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
of_o the_o latitude_n from_o one_o pole_n to_o another_o be_v circular_a furthermore_o that_o the_o section_n of_o the_o earth_n according_a to_o the_o dimension_n of_o the_o latitude_n from_o one_o pole_n to_o another_o a_o b_o c_o d_o be_v circular_a be_v prove_v by_o many_o celestial_a appearance_n first_o if_o this_o line_n a_o b_o c_o d_o any_o place_n whatsoever_o be_v take_v in_o b_o some_o man_n go_v forward_o towards_o either_o pole_n m_n or_o towards_o the_o star_n near_o it_o he_o observe_v by_o his_o progress_v make_v equal_o that_o he_o approach_v equal_o to_o the_o pole_n but_o this_o can_v not_o be_v do_v unless_o the_o line_n of_o his_o journey_n b_o a_o c_o d_o be_v circular_a and_o it_o be_v commodious_o show_v by_o the_o artificial_a terrestrial_a globe_n second_o because_o a_o b_o c_o d_o be_v the_o meridian_n line_n into_o which_o when_o the_o sun_n come_v it_o be_v midday_n to_o we_o and_o to_o all_o people_n dwell_v in_o this_o line_n a_o b_o c_o experience_n witness_v that_o the_o sun_n in_o the_o line_n a_o b_o c_o do_v perpendicular_o hang_v over_o any_o place_n to_o wit_n in_o the_o torrid_a zone_n for_o example_n p_o and_o if_o we_o take_v equal_a space_n equal_a to_o b_o q_n q_o p_o we_o shall_v perceive_v that_o the_o distance_n of_o the_o sun_n from_o the_o vertex_fw-la or_o top_n of_o q_o be_v equal_a to_o the_o excess_n of_o the_o distance_n of_o the_o sun_n from_o the_o vertex_fw-la of_o b_o above_o the_o distance_n from_o the_o vertical_a point_n of_o q_o which_o can_v by_o no_o mean_n be_v accomplish_v unless_o the_o line_n b_o p_o q_o be_v circular_a three_o the_o same_o be_v the_o reason_n of_o all_o the_o star_n which_o when_o they_o come_v into_o the_o meridian_n a_o b_o c_o their_o distance_n from_o the_o vertex_n p_o qui_fw-fr b_o have_v the_o same_o reason_n as_o the_o distance_n pq_n p_o b_o q_o p._n so_o when_o our_o mariner_n sail_v towards_o the_o south_n the_o star_n which_o before_o be_v not_o conspicuous_a become_v high_o and_o more_o manifest_a to_o the_o eye_n according_a to_o the_o proportion_n of_o their_o sail_v four_o so_o if_o many_o star_n be_v take_v and_o the_o place_n of_o the_o earth_n through_o who_o zenith_n they_o pass_v in_o one_o meridian_n you_o shall_v perceive_v that_o the_o distance_n of_o these_o place_n have_v the_o same_o proportion_n among_o themselves_o as_o the_o distance_n of_o the_o point_n of_o the_o meridian_n in_o which_o those_o star_n keep_v their_o noon_n or_o full_a soâ—th_n point_n now_o forasmuch_o as_o belong_v to_o the_o longitude_n of_o the_o earth_n for_o example_n e_o b_o f_o c_o that_o be_v also_o circular_a and_o that_o the_o earth_n have_v a_o spherical_a tumour_n or_o swell_a according_a to_o this_o dimension_n star_n of_o the_o rise_n and_o set_v of_o the_o star_n be_v prove_v by_o that_o because_o the_o sun_n and_o star_n do_v soon_o by_o a_o great_a deal_n rise_v to_o those_o people_n which_o live_v from_o we_o towards_o the_o east_n than_o to_o we_o and_o do_v also_o soon_o set_v to_o they_o than_o to_o we_o but_o to_o they_o that_o dwell_v from_o we_o westward_n contrariwise_o they_o rise_v and_o set_v late_a than_o to_o we_o and_o indeed_o according_a to_o that_o proportion_n of_o time_n which_o the_o distance_n of_o the_o meridian_n of_o those_o place_n have_v from_o our_o meridian_n so_o if_o two_o place_n be_v take_v from_o we_o to_o wit_n the_o distance_n of_o one_o meridian_n towards_o the_o east_n 225_o mile_n the_o distance_n of_o the_o other_o 450_o then_o we_o shall_v find_v that_o in_o this_o place_n the_o sun_n rise_v two_o hour_n soon_o than_o with_o we_o but_o in_o the_o other_o place_n it_o rise_v but_o one_o hour_n soon_o than_o in_o we_o the_o argument_n become_v more_o clear_a if_o this_o theorem_n be_v propose_v of_o the_o sun_n come_v to_o the_o meridian_n of_o divers_a place_n sun_n of_o the_o rise_n of_o the_o sun_n for_o indeed_o look_v what_o be_v the_o account_n of_o the_o distance_n of_o place_n from_o we_o and_o the_o same_o will_v be_v observe_v the_o account_n of_o time_n which_o come_v in_o between_o the_o arriving_n to_o those_o meridian_n and_o we_o or_o between_o the_o arch_n of_o the_o equator_fw-la intercept_v between_o their_o meridian_n and_o we_o which_o be_v make_v evident_a by_o the_o eclipse_n for_o these_o thing_n be_v show_v by_o the_o artificial_a globe_n if_o we_o ascribe_v a_o spheric_a form_n to_o the_o earth_n but_o other_o shape_n thereto_o apply_v be_v very_o absurd_a so_o now_o the_o spherical_a form_n have_v as_o well_o be_v demonstrate_v as_o touch_v the_o latitude_n as_o the_o longitude_n of_o the_o earth_n spherical_a other_o reason_n to_o prove_v the_o earth_n spherical_a yea_o but_o the_o spherical_a form_n thereof_o may_v also_o be_v prove_v by_o the_o only_a latitude_n of_o the_o earth_n for_o indeed_o all_o division_n of_o the_o earth_n which_o be_v make_v according_a to_o the_o latitude_n thereof_o in_o divers_a place_n be_v the_o periphery_n of_o the_o place_n but_o they_o pass_v through_o the_o same_o point_n of_o heaven_n to_o wit_n the_o pole_n of_o conversion_n near_o adjacent_a to_o the_o polar_a star_n from_o these_o two_o reason_n we_o may_v solid_o infer_v and_o prove_v that_o the_o figure_n of_o the_o earth_n be_v spherical_a for_o it_o be_v a_o geometrical_a theorem_fw-la which_o therefore_o ought_v to_o be_v demonstrate_v by_o geometrician_n thus_o if_o any_o solid_a body_n be_v cut_v in_o many_o plane_n it_o matter_n not_o how_o pass_v through_o some_o one_o point_n and_o all_o the_o section_n or_o division_n be_v perform_v in_o the_o superficies_n of_o the_o periphery_a of_o the_o circle_n that_o body_n be_v spherical_a reason_n other_o reason_n here_o come_v another_o reason_n take_v from_o the_o shadow_n which_o the_o earth_n on_o her_o averse_a part_n to_o the_o sun_n disperse_v to_o the_o moon_n whereby_o she_o suffer_v a_o eclipse_n forasmuch_o as_o this_o shadow_n be_v conical_a or_o like_o a_o spire_n of_o a_o steeple_n as_o be_v declare_v by_o the_o obscuration_n of_o the_o moon_n but_o if_o we_o deal_v rigid_o the_o argument_n take_v from_o the_o spherical_a roundness_n of_o the_o earth_n from_o the_o view_n and_o consideration_n of_o the_o earth_n be_v these_o follow_v first_o again_o again_o from_o the_o sail_v round_o the_o earth_n because_o our_o man_n of_o europe_n hoist_v sail_n eight_o time_n from_o europe_n with_o a_o direct_a journey_n to_o the_o west_n and_o south_n even_o unto_o the_o strait_n of_o magellan_n afterward_o to_o the_o west_n and_o north_n they_o return_v again_o from_o the_o east_n into_o europe_n and_o all_o those_o appearance_n happen_v to_o they_o which_o arise_v from_o the_o property_n of_o the_o globe_n which_o sure_o have_v not_o be_v do_v if_o the_o earth_n have_v not_o be_v round_o and_o certain_o upon_o the_o supposition_n of_o that_o figure_n of_o the_o earth_n all_o those_o circumnavigation_n be_v ground_v which_o therefore_o have_v not_o take_v such_o happy_a success_n if_o the_o form_n have_v be_v otherwise_o second_o furthermore_n furthermore_n when_o either_o by_o sea_n or_o land_n we_o take_v our_o departure_n from_o high_a tower_n and_o mountain_n than_o the_o low_a part_n thereof_o be_v abscond_v from_o we_o and_o by_o degree_n more_o and_o more_o till_o at_o last_o the_o very_a top_n thereof_o be_v quite_o take_v from_o our_o sight_n in_o the_o same_o manner_n when_o as_o for_o a_o long_a distance_n we_o come_v to_o a_o tower_n or_o mountain_n first_o the_o top_n present_v itself_o to_o our_o view_n than_o the_o inferior_a part_n till_o at_o last_o through_o our_o near_a distance_n the_o foot_n thereof_o be_v see_v and_o this_o increase_n of_o apparition_n and_o occultation_n be_v altogether_o make_v according_a to_o such_o a_o proportion_n as_o the_o spherical_a tumour_n or_o swell_a of_o the_o earth_n be_v able_a to_o make_v neither_o can_v it_o be_v explicate_v by_o any_o other_o figure_n the_o diagram_n will_v make_v the_o proposition_n more_o clear_a three_o because_o that_o the_o measure_v the_o height_n of_o mountain_n or_o great_a hill_n which_o be_v ground_v upon_o the_o hypothesis_n of_o the_o globous_a form_n of_o the_o earth_n be_v find_v by_o experience_n to_o agree_v with_o a_o real_a truth_n of_o the_o thing_n itself_o earth_n further_a reason_n to_o prove_v the_o rotundity_n of_o the_o earth_n furthermore_o that_o we_o may_v draw_v together_o the_o whole_a number_n of_o these_o argument_n take_v à _fw-la posteriori_fw-la into_o one_o sum_n although_o they_o may_v be_v handle_v geometrical_o but_o that_o business_n will_v be_v of_o great_a labour_n and_o difficulty_n for_o it_o must_v be_v demonstrate_v that_o this_o or_o that_o different_a property_n be_v put_v that_o the_o line_n be_v circular_a
of_o the_o same_o day_n after_o the_o sun_n and_o in_o the_o morning_n before_o the_o sun_n may_v be_v see_v i_o forbear_v to_o bring_v hither_o any_o more_o appearance_n but_o they_o be_v the_o principal_a from_o which_o i_o think_v a_o argument_n of_o great_a moment_n may_v be_v fetch_v for_o this_o motion_n of_o the_o earth_n when_o as_o by_o this_o motion_n of_o the_o earth_n they_o may_v be_v so_o commodious_o declare_v that_o it_o shall_v rather_o be_v admire_v if_o the_o earth_n can_v not_o be_v move_v by_o such_o evident_a appearance_n these_o be_v the_o easy_a argument_n by_o which_o the_o copernican_n will_v evince_v the_o motion_n of_o the_o earth_n which_o although_o they_o be_v not_o demonstrative_a yet_o they_o make_v this_o hypothesis_n more_o probable_a than_o that_o which_o determine_v the_o heaven_n to_o be_v move_v for_o one_o of_o they_o must_v needs_o be_v admit_v ptolomaians_n the_o reason_n of_o â—ome_o against_o the_o move_n of_o the_o earth_n as_o the_o 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heaviness_n be_v also_o discover_v in_o the_o part_n of_o the_o sun_n and_o moon_n and_o yet_o notwithstanding_o neither_o the_o sun_n nor_o moon_n be_v say_v to_o be_v heavy_a to_o the_o second_o they_o answer_v that_o that_o right_a motion_n of_o the_o part_n of_o the_o earth_n not_o of_o the_o whole_a earth_n and_o the_o circular_a motion_n thereof_o do_v not_o hinder_v the_o straight_o carry_v of_o those_o part_n which_o be_v evidence_v by_o the_o part_n of_o the_o sun_n and_o moon_n to_o the_o three_o argument_n they_o reply_v in_o a_o threefold_a manner_n first_o that_o such_o heavy_a thing_n be_v not_o primary_o carry_v to_o the_o centre_n of_o the_o earth_n and_o therefore_o be_v bear_v by_o a_o very_a short_a line_n to_o the_o superficies_n thereof_o as_o iron_n tend_v not_o to_o the_o centre_n of_o the_o loadstone_n but_o to_o the_o loadstone_n second_o the_o whole_a air_n cleave_v to_o the_o earth_n and_o be_v move_v together_o with_o she_o therefore_o all_o such_o heavy_a 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place_n it_o be_v also_o different_a to_o wit_n how_o much_o the_o near_o the_o place_n be_v to_o the_o equator_fw-la with_o so_o much_o the_o great_a swiftness_n and_o space_n it_o be_v move_v but_o the_o great_a motion_n be_v in_o the_o place_n that_o lie_v in_o the_o equator_fw-la for_o indeed_o because_o every_o place_n of_o the_o earth_n in_o twenty_o four_o hour_n be_v roll_v about_o by_o the_o space_n of_o a_o whole_a periphery_n to_o wit_n by_o 360_o degree_n therefore_o the_o space_n of_o one_o hour_n be_v find_v if_o 360_o be_v divide_v by_o 24_o the_o quotient_n be_v fifteen_o which_o be_v so_o many_o degree_n these_o be_v the_o degree_n by_o which_o the_o place_n lie_v in_o the_o equator_fw-la or_o without_o it_o be_v turn_v about_o in_o one_o hour_n but_o they_o make_v if_o the_o place_n lie_v in_o the_o equator_fw-la two_o hundred_o twenty_o five_o german_a mile_n whence_o she_o will_v be_v turn_v in_o four_o minute_n of_o a_o hour_n through_o one_o degree_n that_o be_v 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depart_v from_o the_o meridian_n for_o that_o be_v equal_a to_o the_o latitude_n of_o the_o place_n proposition_n x._o the_o place_n of_o the_o earth_n situate_v under_o the_o aequator_fw-la have_v no_o latitude_n or_o elevation_n of_o the_o pole_n but_o both_o the_o pole_n lie_v in_o their_o horizon_n latitude_n the_o place_n under_o the_o aequator_fw-la have_v not_o latitude_n the_o place_n under_o the_o pole_n have_v the_o latitude_n of_o 90_o degree_n viz._n the_o pole_n in_o the_o vertex_fw-la and_o the_o aequator_fw-la in_o the_o horizon_n the_o place_n between_o the_o pole_n and_o the_o aequator_fw-la have_v a_o less_o latitude_n than_o ninety_o degree_n the_o truth_n of_o this_o proposition_n be_v evident_a therefore_o it_o need_v no_o explication_n proposition_n xi_o if_o we_o be_v either_o on_o the_o sea_n or_o land_n and_o know_v not_o the_o place_n where_o we_o be_v let_v the_o latitude_n be_v find_v to_o exhibit_v that_o parallel_n in_o the_o globe_n that_o we_o may_v be_v certain_a that_o we_o be_v in_o one_o point_n of_o it_o this_o be_v do_v after_o the_o same_o manner_n that_o we_o have_v show_v in_o the_o six_o proposition_n viz._n a_o parallel_n must_v be_v describe_v at_o the_o give_v or_o observe_v latitude_n and_o this_o be_v the_o parallel_n demand_v the_o same_o be_v also_o easy_a in_o map_n chap._n xxiv_o of_o the_o division_n of_o the_o earth_n into_o zone_n and_o the_o celestial_a appearance_n in_o the_o divers_a zone_n proposition_n i._o from_o the_o proper_a or_o annual_a motion_n of_o the_o sun_n there_o arise_v a_o certain_a division_n of_o the_o superficies_n of_o the_o earth_n into_o five_o part_n or_o zone_n scheme_n the_o division_n of_o the_o earth_n into_o 5_o zone_n see_v scheme_n see_v that_o the_o sun_n do_v not_o always_o continue_v in_o the_o aequator_fw-la but_o decline_v from_o it_o describe_v by_o his_o motion_n a_o path_n which_o cut_v the_o aequator_fw-la so_o that_o his_o great_a declination_n be_v in_o 23½_n degree_n 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
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 scorpio_n from_o the_o 21_o of_o september_n to_o the_o 22_o of_o october_n the_o other_o autumn_n whilst_o the_o sun_n move_v from_o the_o second_o degree_n of_o scorpio_n to_o the_o first_o of_o capricorn_n from_o the_o 22_o of_o october_n to_o the_o 21_o of_o december_n the_o other_o winter_n whilst_o the_o sun_n move_v from_o the_o first_o degree_n of_o capricorn_n to_o the_o 28_o of_o aquarius_n from_o the_o 21_o of_o december_n to_o the_o 19_o of_o february_n the_o other_o spring_n be_v whilst_o the_o sun_n do_v move_v from_o the_o 28_o degree_n of_o aquarius_n to_o the_o first_o of_o aries_n from_o the_o 19_o of_o february_n to_o the_o 21_o of_o march._n all_o these_o be_v easy_o demonstrate_v from_o the_o definition_n lay_v down_o because_o that_o the_o sun_n in_o the_o first_o degree_n of_o aries_n and_o in_o the_o first_o of_o libra_n have_v the_o less_o distance_n in_o the_o meridies_n from_o the_o vertices_fw-la of_o the_o place_n lie_v under_o the_o aequator_fw-la for_o 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place_n and_o situation_n and_o therefore_o very_a unlike_o figure_n arise_v thence_o in_o the_o table_n thence_o it_o come_v to_o pass_v that_o according_a to_o the_o various_a situation_n of_o the_o eye_n which_o we_o attribute_v to_o it_o without_o the_o earth_n or_o without_o that_o part_n which_o it_o ought_v to_o represent_v there_o arise_v a_o various_a representation_n of_o that_o superficies_n on_o the_o table_n for_o as_o there_o exi_v another_o sort_n of_o frontispiece_n of_o the_o wall_n of_o a_o house_n when_o the_o eye_n may_v behold_v it_o from_o a_o situation_n direct_o opposite_a another_o from_o a_o oblique_a situation_n another_o from_o a_o upper_a place_n another_o from_o a_o long_a place_n and_o so_o change_v according_a to_o the_o various_a situation_n of_o the_o eye_n which_o tutor_n may_v explain_v by_o diagram_n so_o there_o arise_v a_o different_a position_n of_o the_o part_n of_o the_o earth_n to_o be_v represent_v on_o the_o table_n if_o that_o the_o eye_n be_v so_o constitute_v or_o conceive_v in_o the_o air_n in_o such_o a_o situation_n that_o it_o may_v hang_v over_o the_o aequator_fw-la of_o the_o earth_n and_o otherwise_o if_o that_o it_o be_v suppose_v to_o exist_v in_o the_o pretend_a axis_n of_o the_o earth_n or_o in_o the_o semi-axis_n of_o the_o hemisphere_n and_o otherwise_o if_o it_o be_v conceive_v to_o be_v eminent_a over_o any_o other_o place_n of_o the_o earth_n thence_o it_o come_v to_o pass_v that_o both_o the_o aequator_fw-la and_o the_o parallel_n as_o well_o as_o the_o meridian_n obtain_v various_a representation_n because_o the_o ray_n draw_v from_o they_o exist_v in_o the_o earth_n to_o the_o eye_n perforate_v the_o table_n in_o divers_a point_n endue_v with_o a_o various_a situation_n which_o the_o reader_n may_v easy_o understand_v profitable_a the_o direction_n of_o a_o tutor_n very_o profitable_a if_o that_o they_o have_v the_o live_a information_n and_o direction_n of_o a_o tutor_n the_o other_o which_o i_o 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be_v not_o only_o remove_v but_o also_o recede_v from_o that_o perpendicular_a line_n than_o the_o like_a projecture_n shall_v not_o arise_v and_o the_o place_n shall_v not_o have_v the_o like_a situation_n on_o the_o earth_n but_o beside_o a_o various_a magnitude_n there_o shall_v also_o be_v a_o notable_a dissimilitude_n in_o the_o situation_n of_o the_o place_n one_o to_o the_o other_o but_o in_o the_o projecture_n of_o all_o body_n as_o also_o in_o the_o projecture_n of_o the_o superficies_n of_o the_o earth_n it_o be_v so_o wont_a to_o happen_v that_o we_o attribute_v such_o a_o situation_n to_o the_o table_n or_o glass_n that_o it_o may_v touch_v the_o body_n or_o superficies_n in_o that_o point_n to_o which_o the_o line_n draw_v be_v perpendicular_a to_o the_o superficies_n of_o the_o body_n or_o which_o be_v draw_v from_o the_o eye_n to_o the_o centre_n of_o the_o earth_n now_o to_o obtain_v the_o lesser_a or_o great_a projecture_n we_o remove_v the_o point_n of_o the_o eye_n 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circle_n of_o the_o earth_n as_o the_o aequator_fw-la the_o parallel_n the_o meridian_n as_o they_o have_v in_o the_o earth_n itself_o so_o that_o from_o those_o table_n the_o parallel_n of_o every_o place_n the_o distance_n from_o the_o aequator_fw-la from_o the_o pole_n the_o zone_n the_o climate_n etc._n etc._n may_v be_v behold_v because_o that_o from_o thence_o many_o property_n of_o the_o region_n and_o celestial_a appearance_n do_v depend_v 2._o that_o the_o magnitude_n of_o every_o region_n may_v have_v that_o proportion_n that_o they_o have_v in_o the_o earth_n itself_o 3._o that_o every_o place_n may_v have_v the_o same_o situation_n to_o the_o other_o mutual_o which_o they_o have_v in_o the_o earth_n itself_o of_o these_o three_o requisite_n all_o map_n or_o table_n ought_v exact_o to_o perform_v the_o first_o and_o for_o the_o most_o part_n exact_o do_v because_o they_o be_v make_v from_o the_o table_n of_o latitude_n and_o longitude_n of_o place_n neither_o do_v the_o 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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
author_n for_o the_o confirmation_n thereof_o do_v use_n they_o propose_v so_o obscure_o and_o confuse_o that_o they_o can_v compel_v or_o convince_v a_o obstinate_a and_o pertinacious_a defender_n of_o the_o contrary_a opinion_n we_o therefore_o as_o much_o as_o may_v be_v will_v most_o clear_o set_v forth_o those_o very_a opinion_n and_o examine_v they_o that_o the_o reader_n may_v have_v a_o distinct_a knowledge_n thereof_o round_o reason_n to_o prove_v the_o earth_n round_o first_o i_o reject_v the_o slight_a reason_n or_o argument_n which_o be_v probable_a or_o rather_o sophistical_a first_o the_o spheric_a figure_n be_v most_o capacious_a therefore_o the_o earth_n ought_v to_o have_v such_o a_o kind_n of_o figure_n second_o all_o the_o part_n of_o the_o earth_n tend_v to_o the_o same_o centre_n therefore_o all_o those_o part_n make_v a_o round_a figure_n three_o when_o as_o in_o the_o creation_n the_o water_n as_o yet_o be_v confuse_o mix_v with_o the_o earth_n without_o doubt_n the_o earth_n be_v moist_a and_o soft_a but_o the_o figure_n or_o shape_n of_o liquid_a thing_n be_v round_o or_o spherical_a therefore_o such_o also_o the_o figure_n of_o the_o earth_n remain_v after_o the_o separation_n of_o the_o moist_a from_o the_o dry_a these_o and_o the_o like_a argument_n be_v slight_v let_v we_o view_v and_o consider_v the_o strong_a and_o most_o solid_a there_o be_v but_o one_o argument_n of_o one_o and_o the_o first_o kind_n which_o be_v take_v à _fw-la priori_fw-la but_o the_o other_o two_o kind_n be_v take_v à _fw-la posteriori_fw-la to_o wit_n some_o argument_n be_v take_v from_o the_o celestial_a appearance_n some_o again_o from_o they_o which_o we_o either_o observe_v in_o the_o earth_n or_o in_o heaven_n as_o for_o the_o first_o argument_n conclude_v à _fw-la priori_fw-la it_o be_v take_v from_o the_o nature_n of_o water_n and_o this_o demonstration_n be_v wont_a to_o be_v take_v either_o from_o aristotle_n or_o archimedes_n aristotle_n in_o his_o second_o book_n de_fw-fr coelo_fw-la chap._n 5._o have_v propose_v his_o demonstration_n in_o these_o very_a word_n round_o the_o superficies_n of_o the_o water_n round_o it_o shall_v manifest_o appear_v that_o the_o superficies_n or_o surface_n of_o the_o water_n be_v round_o if_o we_o shall_v take_v the_o supposition_n that_o water_n of_o its_o own_o nature_n make_v its_o confluence_n always_o to_o a_o hollow_a place_n and_o that_o that_o place_n be_v more_o concavous_a which_o be_v near_o the_o centre_n therefore_o from_o the_o centre_n a_o let_v the_o strait_a line_n a_o b_o and_o a_o g_o be_v draw_v and_z from_z b_o unto_z g_z let_v the_o line_n b_o g_o be_v draw_v scheme_n see_v scheme_n unto_o which_o from_o a_o let_v a_o perpendicular_a line_n a_o d_o be_v draw_v into_o e._n it_o be_v manifest_a therefore_o that_o the_o line_n a_o d_o be_v less_o than_o the_o line_n a_o b_o and_z a_o g_z by_o the_o 18_o of_o the_o first_o book_n of_o euclid_n element_n geometrical_a therefore_o this_o place_n d_o be_v more_o concavous_a wherefore_o the_o water_n shall_v flow_v from_o b_o and_z g_z until_o the_o line_n a_o b_o a_o d_o a_o g_o may_v be_v equal_a but_o a_o e_o be_v equal_a to_o a_o b_o a_o g_o therefore_o it_o must_v needs_o be_v that_o the_o very_a water_n shall_v be_v in_o these_o line_n which_o be_v draw_v in_o the_o centre_n this_o part_n of_o the_o demonstration_n be_v clear_o know_v but_o a_o e_o etc._n etc._n make_v nothing_o for_o the_o demonstration_n but_o that_o line_n which_o touch_v they_o which_o be_v draw_v from_o the_o centre_n be_v the_o circumference_n therefore_o the_o superficies_n of_o the_o water_n which_o true_o be_v b_o e_o g_o be_v round_o note_v thing_n to_o be_v note_v this_o be_v aristotle_n demonstration_n in_o which_o beside_o the_o confuse_a and_o evil_a composure_n thereof_o these_o thing_n i_o observe_v first_o that_o it_o suppose_v some_o centre_n of_o the_o whole_a universe_n second_o that_o it_o take_v the_o place_n more_o or_o less_o bend_v down_o in_o regard_n of_o that_o centre_n for_o he_o which_o shall_v deny_v the_o shape_n or_o figure_n of_o the_o earth_n to_o be_v spherical_a will_v call_v these_o thing_n into_o question_n yet_o the_o first_o may_v be_v sufficient_o concern_v the_o centre_n of_o the_o universe_n prove_v or_o correct_v for_o we_o must_v say_v that_o either_o the_o star_n be_v wheel_v round_o about_o by_o a_o diurnal_a motion_n or_o that_o the_o earth_n be_v turn_v round_o about_o its_o own_o centre_n for_o this_o the_o apparent_a motion_n of_o the_o star_n force_v and_o cause_v if_o the_o star_n than_o that_o point_n about_o which_o they_o be_v turn_v shall_v be_v the_o centre_n of_o the_o universe_n if_o the_o earth_n than_o the_o middle_a point_n of_o the_o earth_n or_o that_o about_o which_o it_o be_v turn_v shall_v be_v take_v in_o the_o demonstration_n for_o the_o central_n point_n of_o aristotle_n but_o the_o chief_a difficulty_n lie_v in_o the_o second_o supposition_n to_o wit_n that_o the_o lesser_a or_o great_a declivity_n or_o bend_v downward_o aught_o to_o be_v consider_v in_o respect_n of_o that_o centre_n for_o he_o which_o will_v defend_v the_o superficies_n of_o the_o water_n to_o be_v plain_a and_o of_o another_o figure_n he_o will_v deny_v this_o supposition_n and_o will_v say_v that_o the_o declivity_n must_v be_v consider_v according_a to_o our_o sense_n to_o wit_n in_o respect_n of_o our_o horizontal_n plain_a according_a to_o which_o the_o earth_n with_o infinite_a space_n be_v extend_v into_o profundity_n or_o else_o he_o will_v define_v the_o declivity_n in_o another_o manner_n and_o thus_o this_o demonstration_n conclude_v nothing_o at_o all_o unless_o it_o be_v grant_v that_o the_o declivity_n of_o the_o place_n of_o the_o earth_n must_v be_v take_v in_o respect_n of_o that_o centre_n about_o which_o the_o daily_a apparent_a motion_n of_o the_o celestial_a body_n be_v perform_v which_o thing_n although_o it_o may_v be_v true_a and_o all_o other_o definition_n of_o declivity_n according_a to_o which_o the_o water_n may_v be_v move_v may_v also_o be_v confute_v yet_o notwithstanding_o it_o can_v scarce_o be_v admit_v for_o a_o principle_n see_v that_o it_o in_o a_o manner_n suppose_v the_o figure_n of_o the_o earth_n to_o be_v spherical_a aristotle_n archimedes_n his_o demonstration_n by_o some_o prefer_v before_o those_o of_o aristotle_n other_o therefore_o prefer_v archimedes_n his_o demonstration_n before_o this_o of_o aristotle_n which_o be_v find_v in_o his_o first_o book_n concern_v those_o thing_n that_o be_v carry_v in_o the_o water_n this_o indeed_o be_v more_o artificial_a than_o that_o of_o aristotle_n yet_o it_o be_v oppress_v with_o the_o same_o difficulty_n forasmuch_o as_o it_o suppose_v the_o spherical_a figure_n of_o the_o earth_n and_o its_o centre_n in_o respect_n of_o which_o it_o take_v the_o depression_n of_o the_o water_n we_o will_v bring_v hither_o some_o argument_n frame_v from_o those_o that_o be_v take_v from_o celestial_a appearance_n first_o let_v we_o conceive_v the_o meridian_n line_n of_o our_o place_n or_o of_o any_o point_n of_o b_o in_o the_o earth_n scheme_n see_v scheme_n or_o a_o section_n of_o the_o earth_n make_v in_o plane_n which_o through_o the_o pole_n of_o the_o world_n m_o n_n pass_v through_o a_o b_o c_o d_o this_o line_n be_v usual_o call_v the_o latitude_n of_o the_o earth_n and_o the_o line_n which_o be_v draw_v perpendicular_a to_o this_o be_v name_v the_o longitude_n of_o the_o earth_n or_o another_o plain_a parallel_n to_o the_o celestial_a equator_fw-la make_v in_o the_o earth_n the_o line_n e_o b_o f_o c._n i_o say_v as_o well_o the_o line_n a_o b_o c_o d_o as_o the_o line_n e_o b_o f_o c_o in_o the_o earth_n to_o be_v circular_a but_o it_o be_v a_o geometrical_a thorem_fw-la if_o any_o superficies_n according_a to_o one_o dimension_n be_v cut_v through_o any_o point_n and_o the_o section_n be_v make_v in_o the_o periphery_a or_o circumference_n of_o the_o circle_n then_o according_a to_o the_o other_o dimension_n through_o the_o same_o point_n the_o section_n be_v make_v in_o plain_a which_o be_v perpendicular_a to_o the_o former_a plain_n and_o the_o section_n again_o be_v make_v in_o the_o periphery_a of_o the_o circle_n that_o superficies_n be_v spherical_a therefore_o because_o we_o have_v take_v the_o point_n b_o in_o the_o superficies_n of_o the_o earth_n according_a to_o our_o own_o pleasure_n and_o have_v show_v the_o section_n a_o b_o c_o d_o and_o e_o b_o f_o c_o to_o be_v the_o periphery_n of_o the_o circle_n body_n the_o earth_n a_o spherical_a body_n therefore_o by_o the_o aforesaid_a theorem_n we_o conclude_v that_o the_o superficies_n of_o the_o earth_n be_v spherical_a and_o that_o the_o earth_n be_v a_o spherical_a body_n circular_a the_o section_n of_o the_o earth_n according_a to_o the_o dimension_n
command_v the_o great_a construction_n of_o ptolemy_n to_o be_v turn_v out_o of_o greek_a into_o the_o arabian_a language_n which_o be_v call_v by_o the_o arabian_n the_o almage_a of_o ptolemy_n this_o maimon_n i_o say_v have_v assemble_v together_o certain_a skilful_a mathematician_n command_v they_o that_o they_o shall_v search_v after_o the_o perimeter_n of_o the_o earth_n to_o perform_v which_o task_n they_o choose_v the_o field_n of_o mesopotamia_n and_o they_o under_o the_o same_o meridian_n proceed_v from_o the_o north_n to_o south_n until_o the_o elevation_n of_o the_o pole_n have_v decrease_v one_o degree_n find_v after_o a_o even_a level_n that_o the_o space_n or_o journey_n be_v fifty_o six_o or_o fifty_o six_o and_o a_o half_a from_o whence_o it_o be_v find_v that_o the_o perimeter_n according_a to_o they_o â—is_fw-la twenty_o thousand_o and_o sixty_o or_o twenty_o thousand_o three_o hundred_o and_o forty_o mile_n from_o that_o time_n even_o to_o our_o age_n no_o man_n have_v assay_v this_o but_o many_o arabian_n have_v use_v this_o dimension_n of_o their_o own_o mathematician_n latin_n the_o dimension_n of_o the_o earth_n by_o the_o latin_n but_o the_o latin_n when_o they_o begin_v to_o handle_v astronomy_n use_v that_o of_o 18000_o stadiums_n which_o ptolemy_n have_v use_v which_o make_v 324000_o italian_a mile_n or_o 5400_o german_a mile_n for_o 15_o german_n or_o 60_o italian_a mile_n be_v allot_v to_o one_o degree_n when_o as_o there_o ought_v to_o have_v be_v assign_v thereto_o 15_o and_o â—_o 8_o because_o about_o 38_o stadiums_n be_v give_v to_o one_o german_a mile_n and_o so_o the_o perimeter_n shall_v be_v 5625_o german_a mile_n but_o about_o thirty_o year_n ago_o snellius_n a_o famous_a mathematician_n snellius_n it_o be_v dimension_n according_a to_o snellius_n professor_n of_o leyden_n observe_v that_o usual_a perimeter_n of_o the_o earth_n or_o the_o magnitude_n of_o one_o degree_n define_v in_o 15_o mile_n to_o depend_v on_o no_o certain_a demonstration_n but_o to_o be_v uncertain_a therefore_o with_o very_o great_a industry_n he_o set_v upon_o this_o dimension_n and_o happy_o finish_v it_o demonstrate_v the_o magnitude_n of_o one_o degree_n in_o the_o earth_n to_o be_v 28500_o perch_n or_o pole_n every_o one_o of_o which_o contain_v 12_o rhindlandish_a foot_n or_o 19_o dutch_a mile_n and_o the_o whole_a perimeter_n to_o be_v 8640_o mile_n but_o he_o define_v a_o mile_n with_o 1500_o pole_n or_o 18000_o rhindlandish_a foot_n we_o will_v now_o speak_v concern_v the_o manner_n of_o measure_v the_o earth_n but_o indeed_o this_o invention_n depend_v on_o the_o figure_n of_o the_o earth_n which_o in_o the_o forego_n chapter_n we_o have_v prove_v to_o be_v spherical_a for_o indeed_o we_o conceive_v the_o earth_n to_o be_v cut_v by_o a_o plain_a pass_v through_o the_o centre_n this_o section_n or_o division_n make_v the_o great_a circle_n of_o the_o earth_n for_o a_o sphere_n be_v cut_v in_o any_o manner_n the_o section_n be_v make_v a_o circle_n but_o if_o it_o be_v cut_v through_o the_o centre_n it_o shall_v be_v the_o great_a circle_n and_o therefore_o the_o periphery_a of_o this_o circle_n in_o the_o superficies_n of_o the_o earth_n shall_v be_v the_o circumference_n circuit_n and_o perimeter_n of_o the_o earth_n and_o this_o work_n of_o measure_v begin_v from_o the_o magnitude_n of_o this_o periphery_a degree_n the_o circumference_n of_o the_o sphere_n divide_v into_o 360_o degree_n because_o therefore_o this_o periphery_a or_o circumference_n as_o other_o be_v be_v divide_v in_o the_o mind_n into_o three_o hundred_o and_o sixty_o degree_n as_o have_v be_v say_v in_o the_o second_o chap._n but_o indeed_o we_o can_v perform_v the_o magnitude_n of_o the_o whole_a periphery_n and_o therefore_o the_o problem_n be_v thither_o reduce_v that_o we_o may_v find_v out_o the_o magnitude_n of_o one_o degree_n or_o other_o part_n in_o the_o know_a measure_n for_o example_n the_o magnitude_n of_o half_a a_o degree_n the_o necessity_n of_o which_o also_o meet_v in_o other_o problem_n and_o we_o take_v the_o periphery_a of_o the_o earth_n for_o the_o most_o part_n to_o be_v that_o of_o the_o meridian_n circle_n because_o this_o be_v more_o easy_o and_o with_o less_o occasion_n of_o error_n determine_v by_o our_o own_o place_n and_o by_o the_o north_n or_o polar_a star_n or_o other_o mean_n which_o we_o will_v declare_v in_o the_o three_o and_o twenty_o chapter_n the_o first_o mean_a or_o way_n which_o the_o arabian_n and_o other_o mathematician_n have_v use_v let_v the_o horizon_n therefore_o of_o our_o terrestrial_a meridian_n which_o lie_v just_a under_o the_o celestial_a a_o bed_n and_o be_v concentrical_a thereto_o be_v h_n h_o r_z ss_z let_v the_o periphery_n a_o b_o c_o d_o r_o the_o centre_n of_o the_o earth_n our_o place_n b_o the_o vertex_fw-la scheme_n see_v scheme_n or_o supreme_a point_n over_o our_o head_n the_o pole_n of_o the_o earth_n a_o lie_v under_o the_o celestial_a the_o elevation_n of_o the_o pole_n above_o the_o horizon_n shall_v be_v a_o h_n a_o h_o let_v we_o now_o take_v another_o place_n in_o the_o same_o meridian_n a_o b_o c_o d_o or_o g_o lie_v under_o the_o same_o a_o b_o c_o d_o the_o vertex_fw-la g_o the_o horizon_n f_o f_o r_o t_o t._n let_v here_o now_o the_o elevation_n of_o the_o pole_n be_v exact_o observe_v in_o the_o place_n b_o viz._n a_o h_z or_o a_o h_n also_o of_o the_o place_n g_o to_o wit_n f_o a_o or_o f_o a_o and_o let_v f_o a_o be_v take_v away_o from_o h_n a_o and_o the_o remainder_n be_v h_n f_o to_o which_o the_o arch_n b_o g_o intercept_v between_o the_o place_n be_v equal_a after_o that_o the_o interval_n or_o space_n between_o b_o g_z must_v be_v measure_v accurate_o in_o a_o certain_a measure_n for_o example_n how_o many_o perch_n or_o pole_n it_o may_v contain_v or_o how_o many_o mile_n for_o these_o shall_v be_v correspondent_a to_o the_o arch_n b_o g._n and_o by_o the_o golden_a rule_n as_o b_o g_z be_v to_z a_o b_o g_o c_o d_o the_o 360_o degree_n so_o the_o space_n or_o interval_n find_v out_o or_o the_o perch_n or_o mile_n be_v to_o the_o perch_n or_o mile_n of_o the_o whole_a perimeter_n a_o b_o g_o c_o d_o or_o as_o the_o arch_n b_o g_o be_v to_o one_o degree_n so_o the_o perch_n or_o mile_n find_v be_v to_o the_o perch_n or_o mile_n which_o be_v due_a to_o one_o degree_n note_v if_o your_o pleasure_n be_v not_o to_o measure_v the_o interval_n b_o g_o thus_o but_o to_o follow_v the_o vulgar_a determination_n then_o according_a to_o that_o way_n the_o quantity_n must_v be_v determine_v as_o for_o example_n that_o to_o 1_o degree_n 15_o such_o mile_n answer_v as_o between_z b_o g_z may_v be_v 10_o etc._n etc._n london_n elevation_n of_o the_o pole_n at_o london_n example_n b_o london_z where_o the_o elevation_n of_o the_o pole_n a_o h_n a_o h_o be_v 51_o degree_n 32_o minute_n let_v g_o be_v hartford_n lie_v under_o the_o same_o meridian_n with_o london_n the_o elevation_n of_o who_o pole_n a_o f_z a_o f_z be_v 51_o degree_n 54_o minute_n therefore_o f_z h_z or_o b_o g_z be_v 29_o minute_n but_o the_o distance_n between_o london_n and_o hartford_n be_v 20_o english_a mile_n or_o 13875_o rhinlandish_a perch_n of_o 12_o foot_n therefore_o as_o 29_o minute_n be_v to_o 60_o minute_n so_o 9_o ¼_n to_o 19_o holland_n mile_n therefore_o 19_o holland_n mile_n make_v one_o degree_n in_o the_o circumference_n of_o the_o earth_n or_o the_o interval_n b_o g_o be_v account_v to_o be_v 7_o ¼_n german_a mile_n a_o german_a mile_n be_v reckon_v to_o be_v 1900_o rhinlandish_a perch_n therefore_o let_v it_o be_v wrought_v thus_o as_o 29_o part_n be_v to_o 60_o prague_n the_o elevation_n of_o the_o pole_n at_o prague_n so_o be_v 7_o ¼_n to_o 15_o such_o german_a mile_n so_o at_o prague_n the_o elevation_n of_o the_o pole_n be_v 50_o degree_n and_o 6_o minute_n at_o lincium_n it_o be_v 48_o degree_n and_o 16_o minute_n the_o difference_n of_o b_o g_o shall_v be_v one_o degree_n and_o 50_o minute_n and_o it_o be_v think_v to_o be_v distant_a 26_o german_a mile_n therefore_o the_o perimeter_n be_v 5105_o mile_n and_o the_o whole_a circuit_n of_o the_o earth_n be_v 5400_o mile_n the_o second_o manner_n of_o eratosthenes_n scheme_n eratosthenes_n manner_n use_v about_o the_o dimension_n and_o magnitude_n of_o the_o earth_n see_v scheme_n let_v there_o again_o be_v two_o place_n of_o the_o earth_n in_o the_o same_o meridian_n let_v b_o be_v the_o city_n alexandria_n in_o egypt_n let_v g_o be_v syene_n another_o city_n of_o egypt_n under_o the_o tropic_a of_o cancer_n let_v now_o the_o same_o place_n in_o one_o and_o the_o same_o day_n in_o the_o full_a sothe_v of_o the_o sun_n when_o he_o come_v into_o the_o meridian_n line_n
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
moon_n from_o the_o earth_n it_o be_v worthy_a observation_n that_o 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 as_o well_o in_o assign_v the_o distance_n of_o the_o planet_n from_o the_o earth_n and_o from_o themselves_o as_o in_o number_v and_o compute_v their_o magnitude_n so_o we_o say_v that_o the_o sun_n be_v distant_a from_o the_o earth_n ubout_fw-fr 1200_o half_a diameter_n the_o moon_n 40_o etc._n etc._n but_o see_v in_o geography_n we_o do_v not_o only_o consider_v the_o great_a circle_n of_o the_o earth_n as_o the_o equator_fw-la etc._n etc._n but_o also_o the_o parallel_n of_o the_o equator_fw-la therefore_o we_o must_v likewise_o determine_v how_o many_o mile_n or_o perch_n answer_v one_o degree_n in_o every_o parallel_n we_o have_v take_v the_o account_v of_o the_o perch_v out_o of_o snellius_n but_o i_o myself_o have_v reckon_v up_o the_o mile_n to_o wit_n 1900_o perch_n for_o a_o german_a mile_n 1500_o for_o a_o belgic_a or_o holland_n mile_n 475_o for_o a_o italian_a mile_n a_o table_n of_o the_o quantity_n of_o one_o degree_n in_o every_o parallel_n the_o degree_n in_o which_o the_o parallel_n be_v distant_a from_o the_o equator_fw-la or_o the_o elevation_n of_o the_o pole_n of_o the_o parallel_n equator_fw-la of_o the_o perch_n of_o one_o degree_n holland_n mile_n german_n italian_n the_o latitude_n of_o a_o perch_n of_o one_o degree_n holland_n mile_n german_n italian_n  _fw-fr  _fw-fr mil._n per._n mile_n min._n mile_n min._n  _fw-fr  _fw-fr mil._n per._n mile_n min._n mile_n min._n  _fw-fr 28500_o 19_o 0_o 15._o 0_o 60._o 0_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 1_o 28496_o 18._o 1496_o 14._o 59_o 59_o 56_o 46_o 19798_o 13._o 298_o 10._o 25_o 41._o 40_o 2_o 28483_o 18._o 1483_o 14._o 59_o 59_o 55_o 47_o 19437_o 13._o 0_o â—0_n 14_o 41._o 0_o 3_o â—8461_n 18._o 1461_o 14._o 58_o 59_o 52_o 48_o 19070_o 12._o 1070_o 10._o 2_o 40._o 8_o 4_o 28431_o 18._o 1431_o 14._o 57_o 59_o 50_o 49_o 18698_o 12._o 698_o 9_o 50_o 39_o 20_o 5_o 28392_o 18._o 1392_o 14._o 56_o 59_o 46_o 50_o 18319_o 12._o 319_o 9_o 38_o 38._o 32_o 6_o 28344_o 18._o 1344_o 14._o 55_o 59_o 40_o 51_o 17936_o 11._o 1436_o 9_o 26_o 37._o 44_o 7_o 28288_o 18._o 1288_o 14._o 53_o 59_o 37_o 52_o 17546_o 11._o 1046_o 9_o 14_o 37._o 0_o 8_o 28223_o 18._o 1223_o 14._o 51_o 59_o 24_o 53_o 17152_o 11._o 652_o 9_o 2_o 36._o 8_o 9_o 28149_o 18._o 1149_o 14._o 48_o 59_o 12_o 54_o 16752_o 11._o 252_o 8._o 49_o 35._o 26_o 10_o 28067_o 18._o 1067_o 14._o 46_o 59_o 4_o 55_o 16347_o 10._o 1347_o 8._o 36_o 34._o 24_o 11_o 27976_o 18._o 976_o 14._o 43_o 58._o 52_o 56_o 15932_o 10._o 937_o 8._o 23_o 33._o 32_o 12_o 27877_o 18._o 877_o 14._o 40_o 58._o 40_o 57_o 15522_o 10._o 522_o 8._o 10_o 32._o 40_o 13_o 27769_o 18._o 769_o 14._o 37_o 58._o 28_o 58_o 15103_o 10._o 103_o 7._o 57_o 31._o 40_o 14_o 27653_o 18._o 653_o 14._o 33_o 58._o 12_o 59_o 14671_o 9_o 1179_o 7._o 44_o 31._o 0_o 15_o 27529_o 18._o 529_o 14._o 29_o 50._o  _fw-fr 60_o 14250_o 9_o 750_o 7._o 30_o 30._o 0_o 16_o 27653_o 18._o 453_o 14._o 25_o 57_o 40_o 61_o 13817_o 9_o 317_o 7._o 16_o 29._o 4_o 17_o 27255_o 18._o 255_o 14._o 21_o 57_o 20_o 62_o 13380_o 8._o 1380_o 7._o 2_o 28._o 8_o 18_o 27105_o 18._o 105_o 14._o 16_o 57_o 4_o 63_o 12939_o 8._o 939_o 6._o 48_o 27._o 12_o 19_o 26947_o 18._o 0_o 14._o 11_o 56._o 44_o 64_o 12494_o 8._o 994_o 6._o 34_o 26._o 16_o 20_o 26781_o 18._o 0_o 14._o 6_o 56._o 24_o 65_o 12045_o 8._o 45_o 6._o 20_o 25._o 20_o 21_o 26607_o 17._o 1107_o 14._o 0_o 56._o 0_o 66_o 11592_o 7._o 1092_o 6._o 6_o 24._o 24._o 22_o 26423_o 17._o 925_o 13._o 54_o 55._o 36_o 67_o 11136_o 7._o 636_o 5._o 52_o 23._o 28_o 23_o 26234_o 17._o 734_o â—3_n 48_o 55._o 12_o 68_o 10676_o 7._o 176_o 5._o 38_o 22._o 32_o 24_o 26036_o 17._o 536_o â—3_n 42_o 54._o 48_o 69_o 10213_o 6._o 1213_o 5._o 23_o 21._o 32_o 25_o 25830_o 17._o 330_o â—3_n 36_o 54._o 24_o 70_o 9748_o 6._o 748_o 5._o 8_o 20_o 32_o 26_o 25616_o 17._o 116_o 13._o 29_o 54._o 0_o 71_o 9279_o 6._o 279_o 4._o 53_o 19_o 32_o 27_o 25394_o 16._o 1394_o 13._o 22_o 53._o 28_o 72_o 8807_o 5._o 1307_o 4._o 38_o 18._o 32_o 28_o 25164_o 16._o 1164_o 13._o 15_o 53._o 0_o 73_o 8333_o 5._o 933_o 4._o 23_o 17._o 32_o 29_o 24927_o 16._o 927_o 13._o 7_o 52._o 28_o 74_o 7846_o 5._o 346_o 4._o 8_o 16._o 32_o 30_o â—4681_n 16._o 681_o 13._o 59_o 51._o 56_o 75_o 7376_o 4._o 1376_o 3._o 53_o 15._o 32_o 31_o 24429_o 10._o 429_o 12._o 51_o 51._o 24_o 76_o 6895_o 4._o 895_o 3._o 38_o 14_o 32_o 32_o 24169_o 16._o 169_o 12._o 43_o 50._o 52_o 77_o 6411_o 4._o 411_o 3._o 23_o 13._o 32_o 33_o 23902_o 15._o 1402_o 12._o 35_o 50._o 20_o 78_o 5925_o 3._o 1425_o 3._o 8_o 12._o 32_o 34_o 23628_o 15._o 1128_o 12._o 26_o 49._o 44_o 79_o 5438_o 3._o 938_o 2._o 52_o 11._o 28_o 35_o 23346_o 15._o 846_o 12._o 17_o 49._o 8_o 80_o 4949_o 3._o 449_o 2._o 36_o 10._o 24_o 36_o 23057_o 15._o 557_o 12._o 8_o 48._o 32_o 81_o 4458_o 2._o 1458_o 2._o 20_o 9_o 20_o 37_o 22761_o 15._o 261_o 11._o 59_o 47._o 56_o 82_o 3966_o 2._o 966_o 2._o 5_o 8._o 20_o 38_o 22458_o 15._o 0_o 11._o 49_o 47._o 16_o 83_o 3473_o 2._o 473_o 1._o 50_o 7._o 20_o 39_o 22149_o 14._o 1149_o 11._o 39_o 46._o 36_o 84_o 2979_o 1._o 1479_o 1._o 34_o 6._o 12_o 40_o 21832_o 14._o 832_o 11._o 29_o 46._o 0_o 85_o 2484_o 1._o 984_o 1._o 18_o 5._o 12_o 41_o 21509_o 14._o 509_o 11._o 19_o 45._o 16_o 86_o 1988_o 1._o 488_o 1._o 3_o 4._o 12_o 42_o 21180_o 14._o 180_o 11._o 9_o 44._o 36_o 82_o 1492_o 0._o 1492_o 0._o 47_o 3._o 12_o 43_o 20843_o 13._o 1343_o 10._o 58_o 43._o 52_o 88_o 995_o 0._o 995_o 0._o 31_o 2._o 4_o 44_o 20501_o 13._o 1001_o 10._o 47_o 43._o 8_o 89_o 497_o 0._o 497_o 0._o 16_o 1._o 4_o 45_o 20152_o 13._o 652_o 10._o 36_o 42._o 24_o 90_o 0_o 0._o 0_o 0._o 0_o 0._o 0_o chap._n v._o appearance_n the_o pythagorical_a motion_n of_o the_o earth_n be_v the_o cause_n of_o many_o celestial_a appearance_n the_o pythagorical_a motion_n or_o turn_v the_o earth_n about_o as_o with_o a_o wheel_n not_o that_o quake_a and_o shake_v be_v the_o cause_n of_o very_a many_o celestial_a appearance_n according_a to_o the_o copernican_n opinion_n see_v that_o without_o it_o every_o place_n will_v have_v a_o perpetual_a constancy_n of_o these_o but_o indeed_o there_o be_v no_o property_n or_o quality_n of_o the_o earth_n concern_v which_o there_o can_v be_v great_a disputation_n fith_o that_o not_o very_o long_o ago_o it_o have_v suffer_v the_o censure_n of_o the_o church_n of_o rome_n yet_o because_o to_o many_o man_n it_o seem_v likely_a to_o be_v true_a that_o such_o a_o motion_n of_o the_o earth_n may_v be_v give_v therefore_o i_o will_v endeavour_v brief_o to_o unfold_v the_o same_o appearance_n the_o motion_n of_o the_o sun_n moon_n and_o star_n and_o their_o appearance_n it_o be_v not_o unknown_a to_o any_o of_o the_o very_a vulgar_a sort_n that_o the_o sun_n moon_n and_o all_o the_o star_n of_o heaven_n appear_v every_o day_n that_o be_v in_o the_o space_n of_o 24_o hour_n to_o be_v move_v from_o east_n to_o west_n and_o common_o to_o return_v to_o the_o same_o place_n of_o heaven_n it_o must_v therefore_o needs_o be_v that_o either_o they_o be_v real_o move_v or_o that_o we_o be_v move_v and_o that_o our_o motion_n or_o move_a be_v impute_v to_o the_o star_n for_o if_o two_o thing_n change_v their_o dâ—stance_n one_o of_o they_o at_o least_o be_v move_v which_o principle_n be_v most_o manifest_a etc._n the_o opinion_n of_o the_o ptolomaians_n and_o pythagorean_n concern_v the_o motion_n of_o the_o star_n etc._n etc._n that_o the_o earth_n stand_v still_o and_o that_o the_o star_n with_o the_o heaven_n be_v move_v be_v and_o be_v yet_o the_o common_a opinion_n of_o astronomer_n which_o be_v call_v ptolomaians_n or_o of_o such_o as_o follow_v the_o doctrine_n of_o ptolemy_n yet_o the_o pythagorean_n long_v ago_o maintain_v that_o the_o star_n hold_v their_o place_n constant_o without_o budge_v from_o thence_o and_o that_o the_o earth_n be_v roll_v and_o wheel_v about_o its_o centre_n one_o of_o who_o be_v the_o famous_a aristarchus_n of_o samos_n who_o for_o his_o defend_v this_o opinion_n be_v by_o his_o adversary_n accuse_v of_o profane_v and_o violate_v religion_n before_o the_o most_o famous_a and_o severe_a bench_n of_o the_o areopagite_n but_o he_o be_v nevertheless_o quit_v by_o the_o sentence_n of_o those_o
five_o mile_n distance_n four_o some_o gulf_n or_o whirlpool_n be_v find_v in_o the_o sea_n five_o earthquake_n do_v also_o prove_v the_o be_v of_o cavity_n under_o the_o earth_n six_o some_o river_n bury_v themselves_o under_o the_o earth_n as_o niger_n tigris_n etc._n etc._n seven_o salt-spring_n which_o without_o doubt_n for_o the_o great_a part_n spring_n and_o flow_v from_o the_o sea_n be_v find_v in_o many_o place_n eight_o so_o in_o many_o place_n the_o ground_n at_o the_o entrance_n of_o man_n walk_v tremble_v and_o shake_v as_o about_o the_o abbey_n of_o st._n omer_n in_o flanders_n in_o the_o province_n of_o brabant_n die_v peel_n proposition_n iu._n the_o superficies_n or_o surface_n of_o the_o land_n be_v continual_a but_o that_o of_o the_o water_n be_v not_o so_o indeed_o the_o superficies_n of_o the_o earth_n or_o land_n appear_v out_o above_o the_o water_n be_v continue_v or_o always_o the_o same_o to_o the_o superficies_n of_o the_o channel_n of_o the_o sea_n and_o this_o of_o the_o sea_n again_o be_v continue_v to_o the_o other_o part_n of_o the_o land_n appear_v above_o river_n one_o continual_a superficies_n of_o the_o ocean_n bays_n and_o river_n so_o there_o be_v one_o continual_a superficies_n of_o the_o ocean_n the_o bays_n and_o river_n but_o not_o of_o all_o water_n because_o there_o be_v some_o lake_n which_o be_v not_o join_v with_o the_o ocean_n in_o the_o superficies_n as_o the_o lake_n parime_n and_o the_o caspian_a sea_n proposition_n v._o it_o be_v certain_a how_o or_o in_o what_o manner_n the_o part_n of_o the_o earth_n which_o be_v remove_v from_o the_o surface_n that_o be_v from_o our_o habitation_n towards_o the_o centre_n some_o man_n think_v that_o the_o water_n be_v in_o the_o bottom_n about_o the_o centre_n of_o the_o earth_n loadstone_n the_o body_n of_o the_o earth_n within_o according_a to_o gilbert_n a_o english_a man_n be_v a_o hard_a loadstone_n but_o it_o be_v most_o likely_a true_a that_o the_o earth_n occupy_v that_o place_n gilbert_n a_o english_a man_n be_v of_o opinion_n that_o the_o body_n of_o the_o earth_n within_o be_v nothing_o else_o but_o a_o most_o hard_a loadstone_n but_o that_o those_o part_n to_o which_o man_n have_v admittance_n by_o dig_v and_o in_o which_o herb_n grow_v and_o we_o also_o live_v be_v as_o it_o be_v the_o shell_n or_o crust_n of_o the_o earth_n wherein_o continual_a generation_n and_o corruption_n be_v make_v scheme_n make_v see_v fig._n but_o cartesius_n be_v of_o a_o different_a opinion_n see_v scheme_n cartesius_n his_o opinion_n be_v not_o much_o different_a from_o this_o who_o think_v that_o there_o be_v three_o region_n or_o part_n of_o divers_a substance_n in_o the_o body_n of_o the_o earth_n the_o most_o inward_a region_n of_o the_o earth_n he_o deem_v to_o be_v about_o the_o centre_n thereof_o the_o second_o he_o judge_v to_o be_v thick_a and_o dusky_a of_o very_o small_a part_n the_o three_o he_o think_v wherein_o man_n be_v employ_v to_o be_v make_v up_o of_o little_a parcel_n not_o well_o cleave_v together_o but_o indeed_o touch_v this_o thing_n there_o can_v scarce_o any_o certainty_n be_v affirm_v it_o be_v manifest_a by_o the_o hotbath_n that_o in_o very_a many_o place_n under_o the_o earth_n fire_n and_o fume_n be_v lift_v up_o from_o sulphur_n proposition_n vi_o the_o consistency_n or_o stand_v and_o fast_o cleave_v together_o of_o the_o earth_n be_v from_o salt_n salt_n in_o all_o kind_n of_o earth_n may_v be_v find_v a_o certain_a kind_n of_o salt_n the_o artificial_a resolve_v of_o the_o part_n of_o the_o earth_n show_v that_o in_o all_o earth_n may_v be_v find_v a_o certain_a kind_n of_o salt_n and_o so_o much_o the_o more_o as_o the_o hard_a the_o body_n be_v a_o few_o oily_a one_o be_v except_v as_o in_o metal_n stone_n etc._n etc._n and_o that_o the_o concretion_n or_o hard_o grow_v together_o of_o all_o thing_n be_v by_o reason_n of_o salt_n be_v manifest_a by_o stone_n which_o we_o may_v by_o art_n make_v very_o hard_a with_o salt_n burr_n if_o you_o separate_v the_o salt_n from_o the_o earth_n she_o will_v no_o long_o cleave_v or_o stick_v together_o but_o will_v be_v a_o powder_n neither_o can_v it_o be_v reduce_v to_o hardness_n without_o the_o admixtion_n of_o salt_n thereto_o proposition_n vii_o the_o kind_n of_o earth_n be_v divers_a way_n mix_v together_o in_o the_o earth_n mine_n of_o metal_n find_v in_o mine_n thus_o in_o mine_n be_v find_v small_a piece_n of_o gold_n silver_n lead_v etc._n etc._n not_o heap_v together_o and_o join_v apart_o from_o other_o but_o both_o mix_v among_o themselves_o and_o also_o with_o unprofitable_a earth_n according_a to_o the_o least_o part_n that_o artificer_n not_o at_o the_o first_o sight_n but_o by_o divers_a sign_n do_v find_v out_o what_o may_v be_v contain_v in_o any_o metalline_a earth_n in_o the_o same_o manner_n in_o the_o field_n sand_n be_v mix_v with_o clay_n or_o loam_n lime_n salt_n etc._n etc._n amsterdam_n of_o the_o different_a sort_n of_o earth_n as_o do_v appear_v by_o the_o well_o dig_v at_o amsterdam_n when_o as_o on_o a_o certain_a time_n at_o amsterdam_n for_o make_v a_o well_o the_o earth_n be_v dig_v out_o even_o to_o the_o depth_n of_o 232_o foot_n these_o sort_n of_o earth_n be_v show_v to_o the_o beholder_n viz._n of_o garden-earth_n 7_o foot_n of_o black-earth_n fit_v for_o fire_n which_o be_v call_v peat_n 9_o foot_n of_o soft-clay_n 9_o foot_n of_o sand_n 8_o foot_n of_o earth_n 4_o foot_n of_o clay_n 10_o foot_n of_o earth_n 4_o foot_n of_o sand_n upon_o which_o the_o house_n of_o amsterdam_n be_v wont_a to_o be_v ram_v and_o pave_v 10_o foot_n of_o clay_n 2_o foot_n of_o white-loam_n 4_o foot_n of_o dry-earth_n 5_o foot_n of_o muddy_a 1_o foot_n of_o sand_n 14_o foot_n of_o sandy-clay_n 3_o foot_n of_o sand_n mix_v with_o clay_n 5_o foot_n of_o sand_n mix_v with_o sea-fish_n shell_n 4_o foot_n than_o a_o bottom_n of_o clay_n to_o the_o depth_n of_o 102_o foot_n and_o last_o of_o loam_n 31_o foot_n where_o the_o dig_v cease_v and_o they_o come_v to_o water_n the_o figure_n of_o which_o see_v among_o the_o scheme_n proposition_n viii_o the_o cavity_n of_o the_o earth_n and_o as_o well_o the_o outward_a disposition_n thereof_o and_o the_o position_n of_o its_o part_n be_v not_o perpetual_o the_o same_o but_o be_v at_o divers_a time_n divers_a substance_n the_o water_n of_o the_o seamake_v divers_a change_n and_o ruin_n in_o the_o earth_n where_o likewise_o lie_v hide_v spirit_n and_o sulphureous_a substance_n indeed_o not_o only_o the_o water_n of_o the_o sea_n make_v divers_a change_n and_o ruin_n in_o the_o part_n of_o the_o earth_n whilst_o certain_a hole_n be_v stop_v up_o some_o be_v make_v more_o broad_a but_o also_o spirit_n and_o sulphury_a substance_n lie_v hide_v here_o and_o there_o in_o the_o earth_n when_o they_o begin_v to_o increase_v and_o to_o be_v resolve_v into_o vapour_n do_v impetuous_o shake_v and_o thrust_v forward_o the_o part_n of_o the_o earth_n as_o it_o be_v manifest_a by_o earthquake_n and_o it_o be_v likely_a that_o such_o like_a motion_n be_v make_v in_o the_o interior_a part_n and_o bowel_n of_o the_o earth_n the_o great_a part_n of_o which_o we_o feel_v not_o neither_o perceive_v but_o we_o will_v speak_v of_o the_o mutual_a change_n of_o the_o water_n and_o earth_n in_o the_o superficies_n of_o the_o earth_n in_o the_o eighteen_o chapter_n the_o earth_n be_v divide_v into_o land_n and_o water_n the_o superficies_n of_o the_o earth_n extant_a out_o of_o the_o water_n by_o the_o interflux_n of_o the_o sea_n be_v distinguish_v into_o these_o four_o part_n 1._o into_o great_a continent_n or_o great_a island_n of_o which_o four_o be_v reckon_v by_o we_o 1._o the_o old_a world_n who_o part_n be_v asia_n africa_n and_o europe_n the_o bound_n of_o this_o continent_n be_v on_o the_o north_n the_o freeze_a and_o tartarian_a ocean_n on_o the_o east_n the_o pacifick_n and_o indian_a ocean_n on_o the_o south_n the_o southern_a ocean_n on_o the_o west_n the_o atlantic_a ocean_n 2._o the_o new_a world_n or_o america_n who_o part_n be_v meridionalis_fw-la septentrionalis_n the_o bound_n of_o it_o be_v on_o the_o north_n davis_n streights_n on_o the_o east_n the_o atlantic_a ocean_n on_o the_o south_n the_o pacifick_n ocean_n on_o the_o west_n the_o strait_n of_o magellan_n 3._o the_o polary_a north-land_n or_o greenland_n be_v every_o where_o encompass_v by_o the_o sea_n and_o streights_n 4._o the_o south-land_n and_o land_n of_o magellan_n yet_o undiscovered_a 2._o into_o peninsulas_fw-la or_o chersonesus_n which_o be_v part_n of_o those_o continent_n round_o who_o latitude_n and_o longitude_n be_v equal_a about_o africa_n itself_o peloponesus_fw-la the_o chersonesus_n of_o grecia_n chersonesus_n taurica_n or_o tartary_n
the_o air_n and_o a_o pressure_n towards_o the_o earth_n therefore_o the_o air_n be_v force_v to_o the_o sea_n endeavour_v to_o drive_v it_o from_o its_o place_n and_o by_o reason_n of_o the_o sea_n be_v fluid_a and_o not_o able_a to_o resist_v the_o force_a air_n therefore_o it_o be_v move_v from_o its_o place_n towards_o the_o place_n of_o the_o opposite_a quarter_n and_o force_v another_o water_n and_o this_o another_o and_o so_o on_o now_o see_v that_o there_o be_v always_o some_o wind_n in_o the_o air_n sometime_o in_o this_o place_n and_o sometime_o in_o that_o and_o sometime_o diverse_a in_o divers_a place_n at_o one_o and_o the_o same_o time_n thence_o it_o follow_v that_o there_o be_v certain_a contingent_a motion_n always_o in_o the_o sea_n which_o be_v more_o discernible_a in_o the_o part_n near_o the_o wind_n and_o therefore_o the_o rather_o by_o reason_n that_o the_o sea_n do_v most_o easy_o receive_v a_o impression_n because_o it_o be_v fluid_a proposition_n vii_o the_o general_a motion_n of_o the_o sea_n be_v twofold_a one_o continual_o from_o the_o east_n to_o the_o west_n the_o other_o compose_v of_o two_o contrary_a motion_n which_o be_v term_v the_o flux_n and_o reflux_n of_o the_o sea_n in_o which_o the_o sea_n at_o certain_a hour_n flow_v to_o the_o shore_n and_o in_o certain_a other_o flow_v back_o again_o we_o shall_v first_o treat_v of_o the_o first_o twofold_a the_o motion_n of_o the_o sea_n twofold_a that_o the_o sea_n move_v from_o the_o east_n to_o the_o west_n continual_o be_v chief_o prove_v from_o the_o motion_n of_o that_o sea_n which_o lie_v in_o the_o torrid_a zone_n between_o the_o tropic_n for_o because_o the_o motion_n be_v more_o strong_a hence_o it_o be_v less_o hinder_v by_o other_o motion_n this_o motion_n of_o the_o sea_n be_v manifest_o find_v by_o those_o that_o sail_n from_o india_n to_o madagascar_n and_o africa_n also_o in_o the_o pacifick_n ocean_n between_o new_a spain_n china_n and_o the_o moluccoe_n also_o in_o the_o ocean_n between_o africa_n and_o brasil_n so_o through_o the_o strait_n of_o magellan_n the_o sea_n be_v carry_v from_o the_o east_n to_o the_o west_n with_o a_o vehement_a motion_n so_o through_o the_o streights_n manillan_n through_o channel_n between_o the_o isle_n maldives_n the_o motion_n of_o the_o sea_n carry_v ship_n from_o the_o east_n the_o sea_n glide_v impetuous_o between_o cuba_n and_o jucatan_n into_o the_o gulf_n of_o mexico_n and_o flow_v out_o into_o cuba_n and_o florida_n at_o the_o gulf_n of_o paria_fw-la there_o be_v a_o violent_a influx_n so_o that_o that_o gulf_n be_v term_v os_fw-la draconis_fw-la the_o dragon_n mouth_n famous_a also_o be_v the_o flux_n at_o the_o land_n of_o canada_n from_o the_o tartarian_a ocean_n the_o sea_n move_v through_o the_o strait_n of_o nova_n zembla_n and_o waigat_n strait_n which_o be_v prove_v both_o from_o the_o very_a motion_n itself_o and_o also_o from_o the_o abundance_n of_o ice_n which_o the_o tartarian_a ocean_n cast_v up_o at_o the_o strait_n of_o zembla_n and_o at_o the_o northern_a shore_n of_o america_n in_o the_o pacifick_n ocean_n the_o motion_n be_v towards_o the_o straight_a anian_a also_o from_o japan_n the_o sea_n be_v move_v towards_o china_n so_o in_o the_o straight_a manillan_n the_o motion_n be_v from_o east_n to_o west_n so_o also_o in_o the_o straight_a java_n and_o when_o the_o atlantic_a ocean_n be_v move_v towards_o the_o coast_n of_o america_n the_o contrary_a be_v find_v in_o the_o pacifick_n ocean_n for_o this_o be_v move_v from_o the_o shore_n which_o be_v the_o most_o conspicuous_a at_o cabo_n dez_fw-fr correntes_fw-la between_o panama_n and_o lima._n proposition_n viii_o the_o wind_n oftentimes_o change_v the_o general_a motion_n of_o the_o sea_n especial_o those_o fix_a wind_n which_o we_o shall_v show_v to_o be_v term_v motion_n in_o the_o xxi_o chap._n wind_n the_o motion_n of_o the_o sea_n ofttimes_o change_v by_o the_o wind_n for_o because_o that_o most_o of_o these_o do_v blow_n from_o the_o south_n and_o north_n or_o from_o the_o collateral_a quarter_n of_o these_o thence_o it_o come_v to_o pass_v that_o the_o sea_n by_o reason_n of_o its_o general_a motion_n tend_v towards_o the_o west_n it_o move_v towards_o the_o collateral_a quarter_n of_o the_o west_n viz._n northwest_n or_o south-west_n yea_o the_o general_a wind_n when_o that_o it_o seldom_o blow_v from_o the_o east_n but_o most_o common_o from_o the_o collateral_a quarter_n of_o the_o east_n change_v this_o general_a motion_n of_o the_o sea_n much_o more_o do_v the_o north_n wind_n in_o the_o northern_a sea_n where_o the_o general_a motion_n be_v little_a discernible_a in_o the_o part_n of_o the_o ocean_n proposition_n ix_o the_o cause_n of_o this_o general_a motion_n of_o the_o sea_n from_o the_o east_n to_o the_o west_n be_v uncertain_a west_n the_o opinion_n of_o aristotle_n and_o copernicus_n concern_v the_o general_a motion_n of_o the_o sea_n from_o east_n to_o west_n the_o aristotelian_o suppose_v although_o it_o be_v unknown_a unto_o aristotle_n and_o his_o follower_n and_o indeed_o to_o all_o the_o european_a philosopher_n before_o the_o navigation_n of_o the_o portugal_n through_o the_o ocean_n of_o the_o torrid_a zone_n that_o it_o be_v cause_v by_o the_o prime_a motion_n of_o the_o heaven_n which_o be_v not_o only_o common_a to_o all_o the_o star_n but_o also_o to_o the_o air_n in_o part_n and_o to_o the_o ocean_n by_o which_o all_o be_v carry_v from_o the_o east_n to_o the_o west_n but_o some_o that_o follow_v copernicus_n as_o kepler_n although_o they_o also_o acknowledge_v the_o moon_n also_o the_o cause_n of_o this_o motion_n yet_o they_o determine_v that_o the_o motion_n of_o the_o earth_n do_v not_o a_o little_a contribute_v unto_o this_o motion_n viz._n they_o suppose_v that_o the_o water_n see_v that_o it_o be_v not_o continuous_a but_o only_o contiguous_a unto_o the_o earth_n can_v follow_v the_o circumrotation_n of_o the_o earth_n and_o resist_v it_o towards_o the_o west_n whilst_o the_o earth_n withdraw_v itself_o towards_o the_o east_n and_o therefore_o that_o the_o sea_n move_v not_o from_o one_o part_n of_o the_o earth_n unto_o another_o but_o that_o the_o earth_n leave_v part_n of_o the_o water_n one_o after_o another_o othersome_a who_o be_v not_o please_v neither_o with_o the_o solution_n of_o aristotle_n nor_o copernicus_n have_v recourse_n unto_o the_o moon_n will_v have_v she_o to_o be_v empress_n of_o the_o water_n and_o that_o she_o lead_v about_o with_o she_o and_o draw_v the_o ocean_n from_o the_o east_n to_o the_o west_n if_o it_o be_v demand_v how_o they_o reply_n there_o be_v a_o occult_a faculty_n influence_n sympathy_n vicinity_n to_o the_o earth_n and_o such_o like_a indeed_o it_o be_v very_o probable_a that_o the_o moon_n be_v the_o causer_n of_o this_o motion_n by_o reason_n that_o in_o the_o new_a and_o full_a moon_n this_o motion_n be_v more_o violent_a than_o in_o the_o quarter_n where_o the_o 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b_o and_o t_o be_v render_v more_o angust_n and_o thence_o it_o follow_v that_o the_o celestial_a matter_n flow_v there_o more_o quick_a between_o b_o and_o t_n and_o therefore_o more_o press_v the_o superficies_n of_o the_o air_n in_o 6_o and_o also_o the_o superficies_n of_o the_o water_n in_o 2._o then_o if_o the_o moon_n be_v not_o in_o the_o diameter_n of_o the_o vortex_n b_o d_o and_o see_v that_o both_o the_o body_n of_o the_o air_n and_o water_n be_v fluid_a and_o easy_o pliant_a to_o this_o pression_n it_o must_v not_o be_v so_o high_a above_o the_o part_n of_o the_o earth_n f_o as_o if_o the_o moon_n be_v without_o the_o diameter_n b_o d._n and_o on_o the_o contrary_n must_v be_v more_o high_a towards_o e._n but_o whilst_o that_o the_o earth_n be_v carry_v from_o e_o through_o f_o towards_o g_z or_o from_o the_o
the_o point_n d_o and_o so_o consequent_o or_o rather_o because_o that_o the_o moon_n in_o the_o mean_a space_n do_v somewhat_o proceed_v forward_o from_o b_o towards_z c_z as_o running_z in_o a_o month_n space_n through_o the_o circle_n a_o b_o c_o d_o part_n of_o the_o earth_n that_o be_v now_o in_o f_o on_o the_o opposite_a region_n of_o the_o body_n of_o the_o moon_n after_o six_o hour_n and_o twelve_o minute_n either_o more_o or_o less_o shall_v be_v beyond_o the_o point_n g_o in_o that_o diameter_n of_o the_o vortex_n a_fw-it b_o c_o d_o which_o intersect_v that_o diameter_n of_o the_o same_o vortex_n in_o which_o the_o moon_n shall_v then_o be_v at_o right_a angle_n and_o then_o shall_v the_o water_n be_v there_o most_o high_a and_o after_o six_o hour_n with_o twelve_o minute_n it_o shall_v be_v beyond_o the_o point_n h._n in_o the_o place_n where_o the_o water_n shall_v be_v very_o low_a etc._n etc._n whence_o it_o be_v clear_o discover_v that_o the_o water_n of_o the_o sea_n in_o every_o twelve_o hour_n and_o twenty_o four_o minute_n shall_v flow_v and_o re-flow_a in_o one_o and_o the_o same_o place_n this_o be_v the_o demonstration_n of_o cartesius_n in_o which_o that_o be_v especial_o ingenious_a that_o it_o apt_o show_v not_o only_a how_o the_o flux_n or_o intumescency_n be_v make_v at_o the_o place_n when_o that_o the_o moon_n be_v move_v at_o its_o vertex_fw-la or_o meridian_n but_o also_o when_o that_o the_o moon_n beneath_o the_o horizon_n be_v move_v to_o the_o meridian_n of_o midnight_n we_o have_v say_v in_o the_o end_n of_o the_o nine_o proposition_n what_o any_o one_o may_v seem_v to_o require_v in_o this_o demonstration_n especial_o that_o which_o seem_v to_o be_v admire_v at_o that_o cartesius_n shall_v not_o so_o much_o as_o think_v that_o according_a unto_o this_o demonstration_n that_o the_o least_o altitude_n of_o water_n and_o all_o kind_n of_o detumescency_n aught_o to_o be_v when_o that_o the_o moon_n come_v to_o the_o meridian_n as_o the_o moon_n be_v in_o b_o the_o least_o altitude_n of_o water_n be_v in_o 2_o and_o 4_o and_o on_o the_o contrary_a the_o water_n increase_v with_o the_o departure_n of_o the_o moon_n or_o earth_n so_o that_o when_o f_o shall_v be_v in_o g._n that_o be_v six_o hour_n from_o the_o moon_n it_o shall_v have_v the_o great_a altitude_n which_o in_o truth_n be_v contrary_a to_o all_o experience_n for_o with_o the_o access_n of_o the_o moon_n to_o the_o meridian_n the_o water_n increase_v and_o with_o the_o departure_n of_o the_o same_o decrease_v but_o the_o word_n of_o cartesius_n as_o well_o as_o the_o diagramma_fw-la assert_v the_o contrary_n but_o i_o suppose_v this_o absurdity_n may_v be_v remove_v from_o the_o demonstration_n and_o that_o by_o this_o mode_n so_o that_o it_o may_v be_v approve_v of_o by_o cartesius_n for_o let_v we_o place_v the_o vortex_n of_o the_o earth_n a_o b_o c_o d_o to_n be_v without_o the_o moon_n and_o the_o water_n 1_o 2_o 3_o 4_o to_o be_v equal_o distant_a from_o the_o centre_n t_o without_o any_o tumour_n but_o yet_o to_o be_v move_v round_o with_o the_o earth_n and_o celestial_a matter_n between_o a_o b_o c_o d_o and_z 5_o 6_o 7_o 8._o now_o let_v the_o body_n of_o the_o moon_n draw_v near_o unto_o this_o vortex_n for_o example_n into_o b_o and_o therefore_o the_o space_n t_o b_o become_v more_o narrow_a and_o the_o celestial_a matter_n whilst_o that_o it_o endeavour_v to_o pass_v through_o it_o press_v the_o water_n in_o 2_o towards_o e._n therefore_o whilst_o that_o the_o water_n be_v expel_v from_o 2_o towards_o e_o it_o be_v demand_v where_o the_o great_a tumour_n of_o water_n will_v be_v whether_o in_o the_o place_n e_o which_o be_v a_o quarter_n distant_a from_o the_o place_n f_o unto_o which_o the_o moon_n be_v vertical_a or_o whether_o in_o a_o place_n nigh_o unto_o f_o towards_o e_z if_o that_o you_o assert_v the_o first_o viz._n that_o the_o tumour_n ought_v to_o be_v in_o e_o experience_n do_v then_o gainsay_v but_o that_o the_o second_o be_v true_o so_o experience_n confirm_v and_o reason_n do_v induce_v to_o believe_v viz._n whilst_o that_o the_o moon_n consist_v above_o the_o place_n e_o the_o water_n be_v expel_v from_o 2_o towards_o i_o but_o the_o great_a tumour_n will_v be_v in_o the_o place_n near_o to_o 2_o not_o in_o i._o for_o this_o be_v manifest_a by_o experience_n because_o the_o occidental_a place_n do_v late_a discover_v the_o intumescency_n but_o reason_n and_o the_o motion_n of_o the_o water_n do_v altogether_o require_v the_o same_o law_n for_o if_o the_o water_n be_v pour_v forth_o into_o 2_o that_o it_o may_v flow_v towards_o e_o the_o great_a quantity_n will_v be_v in_o the_o place_n e_o a_o little_a less_o in_o the_o place_n near_o to_o that_o and_o yet_o far_o less_o in_o the_o place_n nigh_o to_o that_o and_o least_o of_o all_o in_o e._n so_o also_o when_o that_o water_n be_v drive_v from_o 2_o towards_o e_o its_o great_a quantity_n and_o accumulation_n shall_v be_v in_o the_o 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the_o motion_n be_v find_v the_o least_o of_o all_o and_o so_o also_o in_o the_o intumescency_n violent_a in_o full_a and_o new_a moon_n the_o motion_n of_o the_o sea_n from_o east_n to_o west_n most_o violent_a experience_v sufficient_o prove_v this_o proposition_n for_o mariner_n testify_v that_o the_o sea_n do_v foam_n and_o swell_v in_o new_a and_o full_a moon_n and_o in_o the_o quarter_n be_v calm_a now_o it_o be_v easy_o demonstrate_v according_a to_o the_o hypothesis_n of_o the_o precede_a proposition_n for_o the_o moon_n when_o it_o be_v either_o full_a or_o new_a be_v more_o near_o the_o earth_n than_o at_o any_o other_o time_n and_o in_o the_o quarter_n more_o remote_a as_o astronomer_n do_v demonstrate_v now_o when_o the_o moon_n be_v more_o near_o the_o earth_n that_o be_v when_o that_o the_o space_n b_o t_n be_v less_o the_o celestial_a matter_n be_v hinder_v more_o vehement_o press_v the_o water_n from_o 2_o to_o 1_o because_o it_o be_v more_o near_o but_o on_o the_o 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on_o the_o mountain_n carpathus_n in_o hungaria_n which_o because_o it_o make_v not_o a_o little_a to_o the_o confirm_v our_o judgement_n concern_v the_o altitude_n of_o the_o air_n and_o the_o constitution_n of_o its_o region_n i_o therefore_o have_v think_v fit_a to_o annex_v it_o here_o although_o it_o ought_v to_o have_v be_v adjoin_v to_o the_o 18_o proposition_n of_o the_o mountain_n of_o hungaria_n carpathus_n say_v he_o be_v the_o chief_a by_o which_o vulgar_a appellation_n all_o the_o tract_n of_o the_o sarmatian_a mountain_n be_v denominate_v which_o separate_a hungary_n from_o rutheni_n the_o polonian_n moravian_o the_o silesian_n and_o that_o part_n of_o austria_n which_o be_v on_o this_o side_n the_o danube_n their_o more_o high_a and_o astonish_a top_n be_v in_o the_o earldom_n sepusia_n at_o my_o native_a country_n caesariopolis_n now_o by_o reason_n that_o they_o be_v almost_o cover_v with_o perpetual_a snow_n they_o be_v term_v by_o the_o sclavonian_n tatry_a or_o 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the_o passenger_n after_o i_o be_v ascend_v another_o more_o high_a be_v discover_v by_o i_o and_o so_o some_o lesser_a top_n the_o latter_a of_o which_o always_o exceed_v the_o former_a in_o altitude_n through_o so_o many_o valley_n be_v i_o force_v to_o pass_v with_o the_o great_a hazard_n of_o my_o life_n until_o i_o have_v arrive_v unto_o the_o uppermost_a top_n of_o all_o and_o when_o that_o i_o survey_v the_o valley_n beneath_o beset_v with_o huge_a tree_n from_o the_o declivity_n of_o the_o mountain_n i_o can_v observe_v nothing_o but_o a_o obscure_a night_n or_o a_o bluish_a colour_n like_v unto_o profound_a air_n and_o it_o seem_v to_o i_o that_o if_o i_o shall_v chance_v to_o fall_v from_o the_o mountain_n that_o i_o shall_v not_o light_v on_o the_o earth_n but_o fall_v direct_o into_o the_o firmament_n for_o by_o the_o overmuch_a declivity_n the_o visible_a object_n be_v extenuate_v and_o dull_v but_o whilst_o that_o i_o ascend_v a_o more_o high_a mountain_n i_o be_v 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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 matter_n viz._n the_o notation_n of_o the_o wind_n which_o at_o that_o time_n be_v observe_v in_o each_o region_n whether_o in_o every_o year_n the_o same_o never_o return_v yet_o if_o that_o any_o thing_n must_v be_v say_v to_o the_o question_n these_o seem_v convenient_a 1._o we_o can_v deny_v but_o that_o the_o north_n wind_n often_o blow_v in_o our_o canicular_a or_o dog_n day_n 2._o that_o it_o be_v discover_v less_o continual_a and_o in_o each_o year_n peradventure_o the_o cause_n be_v the_o often_o blow_v of_o other_o wind_n which_o hinder_v the_o discovery_n of_o the_o same_o 3._o we_o may_v say_v that_o the_o mountain_n from_o which_o this_o first_o resolution_n of_o the_o snow_n begin_v be_v situate_v direct_o from_o greece_n and_o therefore_o the_o first_o canicular_a wind_n be_v carry_v hither_o but_o the_o vapour_n be_v carry_v hither_o from_o the_o snow_n of_o the_o other_o mountain_n because_o that_o here_o they_o find_v a_o free_a passage_n make_v but_o i_o shall_v 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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
del_fw-it majo_n with_o the_o southern-motion_n in_o the_o end_n of_o august_n in_o 35_o degree_n of_o the_o meridian_n of_o tristian_a de_fw-fr cunha_n in_o may_n in_o the_o new_a moon_n the_o west-wind_n rage_v and_o shipwreck_n but_o in_o 33_o degree_n of_o the_o same_o meridian_n the_o north_n and_o north-east_n wind_n predominate_v 8._o in_o june_n and_o july_n in_o the_o sea_n of_o china_n at_o pulon_n timor_fw-la the_o west-wind_n be_v violent_a and_o dangerous_a 9_o between_o china_n and_o japan_n many_o storm_n be_v from_o the_o new_a moon_n of_o july_n to_o the_o twelve_o day_n of_o the_o moon_n 10._o there_o if_o in_o june_n other_o wind_n blow_v beside_o the_o motion_n sometime_o from_o this_o sometime_o from_o that_o quarter_n until_o that_o they_o be_v settle_v in_o the_o north-east_n quarter_n of_o a_o certain_a a_o storm_n follow_v the_o second_o book_n of_o general_n geography_n concern_v the_o affection_n of_o the_o place_n of_o the_o earth_n depend_v on_o the_o apparent_a motion_n of_o the_o star_n chap._n xxii_o of_o thing_n requisite_a to_o be_v foreknow_v in_o the_o knowledge_n of_o geography_n itherto_o we_o have_v be_v employ_v in_o a_o absolute_a contemplation_n of_o the_o earth_n we_o now_o draw_v near_o the_o second_o part_n of_o this_o doctrine_n in_o which_o we_o shall_v consider_v those_o property_n or_o affection_n which_o happen_v to_o the_o earth_n from_o the_o apparent_a motion_n of_o the_o sun_n and_o star_n neither_o will_v they_o be_v except_o this_o motion_n be_v evident_a the_o explication_n of_o which_o affection_n will_v with_o great_a right_n appertain_v unto_o geography_n if_o so_o be_v that_o same_o motion_n be_v attribute_v unto_o the_o earth_n itself_o of_o which_o we_o have_v treat_v in_o the_o six_o chapter_n now_o for_o the_o right_a knowledge_n of_o these_o affection_n these_o follow_a hypothesis_n and_o definition_n be_v necessary_a to_o be_v understand_v definition_n glâ—be_n a_o artificial_a terrestrial_a globe_n term_v a_o factitious_a glâ—be_n first_o the_o artificial_a terrestrial_a globe_n be_v term_v a_o factitious_a globe_n from_o who_o superficies_n the_o part_n of_o the_o earth_n and_o their_o situation_n aâ—_n 〈◊〉_d present_v as_o they_o have_v a_o existence_n in_o the_o earth_n itself_o according_a â—o_o the_o proportion_n of_o this_o superficies_n to_o the_o superficies_n of_o the_o earth_n consist_v a_o map_n a_o plain_a figure_n and_o of_o what_o line_n it_o consist_v a_o map_n or_o geographical_a card_n be_v a_o plain_a figure_n in_o which_o the_o situation_n of_o the_o terrestrial_a superficies_n be_v represent_v and_o this_o again_o be_v either_o universal_a or_o particular_a the_o first_o exhibit_v the_o whole_a superficies_n of_o the_o earth_n the_o other_o some_o one_o or_o other_o region_n some_o map_n consist_v of_o strait_a line_n and_o other_o of_o crooked_a these_o of_o straight_o be_v such_o in_o which_o the_o periphery_n or_o circumference_n of_o the_o 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diameter_n of_o the_o earth_n about_o which_o the_o diurnal_a motion_n of_o the_o star_n or_o earth_n itself_o be_v perfect_v now_o the_o pole_n be_v say_v to_o be_v the_o extreme_a point_n of_o the_o axis_n in_o the_o superficies_n of_o the_o terrestrial_a globe_n and_o that_o pole_n which_o be_v subject_v to_o the_o constellation_n term_v the_o bear_n be_v call_v the_o arctic_a septentrional_n or_o northern_a pole_n the_o other_o be_v call_v the_o antarctic_a or_o southern_a pole_n these_o be_v by_o more_o facility_n explain_v by_o a_o artificial_a terrestrial_a globe_n than_o by_o word_n if_o the_o former_a be_v wheel_v round_o those_o two_o immovable_a point_n will_v appear_v which_o be_v the_o pole_n and_o the_o diameter_n imaginarily_o draw_v from_o one_o pole_n to_o the_o other_o through_o the_o centre_n of_o the_o earth_n shall_v be_v the_o axis_n line_n the_o aequator_fw-la or_o aequinoctial_a line_n three_o the_o aequator_fw-la be_v say_v to_o be_v the_o periphery_a or_o circumference_n of_o the_o great_a circle_n in_o the_o globe_n of_o the_o earth_n equal_o distant_a from_o both_o the_o pole_n or_o place_v in_o the_o middle_n between_o the_o pole_n or_o who_o pole_n be_v the_o same_o with_o the_o pole_n of_o the_o earth_n it_o be_v also_o term_v the_o aequinoctial_a line_n and_o that_o by_o mariner_n all_o the_o star_n in_o their_o diurnal_a motion_n make_v periphery_n equidistant_a or_o parallel_n to_o the_o aequator_fw-la wherefore_o the_o aequator_fw-la be_v the_o rule_n of_o diurnal_a motion_n parallel_n parallel_n four_o the_o parallel_n of_o the_o aequator_fw-la be_v say_v to_o be_v lesser_a periphery_n which_o be_v parallel_v to_o the_o aequator_fw-la in_o a_o artificial_a globe_n the_o aequator_fw-la by_o reason_n of_o its_o magnitude_n be_v more_o conspicuous_a than_o the_o other_o and_o its_o name_n be_v ascribe_v and_o it_o be_v divide_v into_o 360_o degree_n the_o parallel_n be_v also_o conspicuous_a which_o be_v likewise_o term_v the_o circle_n of_o the_o latitude_n of_o place_n as_o we_o shall_v show_v in_o the_o follow_a chapter_n map_n of_o map_n these_o may_v also_o be_v show_v in_o geographical_a map_n that_o be_v universal_a indeed_o in_o map_n of_o right_a line_n the_o pole_n be_v not_o represent_v but_o the_o extremity_n of_o every_o meridian_n be_v the_o pole_n but_o in_o map_n consist_v of_o crooked_a line_n the_o pole_n be_v those_o point_n in_o which_o the_o crooked_a line_n do_v meet_v the_o aequator_fw-la be_v transverse_a in_o both_o kind_n of_o map_n pass_v through_o the_o middle_n of_o they_o and_o have_v a_o great_a latitude_n than_o the_o other_o line_n and_o withal_o it_o be_v a_o strait_a line_n although_o in_o the_o particular_a map_n of_o asia_n and_o europe_n it_o be_v make_v crooked_a the_o parallel_n of_o the_o aequator_fw-la in_o strait-lined_n map_n be_v strait-lâ—â—â—s_a and_o in_o crooked-lined_n map_n they_o be_v crooked_a ecliptic_a the_o ecliptic_a five_o the_o ecliptic_a be_v the_o great_a circle_n of_o the_o heaven_n which_o the_o sun_n describe_v in_o his_o annual_a motion_n in_o truth_n it_o exi_v not_o in_o the_o earth_n but_o by_o reason_n of_o its_o notable_a use_n it_o be_v mark_v in_o the_o artificial_a globe_n as_o also_o in_o geographical_a map_n tropic_n the_o tropic_n six_o the_o tropic_n be_v two_o parallel_n of_o the_o aequator_fw-la which_o be_v distant_a from_o the_o aequator_fw-la by_o so_o great_a a_o interval_n as_o the_o great_a recess_n of_o the_o sun_n be_v from_o the_o aequator_fw-la towards_o the_o pole_n or_o as_o the_o great_a declination_n of_o the_o sun_n or_o obliquity_n of_o the_o ecliptic_a the_o tropic_a of_o cancer_n be_v that_o which_o be_v interpose_v between_o the_o aequator_fw-la and_o pole_n arctic_a the_o tropic_a of_o capricorn_n be_v that_o which_o be_v between_o the_o aequator_fw-la and_o the_o southern_a pole_n circle_n the_o polary_a circle_n in_o the_o globe_n and_o in_o map_n they_o be_v wont_v to_o be_v note_v by_o a_o double_a periphery_n and_o the_o same_o appellation_n be_v ascribe_v the_o polary_a circle_n be_v two_o parallel_n so_o call_v whereof_o one_o be_v distant_a from_o the_o pole_n arctic_a the_o other_o from_o the_o antarctic_a so_o many_o degree_n as_o the_o sun_n be_v from_o the_o aequator_fw-la in_o his_o great_a recess_n and_o the_o first_o be_v term_v the_o arctic_a circle_n and_o the_o other_o the_o antarctic_a the_o circle_n hitherto_o explain_v do_v not_o depend_v on_o certain_a place_n such_o as_o the_o follow_a do_v which_o in_o divers_a place_n be_v various_a and_o different_a meridian_n the_o meridian_n seven_o the_o meridian_n of_o any_o place_n in_o the_o superficies_n of_o the_o earth_n be_v a_o line_n so_o term_v which_o pass_v through_o that_o place_n in_o which_o when_o the_o sun_n come_v the_o meridies_n be_v in_o that_o place_n now_o the_o meridies_n be_v that_o moment_n of_o the_o day_n which_o be_v equal_o distant_a from_o the_o rise_n and_o set_v of_o the_o
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circle_n to_o 12_o let_v the_o globe_n be_v turn_v round_o until_o the_o place_n of_o the_o sun_n come_v to_o the_o occidental_a horizon_n the_o index_n will_v show_v the_o number_n of_o the_o hour_n of_o the_o day_n the_o other_o at_o 24_o will_v show_v the_o hour_n of_o the_o night_n proposition_n v._o in_o all_o place_n seat_v between_o the_o aequator_fw-la and_o the_o pole_n arctic_a the_o long_a day_n and_o short_a night_n be_v when_o the_o sun_n enter_v the_o first_o degree_n of_o cancer_n and_o the_o short_a day_n and_o long_a night_n be_v when_o the_o sun_n enter_v the_o first_o degree_n of_o capricorn_n but_o in_o the_o place_n seat_v between_o the_o aequator_fw-la and_o the_o antarctick_a pole_n it_o be_v just_a contrary_n capricora_n of_o place_n seat_v between_o the_o aequator_fw-la and_o the_o pole_n arctic_a the_o day_n long_o and_o night_n short_a when_o the_o sun_n enter_v into_o cancer_n and_o day_n short_a and_o night_n long_o when_o into_o capricora_n to_o show_v this_o on_o the_o globe_n take_v what_o place_n you_o please_v and_o let_v the_o pole_n be_v elevate_v according_a to_o its_o latitude_n then_o according_a to_o the_o precede_a proposition_n find_v out_o the_o number_n of_o the_o hour_n when_o the_o sun_n be_v in_o the_o first_o degree_n of_o cancer_n than_o any_o other_o point_n of_o the_o ecliptic_a be_v take_v for_o any_o day_n of_o the_o year_n let_v the_o number_n of_o the_o hour_n again_o be_v find_v for_o that_o day_n and_o it_o will_v be_v manifest_a that_o the_o number_n of_o the_o hour_n of_o the_o day_n when_o the_o sun_n be_v in_o the_o first_o degree_n of_o cancer_n be_v great_a than_o the_o number_n of_o the_o hour_n of_o another_o day_n and_o because_o this_o other_o day_n be_v take_v at_o pleasure_n and_o in_o every_o day_n the_o same_o demonstration_n be_v in_o force_n therefore_o the_o day_n when_o the_o sun_n be_v in_o the_o first_o degree_n of_o cancer_n be_v the_o long_a of_o all_o day_n and_o consequent_o the_o 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seat_v southern_o we_o shall_v show_v the_o proposition_n by_o such_o like_a method_n the_o demonstration_n will_v be_v more_o perspicuous_a if_o that_o it_o be_v do_v through_o the_o parallel_n arch_n which_o be_v above_o and_o under_o the_o horizon_n proposition_n vii_o if_o the_o place_n of_o the_o earth_n be_v more_o remote_a from_o the_o aequator_fw-la or_o more_o propincate_a to_o the_o pole_n than_o another_o place_n short_a according_a to_o the_o situation_n of_o the_o place_n of_o earth_n to_o the_o aequator_fw-la and_o the_o pole_n the_o day_n and_o night_n be_v long_o and_o short_a the_o difference_n be_v great_a between_o the_o day_n and_o the_o night_n and_o the_o long_a day_n be_v great_a and_o the_o short_a night_n be_v less_o contrariwise_o if_o the_o place_n be_v more_o nigh_o the_o aequator_fw-la the_o difference_n between_o the_o quantity_n of_o the_o day_n and_o night_n be_v lesser_a and_o the_o long_a day_n besser_n and_o the_o short_a night_n great_a so_o that_o the_o place_n near_o the_o aequator_fw-la or_o situate_a in_o the_o torrid_a zone_n have_v almost_o all_o the_o day_n equal_a to_o the_o night_n as_o the_o place_n of_o the_o aequator_fw-la itself_o and_o the_o excess_n of_o the_o long_a day_n above_o that_o of_o the_o aequinoctial_a about_o one_o hour_n take_v in_o the_o globe_n two_o place_n one_o more_o remote_a from_o the_o aequator_fw-la the_o other_o more_o nigh_o and_o take_v what_o day_n of_o the_o year_n you_o please_v except_o the_o aequinox_n you_o may_v show_v that_o in_o the_o place_n more_o remote_a the_o day_n more_o differ_v from_o the_o quantity_n of_o the_o night_n than_o in_o a_o place_n more_o near_o the_o aequator_fw-la let_v the_o place_n of_o the_o sun_n in_o the_o ecliptic_a be_v
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 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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
autumn_n and_o the_o beginning_n of_o the_o winter_n in_o those_o place_n be_v when_o the_o sun_n obtain_v the_o great_a distance_n that_o possible_o he_o can_v from_o the_o vertex_fw-la of_o those_o place_n as_o it_o be_v lay_v down_o in_o the_o definition_n and_o it_o be_v true_a concern_v all_o the_o place_n of_o the_o torrid_a northern_a zone_n that_o the_o sun_n enter_v into_o the_o first_o degree_n of_o capricorn_n acquire_v the_o great_a distance_n in_o the_o meridies_n from_o the_o vertex_fw-la of_o those_o place_n because_o that_o in_o all_o the_o other_o day_n he_o be_v more_o near_o to_o those_o place_n therefore_o the_o sun_n be_v enter_v into_o the_o first_o degree_n of_o capricorn_n the_o beginning_n of_o the_o winter_n happen_v to_o all_o those_o place_n and_o also_o the_o end_n of_o autumn_n which_o be_v the_o first_o part_n of_o this_o proposition_n the_o other_o part_n be_v also_o easy_o prove_v for_o if_o these_o place_n be_v of_o a_o diverse_a latitude_n than_o the_o sun_n be_v not_o vertical_a in_o the_o meridies_n to_o those_o place_n in_o the_o same_o day_n but_o in_o diverse_a for_o than_o be_v the_o begin_n of_o the_o summer_n of_o any_o place_n of_o this_o torrid_a zone_n when_o the_o sun_n by_o his_o ascent_n from_o the_o first_o of_o capricorn_n come_v to_o that_o degree_n of_o the_o northern_a ecliptic_a that_o he_o be_v vertical_a to_o that_o place_n so_o that_o in_o divers_a day_n the_o beginning_n of_o summer_n may_v be_v in_o those_o divers_a place_n yet_o in_o all_o those_o place_n its_o beginning_n fall_v between_o the_o 21_o of_o march_n and_o the_o 21_o of_o june_n the_o summer_n shall_v also_o end_v in_o different_a day_n and_o the_o autumn_n begin_v because_o the_o sun_n in_o divers_a day_n come_v to_o his_o mean_a distance_n or_o to_o the_o point_n of_o the_o ecliptic_a which_o have_v a_o moderate_a distance_n from_o those_o place_n because_o these_o point_n be_v different_o seat_v between_o the_o first_o of_o libra_n and_o the_o first_o of_o capricorn_n notwitstand_v this_o beginning_n fall_v out_o between_o the_o 21_o of_o september_n and_o the_o 21_o of_o december_n after_o the_o same_o mode_n in_o divers_a day_n the_o winter_n shall_v have_v a_o end_n and_o the_o spring_n begin_v because_o the_o point_n of_o the_o ecliptic_a again_o of_o a_o moderate_a distance_n be_v divers_a from_o the_o vertices_fw-la of_o those_o place_n now_o the_o sun_n touch_v they_o cause_v the_o beginning_n of_o the_o spring_n which_o yet_o happen_v in_o all_o between_o the_o 21_o of_o december_n and_o the_o 21_o of_o march_n 3._o all_o the_o place_n of_o the_o earth_n situate_v in_o the_o torrid_a southern_a zone_n have_v also_o the_o end_n of_o the_o autumn_n and_o the_o beginning_n of_o the_o winter_n together_o at_o one_o time_n viz._n the_o 21_o of_o june_n but_o they_o have_v not_o the_o beginning_n and_o end_n of_o the_o spring_n as_o also_o the_o beginning_n of_o the_o autumn_n together_o but_o divers_a place_n have_v it_o in_o different_a day_n yet_o so_o that_o the_o begin_n of_o the_o summer_n of_o all_o those_o place_n do_v fall_v between_o the_o 21_o of_o september_n and_o the_o 21_o of_o december_n the_o beginning_n of_o autumn_n and_o the_o end_n of_o summer_n 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 the_o spring_n and_o the_o end_n of_o winter_n between_o the_o 21_o of_o june_n and_o the_o 21_o of_o september_n the_o part_n of_o this_o proposition_n be_v prove_v after_o the_o same_o manner_n as_o the_o former_a for_o on_o the_o 21_o of_o june_n the_o sun_n be_v in_o the_o first_o degree_n of_o cancer_n and_o therefore_o have_v the_o great_a distance_n that_o be_v possible_a from_o the_o place_n of_o the_o austrial_a torrid_a zone_n then_o therefore_o all_o of_o they_o shall_v have_v the_o beginning_n of_o winter_n but_o the_o begin_n of_o summer_n the_o spring_n and_o autumn_n shall_v happen_v on_o divers_a day_n because_o the_o sun_n in_o sundry_a point_n of_o the_o ecliptic_a become_v vertical_a unto_o divers_a place_n and_o acquire_v also_o a_o moderate_a distance_n from_o those_o place_n in_o many_o place_n 4._o those_o place_n of_o the_o earth_n in_o the_o torrid_a zone_n have_v something_o peculiar_a which_o lie_v between_o the_o aequator_fw-la and_o the_o eight_o degree_n of_o latitude_n as_o well_o towards_o the_o north_n as_o south_n for_o the_o sun_n by_o his_o proper_a motion_n or_o by_o his_o access_n or_o recess_n make_v two_o summer_n in_o they_o two_o spring_n but_o yet_o but_o one_o autumn_n and_o one_o winter_n and_o that_o by_o a_o confuse_a kind_n of_o order_n viz._n this_o the_o spring_n the_o summer_n the_o spring_n the_o summer_n again_o then_o autumn_n and_o then_o winter_n latitude_n the_o place_n in_o the_o torrid_a zone_n have_v something_o peculiar_a to_o they_o which_o lie_v between_o the_o aequator_fw-la and_o the_o 8_o degree_n of_o latitude_n the_o cause_n of_o this_o paradox_n be_v because_o the_o sun_n recede_v from_o the_o vertices_fw-la of_o those_o place_n which_o lie_v between_o the_o aequator_fw-la and_o the_o 8_o degree_n of_o the_o boreal_a or_o northern_a latitude_n where_o it_o make_v the_o beginning_n of_o the_o first_o summer_n and_o go_v forward_o towards_o the_o beginning_n of_o cancer_n it_o acquire_v here_o a_o a_o moderate_a distance_n when_o it_o return_v from_o the_o vertices_fw-la towards_o those_o vertices_fw-la it_o shall_v not_o make_v autumn_n after_o that_o first_o summer_n but_o another_o spring_n see_v that_o it_o make_v the_o first_o before_o it_o begin_v the_o first_o summer_n where_o it_o obtain_v a_o mean_a distance_n between_o the_o first_o of_o capricorn_n and_o the_o first_o of_o aries_n for_o example_n let_v we_o take_v a_o place_n which_o be_v four_o degree_n from_o the_o aequator_fw-la because_o therefore_o also_o the_o sun_n in_o the_o ten_o degree_n of_o aries_n decline_v and_o be_v distant_a from_o the_o aequator_fw-la four_o degree_n therefore_o he_o be_v in_o the_o ten_o of_o aries_n shall_v cause_v the_o beginning_n of_o summer_n in_o that_o place_n moreover_o the_o great_a distance_n which_o this_o place_n can_v have_v in_o the_o meridies_n be_v 27_o degree_n 30_o minute_n viz._n in_o the_o first_o degree_n of_o capricorn_n where_o his_o declination_n from_o the_o aequator_fw-la be_v 30_o minnte_n 23_o degree_n to_o which_o let_v the_o northerm_n distance_n of_o the_o place_n from_o the_o aequator_fw-la 4_o degree_n be_v add_v therefore_o see_v his_o mean_a distance_n be_v 0_o degree_n let_v 0_o degree_n be_v his_o middle_a distance_n 13_o degree_n 45_o minute_n wherefore_o when_o the_o sun_n shall_v be_v in_o the_o point_n of_o the_o ecliptic_a which_o be_v distant_a from_o the_o place_n take_v or_o the_o parallel_n of_o the_o place_n 13_o degree_n 45_o minute_n then_o the_o sun_n shall_v make_v either_o spring_n or_o autumn_n in_o that_o place_n the_o spring_n if_o the_o sun_n be_v move_v 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the_o twenty_o chapter_n whence_o rain_n and_o cloud_n proceed_v by_o which_o the_o heat_n and_o light_n of_o the_o sun_n be_v very_o much_o obstruct_v and_o the_o celestial_a cause_n of_o the_o season_n be_v disturb_v there_o be_v few_o of_o the_o place_n of_o the_o torrid_a zone_n which_o want_v those_o ridge_n as_o the_o inward_a africa_n mexico_n and_o the_o like_a 9_o the_o effect_n of_o the_o wind_n in_o the_o torrid_a zone_n be_v various_a and_o notable_a for_o a_o general_a wind_n blow_v from_o the_o side_n plagas_fw-la of_o the_o east_n or_o from_o the_o east_n continual_o towards_o the_o west_n refrigerate_v the_o maritime_a place_n which_o regard_v the_o east_n as_o brazilia_n the_o oriental_a coast_n of_o africa_n but_o not_o so_o to_o those_o towards_o the_o west_n as_o guiney_n congo_n angola_n and_o the_o coast_n of_o peru._n some_o wind_n be_v appropriate_v as_o the_o south_n in_o peru_n which_o wind_n dispel_v vapour_n towards_o the_o plaga_fw-la in_o which_o they_o blow_v some_o be_v fix_v wind_n of_o which_o we_o have_v large_o treat_v in_o the_o one_o and_o twenty_o chapter_n now_o these_o wind_n do_v very_o much_o disturb_v the_o celestial_a cause_n of_o the_o season_n for_o they_o be_v almost_o as_o equal_o constant_a and_o observe_v order_n as_o the_o motion_n of_o the_o heaven_n itself_o they_o bring_v down_o the_o air_n compel_v the_o vapour_n towards_o the_o top_n of_o the_o mountain_n and_o by_o other_o mode_n alter_v the_o season_n ten_o anniversary_n rain_n be_v in_o many_o place_n of_o the_o torrid_a zone_n and_o take_v away_o the_o celestial_a cause_n see_v that_o they_o be_v as_o equal_o constant_a as_o the_o motion_n of_o the_o sun_n itself_o for_o those_o err_v who_o suppose_v that_o this_o our_o sublunary_a orb_n observe_v all_o with_o inconstancy_n and_o without_o order_n and_o that_o the_o celestial_a only_o have_v a_o constant_a motion_n see_v that_o the_o cause_n hitherto_o speak_v of_o be_v so_o various_a to_o be_v able_a to_o cause_v the_o heat_n and_o the_o property_n of_o the_o season_n and_o in_o one_o place_n some_o be_v from_o other_o cause_n in_o another_o other_o be_v of_o force_n or_o concur_v in_o divers_a season_n of_o the_o year_n or_o mutual_o impede_fw-la one_o another_o hence_o we_o discover_v why_o the_o cause_n and_o condition_n of_o the_o season_n of_o the_o torrid_a zone_n be_v so_o various_a proposition_n xi_o how_o the_o spring_n summer_n autumn_n and_o winter_n terrestrial_a do_v behave_v themselves_o and_o in_o what_o month_n of_o the_o year_n they_o commence_v in_o the_o divers_a place_n of_o the_o torrid_a zone_n zone_n of_o the_o beginning_n of_o the_o season_n in_o place_n in_o the_o torrid_a zone_n we_o have_v say_v before_o and_o especial_o in_o the_o second_o proposition_n that_o
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 the_o pole_n and_z 15_o beneath_o the_o same_o jupiter_n 6_o year_n beneath_o and_o 6_o above_o the_o same_o horizon_n mars_n 1_o year_n venus_n and_o mercury_n about_o half_a a_o year_n from_o this_o cause_n it_o be_v likely_a that_o there_o be_v great_a diversity_n of_o the_o motion_n of_o the_o air_n and_o season_n in_o divers_a year_n 6._o the_o land_n in_o most_o place_n of_o the_o frigid_a zone_n be_v stony_a rocky_a and_o as_o hard_o as_o flint_n in_o few_o place_n chalky_a sulphureous_a and_o fat_a in_o these_o place_n there_o be_v a_o moderate_a fertility_n in_o the_o other_o a_o sterility_n 7._o those_o region_n be_v encompass_v with_o the_o sea_n but_o for_o the_o mediterranean_a we_o as_o yet_o have_v no_o certain_a account_n 8._o some_o of_o the_o region_n of_o the_o frigid_a zone_n have_v mountain_n of_o a_o moderate_a height_n but_o most_o want_v they_o run_v on_o a_o plain_a for_o a_o long_a space_n 9_o the_o cold_a wind_n there_o frequent_o blow_v from_o the_o polary_n 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
ecliptic_a be_v note_v and_o bring_v to_o the_o meridan_n let_v the_o index_n be_v place_v at_o the_o 12_o hour_n at_o noon_n of_o the_o cycle_n let_v the_o globe_n be_v turn_v until_o the_o index_n show_v the_o hour_n give_v then_o the_o globe_n be_v immovable_a let_v the_o index_n be_v bring_v to_o the_o 12_o hour_n and_o this_o be_v do_v let_v the_o globe_n be_v turn_v towards_o the_o east_n until_o the_o place_n of_o the_o sun_n be_v behold_v in_o the_o occidental_a horizon_n then_o let_v the_o hour_n be_v number_v from_o 12_o to_o the_o index_n near_o the_o quarter_n of_o his_o motion_n for_o these_o shall_v be_v the_o italian_a hour_n of_o numeration_n proposition_n ix_o the_o hour_n from_o the_o set_n of_o the_o sun_n or_o of_o italic_a numeration_n be_v give_v to_o find_v what_o hour_n it_o be_v of_o our_o numeration_n from_o the_o midnoon_n or_o midnight_n let_v the_o pole_n be_v elevate_v for_o the_o latitude_n of_o the_o place_n give_v let_v the_o place_n of_o the_o sun_n in_o the_o ecliptic_a be_v note_v and_o bring_v to_o the_o meridian_n let_v the_o index_n be_v place_v at_o the_o hour_n 12_o let_v the_o globe_n be_v turn_v to_o the_o set_n until_o the_o index_n show_v the_o give_v italic_a hour_n then_o the_o globe_n remain_v immovable_a let_v the_o index_n be_v bring_v to_o the_o 12_o hour_n this_o be_v do_v let_v the_o place_n of_o the_o sun_n be_v turn_v back_o to_o that_o semicircle_n of_o the_o meridian_n which_o it_o do_v near_o pass_v through_o so_o the_o hour_n interrupt_v between_o 12_o and_o the_o index_n number_v from_o 12_o towards_o the_o rise_a be_v the_o hour_n from_o the_o meridies_n or_o midnight_n according_a to_o our_o numeration_n or_o reckon_n proposition_n x._o a_o hour_n of_o our_o numeration_n be_v give_v on_o the_o day_n give_v to_o find_v what_o hour_n of_o the_o day_n that_o hour_n be_v according_a to_o the_o ancient_a judaic_a account_n and_o that_o of_o other_o nation_n night_n the_o jew_n division_n of_o the_o day_n and_o night_n in_o ancient_a time_n the_o jew_n and_o other_o nation_n astronomy_n be_v not_o yet_o polish_v divide_v every_o day_n from_o the_o rise_n of_o the_o sun_n to_o his_o set_n into_o 12_o hour_n and_o the_o night_n into_o as_o many_o which_o hour_n be_v therefore_o term_v judaical_a hour_n planetary_a hour_n for_o another_o reason_n but_o more_o fit_o unequal_a hour_n for_o see_v that_o neither_o the_o day_n or_o night_n be_v equal_a among_o themselves_o or_o of_o equal_a longitude_n but_o increase_n for_o half_a a_o year_n 25._o see_v chap._n 25._o and_o decrease_v the_o other_o half_n except_o in_o the_o place_n of_o the_o aequator_fw-la thence_o it_o come_v to_o pass_v that_o those_o hour_n be_v sometime_o great_a and_o sometime_o lesser_a for_o they_o increase_v with_o the_o longitude_n of_o the_o day_n and_o decrease_v with_o the_o decrease_n of_o the_o same_o but_o in_o place_n near_o the_o aequator_fw-la this_o increase_n be_v not_o great_a as_o we_o have_v show_v in_o the_o 25_o chapter_n but_o all_o the_o day_n of_o the_o whole_a year_n be_v almost_o equal_a and_o thence_o it_o come_v to_o pass_v that_o the_o people_n more_o remote_a from_o the_o aequator_fw-la as_o those_o of_o europe_n never_o use_v these_o hour_n but_o only_o those_o people_n who_o be_v not_o far_o remove_v from_o or_o that_o dwell_v under_o the_o torrid_a zone_n therefore_o the_o problem_n may_v be_v thus_o more_o clear_o propound_v viz._n a_o equal_a hour_n be_v give_v in_o a_o give_v day_n to_o find_v a_o unequal_a hour_n a_o equal_a hour_n be_v term_v the_o 12_o part_n of_o any_o day_n or_o night_n or_o of_o the_o time_n in_o which_o the_o sun_n do_v remain_v above_o or_o beneath_o the_o horizon_n a_o unequal_a hour_n be_v term_v the_o 24_o part_n of_o that_o time_n in_o which_o the_o sun_n be_v move_v from_o the_o semicircle_n of_o the_o meridian_n until_o it_o return_v again_o to_o the_o same_o semicircle_n which_o time_n be_v call_v a_o astronomical_a day_n now_o for_o the_o solution_n of_o this_o problem_n we_o must_v thus_o act_v let_v the_o pole_n he_o elevate_v for_o the_o latitude_n of_o the_o place_n give_v let_v the_o place_n of_o the_o sun_n in_o the_o ecliptic_a be_v note_v and_o bring_v to_o the_o east_n the_o index_n to_o the_o 12_o hour_n of_o the_o cycle_n let_v the_o globe_n be_v turn_v until_o the_o note_a place_n of_o the_o sun_n come_v to_o the_o west_n the_o index_n will_v show_v the_o hour_n for_o the_o longitude_n of_o this_o day_n or_o the_o stay_n of_o the_o sun_n above_o the_o horizon_n which_o must_v be_v observe_v then_o set_v it_o be_v find_v what_o be_v the_o hour_n give_v from_o the_o east_n or_o rise_n or_o from_o the_o west_n and_o set_v if_o that_o any_o hour_n be_v give_v after_o the_o set_n of_o the_o sun_n according_a to_o the_o 6_o or_o 8_o proposition_n 8._o see_v proposition_n 6_o and_o 8._o and_o let_v the_o proportion_n be_v compare_v after_o this_o mode_n that_o as_o the_o note_a hour_n of_o the_o longitude_n of_o the_o whole_a day_n or_o night_n be_v unto_o 2_o hour_n so_o the_o hour_n find_v from_o the_o rise_n or_o set_v if_o that_o a_o hour_n of_o the_o night_n be_v give_v be_v to_o the_o number_n of_o the_o judaic_a hour_n proposition_n xi_o the_o judaic_a hour_n be_v give_v in_o the_o day_n give_v to_o find_v what_o hour_n that_o be_v according_a to_o our_o numeration_n or_o account_n or_o to_o reduce_v a_o give_v unequal_a hour_n to_o a_o equal_a hour_n hour_n of_o the_o judaic_a hour_n let_v the_o pole_n be_v elevate_v for_o the_o latitude_n of_o the_o place_n give_v the_o place_n of_o the_o sun_n in_o the_o ecliptic_a from_o the_o day_n give_v be_v find_v let_v it_o be_v bring_v to_o the_o east_n the_o index_n to_o the_o 12_o hour_n and_o let_v the_o globe_n be_v turn_v to_o the_o west_n that_o the_o longitude_n of_o that_o day_n may_v appear_v in_o unequal_a hour_n on_o the_o horary_a cycle_n which_o be_v note_v then_o 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 unto_o 12_o and_o let_v the_o place_n of_o the_o sun_n be_v turn_v round_o to_o the_o oriental_a honrizon_n the_o index_n will_v show_v the_o hour_n of_o the_o rise_n then_o let_v it_o so_o be_v bring_v to_o pass_v that_o 12_o be_v add_v to_o the_o number_n of_o the_o judaic_a hour_o so_o also_o let_v the_o find_v out_o latitude_n of_o the_o whole_a be_v add_v to_o the_o other_o number_n which_o if_o that_o be_v add_v to_o the_o hour_n of_o the_o rise_n we_o shall_v have_v the_o hour_n from_o the_o midnight_n according_a to_o our_o numeration_n if_o that_o the_o number_n of_o these_o hour_n be_v more_o than_o 12_o let_v 12_o cast_v away_o and_o the_o remainder_n will_v show_v the_o hour_n from_o noon_n those_o judaic_a hour_n which_o be_v relate_v in_o the_o sermon_n of_o christ_n can_v accurate_o be_v reduce_v to_o the_o hour_n of_o our_o account_n because_o the_o day_n of_o the_o year_n be_v not_o add_v so_o that_o the_o three_o hour_n of_o that_o day_n may_v be_v our_o 8_o 9th_o or_o 10_o so_o that_o the_o 11_o hour_n of_o that_o sermon_n may_v be_v our_o seven_o 6_o or_o 5_o viz_o as_o that_o day_n may_v be_v take_v either_o according_a to_o the_o summer_n or_o winter_n solstice_n or_o the_o aequinoctial_a proposition_n xii_o those_o who_o go_v from_o some_o one_o part_n of_o the_o earth_n or_o sail_v towards_o the_o sun_n rise_v and_o the_o whole_a globe_n of_o the_o earth_n be_v encompass_v by_o they_o they_o return_v to_o the_o same_o place_n whence_o they_o set_v forth_o they_o in_o the_o mean_a space_n at_o once_o have_v often_o have_v the_o sun_n rise_v set_v the_o meridies_n and_o the_o midnight_n the_o very_a same_o with_o the_o inhabitant_n of_o the_o place_n from_o which_o they_o go_v from_o and_o therefore_o when_o they_o return_v they_o number_v one_o day_n of_o a_o year_n more_o than_o in_o that_o place_n for_o example_n if_o in_o this_o place_n it_o be_v the_o first_o day_n of_o january_n they_o reckon_v the_o second_o of_o january_n if_o they_o account_v it_o to_o be_v saturday_n they_o reckon_v sunday_n and_o if_o they_o shall_v have_v sail_v about_o the_o earth_n twice_o thrice_o or_o four_o time_n they_o shall_v still_o number_v so_o many_o more_o day_n earth_n of_o the_o compass_n of_o the_o earth_n those_o who_o by_o a_o determine_a course_n sail_v about_o the_o whole_a earth_n towards_o the_o west_n they_o in_o the_o mean_a while_n for_o one_o space_n have_v the_o set_n or_o rise_v sun_n the_o meridies_n and_o midnight_n more_o rare_a and_o therefore_o when_o they_o return_v they_o number_v one_o day_n less_o than_o in_o that_o
place_n to_o wit_n the_o 31_o of_o december_n if_o in_o that_o place_n it_o be_v the_o first_o of_o january_n and_o saturday_n or_o the_o last_o day_n of_o the_o week_n when_o in_o this_o place_n it_o shall_v be_v sunday_n or_o the_o first_o day_n of_o a_o new_a week_n and_o if_o they_o have_v sail_v round_o the_o earth_n twice_o thrice_o or_o soin_fw-fr time_n they_o shall_v also_o reckon_v so_o many_o day_n less_o this_o be_v a_o matter_n of_o wonder_n and_o admiration_n some_o age_n ago_o to_o mâ—â—â—â—_n and_o other_o but_o the_o frequency_n of_o this_o experiment_n have_v lessehen_fw-ge the_o admination_n and_o have_v administer_v occasion_n to_o mathemnâ—â—â—_n to_o 〈…〉_o the_o cause_n neither_o be_v it_o difficult_a to_o explain_v the_o same_o so_o that_o the_o motion_n of_o the_o sun_n and_o the_o meridian_n of_o the_o place_n of_o the_o earth_n be_v well_o apprehend_v and_o a_o certain_a day_n of_o the_o year_n be_v propose_v â—_o for_o it_o dependetiâ—â—_n the_o diurual_a cirâ—â—â—voluationâ—_n of_o the_o sun_n not_o from_o his_o proper_a nation_n as_o some_o have_v think_v which_o we_o may_v begin_v from_o any_o circle_n but_o for_o our_o more_o easy_a understanding_n it_o be_v very_o convenient_a to_o begin_v from_o the_o meridies_n that_o the_o day_n may_v be_v the_o time_n from_o one_o meridies_n to_o the_o follow_a meridies_n or_o noon_n or_o whilst_o the_o sun_n return_v from_o the_o semicircle_n of_o one_o meridiany_n to_o the_o same_o semicircle_n therefore_o because_o that_o those_o who_o sail_n towards_o the_o east_n or_o rise_v come_v to_o those_o place_n where_o the_o sun_n first_o rise_v and_o make_v his_o meridian_n than_o in_o the_o place_n from_o whence_o they_o depart_v thence_o it_o come_v to_o pass_v that_o the_o sun_n be_v in_o the_o meridian_n of_o the_o place_n to_o which_o they_o have_v arrive_v they_o begin_v to_o reckon_v a_o new_a day_n for_o example_n the_o second_o day_n of_o january_n where_o in_o the_o place_n of_o their_o departure_n hitherto_o they_o have_v number_v the_o first_o day_n of_o january_n if_o that_o they_o set_v sail_n on_o the_o same_o and_o the_o difference_n shall_v be_v one_o or_o two_o hour_n this_o anticipation_n daily_o increase_v until_o they_o come_v towards_o the_o east_n so_o that_o it_o shall_v make_v the_o hour_n of_o half_a a_o day_n when_o they_o come_v to_o the_o opposite_a semicircle_n of_o the_o meridian_n for_o here_o they_o shall_v have_v the_o meridies_n of_o a_o new_a day_n when_o in_o the_o place_n of_o their_o set_n forth_o it_o shall_v be_v the_o midnight_n of_o the_o precede_a day_n and_o where_o they_o shall_v come_v to_o the_o meridian_n 1â—_n degree_n more_o remote_a be_v in_o that_o they_o shall_v have_v the_o meridies_n 13_o hour_n soon_o than_o in_o the_o place_n of_o their_o set_n forth_o and_o when_o again_o they_o shall_v come_v to_o a_o meridian_n more_o remote_a 15_o degree_n there_o they_o shall_v have_v the_o minidiesâ—4_n â—4_z hour_n soon_o than_o in_o the_o place_n of_o their_o set_n forth_o and_o so_o moreover_o as_o they_o shall_v come_v to_o the_o meridian_n or_o place_v more_o remote_a 15_o degree_n they_o shall_v have_v the_o meridies_n 15_o 16_o 17_o hour_n soon_o and_o shall_v begin_v to_o account_v a_o new_a day_n soon_o than_o in_o their_o place_n of_o their_o set_n forth_o so_o that_o when_o at_o length_n they_o shall_v have_v return_v to_o the_o place_n they_o shall_v then_o number_v the_o meridies_n of_o a_o new_a day_n soon_o by_o 24_o hour_n where_o in_o the_o place_n also_o the_o meridies_n be_v which_o yet_o may_v answer_v in_o number_n to_o the_o meridies_n which_o the_o mariner_n have_v the_o former_a day_n but_o it_o be_v contrary_a with_o those_o who_o sail_n towards_o the_o west_n when_o they_o return_v to_o the_o place_n from_o whence_o they_o set_v forth_o for_o by_o how_o much_o the_o more_o they_o recede_v from_o this_o place_n by_o so_o much_o the_o more_o they_o shall_v have_v the_o sun_n late_a in_o the_o meridies_n because_o they_o be_v in_o a_o more_o remote_a meridian_n and_o therefore_o do_v late_a begin_v the_o account_n of_o their_o new_a day_n than_o in_o the_o place_n whence_o they_o set_v forth_o so_o that_o this_o proposition_n take_v away_o a_o whole_a day_n in_o the_o return_n corollary_n 1._o corollary_n corollary_n if_o that_o two_o at_o the_o same_o time_n set_v forth_o from_o any_o place_n of_o the_o earth_n the_o one_o towards_o the_o east_n the_o other_o towards_o the_o west_n and_o they_o shall_v return_v both_o together_o to_o the_o same_o place_n the_o whole_a earth_n be_v sail_v about_o he_o that_o take_v his_o journey_n towards_o the_o east_n shall_v reckon_v two_o day_n more_o than_o he_o which_o take_v it_o towards_o the_o west_n and_o if_o they_o have_v sail_v the_o earth_n about_o twice_o they_o shall_v reckon_v a_o day_n more_o if_o thrice_o 6_o day_n more_o etc._n etc._n but_o the_o day_n of_o these_o be_v long_o of_o those_o short_a corollary_n 2._o the_o same_o will_v happen_v if_o that_o in_o any_o place_n of_o the_o earth_n any_o two_o meet_v one_o the_o other_o and_o from_o hence_o first_o and_o then_o often_o afterward_o be_v this_o apparent_o discover_v for_o when_o ferdinando_n magellanes_n by_o a_o direct_a course_n into_o the_o west_n have_v enter_v the_o indies_n by_o the_o strait_n denominate_v from_o he_o it_o be_v find_v out_o by_o the_o mariner_n which_o there_o meet_v with_o other_o european_n bring_v towards_o the_o east_n by_o a_o ordinary_a journey_n that_o the_o kaleudar_n or_o the_o numeration_n of_o the_o day_n differ_v a_o whole_a day_n the_o same_o have_v be_v observe_v by_o all_o which_o have_v sail_v round_o the_o earth_n when_o they_o have_v come_v into_o the_o indies_n corillary_n 10._o this_o also_o be_v the_o cause_n that_o in_o two_o near_a place_n the_o account_n of_o a_o different_a day_n 〈◊〉_d observe_v viz._n in_o the_o philippine_n isle_n and_o in_o the_o city_n of_o marrow_n on_o the_o chaste_a of_o china_n isle_n the_o day_n in_o macoa_n not_o the_o same_o as_o in_o the_o philippine_n isle_n although_o they_o lie_v under_o the_o same_o meridian_n yet_o they_o reckon_v the_o day_n of_o the_o calendar_n soon_o in_o macoa_n than_o in_o the_o philippine_n isle_n and_o that_o by_o the_o anticipation_n of_o one_o day_n so_o that_o it_o be_v sunday_n in_o moacoa_n when_o but_o saturday_n in_o the_o philippine_n isle_n the_o cause_n of_o this_o diversity_n be_v this_o that_o the_o rortuâ—â—â—_n possess_v the_o city_n of_o macoa_n come_v thither_o from_o europe_n towards_o the_o east_n by_o asseccourse_n out_o of_o india_n but_o the_o spaniard_n which_o possess_v the_o philippine_n isle_n come_v thither_o from_o europe_n towards_o the_o west_n by_o a_o set_a course_n from_o america_n therefore_o it_o be_v in_o fer_v from_o the_o precede_a corollary_n because_o here_o in_o mâ—â—a_n and_o the_o philippines_n they_o almost_o meet_v 〈◊〉_d â—ome_v into_o the_o same_o meridian_n that_o they_o shall_v â—â—ceâ—d_v by_o one_o day_n the_o day_n of_o the_o other_o chap._n xxx_o of_o the_o various_a rise_v set_v altitude_n of_o the_o sun_n and_o other_o appearance_n in_o the_o divers_a part_n of_o the_o earth_n proposition_n 1._o to_o place_n or_o hang_v a_o terrestrial_a globe_n so_o that_o when_o the_o sun_n shine_v those_o part_n of_o the_o globe_n may_v be_v illuminate_v which_o the_o sun_n enlighten_v in_o the_o earth_n at_o any_o time_n and_o that_o it_o also_o may_v appear_v unto_o what_o people_n the_o sun_n rise_v and_o to_o who_o it_o set_v to_o who_o it_o make_v the_o meridies_n and_o to_o who_o it_o be_v altogether_o abscond_v to_o what_o place_n it_o be_v vertical_a also_o to_o find_v the_o place_n of_o the_o sun_n in_o the_o ecliptic_a and_o the_o day_n of_o the_o year_n also_o the_o hour_n of_o the_o place_n globe_n the_o motion_n of_o the_o sun_n show_v by_o the_o globe_n let_v the_o place_n in_o which_o the_o globe_n be_v place_v be_v note_v on_o the_o globe_n and_o bring_v to_o the_o meridian_n and_o let_v a_o mark_n be_v make_v with_o a_o chalk_n on_o that_o point_n of_o the_o meridian_n therefore_o if_o the_o globe_n be_v to_o be_v hang_v by_o a_o cord_n the_o cord_n must_v be_v tie_v to_o the_o point_n of_o the_o meridian_n but_o if_o that_o it_o must_v be_v place_v firm_o in_o any_o place_n a_o iron_n piâ—_n must_v be_v bring_v through_o the_o centre_n of_o the_o globe_n even_o to_o the_o opposite_a point_n and_o this_o iron_n pin_n must_v be_v close_o fix_v to_o the_o horizontal_n plain_a that_o it_o may_v remain_v immovable_a the_o globe_n must_v be_v dispose_v according_a to_o the_o four_o quarter_n of_o the_o world_n viz_o that_o the_o north_n part_n of_o the_o globe_n may_v regard_v the_o north_n part_n of_o the_o earth_n
parallel_n direct_o ascend_v from_o the_o horizon_n to_o the_o meridian_n then_o let_v the_o pole_n be_v elevate_v for_o the_o latitude_n of_o any_o other_o place_n and_o it_o will_v appear_v that_o the_o parallel_n be_v so_o much_o the_o more_o oblique_a to_o the_o horizon_n by_o how_o much_o the_o more_o the_o pole_n be_v elevate_v that_o be_v by_o the_o wooden_a horizon_n become_v the_o horizon_n of_o the_o place_n more_o remote_a from_o the_o aequator_fw-la or_o near_o to_o the_o pole_n proposition_n vii_o by_o how_o much_o the_o place_n be_v more_o remote_a from_o the_o aequator_fw-la by_o so_o much_o the_o more_o the_o sign_n of_o the_o zodiac_n and_o the_o other_o constellation_n require_v the_o great_a time_n to_o arise_v and_o set_v and_o they_o pass_v through_o the_o meridian_n of_o all_o place_n at_o a_o equal_a time_n let_v two_o place_n be_v take_v on_o the_o globe_n unequal_o distant_a from_o the_o aequator_fw-la and_o let_v the_o pole_n be_v elevate_v and_o observe_v separately_z for_o each_o of_o they_o how_o much_o time_n any_o sign_n of_o the_o zodiac_n require_v to_o ascend_v above_o the_o horizon_n viz._n the_o entrance_n of_o the_o sign_n be_v bring_v to_o the_o oriental_a horizon_n let_v the_o index_n be_v place_v at_o the_o 12_o hour_n and_o the_o globe_n be_v turn_v round_o until_o the_o whole_a sign_n be_v rise_v the_o index_n will_v show_v the_o hour_n elapse_v in_o the_o space_n whilst_o the_o sign_n arise_v for_o by_o the_o comparison_n of_o the_o time_n the_o truth_n of_o the_o proposition_n will_v be_v manifest_a proposition_n viii_o the_o day_n of_o the_o year_n be_v give_v to_o find_v or_o show_v on_o the_o globe_n those_o place_n in_o which_o the_o sun_n arise_v in_o any_o give_a quarter_n globe_n to_o find_v the_o rise_n of_o the_o sun_n in_o any_o quarter_n by_o the_o globe_n this_o problem_n and_o those_o that_o follow_v shall_v be_v propound_v and_o resolve_v concern_v the_o earth_n itself_o if_o that_o we_o will_v act_v according_a to_o art_n for_o these_o affection_n belong_v unto_o it_o but_o they_o be_v propound_v concern_v the_o globe_n because_o here_o it_o represent_v the_o earth_n although_o another_o method_n must_v be_v use_v in_o the_o earth_n or_o another_o construction_n which_o although_o it_o can_v only_o be_v comprehend_v by_o the_o mind_n be_v sufficient_a that_o it_o may_v hinder_v in_o the_o practice_n by_o reason_n of_o the_o obstacle_n this_o be_v the_o same_o with_o that_o problem_n the_o day_n and_o the_o quarter_n be_v give_v in_o which_o the_o rise_n of_o the_o sun_n be_v observe_v to_o find_v the_o latitude_n of_o that_o place_n or_o its_o parallel_n in_o any_o point_n of_o which_o it_o be_v manifest_a that_o we_o be_v place_v 11._o see_v chap._n 23._o proposit_n 11._o the_o solution_n of_o which_o we_o have_v deliver_v in_o the_o 23_o chapter_n proposition_n 11._o proposition_n ix_o the_o day_n and_o the_o hour_n or_o part_n of_o the_o hour_n be_v give_v to_o show_v the_o place_n on_o the_o globe_n to_o which_o the_o sun_n be_v then_o vertical_a first_o let_v the_o place_n of_o the_o sun_n from_o the_o give_v day_n be_v find_v be_v note_v on_o the_o ecliptic_a of_o the_o globe_n and_o that_o be_v bring_v to_o the_o meridian_n let_v a_o mark_n be_v make_v with_o a_o chalk_n on_o the_o supereminent_a point_n then_o let_v those_o place_n be_v find_v in_o who_o meridian_n the_o sun_n be_v at_o the_o give_v moment_n of_o time_n and_o let_v they_o be_v bring_v to_o the_o brazen_a meridian_n these_o be_v do_v that_o place_n which_o be_v subject_a to_o the_o note_a point_n of_o the_o meridian_n be_v the_o place_n which_o be_v demand_v viz._n that_o to_o which_o the_o sun_n be_v vertical_a at_o the_o give_v moment_n of_o time_n proposition_n x._o note_v further_o note_v the_o day_n and_o the_o hour_n be_v give_v to_o show_v all_o the_o place_n on_o the_o globe_n from_o who_o vertex_fw-la the_o sun_n be_v distant_a the_o give_v degree_n at_o that_o hour_n but_o the_o give_v degree_n must_v not_o exceed_v a_o hundred_o and_o eighty_o or_o the_o day_n and_o the_o hour_n be_v give_v to_o show_v on_o the_o globe_n those_o place_n above_o who_o horizon_n the_o sun_n have_v the_o give_v altitude_n or_o the_o give_v depression_n beneath_o it_o but_o the_o altitude_n give_v must_v not_o exceed_v 90_o degree_n as_o likewise_o the_o depression_n let_v the_o place_n be_v find_v on_o the_o globe_n to_o which_o the_o sun_n be_v vertical_a at_o the_o hour_n give_v and_o let_v this_o be_v bring_v to_o the_o meridian_n and_o let_v the_o quadrant_n be_v affix_v to_o the_o imminent_a point_n of_o the_o meridian_n let_v the_o degree_n of_o distance_n from_o the_o vertex_fw-la give_fw-mi be_v note_v and_o the_o quadrant_n be_v turn_v round_o the_o globe_n remain_v immovable_a all_o the_o place_n of_o the_o earth_n through_o which_o the_o note_a degree_n of_o the_o quadrant_n pass_v be_v those_o from_o who_o the_o sun_n have_v the_o give_v distance_n or_o above_o who_o horizon_n the_o sun_n have_v the_o give_v altitude_n proposition_n xi_o at_o the_o give_v hour_n of_o the_o day_n to_o show_v on_o the_o globe_n all_o plain_n unto_o which_o the_o sun_n rise_v and_o set_v and_o to_o which_o he_o be_v fix_v at_o the_o meridian_n and_o all_o that_o be_v illuminate_v and_o not_o illuminate_v day_n further_o concern_v the_o rise_n and_o set_v of_o the_o sun_n find_v out_o by_o the_o globe_n at_o any_o day_n or_o hour_n of_o the_o day_n let_v the_o place_n be_v find_v in_o the_o globe_n to_o which_o the_o sun_n at_o the_o time_n give_v be_v vertical_a and_o let_v the_o place_n be_v bring_v to_o the_o meridian_n and_o the_o pole_n elevate_v for_o the_o latitude_n of_o that_o place_n or_o let_v that_o place_n be_v place_v in_o the_o vertex_fw-la of_o the_o horizon_n so_o all_o those_o place_n which_o be_v discover_v under_o the_o semicircle_n of_o the_o meridian_n above_o the_o horizon_n shall_v have_v the_o meridies_n but_o those_o place_n which_o be_v behold_v in_o the_o oriental_a semicircle_n of_o the_o horizon_n be_v those_o to_o which_o the_o sun_n than_o set_v but_o to_o those_o which_o lie_v in_o the_o occidental_a semicircle_n of_o the_o horizon_n the_o sun_n rise_v at_o the_o give_v time_n and_o all_o the_o place_n which_o be_v above_o the_o horizon_n be_v illuminate_v by_o the_o sun_n on_o the_o contrary_a all_o the_o place_n situate_v beneath_o the_o same_o then_o want_v the_o presence_n of_o the_o sun_n note_v that_o the_o problem_n must_v be_v understand_v of_o the_o rise_n and_o set_v of_o the_o body_n of_o the_o centre_n of_o the_o sun_n for_o the_o body_n of_o the_o sun_n illustrate_v part_n of_o the_o earth_n somewhat_o big_a than_o the_o hemisphere_n which_o how_o big_a it_o be_v shall_v be_v discover_v in_o the_o follow_a proposition_n therefore_o we_o may_v show_v the_o place_n to_o which_o the_o sun_n rise_v or_o set_v when_o we_o have_v noon_n or_o midnight_n and_o contrariwise_o those_o in_o which_o he_o set_v when_o he_o arise_v to_o we_o who_o then_o have_v midnight_n or_o midday_n proposition_n xii_o the_o semidiameter_n of_o the_o sun_n and_o earth_n be_v give_v and_o the_o distance_n of_o the_o sun_n from_o the_o earth_n be_v know_v to_o find_v out_o the_o part_n of_o the_o earth_n which_o the_o sun_n illuminate_v scheme_n see_v scheme_n let_v the_o semidiameter_n of_o the_o earth_n be_v a_o b_o a_o c_o a_o the_o centre_n a_o b_o c_o d_o e_o the_o great_a circle_n of_o the_o earth_n s_n the_o centre_n of_o the_o sun_n s_o l_o s_o o_o the_o semidiameter_n of_o the_o sun_n l_o b_o o_o c_o the_o ray_n touch_v the_o globe_n of_o the_o sun_n and_o earth_n for_o these_o distinguish_v the_o part_n illuminate_v from_o the_o part_n not_o illuminate_v therefore_o the_o arch_n b_o d_o c_o represent_v the_o part_n of_o the_o superficies_n of_o the_o earth_n illuminate_v and_o the_o arch_n blc_n the_o part_n not_o illuminate_v let_v the_o tangent_n lb_n o_o c_o be_v extend_v until_o they_o concur_v in_o r_n and_z b_o n_n parallel_v to_o a_o s_n therefore_o in_o the_o triangle_n b_o n_o l_o let_v n_n l_o be_v give_v the_o excess_n s_o l_o above_o a_o b_o and_z b_o n_z of_o equal_a distance_n to_o a_o s_n the_o angle_n b_o n_o l_o be_v direct_a because_o that_o b_o l_o touch_v the_o circle_n wherefore_o in_o the_o triangle_n b_o l_o n_o let_v the_o angle_n n_o b_o l_o be_v find_v according_a to_o this_o proposition_n that_o as_o b_o n_n be_v to_o n_n l_o so_fw-mi be_v the_o whole_a sign_n to_o the_o tangent_fw-la of_o the_o angle_n n_o b_o l._n moreover_n the_o two_o angle_n l_o n_n b_o n_o b_o l_o be_v together_o equal_a to_o one_o straight_o or_o 90_o
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
be_v wet_v so_o it_o be_v ready_o apply_v but_o the_o place_n in_o that_o paper_n before_o they_o be_v apply_v be_v consign_v to_o their_o fit_a degree_n of_o longitude_n and_o latitude_n proposition_n vi_o to_o compose_v geographical_a map_n we_o may_v thus_o propound_v the_o problem_n in_o a_o mathematical_a style_n map_n of_o the_o compose_n geographical_a map_n the_o situation_n of_o a_o infinite_a plain_n or_o one_o to_o be_v produce_v at_o pleasure_n be_v give_v to_o represent_v in_o that_o the_o place_n of_o the_o superficies_n of_o the_o earth_n according_a to_o the_o rule_n of_o perspective_n or_o thus_o more_o general_o a_o point_n be_v give_v on_o any_o plain_a which_o be_v put_v to_o represent_v any_o place_n of_o the_o superficies_n of_o the_o earth_n to_o find_v on_o the_o same_o plain_a infinite_a divers_z other_o point_n and_o line_n which_o as_o commodious_o may_v be_v may_v represent_v to_o the_o life_n the_o place_n and_o line_n of_o the_o superficies_n of_o the_o 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that_o it_o may_v be_v have_v in_o the_o large_a map_n but_o we_o shall_v more_o full_o explicate_v this_o in_o the_o description_n only_o this_o we_o shall_v here_o advise_v in_o general_a that_o in_o all_o map_n which_o we_o have_v or_o which_o be_v sell_v by_o artificer_n viz._n those_o that_o be_v universal_a that_o place_n must_v be_v take_v for_o the_o point_n which_o shall_v be_v direct_o subject_a to_o the_o eye_n in_o the_o projecture_n that_o place_n i_o say_v of_o the_o earth_n which_o be_v seat_v in_o the_o middle_n of_o the_o table_n for_o here_o we_o must_v conceive_v the_o eye_n to_o hang_v over_o this_o have_v place_n in_o many_o particular_a one_o yet_o not_o in_o all_o moreover_o you_o may_v make_v the_o follow_a rule_n to_o be_v more_o plain_a if_o that_o you_o make_v use_v of_o several_a map_n use_v map_n necessary_a to_o be_v use_v which_o will_v the_o more_o illustrate_v and_o explain_v our_o rule_n by_o the_o example_n the_o first_o easy_a mode_n the_o eye_n be_v 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to_o be_v emit_v from_o all_o the_o place_n and_o periphery_n of_o the_o arctic_a hemisphere_n whether_o it_o possess_v the_o antarctick_a or_o other_o point_n of_o the_o axis_n which_o ray_n therefore_o shall_v penetrate_v the_o place_n of_o the_o aequator_fw-la the_o point_n in_o which_o the_o perforation_n be_v make_v shall_v exhibit_v every_o place_n of_o that_o hemisphere_n of_o the_o earth_n and_o the_o point_v make_v from_o the_o perforate_n ray_n the_o periphery_n of_o the_o tropic_a if_o they_o be_v join_v do_v exhibit_v the_o line_n which_o represent_v those_o periphery_n by_o this_o method_n it_o come_v to_o pass_v that_o the_o aequator_fw-la become_v the_o term_n of_o this_o projecture_n the_o pole_n of_o the_o earth_n may_v be_v represent_v from_o the_o centre_n of_o this_o circle_n or_o of_o the_o aequator_fw-la the_o meridian_n make_n right_a line_n all_o pass_v through_o the_o pole_n even_o to_o the_o aequator_fw-la the_o parallel_n of_o the_o aequator_fw-la or_o the_o circle_n of_o latitude_n the_o tropic_a of_o cancer_n the_o arctic_a pole_n and_o the_o like_a also_o by_o this_o projecture_n may_v be_v make_v these_o circle_n or_o periphery_n who_o centre_n be_v the_o same_o with_o that_o of_o the_o aequator_fw-la viz._n the_o point_n which_o represent_v the_o pole_n arctic_a but_o the_o place_n of_o the_o earth_n be_v represent_v every_o one_o in_o their_o periphery_n of_o latitude_n and_o the_o meridian_n line_n viz._n where_o the_o meridian_n line_n of_o the_o place_n cut_v the_o parallel_n of_o the_o place_n the_o point_n of_o the_o section_n be_v the_o representation_n of_o the_o place_n but_o all_o the_o other_o periphery_n and_o semiperiphery_n which_o may_v be_v conceive_v in_o that_o hemisphere_n do_v not_o make_v in_o projecture_n straight_o line_n or_o circular_a but_o eclipse_n for_o example_n if_o we_o will_v represent_v the_o horizon_n and_o vertical_a circle_n of_o any_o place_n all_o these_o in_o their_o projecture_n shall_v make_v 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may_v be_v take_v at_o pleasure_n but_o the_o other_o point_n and_o periphery_n shall_v be_v find_v from_o they_o let_v the_o aequator_fw-la be_v divide_v into_o 360_o deg_fw-la and_o straight_a line_n be_v draw_v through_o the_o centre_n and_o the_o beginning_n of_o every_o deg_fw-la these_o shall_v be_v the_o meridian_n from_o which_o that_o which_o be_v draw_v at_o the_o begin_n of_o the_o first_o degree_n from_o these_o 360_o shall_v be_v take_v for_o the_o first_o so_o the_o rest_n of_o the_o line_n shall_v show_v the_o rest_n of_o the_o meridian_n and_o longitude_n of_o the_o earth_n from_o the_o first_o meridian_n now_o the_o parallel_n of_o latitude_n must_v be_v describe_v there_o be_v four_o quadrant_n or_o quarter_n of_o the_o aequator_fw-la the_o first_o 0,90_o the_o second_o 90,108_o the_o three_o 180,270_o and_o the_o four_o 270,0_o let_v those_o be_v note_v for_o the_o more_o easy_a appellation_n with_o the_o letter_n a_o b_o b_o c_o cd_o d_o a_o and_o let_v one_o be_v 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from_o the_o earth_n viz._n the_o region_n about_o e_o be_v lesser_a about_o a_o c_o great_a than_o they_o ought_v by_o proportion_n to_o be_v after_o the_o same_o manner_n the_o region_n about_o the_o pole_n b_o d_o be_v make_v big_a than_o they_o ought_v second_o the_o situation_n of_o one_o place_n to_o another_o can_v be_v commodious_o examine_v neither_o thence_o can_v we_o find_v the_o distance_n of_o place_n the_o three_o four_o and_o five_o mode_n of_o right_o line_v map_n place_n the_o 3d._n four_o 5_o mode_n of_o right_o line_v map_n see_v scheme_n in_o place_n there_o be_v sell_v by_o artificer_n universal_a geographical_a map_n of_o right_a line_n viz._n in_o which_o both_o the_o circle_n of_o longitude_n meridian_n and_o of_o latitude_n parallel_n be_v design_v by_o right_a line_n which_o be_v impossible_a according_a to_o the_o rule_n of_o perspective_n neither_o can_v there_o be_v any_o situation_n or_o position_n assign_v to_o the_o eye_n or_o glass_n that_o both_o 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a_o the_o occident_n c_o the_o oriental_a cardo_n or_o show_v the_o place_n which_o be_v distant_a 90_o degree_n in_o the_o primary_n vertical_a point_n all_o the_o vertical_a point_n be_v represent_v in_o straight_a line_n draw_v through_o the_o centre_n e_o to_o every_o degree_n of_o the_o horizon_n but_o to_o shun_v confusion_n it_o be_v better_a to_o omit_v they_o and_o to_o adjoyn_v a_o circumductile_a rule_n to_o the_o paxil_n affix_v in_o e._n then_o let_v b_o d_o be_v divide_v into_o 180_o degree_n as_o in_o the_o former_a mode_n by_o draw_v right_a line_n from_o a_o to_o every_o degree_n of_o the_o semiperiphery_n b_o c_o d._n that_o point_n
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
church_n and_o a_o bulky_a tall_a steeple_n on_o a_o hill_n describe_v county_n of_o surrey_n describe_v surrey_n a_o county_n of_o a_o different_a soil_n not_o over_o fertile_a especial_o in_o the_o midst_n yet_o the_o part_n near_o the_o thames_n which_o be_v plain_a and_o champain_n be_v grateful_a to_o the_o husbandman_n and_o the_o part_n call_v holmesdale_n by_o reason_n of_o the_o aspire_a hill_n rivers_n park_n meadow_n grove_n and_o field_n be_v a_o place_n of_o great_a delight_n the_o air_n be_v very_o healthful_a it_o be_v garnish_v with_o the_o seat_n of_o several_a gentleman_n and_o be_v better_a store_v with_o game_n than_o grain_n here_o be_v seat_v 140_o parish_n church_n and_o have_v the_o accommodation_n of_o 9_o market_n to_n southwark_n or_o the_o borough_n of_o southwark_n southwark_n southwark_n on_o the_o southside_n of_o the_o thames_n opposite_a to_o the_o city_n of_o london_n to_o which_o it_o be_v join_v by_o a_o stately_a stone-bridge_n and_o be_v a_o 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iron_n unwrought_a and_o wrought_v into_o gun_n etc._n etc._n corn_n cattle_n sheep_n wool_n and_o wood._n this_o county_n be_v sever_v into_o 6_o rape_n all_o which_o traverse_v the_o shire_n and_o have_v each_o of_o they_o their_o particular_a river_n forest_n and_o castle_n and_o in_o these_o rape_n be_v 65_o hundred_o in_o which_o be_v number_v 312_o parish_n church_n and_o be_v trade_v unto_o by_o 16_o market_n to_n in_o chichester_n rape_n be_v 7_o hundred_o and_o its_o chief_a place_n be_v chichester_n chichester_n chichester_n seat_v on_o the_o bank_n of_o the_o levant_n which_o at_o a_o small_a distance_n fall_v into_o the_o sea_n it_o be_v a_o indifferent_a large_a city_n contain_v 5_o or_o 6_o parish_n church_n beside_o its_o cathedral_n it_o be_v grace_v with_o good_a building_n and_o spacious_a street_n especial_o the_o 4_o which_o lead_v from_o the_o 4_o gate_n of_o its_o wall_n and_o cross_v one_o another_o at_o the_o marketplace_n which_o be_v a_o fair_a 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the_o place_n and_o that_o in_o the_o first_o season_n if_o the_o sun_n become_v vertical_a to_o that_o place_n in_o two_o season_n the_o end_n that_o day_n in_o who_o meridies_n the_o sun_n receive_v a_o moderate_a distance_n from_o the_o first_o vertex_fw-la of_o that_o place_n or_o whether_o it_o be_v lesser_a than_o that_o of_o all_o other_o day_n of_o the_o year_n 2._o that_o be_v term_v the_o winter_n of_o any_o place_n the_o beginning_n of_o which_o be_v that_o day_n in_o who_o meridies_n the_o sun_n obtain_v the_o great_a distance_n from_o the_o vertex_fw-la of_o that_o place_n and_o the_o end_n that_o day_n in_o who_o meridies_n the_o sun_n acquire_v a_o moderate_a distance_n from_o the_o vertex_fw-la of_o that_o place_n 3._o that_o season_n be_v term_v the_o spring_n of_o any_o place_n which_o fall_v between_o the_o end_n of_o the_o winter_n and_o the_o beginning_n of_o the_o summer_n or_o who_o beginning_n be_v that_o day_n in_o the_o meridies_n of_o which_o the_o sun_n have_v acquire_v a_o moderate_a distance_n from_o the_o vertex_fw-la when_o he_o have_v come_v from_o a_o great_a distance_n and_o the_o end_n be_v that_o day_n where_o in_o who_o meridies_n the_o sun_n have_v acquire_v a_o very_a small_a distance_n from_o the_o first_o vertex_fw-la of_o the_o place_n 4._o the_o autumn_n of_o any_o place_n be_v term_v that_o season_n of_o the_o year_n fall_v between_o the_o end_n of_o summer_n and_o the_o beginning_n of_o winter_n or_o who_o beginning_n be_v that_o day_n in_o the_o meridies_n of_o which_o the_o sun_n receive_v a_o mean_a distance_n from_o the_o vertex_fw-la of_o the_o place_n come_v from_o a_o lesser_a and_o the_o end_n that_o day_n in_o the_o meridies_n of_o which_o the_o sun_n have_v obtain_v a_o very_a great_a distance_n from_o the_o vertex_fw-la of_o the_o place_n according_a to_o these_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