only_o 12_o second_n hereof_o that_o be_v the_o part_n proportional_a answerable_a to_o the_o excess_n of_o 9_o sec._n above_o 4_o sec._n where_o maginus_fw-la after_o the_o prutenick_n account_n make_v it_o to_o be_v in_o 0_o degr_n 25_o min._n of_o aries_n that_o be_v 33_o minute_n want_v of_o the_o truth_n find_v by_o observation_n the_o like_a difference_n i_o have_v often_o find_v by_o many_o and_o diligent_a observation_n especial_o for_o the_o space_n of_o the_o four_o year_n before_o mention_v the_o whole_a catalogue_n of_o which_o observation_n i_o think_v good_a for_o thy_o further_a satisfaction_n herein_o to_o set_v down_o in_o a_o table_n after_o i_o have_v first_o show_v with_o what_o instrument_n and_o after_o what_o manner_n i_o observe_v the_o same_o that_o if_o any_o error_n herein_o have_v be_v commit_v it_o may_v the_o more_o easy_o appear_v and_o be_v amend_v chap._n xix_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 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much_o of_o it_o make_v flat_a and_o thin_a as_o be_v between_o the_o top_n and_o base_a of_o that_o square_a hole_n this_o wire_n serve_v for_o observe_v the_o star_n the_o flat_a side_n whereof_o be_v to_o be_v turn_v towards_o the_o eye_n in_o observe_v of_o great_a star_n and_o the_o narrow_a side_n or_o edge_n of_o it_o be_v turn_v to_o the_o eye-ward_n when_o small_a star_n be_v to_o be_v observe_v through_o the_o midst_n of_o the_o nether_a sight_n from_o the_o top_n of_o it_o to_o the_o base_a thereof_o be_v make_v a_o narrow_a slit_n perpendicular_o erect_v likewise_o from_o the_o fiducial_a line_n and_o plain_a of_o the_o ruler_n and_o quadrant_n when_o i_o observe_v the_o star_n i_o look_v through_o this_o slit_n elevate_a and_o depress_v the_o ruler_n till_o the_o wire_n be_v first_o fit_v to_o bigness_n of_o the_o star_n do_v even_o cover_v the_o star_n from_o my_o sight_n in_o such_o sort_n that_o i_o may_v see_v both_o edge_n of_o the_o star_n alike_o on_o either_o 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circumference_n equidistant_o from_o the_o top_n and_o side_n thereof_o for_o then_o the_o upper_a edge_n of_o the_o ruler_n show_v precise_o the_o height_n of_o the_o sun_n desire_v in_o degree_n and_o minute_n upon_o the_o limb_n of_o the_o quadrant_n save_v that_o one_o whole_a degree_n be_v always_o to_o be_v add_v thereto_o because_o the_o breadth_n of_o that_o part_n of_o the_o ruler_n that_o lie_v upon_o the_o limb_n of_o the_o quadrant_n be_v make_v to_o be_v just_o equal_a to_o two_o degree_n that_o be_v on_o either_o side_n one_o degree_n from_o the_o fiducial_a line_n now_o for_o find_v out_o the_o meridian_n altitude_n of_o the_o sun_n and_o star_n i_o first_o find_v the_o meridian_n line_n thus_o with_o the_o quadrant_a rectify_v and_o use_v as_o before_o be_v show_v i_o observe_v the_o height_n of_o the_o sun_n in_o the_o forenoon_n and_o so_o wary_o let_v the_o quadrant_n stand_v immovable_a and_o lay_v the_o side_n of_o a_o straight_a ruler_n that_o be_v about_o seven_o foot_n in_o length_n close_v along_o to_o the_o perpendicular_a side_n of_o the_o quadrant_n close_o by_o the_o end_n of_o that_o side_n of_o the_o ruler_n touch_v the_o floor_n of_o the_o chamber_n i_o make_v a_o prick_n upon_o the_o floor_n also_o lay_v the_o side_n of_o the_o ruler_n to_o the_o perpendicular_a side_n and_o limb_n of_o the_o quadrant_n i_o make_v in_o like_a manner_n another_o prick_n so_o far_o as_o convenient_o i_o can_v from_o the_o former_a upon_o the_o floor_n close_o by_o the_o corner_n of_o that_o side_n of_o the_o ruler_n by_o these_o two_o prick_n i_o draw_v a_o right_a line_n which_o represent_v the_o intersection_n of_o the_o sun_n azimuth_n or_o of_o the_o continue_a plain_n of_o the_o quadrant_n and_o of_o the_o plain_a of_o the_o floor_n in_o the_o time_n of_o observation_n likewise_o in_o the_o afternoon_n the_o ruler_n of_o the_o quadrant_n carry_v the_o sight_n be_v fix_v in_o the_o same_o place_n where_o it_o be_v in_o time_n of_o observation_n in_o the_o forenoon_n i_o observe_v diligent_o till_o the_o sun_n come_v to_o the_o same_o height_n that_o he_o have_v when_o i_o observe_v in_o the_o forenoon_n which_o i_o do_v by_o follow_v the_o motion_n of_o the_o sun_n shadow_n with_o the_o quadrant_n till_o the_o edge_n of_o the_o top_n and_o side_n of_o the_o shadow_n of_o the_o upper_a sight_n fall_v upon_o the_o nether_a sight_n equidistant_o from_o the_o top_n and_o side_n thereof_o then_o careful_o let_v the_o quadrant_a stand_v immovable_a and_o draw_v the_o line_n of_o intersection_n of_o the_o floor_n and_o sun_n azimuth_n in_o time_n of_o the_o afternoon_n observation_n in_o like_a manner_n as_o i_o do_v in_o the_o forenoon_n set_v one_o foot_n of_o the_o compass_n in_o the_o
55_o 160_o 401.357_o 537.178_o 251.865.582_o  _fw-fr 56_o 160_o 938.535_o 545.704_o 260.459.920_o 8.594.338_o 57_o 161_o 484.239_o 554.505_o 271_o 919.077_o 11.459.157_o 58_o 162_o 038_o 744_o 563.594_o 289_o 107.811_o 17.188.734_o 59_o 162.602.338_o 572.986_o 323.485.279_o 34.377.468_o chap._n iii_o the_o use_n of_o the_o two_o first_o column_n of_o the_o table_n of_o latitude_n for_o graduate_v a_o meridian_n in_o the_o general_a sea-chart_n before_o you_o can_v make_v use_n of_o this_o table_n for_o the_o true_a graduate_n or_o divide_v of_o a_o meridian_n of_o this_o chart_n into_o his_o degree_n or_o other_o part_n of_o latitude_n increase_v from_o the_o aequinoctial_a towards_o the_o north_n and_o south_n in_o such_o proportion_n as_o before_o have_v be_v show_v there_o must_v be_v first_o some_o preparation_n make_v to_o that_o end_n which_o may_v be_v do_v after_o this_o manner_n overthwart_o the_o midst_n of_o the_o plain_a superficies_n whereupon_o you_o will_v draw_v the_o 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24_o 47_o 69_o 17_o 77_o 86_o 48_o 18_o 34_o 0_o 48_o 70_o 9_o 78_o 87_o 8_o 19_o 35_o 36_o 49_o 70_o 59_o 79_o 87_o 26_o 20_o 37_o 9_o 50_o 71_o 48_o â—0_n 87_o 44_o 21_o 38_o 41_o 51_o 72_o 36_o 81_o 88_o 1_o 22_o 40_o 11_o 52_o 73_o 23_o 82_o 88_o 17_o 23_o 41_o 39_o 53_o 74_o 8_o 83_o 88_o 33_o 24_o 43_o 6_o 54_o 74_o 52_o 84_o 88_o 47_o 25_o 44_o 30_o 55_o 75_o 35_o 85_o 89_o 1_o 26_o 45_o 54_o 56_o 76_o 17_o 86_o 89_o 14_o 27_o 47_o 15_o 57_o 76_o 57_o 87_o 89_o 27_o 28_o 48_o 36_o 58_o 77_o 37_o 88_o 89_o 39_o 29_o 49_o 54_o 59_o 78_o 15_o 89_o 89_o 50_o 30_o 51_o 11_o 60_o 78_o 53_o 90_o 90_o 0_o who_o compliment_n to_o a_o quadrant_a be_v the_o angle_n seek_v for_o arz_n according_a to_o this_o diagram_n and_o demonstration_n be_v calculate_v the_o table_n here_o follow_v the_o first_o column_n whereof_o contain_v the_o height_n of_o the_o pole_n for_o every_o whole_a degree_n the_o second_o column_n show_v the_o inclination_n or_o dip_v of_o the_o magnetical_a needle_n 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the_o other_o foot_n extend_v therein_o that_o way_n which_o the_o number_n succeed_v will_v show_v you_o the_o distance_n as_o for_o example_n london_n and_o cape_n blanco_n near_o the_o coast_n of_o new-found_a land_n have_v both_o northerly_a and_o almost_o equal_a latitude_n of_o 51_o degree_n 32_o minute_n have_v therefore_o draw_v as_o well_o the_o diameter_n bc_n and_o dl_o from_o b_o determine_v the_o longitude_n of_o london_n viz._n 22_o degree_n and_o from_o the_o point_n of_o the_o longitude_n of_o cape_n blanco_n which_o admit_v to_o be_v 331_o degree_n as_o also_o the_o perpendicular_o or_o sin_n of_o both_o their_o latitude_n of_o and_o kl_n as_o before_o be_v show_v cross_v the_o diameter_n in_o f_o and_o l_o the_o distance_n fl_fw-mi take_v with_o the_o compass_n and_o translate_v into_o the_o circle_n as_o in_o the_o former_a example_n will_v show_v you_o the_o distance_n of_o cape_n blanco_n from_o london_n to_o be_v almost_o 31_o degree_n of_o a_o great_a circle_n 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2325_o mile_n but_o if_o the_o latitude_n be_v of_o divers_a denomination_n that_o be_v one_o northerly_a and_o the_o other_o southerly_a continue_v forth_o the_o perpendicular_a that_o cross_v the_o diameter_n wherein_o the_o foresay_a prick_n be_v make_v till_o it_o be_v equal_a to_o both_o perpendicular_o that_o be_v to_o the_o sin_n of_o both_o latitude_n the_o distance_n of_o the_o end_n of_o this_o continue_a perpendicular_a from_o the_o prick_n aforesaid_a in_o the_o diameter_n take_v with_o the_o compass_n and_o translate_v into_o the_o graduated_a peripherie_n of_o the_o circle_n as_o before_o will_v show_v you_o how_o many_o degree_n of_o a_o great_a circle_n be_v contain_v between_o both_o place_n to_o shut_v up_o this_o matter_n with_o one_o example_n suppose_v you_o will_v know_v how_o far_o cusco_n in_o peru_n be_v from_o london_n let_v the_o longitude_n of_o cusco_n be_v 295_o degree_n the_o latitude_n 11_o degree_n southerly_a the_o longitude_n of_o london_n as_o 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upon_o the_o margin_n of_o letter_n n._n fol._n 65._o so_o as_o it_o may_v lie_v open_a all_o the_o while_n the_o foregoing_a matter_n of_o the_o same_o chap._n be_v read_v also_o because_o all_o the_o sin_n of_o latitude_n be_v perpendicular_a to_o the_o same_o plain_a of_o the_o aequinoctial_a be_v parallel_n by_o the_o 5._o e_fw-la 21._o ram._n 6._o pr._n 11._o eucl._n therefore_o by_o the_o 11._o e_fw-la 2._o ram._n or_o 35._o d._n 1._o eucl._n fl_fw-mi be_v the_o line_n subtend_v the_o distance_n of_o london_n and_o cape_n â—â—anco_n again_o because_o fp_n whereto_o of_o be_v perpendicular_a be_v make_v equal_a to_o foe_n the_o distance_n of_o the_o sin_n of_o london_n and_o jerusalem_n to_o which_o distance_n of_o be_v also_o perpendicular_a in_o the_o globe_n and_o eq_n also_o equal_a to_o no_o therefore_o fq_n be_v the_o difference_n 〈◊〉_d the_o sin_n of_o london_n and_o hierusalems_n latitude_n there_o must_v needs_o be_v the_o same_o distance_n betwixt_o p_o and_o q_o that_o 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triangle_n have_v always_o two_o side_n give_v which_o be_v the_o sin_n of_o the_o compliment_n of_o the_o latitude_n of_o the_o two_o place_n as_o open_v fp_n lp_v fp_n rp_n fp_n ap_n fp_n together_o with_o the_o angle_n contain_v between_o they_o that_o be_v the_o difference_n of_o their_o longitude_n whereby_o favorina_n foyes_n fl_fw-mi fs_n the_o distance_n of_o the_o sin_n of_o latitude_n be_v find_v by_o 〈◊〉_d 2_o 3_o 4_o 5_o copernic_n de_fw-fr triang_n planis_fw-la the_o line_n also_o subtend_v the_o distance_n of_o the_o place_n may_v most_o easy_o be_v find_v by_o the_o 3._o copernic_n de_fw-fr triang_n plan_n for_o the_o square_n of_o the_o distance_n of_o the_o sin_n and_o of_o the_o difference_n of_o the_o sin_n of_o their_o latitude_n if_o both_o be_v northerly_a or_o both_o southerly_a or_o of_o the_o sum_n of_o the_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
cast_v his_o point_n in_o manner_n follow_v and_o he_o shall_v errer_n as_o little_a as_o be_v possible_a let_v he_o examine_v according_a to_o the_o ordinary_a run_v of_o his_o ship_n how_o much_o way_n she_o may_v make_v every_o day_n that_o he_o have_v sail_v and_o the_o league_n that_o shall_v amount_v in_o all_o the_o day_n let_v he_o take_v between_o the_o point_n of_o one_o compass_n and_o let_v he_o place_v one_o point_n thereof_o upon_o the_o place_n from_o whence_o he_o depart_v and_o take_v another_o compass_n let_v he_o set_v one_o point_n thereof_o upon_o the_o graduation_n according_a to_o the_o height_n which_o he_o have_v take_v and_o the_o other_o point_n upon_o the_o next_o east_n and_o west_n rumb_n now_o let_v this_o compass_v run_v by_o his_o east_n and_o west_n rumb_n till_o the_o point_n come_v from_o the_o graduation_n meet_v with_o the_o second_o point_n of_o the_o other_o compass_n which_o he_o hold_v not_o upon_o the_o chart_n and_o in_o the_o place_n where_o they_o meet_v he_o may_v say_v that_o there_o be_v his_o point_n and_o his_o ship_n and_o because_o in_o this_o case_n all_o pilot_n do_v not_o use_v this_o point_n of_o imagination_n and_o height_n there_o grow_v great_a diversity_n among_o they_o concern_v their_o distance_n from_o land_n when_o as_o in_o long_a voyage_n they_o confer_v and_o communicate_v their_o opinion_n one_o with_o another_o insomuch_o that_o one_o according_a to_o his_o conjecture_n judge_v himself_o to_o be_v 50_o league_n from_o land_n another_o 100_o another_o 200_o and_o another_o think_v he_o be_v hard_a by_o the_o land_n the_o reason_n be_v because_o some_o of_o they_o cast_v their_o point_n by_o traverse_v other_o by_o imagination_n only_o and_o other_o by_o imagination_n and_o height_n who_o be_v always_o more_o certain_a than_o the_o rest_n chap._n xxiv_o what_o it_o be_v to_o increase_v or_o diminish_v in_o height_n the_o mariner_n call_v it_o increase_v in_o height_n when_o they_o go_v further_o and_o further_o from_o the_o equinoctial_a and_o diminish_v in_o height_n when_o they_o approach_v near_o to_o the_o equinoctial_a so_o that_o in_o our_o navigation_n we_o either_o sail_n from_o a_o great_a to_o a_o less_o altitude_n of_o the_o pole_n and_o then_o we_o go_v towards_o the_o equinoctial_a and_o then_o the_o height_n be_v say_v to_o be_v diminish_v or_o we_o sail_v from_o a_o less_o to_o a_o great_a height_n of_o the_o pole_n and_o then_o we_o go_v from_o the_o equinoctial_a and_o be_v say_v to_o increase_v our_o height_n and_o hence_o it_o be_v that_o cast_v our_o point_n by_o imagination_n and_o afterward_o have_v take_v the_o height_n amend_v it_o by_o traverse_v either_o the_o height_n wherein_o we_o find_v ourselves_o be_v take_v by_o the_o sun_n or_o star_n be_v great_a or_o else_o it_o be_v less_o than_o that_o which_o we_o make_v account_n of_o by_o imagination_n and_o hence_o do_v arise_v four_o rule_n the_o first_o be_v that_o when_o in_o sail_v we_o do_v increase_v the_o height_n if_o the_o point_n amend_v by_o traverse_v be_v of_o great_a height_n than_o the_o point_n of_o imagination_n the_o ship_n have_v go_v more_o than_o the_o point_n of_o imagination_n show_v we_o the_o second_o when_o we_o increase_v our_o height_n if_o the_o point_n amend_v by_o traverse_v be_v in_o less_o height_n than_o the_o point_n find_v by_o imagination_n then_o have_v the_o ship_n go_v less_o way_n than_o we_o imagine_v the_o three_o be_v when_o we_o diminish_v our_o height_n in_o sail_v if_o the_o point_n amend_v by_o traverse_v be_v in_o a_o great_a height_n than_o the_o point_n find_v by_o imagination_n then_o have_v the_o ship_n make_v less_o way_n than_o we_o guess_v by_o our_o imagination_n the_o four_o be_v when_o we_o diminish_v our_o height_n if_o the_o point_n amend_v by_o traverse_n be_v in_o less_o height_n than_o the_o point_n find_v by_o imagination_n then_o have_v the_o ship_n make_v more_o way_n than_o we_o imagine_v chap._n xxv_o how_o you_o may_v cast_v a_o traverse_n point_n without_o compass_n if_o a_o mariner_n chance_v to_o lose_v his_o compass_n he_o may_v cast_v his_o point_n of_o traverse_n after_o this_o manner_n let_v he_o take_v two_o slender_a thread_n and_o put_v the_o end_n of_o one_o of_o they_o upon_o the_o place_n from_o whence_o he_o depart_v let_v he_o stretch_v it_o in_o equal_a distance_n from_o the_o rumb_n by_o which_o he_o have_v sail_v and_o put_v another_o thread_n in_o equal_a distance_n from_o the_o next_o east_n and_o west_n rumb_n let_v he_o make_v it_o to_o pass_v by_o the_o degree_n of_o height_n in_o which_o he_o find_v himself_o and_o where_o the_o two_o thread_n cross_v one_o another_o there_o be_v the_o point_n of_o the_o ship_n and_o always_o the_o first_o thread_n if_o it_o have_v not_o change_v the_o course_n show_v the_o way_n which_o the_o ship_n have_v go_v and_o the_o second_o the_o parallel_n wherein_o the_o ship_n be_v chap._n xxvi_o of_o another_o kind_n of_o cast_v a_o point_n by_o traverse_n examine_v the_o difference_n of_o the_o degree_n of_o distance_n from_o the_o equinoctial_a which_o be_v between_o the_o place_n from_o whence_o the_o ship_n set_v forth_o and_o the_o place_n where_o the_o ship_n be_v then_o take_v the_o heighth_n of_o both_o place_n very_o precise_o and_o subtract_v the_o lesser_a out_o of_o the_o great_a that_o which_o remain_v be_v the_o difference_n which_o difference_n you_o must_v multiply_v by_o the_o league_n which_o answer_n to_o one_o degree_n in_o the_o rumb_n by_o which_o you_o have_v sail_v and_o those_o league_n which_o the_o degree_n and_o minute_n of_o difference_n shall_v make_v you_o shall_v take_v between_o the_o point_n of_o a_o pair_n of_o compass_n out_o of_o your_o scale_n of_o league_n and_o hold_v the_o say_a compass_n so_o open_a set_v one_o foot_n thereof_o upon_o the_o point_n from_o whence_o the_o ship_n depart_v and_o the_o other_o foot_n stretch_v towards_o the_o place_n whithre_o the_o ship_n have_v sail_v you_o must_v hold_v up_o a_o little_a from_o the_o chart_n and_o you_o must_v set_v one_o foot_n of_o the_o other_o compass_n at_o the_o degree_n of_o the_o distance_n wherein_o your_o ship_n be_v from_o the_o equinoctial_a when_o the_o say_a point_n be_v seek_v for_o and_o the_o other_o point_n you_o must_v place_n upon_o the_o next_o east_n and_o west_n parallel_v and_o let_v this_o second_o compass_n run_v by_o his_o next_o east_n and_o west_n rumb_n until_o the_o point_n of_o the_o first_o compass_n lift_v up_o be_v set_v down_o that_o point_n of_o the_o second_o compass_n which_o come_v from_o the_o say_a degree_n do_v meet_v therewithal_o and_o where_o those_o two_o point_n shall_v meet_v there_o be_v the_o true_a point_n of_o the_o ship_n chap._n xxvii_o of_o the_o league_n which_o in_o navigation_n answer_v to_o each_o degree_n of_o latitude_n in_o every_o rumb_n if_o we_o suppose_v as_o we_o have_v before_o say_v in_o the_o chap._n of_o the_o quantity_n of_o the_o earth_n that_o the_o great_a circle_n thereof_o conain_v in_o compass_n 6300_o common_a spanish_a league_n then_o unto_o every_o degree_n of_o the_o meridian_n which_o be_v the_o great_a circle_n do_v answer_v 17_o spanish_a leagus_n and_o a_o half_a so_o that_o sail_a north_n and_o south_n if_o your_o height_n of_o the_o pole_n or_o your_o distance_n from_o the_o equinoctial_a be_v vary_v one_o degree_n you_o may_v say_v that_o you_o have_v go_v seventeen_o league_n and_o a_o half_a but_o if_o you_o vary_v one_o degree_n and_o hold_v your_o course_n upon_o the_o first_o point_n then_o have_v you_o sail_v 17_o league_n and_o ⅙_n and_o you_o have_v decline_v from_o the_o meridian_n or_o right_a line_n which_o pass_v by_o the_o place_n from_o which_o you_o depart_v three_o leagus_n and_o a_o half_a and_o if_o you_o sail_v upon_o the_o second_o point_n from_o the_o north_n or_o south_n till_o your_o height_n of_o the_o pole_n be_v change_v one_o degree_n you_o have_v then_o go_v 19_o league_n and_o ⅜_n and_o be_v distant_a from_o your_o right_a line_n 7_o league_n and_o ¼_n and_o vary_v a_o degree_n upon_o the_o three_o point_n of_o the_o compass_n from_o north_n or_o south_n you_o have_v go_v 21_o league_n and_o be_v depart_v from_o your_o right_a line_n 11_o league_n and_o ⅔_n sail_v upon_o the_o four_o point_n of_o the_o compass_n there_o do_v answer_v unto_o every_o degree_n 24_o league_n and_o three_o fourth_n and_o you_o be_v distant_a from_o the_o right_a line_n or_o meridian_n 17_o league_n and_o a_o half_a upon_o the_o five_o point_n you_o must_v allow_v for_o one_o degree_n 31_o league_n and_o a_o half_a and_o then_o be_v you_o distant_a from_o your_o right_a line_n 26_o league_n and_o ⅕_n upon_o the_o six_o point_n do_v