o the_o style_n by_o how_o much_o the_o more_o he_o be_v elevate_v above_o the_o horizon_n therefore_o the_o ray_n of_o the_o sun_n terminate_a the_o shadow_n become_v also_o more_o nigh_o the_o style_n and_o on_o that_o account_n the_o shadow_n become_v lesser_a moreover_o the_o sun_n have_v the_o great_a altitude_n in_o the_o meridies_n therefore_o the_o longitude_n of_o the_o shadow_n than_o shall_v be_v lesser_a but_o in_o the_o rise_n and_o set_v of_o the_o sun_n there_o be_v no_o altitude_n therefore_o the_o longitude_n of_o the_o shadow_n shall_v be_v infinite_a proposition_n xvi_o the_o longitude_n of_o the_o style_n and_o the_o shadow_n be_v give_v to_o find_v the_o altitude_n of_o the_o sun_n above_o the_o horizon_n and_o thence_o the_o hour_n of_o the_o day_n if_o that_o moreover_o the_o latitude_n of_o the_o place_n and_o day_n of_o the_o year_n be_v know_v the_o longitude_n of_o the_o style_n the_o shadow_n and_o the_o ray_n terminate_a the_o shadow_n make_v a_o right_a angle_a triangle_n therefore_o let_v the_o proportion_n be_v institute_v according_a to_o the_o 15_o proposition_n of_o the_o second_o chapter_n as_o the_o longitude_n of_o the_o shadow_n be_v to_o the_o longitude_n of_o the_o style_n so_o be_v the_o whole_a sign_n to_o the_o tangent_fw-la of_o the_o angle_n which_o show_v the_o altitude_n of_o the_o sun_n from_o this_o altitude_n and_o latitude_n of_o the_o place_n 29._o see_v proposit_n 3._o chap._n 29._o and_o day_n of_o the_o year_n shall_v the_o hour_n of_o the_o day_n be_v find_v out_o proposition_n xvii_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 to_o find_v out_o the_o longitude_n of_o the_o shadow_n which_o the_o whole_a earth_n cast_v towards_o heaven_n shadow_n of_o the_o longitude_n of_o the_o shadow_n the_o shadow_n of_o the_o earth_n be_v conical_a as_o the_o optic_n demonstrate_v and_o be_v easy_o show_v by_o a_o diagram_n therefore_o the_o distance_n of_o the_o vertex_fw-la of_o this_o cone_n which_o cause_v the_o eclipse_n of_o the_o moon_n from_o the_o earth_n be_v seek_v that_o be_v find_v by_o this_o proposition_n for_o as_o the_o distance_n of_o the_o semidiameter_n of_o the_o sun_n and_o earth_n be_v to_o the_o distance_n give_v so_o be_v the_o semidiameter_n of_o the_o earth_n to_o the_o longitude_n of_o the_o shadow_n of_o the_o earth_n or_o to_o the_o axis_n of_o the_o shady_a cone_n proposition_n xviii_o the_o distance_n of_o the_o moon_n from_o the_o earth_n and_o the_o longitude_n of_o the_o shadow_n of_o the_o earth_n be_v give_v to_o find_v how_o great_a a_o part_n of_o the_o moon_n be_v opscure_v how_o great_a the_o eclipse_n will_v be_v if_o that_o the_o moon_n remain_v in_o the_o ecliptic_a moon_n of_o the_o eclipse_n of_o the_o moon_n let_v the_o rule_n of_o three_o be_v institute_v according_a to_o this_o proportion_n as_o the_o longitude_n of_o the_o shadow_n be_v to_o the_o excess_n of_o this_o longitude_n above_o the_o distance_n of_o the_o moon_n so_o the_o semidiameter_n of_o the_o earth_n be_v to_o that_o shady_a cone_n of_o the_o earth_n in_o that_o part_n where_o the_o moon_n enter_v it_o furthermore_o as_o the_o distance_n of_o the_o moon_n be_v to_o the_o find_v out_o semidianeter_n of_o the_o shadow_n so_o be_v the_o whole_a sign_n of_o the_o canon_n to_o the_o tangent_fw-la of_o the_o angle_n of_o sight_n which_o the_o half_a diameter_n of_o shadow_n subtend_v to_o our_o eye_n which_o if_o it_o be_v double_v the_o angle_n of_o sight_n be_v account_v for_o the_o whole_a diameter_n of_o the_o shadow_n with_o this_o angle_n let_v the_o angle_n of_o sight_n or_o the_o apparent_a semidiameter_n of_o the_o moon_n which_o be_v in_o opposition_n of_o the_o sun_n or_o in_o time_n of_o eclipse_n be_v compare_v from_o this_o comparation_n the_o quantity_n of_o the_o obcsurity_n will_v be_v make_v manifest_a which_o if_o you_o desire_v to_o have_v in_o digit_n institute_v a_o rule_n of_o proportion_n after_o this_o manner_n as_o the_o diameter_n of_o the_o moon_n be_v to_o twelve_o digit_n so_o be_v the_o apparent_a diameter_n of_o the_o shadow_n or_o angle_n of_o sight_n to_o the_o ecliptic_a digit_n proposition_n xix_o by_o how_o much_o the_o place_n of_o the_o earth_n every_o day_n be_v more_o remote_a from_o the_o aequator_fw-la or_o from_o the_o parallel_n of_o the_o sun_n by_o so_o much_o the_o more_o both_o the_o meridian_n shadow_n as_o well_o as_o the_o shadow_n of_o the_o rest_n of_o the_o hour_n be_v long_o for_o because_o the_o sun_n be_v more_o remote_a from_o the_o vertex_fw-la of_o those_o place_n therefore_o also_o the_o ray_n of_o the_o sun_n terminate_a the_o shadow_n be_v more_o remote_a from_o the_o style_n and_o therefore_o the_o shadow_n be_v so_o much_o the_o long_o extend_v proposition_n xx._n if_o that_o the_o style_n be_v place_v in_o any_o plain_a after_o such_o a_o mode_n that_o it_o become_v part_n of_o the_o axis_n of_o the_o world_n or_o that_o it_o be_v parallel_n to_o that_o axis_n the_o shadow_n of_o that_o style_n shall_v fall_v on_o a_o certain_a hour_n on_o the_o very_a line_n of_o that_o plain_a in_o which_o this_o line_n be_v cut_v by_o the_o great_a horary_a circle_n whether_o of_o declination_n or_o from_o the_o meridian_n in_o which_o the_o sun_n be_v at_o that_o hour_n hour_n a_o moment_n or_o small_a space_n of_o a_o hour_n for_o the_o shadow_n of_o the_o axis_n of_o the_o world_n or_o the_o style_n so_o place_v fall_v on_o the_o plain_a of_o the_o horary_a or_o meridian_n circle_n in_o which_o the_o sun_n be_v at_o that_o moment_n of_o time_n for_o neither_o can_v it_o fall_v beyond_o the_o plain_n see_v that_o the_o sun_n the_o opac_a body_n and_o the_o shadow_n be_v in_o one_o plain_n upon_o which_o the_o style_n be_v place_v wherefore_o see_v this_o style_n be_v upon_o this_o plain_a as_o also_o on_o the_o plain_a of_o the_o meridian_n which_o the_o sun_n keep_v for_o a_o moment_n thence_o it_o follow_v that_o this_o shadow_n may_v fall_v on_o the_o common_a section_n of_o this_o plain_a or_o the_o plain_a of_o the_o meridian_n or_o of_o the_o horary_a circle_n for_o if_o any_o line_n be_v in_o two_o or_o more_o plain_n it_o shall_v be_v in_o the_o common_a section_n of_o those_o plain_n proposition_n xxi_o to_o describe_v the_o aequinoctial_a night-dial_n night-dial_n aequinoctial_a night-dial_n a_o plain_a of_o wood_n paper_n brass_n or_o other_o metal_n must_v be_v erect_v above_o the_o horizon_n so_o many_o degree_n as_o the_o aequator_fw-la be_v elevate_v above_o the_o horizon_n or_o so_o many_o degree_n as_o be_v in_o the_o compliment_n of_o the_o latitude_n of_o the_o place_n before_o it_o be_v erect_v it_o be_v necessary_a to_o draw_v the_o line_n of_o the_o scioterick_n therefore_o let_v what_o point_n you_o please_v be_v take_v in_o that_o plain_a and_o let_v the_o periphery_a of_o the_o circle_n be_v describe_v from_o it_o as_o from_o a_o centre_n let_v a_o line_n parallel_n to_o the_o horizon_n be_v draw_v through_o that_o centre_n or_o let_v the_o line_n be_v parallel_n to_o the_o common_a section_n of_o the_o aequator_fw-la and_o the_o horizon_n which_o shall_v be_v the_o line_n of_o the_o shadow_n of_o the_o hour_n of_o six_o in_o the_o evening_n and_o six_o in_o the_o morning_n let_v a_o line_n perpendicular_a to_o this_o be_v draw_v from_o the_o centre_n which_o shall_v be_v the_o shadow_n of_o the_o twelve_o hour_n then_o let_v both_o the_o quadrant_n be_v divide_v into_o three_o part_n and_o every_o one_o of_o those_o three_o into_o two_o so_o that_o the_o six_o arch_n may_v be_v in_o every_o one_o of_o they_o whereof_o every_o one_o shall_v be_v of_o fifteen_o degree_n and_o let_v they_o be_v draw_v from_o the_o centre_n to_o the_o term_n or_o bound_n of_o the_o arch_n of_o the_o right_a line_n these_o shall_v be_v the_o line_n of_o the_o shadow_n for_o the_o beginning_n of_o the_o remain_a hour_n which_o fall_v between_o twelve_o and_o six_o who_o number_n and_o order_n must_v be_v set_v down_o at_o the_o extremity_n of_o the_o line_n draw_v the_o same_o
34_o a_o 242_o 4_o lucida_n aquarii_n 31_o 24_o a_o 339_o 28_o arcturus_n bootis_n 21_o 4_o s_n 209_o 59_o lucida_n lyrae_fw-la 38_o 30_o s_n 206_o 17_o cauda_fw-la cygni_fw-la 44_o 3_o s_n 307_o 23_o capella_n 45_o 35_o s_n 72_o 44_o pes_fw-la orionis_n sinister_a 8_o 38_o a_o 74_o 29_o sirius_n canis_n major_n 16_o 13_o a_o 97_o 26_o humerus_fw-la dexter_n orionis_n 7_o 18_o a_o 84_o 7_o canis_fw-la minor_n 6_o 6_o s_n 110_o 17_o chap._n xxxii_o of_o the_o mutual_a situation_n of_o place_n and_o composition_n of_o the_o terrestrial_a globe_n and_o map_n proposition_n i._o a_o place_n be_v give_v in_o the_o earth_n to_o find_v the_o situation_n of_o other_o place_n at_o that_o place_n etc._n of_o find_v of_o the_o situation_n of_o place_n in_o the_o earth_n etc._n etc._n now_o the_o situation_n of_o one_o place_n to_o the_o other_o be_v term_v that_o plaga_fw-la in_o which_o this_o lie_v at_o or_o a_o angle_n of_o position_n that_o be_v a_o angle_n which_o the_o meridian_n of_o the_o give_v place_n make_v with_o a_o line_n or_o periphery_n draw_v from_o this_o place_n to_o the_o other_o for_o example_n if_o we_o be_v in_o amsterdam_n and_o desire_v to_o know_v in_o what_o situation_n other_o place_n lie_v unto_o it_o as_o rome_n leyden_n the_o hague_n or_o the_o like_a the_o first_o mode_n mode_n the_o first_o mode_n to_o those_o place_n that_o a_o prospect_n be_v grant_v from_o the_o place_n give_v their_o situation_n may_v exact_o be_v observe_v to_o this_o place_n by_o instrument_n let_v a_o geometrical_a instrument_n be_v place_v in_o a_o high_a tower_n or_o the_o place_n of_o the_o give_v place_n so_o that_o it_o may_v be_v parallel_n to_o the_o horizon_n and_o the_o meridian_n line_n be_v find_v let_v one_o rule_n of_o the_o instrument_n be_v apply_v unto_o it_o and_o the_o other_o have_v a_o perspective_n must_v be_v direct_v to_o the_o conspicuous_a place_n the_o arch_n of_o the_o periphery_a intercept_v between_o the_o two_o rule_n be_v the_o angle_n of_o the_o position_n of_o the_o place_n observe_v at_o this_o place_n and_o from_o thence_o his_o quarter_n shall_v be_v know_v so_o the_o situation_n or_o position_n of_o all_o other_o vicine_fw-la places_z shall_v be_v observe_v then_o let_v we_o go_v to_o these_o place_n and_o from_o they_o by_o the_o same_o mode_n we_o shall_v again_o discover_v the_o situation_n of_o other_o place_n and_o then_o we_o may_v so_o act_v over_o the_o whole_a superficies_n of_o the_o earth_n except_o that_o other_o way_n be_v know_v by_o which_o we_o may_v come_v more_o easy_o to_o the_o demand_v place_n the_o second_o mode_n mode_n the_o second_o mode_n if_o that_o the_o propose_a place_n may_v be_v have_v on_o the_o globe_n let_v the_o place_n give_v be_v bring_v to_o the_o meridian_n and_o let_v the_o pole_n be_v elevate_v for_o its_o latitude_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 one_o and_o the_o other_o place_n who_o situation_n we_o desire_v to_o know_v at_o our_o place_n the_o extremity_n of_o the_o quadrant_n in_o the_o horizon_n will_v show_v the_o angle_n of_o position_n and_o the_o quarter_n seek_v for_o and_o therefore_o we_o shall_v say_v that_o rome_n constantinople_n lie_v from_o amsterdam_n towards_o this_o or_o that_o find_v out_o quarter_n which_o that_o we_o may_v conceive_v in_o the_o world_n we_o ought_v to_o know_v the_o meridian_n line_n or_o quarter_n of_o the_o north_n and_o south_n also_o the_o east_n and_o west_n aequinoctial_a for_o from_o these_o be_v well_o conceive_v of_o the_o intermedial_a quarter_n may_v easy_o be_v conceive_v here_o must_v be_v collect_v what_o have_v be_v say_v concern_v quarter_n in_o the_o 20_o chapter_n 20._o see_v chap._n 20._o the_o three_o mode_n mode_n the_o three_o mode_n from_o map_n of_o straight_a line_n if_o that_o the_o place_n propound_v be_v to_o be_v find_v in_o they_o it_o be_v easy_a to_o discover_v the_o situation_n of_o those_o place_n to_o this_o by_o the_o eye_n for_o through_o the_o give_v place_n a_o right_a meridian_n line_n be_v conceive_v show_v the_o north_n and_o south_n and_o another_o line_n transverse_a or_o show_v the_o parallel_n of_o the_o place_n which_o discover_v the_o eastern_a and_o western_a quarter_n from_o these_o the_o intermedial_a quarter_n in_o which_o every_o place_n be_v behold_v be_v easy_o discover_v or_o else_o they_o be_v more_o accurate_o know_v by_o line_n draw_v on_o the_o quadrant_n of_o the_o periphery_a if_o that_o there_o be_v need_n of_o a_o more_o accurate_a knowledge_n but_o yet_o this_o method_n be_v not_o complete_a except_o in_o particular_a map_n in_o map_n of_o crooked_a line_n the_o quarter_n or_o situation_n of_o place_n be_v not_o so_o a_o accurate_o seek_v as_o the_o other_o place_n the_o four_o mode_n mode_n the_o four_o mode_n the_o latitude_n and_o longitude_n of_o two_o place_n bege_v give_v the_o situation_n of_o one_o to_o the_o other_o be_v exact_o find_v by_o a_o trigonometrical_a compute_v both_o that_o which_o be_v vulgar_a as_o that_o which_o be_v logorithmetical_a or_o by_o a_o catholic_n planisphere_n or_o also_o by_o the_o globe_n for_o let_v a_o spherical_a triangle_n be_v have_v in_o which_o three_o thing_n be_v give_v viz._n the_o compliment_n of_o the_o latitude_n of_o both_o place_n and_o the_o angle_n comprehend_v from_o these_o which_o be_v know_v from_o the_o difference_n of_o longitude_n now_o let_v the_o opposite_a angle_n or_o adjacent_a to_o either_o of_o the_o two_o side_n be_v seek_v for_o this_o will_v show_v the_o angle_n of_o position_n of_o one_o place_n to_o the_o other_o and_o the_o very_a quarter_n a_o diagram_n and_o the_o lively_a instruction_n of_o a_o tutor_n will_v make_v these_o more_o clear_a and_o hence_o appear_v the_o use_n of_o the_o table_n of_o longitude_n and_o latitude_n of_o place_n the_o five_o mode_n from_o the_o give_a distance_n of_o a_o place_n from_o two_o place_n or_o from_o the_o give_v distance_n and_o latitude_n mode_n the_o five_o mode_n his_o quarter_n or_o situation_n to_o the_o other_o place_n be_v find_v out_o by_o the_o solution_n of_o the_o spherical_a triangle_n the_o six_o mode_n the_o latitude_n of_o two_o place_n be_v give_v the_o distance_n of_o the_o quarter_n of_o one_o be_v find_v to_o the_o other_o by_o a_o threefold_a method_n mode_n the_o six_o mode_n as_o have_v be_v say_v other_o thing_n give_v may_v be_v propound_v by_o which_o we_o may_v find_v out_o the_o quarter_n proposition_n ii_o a_o place_n be_v give_v on_o the_o earth_n or_o globe_n to_o exhibit_v all_o place_n which_o lie_v at_o the_o give_v place_n in_o some_o one_o give_v quarter_n or_o situation_n amsterdam_n of_o the_o know_v the_o place_n in_o the_o north-east_n quarter_n from_o amsterdam_n for_o example_n we_o desire_v to_o know_v all_o the_o place_n which_o lie_v in_o the_o north-east_n quarter_n from_o amsterdam_n let_v the_o pole_n be_v elevate_v for_o the_o latitude_n of_o the_o give_v place_n and_o let_v the_o place_n be_v bring_v to_o the_o meridian_n let_v the_o quadrant_n be_v affix_v to_o the_o vertex_fw-la and_o leâ—_n the_o other_o extremity_n be_v apply_v to_o the_o give_v quarter_n of_o the_o horizon_n so_o we_o shall_v behold_v the_o half_a part_n of_o the_o place_n seek_v for_o viz._n those_o which_o be_v adjacent_a in_o the_o globe_n to_o the_o margin_n of_o the_o quadrant_n the_o other_o half_a part_n be_v beneath_o the_o horizon_n at_o the_o point_n opposite_a to_o the_o vertex_fw-la but_o the_o construction_n be_v more_o easy_a for_o the_o earth_n itself_o to_o wit_n let_v the_o periphery_a of_o the_o great_a circle_n be_v bring_v to_o the_o place_n give_v which_o with_o the_o meridian_n of_o that_o place_n may_v make_v the_o give_v angle_n of_o the_o position_n all_o the_o place_n in_o the_o half_a periphery_n be_v those_o seek_v for_o proposition_n iii_o a_o place_n be_v give_v in_o the_o earth_n or_o on_o the_o globe_n to_o exhibit_v all_o those_o place_n at_o which_o the_o give_v place_n have_v some_o one_o give_v situation_n or_o quarter_n amsterdam_n of_o the_o know_v the_o place_n which_o lie_v north-west_n to_o amsterdam_n for_o example_n we_o desire_v to_o know_v all_o the_o place_n unto_o every_o one_o of_o which_o amsterdam_n lie_v in_o the_o north-west_n quarter_n but_o the_o problem_n may_v with_o more_o delight_n be_v thus_o propound_v any_o place_n in_o the_o earth_n or_o on_o the_o globe_n be_v give_v as_o in_o amsterdam_n to_o show_v all_o those_o place_n from_o which_o whilst_o we_o desire_v to_o go_v to_o the_o give_v place_n amsterdam_n we_o must_v direct_v our_o course_n from_o every_o one_o of_o the_o place_n to_o one_o and_o the_o same_o give_v quarter_n the_o precede_a problem_n be_v local_o plain_a
tangent_n be_v draw_v to_o plain_a line_n to_o a_o curvature_n for_o in_o solid_a line_n infinite_a tangent_n may_v be_v bring_v to_o any_o point_n moreover_o that_o definition_n may_v agree_v also_o to_o other_o draught_n of_o line_n when_o unto_o any_o point_n of_o such_o a_o menidian_n such_o a_o tangent_fw-la and_o crooked_a line_n may_v be_v conceive_v to_o be_v draw_v from_o the_o vicine_fw-la meridian_n also_o our_o definition_n may_v be_v thus_o propose_v loxodromy_n be_v a_o crooked_a line_n encompass_v the_o earth_n with_o many_o wind_n every_o point_n of_o which_o lie_v from_o all_o its_o other_o point_n in_o appearance_n in_o one_o and_o the_o same_o quarter_n or_o in_o which_o if_o that_o two_o point_n be_v take_v one_o point_n lie_v from_o another_o and_o all_o the_o intermedial_a point_n in_o one_o quarter_n or_o from_o any_o point_n of_o which_o if_o that_o circular_a arch_n be_v draw_v unto_o all_o the_o rest_n of_o the_o point_n these_o arch_n make_v equal_a angle_n with_o the_o meridian_n which_o pass_v through_o all_o these_o several_a point_n this_o definition_n be_v essential_a proposition_n xi_o if_o that_o a_o voyage_n be_v undertake_v from_o one_o place_n to_o another_o which_o be_v not_o situate_v with_o the_o former_a in_o the_o same_o meridian_n or_o aequator_fw-la nor_o parallel_n and_o in_o the_o whole_a voyage_n the_o ship_n be_v direct_v unto_o that_o quarter_n in_o which_o the_o place_n design_v be_v situate_v from_o the_o place_n of_o the_o departure_n you_o shall_v never_o by_o this_o voyage_n come_v to_o the_o place_n design_v but_o continual_o the_o ship_n shall_v be_v remove_v more_o and_o more_o from_o it_o navigation_n a_o notable_a property_n in_o navigation_n this_o notable_a property_n of_o navigation_n seem_v miraculous_a to_o mariner_n when_o that_o it_o be_v first_o observe_v which_o happen_v in_o the_o time_n of_o petrus_n nonnius_n the_o portuguez_n mathematician_n who_o write_v two_o book_n of_o this_o subject_a after_o he_o many_o mathematician_n labour_v in_o the_o explication_n of_o this_o matter_n or_o crooked_a line_n and_o last_o mariner_n find_v it_o necessary_a for_o the_o nautick_a use_n and_o thence_o table_n be_v make_v thereeof_o the_o cause_n thereeof_o but_o the_o cause_n of_o this_o phoenomenon_n be_v that_o the_o ship_n be_v continual_o direct_v unto_o that_o quarter_n in_o which_o the_o second_o place_n from_o the_o first_o be_v situate_v it_o remain_v not_o in_o the_o periphery_a intercept_v between_o these_o place_n but_o whilst_o that_o it_o come_v to_o one_o point_n because_o here_o be_v a_o new_a horizon_n and_o another_o quarter_n the_o extension_n of_o the_o assume_v course_n and_o this_o be_v continual_o do_v in_o the_o follow_a point_n thence_o exi_v the_o crooked_a helicoidical_a line_n in_o which_o whilst_o that_o the_o ship_n be_v move_v in_o some_o place_n it_o be_v more_o and_o more_o remove_v from_o the_o determine_a place_n and_o else_o where_o it_o approach_v more_o near_o proposition_n xii_o 1._o when_o a_o voyage_n be_v to_o be_v undertake_v from_o one_o place_n towards_o another_o situate_v in_o the_o same_o meridian_n or_o towards_o the_o quarter_n of_o the_o north_n or_o south_n the_o ship_n be_v continual_o to_o be_v direct_v to_o this_o quarter_n of_o the_o north_n or_o south_n or_o a_o meridian_n be_v to_o be_v choose_v for_o the_o way_n of_o the_o ship_n and_o it_o will_v arrive_v at_o the_o other_o place_n voyage_n observation_n about_o voyage_n 2._o when_o a_o voyage_n be_v to_o be_v undertake_v from_o one_o place_n to_o another_o and_o both_o be_v in_o the_o aequator_fw-la the_o ship_n shall_v be_v guide_v into_o that_o quarter_n in_o which_o the_o other_o place_n lie_v from_o the_o first_o that_o be_v to_o the_o quarter_n of_o the_o east_n or_o west_n or_o the_o line_n of_o the_o aequator_fw-la be_v to_o be_v take_v for_o the_o way_n of_o the_o ship_n 3._o when_o a_o voyage_n be_v to_o be_v undertake_v from_o one_o place_n to_o another_o and_o that_o they_o be_v both_o situate_v in_o one_o parallel_n of_o the_o aequator_fw-la the_o ship_n be_v not_o to_o be_v guide_v unto_o that_o quarter_n in_o which_o this_o other_o place_n from_o the_o first_o lie_v or_o which_o be_v extend_v from_o the_o first_o to_o the_o other_o for_o the_o ship_n will_v never_o arrive_v at_o the_o other_o place_n but_o will_v go_v with_o infinite_a wind_n about_o the_o earth_n towards_o the_o pole_n but_o the_o course_n must_v be_v make_v into_o the_o quarter_n of_o the_o east_n or_o west_n for_o whilst_o that_o the_o ship_n tend_v unto_o that_o it_o describe_v by_o its_o motion_n the_o parallel_n of_o the_o aequator_fw-la and_o so_o arrive_v at_o the_o other_o place_n 4._o when_o a_o voyage_n be_v to_o be_v make_v from_o one_o place_n to_o another_o which_o be_v neither_o in_o one_o meridian_n neither_o both_o in_o the_o aequator_fw-la nor_o in_o one_o parallel_n of_o the_o aequator_fw-la the_o ship_n must_v not_o be_v guide_v unto_o that_o quarter_n in_o which_o the_o other_o place_n from_o the_o first_o lie_v for_o it_o will_v never_o arrive_v to_o the_o other_o place_n but_o the_o motion_n of_o the_o ship_n will_v describe_v the_o loxodrome_n which_o will_v not_o pass_v through_o another_o place_n but_o the_o course_n must_v be_v direct_v unto_o that_o quarter_n into_o which_o whilst_o that_o the_o ship_n move_v it_o describe_v the_o loxodrome_n which_o pass_v through_o another_o place_n into_o that_o quarter_n who_o angle_n with_o the_o meridian_n be_v equal_a to_o the_o inclination_n of_o the_o loxodrome_n which_o pass_v through_o those_o two_o place_n all_o these_o follow_v from_o the_o precede_a proposition_n proposition_n xiii_o infinite_a loxodrome_n may_v proceed_v or_o be_v conceive_v from_o any_o place_n of_o the_o earth_n as_o there_o be_v infinite_a vertical_o but_o yet_o there_o be_v only_o 28_o reckon_v about_o every_o place_n viz._n 7_o in_o the_o quadrant_n between_o the_o meridian_n of_o the_o place_n and_o the_o parallel_n of_o the_o place_n so_o that_o they_o divide_v that_o right_a angle_n into_o 8_o equal_a part_n and_o the_o 2_o vicine_fw-la be_v distant_a a_o equal_a angle_n yet_o the_o parallel_n itself_o be_v term_v a_o eight_o loxodrome_n loxodrome_n of_o the_o number_n of_o loxodrome_n but_o they_o be_v call_v by_o the_o same_o name_n by_o which_o the_o wind_n or_o quarter_n be_v name_v on_o the_o globe_n they_o be_v behold_v to_o proceed_v and_o turn_v round_o about_o the_o earth_n from_o the_o centre_n of_o the_o compass_n or_o also_o from_o other_o point_n of_o the_o meridian_n but_o in_o nautick_a use_n the_o intermedial_a loxodrome_n be_v denominate_v by_o a_o distance_n from_o the_o adjacent_a loxodrome_n for_o example_n in_o a_o three_o part_n a_o four_o part_v more_o north_n more_o east_n proposition_n fourteen_o a_o loxodrome_n intercept_v between_o two_o place_n be_v almost_o or_o according_a to_o the_o sense_n equal_a to_o the_o hypotenusa_fw-la of_o a_o right_n line_v plain_a triangle_n who_o one_o cathetus_n be_v of_o a_o equal_a distance_n of_o latitude_n of_o those_o two_o place_n the_o other_z cathetus_n be_v of_o a_o equal_a difference_n of_o longitude_n of_o the_o place_n take_v in_o the_o parallel_n which_o be_v in_o the_o middle_n between_o the_o parallel_n of_o those_o two_o place_n loxodrome_n what_o triangle_n be_v term_v loxodrome_n such_o triangle_n be_v term_v loxodromical_a but_o place_n very_o near_o be_v to_o be_v take_v for_o a_o accurate_a calculation_n that_o a_o small_a portion_n may_v be_v interpose_v viz._n place_n who_o difference_n of_o latitude_n be_v only_o of_o one_o scruple_n proposition_n xv._o the_o part_n of_o the_o loxodrome_n intercept_v between_o parallel_n distant_a by_o a_o equal_a interval_n be_v equal_a therefore_o many_o small_a loxodromical_a triangle_n be_v conceive_v in_o each_o loxodrome_n of_o which_o if_o that_o the_o loxodrome_n of_o one_o be_v suppute_v you_o have_v the_o quantity_n of_o the_o loxodrome_n from_o one_o place_n into_o another_o who_o latitude_n be_v know_v proposition_n xvi_o the_o latitude_n and_o difference_n of_o longitude_n of_o two_o place_n be_v give_v to_o find_v out_o the_o loxodrome_n by_o which_o you_o may_v sail_v from_o one_o place_n to_o another_o or_o two_o place_n be_v give_v on_o the_o globe_n or_o in_o a_o map_n to_o find_v out_o the_o quarter_n unto_o which_o the_o ship_n be_v to_o sail_n or_o to_o be_v bring_v from_o one_o place_n to_o the_o other_o refer_v the_o chief_a problem_n in_o the_o art_n of_o navigation_n to_o which_o all_o the_o rest_n be_v refer_v this_o be_v the_o chief_a or_o rather_o the_o only_a problem_n of_o the_o whole_a art_n of_o navigation_n unto_o which_o all_o the_o rest_n be_v refer_v if_o that_o there_o be_v no_o difference_n of_o latitude_n the_o loxodrome_n shall_v not_o be_v the_o way_n of_o the_o ship_n but_o the_o
those_o under_o the_o seven_o which_o be_v subject_a to_o the_o moon_n pass_v through_o germany_n the_o low_a country_n and_o england_n which_o say_v planet_n have_v their_o operation_n or_o influence_n on_o the_o inhabitant_n dwell_v under_o each_o of_o the_o say_a clime_n so_o that_o although_o the_o glorious_a and_o eternal_a luminary_n of_o heaven_n have_v a_o efficacious_a operation_n yet_o notwithstanding_o the_o disposition_n of_o the_o earth_n have_v a_o far_o great_a prevalency_n see_v that_o through_o the_o various_a situation_n of_o hill_n and_o valley_n we_o experimental_o find_v more_o great_a and_o different_a effect_n of_o the_o celestial_a ray_n which_o be_v also_o contemporate_v by_o the_o river_n and_o lake_n this_o can_v be_v deny_v by_o no_o man_n that_o nature_n be_v admirable_a in_o her_o work_n sometime_o as_o it_o be_v on_o set_v purpose_n delude_v the_o curiosity_n of_o humane_a wisdom_n by_o recede_v from_o the_o ordinary_a law_n of_o cause_n who_o can_v render_v a_o sufficient_a reason_n of_o that_o which_o be_v testify_v by_o mariner_n concern_v the_o region_n of_o maliapur_n in_o which_o be_v seat_v calicut_n a_o exceed_o high_a mountain_n top_v the_o cloud_n divide_v this_o province_n throughout_o and_o end_v in_o a_o promontory_n which_o be_v now_o call_v comorium_n which_o although_o it_o have_v the_o same_o altitude_n of_o the_o pole_n yet_o when_o the_o winter_n rage_v and_o the_o water_n swell_v on_o the_o one_o side_n on_o the_o other_o side_n the_o field_n and_o town_n be_v scorch_a with_o excessive_a heat_n and_o the_o sea_n calm_a wherefore_o this_o diversity_n which_o be_v discover_v in_o the_o climate_n the_o situation_n of_o province_n contemporation_n of_o the_o air_n and_o element_n do_v various_o discriminate_a the_o constitution_n of_o man_n and_o those_o constitution_n their_o nature_n for_o the_o manner_n of_o the_o mind_n follow_v the_o temperament_n and_o disposition_n of_o the_o body_n the_o septentrional_a or_o northern_a people_n be_v remote_a from_o the_o sun_n and_o by_o consequence_n inhabit_v in_o cold_a country_n be_v sanguine_a robu_v full_a of_o valour_n and_o animosity_n hence_o they_o have_v always_o be_v victorious_a and_o predominant_a over_o the_o meridional_a or_o southern_a nation_n as_o the_o assyrian_n over_o the_o chaldean_n the_o mede_n over_o the_o assyrian_n the_o parthian_n over_o the_o grecian_n the_o turk_n over_o the_o arabian_n the_o goths_z over_o the_o german_n the_o romans_z over_o the_o african_n and_o the_o english_a over_o the_o french_z they_o love_v freedom_n and_o liberty_n as_o those_o also_o do_v which_o be_v mountaineer_n as_o the_o helvetian_o grison_n and_o cantabrians_n the_o nation_n proximate_v to_o the_o sun_n have_v their_o blood_n whole_o exsiccate_v by_o immoderate_a heat_n hence_o the_o inhabitant_n of_o those_o place_n be_v melancholy_a and_o profound_a in_o the_o penetrate_a of_o the_o secret_n of_o nature_n for_o all_o the_o northern_a nation_n receive_v the_o mystery_n of_o the_o science_n from_o the_o egyptian_n and_o arabian_n the_o province_n which_o be_v immediate_o between_o both_o torrid_a zone_n enjoy_v a_o a_o benign_a heaven_n so_o that_o they_o flourish_n in_o religion_n justice_n and_o prudence_n the_o mutation_n of_o government_n the_o transmigration_n and_o emission_n of_o colony_n converse_n matrimony_n war_n and_o peace_n also_o the_o motion_n of_o the_o celestial_a sphere_n which_o drive_v from_o the_o pole_n and_o the_o zodiac_n of_o the_o primum_fw-la mobile_n the_o heavenly_a image_n on_o these_o inferior_a body_n do_v change_n and_o alter_v the_o habit_n manner_n and_o also_o nature_n itself_o if_o we_o have_v recourse_n unto_o history_n we_o shall_v find_v the_o german_n note_v of_o old_a for_o lofty_a mind_n and_o the_o italian_n on_o the_o contrary_a too_o abject_a and_o low_a which_o difference_n now_o can_v be_v discern_v nation_n have_v sway_v and_o be_v predominate_a by_o turn_n and_o as_o long_o as_o the_o monarchy_n have_v have_v duration_n among_o they_o virtue_n have_v flourish_v art_n and_o arm_n have_v go_v hand_n in_o hand_n which_o afterward_o with_o the_o ruin_n of_o the_o empire_n have_v be_v smother_v in_o its_o ash_n and_o receive_v vivification_n in_o another_o place_n yet_o notwithstanding_o these_o obstacle_n every_o nation_n have_v certain_a propension_n and_o fix_a affection_n appropriate_v to_o every_o one_o which_o will_v adhere_v to_o foreigner_n if_o that_o they_o long_o remain_v among_o they_o the_o intelligent_a reader_n who_o desire_v a_o knowledge_n in_o these_o and_o other_o particular_n with_o a_o throughout_o prospect_n of_o the_o utility_n of_o cosmography_n and_o geography_n may_v consult_v the_o work_n itself_o richard_z blome_n the_o content_n of_o the_o section_n and_o chapter_n general_z geography_n which_o may_v be_v divide_v into_o iii_o part_n 1._o the_o absolute_a part_n divide_v into_o five_o section_n the_o first_o section_n of_o thing_n to_o be_v foreknow_v chap._n 1._o of_o the_o precognita_n pag._n 1_o ch._n 2._o thing_n necessary_a to_o geometry_n and_o trigonometry_n p._n 6_o the_o second_o section_n explain_v the_o affection_n of_o the_o whole_a earth_n chap._n 3._o of_o the_o figure_n of_o the_o earth_n p._n 11_o chap._n 4._o of_o the_o dimension_n and_o magnitude_n of_o the_o same_o 15_o chap._n 5._o of_o the_o motion_n of_o the_o same_o p._n 23_o chap._n 6._o of_o its_o place_n in_o the_o system_fw-la of_o the_o world_n p._n 27_o chap._n 7._o of_o its_o substance_n and_o constitution_n p._n 30_o the_o three_o section_n in_o which_o the_o constitution_n and_o part_n of_o the_o earth_n be_v explain_v chap._n 8._o of_o the_o division_n of_o the_o earth_n by_o water_n p._n 35_o chap._n 9_o of_o mountain_n in_o general_a p._n 40_o chap._n 10._o of_o the_o difference_n of_o mountain_n p._n 46_o chap._n 11._o of_o wood_n desert_n and_o mine_n p._n 54_o the_o four_o section_n of_o hydrography_n in_o which_o the_o water_n and_o their_o property_n be_v explain_v chap._n 12._o of_o the_o division_n of_o the_o ocean_n throughout_o the_o earth_n p._n 57_o chap._n 13._o of_o the_o ocean_n and_o its_o part_n p._n 65_o chap._n 14._o of_o the_o motion_n of_o the_o sea_n especial_o of_o the_o flux_n and_o reflux_n p._n 83_o chap._n 15._o of_o lake_n pool_n and_o marsh_n p._n 102_o chap._n 16._o of_o river_n p._n 108_o chap._n 17._o of_o mineral_n water_n bath_n spaw_n etc._n etc._n p._n 130_o chap._n 18._o of_o the_o mutation_n of_o dry_a place_n into_o watery_a and_o the_o contrary_a p._n 142_o the_o five_o section_n of_o the_o atmosphere_n and_o wind_n chap._n 19_o of_o the_o atmosphere_n and_o air_n p._n 154_o chap._n 20._o of_o the_o wind_n in_o general_a p._n 179_o chap._n 21._o of_o the_o difference_n of_o wind_n and_o of_o they_o in_o particular_a p._n 187_o 2._o the_o respective_a part_n explain_v the_o celestial_a affection_n chap._n 22._o of_o the_o celestial_a affection_n in_o general_a p._n 2â—3_n ch._n 23._o of_o the_o latitude_n of_o a_o place_n and_o the_o elevation_n of_o the_o pole_n p._n 207_o chap._n 24._o of_o the_o division_n of_o the_o earth_n into_o zone_n p._n 213_o chap._n 25._o of_o the_o longitude_n of_o the_o day_n and_o division_n of_o the_o earth_n into_o climate_n p._n 220_o chap._n 26._o of_o the_o light_n heatt_z cold_a rains_n with_o other_o property_n of_o the_o zone_n according_a to_o the_o season_n of_o the_o year_n p._n 231_o chap._n 27._o of_o shadow_n and_o the_o division_n of_o the_o inhabitant_n in_o respect_n of_o the_o shadow_n p._n 259_o chap._n 28._o of_o the_o comparation_n of_o the_o celestial_a affection_n in_o divers_a place_n where_o be_v treat_v concern_v the_o antoeci_n perioeci_n and_o antipode_n p._n 269_o chap._n 29._o of_o the_o diversity_n of_o time_n in_o divers_a place_n p._n 275_o chap._n 30._o of_o the_o divers_a rise_n of_o the_o sun_n and_o moon_n and_o of_o the_o other_o appearance_n p._n 280_o 3._o the_o comparative_a part_n consider_v the_o affection_n which_o do_v arise_v from_o the_o compare_v of_o one_o place_n to_o another_o chap._n 31._o of_o the_o longitude_n of_o place_n p._n 291_o chap._n 32._o of_o the_o situation_n of_o place_n one_o to_o another_o p._n 309_o chap._n 33._o of_o the_o mutual_a distance_n of_o place_n p._n 335_o chap._n 34._o of_o the_o visible_a horizon_n p._n 342_o chap._n 35._o of_o the_o art_n of_o navigation_n in_o general_n and_o of_o the_o building_n of_o ship_n p._n 344_o chap._n 36._o of_o the_o lade_n or_o ballace_v of_o ship_n p._n 345_o chap._n 37._o of_o the_o directory_n of_o the_o nautick_a art_n in_o the_o first_o part_n the_o knowledge_n of_o the_o distance_n p._n 347_o chap._n 38._o thâ—â—â—â—ond_a part_n the_o knowledge_n of_o the_o quarter_n p._n 348_o chap._n 39_o the_o three_o part_n of_o histiodromia_n or_o the_o course_n of_o a_o ship_n p._n 353_o chap._n 40._o the_o four_o part_n of_o the_o
these_o be_v the_o three_o sort_n of_o property_n to_o be_v declare_v in_o special_a geography_n although_o those_o terrestrial_a property_n which_o make_v up_o the_o three_o rank_n be_v not_o so_o right_o refer_v to_o geography_n but_o we_o must_v yield_v somewhat_o to_o custom_n and_o the_o profit_n of_o learner_n we_o will_v beside_o these_o join_v many_o chapter_n to_o particular_a geography_n concern_v the_o practice_n of_o geography_n but_o in_o general_n geography_n which_o we_o will_v unfold_v in_o this_o book_n first_o the_o absolute_a property_n of_o the_o earth_n and_o its_o constitution_n be_v consider_v last_o in_o the_o comparative_a part_n those_o thing_n shall_v be_v propose_v which_o be_v offer_v unto_o we_o in_o the_o compare_v one_o place_n with_o another_o the_o principle_n of_o geography_n the_o principle_n which_o geography_n use_v for_o the_o confirm_v the_o truth_n of_o her_o proposition_n be_v threefold_a 1._o geometrical_a arithmetical_a and_o trigonometrical_a proposition_n 2._o astronomical_a precept_n and_o theorem_n although_o it_o may_v seem_v like_o a_o miracle_n for_o the_o knowledge_n of_o the_o earth_n in_o which_o we_o dwell_v to_o use_v the_o celestial_a body_n which_o be_v so_o many_o thousand_o mile_n remote_a from_o we_o 3._o experience_n for_o indeed_o the_o great_a part_n of_o geography_n especial_o that_o which_o be_v particular_a be_v uphold_v by_o the_o only_a experience_n and_o observation_n of_o man_n who_o have_v describe_v every_o country_n the_o order_n of_o geography_n concern_v the_o order_n which_o i_o esteem_v sit_v to_o observe_v in_o this_o art_n of_o geography_n it_o have_v be_v already_o speak_v in_o the_o division_n and_o explication_n of_o the_o property_n thereof_o yet_o here_o meet_v we_o a_o certain_a difficulty_n concern_v the_o order_n to_o be_v observe_v in_o the_o explication_n of_o these_o property_n forsooth_o whether_o to_o all_o country_n their_o own_o property_n be_v to_o be_v attribute_v or_o whether_o the_o country_n themselves_o be_v to_o be_v ascribe_v to_o the_o property_n general_o explicate_v aristotle_n in_o the_o first_o book_n of_o the_o history_n of_o live_v creature_n as_o also_o in_o his_o first_o book_n of_o the_o part_n of_o live_a creature_n move_v the_o like_a doubt_n and_o dispute_v it_o at_o large_a whether_o according_a to_o the_o single_a â—orts_n of_o live_a creature_n their_o property_n be_v single_o to_o be_v reckon_v up_o or_o else_o whether_o these_o property_n be_v general_o to_o be_v declare_v and_o the_o live_a creature_n in_o which_o the_o may_v be_v find_v be_v then_o to_o be_v subjoin_v the_o like_a difficulty_n occur_v also_o in_o other_o part_n of_o philosophy_n we_o in_o general_n geography_n have_v general_o unfold_v some_o property_n which_o in_o special_a geography_n we_o will_v apply_v to_o the_o application_n of_o single_a country_n the_o method_n of_o geography_n as_o touch_v the_o method_n and_o manner_n of_o prove_v the_o truth_n of_o geographical_a tenant_n very_o many_o be_v prove_v in_o general_a geography_n by_o demonstration_n proper_o so_o call_v especial_o celestial_a property_n but_o in_o special_a geography_n the_o celestial_a property_n only_o except_v which_o may_v be_v demonstrate_v be_v in_o a_o manner_n declare_v without_o demonstration_n because_o experience_n and_o observation_n do_v confirm_v they_o neither_o can_v they_o be_v prove_v by_o any_o other_o mean_n also_o very_a many_o proposition_n be_v prove_v or_o rather_o demonstrate_v by_o the_o terrestrial_a artificial_a globe_n and_o also_o by_o geographical_a map_n and_o some_o of_o these_o proposition_n which_o be_v thus_o explain_v upon_o the_o globe_n etc._n etc._n may_v be_v confirm_v by_o lawful_a demonstration_n again_o some_o proposition_n can_v in_o no_o wise_n be_v so_o prove_v but_o be_v therefore_o receive_v because_o we_o suppose_v that_o all_o place_n in_o the_o globe_n and_o map_n be_v so_o dispose_v even_o as_o they_o lie_v on_o the_o earth_n yet_o in_o these_o thing_n we_o will_v rather_o follow_v the_o description_n make_v by_o author_n of_o geography_n the_o globe_n and_o map_n serve_v for_o the_o clear_n and_o more_o easy_a comprehension_n thereof_o the_o original_a of_o geography_n the_o original_a of_o geography_n be_v not_o new_a nor_o bring_v into_o the_o world_n at_o one_o birth_n neither_o come_v she_o to_o we_o from_o one_o man_n but_o her_o principle_n and_o foundation_n be_v lay_v long_o ago_o yea_o many_o age_n since_o although_o ancient_a geographer_n be_v employ_v only_o in_o describe_v country_n which_o be_v the_o part_n of_o chorography_n and_o topography_n the_o roman_n be_v accustom_v when_o any_o country_n by_o they_o be_v subdue_v to_o show_v in_o their_o triumph_n the_o chorography_n thereof_o lively_o pencil_v and_o draw_v on_o a_o table_n and_o flourish_v with_o picture_n to_o the_o beholder_n there_o be_v beside_o at_o rome_n in_o lucullus_n his_o porch_n many_o table_n of_o geography_n expose_v to_o the_o view_n of_o all_o man_n the_o senate_n of_o rome_n about_o a_o hundred_o year_n before_o christ_n birth_n send_v surveyor_n and_o geographer_n into_o divers_a part_n of_o the_o world_n that_o they_o may_v measure_v out_o the_o earth_n but_o they_o come_v far_o short_a thereof_o neco_n king_n of_o the_o egyptian_n many_o age_n before_o the_o birth_n of_o christ_n command_v that_o the_o whole_a outer-side_n of_o africa_n shall_v be_v discover_v by_o the_o phoenician_n in_o three_o year_n space_n king_n darius_n command_v that_o the_o mouth_n of_o the_o river_n indus_n and_o the_o ethiopian_a eastern-sea_n shall_v be_v search_v out_o alexander_n the_o great_a in_o his_o voyage_n to_o asia_n take_v with_o he_o diognetus_n and_o beton_n as_o pliny_n note_v two_o surveyor_n and_o describer_n of_o his_o journey_n out_o of_o who_o annotation_n and_o journal_o geographer_n of_o succeed_a age_n take_v many_o thing_n imperfect_a ancient_a geography_n very_o imperfect_a but_o the_o geography_n of_o the_o ancient_n be_v very_o lame_a and_o imperfect_a for_o first_o they_o know_v not_o america_n in_o the_o least_o 2._o the_o northern-land_n 3._o the_o south-land_n and_o magellan_n be_v utter_o unknown_a to_o they_o 4._o they_o know_v not_o whether_o the_o earth_n may_v be_v sail_v about_o or_o the_o main_a ocean_n with_o a_o continual_a trace_n do_v encompass_v it_o but_o yet_o i_o deny_v not_o but_o that_o some_o of_o the_o ancient_n be_v of_o that_o opinion_n yet_o i_o utter_o deny_v they_o know_v it_o certain_o 5._o they_o know_v not_o whether_o the_o torrid_a zone_n be_v habitable_a 6._o they_o be_v ignorant_a of_o the_o true_a dimension_n of_o the_o earth_n although_o they_o write_v many_o thing_n in_o this_o business_n the_o excellency_n of_o geography_n first_o the_o study_n of_o geography_n be_v commend_v to_o we_o by_o the_o great_a worthiness_n thereof_o because_o it_o most_o of_o all_o become_v man_n be_v a_o inhabitant_n of_o the_o earth_n and_o endue_v with_o reason_n above_o all_o live_a creature_n second_o it_o be_v also_o a_o pleasant_a thing_n and_o indeed_o a_o honest_a recreation_n to_o contemplate_v the_o kingdom_n and_o property_n of_o the_o earth_n three_o the_o commodity_n and_o necessity_n of_o it_o be_v notable_a insomuch_o as_o neither_o divine_n physician_n lawyer_n historian_n nor_o other_o professor_n can_v want_v the_o knowledge_n thereof_o but_o the_o excellency_n of_o geography_n have_v be_v sufficient_o handle_v i_o place_v hereunder_o a_o table_n which_o open_v the_o order_n in_o special_a geography_n to_o the_o observe_v the_o explication_n of_o single_a country_n special_a geography_n consider_v in_o every_o region_n ten_o terrestrial_a 1._o limit_n and_o circumscription_n 2._o longitude_n of_o place_n and_o situation_n 3._o figure_n 4._o magnitude_n 5._o mountain_n the_o appellation_n situation_n and_o altitude_n their_o property_n and_o thing_n contain_v in_o they_o 6._o mine_n 7._o wood_n and_o desert_n 8._o water_n the_o sea_n lakes_n marsh_n river_n their_o spring_n inlet_n tract_n and_o latitude_n the_o quantity_n of_o water_n the_o celerity_n the_o quantity_n the_o cataract_n 9_o fertility_n sterility_n and_o fruit_n 10._o the_o animal_n eight_o celestial_a 1._o the_o distance_n of_o place_n from_o the_o aequator_fw-la and_o pole_n 2._o the_o obliquity_n of_o motion_n above_o the_o horizon_n 3._o the_o quantity_n of_o day_n 4._o the_o clime_n and_o zone_n 5._o the_o heat_n the_o season_n of_o the_o year_n the_o wind_n rain_n and_o other_o meteor_n 6._o the_o rise_n and_o stay_v of_o the_o star_n above_o the_o horizon_n 7._o the_o star_n pass_v through_o the_o vertex_fw-la of_o the_o place_n 8._o the_o celerity_n or_o quantity_n of_o their_o motion_n according_a to_o the_o hypothesis_n of_o copernicus_n ten_o human_a thing_n 1._o the_o stature_n life_n meat_n and_o drink_n and_o the_o original_a of_o the_o inhabitant_n 2._o the_o income_n art_n merchandise_n or_o traffic_n 3._o virtue_n and_o vice_n the_o genius_n and_o erudition_n 4._o
a_o b_o c_o d_o the_o distance_n from_o the_o verticle_n b_o g_o be_v observe_v by_o a_o quadrant_n let_v at_o alexandria_n in_o the_o day_n of_o the_o solstice_n 21_o of_o june_n g_o f_o or_o g_o f_o be_v observe_v 1_o 50_o of_o the_o periphery_a or_o 7_o degree_n 12_o minute_n but_o in_o syene_n let_v there_o be_v no_o distance_n the_o sun_n hang_v perpendicular_o over_o their_o head_n therefore_o b_o g_z shall_v be_v the_o arch_n intercept_v between_o those_o two_o place_n and_o because_o the_o distance_n put_v be_v 5000_o stadiums_n therefore_o according_a to_o the_o golden_a rule_n it_o shall_v be_v as_o 7_o degree_n 12_o part_n to_o one_o degree_n or_o as_o 1_o 50_o to_o 1_o 360_o or_o as_o 5_o to_o 36_o so_o 5000_o to_o 694_o 4_o 9_o stadiums_n which_o be_v requisite_a for_o one_o degree_n or_o as_o 1_o 50_o be_v to_o 50_o or_o as_o 1_o to_o 50_o so_o 5000_o to_o 250000_o stadiums_n of_o the_o whole_a periphery_n a_o b_o c_o d_o according_a to_o this_o measure_n yet_o see_v there_o be_v divers_a way_n to_o take_v the_o meridian_n altitude_n of_o the_o sun_n and_o the_o distance_n from_o the_o vertical_a point_n g_o b_o eratosthenes_n wrought_v it_o by_o a_o hollow_a spherical_a scioterick_n or_o sundial_n which_o they_o call_v scaphe_n where_o the_o style_n b_o x_o show_v the_o vertex_fw-la o_o x_o z_o but_o the_o radius_fw-la or_o beam_n of_o the_o sun_n terminaitng_a the_o shadow_n of_o the_o style_n or_o pin_n mark_v out_o b_o z_o how_o much_o the_o distance_n of_o the_o sun_n o_o b_o from_o the_o vertex_fw-la 7_o degree_n 12_o fir_v at_o alexandria_n but_o in_o the_o city_n syene_n the_o style_n g_o x_o make_v no_o shadow_n that_o day_n because_o o_o the_o sun_n hang_v perpendicular_o over_o it_o and_o therefore_o there_o be_v no_o distance_n of_o the_o sun_n then_o because_o therefore_o the_o angle_n b_o x_o z_o be_v equal_a to_o the_o angle_n b_o x_o o_o who_o measure_n be_v b_o o_o or_o b_o z_o there_o b_o o_fw-fr be_v equal_a to_o b_o z_o 7_o degree_n 12_o first_o minute_n or_o 1_o 50_o of_o the_o periphery_a the_o other_o thing_n be_v perform_v as_o it_o have_v be_v say_v the_o three_o manner_n of_o posidonius_n earth_n posidonius_n manner_n use_v about_o the_o magnitude_n etc._n etc._n of_o the_o earth_n let_v two_o place_n b_o g_z be_v under_o the_o same_o meridian_n posidonius_n take_v b_o rhodes_n and_o g_o the_o city_n alexandria_n in_o egypt_n let_v the_o altitude_n of_o some_o star_n in_o these_o two_o place_n when_o it_o come_v into_o the_o meridian_n above_o the_o horizon_n and_o that_o in_o the_o same_o day_n or_o in_o divers_a day_n which_o matter_n not_o at_o all_o posidonius_n take_v the_o shine_a star_n canobus_n which_o be_v of_o the_o first_o magnitude_n in_o argonavi_n scheme_n see_v scheme_n but_o this_o star_n do_v not_o rise_v above_o the_o horizon_n of_o rhodes_n h_o h_n s_n but_o do_v only_o touch_v the_o horizon_n in_o s_n yet_o it_o be_v elevate_v above_o the_o horizon_n of_o alexandria_n f_o r_o t_o in_o the_o arch_n t_o s_o 1_o 48_o part_n of_o the_o whole_a periphery_n or_o 7_o degree_n 30_o minute_n therefore_o the_o distance_n of_o the_o arch_n t_o s_o that_o be_v b_o g_o shall_v be_v 7_o degree_n 30_o minute_n unto_o 1_o degree_n or_o as_o 1_o 48_o part_n unto_o 1_o 360_o that_o be_v as_o 1_o to_o 48_o so_o 5000_o to_o 240000_o stadiums_n of_o the_o whole_a perimeter_n of_o the_o earth_n according_a to_o these_o hypothesis_n of_o posidonius_n the_o four_o manner_n or_o way_n of_o snellius_n earth_n snellius_n way_n about_o the_o dimension_n and_o magnitude_n of_o the_o earth_n because_o in_o the_o former_a way_n we_o have_v take_v two_o place_n b_o g_z lying_z under_o the_o same_o meridian_n and_o yet_o the_o place_n fit_a for_o this_o business_n may_v lie_v under_o divers_a meridian_n therefore_o we_o think_v it_o requisite_a that_o a_o example_n and_o that_o of_o snellius_n shall_v be_v also_o concern_v this_o case_n here_o propose_v let_v therefore_o a_o b_o c_o d_o be_v the_o meridian_n of_o alcmaria_n b_o alcmaria_n itself_o the_o elevation_n of_o the_o pole_n h_o a_o 52_o degree_n 40_o ½_n minute_n the_o distance_n from_o the_o pole_n b_o a_o 37_o degree_n 19_o minute_n 30_o second_n scheme_n see_v scheme_n let_v the_o other_o place_n be_v p_o bergenapsome_n the_o meridian_n a_o p_o v_o v_o the_o distance_n from_o the_o pole_n that_o be_v the_o compliment_n of_o the_o elevation_n 51_o degree_n 29_o minute_n a_o p_o be_v 38_o degree_n 31_o minute_n therefore_o p_o g_o a_o perpendicular_a line_n be_v draw_v to_o a_o b_o g_o the_o difference_n of_o the_o distance_n from_o the_o pole_n be_v b_o g_o 71_o minute_n 30_o second_n or_o 1_o degree_n 11_o minute_n 30_o second_n moreover_o snellius_n by_o a_o laborious_a geodesie_n or_o earth-meeting_n find_v the_o distance_n of_o alcmaria_n from_o bergen_n b_o p_o to_o be_v 34710_o rhindlandish_a perch_n and_o the_o angle_n of_o position_n p_o b_o g_o to_o be_v 11_o degree_n 26_o minute_n 2_o second_n therefore_o in_o the_o triangle_n straight_o angle_v p_o b_o g_o the_o hypotenuse_n b_o p_o and_o the_o angle_n b_o p_o g_o be_v give_v therefore_o by_o the_o problem_n of_o the_o second_o chapter_n b_o g_z be_v find_v 34018_o for_o which_o snellius_n take_v 33930_o for_o he_o detract_v 88_o perch_n from_o the_o station_n of_o the_o elevation_n of_o the_o pole_n but_o the_o arch_n b_o g_o 71_o ½_n scruple_n be_v the_o difference_n of_o the_o elevation_n of_o the_o pole_n therefore_o as_o 71_o ½_n minute_n be_v to_o 1_o degree_n or_o 60_o minute_n so_o be_v 33930_o or_o 34018_o to_o 28473_o perch_n for_o one_o degree_n or_o according_a to_o the_o round_a number_n 28500_o or_o 19_o holland_n mile_n they_o which_o understand_v spherical_a trigonometry_n from_o the_o give_v a_o b_o a_o p_o the_o angle_n a_o b_o p_o may_v find_v the_o arch_n b_o p_o to_n be_v 1_o degree_n 14_o minute_n which_o when_o they_o be_v equal_a with_o 34710_o perch_n 1_o degree_n shall_v be_v equal_a to_o the_o perch_n or_o of_o 18_o mile_n and_o ⅘_n but_o the_o cause_n that_o this_o number_n differ_v from_o that_o of_o snellius_n be_v first_o that_o snellius_n do_v not_o take_v the_o very_a point_n of_o the_o tower_n b_o p_o by_o which_o he_o obtain_v the_o angle_n g_o b_o p_o for_o the_o know_v the_o elevation_n of_o the_o pole_n but_o he_o take_v the_o place_n a_o little_a distant_a from_o they_o 197._o see_v snellius_n in_o page_n 197._o notwithstanding_o no_o man_n can_v doubt_v but_o the_o same_o may_v be_v find_v to_o be_v the_o altitude_n of_o the_o pole_n the_o other_o cause_n be_v that_o he_o take_v the_o line_n b_o g_z b_o p_o p_o g_o as_o straight_o which_o nevertheless_o be_v not_o straight_o although_o this_o discord_n may_v seem_v to_o make_v little_a or_o no_o difference_n of_o any_o moment_n but_o let_v snellius_n his_o quantity_n of_o a_o degree_n of_o 28500_o perch_n be_v take_v mine_n of_o 28300_o perch_n his_o make_v 19_o 147_o 150_o mile_n mine_n 18_o ⅘_n mile_n the_o perimeter_n or_o circuit_n according_a to_o snellius_n shall_v be_v 10260000_o perch_n 123120000_o foot_n or_o 8640_o holland_n mile_n the_o five_o manner_n be_v the_o first_o terrestrial_a way_n of_o measure_v the_o earth_n earth_n the_o first_o terrestrial_a way_n for_o the_o find_v out_o the_o magnitude_n etc._n etc._n of_o the_o earth_n the_o three_o follow_a manner_n or_o way_n be_v terrestrial_a perform_v the_o work_n without_o the_o heaven_n or_o meridian_n line_n let_v b_o p_o be_v the_o altitude_n of_o the_o tower_n this_o be_v to_o be_v seek_v out_o in_o a_o land-measuring_a way_n then_o let_v p_o s_o be_v the_o distance_n of_o the_o most_o remote_a term_n from_o whence_o the_o tower_n may_v be_v see_v and_o although_o p_o be_v be_v not_o a_o strait_a line_n yet_o because_o it_o be_v the_o least_o part_n of_o the_o periphery_a of_o the_o whole_a earth_n therefore_o it_o be_v take_v for_o a_o strait_a line_n and_o the_o triangle_n straight_o angle_v b_o p_o s_o in_o which_o by_o the_o give_v b_o p_o p_o s_o the_o angle_n b_o s_o p_o be_v find_v to_o who_o b_o r_z s_z be_v equal_a who_o measure_n be_v the_o arch_n s_o p._n therefore_o as_o this_o arch_n be_v to_o one_o degree_n so_o p_o s_o the_o find_v distance_n scheme_n see_v scheme_n be_v to_o the_o quantity_n of_o one_o degree_n as_o for_o example_n let_v b_o p_o the_o altitude_n be_v 480_o pace_n and_o let_v the_o distance_n p_o s_z of_o the_o point_n s_o which_o end_v the_o sight_n be_v 40000_o pace_n or_o 10_o german_a mile_n therefore_o let_v it_o be_v wrought_v according_a to_o the_o problem_n of_o the_o second_o chapter_n as_o
p_o s_o 40000_o pace_n be_v to_o b_o p_o 480_o pace_n so_o the_o whole_a sine_fw-la 10000000_o be_v to_o 11904_o the_o tangent_fw-la of_o the_o angle_n b_o s_o p_o or_o s_o r_o p_o or_o of_o the_o arch_n s_o p_o to_o wit_n 41_o minute_n therefore_o as_o 41_o minute_n be_v to_o 60_o minute_n so_o 40000_o pace_n be_v to_o 59000_o pace_n that_o be_v about_o 15_o mile_n for_o 1_o degree_n or_o the_o diameter_n p_o r_o may_v be_v find_v without_o the_o table_n of_o sines_n or_o without_o the_o find_v the_o perimeter_n for_o as_o b_o p_o be_v to_o p_o s_o so_o p_o s_n be_v to_o p_o r_o as_o 480_o be_v to_o 40000_o so_o 40000_o be_v to_o 3333333_o pace_n for_o the_o half_a diameter_n r_o p._n the_o six_o manner_n of_o measure_v the_o earth_n be_v the_o second_o terrestrial_a without_o the_o knowledge_n of_o the_o distance_n earth_n the_o second_o terrestrial_a way_n for_o the_o measure_v the_o earth_n but_o true_o the_o same_o half_a diameter_n r_o p_o shall_v also_o be_v conclude_v in_o this_o manner_n let_v b_o p_o be_v the_o high_a tower_n to_o wit_n the_o plummet_n be_v let_v down_o from_o the_o hole_n the_o height_n thereof_o may_v be_v find_v to_o be_v 100_o pace_n or_o if_o the_o height_n of_o the_o mountain_n p_o b_o be_v know_v by_o another_o geodesie_n or_o survey_v 4000_o pace_n afterward_o the_o instrument_n be_v apply_v in_o the_o top_n of_o b_o let_v the_o angle_n of_o the_o last_o sight_n be_v find_v p_o b_o s_o 88_o degree_n 37_o minute_n therefore_o b_o r_o s_o shall_v be_v one_o degree_n 23_o minute_n out_o of_o the_o canon_n of_o sines_n let_v the_o sine_fw-la of_o 88_o degree_n 37_o minute_n be_v take_v and_o let_v this_o be_v subtract_v from_o the_o whole_a sine_fw-la 10000000._o and_o let_v it_o be_v dispatch_v thus_o as_o the_o remainder_n be_v to_o the_o sine_fw-la of_o 88_o degree_n 37_o minute_n so_o b_o p_o of_o 1000_o pace_n be_v to_o the_o half_a diameter_n s_o r_n in_o pace_n the_o seven_o manner_n be_v the_o three_o terrestrial_a earth_n the_o three_o terrestrial_a way_n for_o the_o measure_v the_o magnitude_n of_o the_o earth_n this_o way_n or_o manner_n shall_v seem_v more_o accurate_a than_o the_o former_a way_n and_o shall_v appear_v more_o applicable_a to_o the_o practice_n take_v two_o mountain_n or_o height_n of_o who_o not_o the_o height_n but_o the_o distance_n may_v be_v know_v which_o may_v be_v find_v geodetical_o or_o by_o the_o art_n of_o survey_v let_v b_o p_o be_v one_o altitude_n of_o the_o mountain_n tower_n etc._n etc._n s_o t_o the_o other_o height_n let_v t_n p_o be_v the_o distance_n of_o five_o german_a mile_n scheme_n see_v scheme_n let_v the_o angle_n b_o t_o r_o 89_o degree_n 55_o minute_n be_v find_v by_o the_o instrument_n and_o in_o the_o other_o mountain_n t_o b_o r_o 89_o degree_n 55_o minute_n the_o angle_n p_o r_o s_o shall_v be_v 920_o minute_n because_o the_o three_o angle_n t_o b_o r_o be_v equate_v to_o two_o strait_a angle_n 180_o degree_n wherefore_o according_a to_o the_o golden_a rule_n work_v as_o 20_o degree_n be_v to_o 60_o degree_n so_o 5_o mile_n to_o 15_o mile_n for_o 1_o degree_n these_o be_v the_o principal_a manner_n and_o way_n of_o measure_v the_o earth_n for_o by_o the_o find_v out_o measure_n of_o 1_o degree_n the_o whole_a perimeter_n diameter_n superficies_n and_o solidity_n be_v find_v out_o because_o according_a to_o snellius_n the_o perimeter_n be_v 8640_o holland_n mile_n or_o 10260000_o rhindlandish_a perch_n or_o 123120000_o foot_n therefore_o by_o the_o problem_n of_o the_o second_o chapter_n the_o perimeter_n of_o the_o earth_n be_v find_v to_o be_v 1088_o ¼_n mile_n or_o 1633190_o perch_n or_o 19598300_o foot_n the_o superficies_n of_o the_o earth_n 18811353_o â…—_n square_a holland_n mile_n and_o the_o whole_a solidity_n be_v 409568â—1512_n cubick_a mile_n usual_a the_o calculation_n of_o german_a mile_n usual_a but_o because_o the_o calculation_n by_o german_a mile_n be_v more_o usual_a 15_o of_o which_o make_v 1_o degree_n therefore_o these_o may_v be_v use_v but_o upon_o this_o condition_n that_o such_o mile_n may_v be_v understand_v of_o which_o 15_o may_v make_v 19_o holland_n mile_n or_o that_o 1_o mile_n may_v contain_v 1900_o rhindlandish_a perch_n therefore_o the_o periphery_a of_o the_o earth_n shall_v be_v 5400_o such_o mile_n the_o half_a diameter_n 860_o the_o superficies_n 9278181_o square_a mile_n the_o solidity_n shall_v be_v 265693384_o cubick_a mile_n commodious_a the_o italian_a mile_n most_o commodious_a yet_o the_o italian_a mile_n be_v the_o most_o commodious_a 60_o of_o which_o be_v allow_v to_o 1_o degree_n for_o so_o 1_o mile_n fitting_o answer_v one_o minute_n of_o a_o degree_n but_o such_o a_o italian_a mile_n ought_v to_o be_v understand_v which_o may_v contain_v 475_o rhindlandish_a perch_n so_o the_o circuit_n of_o the_o earth_n shall_v be_v 21600_o such_o mile_n the_o half_a diameter_n 3440_o mile_n mathematician_n reason_n show_v error_n in_o the_o differ_v of_o the_o dimension_n of_o the_o earth_n according_a to_o the_o arabian_n and_o other_o mathematician_n these_o thing_n be_v thus_o expound_v we_o must_v allege_v and_o bring_v hither_o the_o cause_n why_o the_o fore-rehearsed_n dimension_n or_o measuring_n of_o author_n may_v so_o differ_v and_o what_o be_v want_v in_o every_o one_o of_o they_o in_o the_o first_o manner_n of_o dimension_n these_o thing_n occur_v first_o that_o a_o error_n may_v be_v commit_v in_o take_v the_o elevation_n of_o the_o pole_n second_o that_o a_o doubt_n may_v be_v make_v concern_v place_n under_o the_o same_o meridian_n three_o that_o the_o distance_n may_v not_o be_v declare_v distinct_o and_o because_o the_o arabian_n use_v this_o manner_n therefore_o the_o thing_n that_o be_v desire_v in_o their_o dimension_n be_v these_o first_o the_o exact_a quantity_n or_o greatness_n of_o their_o mile_n which_o according_a to_o alfraganus_n be_v 4000_o cubit_n as_o unknown_a to_o we_o second_o the_o arabian_n have_v not_o show_v to_o we_o the_o place_n who_o elevation_n they_o take_v and_o therefore_o we_o can_v make_v further_a search_n concern_v their_o diligence_n three_o neither_o do_v they_o demonstrate_v their_o manner_n by_o which_o they_o measure_v in_o eratosthenes_n dimension_n these_o thing_n deserve_v correction_n first_o that_o to_o the_o arch_n find_v b_o z_o of_o 7_o degree_n 12_o minute_n he_o do_v not_o add_v 15_o minute_n for_o the_o arch_n intercept_v between_o the_o radius_fw-la solis_fw-la x_o z_o which_o be_v to_o be_v take_v second_o that_o he_o do_v not_o prove_v syene_n and_o alexandria_n to_o lie_v under_o the_o same_o meridian_n three_o that_o the_o term_n of_o the_o shadow_n can_v be_v exact_o note_v and_o beside_o that_o the_o place_n about_o syene_n even_o to_o 150_o stadiums_n have_v this_o property_n that_o the_o style_n be_v without_o a_o shadow_n fourâ—â—ly_o that_o he_o take_v the_o distance_n between_o syene_n and_o alexandria_n according_a to_o the_o opinion_n of_o the_o vulgar_a sort_n which_o neglect_v and_o have_v no_o care_n of_o exactness_n neither_o can_v the_o magnitude_n of_o the_o stadium_n be_v certain_o manifest_a unto_o we_o in_o posidonius_n his_o manner_n these_o blemish_n be_v judge_v to_o be_v first_o that_o he_o think_v canobus_n be_v not_o lift_v up_o above_o the_o horizon_n of_o rhodes_n whenas_o notwithstanding_o it_o may_v be_v elevate_v 2_o degree_n above_o it_o sure_o he_o can_v not_o know_v that_o it_o exact_o touch_v it_o second_o that_o he_o determine_v the_o distance_n between_o rhodes_n and_o alexandria_n by_o conjecture_n and_o common_a journey_n three_o that_o his_o stadiasm_n or_o measure_n of_o a_o stadium_n be_v not_o sufficient_o determinate_a four_o because_o it_o may_v be_v doubtful_a whether_o alexandria_n and_o rhodes_n lie_v under_o the_o same_o meridian_n etc._n etc._n in_o the_o terrestrial_a â—_z of_o measure_v the_o earth_n there_o be_v this_o defect_n first_o that_o in_o the_o exact_a measure_n of_o hill_n a_o fault_n may_v easy_o be_v commit_v second_o the_o furthermost_a point_n of_o the_o sight_n can_v be_v know_v accurate_o both_o because_o of_o the_o refraction_n as_o also_o for_o the_o weakness_n of_o the_o eye_n it_o may_v suffice_v to_o have_v speak_v thus_o much_o concern_v the_o great_a circuit_n of_o the_o earth_n its_o half_a diameter_n superficies_n and_o solidity_n we_o may_v if_o it_o be_v a_o similar_v body_n by_o the_o solidity_n of_o the_o earth_n judge_v of_o its_o weight_n but_o because_o part_n of_o a_o different_a weight_n who_o proportion_n be_v hide_v from_o we_o be_v in_o it_o therefore_o its_o weight_n can_v but_o by_o a_o conceive_a supposition_n be_v determine_v earth_n the_o half_a diameter_n of_o the_o earth_n be_v the_o measure_n of_o all_o celestial_a dimension_n the_o distance_n of_o the_o sun_n and_o
xenagoras_n the_o son_n of_o eumelus_n use_v this_o manner_n or_o way_n of_o measure_v in_o find_v out_o and_o know_v the_o height_n of_o the_o mountain_n olympus_n and_o to_o have_v find_v the_o angle_n a_o f_o c_o to_o be_v 88_o degree_n 29_o minute_n but_o the_o angle_n a_o c_o f_o 57_o degree_n 30_o minute_n therefore_o c_z a_o f_o shall_v be_v 34_o degree_n 13_o minute_n and_o by_o measure_n he_o find_v f_o c_o to_o be_v 400_o grecian_a foot_n or_o two_o three_o part_n of_o one_o stadium_n therefore_o it_o shall_v be_v as_o the_o sign_n of_o the_o angle_n c_o a_o f_o 34_o degree_n 13_o minute_n to_o the_o sign_n of_o the_o angle_n a_o c_o f_o 57_o degree_n 13_o minute_n so_o c_o f_o 400_o the_o foot_n of_o the_o mountain_n to_o the_o distance_n f_o a_o to_o wit_n as_o 50226_o to_o 84339_o so_o be_v 400_o to_o 600_o therefore_o f_o a_o be_v 600_o foot_n furthermore_o let_v the_o angle_n b_o f_o a_o be_v find_v 84_o degree_n 23_o minute_n it_o shall_v be_v in_o the_o triangle_n f_o a_o b_o as_o 100000_o to_o the_o tangent_fw-la of_o the_o angle_n b_o f_o a_o 1016000_o so_o 600_o to_o 6096_o foot_n for_o a_o b_o the_o height_n of_o the_o mountain_n olympus_n but_o 600_o foot_n make_v a_o stadium_n therefore_o 6096_o being_n divide_v by_o 600_o there_o be_v find_v 10_o stadium_n and_o 96_o greek_a foot_n for_o the_o height_n of_o the_o mountain_n olympus_n just_o so_o much_o as_o xenagoras_n find_v it_o to_o be_v but_o these_o stadium_n make_v ¼_n of_o a_o german_a mile_n with_o 2_o 32_o or_o about_o 1_o 16._o aristotle_n the_o mountain_n olympus_n say_v to_o be_v very_o high_a by_o aristotle_n aristotle_n with_o many_o other_o writer_n affirm_v that_o the_o height_n of_o the_o mountain_n olympus_n be_v so_o great_a that_o the_o top_n thereof_o feel_v no_o motion_n of_o the_o air_n or_o shower_n of_o rain_n and_o also_o that_o it_o be_v elevate_v above_o the_o second_o region_n of_o the_o air_n and_o the_o ancient_n gather_v that_o by_o the_o ash_n leave_v thereon_o be_v never_o move_v thence_o by_o any_o wind_n and_o by_o the_o draught_n and_o form_n of_o letter_n be_v no_o whit_n consume_v but_o find_v there_o after_o divers_a year_n fresh_a and_o as_o they_o be_v there_o draw_v at_o the_o first_o it_o be_v to_o be_v note_v that_o in_o divers_a place_n the_o height_n of_o the_o mountain_n be_v also_o diverse_a therefore_o the_o consequence_n avail_v not_o the_o cloud_n do_v likewise_o cover_v this_o mountain_n therefore_o it_o be_v as_o high_a for_o indeed_o in_o the_o northern_a part_n and_o coast_n of_o the_o world_n the_o cloud_n be_v a_o great_a deal_n low_o there_o be_v also_o another_o manner_n of_o measure_v in_o plane_n the_o mountain_n by_o two_o stadium_n in_o the_o same_o strait_a line_n with_o the_o mountain_n but_o it_o be_v prone_a to_o error_n by_o reason_n of_o the_o small_a difference_n of_o the_o angles_n scheme_n another_o way_n to_o find_v the_o height_n of_o a_o mountain_n see_v scheme_n yet_o by_o one_o height_n know_v as_o for_o example_n by_o a_o tower_n who_o height_n be_v know_v and_o the_o distance_n from_o the_o mountain_n we_o shall_v more_o accurate_o gain_v the_o height_n of_o the_o mountain_n viz._n if_o we_o suppose_v f_o to_o be_v the_o tower_n 300_o foot_n high_a and_o on_o the_o top_n thereof_o or_o in_o some_o commodious_a place_n the_o angle_n b_o f_o p_o be_v observe_v to_o be_v 83_o degree_n 30_o minute_n p_o b_o shall_v be_v find_v to_o be_v 5896_o foot_n to_o who_o b_o a_o the_o height_n of_o the_o tower_n must_v be_v add_v proposition_n iii_o the_o height_n of_o the_o see_v mountain_n be_v give_v or_o know_v to_o find_v out_o geodetical_o or_o by_o land-measuring_a how_o great_a distance_n we_o be_v from_o it_o if_o we_o have_v either_o a_o geometrical_a instrument_n or_o radius_fw-la or_o altimetrical_a scale_n with_o we_o that_o be_v to_o say_v a_o height-measuring_a scale_n mountain_n another_o way_n to_o find_v the_o height_n of_o a_o mountain_n let_v a_o b_o be_v again_o the_o height_n of_o the_o mountain_n be_v now_o know_v by_o the_o description_n of_o the_o other_o 10_o stadium_n and_o 96_o greek_a foot_n or_o 6096_o foot_n let_v f_o be_v our_o place_n and_o let_v we_o desire_v to_o know_v the_o distance_n f_o a._n let_v the_o angle_n b_o f_o a_o be_v take_v by_o a_o geometrical_a instrument_n or_o quadrant_n let_v it_o be_v for_o example_n 48_o degree_n 23_o minute_n therefore_o the_o triangle_n straight_o angle_v b_o at_fw-fr f_o when_o three_o be_v know_v it_o shall_v be_v as_o the_o whole_a sign_n to_o the_o tangent_fw-la of_o the_o angle_n a_o b_o f_o scheme_n see_v scheme_n 5_o degree_n 37_o minute_n so_o b_o a_o the_o know_a height_n shall_v be_v to_o the_o demand_v a_o f._n as_o 100000_o be_v to_o 9234_o so_o 6096_o to_o 600_o foot_n or_o one_o stadium_n therefore_o at_o so_o great_a a_o distance_n which_o be_v f_o a_o we_o be_v from_o the_o mountain_n if_o we_o use_v a_o land-measuring_a quadrant_n or_o square_a or_o radius_fw-la we_o shall_v not_o then_o need_v the_o canon_n of_o sign_n which_o be_v manifest_a by_o the_o declaration_n and_o explication_n of_o the_o instrument_n but_o yet_o the_o calculation_n or_o computation_n become_v thereby_o not_o so_o accurate_a by_o reason_n of_o the_o want_n of_o true_a proportion_n note_v in_o these_o two_o problem_n i_o have_v add_v geodetical_o because_o the_o manner_n of_o measure_v be_v otherwise_o when_o we_o use_v a_o semidiameter_n or_o periphery_n of_o the_o earth_n as_o we_o shall_v now_o propose_v for_o in_o the_o former_a we_o have_v take_v the_o distance_n f_o a_o as_o a_o strait_a line_n because_o there_o be_v but_o a_o small_a difference_n between_o that_o and_o a_o crooked_a line_n proposition_n iu._n a_o distance_n be_v give_v from_o who_o term_n or_o extreme_a boundary_a the_o top_n of_o the_o mountain_n be_v first_o see_v to_o find_v thereby_o the_o height_n of_o the_o mountain_n by_o geography_n scheme_n a_o distance_n of_o a_o mountain_n be_v give_v to_o find_v the_o height_n see_v scheme_n let_v we_o take_v the_o most_o high_a mountain_n of_o teneriff_n call_v el_n pico_n or_o the_o pike_n and_o let_v a_o b_o c_o d_o f_o be_v the_o periphery_a of_o the_o earth_n and_o indeed_o the_o meridian_n of_o that_o mountain_n let_v the_o centre_n be_v r_o the_o mountain_n itself_o a_o b_o let_v from_o b_o a_o strait_a tangent-line_n be_v draw_v to_o the_o periphery_n b_o f._n f_o then_o shall_v be_v the_o furthermost_a or_o first_o point_n from_o which_o the_o top_n of_o the_o mountain_n b_o shall_v be_v see_v let_v f_o r_n be_v draw_v but_o some_o mariner_n do_v testify_v that_o when_o they_o be_v four_o degree_n distant_a from_o it_o in_o the_o meridian_n they_o can_v descry_v the_o top_n of_o that_o mountain_n therefore_o the_o arch_n a_o f_o shall_v be_v four_o degree_n let_v we_o therefore_o suppose_v that_o this_o relation_n of_o our_o seaman_n be_v true_a and_o that_o the_o first_o visive_a ray_n b_o f_o come_v direct_o 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mountain_n a_o b_o which_o be_v almost_o incredible_a and_o altogether_o against_o the_o ancient_n and_o old_a geographer_n therefore_o it_o be_v to_o be_v know_v that_o there_o be_v two_o thing_n take_v in_o the_o problem_n which_o be_v false_a first_o that_o that_o radius_fw-la or_o ray_n which_o come_v from_o b_o first_o strikes_z the_o eye_n be_v direct_v when_o as_o yet_o by_o reason_n of_o the_o thickness_n of_o the_o air_n it_o be_v refract_v or_o turn_v indeed_o from_o b_o the_o top_n of_o the_o hill_n there_o can_v be_v a_o strait_a line_n draw_v to_o f_o if_o f_o a_o be_v four_o degree_n but_o that_o first_o it_o must_v incur_v
or_o run_v upon_o the_o earth_n and_o therefore_o the_o top_n b_o can_v be_v see_v direct_o in_o the_o place_n of_o f_o but_o by_o a_o refracted_a radius_fw-la to_o wit_n b_o t_o f_o which_o be_v break_v and_o indeed_o the_o first_o of_o the_o break_a ray_n which_o may_v reach_v to_o f._n if_o therefore_o we_o suppose_v that_o this_o refraction_n bring_v it_o to_o pass_v that_o this_o mountain_n may_v be_v soon_o see_v by_o one_o degree_n than_o it_o will_v be_v see_v if_o it_o be_v without_o this_o refraction_n to_o wit_n with_o a_o direct_a ray_n b_o f_o to_o be_v see_v from_o three_o degree_n a_o f_o the_o height_n a_o b_o shall_v be_v find_v out_o according_a to_o the_o declare_a form_n of_o five_o italian_a mile_n or_o 40_o stadium_n but_o because_o it_o be_v also_o likely_a which_o be_v the_o second_o that_o our_o seaman_n speak_v more_o at_o large_a and_o not_o with_o so_o accurate_a a_o dimension_n if_o we_o therefore_o subtract_v yet_o half_a a_o degree_n so_o as_o we_o may_v resolve_v that_o it_o be_v see_v 2_o ½_n degree_n thence_o or_o 38_o german_a mile_n for_o f_o a_o this_o i_o say_v be_v put_v and_o our_o calculation_n be_v order_v as_o at_o first_o the_o height_n of_o the_o mountain_n a_o b_o shall_v be_v find_v to_o be_v about_o one_o mile_n if_o the_o mountain_n may_v be_v see_v from_o the_o distance_n of_o two_o degree_n the_o refraction_n be_v set_v apart_o it_o shall_v be_v 2_o ½_n italian_a mile_n high_a but_o if_o it_o can_v be_v see_v at_o one_o degree_n distance_n or_o 15_o german_a mile_n it_o shall_v be_v in_o height_n half_a a_o italian_a mile_n or_o about_o 5_o stadium_n high_a to_o this_o end_n we_o add_v the_o table_n follow_v if_o the_o height_n of_o the_o mountain_n be_v ⅛_n mile_n germ._n 1_o 7_o mile_n ⅙_n ⅕_n ¼_n ⅓_n ½_n 1_o then_o it_o shall_v be_v see_v from_o the_o distance_n of_o mile_n 14_o 18_o 20_o 25_o 26_o 27_o ½_n 28_o 29_o ¼_n but_o all_o these_o thing_n be_v to_o be_v understand_v without_o refraction_n which_o for_o the_o most_o part_n increase_v the_o see_v height_n of_o the_o mountain_n and_o the_o distance_n of_o the_o sight_n as_o you_o may_v perceive_v by_o the_o description_n for_o the_o refract_v radius_fw-la t_o f_o produce_v give_v the_o height_n n_o a._n proposition_n v._o the_o top_n of_o any_o mountain_n be_v first_o see_v who_o height_n be_v know_v to_o find_v by_o geography_n how_o great_a space_n we_o be_v from_o it_o distance_n see_v scheme_n the_o top_n of_o a_o mountain_n who_o height_n be_v know_v to_o find_v at_o the_o first_o sight_n its_o distance_n this_o be_v the_o consequent_a of_o the_o former_a proposition_n and_o the_o solution_n thereof_o may_v be_v fetch_v from_o the_o table_n before_o describe_v but_o the_o calculation_n will_v show_v a_o more_o accurate_a solution_n let_v therefore_o the_o know_a height_n of_o the_o mountain_n be_v a_o b_o and_o let_v it_o be_v see_v in_o f_o it_o may_v please_v we_o to_o know_v the_o distance_n a_o f_o b_o f_o touch_v the_o periphery_a in_o the_o triangle_n straight_o angle_v b_o f_o r_n the_o angle_n f_o be_v be_v straight_o and_o the_o two_o side_n r_o f_o the_o half_a diameter_n of_o the_o earth_n and_o r_o b_o the_o same_o half_a diameter_n with_o a_o b_o be_v know_v which_o we_o may_v put_v to_o be_v half_o a_o german_a mile_n and_o because_o r_n f_o and_o r_o a_o be_v 860_o r_n b_o shall_v be_v 860_o ½_n and_o it_o may_v be_v wrought_v as_o r_z b_o be_v to_z r_o f_o so_o the_o whole_a sign_n to_o the_o sign_n of_o the_o angle_n r_o b_o f._n in_o rhindlandish_a foot_n as_o 860_o ½_n to_o 860_o so_o 10000000_o to_o as_o 19609700_o to_o 19598300_o so_o 10000000_o to_o 9994186_o the_o sign_n 88_o degree_n 2_o minuees_fw-la 40_o for_o r_o b_o f._n therefore_o b_o r_n f_o that_o be_v the_o arch_n a_o f_o shall_v be_v one_o degree_n 55_o minute_n 20_o second_n therefore_o from_o this_o distance_n the_o mountain_n shall_v be_v see_v with_o refraction_n of_o ray_n if_o it_o be_v half_a a_o mile_n high_a to_o which_o for_o the_o argument_n of_o refraction_n we_o may_v add_v eight_o mile_n insomuch_o that_o it_o may_v be_v see_v at_o the_o ordinary_a distance_n of_o 37_o mile_n but_o the_o refraction_n also_o vary_v according_a to_o the_o diverse_a altitude_n of_o the_o sun_n neither_o be_v it_o absent_a before_o the_o rise_n or_o after_o the_o set_n of_o the_o sun_n but_o we_o will_v treat_v more_o at_o large_a concern_v this_o business_n in_o the_o chapter_n touch_v the_o air_n and_o the_o three_o part_n of_o this_o book_n where_o we_o shall_v discourse_v of_o the_o visible_a horizon_n proposition_n vi_o the_o length_n of_o the_o shadow_n be_v give_v which_o any_o mountain_n cast_v and_o the_o height_n of_o the_o sun_n be_v give_v to_o that_o time_n to_o find_v out_o the_o altitude_n of_o the_o mountain_n etc._n to_o find_v out_o the_o altitude_n of_o a_o mountain_n by_o its_o shadow_n know_v the_o height_n of_o the_o sun_n of_o the_o mountain_n athos_n its_o height_n etc._n etc._n we_o will_v propose_v this_o problem_n rather_o for_o its_o antiquity_n and_o pleasantness_n than_o that_o we_o think_v that_o the_o altitude_n may_v accurate_o by_o the_o shadow_n be_v obtain_v plutarch_n and_o pliny_n have_v write_v that_o the_o mountain_n athos_n will_v cover_v or_o hide_v the_o side_n of_o the_o lemnian_a heifer_n because_o the_o mountain_n athos_n situate_v on_o the_o shore_n of_o macedonia_n be_v so_o high_o elevate_v that_o its_o cast_v its_o shadow_n into_o the_o island_n lemnos_n the_o sun_n be_v in_o cancer_n and_o indeed_o into_o the_o market_n of_o the_o city_n myrrhina_n where_o the_o boundary_a or_o end_n of_o the_o shadow_n be_v signify_v by_o a_o brazen_a heifer_n there_o erect_v which_o the_o inhabitant_n place_v there_o for_o the_o strangeness_n and_o wonder_n of_o the_o matter_n and_o pliny_n write_v that_o the_o interval_n or_o distance_n between_o the_o mountain_n athos_n and_o the_o isle_n lemnos_n be_v judge_v to_o be_v 87000_o pace_n or_o 87_o italian_a mile_n but_o writer_n have_v not_o note_v the_o alitude_n of_o the_o sun_n according_a to_o the_o shadow_n thereof_o but_o yet_o it_o be_v likely_a that_o this_o shadow_n cast_v from_o the_o sun_n be_v at_o the_o point_n of_o set_v or_o when_o it_o begin_v to_o be_v hide_v from_o the_o city_n myrrhina_n by_o the_o mountain_n athos_n for_o athos_n stand_v westward_o from_o the_o isle_n lemnos_n or_o when_o in_o it_o it_o be_v hide_v from_o the_o vertical_a point_n of_o myrrhina_n which_o be_v draw_v through_o the_o mountain_n athos_n but_o although_o we_o may_v put_v that_o the_o sun_n be_v then_o as_o it_o be_v in_o the_o horizon_n of_o myrrhina_n f_o o_o and_o so_o that_o the_o radius_fw-la o_o f_o pass_v through_o the_o top_n of_o the_o mountain_n b_o proposition_n see_v the_o scheme_n to_o the_o five_o proposition_n and_o cast_v the_o shadow_n a_o f_o and_o o_o f_o shall_v be_v the_o tangent_fw-la of_o the_o periphery_a and_o because_o f_o r_n be_v give_v and_o the_o angle_n f_o r_o b_o or_o by_o take_v the_o triangle_n b_o a_o f_o and_o f_o a_o as_o a_o strait_a line_n b_o a_o shall_v be_v find_v to_o be_v eight_o stadium_n the_o height_n of_o the_o mountain_n but_o because_o notwithstanding_o in_o this_o position_n of_o the_o sun_n the_o term_n or_o boundary_a of_o the_o shadow_n can_v be_v note_v because_o it_o be_v infinite_a and_o beside_o that_o the_o building_n of_o the_o city_n myrrhina_n may_v hinder_v both_o the_o shadow_n and_o the_o near_a ray_n of_o the_o sun_n near_o to_o the_o shadow_n therefore_o it_o be_v to_o be_v determine_v that_o the_o sun_n at_o the_o least_o be_v elevate_v two_o degree_n above_o the_o horizon_n of_o myrrhina_n for_o example_n in_o s_n that_o the_o angle_n s_o f_o o_o be_v two_o degree_n and_o the_o radius_fw-la of_o the_o sun_n pass_v through_o the_o top_n of_o the_o mountain_n t_o and_o end_v the_o shadow_n in_o f._n therefore_o in_o the_o oblique_a angle_a triangle_n r_o t_o f_o the_o give_v angle_n shall_v be_v t_o f_o r_n 92_o degree_n and_o f_o r_o t_n be_v give_v one_o degree_n 16_o minute_n and_o therefore_o f_o t_n r_n be_v 86_o degree_n 45_o minute_n and_o the_o half_a diameter_n f_o r_n be_v know_v 860_o german_a mile_n therefore_o t_n r_n shall_v be_v find_v according_a to_o the_o proportion_n as_o the_o sign_n of_o the_o angle_n f_o t_o r_n 86_o degree_n 54_o minute_n to_o the_o sign_n of_o the_o angle_n t_o f_o r_n 92_o degree_n so_o f_o r_n to_o r_n t_o 860._o therefore_o r_n t_n shall_v be_v 861_o german_a mile_n and_o a_o t_o the_o height_n of_o the_o mountain_n athos_n somewhat_o
like_a and_o chemical_a water_n in_o wâ—â—â—_n metal_n be_v dissolve_v water_n spirituous_a water_n spirituous_a water_n be_v 〈◊〉_d that_o contain_v only_o a_o volatile_a spirit_n such_o as_o be_v find_v in_o mineral_n but_o no_o fix_a particle_n and_o therefore_o none_o can_v be_v elicitate_v from_o they_o apparent_a to_o the_o sight_n these_o be_v term_v corporeal_a and_o spirituous_a water_n together_o by_o i_o which_o have_v both_o fix_v or_o solid_a and_o volatile_a or_o spirituous_a particle_n of_o mineral_n in_o they_o we_o shall_v allege_v example_n of_o the_o species_n of_o they_o in_o the_o follow_a proposition_n proposition_n iii_o to_o explain_v how_o mineral_n water_n be_v generate_v water_n of_o the_o generation_n of_o mineral_n water_n 1._o if_o that_o water_n be_v carry_v by_o a_o violent_a torrent_n or_o course_n through_o subterraneous_a passage_n in_o which_o metallick_n earth_n and_o mineral_n be_v less_o thick_a it_o be_v manifest_a that_o the_o water_n may_v take_v and_o carry_v away_o from_o these_o with_o it_o grain_n of_o those_o mineral_n water_n this_o therefore_o be_v the_o generation_n of_o corporeal_a mineral_n water_n that_o carry_v grain_n 2._o if_o that_o the_o mineral_n be_v imperfect_a or_o less_o dense_a as_o vitriol_n sulphur_n and_o the_o like_a or_o also_o the_o salt_n which_o of_o their_o own_o nature_n be_v easy_o unite_v to_o the_o water_n if_o that_o the_o water_n or_o riveret_n be_v carry_v through_o these_o earth_n without_o channel_n or_o aqueduct_v as_o we_o have_v explain_v in_o the_o generation_n of_o fountain_n the_o water_n come_v to_o the_o fountain_n this_o will_v have_v the_o atom_n of_o these_o mineral_n admix_v and_o it_o will_v be_v a_o corporeal_a mineral_n water_n of_o a_o subtle_a conjunction_n according_a to_o the_o atom_n now_o whether_o that_o the_o water_n can_v unite_v the_o atom_n of_o metal_n after_o this_o manner_n to_o itself_o be_v question_v because_o that_o they_o be_v hard_a and_o solid_a neither_o be_v they_o easy_o unite_v to_o the_o water_n i_o suppose_v it_o possible_a to_o be_v do_v but_o not_o by_o simple_a water_n but_o by_o a_o salt_n vitriolated_a water_n which_o be_v like_a unto_o the_o aqua_fw-la fortis_fw-la of_o the_o chemist_n for_o as_o these_o water_n of_o aqua_fw-la fortis_fw-la dissolve_v metal_n into_o atom_n and_o intimate_o unite_v they_o to_o themselves_o so_o that_o they_o sink_v not_o to_o the_o bottom_n unless_o that_o they_o be_v separate_v by_o art_n so_o also_o if_o that_o such_o water_n be_v carry_v through_o metallary_n earth_n they_o be_v able_a to_o dissolve_v the_o metallic_a particle_n and_o unite_v they_o to_o themselves_o after_o this_o mode_n be_v the_o generation_n of_o mineral_n corporeal_a water_n of_o the_o second_o classis_fw-la explain_v 3._o in_o the_o bowel_n of_o the_o earth_n before_o that_o metal_n be_v generate_v vapour_n and_o fume_n be_v condense_v unto_o the_o extant_a angle_n of_o the_o rock_n unto_o which_o they_o adhere_v and_o first_o they_o meet_v together_o in_o a_o soft_a substance_n and_o at_o length_n they_o be_v condense_v therefore_o if_o that_o the_o water_n be_v carry_v or_o glide_v through_o the_o earth_n where_o such_o vapour_n be_v and_o be_v raise_v they_o be_v impregnate_v by_o they_o and_o so_o spirituous_a mineral_n water_n be_v make_v but_o imperfect_a mineral_n after_o another_o mode_n cause_n mineral_n water_n of_o their_o own_o nature_n viz._n because_o that_o be_v heat_v by_o their_o own_o or_o subterraneous_a heat_n they_o send_v forth_o spirit_n and_o vapour_n as_o salt_n sulphur_n vitriol_n coal_n and_o such_o like_a and_o such_o fume_n and_o exhalation_n be_v continual_o make_v in_o place_n of_o such_o mineral_n through_o which_o if_o that_o the_o water_n glide_v it_o be_v impregnate_v with_o the_o spirit_n there_o be_v some_o that_o suppose_v these_o spirituous_a water_n may_v be_v generate_v only_o by_o be_v carry_v through_o the_o metallic_a earth_n or_o by_o a_o continual_a stay_n upon_o they_o or_o in_o their_o mine_n but_o it_o be_v certain_a by_o experience_n that_o the_o water_n receive_v no_o quality_n from_o the_o metal_n and_o mineral_n if_o that_o they_o shall_v lie_v 100_o year_n immerse_v in_o they_o therefore_o lay_v aside_o this_o opinion_n we_o affirm_v that_o those_o water_n be_v generate_v or_o spirit_n receive_v from_o first_o the_o seed_n of_o metal_n as_o i_o may_v so_o say_v or_o their_o primordia_fw-la or_o second_o we_o may_v say_v that_o those_o water_n be_v now_o impregnate_v by_o other_o subtle_a spirit_n of_o vitriol_n or_o salt_n by_o the_o benefit_n of_o which_o a_o spirit_n be_v extract_v from_o the_o hard_a metal_n but_o i_o attribute_v the_o less_o to_o this_o cause_n or_o mode_n of_o generation_n because_o here_o arise_v a_o question_n again_o concern_v the_o generation_n of_o the_o spirituous_a water_n of_o mineral_n vitriol_n and_o salt_n 4._o from_o these_o together_o it_o be_v evident_a how_o mineral_n water_n that_o be_v both_o corporeal_a and_o spirituous_a be_v generate_v proposition_n iu._n there_o be_v innumerable_a kind_n of_o mineral_n water_n according_a to_o the_o variety_n and_o diversity_n of_o the_o particle_n which_o they_o contain_v of_o divers_a mineral_n in_o the_o precedent_a proposition_n we_o have_v explain_v how_o that_o mineral_n water_n may_v receive_v those_o particle_n from_o which_o their_o admirable_a quality_n do_v arise_v from_o mineral_n or_o fossils_n water_n many_o kind_n of_o mineral_n water_n now_o because_o that_o there_o be_v various_a sort_n of_o mineral_n thence_o it_o come_v to_o pass_v that_o the_o mineral_n water_n be_v various_a and_o different_a in_o their_o quality_n yea_o they_o be_v almost_o infinite_a for_o neither_o only_a be_v every_o one_o of_o these_o water_n impregnate_v by_o one_o kind_n of_o mineral_n but_o together_o many_o of_o many_o wherefore_o mineral_n water_n will_v either_o be_v simple_a or_o mix_v and_o the_o mix_a will_v have_v something_o either_o from_o three_o or_o four_o or_o from_o many_o fossils_n or_o mineral_n thence_o 1._o be_v metallick_n water_n viz._n of_o gold_n silver_n copper_n tin_n lead_v iron_n 2._o salt_n water_n viz._n of_o common_a salt_n niter_n alum_n vitriol_n 3._o bituminous_a water_n sulphureous_a antimonial_a of_o coal_n and_o of_o amber_n 4._o the_o water_n of_o the_o earth_n and_o stone_n viz._n lime-water_n chalk_n ochre_n marble_n alabaster_n 5._o mercurial_a water_n and_o the_o like_a these_o denomination_n or_o kind_n of_o water_n ii_o see_v prosition_n ii_o be_v to_o be_v understand_v according_a to_o the_o triple_a mode_n by_o which_o in_o the_o second_o propasition_n we_o say_v that_o mineral_n water_n be_v 1._o some_o corporeal_a and_o even_o manifest_a to_o the_o sense_n or_o corporeal_a by_o a_o subtle_a and_o accurate_a commixion_n 2._o that_o other_o be_v spirituous_a 3._o that_o other_o be_v corporeal_a and_o also_o spirituous_a these_o difference_n must_v be_v apply_v to_o every_o kind_n of_o mineral-water_n viz._n to_o demonstrate_v by_o one_o or_o another_o example_n gold-water_n be_v 1._o corporeal_a which_o carry_v grain_n of_o gold_n of_o that_o magnitude_n that_o with_o little_a trouble_n they_o be_v discernible_a to_o the_o sense_n neither_o have_v they_o any_o accurate_a coherency_n admix_v unto_o they_o 2_o corporeal_a water_n which_o possess_v very_o small_a particle_n of_o gold_n and_o indeed_o very_o close_o connex_v to_o the_o water_n such_o water_n i_o suppose_v to_o be._n although_o the_o nature_n of_o gold_n be_v such_o that_o the_o least_o grain_n in_o the_o water_n sink_v to_o the_o bottom_n yet_o that_o such_o may_v be_v be_v manifest_a from_o the_o aqua_fw-la regius_fw-la of_o the_o chemist_n in_o which_o gold_n be_v dissolve_v into_o atom_n but_o this_o aqua_fw-la regius_fw-la be_v not_o simple_a therefore_o neither_o do_v those_o water_n that_o be_v find_v in_o nature_n to_o have_v atom_n of_o gold_n admix_v want_v other_o particle_n of_o mineral_n 3._o spiritual_a golden-water_n which_o conceive_v a_o spirit_n and_o vapour_n in_o the_o earth_n from_o whence_o gold_n be_v wont_a to_o be_v generate_v 4._o golden_a corporeal-water_n and_o also_o spiritual_a which_o possess_v both_o atom_n of_o gold_n and_o a_o vapour_n generate_a gold_n water_n a_o fourfold_a difference_n of_o mineral_n water_n after_o the_o same_o manner_n the_o reader_n must_v apply_v this_o fourfold_a difference_n unto_o every_o kind_n of_o mineral_n water_n both_o simple_a and_o admix_v whence_o innumerable_a kind_n do_v exist_v for_o either_o the_o body_n of_o the_o mineral_n or_o the_o spirit_n or_o the_o body_n of_o one_o with_o the_o spirit_n of_o another_o be_v conjoin_v in_o the_o water_n so_o leaden-water_n be_v fourfold_a viz._n 1._o manifest_o corporeal_a 2._o corporeal_a of_o a_o subtle_a mixture_n 3._o infect_v with_o a_o spirit_n of_o lead_n and_o 4._o impregnated_a both_o with_o the_o spirit_n and_o atom_n of_o lead_n so_o those_o four_o divers_a
air_n f_o h_n be_v rarify_v now_o require_v more_o space_n now_o you_o will_v find_v the_o degree_n of_o accretion_n and_o diminution_n of_o the_o heat_n and_o cold_a if_o that_o you_o divide_v the_o line_n f_o a_o on_o the_o table_n into_o certain_a part_n of_o number_n or_o without_o put_v a_o vessel_n under_o set_v the_o glass_n l_o h_n even_o at_o the_o extremity_n l_o have_v a_o globe_n with_o a_o little_a hole_n from_o the_o side_n and_o let_v this_o globular_a vessel_n be_v fill_v with_o air_n for_o so_o also_o the_o degree_n of_o heat_n will_v be_v show_v by_o the_o ascent_n and_o descent_n of_o the_o water_n proposition_n x._o the_o serene_a air_n may_v be_v carry_v so_o by_o a_o most_o vehement_a fire_n that_o it_o may_v occupy_v a_o space_n 70_o time_n great_a than_o it_o do_v before_o on_o the_o contrary_a it_o may_v be_v so_o condense_v in_o a_o windgun_n that_o it_o may_v only_o possess_v a_o 60_o part_n of_o the_o former_a space_n but_o the_o heat_n of_o the_o sun_n bring_v not_o so_o great_a a_o rarification_n or_o the_o cold_a so_o great_a a_o condensation_n to_o the_o air_n the_o same_o be_v prove_v from_o that_o that_o if_o you_o take_v a_o aeolopile_n and_o heat_n it_o with_o fire_n so_o that_o it_o may_v then_o contain_v 13_o ounce_n but_o the_o same_o be_v cold_a and_o return_v to_o its_o former_a natural_a estate_n it_o will_v contain_v 13_o ounce_n a_o dram_n and_o a_o half_a therefore_o the_o space_n that_o the_o air_n occupy_v whilst_o that_o it_o be_v hot_a be_v great_a than_o the_o space_n that_o the_o air_n possess_v when_o refrigerated_a that_o the_o difference_n of_o the_o space_n be_v that_o part_n of_o the_o aeolopile_n that_o receive_v half_o a_o dram_n of_o water_n if_o that_o the_o whole_a receive_v 13_o ounce_n with_o half_a a_o dram_n and_o the_o part_n of_o this_o aeolopile_n be_v almost_o the_o 70_o part_n of_o the_o whole_a space_n in_o the_o aeolopile_n therefore_o the_o air_n be_v hot_a have_v possess_v a_o space_n 70_o time_n great_a than_o it_o do_v when_o it_o return_v to_o its_o natural_a estate_n proposition_n xi_o why_o in_o the_o place_n in_o the_o frigid_a zone_n at_o the_o time_n in_o which_o the_o sun_n arise_v not_o altogether_o unto_o they_o on_o some_o day_n the_o air_n be_v clear_a and_o serene_a and_o for_o the_o most_o part_n cloudy_a and_o foggy_a zone_n of_o the_o air_n in_o place_n of_o the_o frigid_a zone_n i_o answer_v the_o cause_n of_o this_o gross_a and_o almost_o perpetual_a mist_n or_o fog_n be_v the_o small_a heat_n of_o the_o subterraneous_a earth_n itself_o or_o else_o it_o be_v derive_v from_o the_o sun_n and_o likewise_o the_o moon_n which_o in_o the_o time_n of_o the_o obscurity_n of_o the_o sun_n remain_v many_o day_n and_o night_n continual_o above_o the_o horizon_n &_o the_o other_o star_n which_o heat_n because_o it_o be_v weak_a can_v dissipate_v this_o mist_n now_o that_o some_o day_n or_o night_n afford_v a_o serenity_n of_o the_o air_n this_o happen_v not_o because_o the_o thick_a vapour_n be_v attenuate_v but_o because_o that_o they_o either_o sink_v down_o into_o the_o earth_n or_o else_o be_v force_v into_o other_o place_n by_o the_o wind_n proposition_n xii_o why_o oftentimes_o in_o the_o great_a cold_a of_o the_o winter_n the_o air_n be_v yet_o subtle_a and_o serene_a when_o that_o yet_o the_o cold_a condensate_v and_o contract_v the_o air_n winter_n the_o air_n subtle_a and_o serene_a in_o the_o great_a cold_a of_o the_o winter_n cold_n be_v twofold_a moderate_a or_o extreme_a moderate_a cold_a render_v not_o the_o air_n serene_a but_o cloudy_a by_o reason_n that_o vapour_n be_v elevate_v but_o not_o discuss_v by_o that_o little_a heat_n which_o be_v mix_v or_o adjoin_v to_o that_o cold_a but_o a_o extreme_a cold_a make_v the_o air_n serene_a for_o a_o twofold_a reason_n 1._o because_o it_o render_v the_o grosser_n vapour_n of_o the_o air_n more_o gross_a and_o so_o cause_v they_o to_o fall_v and_o make_v the_o air_n more_o subtle_a 2._o because_o that_o the_o pore_n of_o the_o earth_n be_v shut_v and_o bind_v up_o and_o the_o vapour_n themselves_o can_v exhale_v and_o render_v the_o air_n turbid_v the_o sea_n itself_o indeed_o be_v not_o bind_v up_o with_o ice_n yet_o the_o particle_n be_v so_o condensated_a with_o ice_n that_o it_o be_v not_o so_o apt_a for_o exhalation_n although_o it_o send_v forth_o many_o for_o the_o condition_n of_o it_o and_o the_o earth_n be_v different_a proposition_n xiii_o why_o the_o air_n be_v behold_v at_o the_o horizontal_n line_n appear_v more_o thick_a and_o cloudy_a than_o that_o in_o which_o we_o be_v the_o cause_n be_v twofold_a 1._o because_o that_o the_o air_n about_o the_o horizon_n be_v indeed_o more_o cloudy_a the_o other_o be_v a_o fallacy_n or_o deception_n of_o the_o sight_n or_o judgement_n from_o our_o sight_n for_o the_o eye_n apprehend_v the_o distance_n of_o column_n place_v in_o a_o long_a order_n and_o series_n and_o therefore_o as_o the_o judgement_n suppose_v the_o remote_a column_n to_o be_v conjoin_v so_o also_o it_o apprehend_v not_o the_o distance_n of_o the_o particle_n of_o the_o horizontal_n air_n but_o imagine_v they_o conjoin_v but_o the_o eye_n behold_v the_o distance_n of_o the_o elevate_a air_n under_o great_a angle_n and_o therefore_o better_a apprehend_v it_o the_o same_o be_v the_o reason_n why_o the_o air_n which_o appear_v cloudy_a to_o we_o remove_v from_o it_o when_o we_o come_v to_o it_o or_o be_v in_o it_o seem_v less_o misty_a or_o cloudy_a proposition_n fourteen_o whether_o that_o the_o altitude_n of_o the_o atmosphere_n or_o air_n above_o the_o earth_n be_v the_o same_o in_o all_o place_n at_o one_o and_o the_o same_o time_n and_o whether_o its_o figure_n be_v spherical_a atmosphere_n of_o the_o altitude_n of_o the_o atmosphere_n that_o the_o altitude_n be_v not_o the_o same_o but_o divers_a in_o sundry_a place_n seem_v to_o follow_v from_o thence_o that_o the_o sun_n be_v only_o vertical_a to_o one_o place_n at_o one_o time_n and_o it_o send_v forth_o oblique_a ray_n and_o therefore_o more_o weak_a unto_o other_o place_n by_o how_o much_o the_o place_n be_v more_o remote_a from_o the_o sun_n and_o near_o to_o the_o pole_n therefore_o the_o pore_n of_o the_o ray_n of_o the_o sun_n be_v very_o different_a to_o the_o elevate_n of_o the_o vapour_n and_o therefore_o they_o be_v raise_v to_o different_a altitude_n to_o wit_n in_o a_o place_n unto_o which_o the_o sun_n be_v vertical_a his_o altitude_n be_v the_o great_a in_o the_o opposite_a place_n the_o lesser_a in_o the_o place_n about_o the_o pole_n moderate_a so_o that_o the_o air_n receive_v a_o oval_a figure_n but_o the_o contrary_n be_v more_o probable_a viz._n that_o the_o altitude_n of_o the_o atmosphere_n be_v the_o same_o in_o all_o place_n for_o although_o that_o the_o vapour_n and_o air_n be_v more_o elevate_v in_o some_o place_n than_o in_o other_o yet_o because_o that_o the_o air_n be_v fluid_a and_o tend_v by_o its_o gravity_n to_o the_o centre_n of_o the_o earth_n therefore_o the_o more_o elevate_a part_n of_o the_o air_n press_v down_o the_o air_n place_v under_o it_o and_o this_o thrust_v down_o another_o more_o depress_v until_o all_o the_o part_n acquire_v the_o same_o altitude_n and_o after_o the_o same_o mode_n the_o spherical_a figure_n of_o the_o air_n shall_v be_v demonstrate_v as_o in_o the_o thirteen_o chapter_n we_o have_v prove_v with_o archimedes_n concern_v the_o water_n by_o reason_n that_o the_o same_o hypothesis_n be_v prevalent_a here_o which_o we_o there_o assume_v to_o wit_n that_o the_o part_n of_o the_o air_n less_o press_v be_v expel_v by_o that_o which_o be_v more_o press_v for_o every_o part_n be_v press_v by_o the_o air_n that_o be_v above_o it_o wherefore_o the_o figure_n of_o the_o air_n be_v spherical_a not_o oval_a as_o some_o will_v have_v it_o but_o if_o the_o forementioned_a hypothesis_n be_v not_o grant_v the_o demonstration_n fall_v des_fw-mi cartes_n also_o make_v the_o air_n oval_n in_o figure_n for_o a_o peculiar_a reason_n see_v chapter_n fourteen_o proposition_n xv._o condensation_n or_o rarefaction_n of_o air_n change_v not_o its_o altitude_n altitude_n condensation_n of_o air_n change_v not_o its_o altitude_n because_o that_o the_o whole_a atmosphere_n be_v not_o condense_v but_o only_o some_o part_n and_o at_o all_o time_n some_o part_n be_v condense_v sometime_o these_o sometime_o those_o wherefore_o the_o condensation_n or_o rarefaction_n of_o one_o time_n do_v no_o more_o alterare_fw-la the_o air_n than_o the_o condensation_n or_o rarefaction_n of_o the_o first_o time_n there_o only_o seem_v to_o be_v a_o difference_n that_o at_o one_o time_n there_o may_v be_v a_o great_a condensation_n or_o rarefaction_n than_o at_o another_o but_o this_o
difference_n can_v little_o augment_v the_o altitude_n proposition_n xvi_o the_o altitude_n of_o the_o atmosphere_n or_o air_n be_v not_o only_o the_o same_o in_o divers_a place_n but_o it_o remain_v the_o same_o and_o that_o constant_o at_o all_o time_n both_o winter_n and_o summer_n place_n the_o altitude_n of_o the_o atmosphere_n be_v always_o the_o same_o in_o divers_a place_n for_o although_o that_o heat_n in_o the_o summer_n of_o our_o place_n may_v more_o elevate_v also_o our_o air_n more_o than_o in_o winter_n yet_o because_o that_o the_o winter_n be_v at_o the_o same_o in_o another_o place_n of_o the_o earth_n the_o air_n be_v less_o raise_v in_o it_o wherefore_o part_n of_o our_o air_n shall_v be_v move_v towards_o the_o air_n of_o those_o place_n where_o the_o air_n be_v less_o elevate_v viz._n to_o the_o more_o depress_a place_n as_o we_o have_v show_v in_o the_o fourteen_o proposition_n and_o on_o the_o contrary_a whilst_o that_o the_o air_n of_o the_o place_n where_o we_o be_v be_v depress_v by_o reason_n of_o the_o cold_a of_o the_o winter_n part_n of_o this_o air_n where_o the_o summer_n or_o the_o great_a heat_n be_v shall_v be_v move_v towards_o our_o place_n viz._n until_o the_o whole_a air_n be_v equal_o distant_a from_o the_o centre_n of_o the_o earth_n the_o same_o be_v the_o reason_n concern_v the_o day_n and_o the_o night_n for_o whilst_o that_o the_o air_n be_v depress_v and_o contract_v in_o the_o night_n to_o we_o in_o another_o place_n it_o be_v more_o rarefy_a and_o so_o be_v move_v towards_o the_o air_n of_o our_o place_n until_o it_o again_o make_v a_o spherical_a figure_n and_o because_o that_o all_o be_v equal_a on_o every_o side_n therefore_o the_o name_n altitude_n shall_v remain_v in_o every_o time_n but_o because_o that_o the_o air_n be_v condense_v more_o in_o one_o time_n and_o place_n than_o in_o another_o that_o difference_n see_v that_o it_o be_v very_o small_a can_v very_o little_o vary_v the_o altitude_n as_o we_o have_v show_v in_o the_o precedent_a proposition_n the_o same_o be_v the_o account_n of_o rains_n or_o mist_n or_o vapour_n that_o be_v in_o we_o or_o in_o another_o place_n for_o to_o these_o it_o seem_v that_o the_o altitude_n of_o the_o air_n shall_v be_v less_o or_o more_o but_o i_o answer_v that_o there_o be_v scarce_o any_o time_n in_o which_o in_o some_o place_n of_o the_o earth_n it_o rain_v not_o and_o that_o the_o mist_n fall_v not_o and_o therefore_o when_o that_o it_o rain_v in_o one_o place_n the_o air_n become_v not_o lesser_a than_o it_o be_v before_o because_o that_o before_o it_o rain_v in_o another_o place_n and_o so_o the_o reason_n be_v equal_a and_o the_o quantity_n of_o the_o air_n be_v neither_o augment_v nor_o diminish_v proposition_n xvii_o by_o how_o much_o the_o air_n be_v more_o cold_a by_o so_o much_o the_o more_o it_o be_v condense_v and_o therefore_o for_o the_o most_o part_n more_o condense_v in_o the_o winter_n than_o in_o the_o summer_n to_o wit_n in_o some_o place_n of_o the_o earth_n also_o in_o the_o night_n than_o in_o the_o day_n now_o watery_a thick_a exhalation_n in_o the_o winter_n and_o the_o night_n cause_n and_o augment_v that_o condensation_n especial_o in_o the_o morning_n and_o evening_n condense_a the_o cold_o the_o air_n the_o more_o condense_a the_o truth_n of_o the_o proposition_n be_v manifest_a from_o the_o precede_a proposition_n neither_o do_v it_o obstruct_v for_o that_o part_n of_o the_o more_o not_o air_n be_v move_v to_o the_o more_o cold_a as_o to_o a_o more_o depress_a place_n because_o that_o not_o that_o itself_o but_o another_o adjoin_a approachment_n by_o reason_n of_o continual_a protrusion_n and_o if_o that_o that_o happen_v yet_o in_o a_o cold_a place_n that_o become_v also_o cold_a proposition_n xviii_o there_o be_v three_o region_n vulgar_o make_v in_o the_o air_n whereof_o the_o middle_a be_v that_o in_o which_o the_o snow_n rain_n and_o hail_n be_v generate_v the_o first_o be_v that_o in_o which_o we_o be_v extend_v itself_o even_o to_o the_o middle_a region_n the_o three_o be_v that_o which_o begin_v the_o uttermost_a bind_v of_o the_o middle_a region_n and_o extend_v itself_o to_o the_o utmost_a superficies_n of_o the_o air_n even_o to_o the_o sublunary_a fire_n as_o the_o aristotelian_o affirm_v air._n three_o region_n in_o the_o air._n the_o middle_a region_n be_v more_o cold_a than_o the_o first_o and_o three_o which_o be_v reckon_v more_o hot_a but_o the_o three_o by_o reason_n that_o it_o contain_v more_o subtle_a fiery_a and_o sulphureous_a part_n of_o exhalation_n which_o fly_v to_o it_o about_o the_o place_n of_o the_o watery_a particle_n or_o be_v thrust_v down_o as_o more_o light_n the_o aristotelian_o say_v that_o it_o be_v hot_a by_o reason_n of_o its_o vicinity_n to_o the_o fiery-sphere_n but_o the_o first_o because_o that_o the_o ray_n of_o the_o sun_n fall_v be_v â—eaâ—_n there_o reflex_v and_o so_o duplicate_v the_o heat_n it_o happen_v that_o some_o particle_n of_o subterraneous_a fire_n exhale_v be_v in_o this_o region_n but_o the_o middle_a region_n iâ—_n more_o cold_a by_o reason_n that_o the_o reflect_a ray_n be_v there_o vicine_fw-la to_o those_o that_o fall_v in_o on_o the_o earth_n neither_o do_v they_o contain_v any_o fiery_a sulphureous_a particle_n but_o watery_a one_o for_o the_o sulphureous_a and_o fiery_a one_o that_o have_v carry_v up_o the_o watery_a one_o fly_v high_o proposition_n xix_o by_o how_o much_o that_o place_n of_o the_o earth_n unto_o which_o the_o sun_n be_v vertical_a recede_v to_o the_o pole_n or_o by_o how_o much_o the_o place_n be_v more_o near_o the_o pole_n by_o so_o much_o the_o less_o distant_a the_o place_n of_o the_o air_n be_v from_o the_o earth_n in_o which_o the_o rain_n snow_n hail_o begin_v to_o be_v generate_v the_o reason_n be_v that_o the_o ray_n of_o the_o sun_n do_v fall_v more_o oblique_o on_o the_o place_n about_o the_o pole_n than_o on_o the_o place_n about_o the_o aequator_fw-la and_o therefore_o the_o ray_n refract_v be_v much_o withdraw_v from_o those_o fall_n in_o and_o so_o cause_v lesser_a heat_n and_o for_o a_o lesser_a space_n than_o the_o ray_n under_o the_o place_n of_o the_o sun_n or_o under_o the_o torrid_a zone_n and_o so_o in_o a_o more_o near_a place_n the_o watery_a vapour_n may_v unite_v to_o generate_v watery_a meteor_n corollary_n the_o superficies_n terminate_a the_o first_o region_n of_o the_o air_n be_v of_o a_o oval_a figure_n or_o rather_o elliptical_a or_o sphere_n like_a protuberate_v in_o the_o torrid_a zone_n proposition_n xx._n by_o how_o much_o the_o place_n of_o the_o earth_n be_v near_a the_o pole_n by_o so_o much_o distance_n the_o region_n of_o the_o air_n be_v distant_a from_o that_o earth_n that_o begin_v the_o three_o or_o in_o which_o the_o more_o subtle_a and_o sulphureous_a particle_n be_v for_o there_o be_v the_o few_o and_o more_o subtle_a particle_n in_o part_n of_o the_o atmosphere_n by_o how_o much_o it_o be_v near_o the_o pole_n because_o that_o the_o heat_n of_o the_o sun_n elicitate_v few_o from_o the_o earth_n therefore_o because_o that_o there_o be_v few_o particle_n of_o the_o three_o region_n under_o the_o frigid_a zone_n than_o in_o the_o temperate_a and_o in_o this_o few_o than_o in_o the_o torrid_a and_o yet_o the_o utmost_a bind_v of_o that_o three_o region_n be_v equal_o distant_a from_o the_o centre_n of_o the_o earth_n 16._o see_v proposition_n 16._o according_a to_o the_o sixteenth_o proposition_n thence_o it_o follow_v that_o the_o begin_n of_o the_o region_n under_o the_o torrid_a zone_n be_v far_o more_o distant_a from_o the_o centre_n of_o the_o earth_n than_o the_o begin_n of_o that_o in_o the_o torrid_a and_o temperate_a zone_n corollary_n the_o superficies_n terminate_a the_o second_o region_n of_o the_o air_n or_o distinguish_v it_o from_o the_o three_o be_v spherical_a and_o protuberate_v in_o the_o frigid_a zone_n all_o these_o must_v be_v show_v to_o youth_n by_o diagram_n proposition_n xxi_o the_o ray_n of_o the_o sun_n moon_n and_o star_n do_v not_o direct_o arrive_v at_o our_o eye_n from_o the_o aether_n through_o the_o air_n but_o where_o they_o enter_v the_o air_n they_o be_v withdraw_v or_o deflect_v a_o little_a from_o a_o direct_a passage_n which_o the_o skilful_a in_o the_o optic_n term_v to_o refract_v the_o ray_n and_o so_o those_o ray_n refract_v come_v to_o our_o eye_n and_o show_v we_o the_o star_n star_n of_o the_o ray_n of_o the_o sun_n moon_n and_o star_n this_o part_n which_o treat_v of_o the_o refraction_n of_o light_n be_v the_o most_o subtle_a part_n of_o the_o science_n of_o the_o optic_n for_o experience_n testify_v that_o ray_n proceed_v from_o any_o visible_a body_n if_o from_o one_o medium_n they_o fall_v in_o upon_o another_o that_o be_v
degree_n and_o b_o n_o l_o be_v equal_a to_o the_o angle_n a_o s_o l_o or_o b_o a_o r._n therefore_o the_o arch_n of_o the_o angle_n n_o b_o l_o be_v equal_a to_o the_o arch_n b_o m_o by_o which_o p_o b_o be_v great_a than_o 90_o degree_n or_o than_o p_o m_o so_o also_o the_o arch_n p_o c._n if_o we_o take_v the_o semidiameter_n of_o the_o sun_n according_a unto_o ptolemy_n of_o 5_o 2_o semidiameter_n of_o the_o earth_n but_o the_o distance_n a_o s_o 1168_o semidiameter_n these_o i_o say_v be_v lay_v down_o the_o arch_n m_o b_o will_v be_v find_v 13_o minute_n in_o which_o the_o sun_n illustrate_v the_o earth_n more_o than_o half_a m_o p_o q._n corollary_n when_o therefore_o the_o centre_n of_o the_o sun_n rise_v to_o some_o place_n than_o his_o limbus_n or_o edge_n rise_v to_o the_o people_n which_o inhabit_v in_o the_o parallel_n of_o the_o horizon_n situate_v 13_o minute_n beneath_o the_o horizon_n also_o after_o the_o same_o mode_n to_o those_o to_o who_o he_o set_v and_o when_o his_o centre_n set_v than_o his_o limbus_n yet_o remain_v conspicuous_a until_o the_o centre_n set_v to_o the_o people_n which_o be_v remote_a 13_o minute_n from_o our_o horizon_n proposition_n xiii_o the_o height_n of_o a_o mountain_n be_v give_v to_o find_v how_o much_o soon_o the_o sun_n seem_v to_o rise_v in_o the_o vertex_fw-la of_o the_o same_o than_o at_o the_o foot_n or_o root_n of_o the_o mountain_n and_o how_o much_o late_a it_o set_v from_o the_o give_a altitude_n 5._o see_v chap._n 9_o proposit_n 5._o by_o the_o five_o proposition_n in_o the_o nine_o chapter_n let_v the_o interval_n or_o arch_n from_o which_o the_o vertex_fw-la of_o the_o mountain_n may_v be_v discover_v or_o in_o the_o bind_v of_o which_o a_o line_n so_o draw_v from_o the_o vertex_fw-la of_o the_o mountain_n that_o it_o may_v be_v the_o tangent_fw-la of_o the_o earth_n refract_v the_o same_o for_o this_o line_n show_v the_o first_o ray_n which_o may_v come_v from_o a_o direct_a passage_n from_o the_o sun_n to_o the_o vertex_fw-la of_o the_o mountain_n moreover_o the_o point_n of_o the_o earth_n in_o which_o this_o be_v touch_v by_o the_o line_n be_v the_o place_n to_o which_o the_o sun_n arise_v when_o he_o begin_v to_o be_v see_v on_o the_o vertex_fw-la of_o the_o mountain_n and_o the_o arch_n interrupt_v between_o that_o point_n and_o the_o foot_n of_o the_o mountain_n be_v equal_a to_o that_o in_o which_o the_o sun_n be_v depress_v as_o yet_o beneath_o the_o horizon_n of_o the_o foot_n of_o the_o mountain_n when_o he_o be_v apparent_a in_o the_o vertex_fw-la therefore_o the_o problem_n be_v reduce_v hither_o the_o depression_n of_o the_o sun_n beneath_o the_o horizon_n be_v give_v to_o find_v the_o time_n which_o be_v spend_v whilst_o the_o sun_n move_v from_o the_o depression_n to_o the_o horizon_n whence_o also_o it_o will_v be_v manifest_a that_o this_o time_n be_v also_o diverse_a in_o the_o divers_a day_n of_o the_o year_n therefore_o let_v the_o place_n of_o the_o root_n of_o the_o mountain_n be_v note_v on_o the_o globe_n and_o let_v the_o pole_n be_v clevate_v for_o the_o latitude_n of_o the_o same_o let_v the_o quadrant_n be_v affix_v to_o the_o vertex_fw-la the_o place_n of_o the_o sun_n be_v find_v in_o the_o ecliptic_a from_o any_o day_n take_v let_v it_o be_v note_v also_o the_o point_n of_o the_o ecliptic_a opposite_a to_o the_o place_n of_o the_o sun_n then_o let_v this_o opposite_a point_n be_v bring_v to_o the_o occidental_a horizon_n and_o let_v the_o index_n be_v place_v at_o the_o hour_n 12._o this_o be_v do_v let_v the_o degree_n of_o depression_n before_o find_v be_v note_v in_o the_o quadrant_n and_o the_o opposite_a point_n be_v turn_v above_o the_o horizon_n until_o it_o have_v a_o altitude_n equal_a to_o the_o arch_n of_o the_o depression_n which_o will_v be_v discover_v from_o the_o application_n of_o the_o quadrant_n so_o the_o place_n of_o the_o sun_n beneath_o the_o oriental_a horizon_n will_v have_v that_o depression_n and_o the_o index_n in_o the_o horaty_a circle_n will_v show_v the_o time_n intercopt_v between_o that_o depression_n of_o he_o and_o his_o emersion_n above_o the_o horizon_n but_o because_o in_o this_o case_n we_o do_v almost_o work_v only_o by_o minute_n therefore_o it_o be_v better_a to_o calculate_v it_o than_o to_o search_v after_o it_o on_o the_o globe_n now_o you_o shall_v find_v it_o if_o that_o the_o altitude_n of_o the_o mountain_n be_v place_v 3_o stadias_fw-la or_o ¾_n of_o a_o german_a mile_n because_o the_o arch_n of_o the_o depression_n be_v about_o three_o degree_n night_n the_o mountain_n of_o caucasus_n and_o casius_n according_a to_o aristotle_n and_o pliny_n be_v illustrate_v with_o the_o sun_n ray_n to_o the_o three_o part_n of_o the_o night_n and_o if_o the_o latitude_n of_o the_o foot_n of_o the_o mountain_n be_v 38_o degree_n and_o the_o place_n of_o the_o sun_n about_o the_o middle_n of_o leo_n the_o time_n in_o which_o the_o sun_n be_v behold_v be_v soon_o in_o the_o vertex_fw-la than_o at_o the_o foot_n of_o the_o mountain_n by_o 13_o minute_n hence_o it_o be_v manifest_a that_o that_o be_v not_o so_o probable_a which_o aristotle_n relate_v of_o the_o high_a part_n of_o caucasus_n and_o pliny_n of_o the_o top_n of_o mount_n casius_n that_o they_o before_o the_o rise_n and_o after_o the_o set_n of_o the_o sun_n be_v illustrate_v with_o the_o sun_n beam_n even_o to_o the_o three_o part_n of_o the_o night_n now_o how_o great_a a_o altitude_n be_v require_v for_o this_o shall_v be_v show_v in_o the_o follow_a proposition_n proposition_n fourteen_o the_o time_n be_v give_v in_o which_o the_o sun_n be_v soon_o discern_v on_o the_o vertex_fw-la of_o the_o mountain_n than_o at_o the_o foot_n of_o the_o same_o to_o find_v the_o altitude_n of_o the_o mountain_n let_v the_o pole_n be_v elevate_v on_o the_o globe_n for_o the_o latitude_n of_o the_o root_n of_o the_o mountain_n and_o the_o point_n be_v note_v which_o be_v oppose_v to_o the_o place_n of_o the_o sun_n in_o the_o ecliptic_a let_v the_o arch_n of_o the_o depression_n of_o the_o sun_n beneath_o the_o horizon_n for_o the_o give_v time_n be_v find_v then_o from_o this_o arch_n as_o from_o a_o interval_n from_o whence_o the_o vertex_fw-la of_o the_o mountain_n be_v discover_v the_o altitude_n of_o the_o mountain_n must_v be_v search_v after_o by_o the_o four_o proposition_n of_o the_o nine_o chapter_n proposition_n xv._o the_o place_n of_o the_o moon_n be_v give_v in_o the_o zodiac_n together_o with_o its_o latitude_n to_o find_v out_o or_o show_v all_o those_o place_n on_o the_o globe_n to_o which_o the_o moon_n be_v vertical_a in_o the_o circumrotation_n of_o that_o day_n let_v the_o place_n of_o the_o moon_n take_v from_o the_o ephemerides_n be_v note_v in_o the_o ecliptic_a then_o let_v one_o end_n of_o the_o quadrant_n be_v apply_v to_o the_o pole_n of_o the_o ecliptic_a the_o other_o to_o the_o point_v note_v in_o the_o ecliptic_a or_o to_o the_o place_n of_o the_o moon_n and_o let_v the_o degree_n of_o the_o latitude_n of_o the_o moon_n be_v account_v on_o the_o quadrant_n and_o let_v a_o mark_n be_v make_v at_o the_o term_n of_o the_o numeration_n on_o the_o globe_n then_o this_o be_v bring_v to_o the_o meridian_n and_o a_o chalk_n apply_v let_v a_o parallel_n be_v describe_v which_o the_o moon_n that_o day_n do_v describe_v by_o her_o circumvolution_n and_o all_o the_o place_n situate_v in_o this_o parallel_n be_v those_o demand_v after_o the_o same_o mode_n we_o act_n with_o the_o other_o planer_n if_o their_o longitude_n and_o latitude_n be_v give_v proposition_n xvi_o the_o place_n of_o the_o moon_n be_v give_v in_o the_o zodiac_n and_o its_o latitude_n and_o the_o day_n of_o the_o year_n to_o find_v the_o hour_n in_o which_o she_o arise_v in_o any_o place_n give_v and_o in_o which_o she_o set_v also_o in_o which_o she_o make_v midnight_n let_v the_o pole_n be_v elevate_v for_o the_o latitude_n of_o the_o place_n of_o the_o earth_n give_v let_v the_o place_n of_o the_o sun_n find_v from_o the_o day_n of_o the_o year_n be_v note_v on_o the_o ecliptic_a then_o let_v a_o point_n also_o be_v note_v on_o the_o globe_n for_o the_o place_n of_o the_o moon_n as_o we_o have_v show_v in_o the_o precede_a proposition_n 15._o see_v proposition_n 15._o this_o be_v do_v let_v the_o place_n of_o the_o sun_n be_v bring_v to_o the_o meridian_n the_o index_n to_o the_o 12_o hour_n of_o the_o circle_n and_o let_v the_o globe_n be_v turn_v round_o until_o the_o moon_n arise_v or_o be_v in_o the_o meridian_n or_o set_v for_o the_o index_n in_o the_o circle_n will_v show_v the_o hour_n of_o her_o rise_n or_o set_v or_o be_v in_o
the_o meridian_n or_o set_v after_o the_o same_o manner_n we_o must_v act_v with_o the_o other_o planet_n proposition_n xvii_o to_o show_v on_o the_o globe_n all_o those_o place_n in_o which_o the_o moon_n arise_v at_o the_o give_v hour_n and_o in_o which_o she_o be_v in_o the_o meridian_n and_o to_o which_o she_o set_v if_o that_o the_o longitude_n and_o latitude_n of_o the_o moon_n be_v know_v hour_n by_o the_o globe_n be_v show_v all_o the_o place_n in_o which_o the_o moon_n arise_v and_o set_v at_o any_o hour_n let_v the_o place_n of_o the_o sun_n as_o also_o of_o the_o moon_n be_v note_v on_o the_o ecliptic_a as_o aforesaid_a and_o the_o place_n of_o the_o sun_n be_v bring_v to_o the_o meridian_n and_o the_o index_n to_o the_o 12_o hour_n of_o the_o circle_n let_v the_o globe_n be_v turn_v until_o the_o place_n of_o the_o moon_n come_v to_o the_o meridian_n and_o let_v the_o hour_n be_v observe_v on_o the_o circle_n which_o be_v note_v or_o let_v a_o mark_n be_v make_v on_o the_o circle_n for_o they_o show_v how_o much_o late_a the_o moon_n come_v to_o the_o meridian_n than_o the_o sun_n moreover_o the_o place_n of_o the_o moon_n be_v constitute_v in_o the_o meridian_n let_v the_o eminent_a point_n be_v note_v in_o this_o or_o let_v the_o parallel_n of_o the_o moon_n be_v describe_v this_o do_v let_v the_o place_n of_o the_o sun_n be_v bring_v to_o the_o meridian_n and_o the_o index_n to_o the_o 12_o hour_n let_v the_o globe_n be_v turn_v until_o the_o hour_n be_v find_v in_o which_o the_o moon_n touch_v the_o meridian_n of_o the_o place_n let_v the_o point_n also_o of_o the_o meridian_n be_v note_v which_o hang_v over_o the_o place_n of_o the_o moon_n moreover_o let_v the_o place_n who_o hour_n be_v give_v be_v bring_v to_o the_o meridian_n the_o index_n to_o the_o hour_n give_v let_v the_o globe_n be_v turn_v until_o the_o index_n show_v the_o 12_o hour_n of_o noon_n or_o midnight_n so_o the_o place_n be_v those_o subject_n to_o the_o semicircle_n of_o the_o meridian_n in_o which_o the_o sun_n make_v the_o meridies_n at_o the_o hour_n give_v let_v the_o index_n be_v reduce_v to_o 12_o and_o let_v the_o globe_n be_v turn_v again_o until_o the_o index_n come_v to_o the_o hour_n note_v before_o in_o the_o circle_n in_o this_o situation_n of_o the_o globe_n the_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 that_o to_o which_o the_o sun_n be_v then_o vertical_a therefore_o let_v this_o place_n be_v constitute_v in_o the_o globe_n in_o the_o vertex_fw-la of_o the_o horizon_n all_o the_o place_n be_v those_o subject_n to_o the_o superior_a semicircle_n of_o the_o meridian_n to_o which_o the_o moon_n be_v then_o in_o the_o meridian_n but_o those_o place_n which_o be_v discern_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 moon_n than_o set_v last_o in_o those_o place_n which_o be_v discern_v in_o the_o occidental_a semicircle_n of_o the_o horizon_n the_o moon_n rise_v at_o the_o give_v moment_n of_o time_n after_o the_o same_o mode_n we_o act_n with_o saturn_n jupiter_n and_o the_o rest_n of_o the_o planet_n if_o that_o their_o longitude_n and_o latitude_n be_v know_v proposition_n xviii_o the_o day_n or_o hour_n be_v give_v in_o which_o the_o ecliptic_a of_o the_o moon_n shall_v be_v or_o have_v be_v to_o exhibit_v on_o the_o globe_n all_o those_o place_n which_o have_v see_v it_o and_o in_o that_o species_n to_o who_o the_o moon_n shall_v in_o the_o meridian_n to_o who_o it_o shall_v arise_v and_o to_o who_o it_o shall_v set_v eclipse_v this_o problem_n little_o differ_v from_o the_o precedent_n but_o yet_o it_o have_v a_o more_o easy_a solution_n from_o the_o day_n give_v let_v the_o place_n of_o the_o sun_n be_v find_v except_o it_o be_v already_o know_v and_o let_v the_o point_n opposite_a to_o it_o be_v note_v on_o the_o ecliptic_a of_o the_o globe_n for_o this_o be_v the_o place_n of_o the_o moon_n 28._o see_v proposition_n 6._o chapter_n 28._o let_v the_o place_n be_v find_v in_o the_o globe_n to_o which_o the_o sun_n be_v vertical_a at_o the_o hour_n and_o let_v the_o antipode_n of_o this_o place_n be_v find_v according_a to_o the_o vi_o proposition_n of_o the_o xxviii_o chapter_n for_o this_o shall_v be_v the_o place_n unto_o which_o the_o moon_n be_v eclipse_v shall_v be_v vertical_a let_v this_o place_n be_v constitute_v in_o the_o vertex_fw-la of_o the_o horizon_n the_o pole_n be_v elevate_v or_o depress_v for_o the_o latitude_n of_o the_o place_n so_o all_o the_o place_n of_o the_o globe_n which_o be_v above_o the_o horizon_n may_v have_v see_v that_o eclipse_n and_o those_o which_o lie_v under_o the_o brazen_a meridian_n shall_v see_v it_o in_o the_o meridian_n those_o which_o lie_v under_o the_o oriental_a semicircle_n shall_v see_v it_o in_o the_o west_n or_o set_v with_o the_o eclipse_n but_o those_o which_o lie_v in_o the_o occidental_a semicircle_n of_o the_o horizon_n shall_v see_v it_o in_o the_o east_n or_o noon_n to_o arise_v eclipse_v but_o see_v that_o a_o eclipse_n be_v not_o perform_v in_o one_o moment_n of_o a_o hour_n but_o dure_v for_o some_o hour_n therefore_o it_o be_v wont_a to_o be_v divide_v into_o the_o beginning_n middle_a and_o end_v and_o the_o moment_n of_o the_o hour_n be_v wont_a to_o be_v note_v therefore_o the_o consideration_n must_v be_v more_o especial_o concern_v the_o middle_a time_n of_o the_o eclipse_n moreover_o see_v that_o the_o moon_n be_v less_o than_o the_o earth_n it_o will_v illustrate_v a_o lesser_a part_n than_o the_o hemisphere_n be_v also_o it_o will_v be_v see_v by_o the_o inhabitant_n of_o a_o lesser_a part_n so_o that_o it_o will_v not_o be_v any_o more_o conspicuous_a to_o those_o which_o lie_v in_o the_o oriental_a semicircle_n of_o the_o horizon_n but_o to_o those_o in_o the_o occidental_a semicircle_n it_o have_v not_o yet_o appear_v but_o a_o certain_a circle_n parallel_n to_o the_o horizon_n be_v to_o be_v see_v which_o terminate_v the_o part_n illustrate_v now_o how_o much_o this_o part_n be_v distant_a from_o the_o hemisphere_n or_o how_o great_a a_o portion_n it_o be_v of_o the_o superficies_n of_o the_o earth_n shall_v be_v the_o enquiry_n of_o the_o follow_a proposition_n proposition_n xix_o the_o semidiameter_n of_o the_o moon_n and_o earth_n be_v give_v scheme_n see_v scheme_n and_o the_o distance_n of_o they_o to_o find_v out_o how_o long_o a_o portion_n of_o the_o earth_n be_v illustrate_v by_o the_o moon_n at_o the_o full._n 11._o see_v proposition_n 11._o this_o problem_n must_v be_v solve_v by_o the_o same_o mode_n that_o we_o have_v use_v in_o the_o eleven_o proposition_n for_o let_v the_o centre_n of_o the_o earth_n be_v s_o the_o great_a circle_n represent_v the_o superficies_n o_o f_o l_o h._n the_o centre_n of_o the_o moon_n a_o the_o great_a circle_n c_o p_o b_o q._n let_v the_o tangent_n l_o b_o o_o c_o be_v draw_v for_o these_o be_v the_o ultimate_a ray_n that_o can_v come_v from_o the_o moon_n to_o the_o earth_n and_o therefore_o the_o arch_n o_o h_n l_o will_v denote_v the_o part_n of_o the_o superficies_n of_o the_o earth_n which_o be_v illustrate_v by_o the_o moon_n and_o who_o inhabitant_n may_v see_v the_o moon_n together_o which_o by_o how_o much_o lesser_a it_o be_v than_o the_o hemisphere_n we_o shall_v know_v if_o we_o find_v the_o angle_n h_o s_o l_o or_o the_o arch_n h_o l._n let_v b_o n_n be_v draw_v from_o b_o parallel_n to_o a_o s_n b_o he_o shall_v be_v equal_a to_o s_o n_n and_o n_n l_o the_o excess_n of_o the_o semidiameter_n of_o the_o earth_n s_o l_o above_o the_o semidiameter_n of_o the_o moon_n a_o b_o and_o b_o n_n be_v of_o a_o equal_a distance_n with_o a_o s_o but_o the_o the_o angle_n n_o l_o b_o be_v direct_a or_o of_o 90_o degree_n therefore_o in_o the_o triangle_n straight_a angle_n n_o b_o l_o we_o shall_v find_v the_o angle_n n_o b_o l_o by_o this_o proportion_n as_o n_z b_o be_v to_z n_o l_o so_fw-mi be_v the_o whole_a sign_n to_o the_o sign_n of_o the_o angle_n l_o b_o n_o who_o arch_n be_v that_o in_o which_o h_n l_o differ_v from_o the_o arch_n 90_o or_o from_o the_o quadrant_n of_o the_o periphery_a of_o the_o earth_n and_o so_o great_a a_o interval_n be_v the_o periphery_a of_o the_o earth_n distant_a from_o the_o great_a circle_n terminanate_v the_o part_n of_o the_o earth_n illuminate_v by_o the_o moon_n let_v we_o suppose_v the_o semidiameter_n of_o the_o moon_n to_o contain_v four_o part_n of_o such_o like_a the_o semidiamiter_n of_o the_o earth_n contain_v 15_o or_o 4_o 15_o of_o the_o semidiamiter_n of_o the_o earth_n now_o the_o great_a distance_n of_o
which_o the_o other_o place_n be_v situate_v at_o the_o place_n which_o be_v represent_v from_o that_o bound_n and_o let_v the_o extension_n of_o the_o quadrant_n be_v note_v with_o chalk_n on_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 other_o bind_v and_o the_o quadrant_n be_v affix_v to_o that_o term_n the_o other_o extremity_n to_o the_o other_o give_v quarter_n the_o point_n in_o which_o the_o quadrant_n shall_v cut_v the_o arch_n mark_v with_o chalk_n shall_v represent_v the_o three_o place_n whence_o it_o be_v easy_a to_o take_v the_o distance_n from_o these_o two_o term_n chap._n xxxiv_o of_o the_o visible_a or_o sensible_a horizon_n a_o sensible_a horizon_n be_v a_o periphery_a on_o the_o superficies_n of_o the_o earth_n which_o bound_v the_o prospect_n of_o the_o eye_n move_v round_o about_o or_o which_o terminate_v part_n of_o the_o superficies_n which_o the_o eye_n move_v about_o may_v see_v or_o from_o whence_o the_o ray_n may_v come_v to_o the_o eye_n his_o semidiameter_n be_v term_v the_o great_a arch_n of_o the_o earth_n intercept_v between_o the_o foot_n of_o the_o spectator_n and_o that_o periphery_n which_o therefore_o be_v perpendicular_a over_o it_o proposition_n i._o the_o extension_n or_o semidiameter_n of_o the_o sensible_a horizon_n various_o exi_v both_o according_a to_o the_o divers_a altitude_n of_o the_o eye_n as_o also_o from_o the_o diversity_n of_o the_o take_v semidiameter_n of_o the_o earth_n what_o a_o sensible_a horizon_n what_o let_v the_o great_a circle_n of_o the_o earth_n be_v m_o p_o n_o q._n let_v t_o be_v the_o centre_n t_o p_o the_o semidiameter_n p_o o_o the_o altitude_n of_o the_o eye_n let_v o_o be_v the_o eye_n let_v the_o tangent_n o_o n_n o_o m_o be_v draw_v from_o o_o and_o let_v we_o conceive_v the_o ray_n n_o o_fw-fr to_o be_v as_o it_o be_v carry_v about_o on_o the_o superficies_n of_o the_o earth_n and_o so_o to_o describe_v the_o periphery_a this_o shall_v be_v the_o sensible_a horizon_n his_o semidiameter_n p_o n_n p_o m_o for_o the_o ray_n n_o o_fw-fr m_o o_o be_v the_o last_o which_o from_o o_o can_v come_v to_o the_o eye_n from_o the_o superficies_n of_o the_o earth_n which_o we_o here_o suppose_v to_o be_v perfect_o round_a and_o it_o be_v manifest_a if_o we_o take_v the_o lesser_a or_o great_a altitude_n than_o p_o o_o that_o also_o the_o arch_n p_o n_o shall_v be_v great_a or_o lesser_a after_o the_o same_o mode_n if_o f_o p_o be_v make_v to_o be_v of_o more_o or_o few_o mile_n p_o n_o shall_v also_o be_v of_o more_o or_o few_o mile_n horizon_n the_o opinion_n of_o the_o ancient_n concern_v this_o horizon_n these_o seem_v to_o be_v the_o cause_n that_o the_o ancient_a author_n have_v follow_v divers_a opinion_n concern_v this_o horizon_n or_o extension_n of_o sight_n for_o macrobius_n assign_v to_o it_o the_o semidiameter_n p_o n_n of_o 180_o stadia_n that_o be_v 22_o ½_n mile_n eratosthenes_n 350_o stadia_n which_o make_v 44_o mile_n albertus_n magnus_n 1000_o which_o make_v 125_o mile_n proclus_n 2000_o stadia_n that_o be_v 250_o mile_n many_o assign_v 500_o stadia_n that_o be_v 62_o ½_n mile_n yet_o i_o suppose_v the_o cause_n of_o the_o diversity_n of_o these_o assignation_n not_o only_o to_o be_v those_o of_o which_o i_o have_v speak_v but_o the_o divers_a assume_v distance_n of_o the_o stadia_fw-la as_o shall_v be_v manifest_a from_o the_o follow_a proposition_n proposition_n ii_o the_o stature_n of_o a_o man_n be_v give_v from_o the_o foot_n to_o the_o eye_n and_o the_o semidiameter_n of_o the_o earth_n be_v give_v to_o find_v out_o the_o semidiameter_n of_o the_o sensible_a horizon_n let_v p_o o_fw-fr be_v the_o stature_n of_o a_o man_n o_o the_o eye_n t_o p_o be_v the_o semidiameter_n o_o n_n be_v the_o ray_n touch_v the_o superficies_n of_o the_o earth_n terminate_a the_o sensible_a horizon_n or_o the_o aspect_n therefore_o p_o n_n be_v the_o semidiameter_n the_o longitude_n of_o this_o be_v demand_v let_v p_o o_fw-fr be_v add_v for_o example_n of_o five_o foot_n to_o t_o p_o the_o semediameter_n 19598300_o so_o you_o shall_v have_v t_o o_fw-fr and_o in_o the_o triangle_n n_o t_o o_o beside_o t_o o_fw-fr and_o t_o n_n we_o know_v the_o angle_n t_o n_o o_o to_o be_v right_a or_o 90_o degree_n therefore_o n_n t_o o_fw-fr be_v find_v according_a to_o this_o proportion_n as_o t_o o_fw-fr be_v to_o t_o n_n so_o be_v the_o whole_a sinus_fw-la to_o the_o sinus_fw-la of_o the_o angle_n n_o o_fw-fr t_o who_o compliment_n at_o 90_o degree_n be_v the_o angle_n n_n t_o o_o or_o the_o arch_n n_o p_o which_o may_v be_v turn_v into_o mile_n corollary_n we_o therefore_o may_v thence_o know_v that_o if_o this_o or_o that_o quantity_n of_o the_o semidiameter_n t_o n_n or_o t_o p_o be_v take_v and_o another_o altitude_n of_o the_o eye_n o_o how_o great_a a_o variation_n there_o thence_o be_v of_o the_o sensible_a horizon_n proposition_n iii_o the_o altitude_n of_o the_o eye_n be_v give_v on_o a_o tower_n or_o mountain_n to_o find_v the_o distance_n of_o the_o last_o point_n unto_o which_o the_o eye_n extend_v itself_o or_o which_o the_o eye_n can_v see_v let_v p_o o_fw-fr be_v the_o give_v altitude_n of_o the_o tower_n in_o which_o the_o eye_n be_v place_v behold_v all_o round_a therefore_o in_o the_o triangle_n right_a angle_n n_n t_o o_o the_o give_v have_v themselves_o after_o the_o same_o mode_n as_o in_o the_o precede_a problem_n therefore_o the_o angle_n n_o t_o p_o and_o the_o arch_n n_o p_o shall_v be_v find_v after_o the_o same_o mode_n which_o we_o have_v use_v in_o the_o solution_n of_o the_o former_a proposition_n iv_o the_o semidiameter_n of_o the_o sensible_a horizon_n be_v give_v or_o the_o great_a distance_n from_o which_o the_o eye_n be_v suppose_v to_o see_v to_o find_v out_o the_o altitude_n of_o the_o eye_n eye_n of_o the_o find_n out_o the_o altitude_n of_o the_o eye_n this_o be_v the_o same_o with_o that_o problem_n the_o great_a distance_n be_v give_v from_o which_o the_o vertex_fw-la of_o the_o mountain_n be_v see_v to_o find_v the_o altitude_n of_o the_o mountain_n in_o the_o triangle_n n_o t_o o_o let_v the_o right_a angle_n t_o n_o o_o be_v give_v and_o the_o angle_n n_o t_o o_o be_v know_v from_o the_o semidiameter_n of_o the_o sensible_a horizon_n p_o n_n moreover_o let_v the_o semidiameter_n of_o the_o earth_n t_o n_n be_v give_v therefore_o t_n o_o shall_v be_v find_v according_a to_o the_o proportion_n as_o the_o whole_a sinus_fw-la be_v to_o the_o secant_fw-la of_o the_o angle_n n_o t_o o_o so_o be_v t_o n_n to_o t_o o._n from_o which_o if_o you_o subtract_v t_o p_o the_o remain_a number_n will_v show_v the_o seek_v for_o altitude_n of_o the_o eye_n proposition_n v._o the_o altitude_n of_o the_o eye_n be_v give_v and_o of_o some_o erect_v scene_a magnitude_n as_o a_o tower_n the_o mast_n of_o a_o ship_n or_o a_o high_a mountain_n to_o find_v the_o distance_n of_o this_o from_o the_o eye_n that_o be_v the_o distance_n of_o the_o ship_n eye_n to_o find_v the_o distance_n of_o a_o ship_n etc._n etc._n by_o the_o eye_n for_o example_n in_o the_o diagram_n in_o the_o precede_a proposition_n let_v p_o o_fw-fr be_v the_o altitude_n of_o the_o eye_n in_o the_o ship_n tower_n or_o mountain_n let_v f_o s_n be_v the_o mast_n of_o another_o ship_n and_o let_v p_o be_v the_o point_n and_o f_o s_o the_o ship_n so_o seat_v that_o in_o p_o the_o first_o top_n of_o the_o mast_n s_o moi_fw-fr be_v see_v therefore_o the_o point_n s_o shall_v be_v in_o the_o line_n o_o n_n which_o be_v the_o tangent_fw-la draw_v from_o the_o eye_n o_o for_o whatsoever_o be_v seat_v beneath_o this_o o_o n_n x_o that_o can_v send_v forth_o no_o direct_a ray_n to_o the_o eye_n o_o but_o it_o must_v so_o draw_v near_o that_o the_o vertex_fw-la or_o point_n may_v fall_v into_o the_o right_a line_n o_o x._o therefore_o the_o distance_n f_o p_o be_v seek_v viz._n in_o which_o the_o first_o ray_n from_o s_n may_v come_v to_o the_o eye_n in_o the_o triangle_n n_o o_fw-fr t_o the_o angle_n n_o t_o o_o be_v find_v from_o the_o give_v n_n t_n t_o o_o and_o from_o the_o right_a angle_n t_o n_o o._n and_o again_o in_o the_o triangle_n right_a angle_n n_n t_o s_o n_o t_o t_o s_o be_v give_v and_o the_o right_a angle_n s_o n_o t_o the_o angle_n n_o t_o s_o shall_v be_v find_v out_o and_o so_o the_o whole_a angle_n o_o t_o s_o shall_v be_v have_v who_o measure_n be_v the_o arch_n p_o s_o the_o distance_n demand_v proposition_n vi_o on_o the_o contrary_a if_o the_o altitude_n of_o the_o eye_n be_v give_v and_o the_o distance_n from_o which_o first_o the_o
wax_n commodity_n commodity_n and_o excellent_a warlike_a horse_n who_o mane_n be_v say_v to_o hang_v down_o to_o their_o foot_n their_o fruit_n be_v good_a and_o in_o great_a plenty_n and_o the_o earth_n be_v enrich_v with_o mine_n of_o several_a metal_n it_o be_v seat_v in_o the_o northern_a temperate_a zone_n between_o the_o seven_o and_o 10_o climate_n which_o make_v the_o long_a day_n to_o be_v 17_o hour_n people_n it_o be_v people_n the_o people_n be_v well_o make_v and_o proportionate_a they_o be_v headstrong_a resolute_a in_o their_o opinion_n and_o of_o no_o ready_a wit_n they_o use_v the_o sclavonian_a language_n they_o be_v christian_n and_o follow_v the_o greek_a church_n the_o kingdom_n at_o present_a be_v divide_v into_o several_a province_n as_o in_o the_o geographical_a table_n of_o turkey_n in_o europe_n be_v set_v down_o all_o which_o be_v subject_a to_o the_o grand_a signior_n transilvania_n province_n of_o transilvania_n the_o province_n of_o transilvania_n have_v for_o its_o chief_a place_n 1._o waranine_n far_o engage_v towards_o the_o west_n and_o it_o be_v a_o frontier_n town_n to_o hungaria_n and_o of_o some_o account_n and_o strength_n 2._o hermensted_n more_o towards_o moldavia_n 3._o weisenburg_n 4._o burges_n 5._o and_o hanyad_n bosnia_n province_n of_o bosnia_n the_o province_n of_o bosnia_n have_v for_o its_o chief_a place_n 1._o saraih_o the_o metropolitan_a city_n seat_v in_o a_o fruitful_a valley_n which_o on_o the_o north_n and_o south_n side_n be_v immure_v with_o ridge_n of_o pleasant_a hill_n of_o a_o easy_a ascent_n this_o city_n be_v say_v to_o contain_v about_o 80_o mescheetoe_n and_o about_o 20000_o house_n which_o for_o the_o most_o part_n be_v but_o mean_o build_v 2._o bagnialuch_v once_o the_o residence_n of_o the_o bosnian_a king_n and_o 3._o jayeza_n the_o usual_a sepulchre_n of_o those_o king_n servia_n province_n of_o servia_n the_o province_n of_o servia_n who_o chief_a city_n be_v 1._o belgrade_n once_o the_o bulwark_n of_o christendom_n valiant_o resist_v the_o power_n of_o amurath_n the_o 6_o and_o mahomet_n the_o great_a but_o yield_v to_o solyman_n anno_fw-la 1520_o when_o this_o whole_a country_n become_v a_o turkish_a province_n 2._o stonebourgh_n once_o the_o seat_n of_o its_o despot_n and_o 3._o samandria_n bulgaria_n province_n of_o bulgaria_n the_o province_n of_o bulgaria_n have_v for_o its_o chief_a place_n 1._o sofia_n the_o seat_n of_o the_o beglerbeg_n of_o greece_n under_o who_o be_v 21_o sangiac_n seat_v almost_o in_o the_o midst_n of_o a_o long_a and_o fruitful_a valley_n beautify_v with_o many_o fair_a hanes_n and_o bath_n the_o chief_a of_o which_o have_v hot_a fountain_n it_o be_v college_n be_v magnificent_a and_o its_o mescheetoe_n be_v many_o and_o beautiful_a especial_o that_o in_o the_o midst_n of_o the_o city_n which_o be_v the_o large_a and_o here_o the_o door_n of_o the_o house_n of_o the_o christian_n and_o jew_n be_v not_o above_o 3_o foot_n high_a which_o be_v so_o make_v to_o keep_v out_o the_o turkish_a horse_n who_o will_v else_o in_o their_o travel_n make_v they_o serve_v instead_o of_o stable_n so_o great_a be_v the_o slavery_n that_o they_o live_v under_o 2._o oesco_n 3._o novi_fw-la 4._o durostoro_fw-it and_o 5._o destor_n all_o which_o be_v seat_v on_o the_o danube_n 6._o proslavia_n seat_v at_o the_o mouth_n of_o one_o of_o the_o branch_n of_o the_o danube_n at_o its_o fall_n into_o the_o euxine_a sea_n 7._o calutra_n and_o 8._o varna_n both_o seat_v on_o the_o euxine_a or_o black_a sea_n moldavia_n province_n of_o moldavia_n the_o province_n of_o moldavia_n who_o chief_a place_n be_v 1._o zuccania_n once_o the_o seat_n of_o the_o vaivod_n 2._o sotzowa_o and_o 3._o lazy_a both_o good_a city_n bessarabia_n country_n of_o bessarabia_n to_o the_o province_n of_o moldavia_n do_v belong_v the_o small_a country_n of_o bessarabia_n which_o lie_v between_o podolia_n and_o bulgaria_n and_o be_v commodious_o seat_v on_o the_o black_a sea_n it_o be_v chief_a place_n be_v kherman_n or_o moncastro_n the_o seat_n of_o the_o turkish_a sargiack_a seat_v on_o the_o river_n tyras_n not_o far_o from_o its_o influx_n into_o the_o sea_n and_o 2._o kilia_n also_o seat_v on_o the_o euxine_a sea_n walachia_n province_n of_o walachia_n the_o province_n of_o walachia_n be_v divide_v from_o bulgaria_n by_o the_o danube_n and_o be_v esteem_v the_o rich_a province_n in_o all_o dacia_n it_o be_v chief_a place_n be_v 1._o targovisco_n the_o seat_n of_o the_o vajuod_n 2._o domboviza_n and_o 3._o brailonum_fw-la greece_n greece_n the_o part_n of_o greece_n the_o rest_n of_o turkey_n in_o europe_n may_v be_v comprehend_v under_o the_o name_n of_o greece_n which_o be_v divide_v into_o several_a part_n to_o wit_n romania_n which_o answer_v to_o the_o ancient_a thrace_n macedonia_n who_o divers_a part_n have_v receive_v divers_a name_n as_o that_o of_o jamboli_n of_o camenolitaria_n of_o migdonia_n or_o particular_a macedonia_n albania_n and_o thessaly_n which_o be_v now_o call_v junna_n epirus_n now_o canina_n achaia_n and_o aetolla_n now_o livadia_n and_o peloponnesus_n now_o the_o morea_n bound_n its_o bound_n greece_n esteem_v the_o mother_n of_o art_n and_o science_n have_v for_o its_o eastern_a bound_n the_o egean_a sea_n the_o hellespont_n propontis_n and_o thracian_a bosphorus_n and_o for_o its_o western_a the_o adriatic_a sea_n and_o italy_n it_o be_v seat_v in_o the_o northern_a temperate_a zone_n under_o the_o 5_o and_o 6_o climate_n the_o long_a day_n be_v 15_o hour_n commoty_n it_o be_v sertllity_n and_o commoty_n the_o soil_n without_o doubt_n be_v very_o rich_a and_o fruitful_a and_o will_v be_v very_o prositable_a to_o the_o husbandman_n if_o pain_n be_v take_v in_o till_v it_o but_o the_o great_a turk_n seize_v on_o their_o estate_n when_o and_o as_o often_o as_o he_o please_v make_v they_o careless_a to_o cultivate_v it_o yet_o here_o be_v find_v several_a good_a commodity_n which_o be_v transport_v to_o other_o place_n as_o wine_n oil_n silk_n both_o raw_a and_o wrought_v into_o severai_fw-fr manufacture_n as_o velvet_n damask_n etc._n etc._n also_o gragram_n brimstone_n copper_n vitriol_n cotton_n sope_n carpet_n cute_v currant_n cuminseed_n anniseed_n etc._n etc._n greek_n the_o ancient_n and_o present_a greek_n the_o grecian_n though_o a_o scatter_a people_n since_o the_o turk_n become_v master_n of_o their_o country_n vet_z still_o retain_v their_o name_n religion_n custom_n and_o language_n as_o indeed_o they_o do_v in_o all_o other_o place_n where_o they_o live_v they_o be_v once_o a_o nation_n so_o excellent_a that_o their_o precept_n and_o example_n do_v yet_o remain_v as_o approve_a canon_n to_o direct_v the_o mind_n to_o virtue_n they_o be_v lover_n of_o freedom_n every_o way_n noble_a in_o matter_n of_o government_n famous_a in_o arm_n glorious_a in_o art_n admirable_a and_o to_o who_o the_o rest_n of_o the_o world_n be_v hold_v barbarian_n but_o since_o they_o become_v under_o the_o turkish_a yoke_n for_o the_o generaliay_v their_o spirit_n be_v so_o low_a that_o their_o knowledge_n be_v turn_v into_o ignorance_n their_o liberty_n into_o content_a slavery_n their_o virtue_n into_o vice_n and_o their_o industry_n in_o art_n and_o science_n into_o idleness_n they_o be_v much_o addict_v to_o drink_v and_o dance_v for_o which_o they_o have_v the_o name_n of_o merry_a greek_n they_o be_v of_o a_o good_a proportion_n and_o of_o a_o swart_a complexion_n their_o woman_n be_v well_o favour_v brown_a and_o excessive_o amorous_a in_o matter_n of_o habit_n they_o differ_v little_a from_o those_o among_o who_o they_o live_v the_o christian_a faith_n be_v here_o establish_v by_o timothy_n to_o who_o st._n paul_n write_v two_o epistle_n the_o father_n which_o this_o church_n most_o adher_v unto_o be_v chrysostom_n basil_n and_o the_o two_o gregory_n and_o the_o church_n be_v govern_v by_o patriarch_n one_o of_o constantinople_n another_o of_o alexandria_n another_o of_o jerusalem_n and_o another_o of_o antioch_n free_o exercise_v their_o religion_n which_o differ_v much_o from_o the_o church_n of_o rome_n as_o i_o shall_v in_o place_n elsewhere_o take_v notice_n oâ—_n and_o have_v every_o where_o their_o temple_n and_o monastery_n if_o a_o patriarch_n die_v another_o be_v elect_v by_o the_o synod_n of_o bishop_n breed_v famous_a man_n here_o breed_v this_o country_n have_v breed_v several_a famous_a man_n as_o alexander_z the_o subverter_n of_o the_o persian_a monarchy_n xenophon_n plutarch_n herodotus_n and_o thucydides_n famous_a historiographer_n epaminondas_n pyrrhus_n miltiades_n and_o aristides_n captain_n plato_n aristotle_n socrates_n and_o theophrastus_n divine_a philosopher_n demosthenes_n aeschines_n and_o isocrates_n eloquent_a orator_n with_o several_a other_o too_o tedious_a to_o name_n but_o to_o proceed_v to_o the_o province_n romania_n province_n of_o romania_n romania_n particular_o so_o call_v a_o country_n of_o itself_o neither_o of_o a_o rich_a soil_n nor_o pleasant_a air_n more_o
shadow_n the_o shadow_n receive_v their_o denomination_n from_o the_o part_n or_o quarter_n of_o the_o world_n into_o which_o they_o be_v cast_v as_o the_o oriental_a shadow_n which_o tend_v into_o the_o east_n from_o the_o sun_n place_v in_o the_o west_n contrariwise_o the_o occidental_a shadow_n which_o go_v into_o the_o western_a plaga_fw-la or_o quater_fw-la but_o here_o be_v chief_o to_o be_v consider_v the_o meridian_n shadow_n which_o be_v situate_v on_o the_o plain_a of_o the_o meridian_n or_o which_o be_v cast_v from_o body_n perpendicular_o erect_v or_o seat_v in_o the_o plain_a of_o the_o meridian_n the_o sun_n then_o be_v in_o the_o meridian_n and_o this_o be_v two_o fold_n viz._n northern_a and_o southern_a the_o inhabitant_n of_o that_o part_n of_o the_o earth_n be_v term_v heteroscij_fw-la where_o the_o meridian_n shadow_n of_o body_n erect_v be_v constant_o carry_v all_o day_n of_o the_o year_n to_o either_o pole_n the_o periscij_fw-la be_v those_o inhabitant_n of_o the_o earth_n where_o the_o shadow_n of_o erect_a body_n in_o one_o and_o the_o same_o day_n be_v carry_v about_o into_o all_o the_o plagas_fw-la of_o the_o horizon_n or_o where_o the_o meridian_n shadow_n in_o one_o and_o the_o same_o day_n be_v cast_v to_o both_o the_o quarter_n of_o the_o meridian_n the_o amphiscij_fw-la be_v those_o inhabitant_n of_o the_o earth_n where_o the_o meridian_n shadow_n of_o the_o erect_a body_n in_o some_o day_n of_o the_o year_n be_v cast_v to_o the_o north_n and_o on_o othersom_a to_o the_o south_n proposition_n i._o the_o shadow_n of_o body_n erect_v above_o the_o horizontal_n plain_a fall_v upon_o the_o quarter_n opposite_a to_o it_o in_o which_o the_o sun_n exi_v dyall_v of_o shadow_n in_o reference_n to_o optic_n and_o dyall_v those_o that_o be_v verse_v in_o the_o optic_n and_o horology_n be_v wont_a to_o say_v that_o a_o shadow_n a_o opac_n and_o luminous_a body_n be_v in_o one_o plain_a but_o the_o term_n or_o bind_v of_o the_o shadow_n the_o extremity_n of_o the_o opac_n and_o the_o sun_n be_v in_o one_o right_a line_n for_o because_o the_o opac_n the_o shadow_n and_o line_n conceal_v from_o the_o extremity_n of_o the_o opac_n to_o the_o extremity_n of_o the_o shadow_n make_v a_o triangle_n now_o every_o triangle_n be_v in_o one_o plain_a therefore_o those_o three_o line_n shall_v be_v in_o one_o plain_a the_o sun_n be_v in_o the_o extremity_n of_o the_o line_n conjoin_v the_o extremity_n of_o the_o opacity_n and_o the_o shadow_n moreover_o a_o erect_a body_n be_v right_a to_o the_o horizontal_n plain_a wherefore_o the_o plain_a draw_v through_o it_o viz._n that_o of_o the_o forementioned_a triangle_n be_v also_o straight_o to_o that_o horizontal_n plain_a and_o therefore_o seat_v in_o the_o vertical_a plain_n and_o because_o a_o body_n erect_v be_v seat_v as_o it_o be_v a_o vertex_fw-la between_o the_o sun_n and_o shadow_n therefore_o the_o sun_n and_o shadow_n shall_v be_v in_o the_o opposite_a quarter_n there_o be_v three_o part_n of_o this_o shadow_n which_o the_o style_v erect_v be_v illuminate_v from_o the_o sun_n do_v cast_v viz._n a_o dense_n shadow_n a_o central_n and_o a_o shadow_n which_o be_v almost_o a_o dense_n shadow_n which_o a_o ray_n come_v from_o the_o uppermost_a edge_n of_o the_o sun_n do_v terminate_v a_o central_n shadow_n be_v that_o which_o be_v intercept_v between_o the_o ray_n of_o the_o superior_a edge_n and_o the_o centrel_n ray_n the_o penumbra_fw-mi be_v that_o which_o be_v intercept_v between_o the_o central_n ray_n and_o the_o ray_n of_o the_o low_a proposition_n ii_o the_o inhabitant_n of_o the_o place_n of_o the_o earth_n which_o in_o the_o tropic_a of_o cancer_n and_o capricorn_n be_v heteroscij_fw-la heteroscij_fw-la the_o people_n in_o the_o tropic_n be_v heteroscij_fw-la for_o when_o the_o sun_n be_v in_o the_o first_o degree_n of_o cancer_n that_o very_a day_n the_o body_n erect_v in_o any_o point_n of_o the_o tropic_a of_o cancer_n do_v absorbe_v the_o shadow_n of_o the_o sun_n possess_v their_o meridian_n because_o that_o then_o the_o sun_n perpendicular_o from_o his_o vertex_fw-la hang_v over_o the_o horizon_n and_o therefore_o illuminate_v all_o part_n of_o it_o neither_o do_v any_o ray_n from_o the_o erect_a opac_n hinder_v like_o this_o which_o perpendicular_o fall_v on_o the_o plain_a of_o the_o horizon_n and_o therefore_o lie_v in_o the_o very_a opac_n but_o in_o other_o day_n of_o the_o year_n because_o the_o sun_n decline_v from_o the_o vertex_fw-la of_o the_o place_n of_o the_o tropic_a towards_o the_o south_n therefore_o the_o shadow_n be_v cast_v in_o the_o meridies_n towards_o the_o north_n never_o towards_o the_o south_n on_o the_o contrary_a in_o the_o place_n of_o the_o tropic_a of_o capricorn_n every_o day_n it_o be_v cast_v towards_o the_o south_n except_o on_o one_o day_n in_o which_o there_o will_v be_v no_o shadow_n never_o towards_o the_o north._n proposition_n iii_o the_o inhabitant_n of_o the_o torrid_a zone_n be_v amphiscii_n amphiscii_n the_o inhabitant_n of_o the_o torrid_a zone_n be_v call_v amphiscii_n let_v any_o place_n of_o the_o torrid_a zone_n be_v take_v in_o the_o globe_n and_o let_v it_o be_v bring_v to_o the_o meridian_n and_o let_v the_o parallel_n of_o the_o latitude_n which_o shall_v cut_v the_o ecliptic_a in_o two_o point_n be_v describe_v by_o chalk_n apply_v when_o therefore_o the_o sun_n shall_v be_v in_o these_o point_n of_o the_o ecliptic_a he_o shall_v describe_v by_o his_o circumvolution_n a_o parallel_n which_o shall_v direct_o hang_v over_o the_o parallel_n describe_v and_o therefore_o on_o those_o two_o day_n in_o which_o he_o obtain_v those_o point_n of_o the_o ecliptic_a in_o the_o assume_v place_n and_o in_o all_o situate_v in_o the_o describe_v parallel_n he_o shall_v be_v vertical_a in_o the_o meridies_n and_o illustrate_v all_o the_o place_n of_o the_o horizon_n and_o therefore_o no_o shadow_n shall_v be_v cast_v on_o these_o two_o day_n and_o the_o inhabitant_n shall_v be_v amphiscii_n without_o any_o shadow_n but_o on_o the_o other_o day_n of_o the_o year_n they_o shall_v not_o be_v so_o but_o the_o meridian_n shadow_n shall_v either_o be_v cast_v to_o the_o north_n or_o to_o the_o south_n to_o the_o north_n whilst_o the_o sun_n move_v in_o that_o part_n of_o the_o ecliptic_a which_o lie_v in_o those_o two_o point_n before_o note_v towards_o the_o south_n on_o the_o contrary_a to_o the_o south_n whilst_o the_o sun_n move_v in_o that_o part_n of_o the_o ecliptic_a which_o be_v situate_v from_o those_o two_o point_n towards_o the_o north._n proposition_n iu._n the_o inhabitant_n of_o the_o temperate_a zone_n be_v heteroscii_n heteroscii_n the_o inhabitant_n of_o the_o temperate_a zone_n be_v call_v heteroscii_n for_o because_o the_o sun_n in_o all_o those_o day_n of_o the_o year_n in_o the_o meridies_n be_v move_v from_o the_o place_n of_o the_o north_n temperate_a zone_n towards_o that_o quarter_n to_o wit_n the_o south_n and_o on_o the_o contrary_a from_o the_o place_n of_o the_o south_n temperate_a zone_n towards_o the_o north_n it_o follow_v from_o the_o first_o proposition_n that_o the_o meridian_n shadow_n of_o the_o place_n of_o the_o north_n temperate_a zone_n bend_v to_o the_o same_o quarter_n all_o the_o day_n of_o the_o year_n viz._n the_o north_n on_o the_o contrary_a to_o the_o south_n in_o the_o place_n of_o the_o south_n temperate_a zone_n proposition_n v._o the_o inhabitant_n of_o the_o frigid_a zone_n be_v periscii_n periscii_n the_o inhabitant_n of_o the_o frigid_a zone_n be_v call_v periscii_n for_o by_o reason_n that_o on_o some_o day_n of_o the_o year_n the_o sun_n set_v not_o in_o these_o place_n but_o move_v round_o about_o the_o horizon_n it_o be_v also_o necessary_a that_o the_o shadow_n shall_v be_v carry_v round_o into_o all_o quarter_n and_o the_o sun_n be_v in_o the_o superior_a semicircle_n of_o the_o meridian_n the_o shadow_n be_v cast_v towards_o the_o north_n and_o when_o the_o sun_n be_v in_o the_o inferior_a semicircle_n the_o shadow_n be_v carry_v towards_o the_o southern_a quarter_n proposition_n vi_o a_o place_n of_o the_o torrid_a zone_n be_v give_v to_o find_v the_o day_n of_o the_o year_n in_o which_o the_o inhabitant_n of_o that_o place_n shall_v be_v without_o any_o shadow_n and_o in_o what_o day_n the_o shadow_n be_v carry_v to_o the_o north_n and_o in_o what_o to_o the_o south_n let_v the_o day_n of_o the_o year_n in_o which_o the_o sun_n become_v vertical_a to_o the_o place_n give_v be_v find_v those_o shall_v be_v the_o day_n in_o which_o the_o inhabitant_n of_o that_o place_n shall_v be_v without_o a_o shadow_n for_o this_o use_v the_o mode_n in_o the_o three_o proposition_n proposition_n vii_o the_o day_n of_o the_o year_n be_v give_v to_o find_v the_o place_n of_o the_o earth_n in_o the_o globe_n who_o inhabitant_n be_v amphiscii_n