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Word A Word B Word C Word D Occurrence Frequency Band MI MI Band Prominent
world_n circle_n point_n pole_n 2,440 5 11.6304 5 false
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ID Title Author Corrected Date of Publication (TCP Date of Publication) STC Words Pages
A67154 Certain errors in navigation detected and corrected by Edw. Wright ; with many additions that were not in the former editions. Wright, Edward, 1558?-1615. 1657 (1657) Wing W3689; ESTC R16243 281,730 362

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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 upper_a superficies_n of_o the_o high_a heaven_n and_o it_o have_v in_o the_o very_a midst_n a_o certain_a point_n to_o wit_n the_o centre_n of_o the_o earth_n by_o which_o we_o do_v imagine_v a_o right_a line_n or_o axtree_n to_o pass_v from_o one_o pole_n to_o another_o upon_o which_o the_o world_n be_v move_v about_o from_o east_n to_o west_n chap._n iii_o of_o the_o division_n of_o the_o sphere_n the_o whole_a sphere_n of_o the_o world_n be_v divide_v into_o two_o part_n or_o region_n the_o elementary_a and_o celestial_a the_o elementary_a part_n or_o region_n have_v four_o part_n the_o first_o whereof_o be_v the_o earth_n which_o together_o with_o the_o element_n of_o water_n which_o be_v the_o second_o make_v one_o perfect_a globe_n and_o round_o about_o both_o these_o be_v two_o other_o element_n namely_o the_o air_n and_o above_o that_o the_o fire_n which_o fill_v the_o space_n between_o the_o air_n and_o the_o sphere_n of_o the_o moon_n of_o which_o element_n by_o virtue_n of_o the_o heat_n of_o the_o heaven_n be_v make_v and_o compound_v all_o corruptible_a thing_n in_o the_o world_n the_o celestial_a region_n consist_v of_o other_o ten_o part_n the_o first_o whereof_o be_v the_o sphere_n of_o the_o moon_n the_o second_o the_o sphere_n of_o mercury_n the_o three_o of_o venus_n the_o four_o be_v the_o sphere_n of_o the_o sun_n the_o five_o of_o mars_n the_o six_o of_o jupiter_n the_o seven_o of_o saturn_n the_o eight_o be_v the_o sphere_n of_o the_o fix_a star_n which_o be_v call_v the_o firmament_n the_o nine_o be_v the_o crystalline_a heaven_n and_o last_o the_o ten_o and_o high_a be_v the_o sphere_n call_v the_o primum_fw-la mobile_a that_o be_v the_o first_o or_o high_a movable_a heaven_n that_o which_o remain_v call_v the_o empyreal_a heaven_n because_o it_o have_v no_o motion_n come_v not_o to_o be_v consider_v on_o in_o the_o art_n of_o navigation_n a_o figure_n wherein_o may_v be_v see_v the_o composition_n of_o the_o whole_a sphere_n of_o the_o 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
what_o part_n of_o the_o world_n we_o be_v and_o in_o it_o in_o the_o sea-chart_n be_v place_v all_o these_o point_n or_o degree_n of_o longitude_n and_o from_o it_o the_o latitude_n be_v account_v so_o that_o the_o equinoctial_a be_v a_o circle_n which_o divide_v the_o world_n into_o two_o equal_a portion_n and_o be_v equal_o distant_a every_o where_o from_o either_o of_o the_o pole_n and_o it_o be_v call_v the_o equinoctial_a circle_n because_o that_o when_o the_o sun_n pass_v under_o it_o upon_o the_o 11_o of_o march_n and_o the_o 13_o of_o september_n it_o make_v the_o day_n equal_a to_o the_o night_n the_o knowledge_n of_o this_o circle_n in_o the_o art_n of_o navigation_n do_v help_v we_o to_o find_v the_o latitude_n or_o distance_n from_o the_o line_n and_o from_o this_o circle_n be_v reckon_v the_o declination_n of_o the_o sun_n in_o the_o regiment_n thereof_o and_o always_o those_o chart_n of_o navigation_n which_o be_v either_o universal_a or_o half_a universal_a have_v this_o equinoctial_a circle_n draw_v with_o a_o great_a red_a line_n which_o pass_v by_o the_o begin_n of_o the_o account_n of_o the_o degree_n of_o latitude_n chap._n x._o of_o the_o pole_n of_o the_o world_n and_o here_o it_o be_v to_o be_v note_v that_o one_o of_o those_o two_o pole_n from_o which_o the_o equinoctial_a be_v equal_o distant_a which_o be_v always_o in_o our_o sight_n because_o it_o be_v continual_o above_o our_o horizon_n be_v call_v the_o pole-artick_a the_o septentrional_a or_o north_n pole_n but_o the_o other_o opposite_a pole_n which_o we_o never_o see_v because_o it_o be_v under_o our_o horizon_n be_v call_v the_o pole-antartick_a and_o the_o meridional_a or_o south_n pole_n and_o so_o that_o part_n of_o the_o world_n which_o be_v between_o the_o equinoctial_a and_o the_o north_n pole_n be_v call_v the_o north_n part_n and_o that_o which_o be_v from_o the_o equinoctial_a to_o the_o south_n pole_n be_v call_v the_o south_n part_n chap_n xi_o of_o the_o ecliptic_a line_n the_o equinoctial_a circle_n be_v divide_v into_o equal_a part_n by_o another_o circle_n call_v the_o ecliptic_a whereof_o one_o half_a be_v between_o the_o equinoctial_a and_o the_o north_n pole_n and_o the_o other_o half_a between_o the_o equinoctial_a and_o the_o south_n pole_n and_o that_o part_v thereof_o which_o be_v further_a distant_a from_o the_o equinoctial_a be_v distant_a from_o the_o same_o about_o 23_o degree_n and_o a_o half_a and_o because_o the_o sun_n move_v in_o this_o circle_n without_o depart_v from_o it_o hereof_o proceed_v the_o declination_n thereof_o and_o this_o circle_n in_o all_o part_n be_v equal_o distant_a from_o the_o pole_n of_o the_o second_o motion_n which_o be_v call_v the_o pole_n of_o the_o ecliptic_a and_o through_o this_o circle_n the_o sun_n be_v continual_o move_v by_o his_o proper_a motion_n from_o east_n to_o west_n by_o mean_n of_o which_o motion_n sometime_o he_o pass_v under_o the_o equinoctial_a and_o at_o other_o time_n depart_v from_o it_o both_o towards_o the_o north_n and_o towards_o the_o south_n and_o the_o quantity_n of_o his_o great_a distance_n be_v about_o 23_o degree_n and_o a_o half_a and_o so_o much_o be_v the_o distance_n of_o the_o pole_n of_o the_o ecliptic_a from_o the_o pole_n of_o the_o equinoctial_a and_o albeit_o this_o circle_n be_v not_o draw_v in_o the_o sea_n chartley_n yet_o be_v it_o in_o some_o sort_n represent_v in_o the_o table_n of_o the_o sun_n declination_n which_o be_v gather_v from_o the_o motion_n which_o the_o sun_n make_v under_o the_o ecliptic_a chap._n xii_o of_o the_o declination_n of_o the_o sun_n the_o motion_n of_o the_o sun_n under_o the_o ecliptic_a be_v the_o cause_n of_o his_o declination_n which_o be_v nothing_o else_o but_o the_o daily_a swarve_n or_o decline_a of_o the_o sun_n from_o the_o equinoctial_a line_n and_o this_o declination_n when_o the_o sun_n be_v under_o the_o equinoctial_a upon_o the_o eleven_o of_o march_n and_o thirteen_o of_o september_n be_v nothing_o at_o all_o so_o likewise_o upon_o the_o twelve_o of_o june_n and_o twelve_o of_o december_n the_o declination_n be_v at_o the_o great_a and_o albeit_o this_o great_a declination_n be_v now_o in_o our_o time_n about_o three_o and_o twenty_o degree_n and_o a_o half_a yet_o have_v it_o at_o other_o time_n be_v find_v otherwise_o by_o reason_n of_o a_o three_o motion_n proper_a to_o the_o eight_o heaven_n but_o it_o always_o keep_v between_o 23_o degree_n 28_o minute_n and_o 23_o degree_n 53_o minute_n from_o hence_o therefore_o we_o do_v infer_v that_o at_o divers_a time_n it_o be_v meet_v to_o make_v new_a and_o divers_a table_n of_o the_o declination_n of_o the_o sun_n chap._n xiii_o of_o the_o colour_n there_o be_v two_o circle_n of_o the_o sphere_n either_o of_o which_o divide_v in_o into_o two_o equal_a part_n and_o they_o be_v call_v colour_n because_o that_o in_o the_o revolution_n which_o they_o make_v by_o force_n of_o the_o primum_fw-la mobile_a they_o do_v not_o show_v themselves_o whole_o unto_o we_o so_o as_o we_o may_v see_v all_o part_n of_o they_o one_o of_o they_o be_v call_v the_o equinoctial_a colour_n because_o it_o pass_v by_o the_o pole_n of_o the_o world_n and_o the_o point_n where_o the_o ecliptic_a cut_v the_o equinoctial_a and_o when_o the_o sun_n by_o his_o own_o proper_a motion_n come_v unto_o it_o he_o make_v the_o day_n and_o the_o night_n equal_a and_o divide_v the_o winter_n from_o the_o spring_n by_o the_o one_o part_n and_o by_o the_o other_o summer_n from_o autumn_n at_o which_o time_n the_o sun_n have_v no_o declination_n at_o all_o the_o other_o be_v call_v the_o solstitial_a colour_n because_o it_o pass_v by_o the_o pole_n of_o the_o world_n and_o of_o the_o ecliptic_a and_o by_o the_o point_n where_o the_o ecliptic_a be_v further_a distant_a from_o the_o equinoctial_a and_o when_o the_o sun_n by_o his_o proper_a motion_n come_v unto_o it_o in_o the_o one_o part_v it_o make_v the_o long_a day_n and_o the_o short_a night_n and_o divide_v the_o spring_n from_o the_o summer_n and_o have_v his_o great_a declination_n towards_o the_o north_n and_o be_v in_o the_o other_o part_n the_o sun_n make_v the_o long_a night_n and_o short_a day_n and_o divide_v winter_n from_o autumn_n and_o be_v in_o his_o great_a southerly_a declination_n these_o two_o colour_n be_v note_v in_o the_o table_n of_o the_o sun_n declination_n because_o the_o equinoctial_a colour_n pass_v by_o the_o two_o point_n where_o there_o be_v no_o declination_n at_o all_o because_o the_o sun_n be_v under_o the_o very_a equinoctial_a circle_n and_o the_o solstitial_a colour_n pass_v by_o that_o place_n where_o the_o sun_n have_v his_o great_a declination_n which_o be_v in_o 23_o degree_n and_o a_o half_a or_o thereabouts_o chap._n fourteen_o of_o the_o meridian_n circle_n the_o meridian_n be_v a_o circle_n draw_v by_o the_o pole_n of_o the_o world_n which_o be_v all_o one_o with_o the_o pole_n of_o the_o equinoctial_a and_o and_o by_o the_o point_n direct_o over_o our_o head_n call_v the_o zenith_n and_o it_o be_v call_v the_o meridian_n because_o that_o when_o the_o sun_n by_o the_o motion_n of_o the_o primum_fw-la mobile_a come_v unto_o this_o circle_n it_o make_v midday_n and_o then_o he_o have_v be_v run_v his_o course_n from_o his_o rise_n till_o he_o come_v thither_o just_o so_o long_a time_n as_o he_o shall_v be_v run_v from_o thence_o to_o the_o place_n of_o his_o set_n the_o zenith_n be_v a_o point_n in_o the_o firmament_n place_v direct_o over_o our_o head_n and_o it_o be_v to_o be_v note_v that_o when_o the_o sun_n be_v in_o that_o circle_n it_o have_v the_o great_a altitude_n above_o our_o horizon_n that_o it_o can_v possible_o have_v the_o same_o day_n by_o this_o and_o the_o declination_n we_o come_v to_o know_v how_o far_o we_o be_v distant_a from_o the_o equinoctial_a either_o towards_o the_o north_n or_o towards_o the_o south_n and_o hence_o it_o be_v that_o the_o height_n of_o the_o sun_n in_o navigation_n be_v understand_v only_o for_o that_o height_n which_o the_o sun_n have_v when_o he_o be_v in_o this_o circle_n and_o so_o the_o height_n of_o the_o sun_n shall_v be_v that_o part_n of_o the_o meridian_n which_o be_v contain_v between_o the_o sun_n and_o our_o horizon_n this_o circle_n in_o the_o sea-chart_n be_v represent_v by_o all_o those_o line_n which_o be_v draw_v from_o north_n to_o south_n chap._n xv._n of_o the_o horizon_n the_o horizon_n be_v a_o circle_n which_o divide_v that_o part_n of_o the_o heaven_n which_o we_o see_v from_o the_o residue_n which_o we_o do_v not_o see_v and_o it_o be_v proper_o that_o circle_n by_o which_o according_a to_o our_o sight_n the_o heaven_n seem_v to_o be_v join_v with_o the_o water_n when_o we_o be_v at_o sea_n without_o sight_n of_o
and_o inconstant_a inequality_n of_o the_o angle_n which_o that_o great_a circle_n make_v with_o every_o new_a meridian_n of_o which_o angle_v the_o invention_n indeed_o by_o the_o chart_n especial_o be_v very_o subtle_a and_o consist_v herein_o to_o wit_n in_o know_v how_o much_o such_o kind_n of_o angle_n do_v decrease_v or_o increase_v as_o the_o ship_n go_v forward_o and_o he_o that_o so_o shape_v his_o course_n go_v the_o straight_a and_o near_a way_n otherwise_o it_o can_v be_v that_o a_o man_n shall_v keep_v a_o straight_a course_n if_o he_o shall_v continual_o follow_v one_o and_o the_o same_o point_n or_o line_n of_o the_o compass_n except_o he_o sail_v under_o a_o meridian_n or_o under_o the_o aequinoctial_a line_n but_o he_o must_v change_v the_o point_n of_o the_o compass_n so_o often_o as_o that_o straight_a course_n shall_v sensible_o require_v and_o therefore_o it_o can_v be_v by_o any_o mean_n that_o the_o mariner_n when_o they_o go_v perpetualy_a towards_o the_o same_o part_n of_o the_o world_n keep_v the_o same_o angle_n of_o position_n in_o respect_n of_o the_o meridian_n or_o the_o same_o point_n of_o the_o compass_n shall_v go_v the_o short_a and_o near_a way_n this_o kind_n of_o sail_v under_o a_o great_a circle_n be_v of_o special_a use_n in_o our_o northern_a navigation_n for_o the_o discovery_n of_o the_o north-east_n or_o north_n west_n passage_n which_o as_o it_o may_v most_o easy_o be_v perform_v by_o help_n of_o a_o hydrographical_a globe_n with_o the_o helisphaericall_a line_n draw_v thereupon_o so_o for_o they_o that_o list_v not_o to_o be_v trouble_v with_o the_o cumbersome_a carriage_n and_o charge_n of_o the_o globe_n it_o may_v be_v do_v in_o a_o manner_n with_o no_o less_o facility_n by_o a_o nautical_a planisphere_n make_v after_o the_o projection_n of_o gemma_fw-la erisius_fw-la his_o astrolabe_n whereof_o more_o hereafter_o when_o god_n shall_v give_v leisure_n there_o be_v some_o also_o that_o hold_v it_o for_o erroneous_a that_o the_o rumb_n in_o the_o mariner_n chart_n shall_v be_v express_v by_o right_a line_n erroneous_a and_o consequent_o that_o the_o meridian_n shall_v be_v parallel_n or_o equidistant_a every_o where_o which_o because_o it_o be_v but_o bare_o affirm_v and_o the_o contrary_n may_v be_v prove_v as_o well_o as_o that_o each_o rumb_n except_o the_o rumb_n of_o north_n and_o south_n make_v equal_a angle_n with_o every_o meridian_n we_o hold_v it_o not_o only_o as_o true_a but_o also_o as_o most_o meet_a and_o commodious_a for_o the_o mariner_n common_a use_n that_o the_o meridian_n in_o the_o sea-chart_n shall_v be_v every_o where_o equidistant_a each_o from_o other_o and_o consequent_o that_o the_o rumb_n shall_v be_v straight_a line_n for_o these_o two_o cause_n first_o because_o the_o rumb_n or_o point_n of_o the_o compass_n may_v so_o most_o easy_o be_v draw_v in_o the_o nautical_a planisphaere_n only_o by_o a_o straight_a ruler_n for_o see_v that_o any_o one_o and_o the_o same_o rumb_n save_v only_o the_o rumb_n of_o north_n and_o south_n which_o be_v all_o one_o with_o the_o meridian_n make_v always_o equal_a angle_n with_o every_o meridian_n without_o either_o sensible_a numerable_a or_o measurable_a though_o not_o without_o intelligible_a error_n for_o indeed_o those_o angle_n be_v less_o and_o less_o as_o they_o come_v near_o to_o the_o pole_n much_o like_a as_o the_o angle_n of_o a_o little_a semicircle_n be_v less_o than_o the_o angle_n of_o a_o great_a semicircle_n all_o the_o rumb_n must_v needs_o be_v straight_a line_n if_o the_o meridian_n be_v equidistant_n and_o right_a line_n by_o the_o 27_o and_o 28_o prop._n 1._o euclid_n second_o the_o respective_a situation_n of_o any_o place_n to_o other_o in_o the_o chart_n which_o they_o common_o call_v the_o lie_a or_o bear_v of_o one_o place_n from_o another_o according_a to_o the_o point_n of_o the_o compass_n may_v most_o easy_o be_v know_v by_o the_o nautical_a planisphaere_n with_o right_n line_v rumb_n and_o equidistant_a meridian_n for_o that_o rumb_n from_o which_o both_o place_n be_v equidistant_a show_v how_o those_o two_o place_n lie_v one_o from_o another_o and_o for_o these_o two_o cause_n of_o so_o great_a facility_n both_o in_o the_o make_n and_o use_v of_o the_o mariner_n chart_n with_o equidistant_a meridian_n and_o straight-lined_n rumb_n it_o ought_v to_o be_v prefer_v before_o any_o other_o instrument_n heretofore_o publish_v to_o that_o end_n for_o the_o common_a use_n of_o the_o mariner_n at_o sea_n especial_o and_o though_o the_o globe_n be_v commend_v by_o some_o as_o most_o absolute_a and_o perfect_a for_o all_o course_n and_o climate_n whatsoever_o yet_o for_o the_o chargeableness_n thereof_o troublesome_a carriage_n stowage_n and_o tedious_a usage_n for_o the_o most_o part_n in_o navigation_n follow_v any_o other_o course_n save_o east_n or_o west_n north_n or_o south_n it_o will_v for_o the_o most_o part_n be_v find_v unmeet_a and_o cumbersome_a and_o nothing_o so_o fit_a and_o ready_a for_o the_o mariner_n common_a use_n at_o sea_n as_o the_o nautical_a planisphaere_n true_o make_v chap._n ii_o how_o the_o former_a error_n may_v be_v avoid_v these_o error_n notwithstanding_o they_o have_v be_v much_o complain_v of_o by_o divers_a as_o namely_o by_o martin_n cortese_fw-it in_o his_o three_o book_n and_o second_o chapter_n of_o the_o art_n of_o navigation_n but_o special_o by_o petrus_n nonius_n in_o his_o second_o book_n of_o geometrical_a observation_n rule_n and_o instrument_n and_o although_o gerardus_n mercator_n in_o his_o universal_a map_n of_o the_o world_n seem_v to_o correct_v they_o by_o make_v the_o distance_n of_o the_o parallel_v great_a and_o great_a towards_o the_o pole_n yet_o none_o of_o they_o teach_v any_o certain_a way_n how_o to_o amend_v such_o gross_a fault_n whereby_o the_o mariner_n may_v be_v deceive_v many_o time_n a_o whole_a point_n of_o the_o compass_n yea_o sometime_o two_o or_o three_o point_n and_o more_o in_o judge_v by_o his_o ordinary_a chart_n how_o one_o place_n bear_v from_o another_o especial_o if_o he_o sail_v far_o northwards_o or_o southwards_o whereby_o we_o may_v easy_o guess_v how_o indirect_a a_o course_n he_o shall_v make_v to_o come_v to_o the_o desire_a haven_n that_o shall_v follow_v so_o false_a and_o erroneous_a direction_n with_o great_a danger_n at_o the_o least_o many_o time_n to_o lose_v ship_n good_n life_n and_o all_o the_o fountain_n of_o all_o the_o error_n aforesaid_a the_o last_o only_o except_v be_v in_o the_o very_a foundation_n and_o groundwork_n of_o the_o mariner_n chart_n that_o be_v in_o the_o first_o geometrical_a lineament_n thereof_o namely_o because_o the_o meridian_n be_v not_o right_o divide_v the_o division_n be_v every_o where_o equal_a nor_o the_o parallel_n right_o draw_v have_v in_o all_o place_n the_o same_o distance_n each_o from_o other_o that_o the_o meridian_n have_v at_o the_o aequinoctial_a whereas_o the_o space_n betwixt_o the_o parallel_n shall_v increase_v more_o and_o more_o as_o you_o go_v from_o the_o aequinoctial_a towards_o either_o of_o the_o pole_n which_o martin_n cortese_fw-it also_o note_v be_v his_o 3_o book_n and_o 2_o chapter_n of_o the_o art_n of_o navigation_n but_o he_o omit_v that_o wherein_o all_o the_o difficulty_n lie_v that_o be_v how_o much_o or_o in_o what_o proportion_n those_o space_n shall_v increase_v which_o that_o it_o may_v the_o better_o be_v perceive_v i_o think_v it_o not_o unmeet_a first_o to_o show_v by_o what_o kind_n of_o projection_n or_o extension_n rather_o the_o nautical_a planisphaere_n may_v not_o unfit_o be_v conceive_v to_o be_v geometrical_o make_v after_o this_o manner_n suppose_v a_o spherical_a superficies_n with_o meridian_n parallel_n rumbe_n and_o the_o whole_a hydrographical_a description_n draw_v thereupon_o to_o be_v inscribe_v into_o a_o concave_n cylinder_n their_o axe_n agree_v in_o one_o let_v this_o spherical_a superficies_n swell_v like_o a_o bladder_n while_o it_o be_v in_o blow_v equal_o always_o in_o every_o part_n thereof_o that_o be_v as_o much_o in_o longitude_n as_o in_o latitude_n till_o it_o apply_v and_o join_v itself_o round_a about_o and_o all_o alongst_o also_o towards_o either_o pole_n unto_o the_o concave_a superficies_n of_o the_o cylinder_n each_o parallel_n upon_o this_o spherical_a superficies_n increase_v successive_o from_o the_o aequinoctial_a towards_o either_o pole_n until_o it_o come_v to_o be_v of_o aequal_a diameter_n with_o the_o cylinder_n and_o consequent_o the_o meridian_n still_o widen_v themselves_o till_o they_o come_v to_o be_v so_o far_o distant_a every_n where_o each_o from_o other_o as_o they_o be_v at_o the_o aequinoctial_a thus_o it_o may_v most_o easy_o be_v understand_v how_o a_o spherical_a superficies_n may_v by_o extension_n be_v make_v a_o cylindrical_a and_o consequent_o a_o plain_a parallelogram_n superficies_n because_o the_o superficies_n of_o a_o cylinder_n be_v nothing_o else_o but_o
the_o sun_n and_o the_o shadow_n be_v both_o one_o way_n then_o i_o look_v for_o the_o height_n which_o be_v 85_o degree_n and_o three_o quarter_n so_o that_o it_o lack_v of_o 90_o degree_n four_o degree_n and_o one_o quarter_n which_o be_v fifteen_o minute_n these_o four_o degree_n and_o fifteen_o minute_n be_v add_v to_o the_o declination_n which_o be_v twenty_o degree_n and_o 41_o minute_n amount_v in_o all_o to_o 24_o degree_n and_o 56_o minute_n and_o so_o much_o be_o i_o distant_a from_o the_o equinoctial_a towards_o the_o north_n which_o be_v the_o part_n of_o the_o sun_n and_o of_o the_o shadow_n a_o example_n of_o the_o five_o rule_n upon_o the_o 17_o of_o october_n 1609_o which_o be_v the_o first_o year_n after_o the_o leap_n year_n the_o sun_n now_o go_v his_o course_n towards_o the_o south_n suppose_v i_o take_v his_o altitude_n in_o 50_o degree_n and_o one_o three_o and_o when_o i_o take_v it_o the_o low_a vain_a of_o my_o astrolabe_n decline_v towards_o the_o north_n of_o my_o compass_n wherefore_o i_o say_v that_o the_o sun_n and_o the_o shadow_n be_v different_a and_o so_o add_v 05_o degree_n and_o 20_o minute_n which_o be_v one_o three_o part_n of_o a_o degree_n with_o 12_o degree_n and_o 55_o minute_n which_o upon_o that_o day_n be_v the_o sun_n declination_n they_o amount_v in_o all_o to_o 63_o degree_n and_o 15_o minute_n which_o be_v less_o than_o 90_o degree_n by_o 26_o degree_n and_o 45_o minute_n and_o so_o far_o i_o be_o distant_a from_o the_o equinoctial_a to_o the_o part_n of_o the_o shadow_n that_o be_v to_o the_o north_n for_o the_o sun_n and_o shadow_n be_v different_a the_o height_n and_o declination_n come_v not_o to_o 90_o degr_n a_o second_o example_n of_o the_o five_o rule_n the_o same_o day_n and_o year_n suppose_v that_o some_o man_n find_v the_o sun_n in_o 77_o degree_n and_o five_o minute_n of_o height_n the_o sun_n itself_o decline_v to_o the_o south_n and_o the_o shadow_n fall_v to_o the_o north_n which_o be_v add_v to_o 12_o degree_n and_o 55_o minute_n of_o declination_n amount_v in_o all_o to_o 90_o degree_n just_a whereby_o i_o know_v that_o the_o ship_n wherein_o this_o altitude_n be_v take_v be_v under_o the_o equinoctial_a because_o the_o sun_n and_o shadow_n be_v different_a the_o height_n and_o declination_n make_v just_a 90_o degree_n the_o three_o example_n of_o the_o five_o rule_n upon_o the_o 20_o of_o may_v 1608_o suppose_v a_o certain_a man_n find_v the_o sun_n height_n to_o be_v 88_o degree_n and_o two_o three_o part_n the_o sun_n and_o shadow_n be_v different_a which_o be_v add_v to_o 21_o degr_n 54_o minute_n the_o sun_n declination_n that_o day_n amount_v to_o 110_o degree_n 34_o minute_n which_o exceed_v 90_o by_o 20_o degree_n and_o 34_o minute_n i_o say_v therefore_o that_o this_o man_n be_v 20_o degree_n 34_o minute_n distant_a from_o the_o equinoctial_a towards_o the_o part_n of_o the_o sun_n which_o be_v to_o the_o north_n because_o the_o sun_n and_o the_o shadow_n be_v diffe●rent_a the_o height_n of_o the_o sun_n and_o the_o declination_n be_v add_v together_o exceed_v 90_o degree_n chap._n viii_o another_o manner_n of_o account_v by_o the_o sun_n as_o they_o use_v in_o portugal_n some_o astrolabe_fw-la there_o be_v who_o account_n begin_v not_o from_o the_o horizon_n but_o from_o the_o zenith_n and_o end_v with_o 90_o degr_n in_o the_o horizon_n and_o the_o height_n take_v by_o they_o be_v nothing_o else_o but_o the_o distance_n of_o the_o sun_n from_o our_o zenith_n and_o to_o make_v a_o account_n of_o the_o sun_n according_a to_o the_o altitude_n take_v with_o such_o astrolabe_fw-la there_o be_v these_o rule_n follow_v to_o be_v observe_v 1._o when_o the_o sun_n and_o the_o shadow_n be_v both_o one_o way_n add_v the_o height_n unto_o the_o declination_n and_o the_o product_n will_v show_v how_o far_o you_o be_v distant_a from_o the_o line_n towards_o the_o part_n of_o the_o sun_n and_o shadow_n 2._o if_o the_o sun_n and_o the_o shadow_n be_v differ_v subduct_v the_o declination_n from_o the_o height_n or_o the_o height_n from_o the_o declination_n the_o lesser_a from_o the_o great_a and_o the_o remainder_n will_v show_v how_o far_o you_o be_v from_o the_o line_n towards_o the_o part_n of_o that_o which_o be_v great_a and_o if_o the_o height_n be_v great_a then_o be_v you_o on_o the_o part_n of_o the_o shadow_n 3._o when_o the_o sun_n be_v in_o the_o line_n and_o have_v no_o declination_n so_o much_o altitude_n as_o you_o shall_v find_v so_o far_o be_v you_o distant_a from_o the_o equinoctial_a towards_o the_o part_n of_o the_o shadow_n 4._o when_o you_o shall_v take_v the_o sun_n in_o your_o zenith_n have_v then_o no_o altitude_n his_o declination_n will_v show_v you_o how_o far_o you_o be_v distant_a from_o the_o line_n towards_o the_o part_n of_o the_o sun_n these_o rule_n because_o they_o be_v so_o easy_a and_o plain_a need_v no_o example_n chap._n ix_o how_o the_o height_n of_o the_o sun_n may_v be_v know_v in_o any_o place_n whatsoever_o without_o a_o astrolabe_n first_o know_v your_o distance_n from_o the_o equinoctial_a some_o pilot_n for_o their_o curiosity_n sake_n desire_v to_o know_v the_o height_n of_o the_o sun_n for_o any_o day_n without_o a_o astrolabe_n for_o the_o performance_n whereof_o it_o be_v expedient_a that_o they_o know_v three_o thing_n that_o be_v to_o say_v the_o declination_n of_o the_o sun_n the_o distance_n of_o the_o place_n from_o the_o equinoctial_a and_o the_o part_n whereunto_o the_o shadow_n do_v incline_v at_o midday_n these_o three_o thing_n be_v know_v you_o shall_v come_v to_o the_o knowledge_n of_o the_o sun_n height_n by_o four_o rule_n 1_o when_o you_o and_o the_o sun_n be_v both_o on_o one_o side_n of_o the_o equinoctial_a if_o your_o distance_n from_o the_o line_n be_v equal_a to_o the_o sun_n declination_n you_o shall_v find_v the_o sun_n in_o your_o zenith_n in_o 90_o degr_n and_o shall_v have_v no_o shadow_n 2_o when_o the_o sun_n have_v no_o declination_n look_v how_o much_o your_o distance_n from_o the_o equinoctial_a want_v of_o 90_o deg_n for_o so_o much_o be_v height_n of_o the_o sun_n 3_o when_o the_o sun_n and_o the_o shadow_n be_v both_o towards_o one_o part_n subtract_v out_o of_o your_o distance_n from_o the_o equinoctial_a the_o declination_n of_o the_o sun_n that_o day_n and_o that_o which_o the_o remainder_n shall_v want_v of_o 90_o deg_n shall_v be_v the_o height_n of_o the_o sun_n 4_o when_o the_o sun_n and_o the_o shadow_n be_v different_a if_o the_o equinoctial_a be_v between_o you_o and_o the_o sun_n add_v the_o declination_n of_o the_o sun_n to_o your_o distance_n from_o the_o equinoctial_a and_o that_o which_o these_o two_o number_n add_v together_o shall_v want_v of_o 90_o deg_n shall_v be_v the_o height_n of_o the_o sun_n but_o if_o you_o be_v between_o the_o sun_n and_o the_o line_n you_o must_v subduct_v your_o distance_n from_o the_o line_n out_o of_o the_o sun_n declination_n and_o then_o that_o which_o the_o remainder_n shall_v want_v of_o 90_o deg_n shall_v be_v the_o height_n of_o the_o sun_n chap._n x._o the_o rule_n or_o regiment_n of_o the_o north-star_n for_o the_o knowledge_n of_o the_o height_n of_o the_o pole_n the_o zenith_n be_v the_o pole_n of_o the_o horizon_n because_o it_o be_v every_o where_o distant_a from_o it_o just_a 90_o deg_n and_o hence_o it_o be_v that_o the_o pole_n of_o the_o world_n be_v so_o much_o elevate_v above_o our_o horizon_n as_o our_o zenith_n be_v distant_a from_o the_o equinoctial_a which_o be_v very_o manifest_a for_o have_v 90_o deg_n of_o the_o meridian_n from_o our_o zenith_n by_o the_o pole_n of_o the_o world_n to_o the_o horizon_n and_o other_o 90_o deg_n of_o the_o meridian_n from_o the_o pole_n of_o the_o world_n by_o our_o zenith_n to_o the_o equinoctial_a because_o they_o be_v two_o quadrant_n of_o one_o and_o the_o same_o circle_n they_o must_v needs_o be_v of_o equal_a quantity_n from_o both_o which_o that_o part_n be_v take_v away_o which_o be_v common_a to_o both_o that_o be_v the_o whole_a distance_n from_o the_o pole_n of_o the_o world_n to_o our_o zenith_n that_o which_o remain_v on_o both_o part_n shall_v be_v equal_a and_o so_o that_o space_n from_o our_o zenith_n to_o the_o equinoctial_a which_o be_v call_v the_o distance_n from_o the_o line_n be_v equal_a ●o_o the_o distance_n that_o be_v between_o the_o pole_n of_o the_o world_n and_o the_o horizon_n which_o be_v call_v the_o height_n of_o the_o pole_n whereby_o it_o be_v manifest_a that_o the_o height_n of_o the_o pole_n be_v so_o much_o as_o our_o distance_n from_o the_o line_n be_v and_o although_o they_o be_v two_o different_a thing_n yet_o the_o one_o be_v take_v for_o the_o other_o
clavius_n his_o gross_a demonstration_n hereof_o 90_o a_o more_o exact_a demonst_a with_o the_o practice_n thereof_o 92_o the_o angle_n of_o dip_v for_o any_o height_n of_o the_o eye_n 96_o 3_o error_n by_o the_o parallax_n of_o the_o sun_n correct_v 96_o 4_o error_n in_o observe_v by_o the_o refraction_n of_o the_o sun_n or_o star_n correct_v 97_o chap._n 16·_a fault_n amend_v in_o the_o table_n of_o the_o sun_n declination_n common_o call_v the_o regiment_n of_o the_o sun_n 97_o chap._n 17._o of_o the_o table_n of_o declination_n of_o every_o minute_n of_o the_o ecliptic_a in_o degree_n min._n and_o sec._n make_v according_a to_o the_o great_a obliquity_n of_o the_o zodiac_n this_o present_a age_n which_o by_o exact_a observation_n be_v find_v to_o be_v 23_o degree_n 31_o min._n and_o a_o half_a 98_o a_o table_n of_o the_o declination_n of_o every_o minute_n of_o the_o ecliptic_a in_o degree_n min._n and_o sec._n 101_o chap._n 18._o the_o use_n of_o the_o former_a table_n of_o declination_n 116_o chap._n 19_o the_o description_n and_o use_n of_o a_o great_a quadrant_n for_o observation_n of_o the_o sun_n on_o land_n 120_o a_o table_n of_o observation_n of_o the_o sun_n meridian_n altitude_n take_v by_o the_o foresay_a quadrant_n in_o the_o year_n 1594_o 1595_o 1596_o 1597_o at_o london_n  _fw-fr chap._n 20._o the_o find_n of_o the_o sun_n apogeum_n and_o eccentricity_n out_o of_o the_o former_a observation_n 142_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 ecliptic_a 142_o chap._n 21._o the_o middle_a motion_n of_o the_o sun_n correct_v out_o of_o the_o former_a observation_n 150_o a_o table_n of_o the_o sun_n middle_a motion_n 152_o chap._n 22._o a_o new_a theoric_n of_o the_o sun_n for_o the_o make_n of_o the_o table_n of_o the_o sun_n prosthaphaereses_n 154_o a_o table_n of_o the_o sun_n prosthaphaereses_n 157_o chap._n 23._o the_o make_n of_o the_o ephemerides_n of_o the_o sun_n 159_o chap._n 24._o how_o to_o reduce_v the_o apparent_a time_n to_o the_o equal_a time_n answer_v thereto_o 162_o a_o table_n of_o the_o aequation_n of_o natural_a day_n 162_o chap._n 25._o a_o table_n of_o aequation_n of_o the_o sun_n ephemerides_n to_o make_v they_o serve_v for_o many_o year_n 163_o ephemerides_n of_o the_o sun_n 164_o chap._n 26._o the_o use_n of_o these_o ephemerides_n 169_o chap._n 27._o the_o make_n of_o the_o table_n of_o the_o sun_n declination_n 170_o prosthaphaereses_n of_o the_o sun_n declination_n 172_o a_o table_n of_o the_o sun_n declination_n 173_o chap._n 28·_a the_o use_n of_o the_o former_a table_n of_o declination_n or_o regiment_n of_o the_o sun_n 181_o chap._n 29_o the_o declination_n of_o the_o principal_a fix_a star_n about_o the_o equinoctial_a correct_v by_o observation_n 183_o a_o table_n of_o fix_a star_n about_o the_o equinoctial_a 198_o chap._n 30._o the_o use_n of_o the_o former_a table_n 199_o chap._n 31._o the_o true_a distance_n of_o certain_a principal_a fix_a star_n from_o the_o north_n pole_n find_v by_o late_a observation_n 199_o chap._n 32._o to_o know_v at_o what_o time_n any_o of_o the_o foresay_a fix_a star_n come_v to_o the_o meridian_n for_o any_o day_n of_o the_o year_n 202_o a_o table_n of_o the_o sun_n right_a ascension_n in_o hour_n and_o minute_n for_o every_o day_n of_o the_o year_n 204_o chap._n 33._o by_o the_o former_a table_n of_o fix_a star_n and_o the_o sun_n right_a ascension_n to_o know_v the_o hour_n of_o the_o night_n at_o any_o time_n of_o the_o year_n 206_o chap._n 34._o of_o find_v the_o elevation_n of_o the_o pole_n by_o observation_n of_o the_o pole_n star_n and_o guard_n 207_o chap._n 35._o the_o description_n and_o part_n of_o the_o sea_n quadrant_n 208_o chap._n 36._o the_o description_n of_o the_o nocturnal_a or_o night_n dial_n 210_o chap._n 37._o the_o use_n of_o the_o sea_n quadrant_n first_o in_o observe_v the_o height_n of_o the_o sun_n look_v only_o to_o the_o horizon_n at_o sea_n 211_o chap._n 38._o how_o with_o this_o quadrant_n to_o observe_v the_o height_n of_o the_o sun_n with_o ●our_n back_o turn_v towards_o the_o sun_n 211_o chap._n 39_o how_o to_o observe_v with_o this_o quadrant_n the_o height_n of_o the_o sun_n or_o star_n look_v both_o to_o the_o sun_n or_o star_n and_o to_o the_o horizon_n 212_o chap_n 40._o how_o to_o find_v the_o height_n of_o the_o pole_n by_o observation_n of_o the_o polestar_n and_o guard_n without_o give_v or_o take_v any_o allowance_n or_o abatement_n at_o any_o time_n when_o the_o polestar_n the_o guard_n and_o horizon_n may_v be_v see_v 213_o to_o know_v the_o hour_n of_o the_o night_n by_o the_o nocturnal_a 213_o a_o answer_n to_o simon_n stevin_n show_v his_o erorr_v in_o blame_v i_o of_o error_n in_o my_o table_n of_o rumb_n 214_o the_o content_n of_o the_o treatise_n of_o the_o art_n of_o navigation_n the_o division_n of_o the_o whole_a art_n of_o navigation_n pag._n 1_o chap._n 1._o the_o definition_n of_o the_o sphere_n 2_o 2._o that_o the_o whole_a world_n be_v a_o sphere_n 2_o 3._o of_o the_o division_n of_o the_o sphere_n 2_o 4._o of_o the_o motion_n of_o the_o heaven_n 4_o 5._o of_o the_o figure_n of_o the_o heaven_n 4_o 6._o that_o the_o earth_n and_o water_n make_v one_o perfect_a globe_n 5_o 7._o that_o the_o earth_n be_v in_o the_o centre_n of_o the_o world_n 5_o 8._o the_o whole_a quantity_n of_o the_o earth_n 5_o 9_o of_o the_o equinoctial_a circle_n 6_o 10._o of_o the_o pole_n of_o the_o world_n 6_o 11._o of_o the_o ecliptic_a line_n 7_o 12._o of_o the_o declination_n of_o the_o sun_n 7_o 13._o of_o the_o colour_n 8_o 14._o of_o the_o meridian_n circle_n 8_o 15._o of_o the_o horizon_n 9_o 16._o of_o the_o 32_o wind_n 10_o 17._o of_o the_o two_o tropic_n 12_o 18._o of_o the_o parallel_n 13_o 19_o of_o the_o degree_n 13_o 20._o what_o be_v mean_v by_o longitude_n and_o latitude_n 14_o the_o second_o part_n of_o the_o art_n of_o navigation_n wherein_o be_v handle_v the_o practic_n part_n show_v the_o make_n and_o use_n of_o the_o principal_a instrument_n belong_v to_o this_o art_n chap._n 1._o the_o make_n of_o the_o astrolabe_n pag._n 15_o chap._n 2._o of_o the_o height_n of_o the_o sun_n pag._n 17_o 3._o of_o the_o shadow_n 18_o 4._o of_o the_o regiment_n and_o rule_n of_o the_o sun_n 19_o 5._o of_o the_o declination_n of_o the_o sun_n and_o of_o the_o table_n thereof_o 20_o how_o the_o declination_n of_o the_o sun_n may_v be_v find_v out_o 21_o 6._o the_o equation_n of_o the_o sun_n declination_n 22_o 7._o four_o example_n for_o the_o plain_a declaration_n of_o that_o which_o be_v say_v before_o 22_o 8._o another_o manner_n of_o account_v by_o the_o sun_n as_o they_o use_v in_o portugal_n 25_o 9_o how_o the_o height_n of_o the_o sun_n may_v be_v know_v in_o any_o place_n whatsoever_o without_o a_o astrolabe_n first_o know_v your_o distance_n from_o the_o equinoctial_a 25_o 10._o the_o rule_n or_o regiment_n of_o the_o north-star_n for_o the_o knowledge_n of_o the_o height_n of_o the_o pole_n 26_o 11._o the_o make_n of_o the_o crosse-staffe_n 27_o 12._o of_o the_o position_n of_o the_o north-star_n and_o the_o guard_n 28_o 13._o of_o the_o height_n of_o the_o star_n take_v with_o the_o crosse-staffe_n 30_o 14._o the_o regiment_n or_o rule_n of_o the_o north_n star_n 30_o 15._o other_o thing_n to_o be_v note_v in_o observe_v the_o height_n of_o the_o pole_n 32_o 16._o of_o the_o crosier_n 34_o 17._o of_o the_o sea-compasse_n 34_o 18._o how_o the_o variation_n of_o the_o compass_n may_v be_v find_v 37_o the_o find_v of_o the_o meridian_n line_n 37_o 19_o of_o the_o sea-chart_n 38_o 20._o of_o the_o point_n of_o imagination_n 41_o 21._o of_o the_o traverse_n or_o geometrical_a point_n 42_o 22._o of_o the_o amend_v of_o the_o point_n of_o imagination_n 42_o the_o amend_v of_o the_o point_n of_o imagination_n by_o the_o traverse_n point_n 43_o the_o amendment_n of_o the_o point_n of_o imagination_n by_o north_n south_n east_n west_n 43_o 23._o the_o point_n by_o imagination_n and_o the_o height_n 44_o 24._o what_o it_o be_v to_o increase_v or_o diminish_v in_o height_n 45_o 25._o how_o you_o may_v cast_v a_o traverse_n point_n without_o compass_n 46_o 26._o of_o another_o kind_n of_o cast_v a_o point_n by_o traverse_n 46_o 27._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 47_o chap._n 28._o how_o you_o may_v come_v to_o know_v the_o longitude_n or_o the_o course_n from_o east_n to_o west_n pag_n 48_o 29._o how_o you_o may_v set_v down_o in_o your_o chart_n a_o new_a land_n never_o before_o discover_v 50_o 30._o see_v two_o know_a point_n or_o cape_n of_o land_n as_o you_o sail_v along_o
0_o 0_o 56_o 15_o about_o midway_n betwixt_o lisbon_n and_o saint_n mic●●●ls_v even_o 0_o 0_o 61_o 40_o wnw_n 0_o 0_o 73_o 7_o betwixt_o s._n michael_n &_o tercaera_n e_o by_o n_o ⅕_n n_o 2_o 0_o 70_o 52_o about_o 3._o leag_n from_o tercaera_n ssw_n e_o by_o n_o ¼_n n_o 2_o 30_o 70_o 53_o at_o saint_n cruz_n in_o flores_n  _fw-fr 29_o 25_o 83_o 30_o these_o observation_n make_v in_o the_o town_n of_o fayal_n and_o the_o former_a also_o at_o s._n cruz_n in_o flores_n be_v take_v by_o m._n william_n borowe_n instrument_n of_o variation_n publish_v in_o his_o book_n of_o the_o variation_n of_o the_o compass_n and_o by_o a_o quadrant_n who_o semidiameter_n be_v almost_o three_o foot_n  _fw-fr 18_o 0_o 73_o 0_o  _fw-fr 16_o 36_o 74_o 40_o  _fw-fr 20_o 30_o 62_o 20_o  _fw-fr 20_o 0_o 62_o 54_o  _fw-fr 19_o 20_o 63_o 35_o  _fw-fr 18_o 16_o 64_o 45_o  _fw-fr 30_o 41_o 57_o 15_o  _fw-fr 46_o 13_o 17_o 53_o  _fw-fr 46_o 18_o 16_o 36_o  _fw-fr 40_o 42_o 32_o 45_o or_o 4_o league_n from_o tercaera_n see_fw-la ease_n ¼_n e_o 0_o 0_o 75_o 50_o from_o s._n mary_n w_n by_o saint_n 6_o league_n wsw_n 13_o 0_o 61_o 50_o from_o s._n mary_n w_n by_o saint_n 6_o league_n w_n by_o saint_n ½_o 0_o 0_o 67_o 25_o from_o s._n mary_n south_n 5._o league_n ease_n ½_o s_o 0_o 0_o 69_o 30_o from_o saint_n mary_n 16_o league_n ease_n ¼_n e_o 0_o 0_o 75_o 50_o nw_n by_o w_n northerly_a ease_n 2_o 30_o 73_o 7_o ½_o from_o s._n george_n se_n by_o e_z 3_o leag_fw-mi ease_n ¼_n e_o 0_o 0_o 75_o 50_o from_o the_o east_n part_n of_o s._n michael_n wsw_n ¼_n s_o 0_o 0_o 59_o 0_o ne_fw-fr by_o n_o about_z 15_o or_o 20_o leag_n ease_n ¼_n e_o 0_o 0_o 70_o 23_o from_o the_o rock_n w_n about_o 66_o leag_n see_fw-la by_o saint_n ⅙_n s_o 26_o  _fw-fr 37_o 30_o from_o c._n finisterre_n n_o easterly_a ease_n ½_o s_o 0_o  _fw-fr 67_o 30_o ease_n ⅔_n s_o 2_o  _fw-fr 65_o 37_o sweet_z 11_o  _fw-fr 39_o 22_o the_o time_n of_o observation_n the_o latitude_n of_o the_o place_n of_o observation_n the_o declination_n of_o the_o sun_n the_o true_a azimuth_n of_o the_o sun_n the_o variation_n of_o the_o compass_n the_o middle_a variation_n the_o part_n of_o variation_n  _fw-fr  _fw-fr de._n mi_fw-mi de._n mi_fw-mi de._n mi_fw-mi de._n mi_fw-mi de._n min._n  _fw-fr jul._n 9_o a_fw-la 39_o 50_o 20_o 53_o 62_o 0_o 7_o 30_o  _fw-fr  _fw-fr eastward_o 12_o bn_n 39_o 0_o 20_o 25_o 63_o 20_o 6_o 45_o  _fw-fr  _fw-fr eastward_o 23_o bn_n 38_o 0_o 17_o 55_o 67_o 0_o 5_o 20_o 5_o 38_o eastward_o 23_o a_o 38_o 0_o 17_o 46_o 67_o 10_o 5_o 57_o eastward_o aug_n 8_o b_o n_o 38_o 20_o 13_o 13_o 74_o 10_o 3_o 18_o  _fw-fr  _fw-fr eastward_o 9_o bn_n 38_o 20_o 12_o 54_o 75_o 0_o 4_o 7_o  _fw-fr  _fw-fr eastward_o 14_o a_o 39_o 50_o 11_o 5_o 79_o 30_o 4_o 0_o  _fw-fr  _fw-fr westward_a se._n 13_o a_fw-la 38_o 54_o 0_o 8_o 74_o 35_o 1_o 35_o 3_o 5_o eastward_o 13_o a_o 38_o 54_o 0_o 9_o 76_o 0_o 1_o 20_o eastward_o 22_o a_o 38_o 54_o 3_o 39_o 67_o 10_o 4_o 50_o eastward_o 22_o a_o 38_o 54_o 3_o 39_o 67_o 30_o 4_o 36_o eastward_o 22_o a_o 38_o 54_o 3_o 30_o 68_o 15_o 4_o 40_o eastward_o 22_o a_o 38_o 54_o 3_o 40_o 69_o 20_o 4_o 35_o eastward_o 23_o bn_n 38_o 54_o 3_o 53_o 54_o 20_o 2_o 55_o eastward_o 23_o bn_n 38_o 54_o 3_o 54_o 14_o 0_o 3_o 53_o eastward_o 23_o bn_n 38_o 54_o 3_o 54_o 13_o 30_o 3_o 6_o eastward_o 23_o a_o 38_o 54_o 4_o 0_o 35_o 15_o 2_o 30_o eastward_o oc._n 18_o bn_n 38_o 20_o 13_o 5_o 73_o 0_o 2_o 5_o  _fw-fr  _fw-fr eastward_o 23_o a_o 37_o 0_o 14_o 50_o 60_o 0_o 1_o 50_o 0_o 55_o westward_n 23_o a_fw-la 37_o 0_o 14_o 51_o 71_o 5_o 3_o 40_o eastward_o 24_o bn_n 37_o 0_o 15_o 2_o 70_o 50_o 3_o 20_o westward_n 26_o bn_n 37_o 30_o 15_o 38_o 69_o 50_o 6_o 0_o 5_o 34_o eastward_o 26_o bn_n 37_o 30_o 15_o 39_o 68_o 0_o 5_o 7_o eastward_o 28_o bn_n 38_o 40_o 16_o 16_o 68_o 45_o 7_o 5_o  _fw-fr  _fw-fr eastward_o no._n 1_o a_fw-la 38_o 40_o 17_o 30_o 67_o 10_o 8_o 10_o  _fw-fr  _fw-fr eastward_o 2_o bn_n 38_o 40_o 17_o 41_o 66_o 50_o 3_o 33_o  _fw-fr  _fw-fr eastward_o 6_o bn_n 38_o 35_o 18_o 43_o 31_o 0_o 6_o 30_o  _fw-fr  _fw-fr eastward_o 12_o bn_n 44_o 25_o 20_o 5_o 61_o 0_o 6_o 30_o 7_o 4_o eastward_o 12_o bn_n 44_o 25_o 20_o 5_o 58_o 0_o 7_o 37_o eastward_o 12_o a_o 44_o 30_o 20_o 11_o 46_o 15_o 6_o 52_o eastward_o notwithstanding_o there_o be_v much_o difference_n betwixt_o some_o of_o these_o variation_n take_v at_o the_o same_o place_n with_o the_o same_o instrument_n yet_o we_o use_v with_o what_o diligence_n we_o can_v such_o instrument_n as_o then_o we_o have_v prepare_v for_o that_o purpose_n which_o i_o speak_v that_o other_o that_o shall_v go_v about_o hereafter_o to_o observe_v the_o variation_n at_o sea_n especial_o may_v be_v the_o more_o circumspect_a to_o foresee_v and_o prevent_v all_o cause_n of_o error_n herein_o exact_a truth_n among_o the_o unconstant_a wave_n of_o the_o sea_n be_v not_o to_o be_v look_v for_o though_o good_a instrument_n be_v never_o so_o well_o apply_v to_o their_o use_n yet_o with_o heedful_a diligence_n we_o may_v come_v so_o near_o the_o truth_n as_o the_o nature_n of_o the_o sea_n and_o of_o our_o sight_n and_o instrument_n will_v give_v we_o leave_v neither_o if_o there_o be_v some_o disagreement_n betwixt_o observation_n be_v they_o all_o by_o and_o by_o to_o be_v reject_v but_o as_o when_o many_o arrow_n be_v shoot_v at_o a_o mark_n and_o the_o mark_n afterward_o take_v away_o he_o may_v be_v think_v to_o work_v according_a to_o reason_n who_o to_o find_v the_o place_n where_o the_o mark_n stand_v shall_v seek_v out_o the_o middle_a place_n among_o all_o the_o arrow_n so_o among_o many_o different_a observation_n the_o middlemost_a be_v like_a to_o come_v near_o the_o truth_n cause_n of_o error_n herein_o some_o can_v be_v avoid_v as_o the_o unsteadinesse_n of_o the_o ship_n the_o imperfection_n of_o the_o sense_n and_o instrument_n the_o weak_a respective_a force_n of_o the_o needle_n or_o wire_n be_v they_o never_o so_o well_o touch_v other_o may_v be_v eschew_v as_o that_o there_o be_v no_o iron_n near_o the_o compass_n in_o the_o time_n of_o observation_n that_o the_o wire_n be_v keep_v clean_o from_o rust_n and_o that_o they_o be_v not_o keep_v too_o long_o untouched_a from_o the_o stone_n that_o such_o instrument_n be_v use_v for_o observation_n as_o need_v least_o work_n afterward_o for_o find_v out_o the_o variation_n wherein_o the_o instrument_n heretofore_o publish_v for_o this_o purpose_n be_v faulty_a be_v such_o as_o serve_v for_o observation_n only_a o●_n land_n as_o also_o require_v many_o work_n afterward_o unfit_a for_o mariner_n before_o the_o matter_n can_v come_v to_o issue_n wherein_o be_v as_o many_o lurk_a hole_n of_o error_n without_o great_a diligence_n i_o have_v therefore_o here_o set_v down_o the_o make_n and_o use_n of_o a_o certain_a instrument_n whereby_o the_o variation_n of_o the_o compass_n and_o time_n of_o the_o day_n be_v present_o give_v together_o with_o the_o observation_n the_o latitude_n of_o the_o place_n be_v know_v and_o that_o universal_o throughout_o the_o world_n both_o at_o sea_n and_o land_n as_o also_o the_o variation_n be_v give_v the_o height_n of_o the_o pole_n and_o hour_n of_o the_o day_n may_v thereby_o be_v know_v without_o those_o inconvenience_n wherewith_o martin_n curtis_n his_o instrument_n chap._n 11._o part_n 3._o of_o the_o art_n of_o navigation_n and_o michael_n coignet_n his_o nautical_a hemisphere_n be_v much_o encumber_v to_o omit_v the_o observation_n of_o the_o height_n of_o the_o sun_n which_o as_o i_o have_v oft_o make_v trial_n at_o sea_n may_v thereby_o be_v more_o exact_o perform_v then_o have_v be_v hitherto_o by_o staff_n ring_n or_o astrolabe_n as_o they_o be_v common_o use_v the_o make_n of_o the_o searing_n the_o figure_n of_o the_o searings_a upon_o the_o concave_a side_n of_o the_o innermost_a ring_n let_v be_v describe_v the_o degree_n of_o the_o sun_n declination_n for_o the_o right_n place_v of_o the_o little_a bead_n upon_o the_o thread_n according_a to_o the_o time_n of_o the_o year_n which_o may_v easy_a be_v do_v after_o this_o manner_n the_o bead_n be_v thus_o right_o place_v put_v aside_o the_o equinoctial_a ring_n from_o the_o brass_n pointer_n represent_v the_o pole_n actick_a that_o it_o may_v cross_v the_o meridian_n at_o right_a angle_n which_o it_o shall_v precise_o do_v if_o you_o bring_v the_o prick_n or_o little_a hole_n upon_o the_o outside_n of_o the_o
excuse_v for_o find_v a_o fault_n herein_o and_o not_o amend_v it_o at_o this_o time_n and_o that_o so_o much_o the_o rather_o because_o that_o according_a to_o promise_v make_v in_o the_o first_o edition_n of_o this_o book_n i_o will_v now_o show_v the_o mean_n how_o by_o observation_n of_o the_o polestar_n and_o guard_n to_o find_v present_o the_o height_n of_o the_o pole_n not_o only_a when_o the_o fore-guard_n be_v in_o some_o one_o of_o those_o eight_o principal_a position_n beforementioned_a as_o the_o manner_n have_v be_v hitherto_o but_o in_o any_o other_o position_n also_o and_o at_o any_o time_n of_o the_o night_n when_o the_o polestar_n and_o guard_n may_v be_v see_v and_o that_o without_o any_o allowance_n or_o abatement_n give_v or_o take_v by_o addition_n or_o subtraction_n of_o any_o equation_n in_o regard_n of_o the_o pole-star_n be_v high_o or_o low_a than_o the_o pole_n all_o which_o beside_o divers_a other_o pleasant_a and_o profitable_a conclusion_n may_v easy_o be_v perform_v by_o mean_n of_o a_o instrument_n by_o i_o divise_v which_o may_v not_o unfit_o be_v call_v the_o sea-quadrant_n the_o description_n and_o use_n whereof_o here_o follow_v the_o figure_n of_o the_o sea-quadrant_a chap._n xxxv_o the_o description_n and_o part_n of_o the_o sea-quadrant_n this_o quadrant_n consist_v of_o many_o part_n whereof_o some_o may_v be_v call_v principal_a and_o some_o less_o principal_a the_o principal_a part_n of_o this_o quadrant_n be_v the_o semidiameter_n thereof_o and_o the_o archippus_n the_o semidiameter_n i_o call_v the_o straight_a square_a ruler_n the_o arch_n i_o call_v that_o part_n of_o the_o quadrant_n that_o be_v make_v crooked_a like_o a_o bow_n the_o less_o principal_a part_n be_v the_o double_a box_n or_o ●ocket_n and_o the_o sight_n or_o vane_n the_o double_a box_n or_o socket_n have_v two_o square_a hole_n make_v crosse-wise_a through_o it_o in_o such_o sort_n that_o the_o arch_n and_o semidiameter_n of_o the_o quadrant_n may_v be_v fit_o put_v through_o they_o the_o flat_a side_n of_o the_o one_o pass_v close_o by_o the_o flat_a side_n of_o the_o other_o by_o mean_n of_o this_o double_a cross_a socket_n the_o arch_n and_o semidiameter_n of_o the_o quadrant_n be_v so_o to_o be_v join_v together_o that_o the_o two_o angle_n make_v by_o the_o hollow_a side_n of_o the_o arch_n with_o the_o semidiameter_n may_v be_v equal_a each_o to_o other_o the_o sight_n or_o vane_n be_v either_o fix_v or_o movable_a there_o be_v two_o fix_a sight_n the_o one_o great_a the_o other_o lesser_a the_o great_a fix_v sight_n be_v fasten_v upon_o the_o double_a socket_n and_o have_v a_o narrow_a slit_n cut_v through_o the_o midst_n thereof_o the_o lesser_a fix_v sight_n be_v fasten_v to_o the_o end_n of_o the_o arch_n of_o the_o quadrant_n and_o have_v a_o small_a sight-hole_n bore_v through_o it_o even_o with_o the_o end_n of_o the_o archippus_n the_o movable_a sight_n be_v three_o in_o number_n whereof_o two_o be_v to_o be_v move_v up_o and_o down_o upon_o the_o arch_n of_o the_o quadrant_n as_o need_n shall_v require_v for_o observation_n the_o three_o be_v to_o be_v put_v on_o or_o take_v off_o that_o end_n of_o the_o semidiameter_n of_o the_o quadrant_n where_o the_o centre_n be_v which_o centre_n be_v show_v by_o the_o little_a round_a hole_n bore_v overthwart_o through_o the_o midst_n of_o the_o thickness_n of_o the_o square_a ruler_n near_o the_o end_n thereof_o which_o ruler_n we_o call_v the_o semidiameter_n of_o the_o quadrant_n this_o sight_n whensoever_o it_o be_v to_o be_v use_v must_v so_o be_v put_v on_o upon_o the_o end_n of_o that_o ruler_n that_o the_o flat_a side_n thereof_o which_o must_v be_v set_v towards_o the_o arch_n of_o the_o quadrant_n may_v divide_v the_o foresay_a round_a hole_n even_o by_o the_o midst_n thereof_o the_o sharp_a edge_n of_o that_o sight_n arise_v perpendicular_o from_o the_o very_a midst_n or_o centre_n of_o that_o hole_n which_o be_v also_o the_o centre_n of_o the_o quadrant_n when_o the_o other_o end_n of_o the_o square_a ruler_n or_o semidiameter_n thereof_o be_v put_v into_o his_o socket_n be_v thrust_v so_o far_o forward_o that_o the_o end_n thereof_o come_v to_o be_v even_o with_o the_o fore-end_n of_o the_o socket_n two_o side_n of_o the_o arch_n of_o the_o quadrant_n that_o be_v to_o say_v one_o of_o the_o straight_a or_o plain_a side_n and_o the_o hollow_a side_n thereof_o be_v divide_v into_o 90_o degree_n and_o every_o degree_n into_o 6_o part_n each_o part_n contain_v 10_o min._n and_o upon_o the_o straight_a side_n of_o the_o quadrant_n there_o be_v figure_n set_v to_o every_o five_o degree_n and_o that_o in_o two_o rank_n or_o limb_n the_o one_o beginning_n from_o that_o end_n of_o the_o arch_n where_o the_o small_a fix_a sight_n be_v place_v the_o other_o beginning_n and_o proceed_v from_o the_o other_o end_n of_o the_o arch_n where_o the_o nocturnal_a be_v to_o be_v fasten_v or_o put_v on_o that_o so_o the_o number_n of_o the_o degree_n and_o minute_n may_v the_o easy_o be_v reckon_v from_o either_o end_n of_o the_o arch_n as_o need_n shall_v require_v chap._n xxxvi_o of_o the_o nocturnal_a or_o night-dial_n the_o nocturnal_a contain_v three_o circle_n that_o be_v the_o hour_n circle_n the_o day_n circle_n and_o the_o polestar_n circle_n the_o big_a of_o these_o circle_n which_o be_v to_o be_v fasten_v to_o the_o end_n of_o the_o arch_n of_o the_o quadrant_n i_o call_v the_o hour-circle_n and_o it_o be_v divide_v into_o 24_o hour_n and_o half_a hour_n with_o figure_n set_v to_o every_o hour_n for_o the_o easy_a reckon_n of_o they_o next_o within_o this_o be_v the_o day-circle_n or_o circle_n of_o day_n because_o it_o contain_v the_o day_n of_o all_o the_o month_n of_o the_o year_n which_o day_n be_v signify_v by_o the_o small_a division_n round_o about_o at_o the_o circumference_n of_o this_o circle_n every_o five_o day_n have_v his_o stroke_n draw_v a_o little_a long_o than_o the_o rest_n that_o so_o any_o day_n you_o desire_v may_v the_o easy_o be_v find_v the_o small_a division_n contain_v but_o one_o day_n apiece_o the_o line_n show_v the_o beginning_n and_o end_n of_o the_o month_n be_v draw_v overthwart_o the_o whole_a breadth_n of_o this_o circle_n the_o beginning_n of_o january_n be_v know_v by_o the_o two_o line_n draw_v near_o together_o overthwart_a this_o circle_n whereof_o one_o show_v the_o end_n of_o the_o month_n of_o december_n and_o the_o other_o show_v the_o beginning_n of_o the_o month_n of_o january_n which_o be_v mark_v with_o two_o prick_n february_n be_v easy_o know_v in_o this_o circle_n because_o it_o have_v but_o only_o 28_o day_n march_n be_v by_o the_o little_a polestar_n circle_n and_o so_o all_o the_o rest_n of_o the_o month_n may_v easy_o be_v know_v by_o their_o order_n upon_o the_o centre_n of_o this_o arch_n which_o represent_v the_o pole_n of_o the_o world_n there_o be_v two_o indices_fw-la fasten_v the_o long_a of_o they_o may_v be_v call_v the_o guard-index_n whereto_o a_o short_a pin_n be_v fasten_v underneath_o which_o serve_v to_o set_v this_o index_n right_a upon_o the_o place_n of_o the_o middle_a guard_n in_o the_o day-circle_n by_o put_v it_o into_o the_o small_a hole_n that_o there_o be_v make_v in_o that_o circle_n the_o short_a index_n reach_v from_o the_o centre_n of_o the_o day-circle_n unto_o the_o limb_n or_o circumference_n thereof_o that_o be_v divide_v into_o day_n may_v be_v call_v the_o day-index_n this_o small_a circle_n place_v between_o the_o centre_n of_o the_o day-circle_n and_o the_o month_n of_o march_n may_v not_o unfit_o be_v call_v the_o polestar_n circle_n because_o the_o distance_n of_o the_o centre_n thereof_o from_o the_o centre_n of_o the_o day-circle_n be_v answerable_a to_o the_o distance_n of_o the_o polestar_n from_o the_o pole_n which_o at_o this_o time_n i_o have_v often_o find_v by_o exact_a observation_n not_o to_o be_v more_o than_o 2_o degree_n and_o 48_o minute_n chap._n xxxvii_o the_o use_n of_o the_o sea-quadrant_n and_o that_o first_o in_o observe_v the_o height_n of_o the_o sun_n look_v only_o by_o the_o sight_n at_o the_o centre_n to_o the_o horizon_n at_o sea_n turn_v the_o centre_n of_o the_o quadrant_n towards_o the_o sun_n so_o as_o the_o shadow_n of_o the_o vane_n or_o sight_n place_v at_o the_o centre_n may_v fall_v upon_o the_o hollow_a side_n of_o the_o arch_n of_o the_o quadrant_n then_o look_v through_o the_o little_a sight_n fasten_v in_o the_o end_n of_o the_o arch_n of_o the_o quadrant_n lay_v the_o upper_a edge_n of_o the_o sight_n place_v at_o the_o centre_n even_o with_o the_o horizon_n and_o at_o the_o same_o instant_n let_v one_o that_o stand_v by_o mark_v deligent_o upon_o what_o degree_n and_o minute_n of_o the_o quadrant_n the_o edge_n of_o the_o shadow_n
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
the_o very_a degree_n of_o the_o compass_n upon_o which_o the_o sun_n rise_v or_o set_v then_o the_o horizon_n be_v set_v fast_o as_o we_o have_v show_v in_o the_o former_a chapter_n mark_v in_o the_o instrument_n by_o which_o part_n or_o degree_n of_o those_o upon_o the_o horizon_n the_o parallel_n of_o the_o sun_n declination_n that_o day_n do_v cross_v the_o same_o count_v in_o the_o number_n of_o the_o horizon_n from_o the_o centre_n towards_o the_o north_n pole_n if_o it_o be_v from_o the_o 11_o of_o march_n to_o the_o 13_o of_o september_n or_o towards_o the_o south_n pole_n the_o other_o half_o of_o the_o year_n and_o mark_v also_o whether_o this_o cross_n be_v so_o many_o deg_n distant_a from_o the_o division_n of_o the_o equinoctial_a of_o your_o instrument_n as_o the_o sun_n in_o his_o rise_n be_v distant_a from_o the_o east_n of_o the_o compass_n or_o at_o his_o go_v down_o be_v distant_a from_o the_o west_n thereof_o for_o than_o you_o may_v say_v that_o the_o compass_n have_v no_o variation_n at_o all_o but_o if_o it_o be_v not_o so_o mark_v the_o rule_n follow_v 1_o when_o the_o sun_n rise_v by_o the_o same_o rumb_n of_o the_o compass_n which_o the_o instrument_n do_v show_v the_o compass_n have_v no_o variation_n at_o all_o 2_o when_o the_o sun_n rise_v more_o to_o the_o north_n of_o the_o compass_n or_o go_v down_o more_o to_o the_o south_n then_o be_v show_v by_o the_o instrument_n all_o the_o difference_n between_o the_o instrument_n and_o the_o compass_n be_v the_o north-easting_a or_o variation_n thereof_o to_o the_o eastward_o 3_o if_o the_o sun_n rise_v more_o to_o the_o south_n of_o the_o compass_n or_o seat_v more_o to_o the_o north_n than_o the_o instrument_n show_v all_o the_o difference_n between_o the_o instrument_n and_o the_o compass_n be_v the_o north-westing_a or_o westerly_a variation_n thereof_o chap._n xxxviii_o at_o what_o hour_n the_o sun_n rise_v and_o set_v every_o day_n in_o all_o part_n of_o the_o world_n the_o height_n of_o the_o pole_n in_o that_o part_n where_o you_o desire_v to_o know_v this_o be_v know_v place_v the_o horizon_n in_o such_o sort_n as_o be_v show_v in_o the_o 36_o chapter_n and_o find_v by_o the_o table_n of_o the_o sun_n declination_n the_o declination_n which_o the_o sun_n have_v that_o day_n count_v the_o same_o from_o the_o equinoctial_a of_o the_o instrument_n towards_o that_o part_n whither_o the_o sun_n decline_v among_o the_o parallel_n and_o then_o mark_v the_o parallel_n whereat_o your_o account_n end_v in_o what_o hour_n and_o in_o what_o part_n of_o the_o hour_n it_o cut_v the_o horizon_n note_v that_o every_o hour_n have_v two_o number_n one_o afternoon_n which_o be_v the_o hour_n of_o the_o sun_n set_v and_o another_o before_o noon_n which_o be_v that_o wherein_o the_o sun_n rise_v chap._n thirty-nine_o of_o the_o length_n of_o the_o day_n and_o of_o the_o night_n the_o hour_n of_o the_o sun_n go_v down_o be_v know_v double_v it_o and_o the_o double_a number_n of_o hour_n will_v show_v you_o the_o length_n of_o the_o day_n also_o the_o hour_n of_o the_o sun_n rise_v be_v know_v and_o double_v will_v manifest_v unto_o you_o the_o length_n of_o the_o night_n in_o that_o part_n of_o the_o year_n when_o you_o desire_v to_o know_v the_o same_o chap._n xl._o of_o a_o night-diall_n by_o the_o north._n that_o be_v know_v which_o be_v before_o declare_v of_o the_o situation_n of_o the_o north_n star_n and_o of_o the_o guard_n we_o may_v easy_o know_v in_o the_o night_n what_o a_o clock_n it_o be_v wheresoever_o we_o can_v see_v the_o north_n star_n presuppose_v that_o upon_o the_o 15_o of_o april_n at_o the_o very_a point_n of_o midnight_n the_o former_a guard_n go_v a-head_n in_o respect_n of_o the_o north_n star_n and_o because_o by_o this_o account_n of_o the_o hour_n of_o the_o night_n we_o must_v take_v for_o a_o beginning_n the_o very_a instant_n when_o the_o former_a guard_n make_v midnight_n the_o rule_n follow_v be_v to_o be_v observe_v the_o rule_n the_o number_n of_o the_o whole_a month_n which_o have_v pass_v since_o the_o 15_o of_o april_n forward_o be_v double_a you_o have_v the_o number_n of_o the_o hour_n wherein_o the_o former_a guard_n make_v midnight_n be_v head-most_a and_o if_o the_o month_n fall_v not_o out_o just_a add_v for_o every_o fifteen_o day_n above_o the_o whole_a month_n one_o day_n and_o for_o every_o day_n four_o minute_n and_o you_o shall_v know_v when_o it_o be_v midnight_n as_o for_o example_n if_o i_o will_v know_v upon_o the_o 15_o of_o november_n where_o the_o former_a guard_n make_v midnight_n i_o account_v the_o whole_a month_n from_o the_o 15_o of_o april_n and_o i_o find_v they_o to_o be_v seven_o which_o be_v double_v make_v fourteen_o i_o say_v therefore_o that_o upon_o the_o 15_o of_o november_n it_o shall_v be_v midnight_n when_o the_o former_a guard_n have_v pass_v before_o the_o north_n or_o head_n fourteen_o hour_n and_o so_o allow_v three_o to_o the_o northwest_n three_o to_o the_o west_n and_o six_o to_o the_o foot_n it_o may_v be_v say_v that_o the_o former_a guard_n go_v two_o hour_n before_o the_o foot_n towards_o the_o south-west_n that_o it_o be_v midnight_n which_o shall_v come_v to_o pass_v when_o the_o former_a guard_n go_v a_o hour_n before_o from_o the_o south-west_n this_o be_v thus_o presuppose_v when_o i_o will_v know_v in_o the_o night_n what_o a_o clock_n it_o be_v i_o must_v note_v two_o thing_n the_o one_o be_v in_o what_o part_n the_o former_a guard_n make_v midnight_n the_o same_o night_n the_o second_o be_v in_o what_o part_n the_o say_a guard_n be_v at_o the_o same_o instant_n when_o i_o will_v know_v the_o time_n of_o the_o night_n which_o be_v understand_v i_o will_v make_v my_o account_n from_o that_o which_o the_o guard_n want_v of_o be_v come_v to_o the_o place_n where_o that_o day_n it_o make_v midnight_n or_o from_o so_o much_o as_o it_o have_v pass_v the_o same_o place_n make_v my_o account_n that_o one_o three_o part_n of_o four_o point_n of_o the_o compass_n be_v a_o hour_n and_o that_o which_o it_o want_v of_o be_v come_v or_o which_o it_o have_v pass_v forward_o be_v the_o hour_n before_o midnight_n if_o it_o be_v not_o come_v to_o the_o place_n or_o after_o midnight_n if_o it_o have_v go_v beyond_o as_o for_o example_n i_o see_v the_o former_a guard_n in_o the_o northwest_o upon_o the_o 15_o of_o july_n because_o that_o upon_o the_o 15_o of_o july_n by_o the_o account_n before_o mention_v the_o former_a guard_n make_v midnight_n in_o the_o west_n and_o from_o the_o north_n or_o head_n to_o the_o west_n be_v six_o hour_n and_o from_o the_o northwest_o where_o i_o see_v the_o guard_n to_o the_o west_n where_o it_o make_v midnight_n be_v three_o hour_n i_o say_v therefore_o that_o it_o be_v three_o hour_n before_o midnight_n that_o be_v to_o say_v nine_o of_o the_o clock_n at_o night_n finis_fw-la because_o the_o table_n of_o the_o sun_n declination_n that_o have_v be_v most_o in_o use_n among_o english_a seaman_n do_v both_o in_o fashion_n and_o manner_n of_o use_v something_o differ_v from_o those_o before_o set_v down_o pag._n 173_o 174_o etc._n etc._n lest_o any_o therefore_o of_o the_o meanner_n sort_n may_v be_v mistake_v or_o shall_v not_o right_o conceive_v the_o manner_n of_o use_v these_o table_n i_o think_v good_a to_o adjoyn_v these_o also_o here_o follow_v bear_v in_o a_o manner_n the_o same_o form_n and_o shape_n and_o therefore_o also_o to_o be_v use_v altogether_o almost_o in_o the_o same_o sort_n that_o those_o table_n have_v be_v which_o for_o these_o many_o year_n have_v be_v most_o use_v by_o english_a mariner_n this_o table_n of_o the_o sun_n declination_n contain_v twelve_o particular_a table_n show_v the_o declination_n of_o the_o sun_n for_o every_o day_n of_o the_o twelve_o month_n of_o the_o year_n for_o four_o year_n together_o from_o leap_z year_n to_o leap_v year_n in_o the_o head_n of_o every_o one_o of_o these_o table_n be_v first_o set_v down_o the_o month_n for_o which_o that_o table_n be_v make_v under_o this_o be_v place_v the_o year_n of_o our_o lord_n for_o which_o those_o table_n may_v serve_v which_o year_n be_v divide_v into_o four_o rank_n signify_v by_o the_o four_o arithmetical_a character_n 1_o 2_o 3_o 4_o that_o be_v set_v over_o they_o the_o first_o rank_n contain_v the_o first_o year_n immediate_o follow_v after_o the_o leap_n year_n the_o next_o rank_n contain_v the_o second_o year_n after_o the_o leap_n year_n in_o the_o three_o rank_n be_v set_v down_o the_o year_n that_o follow_v three_o year_n after_o the_o leap_n year_n and_o in_o the_o four_o and_o last_o rank_n be_v the_o four_o year_n after_o the_o precedent_n leap_v
two_o guard_n be_v in_o the_o same_o azimuth_n or_o the_o one_o direct_o over_o the_o other_o betwixt_o the_o low_a and_o the_o east_n height_n of_o the_o pole_n star_n height_n of_o the_o pole_n height_n of_o th●_n pole_n star_n height_n of_o ●he_n pole_n height_n of_o the_o pole_n star_n height_n of_o the_o pole_n deg._n degr_n mi._n sec._n deg._n degr_n mi._n sec._n deg._n degr_n mi._n sec._n 1_o 0_o 40_o 50_o 28_o 27_o 58_o 43_o 55_o 55_o 30_o 47_o 2_o 1_o 41_o 27_o 29_o 28_o 59_o 31_o 56_o 56_o 32_o 47_o 3_o 2_o 42_o 3_o 30_o 30_o 0_o 19_o 57_o 57_o 34_o 54_o 4_o 3_o 42_o 39_o 31_o 31_o 1_o 9_o 58_o 58_o 37_o 9_o 5_o 4_o 43_o 16_o 32_o 32_o 1_o 59_o 59_o 59_o 39_o 32_o 6_o 5_o 43_o 52_o 33_o 33_o 2_o 51_o 60_o 60_o 42_o 4_o 7_o 6_o 44_o 29_o 34_o 34_o 3_o 44_o 61_o 61_o 44_o 46_o 8_o 7_o 45_o 6_o 35_o 35_o 4_o 39_o 62_o 62_o 47_o 41_o 9_o 8_o 45_o 43_o 36_o 36_o 5_o 34_o 63_o 63_o 50_o 48_o 10_o 9_o 46_o 20_o 37_o 37_o 6_o 32_o 64_o 64_o 54_o 11_o 11_o 10_o 46_o 58_o 38_o 38_o 7_o 30_o 65_o 65_o 57_o 51_o 12_o 11_o 47_o 36_o 39_o 39_o 8_o 31_o 66_o 67_o 1_o 49_o 13_o 12_o 48_o 14_o 40_o 40_o 9_o 33_o 67_o 68_o 6_o 11_o 14_o 13_o 48_o 52_o 41_o 41_o 10_o 38_o 68_o 69_o 10_o 59_o 15_o 14_o 49_o 31_o 42_o 42_o 11_o 44_o 69_o 70_o 16_o 16_o 16_o 15_o 50_o 10_o 43_o 43_o 12_o 53_o 70_o 71_o 22_o 11_o 17_o 16_o 50_o 50_o 44_o 44_o 14_o 4_o 71_o 72_o 28_o 54_o 18_o 17_o 51_o 30_o 45_o 45_o 15_o 17_o 72_o 73_o 36_o 34_o 19_o 18_o 52_o 10_o 46_o 46_o 16_o 33_o 73_o 74_o 45_o 18_o 20_o 19_o 52_o 52_o 47_o 47_o 17_o 53_o 74_o 75_o 55_o 14_o 21_o 20_o 53_o 33_o 48_o 48_o 19_o 15_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 22_o 21_o 54_o 15_o 49_o 49_o 20_o 41_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 23_o 22_o 54_o 58_o 50_o 50_o 22_o 11_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 24_o 23_o 55_o 42_o 51_o 51_o 23_o 45_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 25_o 24_o 56_o 26_o 52_o 52_o 25_o 23_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 26_o 25_o 57_o 11_o 53_o 53_o 27_o 5_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 27_o 26_o 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