any_o land_n this_o horizon_n be_v of_o two_o sort_n namely_o right_a and_o oblique_a the_o right_a horizon_n be_v that_o which_o they_o have_v that_o live_v under_o the_o equinoctial_a which_o pass_v by_o their_o zenith_n and_o therefore_o the_o equinoctial_a line_n or_o circle_n fall_v perpendicular_o and_o right_o across_o with_o their_o horizon_n and_o both_o the_o south_n and_o the_o north_n pole_n be_v in_o their_o horizon_n the_o oblique_a horizon_n be_v that_o which_o they_o have_v that_o live_v not_o direct_o under_o the_o equinoctial_a for_o unto_o they_o the_o equinoctial_a divide_v the_o horizon_n oblique_o and_o not_o right_o across_o and_o one_o pole_n be_v always_o above_o their_o horizon_n and_o the_o other_o be_v beneath_o their_o horizon_n and_o can_v be_v see_v this_o horizon_n be_v represent_v in_o the_o sea-chart_n by_o a_o certain_a imagine_a circle_n who_o centre_n be_v the_o point_n where_o our_o ship_n be_v from_o which_o centre_n be_v imagine_v to_o proceed_v unto_o the_o say_a circle_n 32_o line_n which_o represent_v the_o 32_o wind_n or_o rumb_n which_o always_o be_v draw_v in_o our_o sea-compasse_n which_o likewise_o in_o a_o little_a piece_n of_o paper_n do_v continual_o represent_v unto_o we_o both_o by_o day_n and_o night_n the_o whole_a horizon_n with_o his_o 32_o division_n chap._n xvi_o of_o the_o 32_o wind_n this_o right_a or_o oblique_a horizon_n be_v divide_v into_o 32_o equal_a part_n by_o 16_o line_n which_o they_o call_v rumb_n and_o they_o cut_v themselves_o in_o the_o point_n where_o we_o stand_v of_o which_o rumb_n that_o which_o pass_v by_o the_o point_n where_o the_o equinoctial_a begin_v and_o end_v which_o be_v where_o the_o sun_n rise_v and_o set_v the_o 11_o of_o march_n and_o the_o 13_o of_o september_n be_v call_v east_n and_o west_n and_o that_o which_o cut_v it_o right_o across_o be_v name_v north_n and_o south_n and_o the_o four_o extreme_n or_o end_n of_o these_o two_o line_n be_v distant_a upon_o the_o horizon_n one_o four_o part_n of_o a_o circle_n and_o they_o make_v four_o quarter_n every_o one_o of_o which_o quarter_n be_v divide_v in_o the_o midst_n do_v make_v four_o other_o point_n and_o that_o which_o fall_v between_o the_o north_n and_o the_o east_n be_v call_v north-east_n and_o that_o between_o the_o north_n and_o the_o west_n northwest_n that_o between_o the_o south_n and_o the_o east_n southeast_n and_o that_o between_o the_o south_n and_o the_o west_n south-west_n and_o so_o the_o horizon_n be_v divide_v by_o four_o line_n or_o numb_v into_o eight_o principal_a wind_n note_v in_o the_o sea-chart_n with_o black_a line_n and_o if_o you_o divide_v every_o one_o of_o those_o eight_o part_n in_o the_o midst_n you_o shall_v have_v other_o eight_o line_n and_o other_o four_o rumb_n which_o in_o all_o be_v 16_o wind_n and_o each_o one_o of_o these_o have_v his_o name_n compound_v of_o the_o name_n of_o those_o principal_a wind_n which_o be_v on_o either_o side_n thereof_o as_o for_o example_n that_o half_a wind_n which_o be_v between_o the_o north_n and_o the_o north-east_n be_v call_v north-north-east_n and_o that_o which_o blow_v between_o the_o east_n and_o the_o north-east_n be_v call_v east-north-east_n and_o that_o between_o the_o east_n and_o the_o southeast_n east-south-east_n and_o that_o between_o the_o south_n and_o the_o southeast_n south-south-east_n and_o that_o between_o the_o south-west_n and_o the_o west_n west-south-west_n and_o that_o between_o the_o west_n and_o northwest_n west-north-west_n and_o that_o between_o the_o northwest_n and_o the_o north_n north-north-west_n and_o these_o be_v note_v in_o the_o chart_n with_o green_a line_n final_o if_o you_o divide_v every_o one_o of_o these_o sixteen_o wind_n in_o the_o midst_n they_o will_v yield_v you_o other_o 16_o wind_n and_o will_v amount_v to_o 32_o wind_n in_o all_o which_o 16_o last_v mention_v be_v draw_v in_o the_o sea-chart_n with_o red_a line_n and_o be_v by_o the_o spaniard_n call_v quarter_n of_o the_o eight_o first_o and_o principal_a wind_n and_o every_o one_o of_o these_o be_v call_v by_o the_o name_n of_o that_o principal_a wind_n which_o be_v next_o it_o together_o with_o a_o addition_n of_o the_o word_n by_o and_o the_o name_n of_o another_o principal_a wind_n which_o be_v next_o unto_o it_o as_o for_o example_n of_o the_o two_o quarter-wind_n which_o fall_v next_o the_o rumb_n of_o the_o north_n that_o which_o lie_v towards_o the_o north-east_n be_v call_v north_n and_o by_o east_n and_o that_o which_o fall_v towards_o the_o northwest_n be_v call_v north_n by_o west_n so_o likewise_o of_o those_o two_o wind_n which_o blow_n next_o the_o north-east_n that_o towards_o the_o north_n be_v call_v north-east_n and_o by_o north_n and_o that_o towards_o the_o east_n north-east_n and_o by_o east_n and_o after_o the_o same_o manner_n you_o may_v name_v all_o the_o rest_n the_o figure_n of_o the_o sea-compasse_n and_o of_o the_o horizon_n divide_v into_o 32_o wind_n by_o 16_o rumb_n but_o here_o be_v to_o be_v note_v wind_n that_o there_o be_v difference_n between_o the_o rumb_n and_o the_o wind_n because_o a_o rumb_n be_v one_o direct_v line_n continue_v with_o two_o contrary_a wind_n as_o the_o rumb_n of_o north_n &_o south_n and_o the_o rumb_n of_o east_n and_o west_n and_o so_o when_o we_o will_v name_v the_o lie_v of_o any_o coast_n we_o will_v say_v that_o it_o lie_v north_n and_o south_n or_o north_n and_o by_o east_n and_o south_n and_o by_o west_n but_o the_o wind_n be_v one_o line_n of_o those_o 32_o into_o which_o the_o horizon_n be_v divide_v and_o it_o be_v one_o part_n of_o those_o two_o which_o together_o be_v call_v the_o rumb_n and_o so_o we_o say_v that_o land_n lie_v from_o we_o towards_o the_o south_n and_o towards_o the_o south_n and_o by_o west_n or_o towards_o the_o south-south-west_n etc._n etc._n chap._n xvii_o of_o the_o two_o tropic_n beside_o the_o six_o circle_n abovementioned_a which_o be_v draw_v upon_o the_o superficies_n of_o the_o sphere_n of_o the_o world_n there_o be_v other_o two_o which_o the_o sun_n describe_v with_o the_o motion_n of_o the_o primum_fw-la mobile_n about_o the_o 12_o day_n of_o june_n and_o of_o december_n of_o which_o two_o circle_n that_o which_o the_o sun_n describe_v the_o 12_o of_o june_n from_o the_o time_n of_o his_o rise_n till_o the_o time_n that_o he_o rise_v the_o day_n follow_v be_v call_v the_o tropic_a of_o the_o summer_n sun-standing_a or_o the_o tropic_a of_o cancer_n for_o the_o sun_n have_v depart_v from_o the_o equinoctial_a and_o increase_v his_o declination_n towards_o the_o north_n when_o he_o come_v to_o describe_v that_o circle_n for_o two_o or_o three_o day_n it_o seem_v that_o he_o come_v no_o near_o to_o our_o zenith_n nor_o depart_v from_o the_o equinoctial_a one_o day_n more_o than_o another_o but_o from_o thence_o forward_o he_o go_v back_o diminish_v his_o declination_n till_o he_o come_v to_o the_o equinoctial_a and_o cross_v the_o same_o he_o go_v on_o the_o other_o side_n increase_v his_o declination_n until_o the_o 12_o of_o december_n upon_o which_o day_n from_o the_o time_n of_o his_o rise_n till_o he_o be_v come_v about_o to_o rise_v again_o the_o next_o morning_n he_o describe_v another_o circle_n call_v the_o tropic_a of_o the_o winter_n sun-standing_a or_o the_o tropic_a of_o capricorn_n for_o the_o sun_n be_v depart_v from_o the_o equinoctial_a and_o increase_v his_o declination_n towards_o the_o south_n when_o he_o come_v to_o describe_v that_o circle_n it_o seem_v for_o two_o or_o three_o day_n that_o he_o return_v not_o one_o whit_n towards_o the_o equinoctial_a nor_o go_v further_o from_o our_o zenith_n one_o day_n more_o than_o other_o but_o from_o thence_o forward_o he_o come_v back_o again_o diminish_v his_o declination_n till_o he_o be_v return_v to_o the_o equinoctial_a and_o from_o thence_o towards_o our_o zenith_n these_o two_o circle_n in_o sea-chart_n be_v mark_v with_o two_o great_a red_a line_n draw_v from_o east_n to_o west_n which_o lie_v on_o either_o side_n of_o the_o equinoctial_a be_v distant_a from_o thence_o about_o 23_o deg_n and_o a_o half_a and_o wheresoever_o our_o ship_n be_v in_o any_o place_n between_o these_o two_o circle_n or_o line_n we_o may_v in_o some_o time_n of_o the_o year_n take_v the_o sun_n in_o our_o zenith_n at_o which_o time_n it_o make_v no_o shadow_n at_o all_o be_v then_o just_a 90_o degr_n high_a above_o our_o horizon_n but_o they_o which_o be_v without_o the_o say_v two_o circle_n or_o line_n shall_v never_o have_v the_o sun_n in_o their_o zenith_n because_o it_o can_v come_v to_o the_o height_n of_o 90_o degr_n above_o their_o horizon_n chap._n xviii_o of_o the_o parallel_n the_o parallel_a circle_n be_v those_o which_o be_v in_o all_o part_n equal_o distant_a from_o the_o
a_o half_a be_v deduct_v out_o of_o the_o height_n of_o the_o north_n star_n the_o remainder_n be_v the_o just_a height_n of_o the_o pole_n the_o six_o rule_n when_o the_o guard_n be_v in_o the_o south-west_n one_o bear_v from_o another_o east_n and_o west_n and_o the_o former_a lie_v from_o the_o north_n star_n north-east_n and_o south-west_n and_o then_o the_o north_n star_n be_v above_o the_o pole_n three_o degree_n and_o a_o half_a which_o three_o degree_n and_o a_o half_a be_v deduct_v out_o of_o the_o height_n of_o the_o star_n that_o which_o remain_v shall_v be_v the_o height_n of_o the_o pole_n the_o seven_o rule_n when_o the_o guard_n be_v at_o the_o low_a the_o former_a guard_n bear_v with_o the_o north_n star_n north_n and_o south_n and_o then_o the_o north_n star_n be_v above_o the_o pole_n three_o degree_n which_o be_v deduct_v the_o remainder_n be_v the_o height_n of_o the_o pole_n the_o eight_o rule_n when_o the_o guard_n be_v in_o the_o southeast_n one_o bear_v from_o another_o north_n and_o south_n and_o the_o former_a bear_v from_o the_o north_n star_v northwest_o and_o southeast_n and_o the_o north_n star_n be_v above_o the_o pole_n half_o a_o degree_n which_o half_a degree_n be_v deduct_v from_o the_o height_n of_o the_o star_n the_o remainder_n be_v the_o height_n of_o the_o pole_n above_o our_o horizon_n and_o just_a so_o much_o be_v we_o distant_a from_o the_o equinoctial_a towards_o the_o north._n this_o be_v the_o account_n which_o always_o have_v be_v make_v of_o the_o north_n star_n from_o the_o time_n that_o it_o have_v have_v three_o degree_n and_o a_o half_a distance_n from_o the_o pole_n unto_o this_o present_a but_o because_o at_o this_o time_n by_o reason_n of_o the_o compound_n motion_n of_o the_o 8_o and_o 9_o heaven_n the_o fix_a star_n have_v notable_o vary_v from_o their_o place_n the_o pole_n star_n have_v also_o approach_v near_o the_o pole_n be_v now_o distant_a therefrom_o not_o above_o three_o degree_n and_o eight_o minute_n and_o so_o i_o think_v it_o convenient_a to_o set_v down_o the_o account_n which_o ought_v now_o to_o be_v make_v thereof_o book_n according_a to_o the_o foresay_a distance_n to_o the_o end_n that_o from_o henceforth_o the_o height_n of_o the_o pole_n take_v by_o the_o star_n may_v agree_v just_o with_o the_o distance_n from_o the_o equinoctial_a take_v by_o the_o sun_n which_o two_o thing_n have_v hitherto_o disagree_v and_o cause_v no_o small_a confusion_n unto_o the_o pilot_n and_o some_o error_n in_o navigation_n the_o guard_n be_v in_o the_o east_n you_o shall_v add_v unto_o the_o height_n take_v by_o the_o crosse-staffe_n 1_o degree_n 20_o minute_n north-east_n 3_o degree_n 8_o minute_n north_n 2_o degree_n 41_o minute_n northwest_o 0_o degree_n 27_o minute_n in_o the_o contrary_a rumb_n to_o these_o you_o must_v deduct_v these_o degree_n from_o the_o height_n of_o the_o star_n which_o you_o take_v with_o your_o crosse-staffe_n and_o then_o you_o shall_v have_v the_o height_n of_o the_o pole_n above_o the_o horizon_n chap._n xv._n other_o thing_n to_o be_v note_v in_o observe_v the_o height_n of_o the_o pole_n next_o unto_o the_o constellation_n of_o the_o horn_n here_o be_v a_o star_n which_o be_v call_v by_o the_o spaniard_n el_fw-es guion_n signify_v before_o by_o the_o letter_n d_o which_o stand_v east_n and_o west_n from_o the_o north-star_n give_v you_o to_o understand_v that_o it_o and_o the_o north_n star_n and_o the_o very_a pole_n be_v east_n and_o west_n and_o so_o take_v the_o height_n of_o the_o north_n star_n when_o it_o be_v thus_o situate_a in_o regard_n of_o the_o guion_n with_o out_o make_v any_o other_o account_n you_o have_v the_o just_a height_n of_o the_o pole_n and_o the_o distance_n from_o the_o equinoctial_a here_o follow_v the_o table_n the_o guard_n be_v in_o the_o east_n the_o three_o star_n be_v in_o the_o southeast_n the_o six_o star_n in_o the_o south_n the_o 9_o the_o star_n in_o the_o south-west_n northeast_n east_n southeast_n south_n north_n northeast_n east_n southeast_n northwest_o north_n north-east_n east_n west_n northwest_o north_n north-east_n southwest_n west_n northwest_o north_n south_n southwest_n west_n northwest_o southeast_n south_n southwest_n west_n in_o this_o table_n the_o first_o column_n serve_v for_o the_o guard_n the_o second_o for_o the_o three_o star_n the_o three_o column_n for_o the_o six_o star_n and_o the_o four_o for_o the_o nine_o star_n insomuch_o as_o if_o you_o seek_v the_o rumb_n see_v any_o of_o these_o four_o star_n in_o this_o table_n right_a against_o the_o same_o do_v answer_v those_o rumb_n where_o the_o other_o three_o be_v although_o we_o can_v see_v they_o in_o the_o heaven_n chap._n xvi_o of_o the_o crosier_n when_o the_o mariner_n pass_v the_o equinoctial_a line_n towards_o the_o south_n so_o that_o they_o can_v see_v the_o north-star_n they_o make_v use_v of_o another_o staâ—_n which_o be_v in_o the_o constellation_n call_v by_o the_o astronomer_n the_o centaur_n which_o star_n with_o other_o three_o notable_a star_n which_o be_v in_o the_o same_o constellation_n make_v the_o figure_n of_o a_o cross_n for_o which_o cause_n they_o call_v it_o the_o crosier_n and_o it_o be_v hold_v for_o certain_a that_o when_o the_o star_n a_o which_o of_o all_o four_o come_v near_a to_o the_o south_n pole_n be_v north_n and_o south_n with_o the_o star_n b_o that_o than_o it_o be_v right_o situate_a to_o take_v the_o height_n by_o and_o because_o this_o star_n a_o which_o they_o call_v the_o cock_n foot_n be_v thirty_o degree_n from_o the_o south_n pole_n it_o come_v to_o pass_v that_o if_o be_v situate_a as_o be_v aforesaid_a we_o take_v the_o height_n thereof_o which_o be_v then_o the_o great_a that_o it_o can_v have_v this_o height_n will_v true_o show_v how_o far_o we_o be_v distant_a from_o the_o equinoctial_a for_o if_o the_o say_a height_n be_v thirty_o degree_n than_o we_o be_v in_o the_o very_a equinoctial_a and_o if_o it_o be_v more_o than_o thirty_o degree_n then_o be_v we_o by_o so_o much_o past_o the_o equinoctial_a towards_o the_o south_n and_o if_o it_o be_v less_o than_o 30_o degree_n so_o much_o as_o it_o want_v be_v we_o to_o the_o north_n of_o the_o equinoctial_a and_o here_o it_o be_v to_o be_v note_v that_o when_o the_o guard_n be_v in_o the_o north-east_n then_o be_v the_o star_n in_o the_o crosier_n fit_o situate_a for_o observation_n because_o than_o they_o be_v in_o the_o meridian_n chap._n xvii_o of_o the_o sea-compass_n the_o sea-compass_n be_v one_o of_o the_o most_o necessary_a instrument_n which_o be_v use_v in_o navigation_n for_o day_n and_o night_n in_o clear_a and_o dark_a weather_n it_o show_v always_o the_o right_a way_n through_o the_o sea_n and_o therefore_o it_o be_v meet_v that_o this_o instrument_n be_v make_v with_o much_o care_n to_o the_o end_n that_o it_o may_v be_v most_o certain_a and_o true_a and_o the_o manner_n of_o make_v it_o be_v that_o upon_o a_o piece_n of_o pasteboard_n you_o draw_v a_o circle_n so_o big_a as_o you_o will_v have_v your_o compass_n to_o be_v which_o be_v divide_v into_o 32_o equal_a part_n as_o we_o have_v already_o show_v in_o the_o chapter_n of_o the_o wind_n with_o sixteen_o line_n cross_v one_o another_o in_o the_o centre_n than_o you_o shall_v adorn_v the_o eight_o principal_a wind_n as_o be_v to_o be_v see_v in_o the_o figure_n follow_v end_v in_o the_o north_n with_o a_o flower_n deluis_fw-la and_o you_o shall_v paint_v the_o north_n and_o south_n and_o east_n and_o west_n with_o blue_a and_o the_o north-east_n and_o south-west_n and_o the_o northwest_n and_o southeast_n with_o red_a and_o then_o take_v two_o steel_n wire_n which_o be_v to_o be_v place_v like_o the_o head_n of_o a_o lance_n you_o must_v fasten_v they_o on_o the_o back_n side_n of_o the_o say_a circle_n in_o such_o sort_n that_o one_o meet_v of_o the_o point_n of_o those_o steel_n wire_n be_v right_a under_o the_o north_n allow_v half_o a_o point_n towards_o the_o north-east_n in_o regard_n of_o the_o north-easting_a of_o the_o needle_n at_o sevil_n and_o the_o other_o meet_v at_o the_o opposite_a point_n which_o be_v south_n and_o half_a a_o point_n towards_o the_o south-west_n and_o touch_v or_o rub_v those_o two_o point_n of_o the_o wire_n with_o the_o end_n of_o the_o loadstone_n which_o look_v to_o the_o north_n and_o to_o the_o south_n to_o wit_n the_o north_n point_v of_o the_o wire_n with_o the_o south_n of_o the_o stone_n &_o the_o south_n point_n of_o the_o wire_n with_o the_o north_n of_o the_o stone_n this_o be_v do_v you_o must_v place_n upon_o the_o centre_n of_o the_o say_a circle_n a_o capitel_a which_o must_v be_v very_o well_o bore_v in_o from_o off_o a_o round_a pyramid_n to_o the_o end_n
after_o it_o be_v touch_v with_o the_o loadstone_n by_o mean_n whereof_o it_o seem_v something_o probable_a that_o seaman_n may_v have_v some_o help_n to_o know_v their_o height_n or_o latitude_n in_o dark_a and_o cloudy_a weather_n when_o neither_o sun_n nor_o star_n for_o many_o day_n appear_v to_o be_v observe_v i_o think_v it_o shall_v not_o be_v impertinent_a to_o this_o place_n to_o set_v down_o the_o theoric_n that_o have_v be_v devise_v of_o this_o magnetical_a inclination_n together_o with_o a_o demonstration_n for_o the_o make_n of_o a_o table_n thereof_o to_o every_o degree_n of_o latitude_n according_a to_o that_o theoric_n to_o the_o end_n that_o such_o of_o our_o seaman_n as_o mean_v to_o be_v diligent_a observer_n hereof_o may_v make_v heedful_a trial_n of_o that_o incline_a property_n and_o compare_v the_o same_o with_o this_o table_n in_o all_o part_n of_o the_o world_n where_o they_o shall_v travel_v especial_o in_o those_o long_a voyage_n to_o the_o east_n and_o 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simon_n stevins_n inconsiderate_a desire_n of_o find_v fault_n with_o my_o table_n of_o rumb_n have_v cause_v i_o to_o conclude_v with_o a_o answer_n to_o he_o plain_o show_v himself_o and_o not_o i_o to_o be_v in_o the_o same_o fault_n that_o he_o will_v find_v with_o i_o to_o this_o treatise_n for_o the_o benefit_n of_o the_o young_a and_o unskilfull_a sort_n of_o seaman_n it_o be_v think_v not_o unmeet_a to_o adjoyn_v the_o short_a treatise_n follow_v contain_v the_o sum_n of_o the_o whole_a art_n of_o navigation_n first_o set_v forth_o in_o spanish_a by_o roderigo_n samorano_n and_o since_o translate_v into_o english_a by_o a_o friend_n of_o i_o for_o the_o benefit_n of_o our_o nation_n which_o treatise_n i_o will_v wish_v all_o they_o that_o be_v but_o new_a beginner_n in_o that_o art_n first_o to_o peruse_v and_o understand_v well_o before_o they_o come_v to_o the_o read_n of_o the_o former_a which_o for_o the_o read_n thereof_o with_o the_o great_a profit_n require_v such_o a_o one_o as_o be_v already_o reasonable_o well_o acquaint_v with_o the_o rule_n and_o principle_n of_o that_o art_n which_o i_o have_v not_o hitherto_o know_v to_o be_v more_o brief_o and_o plain_o nor_o yet_o more_o full_o set_v down_o and_o publish_v in_o any_o other_o book_n than_o they_o be_v in_o that_o little_a treatise_n this_o notwithstanding_o i_o must_v admonish_v the_o reader_n that_o in_o stead_n of_o the_o sea-chart_n therein_o describe_v according_a to_o the_o common_a error_n with_o equal_a degree_n of_o latitude_n he_o follow_v that_o manner_n of_o make_v the_o same_o which_o i_o have_v in_o the_o former_a treatise_n set_v down_o chap._n 3_o 4_o 5_o and_o 6._o and_o that_o in_o stead_n of_o the_o rule_n and_o allowance_n for_o find_v the_o latitude_n by_o the_o height_n of_o the_o polestar_n which_o be_v many_o way_n and_o much_o
55_o 160_o 401.357_o 537.178_o 251.865.582_o  _fw-fr 56_o 160_o 938.535_o 545.704_o 260.459.920_o 8.594.338_o 57_o 161_o 484.239_o 554.505_o 271_o 919.077_o 11.459.157_o 58_o 162_o 038_o 744_o 563.594_o 289_o 107.811_o 17.188.734_o 59_o 162.602.338_o 572.986_o 323.485.279_o 34.377.468_o chap._n iii_o the_o use_n of_o the_o two_o first_o column_n of_o the_o table_n of_o latitude_n for_o graduate_v a_o meridian_n in_o the_o general_a sea-chart_n before_o you_o can_v make_v use_n of_o this_o table_n for_o the_o true_a graduate_n or_o divide_v of_o a_o meridian_n of_o this_o chart_n into_o his_o degree_n or_o other_o part_n of_o latitude_n increase_v from_o the_o aequinoctial_a towards_o the_o north_n and_o south_n in_o such_o proportion_n as_o before_o have_v be_v show_v there_o must_v be_v first_o some_o preparation_n make_v to_o that_o end_n which_o may_v be_v do_v after_o this_o manner_n overthwart_o the_o midst_n of_o the_o plain_a superficies_n whereupon_o you_o will_v draw_v the_o 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unto_o if_o that_o difference_n be_v a_o compound_n number_n that_o may_v be_v divide_v into_o his_o unity_n by_o small_a divisoâ—â—_n but_o if_o it_o fall_v out_o that_o the_o number_n of_o equal_a part_n remine_v 〈◊〉_d either_o a_o prime_a number_n or_o else_o such_o a_o number_n as_o can_v otherwise_o be_v divide_v into_o his_o unity_n but_o by_o some_o great_a divisor_n 〈◊〉_d may_v then_o take_v the_o next_o compound_v number_n that_o be_v great_a 〈◊〉_d the_o say_a difference_n which_o may_v be_v divide_v into_o his_o unity_n 〈◊〉_d small_a divisor_n thus_o have_v divide_v the_o line_n draw_v 〈◊〉_d thwart_o the_o breadth_n of_o the_o chart_n into_o so_o many_o equal_a part_n as_o 〈◊〉_d compound_n number_n contain_v unity_n and_o beginning_n at_o 〈◊〉_d end_n thereof_o which_o be_v suppose_v to_o be_v southwards_o or_o next_o the_o equinoctial_a set_v thereto_o the_o next_o number_n of_o whole_a hundred_o or_o thousand_o less_o than_o the_o number_n of_o equal_a part_n answerable_a 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with_o the_o regiment_n of_o the_o sun_n and_o of_o the_o star_n the_o rule_n of_o the_o moon_n and_o of_o the_o tide_n the_o declaration_n of_o the_o sea-chart_n and_o other_o thing_n appertain_v hereunto_o chap._n i._n the_o definition_n of_o the_o sphere_n a_o sphere_n be_v a_o solid_a or_o massy_a body_n without_o hollowness_n and_o perfect_o round_a in_o the_o midst_n whereof_o there_o be_v a_o prick_n call_v the_o centre_n by_o which_o there_o pass_v a_o right_a line_n name_v the_o axtree_n and_o the_o point_n where_o this_o line_n end_v upon_o the_o superficies_n of_o the_o whole_a body_n be_v call_v pole_n because_o upon_o they_o the_o sphere_n be_v move_v chap._n ii_o that_o the_o whole_a world_n be_v a_o sphere_n and_o so_o it_o be_v evident_a that_o the_o whole_a frame_n of_o the_o world_n wherein_o we_o live_v be_v a_o sphere_n be_v as_o it_o be_v solid_a so_o that_o in_o the_o whole_a world_n there_o be_v no_o empty_a place_n also_o it_o be_v perfect_o round_a upon_o the_o 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world_n chap._n iu._n of_o the_o motion_n of_o the_o heaven_n the_o number_n of_o the_o heaven_n be_v know_v by_o the_o motion_n observe_v in_o they_o which_o be_v ten_o distinct_a one_o from_o another_o for_o the_o moon_n move_v her_o proper_a and_o peculiar_a motion_n in_o 27_o day_n and_o 8_o hour_n which_o be_v one_o revolution_n mercury_n venus_n and_o the_o sun_n finish_v their_o motion_n in_o one_o year_n which_o contain_v 365_o day_n and_o almost_o a_o quarter_n of_o a_o day_n mars_n run_v his_o course_n in_o two_o year_n jupiter_n in_o twelve_o year_n saturn_n in_o thirty_o year_n the_o eight_o sphere_n according_a to_o the_o opinion_n of_o some_o in_o seven_o thousand_o year_n the_o nine_o in_o five_o and_o twenty_o thousand_o and_o eight_o hundred_o year_n and_o the_o ten_o in_o four_o and_o twenty_o hour_n almost_o which_o ten_o motion_n be_v reduce_v unto_o three_o principal_a the_o first_o be_v that_o of_o the_o first_o movable_a upon_o the_o two_o end_n of_o the_o axletree_n which_o be_v call_v the_o pole_n of_o the_o world_n from_o east_n to_o west_n turn_v about_o again_o unto_o the_o east_n in_o 24_o hour_n and_o this_o sphere_n by_o the_o force_n of_o his_o motion_n carry_v about_o with_o it_o all_o the_o other_o low_a sphere_n in_o the_o space_n of_o 24_o hour_n howbeit_o they_o move_v also_o the_o contrary_a way_n with_o a_o second_o motion_n which_o be_v from_o west_n to_o east_n upon_o two_o other_o pole_n distant_a from_o the_o first_o about_o three_o and_o twenty_o and_o a_o half_a such_o part_n whereof_o the_o whole_a compass_n of_o heaven_n contain_v three_o hundred_o and_o sixty_o and_o this_o second_o motion_n be_v accomplish_v in_o each_o of_o the_o low_a heaven_n in_o divers_a space_n of_o time_n as_o be_v before_o say_v the_o three_o motion_n be_v proper_a to_o the_o eight_o heaven_n wherein_o the_o fix_a star_n be_v place_v which_o motion_n be_v the_o cause_n that_o the_o distance_n of_o the_o pole_n of_o the_o first_o motion_n from_o they_o of_o the_o second_o motion_n do_v vary_v be_v sometime_o great_a and_o sometime_o less_o chap._n v._o of_o the_o figure_n of_o the_o heaven_n that_o the_o heaven_n be_v round_o it_o be_v prove_v because_o roundness_n be_v the_o most_o perfect_a figure_n of_o all_o other_o be_v whole_a and_o entire_a have_v no_o need_n of_o any_o joint_n be_v also_o of_o the_o great_a capacity_n of_o all_o figure_n that_o have_v the_o same_o compass_n and_o in_o that_o respect_n most_o fit_a to_o contain_v all_o other_o thing_n also_o the_o principal_a body_n of_o the_o world_n as_o the_o sun_n the_o moon_n and_o the_o star_n be_v of_o this_o figure_n and_o we_o see_v the_o same_o likewise_o in_o those_o thing_n which_o be_v bound_v by_o themselves_o as_o it_o be_v manifest_a in_o drop_n of_o water_n and_o all_o other_o liquid_a thing_n chap._n vi_o that_o the_o earth_n and_o water_n make_v one_o perfect_a globe_n there_o be_v nothing_o that_o show_v more_o clear_o that_o the_o earth_n and_o water_n make_v one_o round_a globe_n than_o the_o shadow_n which_o they_o make_v in_o the_o eclipse_n of_o the_o moon_n which_o shadow_n we_o always_o see_v to_o be_v a_o part_n of_o a_o circle_n for_o if_o the_o body_n which_o be_v the_o cause_n of_o the_o same_o shadow_n be_v threesquare_a or_o foursquare_a the_o shadow_n itself_o also_o will_v appear_v in_o the_o same_o fashion_n wherefore_o the_o shadow_n of_o these_o two_o body_n together_o be_v round_o it_o be_v manifest_a that_o they_o be_v round_o also_o chap._n vii_o that_o the_o earth_n be_v in_o the_o centre_n of_o the_o world_n one_o sign_n we_o have_v to_o be_v assure_v that_o the_o earth_n be_v in_o the_o midst_n and_o centre_n of_o the_o world_n namely_o that_o wheresoever_o we_o be_v upon_o the_o face_n of_o the_o earth_n we_o always_o see_v one_o half_a of_o the_o heaven_n the_o other_o half_o be_v hide_v out_o of_o our_o sight_n moreover_o the_o star_n in_o what_o part_n of_o the_o heaven_n soever_o they_o be_v either_o in_o the_o east_n west_n or_o south_n we_o see_v that_o they_o be_v always_o of_o the_o very_a same_o bigness_n whereby_o we_o may_v easy_o perceive_v that_o they_o be_v always_o equal_o distant_a from_o our_o sight_n and_o whereas_o they_o move_v round_o about_o it_o it_o follow_v that_o we_o be_v upon_o the_o centre_n of_o that_o body_n on_o who_o superficies_n the_o say_a star_n describe_v their_o circle_n chap._n viii_o the_o whole_a quantity_n of_o the_o earth_n and_o albeit_o the_o globe_n of_o the_o earth_n and_o water_n compare_v with_o the_o sphere_n of_o the_o star_n be_v as_o it_o be_v a_o centre_n or_o prick_n yet_o be_v consider_v by_o itself_o it_o contain_v in_o the_o great_a circle_n thereof_o 6300_o common_a spanish_a league_n which_o a_o man_n may_v easy_o perceive_v by_o take_v two_o such_o point_n or_o headland_n of_o the_o earth_n as_o be_v under_o the_o same_o meridian_n and_o which_o differ_v in_o distance_n one_o from_o another_o so_o much_o as_o one_o of_o those_o part_n be_v whereof_o the_o compass_n of_o the_o whole_a world_n contain_v 360_o and_o it_o be_v find_v both_o by_o navigation_n at_o sea_n and_o also_o by_o travel_n on_o land_n that_o the_o two_o foresay_a point_n be_v distant_a each_o from_o other_o 17_o league_n and_o a_o half_a of_o which_o league_n each_o one_o contain_v 4000_o pace_n every_o pace_n 5_o foot_n every_o foot_n 16_o finger_n and_o every_o finger_n 4_o grain_n of_o barley_n chap._n ix_o of_o the_o equinoctial_a circle_n be_v to_o treat_v of_o the_o circle_n of_o the_o sphere_n of_o the_o world_n the_o first_o which_o offer_v itself_o to_o be_v speak_v of_o be_v the_o equinoctial_a circle_n by_o mean_n whereof_o we_o do_v know_v in_o
because_o they_o be_v equal_a this_o height_n of_o the_o pole_n be_v know_v by_o the_o help_n of_o four_o thing_n which_o be_v the_o ballâ—stilla_n or_o crosse-staffe_n the_o position_n of_o the_o north-star_n the_o height_n of_o the_o say_a star_n and_o certain_a rule_n chap._n xi_o the_o make_n of_o the_o crossstaff_n the_o mariner_n crosse-staff_n be_v that_o which_o by_o the_o astronomer_n be_v call_v radius_fw-la astronomicus_fw-la and_o the_o manner_n how_o to_o make_v it_o be_v as_o follow_v first_o upon_o a_o very_a plain_a and_o broad_a table_n you_o may_v draw_v a_o semicircle_n which_o from_o the_o centre_n to_o the_o circumference_n must_v contain_v at_o the_o least_o four_o hand_n breadth_n and_o have_v draw_v through_o the_o centre_n thereof_o the_o line_n abc_n divide_v the_o circumference_n into_o two_o equal_a part_n in_o the_o point_n e_o as_o likewise_o you_o must_v divide_v the_o quadrant_a aec_fw-la in_o the_o very_a midst_n by_o the_o point_n f._n then_o must_v you_o divide_v the_o arch_n of_o into_o 90_o equal_a part_n divide_v it_o first_o into_o three_o and_o every_o of_o these_o three_o into_o other_o three_o and_o every_o of_o those_o nine_o into_o two_o and_o each_o of_o those_o two_o into_o five_o which_o you_o must_v do_v with_o much_o preciseness_n and_o care_n then_o lay_v your_o ruler_n to_o the_o point_n b_o which_o be_v the_o centre_n through_o every_o one_o those_o 90_o division_n of_o the_o half_a quadrant_a you_o must_v draw_v 90_o line_n and_o keep_v this_o quadrant_a so_o divide_v it_o will_v serve_v you_o for_o a_o pattern_n to_o make_v we_o many_o crosse-stave_n as_o you_o think_v good_a of_o what_o bigness_n soever_o you_o will_n but_o to_o make_v the_o crosse-staff_n you_o must_v take_v a_o piece_n of_o wood_n of_o some_o three_o foot_n in_o length_n and_o a_o finger_n thick_a four_o square_a and_o very_o even_o and_o fit_v a_o transversary_n thereto_o which_o may_v with_o facility_n slide_v up_o and_o down_o upon_o the_o staff_n always_o right_o across_o take_v with_o your_o compass_n half_a the_o length_n of_o the_o transversary_n and_o place_v one_o foot_n of_o the_o compass_n upon_o the_o point_n b_o make_v with_o the_o other_o a_o mark_n in_o the_o line_n bc_n which_o may_v serve_v for_o the_o point_n g_o and_o draw_v through_o the_o point_n g_o the_o line_n give_v which_o may_v run_v equal_o distant_a from_o the_o line_n ebb_n final_o lay_v one_o end_n of_o the_o staff_n upon_o the_o point_n g_o let_v it_o lie_v all_o along_o just_a upon_o the_o line_n give_v and_o make_v your_o mark_n upon_o the_o edge_n of_o the_o staff_n by_o which_o you_o may_v draw_v 90_o line_n put_v the_o number_n of_o every_o line_n upon_o the_o say_a edge_n begin_n to_o place_n 90_o where_o the_o line_n be_v do_v cross_v the_o staff_n and_o from_o thence_o descend_v unto_o one_o or_o two_o which_o may_v be_v put_v down_o according_a to_o the_o length_n of_o the_o staff_n and_o the_o largeness_n of_o the_o transversary_n chap._n xii_o of_o the_o position_n of_o the_o north-star_n and_o the_o guard_n among_o the_o 48_o constellation_n which_o the_o astronomer_n place_n in_o the_o heaven_n the_o near_a unto_o the_o pole_n of_o the_o world_n be_v that_o which_o they_o call_v the_o lesser_a bear_n and_o the_o mariner_n bozina_fw-la or_o the_o horn_n in_o regard_n of_o the_o fashion_n thereof_o which_o constellation_n consist_v of_o 7_o star_n which_o be_v place_v after_o this_o manner_n and_o of_o these_o star_n the_o three_o great_a mark_v with_o the_o letter_n abc_n do_v serve_v especial_o for_o our_o purpose_n and_o so_o a_o be_v call_v the_o north-star_n b_o the_o the_o foremost_a guard_n c_z the_o other_z guard_z behind_z and_o they_o be_v so_o call_v because_o that_o by_o force_n of_o the_o motion_n of_o the_o first_o movable_a heaven_n the_o star_n b_o go_v always_o before_o and_o the_o star_n c_o behind_o every_o of_o these_o three_o star_n as_o well_o as_o all_o other_o in_o the_o heaven_n beside_o describe_v thâ—â—_n circle_n round_o about_o the_o pole_n with_o the_o motion_n of_o the_o first_o or_o high_a movable_a heaven_n 〈◊〉_d which_o motion_n sometime_o the_o 〈◊〉_d star_n ab_fw-la be_v just_a of_o 〈…〉_z above_o the_o horizon_n 〈…〉_z they_o be_v say_v to_o be_v east_n and_o west_n one_o from_o another_o sometime_o they_o be_v in_o a_o perpendicular_a line_n to_o the_o horizon_n according_a to_o our_o sight_n and_o then_o they_o be_v say_v to_o be_v north_n and_o south_n and_o sometime_o also_o the_o two_o guard_n bc_n be_v east_n and_o west_n one_o from_o another_o and_o then_o the_o former_a guard_n bear_v from_o the_o north-star_n north-east_n and_o south-west_n and_o when_o these_o two_o guard_n be_v in_o a_o perpendicular_a line_n one_o above_o another_o the_o former_a guard_n bear_v from_o the_o north_n star_n north-east_n and_o south-west_n insomuch_o that_o from_o these_o four_o position_n do_v arise_v eight_o rule_n for_o the_o eight_o rumb_n wherein_o the_o former_a guard_n may_v stand_v be_v consider_v in_o respect_n of_o the_o north_n star_n and_o so_o presuppose_v that_o the_o north_n star_n be_v distant_a from_o the_o pole_n three_o degree_n and_o a_o half_a according_a to_o the_o opinion_n of_o some_o mariner_n who_o love_v number_n that_o have_v not_o any_o fraction_n sometime_o the_o north_n star_n shall_v be_v as_o high_a as_o the_o pole_n itself_o sometime_o three_o degree_n and_o a_o half_a low_o or_o high_a than_o the_o pole_n and_o sometime_o three_o degree_n and_o sometime_o one_o and_o a_o half_a and_o sometime_o half_a a_o degree_n chap._n xiii_o of_o the_o height_n of_o the_o star_n take_v with_o the_o crosse-staffe_n to_o know_v how_o much_o the_o north_n star_n be_v elevate_v above_o the_o horizon_n you_o must_v take_v the_o height_n thereof_o only_o at_o such_o time_n when_o as_o in_o respect_n of_o the_o former_a guard_n it_o be_v in_o some_o one_o of_o these_o four_o rumb_n that_o be_v to_o say_v north_n and_o south_n east_n and_o west_n north-east_n and_o south-west_n and_o northwest_n and_o southeast_n wherefore_o see_n it_o place_v in_o any_o of_o the_o foresay_a rumb_n you_o shall_v put_v that_o end_n of_o the_o crosse-staffe_n which_o be_v next_o 90_o degree_n upon_o your_o cheekbone_n at_o the_o utter_a corner_n of_o your_o eye_n and_o hold_v it_o there_o steadfast_a you_o must_v move_v the_o transversarie_n till_o you_o see_v the_o horizon_n join_v with_o the_o low_a end_n thereof_o and_o the_o north_n star_n with_o the_o high_a end_n then_o mark_v the_o degree_n and_o part_n of_o the_o degree_n which_o the_o transuersarie_n show_v upon_o the_o staff_n for_o that_o be_v the_o height_n of_o the_o star_n chap._n xiiii_o the_o regiment_n or_o rule_n of_o the_o north_n star_n the_o first_o rule_n when_o the_o guard_n be_v in_o the_o east_n the_o former_a guard_n bear_v with_o the_o north_n star_n east_n and_o west_n and_o then_o the_o north_n star_n be_v a_o degree_n and_o half_a under_o the_o pole_n let_v we_o add_v this_o degree_n and_o half_a to_o the_o height_n which_o we_o observe_v with_o the_o crosse-staffe_n and_o the_o whole_a product_n show_v the_o number_n of_o degree_n which_o the_o pole_n be_v elevate_v above_o our_o horizon_n and_o so_o much_o be_v we_o distant_a from_o the_o equinoctial_a towards_o the_o north._n the_o second_o rule_n when_o the_o guard_n be_v in_o the_o north-east_n one_o guard_n bear_v from_o another_o east_n and_o west_n and_o the_o former_a guard_n stand_v from_o the_o north_n star_n north-east_n and_o south-west_n and_o then_o the_o north_n star_n be_v under_o the_o pole_n three_o degree_n and_o one_o half_a which_o be_v add_v to_o the_o height_n of_o the_o star_n will_v show_v you_o the_o height_n of_o the_o pole_n the_o three_o rule_n when_o the_o guard_n be_v at_o the_o high_a than_o the_o former_a guard_n bear_v from_o the_o north_n star_n north_n and_o south_n the_o north_n star_n be_v then_o three_o degree_n under_o the_o pole_n which_o three_o degree_n be_v add_v to_o the_o height_n of_o the_o star_n do_v show_v the_o true_a height_n of_o the_o pole_n the_o four_o rule_n when_o the_o guard_n be_v in_o the_o northwest_n they_o bear_v one_o from_o another_o north_n and_o south_n and_o the_o former_a guard_n lie_v from_o the_o north_n star_n north-east_n and_o south-west_n and_o then_o the_o north_n star_n be_v under_o the_o pole_n half_o a_o degree_n which_o half_a degree_n be_v add_v to_o the_o height_n of_o the_o star_n give_v you_o the_o height_n of_o the_o pole_n the_o five_o rule_n when_o the_o guard_n be_v in_o the_o east_n the_o former_a guard_n lie_v from_o the_o north_n star_n east_n and_o west_n and_o then_o the_o north_n star_n be_v a_o degree_n and_o a_o half_a above_o the_o pole_n which_o degree_n and_o
cast_v his_o point_n in_o manner_n follow_v and_o he_o shall_v errer_n as_o little_a as_o be_v possible_a let_v he_o examine_v according_a to_o the_o ordinary_a run_v of_o his_o ship_n how_o much_o way_n she_o may_v make_v every_o day_n that_o he_o have_v sail_v and_o the_o league_n that_o shall_v amount_v in_o all_o the_o day_n let_v he_o take_v between_o the_o point_n of_o one_o compass_n and_o let_v he_o place_v one_o point_n thereof_o upon_o the_o place_n from_o whence_o he_o depart_v and_o take_v another_o compass_n let_v he_o set_v one_o point_n thereof_o upon_o the_o graduation_n according_a to_o the_o height_n which_o he_o have_v take_v and_o the_o other_o point_n upon_o the_o next_o east_n and_o west_n rumb_n now_o let_v this_o compass_v run_v by_o his_o east_n and_o west_n rumb_n till_o the_o point_n come_v from_o the_o graduation_n meet_v with_o the_o second_o point_n of_o the_o other_o compass_n which_o he_o hold_v not_o upon_o the_o chart_n and_o in_o the_o place_n where_o they_o meet_v he_o may_v say_v that_o there_o be_v his_o point_n and_o his_o ship_n and_o because_o in_o this_o case_n all_o pilot_n do_v not_o use_v this_o point_n of_o imagination_n and_o height_n there_o grow_v great_a diversity_n among_o they_o concern_v their_o distance_n from_o land_n when_o as_o in_o long_a voyage_n they_o confer_v and_o communicate_v their_o opinion_n one_o with_o another_o insomuch_o that_o one_o according_a to_o his_o conjecture_n judge_v himself_o to_o be_v 50_o league_n from_o land_n another_o 100_o another_o 200_o and_o another_o think_v he_o be_v hard_a by_o the_o land_n the_o reason_n be_v because_o some_o of_o they_o cast_v their_o point_n by_o traverse_v other_o by_o imagination_n only_o and_o other_o by_o imagination_n and_o height_n who_o be_v always_o more_o certain_a than_o the_o rest_n chap._n xxiv_o what_o it_o be_v to_o increase_v or_o diminish_v in_o height_n the_o mariner_n call_v it_o increase_v in_o height_n when_o they_o go_v further_o and_o further_o from_o the_o equinoctial_a and_o diminish_v in_o height_n when_o they_o approach_v near_o to_o the_o equinoctial_a so_o that_o in_o our_o navigation_n we_o either_o sail_n from_o a_o great_a to_o a_o less_o altitude_n of_o the_o pole_n and_o then_o we_o go_v towards_o the_o equinoctial_a and_o then_o the_o height_n be_v say_v to_o be_v diminish_v or_o we_o sail_v from_o a_o less_o to_o a_o great_a height_n of_o the_o pole_n and_o then_o we_o go_v from_o the_o equinoctial_a and_o be_v say_v to_o increase_v our_o height_n and_o hence_o it_o be_v that_o cast_v our_o point_n by_o imagination_n and_o afterward_o have_v take_v the_o height_n amend_v it_o by_o traverse_v either_o the_o height_n wherein_o we_o find_v ourselves_o be_v take_v by_o the_o sun_n or_o star_n be_v great_a or_o else_o it_o be_v less_o than_o that_o which_o we_o make_v account_n of_o by_o imagination_n and_o hence_o do_v arise_v four_o rule_n the_o first_o be_v that_o when_o in_o sail_v we_o do_v increase_v the_o height_n if_o the_o point_n amend_v by_o traverse_v be_v of_o great_a height_n than_o the_o point_n of_o imagination_n the_o ship_n have_v go_v more_o than_o the_o point_n of_o imagination_n show_v we_o the_o second_o when_o we_o increase_v our_o height_n if_o the_o point_n amend_v by_o traverse_v be_v in_o less_o height_n than_o the_o point_n find_v by_o imagination_n then_o have_v the_o ship_n go_v less_o way_n than_o we_o imagine_v the_o three_o be_v when_o we_o diminish_v our_o height_n in_o sail_v if_o the_o point_n amend_v by_o traverse_v be_v in_o a_o great_a height_n than_o the_o point_n find_v by_o imagination_n then_o have_v the_o ship_n make_v less_o way_n than_o we_o guess_v by_o our_o imagination_n the_o four_o be_v when_o we_o diminish_v our_o height_n if_o the_o point_n amend_v by_o traverse_n be_v in_o less_o height_n than_o the_o point_n find_v by_o imagination_n then_o have_v the_o ship_n make_v more_o way_n than_o we_o imagine_v chap._n xxv_o how_o you_o may_v cast_v a_o traverse_n point_n without_o compass_n if_o a_o mariner_n chance_v to_o lose_v his_o compass_n he_o may_v cast_v his_o point_n of_o traverse_n after_o this_o manner_n let_v he_o take_v two_o slender_a thread_n and_o put_v the_o end_n of_o one_o of_o they_o upon_o the_o place_n from_o whence_o he_o depart_v let_v he_o stretch_v it_o in_o equal_a distance_n from_o the_o rumb_n by_o which_o he_o have_v sail_v and_o put_v another_o thread_n in_o equal_a distance_n from_o the_o next_o east_n and_o west_n rumb_n let_v he_o make_v it_o to_o pass_v by_o the_o degree_n of_o height_n in_o which_o he_o find_v himself_o and_o where_o the_o two_o thread_n cross_v one_o another_o there_o be_v the_o point_n of_o the_o ship_n and_o always_o the_o first_o thread_n if_o it_o have_v not_o change_v the_o course_n show_v the_o way_n which_o the_o ship_n have_v go_v and_o the_o second_o the_o parallel_n wherein_o the_o ship_n be_v chap._n xxvi_o of_o another_o kind_n of_o cast_v a_o point_n by_o traverse_n examine_v the_o difference_n of_o the_o degree_n of_o distance_n from_o the_o equinoctial_a which_o be_v between_o the_o place_n from_o whence_o the_o ship_n set_v forth_o and_o the_o place_n where_o the_o ship_n be_v then_o take_v the_o heighth_n of_o both_o place_n very_o precise_o and_o subtract_v the_o lesser_a out_o of_o the_o great_a that_o which_o remain_v be_v the_o difference_n which_o difference_n you_o must_v multiply_v by_o the_o league_n which_o answer_n to_o one_o degree_n in_o the_o rumb_n by_o which_o you_o have_v sail_v and_o those_o league_n which_o the_o degree_n and_o minute_n of_o difference_n shall_v make_v you_o shall_v take_v between_o the_o point_n of_o a_o pair_n of_o compass_n out_o of_o your_o scale_n of_o league_n and_o hold_v the_o say_a compass_n so_o open_a set_v one_o foot_n thereof_o upon_o the_o point_n from_o whence_o the_o ship_n depart_v and_o the_o other_o foot_n stretch_v towards_o the_o place_n whithre_o the_o ship_n have_v sail_v you_o must_v hold_v up_o a_o little_a from_o the_o chart_n and_o you_o must_v set_v one_o foot_n of_o the_o other_o compass_n at_o the_o degree_n of_o the_o distance_n wherein_o your_o ship_n be_v from_o the_o equinoctial_a when_o the_o say_a point_n be_v seek_v for_o and_o the_o other_o point_n you_o must_v place_n upon_o the_o next_o east_n and_o west_n parallel_v and_o let_v this_o second_o compass_n run_v by_o his_o next_o east_n and_o west_n rumb_n until_o the_o point_n of_o the_o first_o compass_n lift_v up_o be_v set_v down_o that_o point_n of_o the_o second_o compass_n which_o come_v from_o the_o say_a degree_n do_v meet_v therewithal_o and_o where_o those_o two_o point_n shall_v meet_v there_o be_v the_o true_a point_n of_o the_o ship_n chap._n xxvii_o of_o the_o league_n which_o in_o navigation_n answer_v to_o each_o degree_n of_o latitude_n in_o every_o rumb_n if_o we_o suppose_v as_o we_o have_v before_o say_v in_o the_o chap._n of_o the_o quantity_n of_o the_o earth_n that_o the_o great_a circle_n thereof_o conain_v in_o compass_n 6300_o common_a spanish_a league_n then_o unto_o every_o degree_n of_o the_o meridian_n which_o be_v the_o great_a circle_n do_v answer_v 17_o spanish_a leagus_n and_o a_o half_a so_o that_o sail_a north_n and_o south_n if_o your_o height_n of_o the_o pole_n or_o your_o distance_n from_o the_o equinoctial_a be_v vary_v one_o degree_n you_o may_v say_v that_o you_o have_v go_v seventeen_o league_n and_o a_o half_a but_o if_o you_o vary_v one_o degree_n and_o hold_v your_o course_n upon_o the_o first_o point_n then_o have_v you_o sail_v 17_o league_n and_o ⅙_n and_o you_o have_v decline_v from_o the_o meridian_n or_o right_a line_n which_o pass_v by_o the_o place_n from_o which_o you_o depart_v three_o leagus_n and_o a_o half_a and_o if_o you_o sail_v upon_o the_o second_o point_n from_o the_o north_n or_o south_n till_o your_o height_n of_o the_o pole_n be_v change_v one_o degree_n you_o have_v then_o go_v 19_o league_n and_o ⅜_n and_o be_v distant_a from_o your_o right_a line_n 7_o league_n and_o ¼_n and_o vary_v a_o degree_n upon_o the_o three_o point_n of_o the_o compass_n from_o north_n or_o south_n you_o have_v go_v 21_o league_n and_o be_v depart_v from_o your_o right_a line_n 11_o league_n and_o ⅔_n sail_v upon_o the_o four_o point_n of_o the_o compass_n there_o do_v answer_v unto_o every_o degree_n 24_o league_n and_o three_o fourth_n and_o you_o be_v distant_a from_o the_o right_a line_n or_o meridian_n 17_o league_n and_o a_o half_a upon_o the_o five_o point_n you_o must_v allow_v for_o one_o degree_n 31_o league_n and_o a_o half_a and_o then_o be_v you_o distant_a from_o your_o right_a line_n 26_o league_n and_o ⅕_n upon_o the_o six_o point_n do_v
sake_n have_v need_n to_o note_v and_o when_o he_o have_v expect_v afternoon_n till_o the_o sun_n descend_v by_o the_o same_o instrument_n be_v find_v place_v in_o the_o same_o 25._o degr_v of_o altitude_n than_o the_o box_n itself_o must_v again_o be_v turn_v this_o way_n or_o that_o way_n until_o the_o sun_n again_o shine_v through_o the_o sight_n the_o magnetical_a needle_n do_v point_n to_o the_o begin_n of_o the_o circle_n which_o thing_n be_v thus_o dispatch_v the_o middle_a point_n of_o the_o arch_n in_o the_o horizontall_a plain_a between_o the_o first_o and_o second_o experiment_n be_v the_o north_n point_n and_o how_o much_o the_o needle_n decline_v from_o that_o point_n so_o much_o be_v the_o variation_n seek_v for_o as_o before_o we_o have_v show_v in_o the_o first_o example_n more_o at_o large_a whatsoever_o we_o have_v affirm_v to_o be_v available_a in_o the_o day_n time_n in_o these_o experiment_n of_o the_o sun_n the_o same_o may_v be_v understand_v and_o do_v in_o like_a manner_n in_o the_o night_n by_o any_o of_o the_o fix_a star_n whereof_o there_o be_v the_o same_o use_n in_o this_o matter_n that_o there_o be_v of_o the_o sun_n but_o there_o be_v not_o the_o same_o reason_n of_o the_o moon_n aswell_o because_o of_o the_o swiftness_n of_o her_o proper_a motion_n as_o also_o because_o of_o the_o greatness_n of_o her_o parallax_n as_o they_o call_v it_o which_o the_o overmuch_o neereness_n of_o the_o moon_n to_o the_o globe_n of_o the_o earth_n bring_v forth_o but_o this_o also_o be_v to_o be_v note_v that_o two_o three_o or_o four_o yea_o and_o more_o observation_n may_v be_v make_v in_o the_o foorenoon_n as_o for_o example_n let_v the_o first_o be_v when_o the_o sun_n be_v 10_o degree_n above_o the_o horizon_n the_o second_o when_o it_o be_v 15._o degr_n the_o three_o when_o it_o be_v 20._o degr_n and_o if_o any_o man_n will_v make_v trial_n as_o often_o after_o noon_n he_o shall_v see_v how_o every_o experiment_n agree_v with_o other_o and_o 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thereby_o what_o difference_n of_o variation_n be_v answerable_a to_o any_o determinate_a time_n of_o sail_v and_o so_o find_v a_o way_n whereby_o the_o north_n point_n may_v be_v find_v with_o more_o certainty_n and_o security_n which_o thing_n may_v thus_o also_o be_v do_v if_o a_o man_n diligent_o compare_v the_o variation_n find_v in_o the_o former_a day_n with_o the_o variation_n which_o he_o present_o see_v finis_fw-la error_n in_o the_o proportion_n of_o the_o length_n and_o breadth_n of_o place_n in_o the_o common_a sea-chart_n error_n in_o find_v out_o the_o difference_n of_o longitude_n by_o the_o common_a sea_n chart._n error_n in_o the_o lie_a and_o bear_v of_o place_n one_o from_o another_o in_o the_o common_a sea-chart_n error_n in_o set_v of_o place_n out_o of_o the_o common_a sea-chart_n into_o the_o globe_n error_n in_o show_v the_o distance_n of_o place_n in_o the_o common_a sea-chart_n error_n in_o keep_v always_o the_o same_o point_n of_o the_o compass_n the_o 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the_o quantity_n of_o the_o earth_n semidiameter_n clau_n comm._n in_o 1_o cap_n joan._n de_fw-fr sacrobosc_n height_n of_o the_o eye_n angle_n of_o dip_v foot_n min._n se_fw-la 1_o 1_o 8_o 2_o 1_o 36_o 3_o 1_o 58_o 4_o 2_o 16_o 5_o 2_o 33_o 6_o 2_o 47_o 7_o 3_o 0_o 8_o 3_o 13_o 9_o 3_o 24_o 10_o 3_o 35_o 12_o 3_o 56_o 14_o 4_o 15_o 16_o 4_o 33_o 18_o 4_o 40_o 20_o 5_o 5_o 22_o 5_o 20_o 24_o 5_o 3â—_n 26_o 5_o 40_o 28_o 6_o 1_o 30_o 6_o 13_o 32_o 6_o 25_o 34_o 6_o 38_o 36_o 6_o 49_o 38_o 7_o 0_o 40_o 7_o 11_o 42_o 7_o 21_o 44_o 7_o 32_o 46_o 7_o 42_o 48_o 7_o 52_o 50_o 8_o 2_o sun_n height_n sun_n paralax_n gr_n m_o sec_n 0_o 3_o 0_o 5_o 2_o 59_o 10_o 2_o 57_o 15_o 2_o 54_o 20_o 2_o 50_o 25_o 2_o 44_o 30_o 2_o 36_o 35_o 2_o 27_o 40_o 2_o 18_o 45_o 2_o 7_o 50_o 1_o 56_o 55_o 1_o 43_o 60_o 1_o 30_o 65_o 1_o 16_o 70_o 1_o 2_o 75_o 0_o 46_o 80_o 0_o 31_o 85_o 0_o 15_o the_o sun_n the_o sun_n the_o fix_v st._n altitude_n refraction_n altitude_n refraction_n altitude_n refraction_n de._n mi._n se_fw-la de._n mi._n se_fw-la de._n mi._n se_fw-la 0_o 34_o 0_o 23_o 3_o 10_o 0_o 30_o 0_o 1_o 26_o 0_o 24_o 2_o 50_o 1_o 21_o 30_o 2_o 20_o 0_o 25_o 2_o 30_o 2_o 15_o 30_o 3_o 17_o 0_o 26_o 2_o 15_o 3_o 12_o 30_o 4_o 15_o 30_o 27_o 2_o 0_o 4_o 11_o 0_o 5_o 14_o 30_o 28_o 1_o 45_o 5_o 10_o 0_o 6_o 13_o 30_o 29_o 1_o 35_o 6_o 9_o 0_o 7_o 12_o 45_o 30_o 1_o 25_o 7_o 8_o 15_o 8_o 11_o 15_o 31_o 1_o 15_o 8_o 6_o 45_o 9_o 10_o 30_o 32_o 1_o 5_o 9_o 6_o 0_o 10_o 10_o 0_o 33_o  _fw-fr 55_o 10_o 5_o 30_o 11_o 9_o 30_o 34_o  _fw-fr 45_o 11_o 5_o 0_o 12_o 9_o 0_o 35_o  _fw-fr 35_o 12_o 4_o 30_o 13_o 8_o 30_o 36_o  _fw-fr 30_o 13_o 4_o 0_o 14_o 8_o 0_o 37_o  _fw-fr 25_o 14_o 3_o 30_o 15_o 7_o 30_o 38_o  _fw-fr 20_o 15_o 3_o 0_o 16_o 7_o 0_o 39_o  _fw-fr 15_o 16_o 2_o 30_o 17_o 6_o 30_o 40_o  _fw-fr 10_o 17_o 2_o 0_o 18_o 5_o 45_o 41_o  _fw-fr 9_o 18_o 1_o 30_o 19_o 5_o 0_o 42_o  _fw-fr 8_o 19_o 1_o 0_o 20_o 4_o 30_o 43_o  _fw-fr 7_o 20_o 0_o 30_o 21_o 4_o 0_o 44_o  _fw-fr 6_o 21_o 0_o 0_o 22_o 3_o 30_o 45_o  _fw-fr 5_o  _fw-fr  _fw-fr  _fw-fr 1597_o to_o know_v the_o time_n of_o the_o sun_n come_v to_o any_o point_n of_o the_o ecliptick·_n pag._n 153._o pag._n 154._o pag._n 155._o by_o whole_a degree_n the_o first_o rumbe_n lon·_n latitu_fw-la gr_n m._n gr_n mi._n se._n 1_o 0_o 5_o 1_o 38_o 2_o 0_o 10_o 2_o 6_o by_o tin_n of_o min._n the_o first_o rumb_n lon·_n latitude_n gr_n m._n gr_n mi._n se._n the_o 0_o 10_o 0_o 50_o 16_o 23_o 0_o 20_o 1_o 40_o 32_o 26_o 0_o 30_o 2_o 30_o 47_o 33_o 0_o 40_o 3_o 21_o 1_o 5_o 0_o 50_o 4_o 11_o 12_o 16_o 1_o 0_o 5_o 1_o 20_o 46_o 1_o 10_o 5_o 51_o 25_o 35_o 1_o 20_o 6_o 41_o 26_o 18_o 1_o 30_o 7_o 31_o 22_o 14_o 1_o 40_o 8_o 21_o 12_o 38_o 1_o 50_o 9_o 10_o 57_o 0_o 2_o 0_o 10_o 0_o 34_o 40_o difference_n between_o the_o rumb_n and_o the_o wind_n the_o equinoctial_a be_v call_v the_o line_n because_o it_o be_v the_o principal_a of_o all_o other_o which_o be_v draw_v in_o the_o chart._n these_o league_n must_v be_v count_v in_o the_o 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that_o the_o rose_n or_o fly_n may_v play_v more_o nimble_o upon_o the_o pin_n this_o pin_n must_v be_v make_v of_o lattin_a with_o a_o very_a sharp_a point_n and_o be_v to_o be_v fasten_v upright_o in_o a_o round_a box_n of_o wood_n which_o must_v be_v of_o the_o fashion_n of_o a_o great_a cup-dish_n contain_v the_o rose_n within_o it_o be_v cover_v above_o with_o a_o clear_a round_a glass_n and_o the_o joint_n thereof_o must_v be_v stop_v with_o wax_n to_o the_o end_n that_o no_o wind_n may_v enter_v into_o the_o rose_n to_o disturb_v it_o there_o must_v be_v great_a care_n have_v that_o this_o rose_n with_o the_o wire_n place_v upon_o the_o pin_n may_v go_v nimble_o and_o may_v not_o swerve_v more_o to_o the_o one_o side_n then_o to_o the_o other_o but_o may_v stand_v even_o and_o level_a and_o when_o it_o incline_v towards_o either_o part_n you_o must_v put_v on_o the_o contrary_a part_n a_o little_a wax_n or_o a_o thin_a plate_n of_o lead_n fasten_v under_o the_o pasteboard_n which_o cover_v the_o wire_n this_o box_n wherein_o the_o rose_n play_v up_o and_o down_o hang_v within_o two_o hoop_n of_o lattin_a which_o be_v two_o round_a circle_n enclose_v one_o within_o another_o and_o distant_a asunder_o by_o the_o space_n of_o half_a a_o finger_n breadth_n with_o two_o nail_n of_o lattin_a which_o be_v diametral_o opposite_a and_o the_o box_n be_v fit_o place_v within_o these_o hoop_n you_o must_v make_v in_o the_o outward_a hoop_n two_o hole_n which_o must_v be_v distant_a from_o the_o foresay_a two_o nail_n a_o quarter_n of_o a_o circle_n both_o way_n and_o by_o these_o two_o hole_n must_v the_o outward_a hoop_n or_o circle_n be_v fasten_v within_o a_o square_a box_n or_o a_o round_a so_o as_o although_o that_o uttermost_a box_n be_v toss_v up_o and_o down_o every_o way_n with_o the_o motion_n of_o the_o ship_n yet_o always_o the_o superficies_n and_o glass_n of_o the_o inner_a box_n may_v lie_v level_a with_o the_o horizon_n and_o this_o be_v do_v with_o care_n the_o instrument_n which_o they_o call_v the_o sea-compasse_n be_v full_o finish_v the_o manner_n of_o use_v the_o same_o be_v when_o be_v place_v with_o the_o box_n in_o the_o midst_n of_o the_o poop_n of_o the_o ship_n where_o the_o bittacle_n stand_v in_o a_o right_a line_n which_o pass_v from_o the_o bolt-sprit_n by_o the_o midst_n of_o the_o main_a mast_n to_o the_o poop_n it_o serve_v continual_o to_o govern_v the_o ship_n by_o move_v of_o the_o rudder_n till_o the_o wind_n or_o the_o line_n of_o your_o compass_n towards_o which_o we_o desire_v to_o shape_v our_o course_n stand_v direct_o towards_o the_o prow_n or_o bolt-sprit_n of_o the_o ship_n they_o use_v also_o for_o the_o night_n to_o mark_v a_o point_n within_o the_o inner_a part_n of_o the_o inner_a box_n which_o in_o respect_n of_o the_o capitel_a of_o the_o compass_n may_v stand_v direct_o towards_o the_o prow_n of_o the_o ship_n and_o always_o in_o guide_v the_o ship_n you_o must_v take_v heed_n that_o the_o say_a point_n be_v continual_o join_v with_o the_o wind_n of_o the_o rose_n towards_o which_o you_o intend_v your_o course_n chap._n xviii_o how_o the_o variation_n of_o the_o compass_n may_v be_v find_v the_o mariner_n use_v to_o examine_v whether_o their_o compass_n north-easteth_a or_o south-westeth_a watch_v for_o that_o purpose_n when_o the_o former_a guard_n bear_v with_o the_o north_n star_n north-east_n and_o south-west_n take_v a_o little_a of_o the_o point_n of_o north_n and_o south_n and_o place_v their_o compass_n in_o a_o open_a place_n where_o the_o north_n star_n may_v be_v see_v if_o the_o flowerdeluis_fw-it of_o the_o rose_n look_v direct_o towards_o the_o star_n their_o compass_n vary_v nothing_o at_o all_o but_o if_o the_o star_n be_v to_o the_o north-east_n so_o much_o as_o it_o vary_v from_o the_o point_n of_o the_o flowerdeluis_fw-la so_o much_o the_o compass_n north-westeth_a and_o if_o it_o vary_v to_o the_o northwest_n of_o the_o compass_n how_o much_o the_o star_n swerve_v from_o the_o point_n of_o the_o flowerdeluis_fw-it so_o much_o the_o compass_n north-easteth_a and_o in_o regard_n of_o this_o variation_n of_o the_o compass_n there_o must_v always_o allowance_n be_v make_v in_o the_o course_n which_o be_v hold_v this_o manner_n of_o find_v out_o the_o variation_n i_o do_v account_n to_o be_v somewhat_o subject_a unto_o error_n but_o at_o land_n there_o be_v another_o more_o certain_a way_n by_o the_o meridian_n line_n which_o be_v to_o be_v take_v in_o manner_n follow_v the_o find_n of_o the_o meridian-line_n in_o a_o superficies_n which_o be_v plain_a and_o level_v every_o where_o and_o in_o a_o place_n where_o the_o sun_n shine_v at_o his_o rise_n and_o set_v you_o must_v draw_v certain_a circle_n upon_o one_o centre_n and_o have_v pitch_v a_o stile_n upright_o in_o the_o same_o centre_n the_o head_n whereof_o must_v be_v approve_v with_o a_o pair_n of_o compass_n to_o be_v equal_o distant_a from_o all_o part_n of_o one_o of_o those_o circle_n observe_v you_o in_o the_o morning_n two_o or_o three_o hour_n before_o noon_n when_o the_o point_n of_o the_o shadow_n of_o the_o stile_n touch_v the_o circumference_n of_o any_o of_o those_o circle_n and_o have_v make_v a_o mark_n in_o the_o touch_n take_v diligent_a heed_n in_o the_o afternoon_n also_o when_o the_o same_o point_n of_o the_o shadow_n turn_v about_o to_o touch_v in_o the_o same_o circle_n and_o make_v another_o mark_n in_o that_o second_o touch_n divide_v in_o the_o midst_n that_o part_n of_o the_o circle_n which_o be_v between_o those_o two_o mark_n then_o lay_v your_o ruler_n upon_o the_o point_n of_o the_o division_n and_o upon_o the_o centre_n of_o those_o circle_n draw_v a_o line_n which_o shall_v be_v your_o meridian_n and_o the_o true_a north_n and_o south_n rumb_n upon_o which_o set_v your_o compass_n and_o lay_v your_o ruler_n over_o the_o glass_n that_o it_o may_v pass_v along_o over_o the_o meridian_n and_o over_o the_o centre_n or_o capitel_a of_o the_o rose_n or_o fly_v either_o say_a ruler_n lie_v over_o the_o north_n and_o south_n of_o the_o compass_n and_o then_o be_v the_o compass_n without_o variation_n or_o the_o ruler_n decline_v towards_o the_o north-east_n or_o south-west_n and_o how_o much_o it_o decline_v that_o way_n so_o much_o the_o compass_n north-westeth_a or_o else_o it_o decline_v towards_o the_o northwest_n and_o then_o it_o north-easteth_a so_o much_o as_o the_o ruler_n decline_v that_o way_n but_o to_o know_v the_o variation_n of_o the_o compass_n both_o at_o land_n and_o sea_n we_o will_v deliver_v another_o far_o more_o easy_a and_o certain_a way_n when_o we_o come_v to_o entreat_v of_o the_o universal_a dial._n chap._n xix_o of_o the_o sea-chart_n the_o sea-chart_n be_v nothing_o else_o but_o a_o lively_a picture_n of_o the_o earth_n and_o water_n and_o it_o contain_v five_o notable_a thing_n which_o do_v concern_v as_o well_o the_o true_a make_n of_o the_o chart_n as_o also_o the_o enable_v of_o the_o mariner_n to_o know_v the_o way_n which_o he_o make_v the_o place_n where_o he_o be_v and_o the_o end_n of_o his_o journey_n the_o first_o be_v the_o lay_v out_o of_o the_o coast_n of_o the_o land_n which_o that_o it_o may_v be_v true_o do_v it_o be_v meet_v that_o every_o thing_n be_v set_v down_o in_o the_o chart_n in_o the_o same_o course_n distance_z and_o height_n that_o shall_v be_v find_v in_o navigation_n the_o second_o be_v that_o it_o contain_v not_o only_o the_o coast_n of_o the_o firm_a land_n but_o also_o all_o other_o particularity_n which_o do_v occur_v in_o sail_v as_o namely_o island_n iselet_n bank_n or_o bar_n shoalds_z rock_n and_o flat_n the_o three_o be_v the_o line_n which_o signify_v the_o 32_o wind_n by_o the_o help_n whereof_o we_o may_v see_v whether_o the_o part_n of_o the_o land_n be_v well_o lay_v out_o and_o in_o their_o true_a course_n one_o from_o another_o and_o of_o these_o wind_n the_o black_a be_v the_o eight_o principal_a which_o be_v call_v whole_a wind_n the_o green_a be_v half_a wind_n or_o half_o part_v wind_n and_o the_o red_a be_v the_o quarter_n of_o the_o wind_n you_o may_v know_v in_o your_o chart_n whether_o these_o wind_n be_v well_o draw_v if_o you_o try_v with_o your_o compass_n that_o all_o point_n of_o they_o be_v equal_o distant_a one_o from_o another_o and_o that_o all_o wind_n represent_v the_o same_o rumb_n be_v parallel_n as_o namely_o that_o one_o north-east_n and_o southwest_n rumb_n be_v parallel_n to_o another_o north-east_n and_o southwest_n rumb_n the_o four_o be_v the_o graduation_n in_o all_o part_n whereof_o it_o be_v meet_v that_o the_o degree_n south_n be_v equal_a one_o to_o another_o and_o that_o the_o part_n of_o the_o land_n do_v direct_o lie_v east_n