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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 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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
innermost_a circle_n to_o the_o end_n of_o the_o foresay_a brass_n pointer_n so_o as_o the_o end_n thereof_o may_v enter_v thereinto_o then_o set_v the_o line_n that_o be_v draw_v from_o the_o end_n of_o the_o brass_n pointer_n to_o the_o elevation_n of_o the_o pole_n at_o the_o place_n of_o your_o observation_n and_o so_o have_v you_o all_o part_n of_o your_o instrument_n right_o place_v for_o observation_n now_o when_o you_o will_v make_v observation_n with_o this_o instrument_n instrument_n hang_v the_o same_o by_o this_o ring_n upon_o your_o finger_n as_o you_o do_v when_o you_o observe_v the_o height_n of_o the_o sun_n with_o the_o astrolabe_n turn_v the_o foresay_a brass_n pointer_n northwards_o till_o you_o find_v the_o midst_n of_o the_o shadow_n of_o the_o bead_n to_o fall_v upon_o the_o peripherie_n draw_v round_o about_o through_o the_o midst_n of_o the_o concavitie_n of_o the_o equinoctial_a ring_n which_o peripherie_n we_o call_v the_o parallel_n of_o the_o sun_n and_o so_o keep_v the_o whole_a instrument_n and_o compass_n as_o steady_a as_o you_o can_v till_o the_o fly_n of_o the_o compass_n remain_v quiet_a and_o still_o keep_v in_o the_o mean_a time_n the_o midst_n of_o the_o shadow_n of_o the_o bead_n always_o upon_o the_o foresay_a parallel_n of_o the_o sun_n and_o withal_o look_v close_o by_o the_o graduated_a side_n of_o the_o meridian_n direct_o down_o upon_o the_o midst_n of_o the_o compass_n and_o mark_v what_o degree_n and_o minute_n you_o see_v close_o thereby_o in_o the_o north_n part_n of_o the_o fly_n for_o so_o much_o as_o the_o north_n point_n of_o the_o needle_n or_o wire_n be_v from_o thence_o towards_o the_o east_n or_o west_n so_o much_o be_v the_o variation_n eastward_n or_o westward_n and_o the_o shadow_n of_o the_o bead_n light_v upon_o the_o parallel_n of_o the_o sun_n show_v the_o hour_n and_o time_n of_o the_o day_n the_o best_a time_n for_o the_o take_n of_o these_o observation_n be_v about_o the_o midst_n of_o the_o forenoon_n or_o afternoon_n because_o that_o about_o those_o time_n the_o height_n of_o the_o sun_n alter_v quick_o and_o his_o refraction_n also_o can_v breed_v no_o sensible_a error_n but_o because_o there_o be_v many_o that_o want_v both_o this_o instrument_n and_o also_o the_o globe_n and_o astrolabe_n beforementioned_a i_o have_v for_o their_o sake_n think_v it_o good_a to_o set_v down_o a_o way_n whereby_o the_o declination_n and_o height_n of_o the_o sun_n be_v give_v together_o with_o the_o latitude_n of_o the_o place_n the_o sun_n true_a azimuth_n may_v be_v find_v with_o ruler_n and_o compass_n only_o after_o this_o manner_n draw_v the_o circle_n abcdefgh_o represent_v the_o meridian_n by_o the_o centre_n hereof_o draw_v the_o diameter_n of_o the_o horizon_n af._n from_o a_o the_o end_n of_o this_o diameter_n reckon_v the_o elevation_n of_o the_o equinoctial_a ac_fw-la from_o whence_o draw_v a_o line_n by_o the_o centre_n which_o may_v be_v call_v the_o diameter_n of_o the_o equinoctial_a ac_fw-la from_o c_o the_o end_n of_o this_o diameter_n count_v the_o declination_n of_o the_o sun_n cd_o thereby_o draw_v a_o parallel_n to_o the_o diameter_n of_o the_o equinoctial_a which_o may_v be_v call_v the_o diameter_n of_o the_o sun_n parallel_n dg_n likewise_o from_o the_o diameter_n of_o the_o horizon_n count_v the_o height_n of_o the_o sun_n ab_fw-la know_v by_o observation_n and_o thereby_o also_o draw_v be_v a_o parallel_n to_o the_o diameter_n of_o the_o horizon_n which_o may_v be_v call_v the_o diameter_n of_o the_o sun_n almicantar_n from_o i_o the_o intersection_n of_o these_o two_o parallel_n draw_v ik_fw-mi a_o line_n perpendicular_a to_o the_o diameter_n of_o the_o horizon_n then_o set_v one_o foot_n of_o the_o compass_n in_o l_o the_o midst_n of_o be_v the_o diameter_n of_o the_o sun_n almicantar_n and_o stretch_v out_o the_o other_o foot_n to_o b_o the_o end_n of_o this_o diameter_n from_o thence_o draw_v therewith_o the_o arch_n bk_n till_o you_o come_v to_o the_o say_v perpendicular_a this_o arch_n resolve_v into_o degree_n shall_v give_v you_o the_o true_a azimuth_n of_o the_o sun_n chap._n xiiii_o to_o find_v the_o inclination_n or_o dip_v of_o the_o magnetical_a needle_n under_o the_o horizon_n first_o the_o angle_n oar_n be_v give_v because_o of_o the_o arch_n obr_n measure_v the_o same_o 150_o degree_n and_o consequent_o the_o angle_n at_o r_o 15_o degree_n be_v equal_a to_o the_o equal_a side_v angle_n at_o o_o both_o which_o together_o be_v 30_o degree_n because_o they_o be_v the_o compliment_n of_o the_o angle_n oar_n 150_o degree_n to_o a_o semicircle_n or_o 180_o degree_n second_o in_o the_o triangle_n ars_n all_o the_o side_n be_v give_v be_v the_o radius_fw-la or_o semidiameter_n 10,000,000_o r_n equal_a to_o ro_n the_o subtense_n of_o 150_o degree_n 19,318,516_o and_o as_o equal_a to_o ad_fw-la triple_a in_o power_n to_o ab_fw-la because_o it_o be_v equal_a in_o power_n to_o ab_fw-la and_o bd_o that_o be_v boy_n which_o be_v double_a in_o power_n to_o ab_fw-la or_o else_o thus_o the_o arch_n ob_fw-la being_n 90_o degree_n the_o subtense_n thereof_o ob_fw-la that_o be_v the_o tangent_fw-la bd_o be_v 14,142,126_o which_o seek_v in_o the_o table_n of_o tangent_n shall_v give_v you_o the_o angle_n bid_v 54_o degree_n 44_o minute_n 8_o second_o the_o secant_fw-la whereof_o be_v the_o line_n ad_fw-la that_o be_v as_o 17,320,508_o now_o then_o by_o 4_o axiom_n of_o the_o 2_o book_n of_o ptisc_n as_o the_o base_a or_o great_a side_n sir_n 19,318,516_o be_v to_o the_o sum_n of_o the_o other_o two_o side_n sa_o and_o ar_n 27,320,508_o so_o be_v the_o difference_n of_o they_o sx_v 7,320,508_o to_o the_o segment_n of_o the_o great_a side_n sy_n 10,352,762_o which_o be_v take_v out_o of_o sir_n 19,318,516_o there_o remain_v your_o 8,965,754_o the_o half_a whereof_o rz_n 4,482,877_o be_v the_o sine_fw-la of_o the_o angle_n raz_n 26_o degree_n 38_o minute_n 2_o second_o the_o compliment_n whereof_o 63_o degree_n 21_o minute_n 58_o second_n be_v the_o angle_n arz_n which_o add_v to_o the_o angle_n aro_n 15_o degree_n make_v the_o whole_a angle_n orseolo_n 78_o degree_n â—1_n minute_n 58_o second_o whereof_o 60_o 90_o make_v 52_o degree_n 14_o minute_n 38_o second_n which_o take_v out_o of_o arz_n 63_o degree_n 21_o minute_n 58_o second_n there_o remain_v the_o angle_n tra_n 11_o degree_n 7_o minute_n 20_o second_o the_o compliment_n whereof_o be_v the_o inclination_n seek_v for_o 78_o degree_n 52_o minute_n 40_o second_n the_o sum_n and_o difference_n of_o the_o side_n sa_o and_o be_v be_v always_o the_o same_o viz._n 27,320,508_o and_o 7,320,508_o inclination_n the_o product_n of_o they_o shall_v likewise_o be_v always_o the_o same_o viz._n 199,999,997,378.064_o to_o be_v divide_v by_o the_o side_n sir_n that_o be_v ro_n the_o subtense_n of_o rbo._n therefore_o there_o may_v be_v some_o labour_n save_v in_o make_v the_o table_n of_o magnetical_a inclination_n if_o in_o stead_n of_o the_o say_v product_v you_o take_v continual_o but_o the_o half_a thereof_o that_o be_v 99,999,998,689,032_o and_o so_o divide_v it_o by_o half_a the_o subtense_n ro_n that_o be_v by_o the_o sine_fw-la of_o half_a the_o arch_n obr_n or_o rather_o thus_o as_o half_a the_o base_a r_n that_o be_v as_o the_o sine_z of_o half_a the_o arch_n obr_n be_v to_o half_a the_o sum_n of_o the_o other_o two_o side_n sa_o and_o ar_n 13,660,254_o so_o be_v half_a the_o difference_n of_o they_o 3,660,254_o to_o half_a of_o the_o segment_n sy_n which_o take_v out_o of_o half_a the_o base_a there_o remain_v rz_n the_o sine_fw-la of_o raz_n the_o table_n of_o magnetical_a inclination_n first_o col_fw-fr second_o col_fw-fr first_o col·_fw-la second_o col_fw-fr first_o col_fw-fr second_n col_fw-fr height_n of_o the_o pole_n magnetical_a inclination_n height_n of_o the_o pole_n magnetical_a inclination_n height_n of_o the_o pole_n magnetical_a inclination·_n degree_n degr._fw-la min._n degree_n degr._fw-la min_n degree_n degr._fw-la min._n 1_o 2_o 11_o 31_o 52_o 27_o 61_o 79_o 29_o 2_o 4_o 20_o 32_o 53_o 41_o 62_o 80_o 4_o 3_o 6_o 27_o 33_o 54_o 53_o 63_o 80_o 38_o 4_o 8_o 31_o 34_o 56_o 4_o 64_o 81_o 11_o 5_o 10_o 34_o 35_o 57_o 13_o 65_o 81_o 43_o 6_o 12_o 34_o 36_o 58_o 21_o 66_o 82_o 13_o 7_o 14_o 32_o 37_o 59_o 28_o 67_o 82_o 43_o 8_o 16_o 28_o 38_o 60_o 33_o 68_o 83_o 12_o 9_o 18_o 22_o 39_o 61_o 37_o 69_o 83_o 40_o 10_o 20_o 14_o 40_o 62_o 39_o 70_o 84_o 7_o 11_o 22_o 4_o 41_o 63_o 40_o 71_o 84_o 32_o 12_o 24_o 52_o 42_o 64_o 39_o 72_o 84_o 57_o 13_o 25_o 38_o 43_o 65_o 38_o 73_o 85_o 21_o 14_o 27_o 22_o 44_o 66_o 35_o 74_o 85_o 44_o 15_o 29_o 4_o 45_o 67_o 30_o 75_o 86_o 7_o 16_o 30_o 45_o 46_o 68_o 24_o 76_o 86_o 28_o 17_o 32_o