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
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
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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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
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 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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 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