34_o a_o 242_o 4_o lucida_n aquarii_n 31_o 24_o a_o 339_o 28_o arcturus_n bootis_n 21_o 4_o s_n 209_o 59_o lucida_n lyrae_fw-la 38_o 30_o s_n 206_o 17_o cauda_fw-la cygni_fw-la 44_o 3_o s_n 307_o 23_o capella_n 45_o 35_o s_n 72_o 44_o pes_fw-la orionis_n sinister_a 8_o 38_o a_o 74_o 29_o sirius_n canis_n major_n 16_o 13_o a_o 97_o 26_o humerus_fw-la dexter_n orionis_n 7_o 18_o a_o 84_o 7_o canis_fw-la minor_n 6_o 6_o s_n 110_o 17_o chap._n xxxii_o of_o the_o mutual_a situation_n of_o place_n and_o composition_n of_o the_o terrestrial_a globe_n and_o map_n proposition_n i._o a_o place_n be_v give_v in_o the_o earth_n to_o find_v the_o situation_n of_o other_o place_n at_o that_o place_n etc._n of_o find_v of_o the_o situation_n of_o place_n in_o the_o earth_n etc._n etc._n now_o the_o situation_n of_o one_o place_n to_o the_o other_o be_v term_v that_o plaga_fw-la in_o which_o this_o lie_v at_o or_o a_o angle_n of_o position_n that_o be_v a_o angle_n which_o the_o meridian_n of_o the_o give_v place_n make_v with_o a_o line_n or_o periphery_n draw_v from_o this_o place_n to_o the_o other_o for_o example_n if_o we_o be_v in_o amsterdam_n and_o desire_v to_o know_v in_o what_o situation_n other_o place_n lie_v unto_o it_o as_o rome_n leyden_n the_o hague_n or_o the_o like_a the_o first_o mode_n mode_n the_o first_o mode_n to_o those_o place_n that_o a_o prospect_n be_v grant_v from_o the_o place_n give_v their_o situation_n may_v exact_o be_v observe_v to_o this_o place_n by_o instrument_n let_v a_o geometrical_a instrument_n be_v place_v in_o a_o high_a tower_n or_o the_o place_n of_o the_o give_v place_n so_o that_o it_o may_v be_v parallel_n to_o the_o horizon_n and_o the_o meridian_n line_n be_v find_v let_v one_o rule_n of_o the_o instrument_n be_v apply_v unto_o it_o and_o the_o other_o have_v a_o perspective_n must_v be_v direct_v to_o the_o conspicuous_a place_n the_o arch_n of_o the_o periphery_a intercept_v between_o the_o two_o rule_n be_v the_o angle_n of_o the_o position_n of_o the_o place_n observe_v at_o this_o place_n and_o from_o thence_o his_o quarter_n shall_v be_v know_v so_o the_o situation_n or_o position_n of_o all_o other_o vicine_fw-la places_z shall_v be_v observe_v then_o let_v we_o go_v to_o these_o place_n and_o from_o they_o by_o the_o same_o mode_n we_o shall_v again_o discover_v the_o situation_n of_o other_o place_n and_o then_o we_o may_v so_o act_v over_o the_o whole_a superficies_n of_o the_o earth_n except_o that_o other_o way_n be_v know_v by_o which_o we_o may_v come_v more_o easy_o to_o the_o demand_v place_n the_o second_o mode_n mode_n the_o second_o mode_n if_o that_o the_o propose_a place_n may_v be_v have_v on_o the_o globe_n let_v the_o place_n give_v be_v bring_v to_o the_o meridian_n and_o let_v the_o pole_n be_v elevate_v for_o its_o latitude_n let_v the_o quadrant_n be_v affix_v to_o the_o vertex_fw-la and_o let_v it_o be_v apply_v to_o one_o and_o the_o other_o place_n who_o situation_n we_o desire_v to_o know_v at_o our_o place_n the_o extremity_n of_o the_o quadrant_n in_o the_o horizon_n will_v show_v the_o angle_n of_o position_n and_o the_o quarter_n seek_v for_o and_o therefore_o we_o shall_v say_v that_o rome_n constantinople_n lie_v from_o amsterdam_n towards_o this_o or_o that_o find_v out_o quarter_n which_o that_o we_o may_v conceive_v in_o the_o world_n we_o ought_v to_o know_v the_o meridian_n line_n or_o quarter_n of_o the_o north_n and_o south_n also_o the_o east_n and_o west_n aequinoctial_a for_o from_o these_o be_v well_o conceive_v of_o the_o intermedial_a quarter_n may_v easy_o be_v conceive_v here_o must_v be_v collect_v what_o have_v be_v say_v concern_v quarter_n in_o the_o 20_o chapter_n 20._o see_v chap._n 20._o the_o three_o mode_n mode_n the_o three_o mode_n from_o map_n of_o straight_a line_n if_o that_o the_o place_n propound_v be_v to_o be_v find_v in_o they_o it_o be_v easy_a to_o discover_v the_o situation_n of_o those_o place_n to_o this_o by_o the_o eye_n for_o through_o the_o give_v place_n a_o right_a meridian_n line_n be_v conceive_v show_v the_o north_n and_o south_n and_o another_o line_n transverse_a or_o show_v the_o parallel_n of_o the_o place_n which_o discover_v the_o eastern_a and_o western_a quarter_n from_o these_o the_o intermedial_a quarter_n in_o which_o every_o place_n be_v behold_v be_v easy_o discover_v or_o else_o they_o be_v more_o accurate_o know_v by_o line_n draw_v on_o the_o quadrant_n of_o the_o periphery_a if_o that_o there_o be_v need_n of_o a_o more_o accurate_a knowledge_n but_o yet_o this_o method_n be_v not_o complete_a except_o in_o particular_a map_n in_o map_n of_o crooked_a line_n the_o quarter_n or_o situation_n of_o place_n be_v not_o so_o a_o accurate_o seek_v as_o the_o other_o place_n the_o four_o mode_n mode_n the_o four_o mode_n the_o latitude_n and_o longitude_n of_o two_o place_n bege_v give_v the_o situation_n of_o one_o to_o the_o other_o be_v exact_o find_v by_o a_o trigonometrical_a compute_v both_o that_o which_o be_v vulgar_a as_o that_o which_o be_v logorithmetical_a or_o by_o a_o catholic_n planisphere_n or_o also_o by_o the_o globe_n for_o let_v a_o spherical_a triangle_n be_v have_v in_o which_o three_o thing_n be_v give_v viz._n the_o compliment_n of_o the_o latitude_n of_o both_o place_n and_o the_o angle_n comprehend_v from_o these_o which_o be_v know_v from_o the_o difference_n of_o longitude_n now_o let_v the_o opposite_a angle_n or_o adjacent_a to_o either_o of_o the_o two_o side_n be_v seek_v for_o this_o will_v show_v the_o angle_n of_o position_n of_o one_o place_n to_o the_o other_o and_o the_o very_a quarter_n a_o diagram_n and_o the_o lively_a instruction_n of_o a_o tutor_n will_v make_v these_o more_o clear_a and_o hence_o appear_v the_o use_n of_o the_o table_n of_o longitude_n and_o latitude_n of_o place_n the_o five_o mode_n from_o the_o give_a distance_n of_o a_o place_n from_o two_o place_n or_o from_o the_o give_v distance_n and_o latitude_n mode_n the_o five_o mode_n his_o quarter_n or_o situation_n to_o the_o other_o place_n be_v find_v out_o by_o the_o solution_n of_o the_o spherical_a triangle_n the_o six_o mode_n the_o latitude_n of_o two_o place_n be_v give_v the_o distance_n of_o the_o quarter_n of_o one_o be_v find_v to_o the_o other_o by_o a_o threefold_a method_n mode_n the_o six_o mode_n as_o have_v be_v say_v other_o thing_n give_v may_v be_v propound_v by_o which_o we_o may_v find_v out_o the_o quarter_n proposition_n ii_o a_o place_n be_v give_v on_o the_o earth_n or_o globe_n to_o exhibit_v all_o place_n which_o lie_v at_o the_o give_v place_n in_o some_o one_o give_v quarter_n or_o situation_n amsterdam_n of_o the_o know_v the_o place_n in_o the_o north-east_n quarter_n from_o amsterdam_n for_o example_n we_o desire_v to_o know_v all_o the_o place_n which_o lie_v in_o the_o north-east_n quarter_n from_o amsterdam_n let_v the_o pole_n be_v elevate_v for_o the_o latitude_n of_o the_o give_v place_n and_o let_v the_o place_n be_v bring_v to_o the_o meridian_n let_v the_o quadrant_n be_v affix_v to_o the_o vertex_fw-la and_o leâ—_n the_o other_o extremity_n be_v apply_v to_o the_o give_v quarter_n of_o the_o horizon_n so_o we_o shall_v behold_v the_o half_a part_n of_o the_o place_n seek_v for_o viz._n those_o which_o be_v adjacent_a in_o the_o globe_n to_o the_o margin_n of_o the_o quadrant_n the_o other_o half_a part_n be_v beneath_o the_o horizon_n at_o the_o point_n opposite_a to_o the_o vertex_fw-la but_o the_o construction_n be_v more_o easy_a for_o the_o earth_n itself_o to_o wit_n let_v the_o periphery_a of_o the_o great_a circle_n be_v bring_v to_o the_o place_n give_v which_o with_o the_o meridian_n of_o that_o place_n may_v make_v the_o give_v angle_n of_o the_o position_n all_o the_o place_n in_o the_o half_a periphery_n be_v those_o seek_v for_o proposition_n iii_o a_o place_n be_v give_v in_o the_o earth_n or_o on_o the_o globe_n to_o exhibit_v all_o those_o place_n at_o which_o the_o give_v place_n have_v some_o one_o give_v situation_n or_o quarter_n amsterdam_n of_o the_o know_v the_o place_n which_o lie_v north-west_n to_o amsterdam_n for_o example_n we_o desire_v to_o know_v all_o the_o place_n unto_o every_o one_o of_o which_o amsterdam_n lie_v in_o the_o north-west_n quarter_n but_o the_o problem_n may_v with_o more_o delight_n be_v thus_o propound_v any_o place_n in_o the_o earth_n or_o on_o the_o globe_n be_v give_v as_o in_o amsterdam_n to_o show_v all_o those_o place_n from_o which_o whilst_o we_o desire_v to_o go_v to_o the_o give_v place_n amsterdam_n we_o must_v direct_v our_o course_n from_o every_o one_o of_o the_o place_n to_o one_o and_o the_o same_o give_v quarter_n the_o precede_a problem_n be_v local_o plain_a
contain_v all_o the_o place_n who_o latitude_n be_v the_o same_o with_o the_o place_n give_v in_o map_n of_o strait_a line_n let_v a_o strait_a line_n be_v draw_v through_o the_o place_n give_v parallel_n to_o the_o aequator_fw-la all_o the_o place_n through_o which_o that_o line_n pass_v shall_v have_v the_o same_o latitude_n with_o the_o place_n give_v in_o map_n of_o crooked_a line_n let_v the_o periphery_n be_v describe_v pass_v the_o place_n give_v from_o the_o pole_n of_o the_o map_n as_o from_o a_o centre_n so_o by_o the_o same_o mean_n as_o before_o the_o place_n seek_v for_o shall_v be_v find_v but_o if_o no_o certain_a place_n but_o a_o latitude_n be_v give_v let_v one_o fool_n of_o the_o compass_n be_v place_v in_o the_o pole_n of_o the_o map_n and_o the_o other_o on_o the_o side_n line_n to_o the_o degree_n of_o latitude_n and_o then_o the_o parallel_n shall_v be_v describe_v proposition_n vii_o to_o find_v the_o meridian_n or_o the_o plaga_fw-la and_o point_n of_o the_o north_n and_o south_n in_o the_o give_v place_n of_o the_o earth_n or_o in_o the_o give_v plane_n there_o be_v divers_a way_n by_o which_o the_o line_n fight_v for_o may_v be_v find_v meridian_n rule_n for_o the_o find_v the_o meridian_n first_o the_o most_o easy_a mode_n be_v that_o which_o make_v use_v of_o the_o magnetical_a needle_n for_o see_v that_o the_o magnetical_a needle_n or_o needle_n of_o the_o compass_n with_o one_o extreme_a look_v to_o the_o south_n and_o the_o other_o to_o the_o north_n the_o extension_n of_o it_o will_v show_v the_o meridian_n line_n but_o because_o in_o very_a few_o place_n it_o have_v respect_n to_o the_o northern_a and_o southern_a point_n or_o clime_n and_o in_o very_a many_o decline_v from_o they_o as_o we_o shall_v show_v elsewhere_o 38th_o see_v in_o chapter_n the_o 38th_o therefore_o the_o meridian_n line_n be_v not_o accurate_o find_v by_o that_o but_o only_o a_o adjoin_a line_n which_o although_o it_o may_v serve_v when_o the_o matter_n be_v not_o much_o material_a for_o which_o we_o desire_v it_o yet_o in_o concernment_n of_o great_a moment_n it_o may_v be_v the_o cause_n of_o a_o great_a error_n first_o draw_v the_o line_n which_o the_o magnetical_a needle_n show_v then_o take_v any_o point_n in_o this_o line_n 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 in_o the_o which_o let_v the_o degree_n of_o the_o declination_n of_o the_o needle_n be_v number_v begin_v from_o the_o false_a draw_v meridian_n line_n and_o that_o towards_o the_o east_n if_o the_o give_v declination_n be_v towards_o the_o west_n and_o contrariwise_o towards_o the_o west_n if_o the_o give_v declination_n be_v towards_o the_o east_n last_o let_v a_o straight_a line_n be_v draw_v through_o the_o term_n of_o the_o numeration_n of_o the_o centre_n of_o the_o periphery_a this_o shall_v be_v the_o true_a meridian_n line_n useful_a the_o mariner_n compass_n useful_a there_o be_v no_o need_n of_o this_o labour_n if_o that_o you_o have_v the_o mariner_n compass_n at_o hand_n in_o the_o which_o the_o declination_n of_o the_o magnetic_a needle_n be_v correct_v to_o the_o place_n propose_v second_o the_o meridian_n line_n be_v more_o accurate_o find_v out_o by_o the_o benefit_n of_o the_o star_n staâ—â—_n the_o meridian_n line_n find_v by_o the_o staâ—â—_n first_o when_o the_o sun_n shine_v a_o style_n or_o pin_n be_v erect_v the_o shadow_n of_o it_o will_v show_v the_o meridian_n line_n but_o by_o reason_n that_o it_o be_v not_o safe_a to_o conside_fw-la in_o dial_n therefore_o this_o mode_n be_v not_o altogether_o accurate_a and_o it_o show_v a_o true_a line_n yet_o a_o little_a distance_n from_o the_o true_a three_o a_o periphery_a be_v draw_v in_o a_o plain_a give_v let_v a_o style_n or_o pin_n be_v erect_v from_o the_o centre_n of_o the_o same_o and_o let_v the_o term_n of_o the_o shadow_n before_o the_o meridies_n be_v note_v or_o first_o the_o extremity_n of_o the_o shadow_n be_v note_v let_v the_o periphery_a or_o circumserence_n be_v describe_v by_o the_o extremity_n of_o the_o shadow_n from_o the_o place_n of_o the_o style_n then_o you_o must_v expect_v so_o long_o after_o the_o meridies_n until_o the_o extremity_n of_o the_o shadow_n touch_v the_o same_o periphery_a out_o the_o latitude_n be_v know_v the_o meridian_n line_n by_o the_o help_n of_o the_o globe_n may_v be_v sound_a out_o four_o if_o that_o the_o elevation_n of_o the_o pole_n or_o latitude_n in_o the_o place_n of_o the_o observation_n be_v know_v we_o may_v be_v the_o benefit_n of_o the_o globe_n find_v out_o the_o meridian_n line_n by_o this_o mean_n first_o by_o observation_n let_v the_o altitude_n of_o the_o sun_n above_o the_o horizon_n be_v find_v out_o then_o let_v a_o strait_a line_n be_v draw_v on_o a_o plain_a in_o which_o the_o sun_n than_o seem_v to_o be_v and_o a_o point_n be_v take_v as_o a_o centre_n in_o this_o line_n whatsoever_o it_o be_v the_o periphery_n be_v describe_v then_o let_v the_o pole_n be_v elevate_v in_o the_o globe_n according_a to_o the_o elevation_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 for_o the_o day_n give_v be_v note_v let_v the_o quadrant_n be_v apply_v to_o the_o vertex_fw-la and_o in_o that_o let_v the_o observe_v altitude_n of_o the_o sun_n be_v mark_v then_o let_v the_o globe_n and_o the_o quadrant_n be_v move_v together_o until_o the_o point_n of_o the_o quadrant_n and_o the_o note_a place_n of_o the_o sun_n do_v meet_v the_o globe_n thus_o remain_v let_v the_o intercept_a degree_n between_o the_o meredian_n and_o the_o quadrant_n of_o the_o verrical_a point_n be_v number_v in_o the_o wooden_a horizon_n let_v so_o may_v degree_n be_v cut_v off_o in_o the_o periphery_n before_o describe_v begin_v from_o the_o line_n of_o the_o plaga_fw-la of_o the_o sun_n towards_o the_o east_n or_o west_n as_o the_o time_n of_o the_o observation_n shall_v be_v and_o let_v a_o right_a line_n be_v draw_v through_o the_o term_n or_o bind_v of_o the_o resection_n and_o centre_n of_o the_o circle_n this_o shall_v be_v the_o true_a meridian_n line_n the_o invention_n will_v be_v far_o more_o easy_a and_o without_o the_o use_n of_o the_o vertical_a quadrant_n if_o the_o plaga_fw-la be_v observe_v or_o a_o line_n draw_v in_o the_o plain_a in_o which_o the_o sun_n either_o rise_v or_o set_v be_v behold_v for_o then_o a_o circle_n be_v again_o describe_v let_v the_o place_n of_o the_o sun_n be_v bring_v to_o the_o horizon_n and_o let_v the_o intercept_a degree_n between_o the_o place_n of_o the_o sun_n and_o the_o north_n or_o south_n be_v number_v let_v so_o many_o degree_n be_v cut_v off_o in_o the_o periphery_a describe_v from_o the_o line_n draw_v and_o let_v a_o right_a line_n be_v draw_v through_o the_o term_n or_o bind_v of_o the_o resection_n and_o centre_n this_o shall_v be_v the_o true_a meridian_n line_n proposition_n viii_o to_o place_v a_o globe_n so_o that_o the_o cardines_fw-la of_o the_o same_o may_v respect_v the_o cardines_fw-la of_o the_o earth_n that_o be_v that_o the_o brazen_a meridian_n may_v be_v seat_v in_o the_o true_a meridian_n of_o the_o place_n globe_n of_o the_o place_n the_o globe_n let_v the_o meridian_n line_n be_v find_v in_o that_o plain_a on_o which_o the_o globe_n stand_v and_o let_v the_o globe_n be_v so_o place_v that_o the_o brazen_a meridian_n may_v exact_o hang_v over_o the_o meridian_n line_n so_o the_o globe_n shall_v be_v fix_v according_a to_o the_o plagas_fw-la or_o climate_n of_o the_o world_n or_o let_v the_o mariner_n compass_n be_v place_v at_o the_o foot_n of_o the_o globe_n and_o let_v the_o globe_n with_o its_o foot_n so_o long_o be_v move_v in_o the_o plain_a until_o the_o brazen_a meridian_n and_o the_o meridian_n line_n of_o the_o compass_n be_v find_v to_o be_v in_o the_o same_o plain_a so_o the_o globe_n shall_v be_v again_o constitute_v according_a to_o the_o plaga_fw-la or_o climate_n of_o the_o earth_n that_o be_v so_o that_o the_o north_n part_n of_o the_o globe_n shall_v have_v respect_n to_o the_o north_n part_n of_o the_o earth_n the_o south_n to_o the_o south_n east_n to_o the_o east_n and_o west_n to_o west_n a_o problem_n may_v be_v propound_v concern_v geographical_a map_n and_o the_o use_n be_v also_o in_o the_o art_n of_o navigation_n viz._n so_o to_o place_v they_o on_o a_o plain_a that_o the_o northern_a place_n of_o they_o may_v look_v towards_o the_o north_n of_o the_o earth_n the_o southern_a to_o the_o south_n and_o the_o like_a the_o solution_n be_v easy_a if_o that_o a_o meridian_n line_n may_v be_v find_v in_o that_o plain_a or_o if_o you_o have_v a_o accurate_a mariner_n compass_n for_o the_o side_n line_n of_o the_o map_n
perioeci_n and_o what_o hour_n they_o do_v not_o see_v it_o together_o let_v the_o place_n of_o the_o stay_n of_o the_o sun_n above_o the_o horizon_n of_o the_o place_n give_v be_v find_v at_o the_o day_n give_v and_o let_v the_o time_n of_o his_o stay_n beneath_o the_o horizon_n that_o be_v the_o quantity_n of_o the_o day_n and_o the_o night_n be_v find_v half_o the_o difference_n between_o the_o quantity_n of_o the_o day_n and_o the_o night_n will_v show_v the_o hour_n or_o part_n of_o the_o hour_n in_o which_o the_o sun_n first_o rise_v to_o one_o place_n before_o he_o set_v to_o another_o and_o set_v late_a also_o to_o that_o place_n than_o he_o arise_v to_o this_o chap._n xxix_o of_o the_o computation_n of_o time_n in_o the_o divers_a place_n of_o the_o earth_n proposition_n i._o the_o hour_n of_o one_o place_n be_v give_v in_o the_o globe_n to_o find_v the_o hour_n of_o another_o place_n give_v out_o by_o the_o globe_n the_o hour_n of_o the_o place_n be_v find_v out_o let_v the_o 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have_v observe_v the_o beginning_n also_o in_o his_o map_n but_o see_v that_o there_o be_v other_o place_n in_o the_o earth_n where_o the_o magnetic_a needle_n do_v the_o same_o neither_o do_v it_o do_v it_o in_o all_o the_o meridian_n of_o this_o place_n therefore_o other_o geographer_n have_v not_o think_v that_o cause_n sufficient_a and_o some_o have_v place_v the_o first_o meridian_n in_o the_o brazilian_n shore_n the_o more_o modern_a especial_o the_o hollander_n have_v go_v back_o to_o the_o fortunate_a or_o canary_n isle_n have_v choose_v in_o one_o of_o they_o call_v teneriffe_n teneriffe_n the_o longitude_n by_o the_o hollander_n begin_v at_o teneriffe_n a_o mountain_n which_o be_v think_v to_o be_v the_o high_a in_o the_o whole_a world_n call_v el_n pico_fw-la de_fw-fr teneriffe_n and_o from_o the_o meridian_n of_o this_o mountain_n they_o judge_v the_o numeration_n of_o the_o longitude_n of_o place_n ought_v to_o be_v begin_v because_o they_o think_v fit_a that_o a_o 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take_v for_o the_o first_o meridian_n in_o which_o the_o magnetic_a needle_n make_v little_a or_o no_o declination_n so_o that_o such_o a_o meridian_n may_v be_v give_v viz._n in_o all_o the_o place_n of_o which_o or_o the_o most_o at_o least_o the_o magnetic_a needle_n will_v do_v it_o but_o see_v that_o the_o hollander_n at_o this_o time_n take_v the_o mountain_n of_o teneriffe_n for_o the_o begin_n of_o their_o longitude_n and_o that_o they_o sail_v at_o this_o day_n into_o all_o part_n of_o the_o world_n therefore_o it_o be_v convenient_a to_o acknowledge_v the_o same_o begin_n with_o they_o for_o the_o better_a understanding_n of_o the_o diaries_n that_o they_o be_v wont_v to_o publish_v now_o you_o must_v know_v that_o the_o read_n of_o author_n where_o mention_n be_v make_v of_o the_o longitude_n of_o a_o place_n or_o of_o a_o certain_a number_v meridian_n that_o then_o you_o ought_v to_o consider_v what_o beginning_n of_o longitude_n that_o author_n determine_v or_o through_o what_o place_n he_o bring_v his_o first_o meridian_n as_o you_o be_v to_o observe_v that_o the_o map_n which_o be_v use_v in_o the_o second_o part_n of_o this_o book_n be_v the_o geographical_a description_n of_o the_o part_n and_o place_n of_o the_o four_o part_n of_o the_o world_n the_o longitude_n i_o say_v of_o those_o place_n be_v take_v according_a to_o the_o french_a account_n begin_v at_o the_o isle_n of_o of_o fer_n be_v one_o of_o the_o canary_n isle_n they_o be_v compose_v by_o monsieur_n sanson_n geographer_n to_o the_o king_n of_o france_n and_o who_o method_n be_v not_o convenient_a to_o be_v allow_v for_o to_o that_o the_o longitude_n of_o other_o place_n must_v be_v bring_v and_o inquire_v of_o proposition_n iii_o the_o latitude_n and_o longitude_n of_o any_o place_n or_o the_o distance_n of_o any_o place_n from_o the_o aequator_fw-la or_o a_o certain_a meridian_n be_v give_v which_o be_v find_v in_o the_o map_n or_o globe_n to_o exhibit_v the_o situation_n and_o 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pay_v which_o be_v not_o of_o facility_n and_o lester_n expense_n for_o the_o make_n of_o one_o globe_n but_o most_o apt_a and_o prompt_a for_o the_o make_n of_o innumerable_a of_o the_o same_o magnitude_n and_o less_o expense_n of_o which_o i_o shall_v speak_v in_o the_o three_o place_n yet_o the_o foundation_n of_o the_o constouction_n of_o it_o depend_v on_o this_o description_n conceive_v on_o the_o globe_n moreover_o where_o peculiar_a terrestrial_a globe_n be_v to_o be_v make_v in_o brass_n of_o a_o notable_a magnitude_n and_o the_o place_n of_o the_o earth_n be_v to_o be_v design_v on_o its_o superficies_n as_o brince_n that_o favour_v the_o mathematics_n be_v wont_a to_o have_v they_o holstein_n a_o great_a globe_n a_o prepare_v for_o frederick_n duke_n of_o holstein_n as_o for_o example_n frederick_n duke_n of_o holstein_n have_v order_v such_o a_o globe_n to_o be_v make_v who_o oavity_n be_v to_o be_v so_o great_a that_o one_o may_v commodious_o set_v in_o it_o and_o in_o 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mark_n with_o a_o chalk_n then_o let_v the_o shank_n apply_v to_o the_o quarter_n be_v move_v until_o the_o other_o note_a point_n of_o the_o shank_n apply_v to_o the_o quarter_n fall_v in_o on_o the_o parallel_n of_o the_o observe_v latitude_n for_o the_o point_n of_o the_o fall_n in_o be_v the_o place_n seek_v viz._n the_o place_n of_o the_o ship_n but_o if_o that_o there_o be_v no_o parallel_n of_o latitude_n observe_v on_o the_o map_n let_v the_o degree_n intercept_v between_o this_o latitude_n and_o the_o vicine_fw-la parallel_n be_v take_v by_o the_o interval_n of_o the_o compass_n on_o the_o lateral_a line_n and_o let_v the_o rule_n in_o the_o line_n of_o the_o quarter_n and_o one_o foot_n of_o the_o compass_n be_v move_v together_o in_o this_o parallel_n until_o the_o other_o foot_n of_o the_o compass_n and_o the_o note_a shank_n do_v meet_v the_o point_n of_o the_o meeting_n show_v the_o place_n of_o the_o ship_n seamen_n use_v two_o pair_n of_o compass_n if_o that_o you_o 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know_v when_o the_o latitude_n be_v observe_v you_o have_v the_o situation_n of_o the_o place_n itself_o on_o the_o map_n or_o earth_n the_o four_o or_o 5_o method_n also_o of_o find_v out_o of_o this_o place_n be_v also_o give_v viz._n in_o which_o the_o longitude_n of_o the_o other_o or_o seek_v for_o place_n be_v suppose_v to_o be_v observe_v but_o the_o latitude_n be_v unknown_a but_o because_o that_o very_a seldom_o the_o longitude_n can_v be_v observe_v on_o the_o sea_n therefore_o this_o method_n be_v omit_v as_o unuseful_a metius_n see_v snellius_n stevens_n and_o metius_n he_o that_o desire_v more_o concern_v this_o method_n let_v he_o read_v snellius_n stevens_n metius_n and_o other_o that_o have_v treat_v at_o large_a of_o it_o proposition_n iii_o to_o conjecture_n unto_o what_o quarter_n the_o ship_n be_v move_v and_o in_o what_o rhombe_n although_o the_o sign_n be_v fallacious_a in_o the_o solution_n of_o the_o former_a proposition_n for_o the_o find_v out_o the_o place_n 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the_o same_o be_v put_v into_o the_o quarter_n of_o the_o ship_n to_o be_v move_v and_o to_o describe_v its_o rhombe_n for_o they_o seldom_o use_v the_o sign_n take_v from_o the_o quarter_n of_o the_o apparent_a rise_n and_o set_v of_o the_o sun_n which_o they_o compute_v these_o sign_n may_v be_v corrupt_v by_o divers_a cause_n so_o that_o they_o may_v deceive_v in_o show_v the_o rhombe_n or_o quarter_n 1._o if_o that_o the_o declination_n of_o the_o magnetic_a needle_n be_v uncertain_a in_o that_o place_n and_o therefore_o the_o quarter_n of_o the_o compass_n do_v not_o show_v the_o true_a quarter_n 2._o if_o that_o the_o sea_n in_o that_o place_n have_v a_o flux_n to_o a_o certain_a place_n for_o it_o will_v carry_v the_o ship_n from_o the_o true_a rhombe_n although_o the_o ship_n be_v direct_v unto_o the_o same_o quarter_n the_o flux_n and_o reflux_n be_v the_o frequent_a cause_n of_o this_o error_n and_o in_o many_o place_n of_o the_o torrid_a zone_n a_o general_a motion_n be_v of_o force_n and_o in_o many_o place_n a_o state_v and_o fix_v motion_n from_o state_v wind_n 3._o wind_n especial_o storm_n remove_v the_o ship_n from_o the_o rhombe_n of_o their_o voyage_n although_o they_o ply_v in_o the_o same_o quarter_n 4._o the_o flux_n of_o the_o sea_n which_o be_v carry_v towards_o other_o quarter_n and_o carry_v the_o ship_n with_o it_o 5._o the_o rudder_n or_o helm_n can_v be_v move_v by_o he_o that_o steer_v unto_o any_o quarter_n as_o it_o ought_v to_o be_v the_o wave_n of_o the_o sea_n obstruct_v of_o it_o all_o these_o hinder_v the_o ship_n to_o be_v move_v in_o the_o same_o rhombe_n who_o quarter_n be_v show_v by_o the_o compass_n but_o how_o much_o it_o be_v draw_v aside_o must_v be_v learn_v by_o conjecture_n from_o the_o vehemency_n of_o the_o flood_n and_o of_o its_o quarter_n and_o the_o like_a but_o the_o method_n be_v very_o imperfect_a proposition_n iv_o to_o cast_v up_o the_o voyage_n make_v upon_o the_o rhombe_n to_o measure_v it_o at_o the_o give_v time_n from_o the_o give_v place_n etc._n the_o cast_v up_o the_o voyage_n make_v upon_o the_o rhombe_n etc._n etc._n pilot_n conjecture_v the_o same_o 1._o when_o they_o observe_v or_o know_v by_o experience_n what_o course_n a_o ship_n be_v wont_a to_o make_v with_o such_o a_o wind._n 2._o if_o that_o they_o have_v sail_v in_o the_o same_o meridian_n or_o vicine_fw-la line_n with_o any_o wind_n and_o have_v observe_v the_o latitude_n of_o the_o place_n in_o the_o begin_n of_o the_o motion_n and_o the_o latitude_n of_o the_o place_n in_o the_o follow_a time_n for_o the_o difference_n of_o latitude_n turn_v into_o mile_n show_v the_o course_n make_v for_o so_o long_a a_o space_n of_o time_n and_o such_o a_o wind._n whence_o for_o the_o time_n give_v and_o such_o a_o wind_n continue_v the_o course_n make_v be_v collect_v 3._o with_o more_o industry_n they_o measure_v the_o course_n perform_v by_o a_o boat_n and_o string_n one_o end_n of_o which_o be_v fasten_v to_o the_o boat_n and_o the_o other_o with_o the_o globe_n be_v in_o the_o ship_n for_o the_o ship_n remain_v immovable_a sail_v be_v permit_v to_o the_o boat_n until_o it_o be_v remove_v 10_o or_o 12_o orgyas_n of_o the_o string_n and_o the_o time_n elapse_v between_o be_v observe_v and_o from_o this_o for_o any_o time_n of_o the_o perform_v course_n of_o the_o ship_n be_v find_v out_o the_o sign_n of_o the_o perform_v sail_v of_o the_o ship_n be_v corrupt_v and_o render_v uncertain_a by_o divers_a way_n yea_o be_v uncertain_a of_o themselves_o see_v they_o be_v mere_a conjecture_n 1._o oftentimes_o the_o ship_n make_v lesser_a or_o great_a way_n than_o the_o conjecture_n afford_v viz._n because_o in_o many_o place_n of_o the_o sea_n the_o flux_n be_v
unto_o a_o certain_a quarter_n or_o the_o billow_n be_v roll_v unto_o a_o certain_a quarter_n if_o therefore_o the_o ship_n be_v direct_v into_o the_o same_o quarter_n the_o way_n make_v will_v be_v great_a than_o the_o conjecture_n make_v it_o but_o if_o into_o a_o contrary_a it_o will_v be_v lesser_a 2._o because_o the_o ship_n be_v carry_v by_o other_o cause_n into_o other_o quarter_n and_o so_o by_o wind_a arrive_v at_o another_o place_n 3._o the_o wind_n be_v various_o change_v 4._o by_o how_o much_o a_o ship_n have_v the_o great_a altitude_n by_o so_o much_o its_o motion_n seem_v more_o slow_a though_o it_o be_v not_o so_o proposition_n v._o to_o observe_v the_o latitude_n of_o a_o place_n unto_o which_o a_o ship_n be_v arrive_v the_o seaman_n observe_v it_o by_o the_o sun_n in_o the_o day_n time_n and_o by_o the_o star_n in_o the_o night_n as_o we_o have_v show_v in_o the_o xxiii_o chapter_n they_o use_v three_o instrument_n 23._o see_v chap._n 23._o the_o astrolabe_n the_o radius_fw-la and_o the_o triangle_n proposition_n vi_o from_o whence_o it_o be_v manifest_a that_o the_o method_n use_v by_o seaman_n to_o find_v the_o place_n on_o the_o map_n unto_o which_o they_o have_v arrive_v be_v fallacious_a because_o that_o they_o can_v neither_o be_v certain_a of_o the_o rhombe_n or_o quarter_n of_o the_o way_n or_o of_o the_o quantity_n of_o the_o way_n make_v or_o of_o the_o observe_v latitude_n of_o the_o place_n yet_o the_o observation_n of_o the_o latitude_n of_o the_o place_n unto_o which_o they_o be_v arrive_v because_o that_o it_o be_v not_o less_o subject_n to_o error_n especial_o the_o air_n and_o sea_n be_v tranquillous_a may_v be_v exempt_v from_o this_o fallacy_n but_o from_o that_o alone_o the_o place_n itself_o be_v not_o find_v on_o the_o map_n or_o earth_n but_o a_o second_o be_v require_v viz._n either_o a_o distance_n from_o another_o place_n give_v or_o a_o rhombe_n by_o which_o they_o sail_v from_o the_o give_v place_n to_o that_o or_o lasty_a the_o longitude_n of_o that_o place_n from_o this_o we_o have_v say_v that_o the_o observation_n of_o the_o way_n make_v or_o distance_n be_v uncertain_a as_o also_o that_o of_o the_o rhombs_n therefore_o they_o return_v back_o to_o find_v out_o the_o longitude_n of_o the_o place_n for_o the_o latitude_n and_o longitude_n of_o the_o place_n be_v know_v the_o place_n itself_o be_v find_v on_o the_o map_n and_o determine_v on_o the_o globe_n of_o the_o earth_n whence_o it_o be_v evident_a that_o the_o art_n of_o navigation_n require_v the_o solution_n of_o this_o problem_n to_o the_o make_v up_o of_o its_o perfection_n viz._n to_o find_v out_o the_o longitude_n of_o the_o place_n where_o we_o be_v at_o any_o time_n and_o on_o any_o day_n the_o prize_n be_v propound_v let_v he_o win_v who_o can_v a_o map_n or_o general_n carte_n of_o the_o world_n design_v in_o two_o plain_a hemispher_n by_o mounseur_fw-fr sanson_n geograph_n r_o to_o the_o french_a king_n and_o render_v into_o english_a and_o illustrated_n with_o figure_n by_o richard_n blome_n by_o the_o king_n especial_a command_n to_o the_o high_a and_o mighty_a monarch_n charles_n the_o secâ—â—â—_n by_o the_o grace_n of_o god_n king_n of_o england_n scotland_n france_n and_o ireland_n defendor_n of_o the_o faith_n etc._n etc._n this_o map_n in_o all_o humility_n be_v dedicate_v by_o your_o majesty_n obedient_a subject_n and_o sarvant_n richard_n blome_n a_o geographical_a description_n of_o the_o world_n take_v from_o the_o work_n of_o the_o famous_a mounseur_fw-fr sanson_n late_a geographer_n to_o the_o present_a french_a king_n to_o which_o be_v add_v about_o a_o hundred_o geographical_a and_o hydrographical_a table_n of_o the_o kingdom_n country_n and_o isle_n in_o the_o world_n with_o their_o chief_a city_n and_o seaport_n draw_v from_o the_o map_n of_o the_o say_v mounseur_fw-fr sanson_n and_o according_a to_o the_o method_n of_o the_o say_a description_n illustrate_v with_o map_n the_o second_o 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pole_n antarctic_a five_o other_o be_v different_a the_o one_o from_o the_o other_o as_o in_o the_o middle_n of_o the_o zodiac_n as_o the_o ecliptic_a the_o horizon_n as_o the_o horizon_n rational_a the_o horizon_n sensible_a or_o visible_a the_o parallel_n or_o the_o degree_n of_o latitude_n the_o meridian_n or_o the_o degree_n of_o longitude_n two_o colour_n in_o which_o be_v 4_o point_n which_o note_v our_o four_o season_n of_o the_o year_n to_o wit_n above_o the_o colour_n of_o the_o aequinox_n as_o the_o spring_n the_o autumn_n the_o colour_n of_o the_o solstice_n as_o the_o summer_n the_o winter_n three_o sort_n of_o zone_n in_o which_o be_v five_o to_o wit_v one_o torrid_a or_o the_o parch_a two_o temperate_a as_o the_o temperate_a arctic_a or_o northern_o the_o temperate_a antarctic_a or_o southern_o two_o freeze_a or_o cold_a as_o the_o freeze_a arctic_a or_o northern_o the_o freeze_a antarctic_a or_o southern_o three_o sort_n of_o shadow_n which_o diverse_o receive_v the_o inhabitant_n of_o the_o five_o zone_n for_o they_o be_v in_o the_o torrid_a zone_n amphisciens_fw-la in_o the_o temperate_a zone_n northern_o northern_a heterosciens_fw-fr southern_o southern_a heterosciens_fw-fr in_o the_o freeze_a zone_n northern_o northern_a perisciens_fw-fr southern_o southern_a perisciens_fw-fr three_o sort_n of_o position_n as_o the_o inhabitant_n about_o the_o same_o parallel_n opposite_a in_o meridian_n be_v perioeciens_fw-la the_o inhabitant_n about_o one_o meridian_n oppose_v in_o their_o parallel_n be_v antoeciens_fw-la the_o inhabitant_n oppose_v both_o in_o meridian_n and_o in_o parallel_n be_v antipode_n the_o climate_n of_o which_o the_o ancient_n first_o make_v seven_o which_o they_o call_v by_o the_o most_o famous_a place_n sea_n and_o river_n by_o which_o they_o pass_v as_o dia_z that_o be_v through_z meroes_n dia_z sienes_n dia_z alexandrias_n dia_z rhodou_n dia_z pontou_n dia_z boristenon_n then_o mâ—e_v in_o add_v dia_z ripheon_a dia_z danias_n the_o modern_n make_v 30_o to_o wit_n between_o the_o aequator_fw-la and_o the_o polar_a circle_n 24_o by_o half_a hour_n between_o the_o polar_a circle_n and_o the_o pole_n 6_o by_o month_n the_o parallel_n which_o be_v follow_v the_o ancient_n 14_o between_o the_o aequator_fw-la and_o polar_a circle_n 48_o by_o quarter_n of_o hour_n follow_v the_o modern_n 60_o between_o the_o polar_a circle_n and_o the_o pole_n 12_o by_o fourteen_o day_n the_o wind_n whereof_o the_o 4_o first_o and_o whereof_o the_o name_n be_v monosyllable_n shall_v be_v call_v cardinal_n wind_n as_o north_n south_n east_n west_n 4_o second_o and_o whereof_o the_o name_n be_v of_o two_o syllable_n and_o compose_v of_o two_o of_o the_o four_o first_o shall_v be_v call_v collateral_a wind_n as_o north-east_n northwest_n southeast_n south-west_n 8_o three_o and_o have_v their_o name_n of_o three_o syllable_n compose_v of_o one_o of_o the_o four_o first_o and_o of_o one_o of_o the_o four_o second_o as_o north_n north-east_n north_n northwest_n south_n southeast_n south_n south-west_n east_n north-east_n east_n south-west_n west_n northwest_n west_n south-west_n north_n and_o a_o quarter_n by_o north-east_n north_n and_o a_o quarter_n by_o northwest_n north-east_n and_o a_o quarter_n by_o north_n northwest_n and_o a_o quarter_n by_o north._n 16_o fourths_o take_v their_o name_n from_o four_o first_o or_o four_o second_o in_o say_v of_o one_o four_o part_n by_o the_o other_o and_o that_o without_o have_v regard_n to_o the_o eight_o three_o wind_n etc._n etc._n as_o it_o be_v south_n and_o a_o quarter_n by_o southeast_n south_n and_o a_o quarter_n by_o south-west_n southeast_n and_o a_o quarter_n by_o south_n south-west_n and_o a_o quarter_n by_o south_n east_n and_o a_o quarter_n by_o north-east_n east_n and_o a_o quarter_n by_o southeast_n north-east_n and_o a_o quarter_n by_o east_n southeast_n and_o a_o quarter_n by_o east_n west_n and_o a_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 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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
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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
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
the_o meridian_n or_o set_v after_o the_o same_o manner_n we_o must_v act_v with_o the_o other_o planet_n proposition_n xvii_o to_o show_v on_o the_o globe_n all_o those_o place_n in_o which_o the_o moon_n arise_v at_o the_o give_v hour_n and_o in_o which_o she_o be_v in_o the_o meridian_n and_o to_o which_o she_o set_v if_o that_o the_o longitude_n and_o latitude_n of_o the_o moon_n be_v know_v hour_n by_o the_o globe_n be_v show_v all_o the_o place_n in_o which_o the_o moon_n arise_v and_o set_v at_o any_o hour_n let_v the_o place_n of_o the_o sun_n as_o also_o of_o the_o moon_n be_v note_v on_o the_o ecliptic_a as_o aforesaid_a and_o the_o place_n of_o the_o sun_n be_v bring_v to_o the_o meridian_n and_o the_o index_n to_o the_o 12_o hour_n of_o the_o circle_n let_v the_o globe_n be_v turn_v until_o the_o place_n of_o the_o moon_n come_v to_o the_o meridian_n and_o let_v the_o hour_n be_v observe_v on_o the_o circle_n which_o be_v note_v or_o let_v a_o mark_n be_v make_v on_o the_o circle_n for_o they_o show_v how_o much_o late_a the_o moon_n come_v to_o the_o meridian_n than_o the_o sun_n moreover_o the_o place_n of_o the_o moon_n be_v constitute_v in_o the_o meridian_n let_v the_o eminent_a point_n be_v note_v in_o this_o or_o let_v the_o parallel_n of_o the_o moon_n be_v describe_v this_o do_v let_v the_o place_n of_o the_o sun_n be_v bring_v to_o the_o meridian_n and_o the_o index_n to_o the_o 12_o hour_n let_v the_o globe_n be_v turn_v until_o the_o hour_n be_v find_v in_o which_o the_o moon_n touch_v the_o meridian_n of_o the_o place_n let_v the_o point_n also_o of_o the_o meridian_n be_v note_v which_o hang_v over_o the_o place_n of_o the_o moon_n moreover_o let_v the_o place_n who_o hour_n be_v give_v be_v bring_v to_o the_o meridian_n the_o index_n to_o the_o hour_n give_v let_v the_o globe_n be_v turn_v until_o the_o index_n show_v the_o 12_o hour_n of_o noon_n or_o midnight_n so_o the_o place_n be_v those_o subject_n to_o the_o semicircle_n of_o the_o meridian_n in_o which_o the_o sun_n make_v the_o meridies_n at_o the_o hour_n give_v let_v the_o index_n be_v reduce_v to_o 12_o and_o let_v the_o globe_n be_v turn_v again_o until_o the_o index_n come_v to_o the_o hour_n note_v before_o in_o the_o circle_n in_o this_o situation_n of_o the_o globe_n the_o place_n which_o be_v subject_a to_o the_o note_a point_n of_o the_o meridian_n be_v that_o to_o which_o the_o sun_n be_v then_o vertical_a therefore_o let_v this_o place_n be_v constitute_v in_o the_o globe_n in_o the_o vertex_fw-la of_o the_o horizon_n all_o the_o place_n be_v those_o subject_n to_o the_o superior_a semicircle_n of_o the_o meridian_n to_o which_o the_o moon_n be_v then_o in_o the_o meridian_n but_o those_o place_n which_o be_v discern_v in_o the_o oriental_a semicircle_n of_o the_o horizon_n be_v those_o to_o which_o the_o moon_n than_o set_v last_o in_o those_o place_n which_o be_v discern_v in_o the_o occidental_a semicircle_n of_o the_o horizon_n the_o moon_n rise_v at_o the_o give_v moment_n of_o time_n after_o the_o same_o mode_n we_o act_n with_o saturn_n jupiter_n and_o the_o rest_n of_o the_o planet_n if_o that_o their_o longitude_n and_o latitude_n be_v know_v proposition_n xviii_o the_o day_n or_o hour_n be_v give_v in_o which_o the_o ecliptic_a of_o the_o moon_n shall_v be_v or_o have_v be_v to_o exhibit_v on_o the_o globe_n all_o those_o place_n which_o have_v see_v it_o and_o in_o that_o species_n to_o who_o the_o moon_n shall_v in_o the_o meridian_n to_o who_o it_o shall_v arise_v and_o to_o who_o it_o shall_v set_v eclipse_v this_o problem_n little_o differ_v from_o the_o precedent_n but_o yet_o it_o have_v a_o more_o easy_a solution_n from_o the_o day_n give_v let_v the_o place_n of_o the_o sun_n be_v find_v except_o it_o be_v already_o know_v and_o let_v the_o point_n opposite_a to_o it_o be_v note_v on_o the_o ecliptic_a of_o the_o globe_n for_o this_o be_v the_o place_n of_o the_o moon_n 28._o see_v proposition_n 6._o chapter_n 28._o let_v the_o place_n be_v find_v in_o the_o globe_n to_o which_o the_o sun_n be_v vertical_a at_o the_o hour_n and_o let_v the_o antipode_n of_o this_o place_n be_v find_v according_a to_o the_o vi_o proposition_n of_o the_o xxviii_o chapter_n for_o this_o shall_v be_v the_o place_n unto_o which_o the_o moon_n be_v eclipse_v shall_v be_v vertical_a let_v this_o place_n be_v constitute_v in_o the_o vertex_fw-la of_o the_o horizon_n the_o pole_n be_v elevate_v or_o depress_v for_o the_o latitude_n of_o the_o place_n so_o all_o the_o place_n of_o the_o globe_n which_o be_v above_o the_o horizon_n may_v have_v see_v that_o eclipse_n and_o those_o which_o lie_v under_o the_o brazen_a meridian_n shall_v see_v it_o in_o the_o meridian_n those_o which_o lie_v under_o the_o oriental_a semicircle_n shall_v see_v it_o in_o the_o west_n or_o set_v with_o the_o eclipse_n but_o those_o which_o lie_v in_o the_o occidental_a semicircle_n of_o the_o horizon_n shall_v see_v it_o in_o the_o east_n or_o noon_n to_o arise_v eclipse_v but_o see_v that_o a_o eclipse_n be_v not_o perform_v in_o one_o moment_n of_o a_o hour_n but_o dure_v for_o some_o hour_n therefore_o it_o be_v wont_a to_o be_v divide_v into_o the_o beginning_n middle_a and_o end_v and_o the_o moment_n of_o the_o hour_n be_v wont_a to_o be_v note_v therefore_o the_o consideration_n must_v be_v more_o especial_o concern_v the_o middle_a time_n of_o the_o eclipse_n moreover_o see_v that_o the_o moon_n be_v less_o than_o the_o earth_n it_o will_v illustrate_v a_o lesser_a part_n than_o the_o hemisphere_n be_v also_o it_o will_v be_v see_v by_o the_o inhabitant_n of_o a_o lesser_a part_n so_o that_o it_o will_v not_o be_v any_o more_o conspicuous_a to_o those_o which_o lie_v in_o the_o oriental_a semicircle_n of_o the_o horizon_n but_o to_o those_o in_o the_o occidental_a semicircle_n it_o have_v not_o yet_o appear_v but_o a_o certain_a circle_n parallel_n to_o the_o horizon_n be_v to_o be_v see_v which_o terminate_v the_o part_n illustrate_v now_o how_o much_o this_o part_n be_v distant_a from_o the_o hemisphere_n or_o how_o great_a a_o portion_n it_o be_v of_o the_o superficies_n of_o the_o earth_n shall_v be_v the_o enquiry_n of_o the_o follow_a proposition_n proposition_n xix_o the_o semidiameter_n of_o the_o moon_n and_o earth_n be_v give_v scheme_n see_v scheme_n and_o the_o distance_n of_o they_o to_o find_v out_o how_o long_o a_o portion_n of_o the_o earth_n be_v illustrate_v by_o the_o moon_n at_o the_o full._n 11._o see_v proposition_n 11._o this_o problem_n must_v be_v solve_v by_o the_o same_o mode_n that_o we_o have_v use_v in_o the_o eleven_o proposition_n for_o let_v the_o centre_n of_o the_o earth_n be_v s_o the_o great_a circle_n represent_v the_o superficies_n o_o f_o l_o h._n the_o centre_n of_o the_o moon_n a_o the_o great_a circle_n c_o p_o b_o q._n let_v the_o tangent_n l_o b_o o_o c_o be_v draw_v for_o these_o be_v the_o ultimate_a ray_n that_o can_v come_v from_o the_o moon_n to_o the_o earth_n and_o therefore_o the_o arch_n o_o h_n l_o will_v denote_v the_o part_n of_o the_o superficies_n of_o the_o earth_n which_o be_v illustrate_v by_o the_o moon_n and_o who_o inhabitant_n may_v see_v the_o moon_n together_o which_o by_o how_o much_o lesser_a it_o be_v than_o the_o hemisphere_n we_o shall_v know_v if_o we_o find_v the_o angle_n h_o s_o l_o or_o the_o arch_n h_o l._n let_v b_o n_n be_v draw_v from_o b_o parallel_n to_o a_o s_n b_o he_o shall_v be_v equal_a to_o s_o n_n and_o n_n l_o the_o excess_n of_o the_o semidiameter_n of_o the_o earth_n s_o l_o above_o the_o semidiameter_n of_o the_o moon_n a_o b_o and_o b_o n_n be_v of_o a_o equal_a distance_n with_o a_o s_o but_o the_o the_o angle_n n_o l_o b_o be_v direct_a or_o of_o 90_o degree_n therefore_o in_o the_o triangle_n straight_a angle_n n_o b_o l_o we_o shall_v find_v the_o angle_n n_o b_o l_o by_o this_o proportion_n as_o n_z b_o be_v to_z n_o l_o so_fw-mi be_v the_o whole_a sign_n to_o the_o sign_n of_o the_o angle_n l_o b_o n_o who_o arch_n be_v that_o in_o which_o h_n l_o differ_v from_o the_o arch_n 90_o or_o from_o the_o quadrant_n of_o the_o periphery_a of_o the_o earth_n and_o so_o great_a a_o interval_n be_v the_o periphery_a of_o the_o earth_n distant_a from_o the_o great_a circle_n terminanate_v the_o part_n of_o the_o earth_n illuminate_v by_o the_o moon_n let_v we_o suppose_v the_o semidiameter_n of_o the_o moon_n to_o contain_v four_o part_n of_o such_o like_a the_o semidiamiter_n of_o the_o earth_n contain_v 15_o or_o 4_o 15_o of_o the_o semidiamiter_n of_o the_o earth_n now_o the_o great_a distance_n of_o
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 earth_n or_o their_o situation_n to_o the_o give_v place_n or_o one_o to_o another_o so_o i_o think_v the_o sense_n of_o the_o proposition_n will_v be_v better_o understand_v by_o reason_n that_o very_o few_o student_n and_o favourer_n of_o geography_n understand_v the_o rule_n of_o perspective_n neither_o can_v they_o attain_v to_o any_o distinct_a knowledge_n of_o the_o construction_n and_o nature_n of_o geographical_a map_n or_o judge_v of_o their_o commodity_n or_o defect_n except_o they_o know_v the_o principle_n according_a unto_o which_o they_o be_v make_v therefore_o here_o a_o few_o thing_n necessary_a in_o this_o doctrine_n must_v be_v explain_v from_o the_o art_n of_o perspective_n geography_n the_o knowledge_n of_o perspective_n necessary_a in_o geography_n now_o that_o art_n as_o most_o know_v be_v conversant_a in_o represent_v all_o object_n or_o body_n on_o some_o table_n or_o platform_n as_o the_o part_n of_o a_o picture_n be_v so_o conform_v and_o seat_v one_o to_o the_o other_o and_o so_o appear_v to_o our_o fight_n the_o eye_n be_v fix_v to_o some_o certain_a place_n as_o the_o part_n of_o the_o body_n which_o it_o represent_v this_o indeed_o be_v the_o end_n of_o the_o perspective_n but_o the_o mode_n by_o which_o they_o endeavour_v to_o obtain_v it_o be_v this_o perspective_n the_o mode_n for_o the_o obtain_v the_o art_n of_o perspective_n then_o they_o will_v represent_v a_o point_n a_o superficies_n or_o any_o body_n of_o what_o shape_n soever_o in_o a_o table_n board_n or_o paper_n whether_o they_o behold_v it_o or_o conceive_v the_o idea_n in_o their_o fancy_n 1._o they_o imagine_v it_o be_v discerner_n by_o the_o eye_n as_o in_o or_o from_o one_o point_n and_o they_o do_v assign_v a_o certain_a situation_n or_o place_n to_o the_o eye_n whence_o the_o sight_n may_v be_v make_v 2._o then_o they_o conceive_v some_o one_o infinite_a plain_n they_o term_v it_o a_o glass_n because_o it_o be_v better_a for_o conception_n if_o that_o the_o plain_a be_v understand_v to_o be_v pellucid_a to_o be_v interpose_v in_o some_o certain_a situation_n between_o the_o eye_n and_o the_o object_n then_o 3._o they_o conceive_v ray_n or_o line_n to_o be_v draw_v through_o that_o plain_a to_o the_o eye_n from_o every_o point_n of_o the_o object_n they_o say_v that_o the_o point_n of_o this_o plain_a by_o which_o the_o ray_n be_v so_o conceive_v to_o penetrate_v to_o the_o eye_n be_v the_o representation_n of_o the_o point_n of_o the_o object_n itself_o or_o the_o shadow_n of_o it_o as_o they_o term_v it_o and_o these_o point_n be_v conjoin_v by_o line_n they_o determine_v the_o figure_n which_o thence_o arise_v in_o the_o table_n to_o be_v the_o representation_n of_o the_o very_a object_n of_o the_o body_n or_o superficies_n in_o such_o a_o situation_n of_o the_o eye_n and_o this_o figure_n of_o a_o plain_a or_o table_n remain_v in_o its_o situation_n do_v not_o otherwise_o appear_v to_o the_o eye_n remain_v in_o its_o situation_n then_o as_o if_o it_o behold_v the_o very_a object_n itself_o which_o yet_o the_o optic_n show_v not_o to_o be_v altogether_o true_a in_o all_o respect_n and_o it_o be_v easy_a to_o understand_v from_o the_o various_a position_n of_o a_o interpose_a plain_n but_o by_o reason_n no_o better_o method_n of_o represent_v body_n be_v yet_o find_v therefore_o we_o must_v be_v content_a with_o this_o for_o example_n let_v the_o superficies_n of_o the_o earth_n and_o all_o its_o periphery_n and_o place_n be_v represent_v on_o a_o table_n and_o therefore_o in_o the_o first_o we_o conceive_v the_o eye_n to_o be_v fix_v or_o situate_v as_o a_o point_n without_o the_o earth_n in_o the_o air._n then_o between_o the_o eye_n and_o the_o earth_n a_o certain_a table_n or_o glass_n plain_a to_o be_v extend_v who_o situation_n although_o it_o may_v be_v take_v at_o pleasure_n yet_o in_o practice_n it_o be_v so_o assume_v to_o a_o better_a and_o more_o ordinate_a figure_n of_o a_o equal_a form_n that_o it_o be_v perpendicular_a to_o the_o line_n which_o be_v draw_v from_o the_o eye_n to_o the_o centre_n of_o the_o earth_n then_o we_o conceive_v line_n to_o be_v draw_v or_o ray_n to_o be_v emit_v through_o the_o table_n or_o glass_n to_o the_o eye_n from_o all_o point_n or_o place_n of_o the_o superficies_n of_o the_o earth_n as_o from_o all_o the_o point_n of_o the_o aequator_fw-la of_o the_o tropic_n polary_a circle_n also_o of_o the_o meridian_n as_o likewise_o from_o all_o city_n source_n of_o water_n and_o the_o like_a every_o one_o of_o these_o ray_n shall_v pierce_v the_o table_n in_o certain_a point_n these_o point_n therefore_o be_v the_o shadow_n or_o representation_n of_o the_o place_n of_o the_o superficies_n of_o the_o earth_n and_o if_o those_o point_n which_o be_v make_v by_o the_o ray_n emit_v from_o some_o one_o periphery_n as_o from_o the_o aequator_fw-la from_o one_o of_o the_o tropic_n from_o a_o polary_a circle_n or_o some_o other_o meridian_n be_v join_v by_o a_o draw_a line_n let_v it_o be_v either_o straight_a or_o crooked_a this_o shall_v be_v the_o representation_n or_o shadow_n of_o this_o periphery_a so_o we_o shall_v have_v all_o the_o circle_n and_o all_o the_o place_n of_o the_o earth_n represent_v on_o a_o table_n be_v the_o whole_a superficies_n of_o the_o earth_n be_v round_o can_v be_v so_o well_o represent_v on_o a_o plain_a as_o otherwise_o it_o be_v but_o because_o the_o earth_n be_v round_o therefore_o the_o whole_a superficies_n of_o the_o earth_n with_o all_o its_o place_n can_v commodious_o be_v represent_v on_o one_o plain_a because_o they_o shall_v make_v two_o place_n one_o and_o the_o same_o point_n on_o the_o plain_a and_o those_o that_o be_v situate_v beyond_o the_o hemisphere_n will_v be_v represent_v with_o a_o false_a face_n therefore_o half_a the_o supersicies_n of_o the_o earth_n must_v be_v represent_v on_o one_o table_n and_o the_o other_o half_a on_o the_o other_o and_o so_o the_o eye_n may_v be_v take_v within_o the_o earth_n itself_o viz._n when_o we_o take_v up_o one_o hemisphere_n to_o be_v represent_v the_o eye_n be_v conceive_v to_o be_v place_v in_o the_o other_o hemisphere_n and_o the_o table_n between_o that_o and_o the_o hemisphere_n to_o be_v represent_v the_o same_o must_v be_v understand_v if_o that_o only_a part_n of_o the_o superficies_n as_o europe_n asia_n spain_n must_v be_v represent_v on_o the_o table_n for_o than_o we_o may_v assume_v the_o place_n of_o the_o eye_n in_o the_o very_a centre_n of_o the_o earth_n if_o we_o please_v from_o these_o i_o think_v the_o reader_n may_v sufficient_o understand_v the_o nature_n and_o mode_n of_o this_o perspective_n art_n by_o which_o the_o place_n of_o the_o earth_n be_v represent_v on_o a_o plain_a the_o other_o two_o be_v more_o full_o to_o be_v explain_v from_o those_o which_o we_o have_v speak_v of_o in_o this_o method_n because_o from_o thence_o depend_v the_o variety_n and_o diversity_n of_o geographical_a table_n we_o have_v say_v that_o a_o point_n must_v be_v take_v for_o the_o representation_n for_o the_o place_n of_o the_o eye_n without_o the_o object_n to_o be_v represent_v as_o without_o the_o hemisphere_n of_o the_o earth_n or_o without_o the_o superficies_n of_o spain_n or_o europe_n and_o therefore_o because_o there_o be_v a_o infinite_a space_n about_o any_o object_n and_o on_o that_o account_n there_o be_v infinite_a point_n in_o which_o the_o eye_n may_v be_v put_v contemplate_v the_o superficies_n of_o the_o earth_n or_o europe_n or_o asia_n if_o that_o a_o particular_a table_n must_v be_v make_v and_o if_o the_o ray_n be_v draw_v to_o divers_a point_n from_o the_o same_o point_n of_o the_o object_n or_o superficies_n which_o may_v penetrate_v the_o same_o table_n the_o penetration_n of_o the_o ray_n be_v make_v in_o a_o very_a different_a
apprehend_v it_o from_o his_o word_n neither_o do_v i_o see_v how_o it_o can_v follow_v from_o his_o hypothesis_n it_o be_v probable_a that_o the_o sun_n and_o general_a wind_n do_v very_o much_o contribute_v to_o this_o intumescency_n of_o the_o water_n and_o see_v that_o the_o sun_n in_o the_o aequinoctial_o do_v incumb_fw-la on_o the_o middle_n of_o the_o sea_n of_o the_o torrid_a zone_n therefore_o either_o he_o or_o the_o wind_n cause_n that_o the_o sea_n than_o swell_v more_o than_o at_o another_o time_n but_o as_o concern_v the_o solstice_n we_o must_v say_v in_o a_o contrary_a mode_n or_o that_o the_o same_o be_v the_o cause_n of_o the_o great_a intumescency_n of_o the_o sea_n in_o the_o time_n of_o the_o aequinoctial_o either_o of_o the_o spring_n or_o autumn_n which_o be_v the_o cause_n of_o more_o frequent_a rain_n wind_n and_o inundadion_n in_o those_o season_n proposition_n fourteen_o in_o some_o part_n of_o the_o ocean_n gulf_n and_o shore_n great_a be_v the_o increase_n and_o decrease_v of_o the_o water_n in_o the_o influx_n and_o deflux_n in_o other_o some_o it_o be_v very_o small_a in_o some_o not_o discernible_a and_o so_o there_o be_v no_o flux_n and_o reflux_n or_o intumescency_n and_o detumescency_n ocean_n the_o increase_n and_o decrease_v of_o the_o water_n in_o several_a part_n of_o the_o ocean_n those_o place_n receive_v great_a augmentation_n and_o decrease_n 1._o that_o be_v under_o the_o torrid_a zone_n between_o the_o tropic_n for_o then_o the_o moon_n press_v for_o the_o most_o part_n be_v there_o carry_v round_o 2._o in_o place_n that_o be_v direct_o extend_v from_o east_n to_o west_n or_o nigh_o the_o collateral_a quarter_n 3._o in_o those_o gulf_n that_o be_v long_a and_o less_o broad_a the_o augmentation_n be_v the_o more_o sensible_a 4._o in_o those_o place_n in_o which_o few_o island_n or_o procurrent_n adjoyn_v to_o the_o earth_n cambaja_n the_o great_a flux_n and_o deflux_n in_o the_o straight_a of_o cambaja_n the_o great_a flux_n and_o deflux_n hitherto_o observe_v be_v that_o which_o be_v in_o the_o straight_a of_o cambaja_n in_o one_o of_o the_o inlet_n of_o the_o river_n indus_n and_o it_o have_v strike_v many_o with_o admiration_n for_o the_o water_n recede_v to_o a_o high_a distance_n and_o that_o very_o speedy_o whence_o not_o without_o reason_n the_o river_n indus_n or_o the_o gulf_n of_o cambaja_n be_v think_v to_o be_v that_o unto_o which_o when_o that_o alexander_n the_o great_a come_v and_o endeavour_v to_o pass_v his_o army_n over_o as_o it_o be_v there_o relate_v the_o water_n present_o go_v back_o and_o leave_v his_o ship_n a_o ground_n hence_o he_o go_v no_o far_o but_o judge_v that_o the_o god_n have_v here_o fix_v the_o bound_n of_o his_o expedition_n with_o a_o prohibition_n of_o proceed_v any_o far_o the_o cause_n be_v the_o small_a or_o narrow_a and_o deep_a depression_n of_o the_o channel_n but_o yet_o it_o be_v probable_a there_o be_v some_o other_o cause_n damman_n fluv_n and_o reflux_n at_o damman_n at_o the_o city_n damman_n in_o india_n not_o far_o from_o surat_n the_o altitude_n of_o the_o water_n by_o flux_n and_o reflux_n be_v vary_v at_o two_o and_o a_o half_a orygas_n and_o the_o sea_n depart_v from_o the_o shore_n the_o space_n of_o half_a a_o mile_n in_o the_o gulf_n of_o cambaja_n the_o flux_n augment_v the_o altitude_n five_o orgyas_n other_o say_v seven_o which_o unusual_a augmentation_n have_v be_v the_o cause_n of_o the_o loss_n of_o many_o ship_n by_o unexperienced_a mariner_n for_o the_o water_n fall_v they_o have_v be_v split_v on_o the_o rock_n red-sea_n no_o constant_a time_n of_o the_o flux_n and_o reflux_n in_o the_o strait_n of_o magellan_n the_o flux_n and_o reflux_n in_o the_o red-sea_n in_o the_o gulf_n and_o shore_n of_o the_o strait_n of_o magellan_n no_o constant_a time_n of_o the_o flux_n and_o reflux_n be_v observe_v for_o sometime_o the_o water_n flow_v and_o reflow_v in_o three_o hour_n othersome_a in_o twelve_o hour_n which_o inconstancy_n be_v to_o be_v ascribe_v to_o the_o violent_a irruption_n of_o the_o ocean_n into_o that_o straight_a and_o from_o the_o various_a agitation_n of_o the_o wind_n about_o malacca_n also_o at_o the_o straight_a of_o sunda_n a_o notable_a flux_n and_o deflux_n be_v observe_v in_o the_o arabian_a gulf_n or_o red_a sea_n some_o of_o the_o ancient_n have_v write_v that_o there_o be_v so_o great_a a_o reflux_n as_o scaliger_n write_v that_o moses_n and_o the_o israelite_n pass_v over_o without_o any_o miracle_n but_o it_o be_v false_a because_o the_o reflux_n be_v not_o there_o so_o great_a as_o to_o leave_v the_o channel_n dry_a on_o the_o coast_n of_o china_n the_o flux_n and_o reflux_n be_v very_o sensible_a as_o also_o at_o the_o isle_n of_o japan_n at_o panama_n on_o the_o coast_n of_o america_n lie_v at_o the_o pacifick_n ocean_n the_o sea_n be_v very_o much_o exalt_v panama_n the_o sea_n at_o the_o flux_n much_o exalt_v at_o panama_n and_o by_o and_o by_o depress_v again_o in_o the_o full_a moon_n the_o flux_n be_v so_o much_o augment_v that_o water_n enter_v into_o the_o house_n of_o the_o city_n yea_o in_o almost_o all_o the_o shore_n of_o the_o south_n sea_n the_o altitude_n of_o the_o water_n be_v wonderful_o augment_v and_o diminish_v so_o that_o in_o the_o reflux_n the_o decrease_n be_v sensible_a for_o two_o mile_n in_o the_o gulf_n of_o bengala_n at_o the_o shore_n of_o sâ—am_n the_o flux_n augment_v the_o altitude_n ten_o foot_n sea_n the_o flux_n not_o perceivable_a in_o the_o mediterranean_a sea_n but_o in_o the_o mediterranean_a sea_n which_o flow_v in_o through_o the_o strait_n of_o gibraltar_n from_o the_o west_n to_o the_o east_n the_o flux_n be_v not_o perceivable_a because_o the_o situation_n be_v contrary_a to_o the_o quarter_n into_o which_o the_o sea_n be_v move_v and_o therefore_o the_o water_n of_o it_o be_v little_o augment_v by_o the_o flux_n so_o that_o it_o be_v not_o discernible_a unless_o in_o the_o gulf_n of_o venice_n which_o by_o reason_n of_o its_o long_a extension_n and_o small_a latitude_n show_v the_o flux_n and_o reflux_n when_o in_o the_o other_o part_n of_o the_o mediterranean_a sea_n by_o reason_n of_o its_o notable_a latitude_n that_o little_a augmentation_n and_o decrease_n be_v not_o discover_v whence_o this_o flux_n and_o reflux_n be_v unknown_a to_o the_o grecian_n as_o also_o to_o the_o roman_n in_o the_o time_n of_o scipio_n africanus_n and_o the_o grecian_n as_o well_v as_o the_o roman_n account_v it_o as_o miraculous_a what_o sometime_o they_o discover_v in_o other_o place_n as_o be_v manifest_a from_o the_o expedition_n of_o alexander_n the_o great_a and_o of_o scipio_n in_o the_o expugnation_n of_o carthage_n but_o in_o the_o time_n of_o cicero_n it_o be_v know_v to_o the_o roman_n yet_o some_o observe_v it_o a_o little_a at_o massilia_n also_o at_o certain_a coast_n of_o barbary_n it_o be_v note_v enough_o out_o the_o flux_n and_o reflux_n in_o the_o baltic_a sea_n not_o yet_o find_v out_o in_o the_o baltic_a ocean_n as_o also_o in_o the_o whole_a northern_a sea_n beyond_o england_n towards_o norway_n and_o greenland_n the_o flux_n and_o reflux_n of_o the_o sea_n be_v not_o yet_o find_v out_o as_o neither_o in_o the_o north_n coast_n of_o the_o pacifick_n ocean_n but_o the_o cause_n be_v not_o yet_o sufficient_o know_v unless_o you_o will_v say_v that_o those_o sea_n be_v remote_a from_o the_o course_n of_o the_o moon_n and_o also_o that_o they_o be_v extend_v from_o the_o west_n to_o the_o east_n and_o north_n moreover_o that_o many_o isle_n and_o procurrency_n of_o land_n do_v hinder_v these_o three_o must_v be_v conjoin_v to_o impede_fw-la the_o flux_n of_o the_o sea_n in_o these_o place_n proposition_n xv._o the_o flux_n and_o reflux_n of_o the_o sea_n be_v a_o violent_a motion_n viz._n a_o impulse_n but_o the_o reflux_n be_v a_o natural_a motion_n of_o the_o water_n for_o the_o flux_n be_v cause_v by_o the_o pression_n of_o the_o moon_n or_o matter_n between_o the_o moon_n and_o the_o earth_n or_o also_o because_o that_o the_o sea_n do_v not_o remain_v in_o that_o situation_n which_o be_v receive_v in_o the_o flux_n this_o be_v a_o sign_n that_o it_o be_v a_o violent_a motion_n but_o in_o the_o reflux_n the_o sea_n be_v move_v from_o a_o more_o high_a place_n to_o a_o more_o depress_a place_n which_o be_v the_o natural_a motion_n of_o water_n lemma_n the_o place_n of_o the_o moon_n be_v give_v in_o the_o ecliptic_a and_o the_o latitude_n and_o hour_n of_o the_o day_n from_o a_o ephemerides_n or_o by_o supputation_n or_o astronomical_a observation_n to_o find_v on_o the_o terrestrial_a globe_n the_o place_n unto_o which_o the_o moon_n at_o the_o hour_n give_v be_v vertical_a also_o to_o exhibit_v all_o those_o place_n of_o the_o earth_n unto_o
which_o the_o moon_n will_v be_v vertical_a that_o day_n viz._n one_o after_o another_o 19_o see_v proposition_n 13._o in_o chap._n 19_o the_o use_n of_o this_o problem_n be_v great_a yea_o very_a necessary_a in_o the_o doctrine_n concern_v the_o flux_n and_o reflux_n of_o the_o sea_n the_o mode_n of_o perform_v of_o the_o same_o you_o shall_v find_v in_o the_o nineteenth_o chapter_n and_o the_o thirteen_o proposition_n for_o there_o it_o be_v more_o convenient_o explain_v yet_o the_o explication_n of_o that_o proposition_n may_v be_v anticipate_v and_o demonstrate_v to_o the_o studious_a in_o this_o chapter_n proposition_n xvi_o in_o those_o place_n of_o the_o sea_n to_o which_o the_o moon_n be_v vertical_a the_o flux_n and_o deflux_n be_v great_a except_o that_o there_o be_v other_o impediment_n which_o we_o have_v reckon_v up_o in_o the_o fourteen_o proposition_n and_o by_o how_o much_o the_o part_n of_o the_o sea_n be_v more_o remote_a from_o the_o place_n by_o so_o much_o the_o flux_n and_o deflux_n be_v lesser_a other_o thing_n be_v equal_a for_o because_o in_o that_o place_n the_o pressure_n be_v great_a and_o the_o tumour_n of_o the_o water_n great_a which_o be_v more_o vicine_fw-la to_o the_o moon_n press_v and_o the_o celestial_a matter_n thence_o follow_v that_o that_o the_o proposition_n intimate_v the_o objection_n concern_v some_o other_o place_n in_o the_o comparison_n of_o which_o the_o contrary_a be_v find_v be_v to_o be_v excuse_v by_o the_o admixtion_n of_o other_o cause_n proposition_n xvii_o the_o quantity_n of_o the_o flux_n and_o reflux_n be_v unconstant_a in_o every_o place_n and_o divers_a on_o several_a day_n and_o by_o so_o much_o the_o great_a or_o lesser_a by_o how_o much_o the_o moon_n be_v more_o remote_a or_o near_o unto_o that_o place_n ecliptic_a the_o moon_n every_o day_n change_v her_o place_n in_o the_o ecliptic_a for_o the_o moon_n every_o day_n change_v her_o place_n in_o the_o ecliptic_a and_o so_o on_o other_o day_n be_v vertical_a to_o other_o place_n and_o by_o consequence_n be_v more_o remote_a from_o any_o place_n or_o more_o near_o which_o be_v observe_v we_o conclude_v from_o the_o precede_a proposition_n that_o there_o be_v a_o divers_a quantity_n of_o the_o flux_n and_o reflux_n in_o one_o and_o the_o same_o place_n on_o divers_a day_n whether_o that_o the_o diversity_n be_v sensible_a or_o insensible_a proposition_n xviii_o the_o great_a intumescency_n of_o water_n in_o any_o place_n and_o term_v of_o the_o flux_n aught_o to_o be_v when_o that_o the_o moon_n do_v occupy_v the_o meridian_n of_o the_o place_n but_o in_o many_o place_n it_o be_v find_v to_o be_v in_o another_o situation_n of_o the_o moon_n for_o than_o be_v the_o moon_n most_o nigh_o to_o any_o place_n of_o the_o earth_n when_o that_o it_o be_v in_o the_o meridian_n of_o that_o place_n because_o that_o the_o hypotenusa_fw-la of_o a_o right_a angle_a triangle_n be_v low_a than_o the_o cathetus_n whence_o it_o be_v infer_v by_o the_o xvi_o proposition_n that_o when_o the_o moon_n be_v in_o the_o meridian_n 16._o see_v proposition_n 16._o there_o ought_v to_o be_v the_o great_a intumescency_n and_o altitude_n of_o water_n and_o immediate_o a_o decrease_n to_o succeed_v but_o when_o the_o moon_n be_v in_o the_o low_a of_o the_o meridian_n than_o the_o narrow_a of_o the_o vortex_n of_o the_o earth_n opposite_a to_o it_o in_o the_o upper_a meridian_n and_o therefore_o do_v effect_v the_o same_o as_o if_o that_o the_o body_n of_o the_o moon_n be_v present_a but_o here_o arise_v a_o great_a difficulty_n for_o there_o be_v many_o place_n and_o coast_n of_o the_o earth_n in_o which_o we_o find_v that_o the_o term_n of_o the_o flux_n be_v not_o when_o that_o the_o moon_n come_v to_o the_o meridian_n as_o the_o philosopher_n hold_v before_o this_o age_n but_o soon_o or_o late_a viz._n when_o that_o the_o moon_n come_v to_o a_o certain_a quarter_n not_o cardinal_n and_o this_o quarter_n be_v not_o constant_o observe_v but_o in_o new_a and_o full_a moon_n for_o the_o most_o part_n the_o great_a intumescency_n be_v and_o the_o begin_n of_o a_o detumescency_n before_o the_o moon_n come_v to_o this_o quarter_n or_o vertical_a circle_n so_o at_o london_n the_o water_n be_v at_o the_o high_a when_o the_o moon_n come_v to_o the_o quarter_n which_o be_v between_o the_o south_n and_o west_n or_o north_n and_o east_n that_o be_v to_o the_o south_n west_n or_o north_n east_n quarter_n at_o the_o coast_n of_o china_n in_o the_o port_n of_o the_o city_n maccau_n portugal_n the_o great_a flux_n at_o the_o coast_n of_o china_n observe_v by_o a_o portugal_n a_o certain_a portugal_n mariner_n observe_v the_o time_n of_o the_o great_a intumescency_n by_o this_o mode_n the_o elevation_n of_o the_o pole_n be_v 22_o degree_n 20_o minute_n in_o the_o year_n 1584._o on_o the_o 19_o of_o september_n the_o moon_n be_v at_o full_a than_o the_o intumescency_n or_o altitude_n of_o the_o high_a water_n be_v observe_v in_o the_o morning_n at_o ½_n or_o ¼_n of_o a_o hour_n past_o 8._o therefore_o then_o the_o moon_n be_v remove_v from_o the_o meridian_n 3_o ¼_n hour_n whence_o the_o quarter_n or_o vertical_a circle_n in_o which_o the_o moon_n at_o that_o moment_n of_o time_n be_v be_v find_v according_a to_o the_o problem_n of_o the_o 30_o chapter_n anno_fw-la 1585._o on_o the_o 16_o of_o february_n in_o the_o full_a moon_n the_o great_a height_n of_o water_n be_v observe_v at_o half_a a_o hour_n past_o a_o eleven_o a_o clock_n at_o noon_n place_n certain_a observation_n take_v by_o a_o dutch_a mariner_n of_o the_o flux_n of_o the_o sea_n in_o many_o place_n a_o certain_a dutch_a mariner_n on_o the_o day_n of_o the_o new_a and_o full_a moon_n note_v the_o hour_n of_o divers_a place_n for_o the_o term_n or_o intumescency_n of_o the_o flux_n from_o which_o i_o have_v extract_v these_o at_o the_o twelve_o hour_n on_o the_o day_n of_o the_o new_a and_o full_a moon_n on_o the_o coast_n of_o flanders_n at_o enchusen_n in_o holland_n at_o horn_n at_o embden_n in_o east_n freezland_n at_o the_o mouth_n of_o the_o elve_n at_o eider_n at_o the_o isle_n of_o jutland_n and_o at_o dover_n at_o england_n at_o 45_o minute_n past_o 12_o at_o flushing_n in_o zealand_n half_o a_o hour_n after_o one_o a_o clock_n at_o the_o occidental_a coast_n of_o the_o isle_n of_o wight_n at_o calis_n at_o the_o mouth_n of_o the_o river_n of_o thames_n at_o the_o shore_n of_o zealand_n in_o the_o mouth_n of_o scald_v in_o mosa_n and_o at_o gore_v a_o quarter_n after_o two_o before_o the_o mouth_n of_o scald_v and_o the_o mouth_n of_o mosa_n at_o three_o a_o clock_n at_o amsterdam_n rotterdam_n dort_n in_o holland_n at_o newcastle_n in_o england_n at_o arment_n in_o flanders_n in_o the_o mouth_n of_o the_o river_n of_o bordeaux_n in_o the_o south_n coast_n of_o britain_n gallocia_n gascoyn_n biscay_n portugal_n and_o spain_n and_o on_o the_o western_a coast_n of_o ireland_n even_o to_o hitland_n a_o quarter_n after_o four_o in_o the_o evening_n at_o rouen_n in_o france_n between_o mosa_n and_o rochel_n in_o the_o river_n of_o bordeaux_n in_o the_o bay_n of_o the_o spanish_a portugal_n and_o gallecian_a coast_n in_o the_o south_n coast_n of_o britain_n in_o france_n gascoyn_n and_o on_o the_o western_a coast_n of_o ireland_n half_n a_o hour_n past_o four_o from_o the_o texel_n at_o the_o south_n coast_n of_o ireland_n a_o quarter_n past_o five_o in_o all_o the_o port_n of_o the_o southern_a coast_n of_o ireland_n at_o plymouth_n in_o england_n and_o other_o southern_a place_n of_o it_o even_o to_o the_o coast_n of_o wales_n at_o six_o in_o the_o evening_n and_o morning_n before_o hamburgh_n in_o the_o elbe_n before_o bremen_n the_o texel_n antwerp_n in_o the_o channel_n between_o england_n and_o brabant_n without_o sorlis_n a_o quarter_n before_o seven_o in_o the_o evening_n between_o fawick_n and_o vaelmuya_n in_o the_o channel_n even_o to_o bristol_n before_o st._n nicholas_n and_o podessembe_n even_o to_o waymouth_n and_o hartepole_n at_o half_a a_o hour_n past_o seven_o in_o the_o haven_n at_o the_o texel_n at_o kilduyna_n in_o the_o middle_n of_o the_o channel_n nigh_o plymouth_n and_o in_o the_o sea_n even_o to_o the_o promontory_n of_o the_o lizard_n a_o quarter_n past_o eight_o in_o the_o evening_n nigh_o the_o isle_n of_o wight_n in_o the_o channel_n even_o to_o bevesier_n without_o the_o fly_n on_o the_o coast_n of_o holland_n at_o nine_o before_o the_o mouth_n of_o the_o river_n ems_n in_o freezland_n before_o the_o fly_n before_o the_o coast_n of_o freezland_n at_o the_o eastern_a coast_n of_o the_o isle_n of_o wight_n at_o half_a a_o hour_n past_o ten_o before_o the_o mouth_n of_o the_o river_n thames_n on_o the_o coast_n of_o normandy_n and_o picardy_n and_o at_o a_o quarter_n
because_o the_o place_n of_o the_o demand_v point_n be_v the_o periphery_a of_o the_o circle_n which_o may_v be_v exhibit_v on_o a_o plain_a and_o be_v always_o situate_v in_o one_o plain_a but_o the_o present_a problem_n be_v solid_a or_o rather_o do_v belong_v to_o the_o superficies_n for_o the_o place_n of_o the_o demand_v point_n in_o the_o superficies_n of_o the_o globe_n be_v not_o any_o periphery_n of_o the_o circle_n except_o when_o the_o quarter_n give_v be_v northern_o or_o southern_o but_o a_o certain_a peculiar_a crooked_a solid_a line_n that_o be_v which_o may_v not_o be_v on_o a_o plain_a but_o a_o crooked_a to_o wit_n a_o spherical_a superficies_n yet_o neither_o be_v it_o a_o loxodromical_a line_n of_o which_o we_o shall_v speak_v in_o a_o peculiar_a chapter_n but_o a_o crooked_a line_n of_o its_o own_o kind_a terminate_v on_o both_o side_n now_o for_o the_o conceive_n of_o this_o line_n or_o the_o place_n themselves_o on_o the_o superficies_n of_o the_o globe_n let_v the_o give_v place_n be_v bring_v to_o the_o meridian_n then_o if_o the_o quarter_n give_v be_v oriental_a it_o be_v certain_a that_o the_o demand_v place_n be_v seat_v in_o the_o part_n of_o the_o globe_n towards_o the_o west_n remove_v from_o the_o meridian_n of_o the_o give_v place_n but_o it_o be_v otherwise_o if_o that_o the_o quarter_n give_v be_v occidental_a and_o if_o the_o quarter_n give_v be_v one_o of_o those_o which_o incline_v from_o the_o east_n or_o west_n towards_o the_o north_n the_o place_n demand_v shall_v lie_v between_o the_o south_n and_o the_o primary_n vertical_a of_o the_o give_v place_n but_o it_o be_v otherwise_o if_o the_o quarter_n give_v be_v one_o of_o those_o which_o incline_v from_o the_o east_n or_o west_n towards_o the_o south_n if_o the_o give_v quarter_n be_v of_o the_o eastern_a or_o western_a aequinoctial_a the_o place_n of_o the_o demand_v place_n shall_v be_v some_o one_o crooked_a line_n begin_v from_o the_o give_v place_n and_o terminate_v in_o the_o vicine_fw-la pole_n seat_v from_o the_o oriental_a part_n of_o the_o meridian_n if_o the_o give_v quarter_n be_v of_o the_o west_n but_o from_o the_o occidental_a if_o that_o the_o give_v quarter_n be_v of_o the_o east_n and_o must_v be_v conceive_v at_o this_o line_n so_o the_o place_n must_v be_v seek_v or_o exhibit_v from_o which_o amsterdam_n lie_v towards_o the_o western_a aequinoctial_o because_o the_o quarter_n or_o vertical_a quadrant_n respect_v the_o eastern_a or_o western_a aequinoctial_a fall_v in_o with_o the_o point_n of_o the_o aequator_fw-la which_o be_v 90_o deg_fw-la absent_a from_o the_o meridian_n of_o every_o place_n therefore_o first_o let_v the_o point_n draw_v from_o the_o give_v place_n be_v conceive_v to_o be_v seat_v at_o the_o aequinoctial_a quarter_n or_o point_n of_o the_o aequator_fw-la in_o the_o horizon_n and_o therefore_o it_o be_v certain_a that_o all_o the_o place_n seek_v ought_v so_o to_o be_v seat_v from_o the_o oriental_a part_n of_o the_o meridian_n of_o amsterdam_n so_o that_o their_o quarter_n or_o primary_n vertical_a quadrant_n respect_v the_o west_n must_v cut_v the_o quadrant_n of_o the_o aequator_fw-la between_o the_o point_n in_o the_o occident_n and_o the_o meridian_n therefore_o from_o every_o one_o of_o the_o point_n of_o this_o quadrant_n let_v the_o great_a periphery_n be_v conceive_v pass_v through_o amsterdam_n and_o the_o meridian_n draw_v from_o these_o point_v as_o from_o the_o pole_n in_o which_o the_o first_o conceive_v periphery_n every_o one_o cut_v their_o meridian_n be_v those_o demand_v they_o make_v such_o a_o crooked_a line_n as_o i_o have_v say_v which_o put_v itself_o into_o the_o pole_n neither_o be_v it_o infinite_a hence_o the_o difference_n be_v manifest_a between_o the_o crooked_a line_n and_o the_o loxodromic_a for_o this_o do_v not_o arise_v in_o journey_n institute_v towards_o the_o eastern_a or_o western_a aequinoctial_a all_o the_o kind_n of_o this_o of_o which_o we_o now_o do_v speak_v be_v such_o that_o be_v contain_v and_o run_v within_o the_o pole_n and_o the_o quadrant_n of_o the_o 2_o merid._n who_o distance_n do_v not_o exceed_v 90_o deg_fw-la but_o where_o any_o quarter_n be_v give_v intermedial_a between_o the_o cardines_fw-la for_o example_n place_n be_v seek_v from_o which_o amsterdam_n lie_v towards_o the_o south-west_n or_o in_o the_o quarter_n remove_v 45_o deg_fw-la from_o the_o meridian_n of_o every_o place_n towards_o the_o west_n from_o the_o south_n first_o therefore_o let_v another_o meridian_n from_o the_o oriental_a part_n of_o amsterdam_n be_v imagine_v for_o in_o this_o it_o be_v manifest_a that_o the_o place_n seek_v aught_o to_o be_v which_o with_o amsterdam_n make_v a_o angle_n of_o 45_o deg_fw-la or_o between_o which_o and_o that_o of_o amsterdam_n the_o intercept_a arch_n of_o the_o aequator_fw-la be_v 45_o deg_fw-la this_o shall_v be_v the_o term_n of_o the_o place_n seek_v for_o neither_o beyond_o it_o can_v any_o place_n be_v find_v in_o any_o meridian_n which_o do_v satisfy_v let_v a_o perpendicular_a periphery_n be_v suppose_v to_o be_v draw_v from_o amsterdam_n into_o this_o meridian_n moreover_o because_o the_o quarter_n give_v seem_v to_o incline_v towards_o the_o south_n from_o the_o west_n thence_o it_o be_v certain_a that_o the_o place_n demand_v shall_v be_v situate_v in_o the_o space_n of_o the_o triangle_n who_o side_n be_v now_o first_o draw_v perpendicular_a second_o part_n of_o this_o meridian_n be_v intercept_v between_o the_o draw_a periphery_n and_o the_o vicine_fw-la pole_n three_o part_n of_o the_o meridian_n of_o amsterdam_n be_v between_o amsterdam_n and_o the_o adjacent_a pole_n in_o this_o space_n the_o crooked_a line_n all_o who_o point_n answer_v the_o demand_n be_v seat_v which_o creep_v forward_o from_o amsterdam_n with_o a_o crooked_a passage_n even_o to_o the_o pole_n for_o the_o description_n of_o it_o many_o meridian_n be_v to_o be_v take_v from_o which_o the_o great_a periphery_n draw_v to_o amsterdam_n may_v make_v with_o the_o meridian_n from_o whence_o it_o be_v draw_v and_o angle_n of_o forty_o five_o degree_n for_o our_o example_n so_o many_o point_n of_o this_o crooked_a line_n to_o be_v describe_v shall_v be_v find_v we_o have_v treat_v full_o of_o this_o crooked_a line_n in_o our_o book_n of_o crooked_a line_n here_o we_o have_v only_o touch_v what_o be_v proper_a to_o geography_n proposition_n iu._n the_o latitude_n of_o one_o place_n be_v give_v and_o the_o distance_n from_o the_o other_o place_n and_o the_o quarter_n in_o which_o this_o other_o place_n in_o seat_v from_o it_o to_o find_v the_o quarter_n of_o this_o other_o place_n in_o which_o the_o former_a place_n be_v seat_v at_o this_o other_o place_n it_o will_v be_v better_o understand_v by_o a_o example_n viz._n let_v the_o quarter_n be_v give_v in_o which_o the_o city_n of_o hamburgh_n be_v seat_v from_o amsterdam_n we_o seek_v the_o quarter_n in_o which_o amsterdam_n be_v seat_v from_o hamburgh_n the_o vulgar_a opinion_n be_v that_o the_o contrary_a quarter_n be_v to_o be_v take_v which_o be_v false_a and_o in_o this_o all_o mariner_n chart_n and_o all_o right_o line_v map_n do_v much_o err_v the_o solution_n be_v easy_a by_o a_o trigonometrical_a calculation_n or_o by_o the_o globe_n or_o by_o the_o plain_a sphere_n proposition_n v._o to_o make_v a_o terrestrial_a globe_n globe_n of_o the_o make_n a_o terrestrial_a globe_n so_o the_o vulgar_a speak_v very_o confuse_o by_o this_o problem_n but_o the_o distinct_a understanding_n of_o it_o be_v thus_o to_o be_v propound_v in_o a_o mathematical_a style_n any_o piont_n be_v give_v in_o the_o superficies_n of_o any_o globe_n which_o be_v put_v to_o represent_v any_o place_n situate_v in_o the_o superficies_n of_o the_o earth_n or_o in_o the_o give_v half_a periphery_n to_o find_v out_o any_o line_n and_o point_n in_o the_o superficies_n of_o the_o same_o globe_n which_o be_v so_o mutual_o seat_v to_o the_o give_v point_n and_o to_o themselves_o as_o the_o place_n and_o line_n in_o the_o superficies_n of_o the_o earth_n which_o ought_v to_o be_v represent_v by_o they_o be_v situate_v to_o the_o place_n first_o take_v and_o mutual_a to_o themselves_o the_o first_o mode_n globe_n the_o first_o mode_n of_o make_v terrestrial_a globe_n the_o best_a most_o easy_a and_o exact_a method_n be_v that_o by_o which_o from_o the_o longitude_n and_o latitude_n of_o place_n in_o the_o superficies_n of_o the_o globe_n itself_o the_o place_n and_o point_v fight_v for_o or_o represent_v the_o part_n of_o the_o superficies_n of_o the_o earth_n be_v consign_v which_o although_o artificer_n do_v not_o use_v in_o make_v of_o terrestrial_a globe_n which_o be_v sell_v in_o a_o great_a number_n because_o that_o this_o may_v be_v do_v another_o way_n where_o from_o the_o abundance_n of_o their_o sale_n the_o cost_n and_o charge_n be_v sufficient_o
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