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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
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 lineament_n of_o the_o chart_n describe_v a_o right_a line_n represent_v the_o aequinoctial_a circle_n which_o you_o shall_v divide_v into_o 360_o part_n or_o degree_n and_o cross_v the_o same_o squirewise_o with_o right_a line_n by_o every_o five_o or_o ten_o degree_n then_o take_v with_o your_o compass_n the_o length_n of_o half_a the_o aequinoctial_a that_o be_v 180_o degree_n and_o set_v one_o foot_n of_o your_o compass_n in_o the_o mutual_a intersection_n of_o the_o aequinoctial_a with_o the_o perpendicular_a or_o meridian_n that_o pass_v by_o either_o end_n of_o the_o aequinoctial_a with_o the_o other_o foot_n make_v a_o prick_n in_o the_o same_o perpendicular_a or_o meridian_n the_o space_n contain_v betwixt_o this_o prick_n and_o the_o aequinoctial_a divide_v first_o into_o three_o equal_a part_n and_o every_o one_o of_o these_o into_o other_o three_o so_o have_v you_o nine_o in_o all_o and_o again_o every_o one_o of_o these_o into_o three_o so_o have_v you_o 27_o part_n and_o 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this_o table_n of_o latitude_n omit_v always_o four_o or_o five_o of_o the_o first_o figure_n towards_o the_o right_a hand_n and_o at_o the_o same_o number_n of_o part_n in_o the_o perpendicular_o make_v prick_n on_o either_o side_n the_o aequinoctial_a by_o which_o prick_n draw_v right_a line_n equidistant_a from_o the_o aequinoctial_a for_o they_o shall_v be_v the_o parallel_n of_o the_o true_a nautical_a planisphere_n or_o sea-chart_n notwithstanding_o these_o parallel_n be_v all_o oâ—â—hem_n a_o little_o further_a distant_a from_o the_o aequinoctial_a then_o in_o truth_n they_o shall_v be_v and_o so_o much_o the_o more_o the_o further_o they_o be_v from_o the_o aequinoctial_a which_o error_n may_v be_v something_o the_o less_o if_o the_o former_a table_n have_v be_v first_o make_v to_o small_a part_n than_o minute_n but_o that_o be_v a_o matter_n more_o curious_a than_o necessary_a the_o table_n here_o before_o set_v down_o be_v so_o near_o the_o truth_n that_o it_o be_v not_o possible_a by_o any_o rule_n or_o instrument_n of_o navigation_n to_o discover_v any_o sensible_a error_n in_o the_o sea-chart_n so_o far_o forth_o as_o it_o shall_v be_v make_v according_a thereto_o the_o figure_n follow_v contain_v only_o one_o part_n of_o the_o nautical_a planisphaere_n from_o the_o aequinoctial_a northwards_o because_o the_o other_o part_n from_o the_o aequinoctial_a southwards_o must_v be_v altogether_o like_a and_o equal_a to_o this_o herein_o first_o i_o draw_v the_o aequinoctial_a line_n ac_fw-la and_o divide_v it_o into_o 36_o equal_a part_n whereof_o every_o one_o be_v understand_v to_o contain_v ten_o degree_n and_o i_o raise_v perpendicular_o from_o every_o one_o of_o those_o part_n which_o be_v the_o meridian_n of_o the_o nautical_a planisphaere_n every_o where_o aequidistant_a each_o from_o other_o then_o i_o take_v half_o the_o length_n of_o the_o aequinoctial_a with_o the_o compass_n and_o set_v one_o foot_n in_o the_o end_n of_o the_o aequinoctial_a at_o c_z with_o the_o other_o foot_n i_o make_v a_o prick_n at_o d_o in_o the_o perpendicular_a or_o meridian_n cd_o the_o space_n contain_v betwixt_o c_o and_o d_o i_o divide_v into_o 1080_o part_n understand_v every_o one_o of_o the_o small_a part_n or_o segment_n of_o the_o line_n cd_o to_o contain_v ten_o lesser_a part_n in_o such_o sort_n as_o before_o have_v be_v show_v and_o set_v figure_n to_o they_o as_o here_o you_o see_v for_o the_o ready_a number_n and_o find_v out_o of_o any_o of_o those_o part_n then_o i_o look_v in_o the_o former_a table_n what_o number_n of_o equal_a part_n of_o the_o meridian_n answer_v to_o every_o ten_o degree_n and_o cast_a away_o five_o of_o the_o first_o figure_n next_o the_o right_a hand_n because_o i_o conceive_v the_o space_n betwixt_o c_o and_o d_o to_o be_v divide_v only_o into_o 1080_o part_n i_o find_v out_o the_o part_n answerable_a to_o the_o number_n remain_v in_o the_o line_n cd_o and_o at_o those_o part_n i_o make_v prick_v by_o 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latitude_n be_v 83_o â—â—_o 73_o 416_o and_o 37_o 639_o 370_o which_o be_v divide_v by_o 600_o â—â—00_n the_o quotient_n be_v 140_o and_o 63_o almost_o show_v the_o breadth_n 〈◊〉_d the_o chart_n from_o the_o equinoctial_a northwards_o and_o southwards_o in_o such_o part_n whereof_o the_o equinoctial_a contain_v 360_o â—hich_v add_v together_o shall_v show_v that_o the_o whole_a breadth_n of_o 〈◊〉_d chart_n from_o north_n to_o south_n must_v be_v about_o 203_o such_o part_n â—aving_a therefore_o divide_v the_o length_n of_o the_o equinoctial_a or_o any_o â—ther_a parallel_n of_o the_o chart_n because_o they_o be_v all_o equal_a into_o â—60_n part_n take_v with_o a_o pair_n of_o compass_n 210_o of_o the_o same_o part_n because_o that_o be_v the_o next_o great_a number_n apt_a for_o division_n and_o so_o keep_v they_o unaltered_a set_v both_o foot_n in_o the_o meridian_n at_o one_o of_o the_o end_n or_o in_o the_o midst_n of_o the_o chart_n and_o divide_v the_o space_n contain_v between_o 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unto_o if_o that_o difference_n be_v a_o compound_n number_n that_o may_v be_v divide_v into_o his_o unity_n by_o small_a divisoâ—â—_n but_o if_o it_o fall_v out_o that_o the_o number_n of_o equal_a part_n remine_v 〈◊〉_d either_o a_o prime_a number_n or_o else_o such_o a_o number_n as_o can_v otherwise_o be_v divide_v into_o his_o unity_n but_o by_o some_o great_a divisor_n 〈◊〉_d may_v then_o take_v the_o next_o compound_v number_n that_o be_v great_a 〈◊〉_d the_o say_a difference_n which_o may_v be_v divide_v into_o his_o unity_n 〈◊〉_d small_a divisor_n thus_o have_v divide_v the_o line_n draw_v 〈◊〉_d thwart_o the_o breadth_n of_o the_o chart_n into_o so_o many_o equal_a part_n as_o 〈◊〉_d compound_n number_n contain_v unity_n and_o beginning_n at_o 〈◊〉_d end_n thereof_o which_o be_v suppose_v to_o be_v southwards_o or_o next_o the_o equinoctial_a set_v thereto_o the_o next_o number_n of_o whole_a hundred_o or_o thousand_o less_o than_o the_o number_n of_o equal_a part_n answerable_a 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the_o distance_n but_o if_o both_o place_n agree_v in_o longitude_n have_v latitude_n also_o of_o like_a denomination_n as_o both_o northerly_a or_o both_o southerly_a subtract_v the_o lesser_a latitude_n out_o of_o the_o great_a the_o distance_n remain_v if_o one_o place_n have_v northerly_a latitude_n and_o the_o other_o southerly_a add_v they_o together_o for_o the_o sum_n be_v the_o distance_n if_o one_o or_o both_o place_n have_v atitude_n land_n differ_v also_o in_o longitude_n in_o a_o great_a circle_n divide_v exact_o into_o degree_n with_o figure_n set_v to_o every_o five_o or_o ten_o degree_n note_v the_o longitude_n of_o both_o place_n now_o if_o one_o place_n only_o have_v latitude_n draw_v a_o diameter_n from_o the_o longitude_n thereof_o note_v in_o the_o circle_n and_o with_o your_o compass_n take_v so_o many_o degree_n and_o minute_n in_o the_o same_o circle_n as_o that_o latitude_n contain_v then_o set_v one_o foot_n of_o the_o compass_n in_o the_o longitude_n of_o that_o place_n with_o the_o other_o make_v a_o prick_n in_o the_o circle_n which_o may_v be_v call_v the_o point_n of_o latitude_n from_o this_o point_n draw_v a_o line_n perpendicular_a cross_v the_o diameter_n draw_v from_o the_o longitude_n of_o that_o place_n take_v with_o your_o compass_n the_o distance_n of_o this_o cross_n from_o the_o point_n of_o the_o other_o place_n longitude_n note_v in_o the_o circle_n and_o leave_v one_o foot_n in_o the_o say_v cross_v with_o the_o other_o make_v a_o prick_n in_o the_o foresay_a diameter_n take_v the_o distance_n of_o this_o prick_n from_o the_o point_n of_o latitude_n note_v in_o the_o circle_n then_o set_v one_o foot_n of_o the_o compass_n in_o that_o point_n of_o the_o circle_n where_o the_o degree_n begin_v to_o be_v number_v the_o other_o foot_n extend_v that_o way_n which_o the_o number_n proceed_v shall_v show_v you_o in_o the_o circle_n the_o distance_n of_o the_o place_n take_v for_o example_n the_o city_n of_o london_n and_o saint_n thomas_n island_n which_o lie_v right_a under_o the_o aequinoctial_a line_n in_o 32_o degree_n of_o longitude_n the_o longitude_n of_o london_n admit_v to_o be_v 22_o degree_n the_o latitude_n 51_o degree_n 32_o minute_n mark_v the_o longitude_n of_o saint_n thomas_n island_n and_o of_o london_n with_o a_o and_o b._n from_o the_o longitude_n of_o london_n because_o london_n have_v also_o latitude_n draw_v the_o diameter_n bc._n have_v take_v with_o the_o compass_n the_o latitude_n of_o london_n in_o the_o circle_n set_v one_o foot_n in_o b_o and_o with_o the_o other_o make_v the_o prick_n e_o in_o the_o circle_n and_o draw_v the_o perpendicular_a of_o cross_v the_o diameter_n bc_n at_o f._n make_v fg_v equal_a to_o favorina_n which_o be_v the_o distance_n of_o saint_n thomas_n island_n from_o the_o sine_fw-la of_o london_n latitude_n then_z ge_n shall_v be_v the_o line_n
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 â—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
because_o they_o be_v equal_a this_o height_n of_o the_o pole_n be_v know_v by_o the_o help_n of_o four_o thing_n which_o be_v the_o ballâ—stilla_n or_o crosse-staffe_n the_o position_n of_o the_o north-star_n the_o height_n of_o the_o say_a star_n and_o certain_a rule_n chap._n xi_o the_o make_n of_o the_o crossstaff_n the_o mariner_n crosse-staff_n be_v that_o which_o by_o the_o astronomer_n be_v call_v radius_fw-la astronomicus_fw-la and_o the_o manner_n how_o to_o make_v it_o be_v as_o follow_v first_o upon_o a_o very_a plain_a and_o broad_a table_n you_o may_v draw_v a_o semicircle_n which_o from_o the_o centre_n to_o the_o circumference_n must_v contain_v at_o the_o least_o four_o hand_n breadth_n and_o have_v draw_v through_o the_o centre_n thereof_o the_o line_n abc_n divide_v the_o circumference_n into_o two_o equal_a part_n in_o the_o point_n e_o as_o likewise_o you_o must_v divide_v the_o quadrant_a aec_fw-la in_o the_o very_a midst_n by_o the_o point_n f._n then_o must_v you_o divide_v the_o arch_n of_o into_o 90_o equal_a part_n divide_v it_o first_o into_o three_o and_o every_o of_o these_o three_o into_o other_o three_o and_o every_o of_o those_o nine_o into_o two_o and_o each_o of_o those_o two_o into_o five_o which_o you_o must_v do_v with_o much_o preciseness_n and_o care_n then_o lay_v your_o ruler_n to_o the_o point_n b_o which_o be_v the_o centre_n through_o every_o one_o those_o 90_o division_n of_o the_o half_a quadrant_a you_o must_v draw_v 90_o line_n and_o keep_v this_o quadrant_a so_o divide_v it_o will_v serve_v you_o for_o a_o pattern_n to_o make_v we_o many_o crosse-stave_n as_o you_o think_v good_a of_o what_o bigness_n soever_o you_o will_n but_o to_o make_v the_o crosse-staff_n you_o must_v take_v a_o piece_n of_o wood_n of_o some_o three_o foot_n in_o length_n and_o a_o finger_n thick_a four_o square_a and_o very_o even_o and_o fit_v a_o transversary_n thereto_o which_o may_v with_o facility_n slide_v up_o and_o down_o upon_o the_o staff_n always_o right_o across_o take_v with_o your_o compass_n half_a the_o length_n of_o the_o transversary_n and_o place_v one_o foot_n of_o the_o compass_n upon_o the_o point_n b_o make_v with_o the_o other_o a_o mark_n in_o the_o line_n bc_n which_o may_v serve_v for_o the_o point_n g_o and_o draw_v through_o the_o point_n g_o the_o line_n give_v which_o may_v run_v equal_o distant_a from_o the_o line_n ebb_n final_o lay_v one_o end_n of_o the_o staff_n upon_o the_o point_n g_o let_v it_o lie_v all_o along_o just_a upon_o the_o line_n give_v and_o make_v your_o mark_n upon_o the_o edge_n of_o the_o staff_n by_o which_o you_o may_v draw_v 90_o line_n put_v the_o number_n of_o every_o line_n upon_o the_o say_a edge_n begin_n to_o place_n 90_o where_o the_o line_n be_v do_v cross_v the_o staff_n and_o from_o thence_o descend_v unto_o one_o or_o two_o which_o may_v be_v put_v down_o according_a to_o the_o length_n of_o the_o staff_n and_o the_o largeness_n of_o the_o transversary_n chap._n xii_o of_o the_o position_n of_o the_o north-star_n and_o the_o guard_n among_o the_o 48_o constellation_n which_o the_o astronomer_n place_n in_o the_o heaven_n the_o near_a unto_o the_o pole_n of_o the_o world_n be_v that_o which_o they_o call_v the_o lesser_a bear_n and_o the_o mariner_n bozina_fw-la or_o the_o horn_n in_o regard_n of_o the_o fashion_n thereof_o which_o constellation_n consist_v of_o 7_o star_n which_o be_v place_v after_o this_o manner_n and_o of_o these_o star_n the_o three_o great_a mark_v with_o the_o letter_n abc_n do_v serve_v especial_o for_o our_o purpose_n and_o so_o a_o be_v call_v the_o north-star_n b_o the_o the_o foremost_a guard_n c_z the_o other_z guard_z behind_z and_o they_o be_v so_o call_v because_o that_o by_o force_n of_o the_o motion_n of_o the_o first_o movable_a heaven_n the_o star_n b_o go_v always_o before_o and_o the_o star_n c_o behind_o every_o of_o these_o three_o star_n as_o well_o as_o all_o other_o in_o the_o heaven_n beside_o describe_v thâ—â—_n circle_n round_o about_o the_o pole_n with_o the_o motion_n of_o the_o first_o or_o high_a movable_a heaven_n 〈◊〉_d which_o motion_n sometime_o the_o 〈◊〉_d star_n ab_fw-la be_v just_a of_o 〈…〉_z above_o the_o horizon_n 〈…〉_z they_o be_v say_v to_o be_v east_n and_o west_n one_o from_o another_o sometime_o they_o be_v in_o a_o perpendicular_a line_n to_o the_o horizon_n according_a to_o our_o sight_n and_o then_o they_o be_v say_v to_o be_v north_n and_o south_n and_o sometime_o also_o the_o two_o guard_n bc_n be_v east_n and_o west_n one_o from_o another_o and_o then_o the_o former_a guard_n bear_v from_o the_o north-star_n north-east_n and_o south-west_n and_o when_o these_o two_o guard_n be_v in_o a_o perpendicular_a line_n one_o above_o another_o the_o former_a guard_n bear_v from_o the_o north_n star_n north-east_n and_o south-west_n insomuch_o that_o from_o these_o four_o position_n do_v arise_v eight_o rule_n for_o the_o eight_o rumb_n wherein_o the_o former_a guard_n may_v stand_v be_v consider_v in_o respect_n of_o the_o north_n star_n and_o so_o presuppose_v that_o the_o north_n star_n be_v distant_a from_o the_o pole_n three_o degree_n and_o a_o half_a according_a to_o the_o opinion_n of_o some_o mariner_n who_o love_v number_n that_o have_v not_o any_o fraction_n sometime_o the_o north_n star_n shall_v be_v as_o high_a as_o the_o pole_n itself_o sometime_o three_o degree_n and_o a_o half_a low_o or_o high_a than_o the_o pole_n and_o sometime_o three_o degree_n and_o sometime_o one_o and_o a_o half_a and_o sometime_o half_a a_o degree_n chap._n xiii_o of_o the_o height_n of_o the_o star_n take_v with_o the_o crosse-staffe_n to_o know_v how_o much_o the_o north_n star_n be_v elevate_v above_o the_o horizon_n you_o must_v take_v the_o height_n thereof_o only_o at_o such_o time_n when_o as_o in_o respect_n of_o the_o former_a guard_n it_o be_v in_o some_o one_o of_o these_o four_o rumb_n that_o be_v to_o say_v north_n and_o south_n east_n and_o west_n north-east_n and_o south-west_n and_o northwest_n and_o southeast_n wherefore_o see_n it_o place_v in_o any_o of_o the_o foresay_a rumb_n you_o shall_v put_v that_o end_n of_o the_o crosse-staffe_n which_o be_v next_o 90_o degree_n upon_o your_o cheekbone_n at_o the_o utter_a corner_n of_o your_o eye_n and_o hold_v it_o there_o steadfast_a you_o must_v move_v the_o transversarie_n till_o you_o see_v the_o horizon_n join_v with_o the_o low_a end_n thereof_o and_o the_o north_n star_n with_o the_o high_a end_n then_o mark_v the_o degree_n and_o part_n of_o the_o degree_n which_o the_o transuersarie_n show_v upon_o the_o staff_n for_o that_o be_v the_o height_n of_o the_o star_n chap._n xiiii_o the_o regiment_n or_o rule_n of_o the_o north_n star_n the_o first_o rule_n when_o the_o guard_n be_v in_o the_o east_n the_o former_a guard_n bear_v with_o the_o north_n star_n east_n and_o west_n and_o then_o the_o north_n star_n be_v a_o degree_n and_o half_a under_o the_o pole_n let_v we_o add_v this_o degree_n and_o half_a to_o the_o height_n which_o we_o observe_v with_o the_o crosse-staffe_n and_o the_o whole_a product_n show_v the_o number_n of_o degree_n which_o the_o pole_n be_v elevate_v above_o our_o horizon_n and_o so_o much_o be_v we_o distant_a from_o the_o equinoctial_a towards_o the_o north._n the_o second_o rule_n when_o the_o guard_n be_v in_o the_o north-east_n one_o guard_n bear_v from_o another_o east_n and_o west_n and_o the_o former_a guard_n stand_v from_o the_o north_n star_n north-east_n and_o south-west_n and_o then_o the_o north_n star_n be_v under_o the_o pole_n three_o degree_n and_o one_o half_a which_o be_v add_v to_o the_o height_n of_o the_o star_n will_v show_v you_o the_o height_n of_o the_o pole_n the_o three_o rule_n when_o the_o guard_n be_v at_o the_o high_a than_o the_o former_a guard_n bear_v from_o the_o north_n star_n north_n and_o south_n the_o north_n star_n be_v then_o three_o degree_n under_o the_o pole_n which_o three_o degree_n be_v add_v to_o the_o height_n of_o the_o star_n do_v show_v the_o true_a height_n of_o the_o pole_n the_o four_o rule_n when_o the_o guard_n be_v in_o the_o northwest_n they_o bear_v one_o from_o another_o north_n and_o south_n and_o the_o former_a guard_n lie_v from_o the_o north_n star_n north-east_n and_o south-west_n and_o then_o the_o north_n star_n be_v under_o the_o pole_n half_o a_o degree_n which_o half_a degree_n be_v add_v to_o the_o height_n of_o the_o star_n give_v you_o the_o height_n of_o the_o pole_n the_o five_o rule_n when_o the_o guard_n be_v in_o the_o east_n the_o former_a guard_n lie_v from_o the_o north_n star_n east_n and_o west_n and_o then_o the_o north_n star_n be_v a_o degree_n and_o a_o half_a above_o the_o pole_n which_o degree_n and_o
5_o i_o divide_v these_o 24_o by_o 5_o and_o i_o find_v the_o quotient_a to_o be_v four_o and_o the_o remainder_n four_o and_o so_o i_o say_v that_o the_o moon_n come_v to_o the_o north-east_n four_o hour_n and_o ⅘_n late_a than_o the_o sun_n and_o because_o the_o sun_n come_v to_o the_o north-east_n at_o three_o a_o clock_n in_o the_o morning_n i_o add_v those_o 4_o hour_n and_o ⅘_n unto_o the_o 3_o hour_n last_o mention_v and_o they_o make_v seven_o hour_n and_o ⅘_n which_o be_v the_o hour_n of_o the_o morning_n wherein_o the_o tide_n or_o full_a sea_n happen_v and_o add_v unto_o these_o seven_o hour_n and_o ⅘_n other_o six_o hour_n and_o ⅕_n they_o make_v in_o all_o fourteen_o hour_n which_o fall_v out_o at_o two_o a_o clock_n in_o the_o afternoon_n which_o be_v the_o hour_n of_o the_o first_o low_a water_n or_o ebb_v and_o add_v unto_o the_o say_a hour_n of_o the_o full_a sea_n twelve_o hour_n and_o ⅖_n it_o will_v amount_v unto_o eight_o of_o the_o clock_n and_o ⅕_n part_v of_o a_o hour_n which_o be_v the_o hour_n of_o the_o night_n wherein_o the_o second_o tide_n or_o high_a water_n be_v and_o add_v unto_o this_o second_o tide_n other_o six_o hour_n and_o ⅕_n and_o they_o make_v two_o of_o the_o clock_n in_o the_o morning_n and_o ⅕_n at_o which_o time_n there_o come_v the_o second_o ebb_n or_o low_a sea_n chap._n xxxiii_o of_o a_o certain_a instrument_n whereby_o you_o may_v in_o general_a judge_n of_o the_o tide_n because_o the_o tide_n it_o be_v suppose_v that_o in_o all_o place_n they_o proceed_v from_o the_o motion_n of_o the_o moon_n run_v not_o in_o every_o part_n of_o the_o world_n by_o one_o and_o the_o same_o rumb_n as_o it_o be_v manifest_a in_o the_o channel_n of_o flanders_n and_o in_o all_o the_o coast_n of_o the_o northern_a sea_n which_o be_v a_o matter_n of_o great_a confusion_n and_o difficulty_n to_o mariner_n i_o think_v good_a here_o to_o set_v down_o a_o instrument_n whereby_o the_o day_n of_o the_o moon_n and_o the_o rumb_n whereupon_o the_o moon_n cause_v the_o tide_n in_o every_o part_n be_v know_v they_o may_v judge_v of_o the_o ebb_n and_o flood_n with_o great_a facility_n draw_v upon_o a_o sheet_n of_o paper_n or_o upon_o a_o plate_n of_o tinn_n or_o any_o other_o matter_n a_o circle_n as_o big_a as_o the_o palm_n of_o a_o man_n hand_n and_o half_a a_o finger_n breadth_n within_o that_o circle_n draw_v another_o circle_n and_o have_v divide_v they_o both_o into_o 32_o equal_a part_n with_o line_n draw_v from_o the_o centre_n to_o the_o circumference_n of_o the_o great_a circle_n upon_o the_o upper_a end_n of_o one_o of_o those_o line_n place_v a_o flowerdeluis_a and_o the_o number_n of_o 12_o and_o in_o the_o next_o line_n thereunto_o towards_o the_o left_a hand_n set_v down_o 12_o and_o ¾_n and_o in_o the_o three_o line_n 1_o ½_o and_o so_o proceed_v forward_o put_v down_o upon_o every_o line_n follow_v ¾_n of_o a_o hour_n more_o until_o you_o come_v again_o to_o the_o number_n of_o 12_o in_o the_o low_a line_n and_o from_o thence_o forward_o set_v down_o the_o same_o number_n that_o you_o do_v at_o the_o first_o these_o 32_o line_n so_o draw_v do_v represent_v the_o 32_o wind_n whereby_o the_o sun_n and_o moon_n pass_v every_o day_n and_o so_o you_o may_v set_v down_o the_o name_n of_o the_o principal_a wind_n to_o the_o end_n that_o you_o may_v know_v they_o and_o those_o that_o be_v next_o they_o and_o then_o in_o like_a manner_n make_v another_o round_a and_o slender_a table_n as_o big_a as_o the_o innermost_a circle_n of_o those_o two_o which_o you_o draw_v in_o the_o first_o table_n and_o divide_v it_o into_o thirty_o equal_a part_n first_o into_o two_o by_o a_o line_n divide_v it_o in_o the_o midst_n and_o then_o either_o of_o those_o two_o into_o three_o and_o every_o of_o those_o three_o into_o five_o these_o division_n will_v represent_v the_o day_n of_o the_o moon_n and_o leave_v upon_o 1_o of_o those_o part_n a_o index_n or_o small_a point_n which_o may_v reach_v without_o the_o circle_n set_v down_o the_o number_n thereof_o beginning_n with_o 30_o in_o that_o part_n where_o that_o point_n end_v and_o the_o number_n of_o 1_o in_o the_o line_n follow_v towards_o the_o left_a hand_n and_o then_o 2_o etc._n etc._n till_o you_o end_n at_o the_o same_o point_n with_o 30_o this_o be_v do_v fasten_v with_o a_o thread_n or_o nail_n the_o second_o table_n or_o circle_n upon_o the_o centre_n of_o the_o first_o so_o that_o it_o may_v free_o without_o impediment_n turn_v round_o about_o the_o use_n of_o this_o instrument_n the_o use_n of_o this_o instrument_n be_v that_o know_v in_o every_o port_n or_o part_n of_o any_o coast_n the_o rumb_n or_o quarter_n on_o which_o the_o moon_n make_v full_a sea_n or_o high_a water_n you_o must_v note_v upon_o the_o outward_a circle_n of_o the_o wind_n that_o quarter_n or_o rumb_n and_o place_v the_o tooth_n or_o point_n of_o the_o inner_a circle_n be_v the_o number_n of_o 30_o be_v upon_o that_o quarter_n or_o rumb_n make_v it_o there_o fast_o put_v a_o little_a wax_n underneath_o that_o it_o may_v not_o move_v then_o account_v the_o day_n of_o the_o moon_n age_n in_o the_o inner_a circle_n and_o over_o against_o the_o end_n of_o your_o account_n you_o shall_v see_v in_o the_o uttermost_a circle_n the_o hour_n of_o the_o full_a sea_n of_o that_o day_n together_o with_o the_o rumb_n where_o the_o sun_n be_v at_o that_o hour_n and_o at_o the_o same_o hour_n when_o it_o be_v in_o the_o contrary_a part_n it_o will_v make_v a_o full_a sea_n the_o place_n of_o the_o moon_n at_o the_o hour_n of_o the_o tide_n be_v always_o either_o where_o the_o point_n be_v or_o at_o the_o point_n right_o over_o against_o it_o and_o hence_o you_o may_v easy_o find_v both_o ebb_n also_o this_o little_a instrument_n although_o it_o be_v but_o of_o small_a invention_n be_v of_o great_a use_n and_o profit_n for_o the_o navigation_n of_o flanders_n france_n england_n ireland_n and_o all_o the_o northern_a region_n where_o you_o have_v much_o variety_n in_o the_o tide_n chap._n xxxiiii_o of_o the_o make_n of_o a_o universal_a dial_n which_o may_v serve_v general_o all_o the_o world_n over_o draw_v upon_o a_o table_n or_o pastboord_n the_o circle_n abcd_v upon_o the_o centre_n e_o and_o half_o a_o finger_n breadth_n within_o that_o circle_n upon_o the_o same_o centre_n draw_v another_o circle_n and_o about_o the_o breadth_n of_o a_o wheat_n corn_n within_o the_o second_o circle_n draw_v a_o three_o and_o place_v your_o ruler_n upon_o the_o centre_n e_o by_o the_o right_a line_n ac_fw-la divide_v the_o two_o inner_a circle_n in_o the_o midst_n abc_n and_o cda_n in_o the_o point_n bd_o upon_o which_o and_o upon_o the_o centre_n e_o the_o ruler_n be_v place_v you_o may_v draw_v the_o line_n bd_o whereby_o every_o one_o of_o the_o foresay_a circle_n shall_v be_v divide_v into_o four_o equal_a part_n and_o divide_v every_o one_o of_o those_o four_o quadrant_n of_o the_o inner_a circle_n to_o wit_n ab_fw-la bc_n cd_o da_n into_o 90_o part_n as_o the_o manner_n be_v in_o the_o make_n of_o a_o astrolabe_n set_v number_n thereto_o from_o 5_o to_o 5._o begin_n your_o account_n from_o the_o two_o point_n ac_fw-la and_o so_o procede_v both_o way_n till_o you_o end_v your_o account_n in_o 90_o at_o the_o point_n bd_o and_o this_o inner_a circle_n thus_o divide_v represent_v the_o meridian_n and_o the_o point_n c_o be_v the_o north_n a_o the_o south_n and_o the_o point_n b_o d_o be_v those_o where_o the_o equinoctial_a cut_v the_o meridian_n then_o count_v 23_o degree_n and_o a_o half_a from_o the_o point_n b_o to_o f_o and_o to_o g_o on_o both_o side_n and_o so_o much_o account_n also_o from_o the_o point_n d_o to_o h_n and_o to_o i._o and_o then_o draw_v two_o right_a line_n fh_n and_o give_v the_o line_n fh_n shall_v represent_v the_o tropic_a of_o cancer_n and_o give_v the_o tropic_a of_o capricorn_n and_o those_o two_o line_n shall_v cut_v the_o line_n ca_n which_o be_v the_o axtree_n of_o the_o world_n and_o the_o circle_n of_o six_o of_o the_o clock_n in_o the_o morning_n and_o evening_n upon_o the_o point_v lm_o then_o count_v fifteen_o degree_n from_o c_o towards_o b_o and_o other_o fifteeen_n from_o a_o towards_o b_o and_o place_v your_o ruler_n on_o either_o side_n upon_o the_o end_n of_o your_o account_n you_o shall_v cut_v the_o equinoctial_a bd_o upon_o a_o certain_a point_n which_o shall_v represent_v unto_o you_o seven_o a_o clock_n in_o the_o morning_n and_o five_o of_o the_o clock_n at_o evening_n and_o count_v other_o fifteen_o degree_n on_o both_o side_n more_o towards_o the_o point_n b_o and_o place_v
the_o ruler_n as_o before_o you_o shall_v cut_v the_o line_n bd_o in_o another_o point_n which_o shall_v represent_v eight_o of_o the_o clock_n in_o the_o morning_n and_o four_o in_o the_o afternoon_n and_o account_v high_o fifteen_o degree_n more_o one_o both_o side_n and_o place_v your_o ruler_n upon_o the_o end_n of_o your_o account_n it_o will_v divide_v the_o line_n bd_o at_o another_o point_n which_o shall_v be_v nine_o a_o clock_n in_o the_o morning_n and_o three_o in_o the_o afternoon_n and_o so_o you_o shall_v proceed_v from_o fifteen_o to_o fifteen_o degree_n till_o you_o come_v to_o eleven_o of_o the_o clock_n in_o the_o morning_n and_o one_o in_o the_o afternoon_n and_o if_o you_o will_v have_v the_o half_a hour_n also_o you_o must_v account_v from_o seven_o degree_n and_o a_o half_a to_o seven_o and_o a_o half_a and_o do_v as_o you_o do_v with_o the_o fifteen_o degree_n you_o shall_v have_v the_o half_a hour_n also_o then_o place_v your_o compass_n upon_o the_o centre_n e_o and_o upon_o every_o division_n of_o the_o line_n ebb_v you_o shall_v draw_v the_o same_o division_n likewise_o upon_o the_o line_n ed_z which_o be_v do_v draw_z certain_z obscure_a line_n from_o the_o point_n a_o to_o the_o division_n of_o the_o line_n ebb_v and_o draw_v the_o right_a line_n gf_n see_v where_o gf_n be_v cut_v at_o the_o high_a of_o the_o obscure_a line_n which_o must_v be_v at_o the_o point_n n_o from_o whence_o the_o line_n no_o be_v to_o be_v draw_v equal_o distant_a from_o the_o line_n be._n and_o this_o line_n no_o shall_v be_v divide_v proportional_o by_o the_o obscure_a line_n even_o as_o the_o line_n be._n then_o let_v the_o division_n of_o the_o line_n no_o be_v transfer_v into_o the_o line_n mg_n mi_fw-mi lf_n lh_n and_o then_o the_o tropic_n also_o shall_v be_v divide_v then_o by_o every_o three_o point_n answerable_a in_o the_o equinoctial_a and_o the_o two_o tropic_n you_o shall_v draw_v certain_a part_n of_o circle_n seek_v the_o centre_n of_o those_o three_o point_n in_o the_o equinoctial_a line_n extend_v forth_o on_o either_o side_n and_o these_o part_n of_o circle_n represent_v the_o hour_n then_o make_v a_o account_n of_o the_o degr_n of_o declination_n from_o the_o point_n b_o and_o from_o d_o on_o both_o side_n by_o every_o 2_o degr_n and_o draw_v line_n parallel_v to_o the_o equinoctial_a from_o one_o to_o another_o and_o those_o shall_v be_v the_o parallel_n of_o the_o sun_n declination_n moreover_o you_o shall_v make_v a_o horizon_n as_o large_a as_o the_o diameter_n of_o the_o inner_a circle_n which_o shall_v be_v divide_v after_o this_o manner_n count_n from_o the_o point_n ac_fw-la towards_o b_o five_o degree_n and_o put_v your_o ruler_n upon_o the_o end_n of_o the_o account_n of_o both_o part_n see_v where_o it_o cut_v the_o line_n ebb_n and_o there_o make_v a_o mark_n and_o then_o count_v on_o both_o side_n other_o five_o degree_n and_o put_v the_o ruler_n once_o again_o at_o the_o end_n of_o your_o account_n make_v another_o mark_n where_o it_o cut_v the_o line_n ebb_n and_o so_o the_o line_n ebb_n must_v be_v divide_v from_o five_o to_o five_o degree_n which_o division_n shall_v be_v remove_v into_o the_o say_a horizon_n fasten_v it_o to_o the_o centre_n and_o lay_v it_o to_o the_o line_n bd_o and_o divide_v it_o both_o way_n as_o the_o line_n ebb_n be_v divide_v and_o set_v number_n thereinto_o from_o 5_o to_o 5_o which_o may_v begin_v in_o the_o midst_n and_o end_n with_o 90_o at_o the_o end_n of_o the_o horizon_n and_o let_v every_o one_o of_o these_o part_n be_v divide_v into_o five_o other_o part_n or_o degree_n then_o account_v from_o the_o centre_n e_o in_o the_o horizon_n eleven_o degree_n and_o ¼_n you_o shall_v set_v there_o a_o mark_n which_o shall_v be_v the_o seven_o point_n from_o north_n and_o south_n that_o be_v it_o shall_v represent_v the_o point_n which_o be_v next_o to_o the_o east_n and_o west_n in_o the_o compass_n and_o account_v another_o eleven_o degree_n and_o a_o quarter_n and_o make_v there_o a_o mark_n it_o shall_v represent_v the_o six_o point_n from_o north_n and_o south_n and_o so_o you_o must_v do_v with_o the_o other_o point_n and_o then_o your_o instrument_n be_v finish_v chap._n xxxv_o of_o the_o part_n of_o this_o instrument_n in_o this_o instrument_n the_o first_o thing_n be_v a_o circle_n divide_v into_o 360_o degree_n which_o be_v the_o meridian_n and_o the_o line_n of_o twelve_o a_o clock_n the_o second_o be_v the_o right_a line_n of_o which_o that_o in_o the_o midst_n be_v the_o equinoctial_a and_o the_o two_o other_o be_v the_o tropic_n of_o cancer_n and_o capricorn_n and_o the_o other_o line_n between_o those_o be_v the_o parallel_n of_o the_o sun_n declination_n which_o have_v their_o number_n agreeable_a to_o they_o and_o those_o that_o be_v between_o the_o equinoctial_a and_o the_o tropic_a of_o cancer_n do_v serve_v from_o the_o 11_o of_o march_n to_o the_o 13_o of_o september_n and_o the_o other_o for_o the_o residue_n of_o the_o year_n the_o crooked_a line_n which_o cross_v those_o parallel_n be_v the_o hour_n line_n and_o the_o point_n of_o the_o meridian_n which_o in_o 90_o degree_n distant_a from_o the_o equinoctial_a towards_o the_o left_a hand_n be_v the_o north_n pole_n and_o the_o point_n opposite_a to_o that_o be_v the_o south_n pole_n in_o the_o horizon_n there_o be_v first_o the_o degree_n and_o then_o the_o point_n of_o the_o compass_n distinguish_v by_o the_o small_a prick_v line_n chap._n xxxvi_o how_o you_o may_v know_v what_o a_o clock_n it_o be_v by_o this_o instrument_n at_o any_o time_n of_o the_o day_n when_o you_o will_v know_v what_o a_o clock_n it_o be_v take_v the_o height_n of_o the_o sun_n with_o your_o astrolabe_n and_o seek_v the_o table_n of_o the_o sun_n declination_n what_o declination_n it_o have_v the_o same_o day_n and_o the_o height_n of_o the_o pole_n which_o a_o good_a mariner_n know_v at_o all_o time_n because_o he_o must_v direct_v his_o course_n thereby_o this_o be_v know_v place_v the_o horizon_n instrument_n on_o the_o one_o side_n under_o the_o north_n and_o on_o the_o other_o side_n above_o the_o south_n so_o many_o degree_n as_o his_o distance_n from_o the_o equinoctial_a be_v the_o same_o day_n and_o fasten_v it_o there_o with_o a_o little_a wax_n that_o it_o may_v not_o move_v then_o count_v in_o the_o meridian_n on_o either_o side_n from_o the_o horizon_n which_o now_o stand_v firm_a the_o height_n of_o the_o sun_n above_o the_o horizon_n take_v with_o your_o astrolabe_n and_o by_o the_o end_n of_o the_o account_n draw_v a_o line_n or_o thread_n overthwart_o which_o shall_v be_v equal_o distant_a from_o the_o horizon_n then_o reckon_v the_o sun_n declination_n in_o the_o parallel_n begin_v from_o the_o equinoctial_a of_o the_o instrument_n that_o way_n which_o the_o sun_n decline_v and_o mark_v the_o line_n or_o parallel_v at_o which_o the_o account_n of_o the_o declination_n end_v where_o and_o at_o what_o hour_n it_o be_v cross_v by_o the_o thread_n for_o that_o hour_n be_v the_o hour_n of_o the_o day_n but_o note_v this_o that_o if_o the_o cross_n of_o the_o thread_n and_o parallel_n do_v fall_v upon_o the_o division_n of_o the_o parallel_n and_o of_o the_o hour_n it_o be_v a_o just_a hour_n but_o if_o it_o fall_v beside_o the_o common_a meeting_n of_o the_o parallel_n and_o of_o the_o hour-line_n upon_o that_o side_n where_o it_o fall_v see_v how_o much_o more_o there_o be_v then_o a_o hour_n whether_o ¼_n or_o 1_o â—_o or_o ½_o etc._n etc._n now_o although_o every_o hour_n line_n have_v two_o number_n one_o of_o the_o morning_n and_o another_o of_o the_o afternoon_n yet_o it_o be_v a_o easy_a matter_n to_o distinguish_v which_o of_o they_o will_v serve_v your_o turn_n if_o you_o know_v whether_o your_o observation_n be_v before_o high_a noon_n or_o after_o which_o be_v to_o be_v know_v by_o your_o astrolabe_n for_o if_o the_o sun_n ascend_v it_o be_v before_o noon_n but_o if_o it_o descend_v it_o be_v afternoon_n chap._n xxxvii_o of_o the_o variation_n of_o the_o compass_n by_o this_o instrument_n if_o you_o will_v know_v by_o this_o instrument_n the_o variation_n of_o the_o compass_n you_o must_v do_v thus_o when_o the_o sun_n rise_v or_o go_v down_o at_o the_o horizon_n observe_v he_o with_o your_o compass_n note_v very_o diligent_o upon_o what_o rumb_n and_o part_n of_o the_o rumb_n he_o rise_v or_o fall_v and_o if_o the_o compass_n be_v divide_v into_o 360_o part_n begin_v to_o reckon_v they_o from_o the_o east_n and_o from_o the_o west_n on_o either_o side_n and_o end_v in_o the_o north_n and_o south_n with_o 90_o degree_n it_o shall_v be_v the_o fit_a for_o this_o purpose_n because_o than_o you_o shall_v see_v
subtend_v the_o distance_n of_o those_o two_o place_n take_v therefore_o the_o length_n of_o ge_n with_o the_o compass_n and_o set_v one_o foot_n in_o h_n where_o the_o degree_n begin_v the_o other_o stretch_v forward_o in_o the_o circle_n will_v point_v you_o out_o the_o distance_n of_o saint_n thomas_n island_n and_o london_n 52_o degree_n of_o a_o great_a circle_n and_o about_o one_o half_a that_o be_v 1050_o league_n or_o 3150_o english_a mile_n if_o both_o place_n have_v latitude_n do_v the_o like_a for_o both_o place_n as_o before_o you_o do_v for_o the_o one_o place_n have_v latitude_n till_o you_o have_v cross_v both_o diameter_n with_o perpendicular_o then_o take_v with_o your_o compass_n the_o distance_n of_o those_o cross_n now_o if_o both_o their_o latitude_n be_v of_o one_o denomination_n that_o be_v both_o northerly_a or_o both_o southerly_a and_o equal_a set_v one_o foot_n of_o the_o compass_n where_o the_o degree_n begin_v to_o be_v number_v in_o the_o circle_n and_o 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 that_o be_v 620_o league_n or_o 1860_o mile_n if_o the_o latitude_n be_v not_o both_o equal_a and_o also_o of_o one_o denomination_n leave_v one_o foot_n of_o the_o compass_n in_o the_o cross_n of_o the_o sine_fw-la or_o perpendicular_a descend_v from_o the_o point_n of_o the_o great_a latitude_n with_o the_o other_o foot_n make_v a_o prick_n in_o the_o same_o diameter_n wherein_o that_o cross_n be_v then_o if_o the_o latitude_n be_v both_o of_o one_o denomination_n â—ake_v with_o the_o compass_n the_o length_n of_o the_o perpendicular_a or_o sine_fw-la draw_v from_o the_o point_n of_o the_o lesser_a latitude_n and_o set_v one_o foot_n in_o the_o point_n of_o the_o great_a latitude_n with_o the_o other_o make_v a_o prick_n in_o the_o perpendicular_a descend_v from_o it_o that_o be_v in_o the_o sine_fw-la thereof_o take_v the_o distance_n of_o this_o prick_n from_o the_o former_a make_v in_o the_o diameter_n this_o distance_n transfer_v into_o the_o circle_n as_o in_o the_o first_o example_n will_v give_v you_o the_o distance_n of_o the_o place_n give_v as_o london_n and_o jerusalem_n have_v both_o northerly_a and_o unequal_a latitude_n hierusalems_n latitude_n be_v only_o 32_o degree_n first_o therefore_o note_v in_o the_o circle_n both_o their_o longitude_n the_o longitude_n of_o london_n viz._n 22_o degree_n as_o before_o with_o b_o the_o longitude_n of_o jerusalem_n 68_o degree_n note_v with_o m_n let_v the_o perpendicular_a or_o the_o sin_n of_o the_o latitude_n of_o london_n and_o jerusalem_n of_o and_o no_o be_v draw_v as_o in_o the_o former_a example_n make_v fp_n equal_a to_o of_o and_o pq_n equal_a to_o no_o the_o space_n betwixt_o p_o and_o q_o take_v with_o the_o compass_n and_o then_o both_o foot_n set_v in_o the_o circle_n in_o such_o sort_n as_o in_o the_o first_o example_n be_v show_v shall_v contain_v between_o they_o the_o desire_a distance_n of_o jerusalem_n from_o london_n 38_o degree_n and_o about_o ¾_n that_o be_v 775_o league_n which_o be_v 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 before_o 22_o degree_n the_o latitude_n 51_o degree_n 32_o minute_n from_o both_o these_o longitude_n note_v in_o the_o circle_n with_o b_o and_o r_o draw_v the_o diameter_n as_o before_o bc_n and_o rv_v as_o also_o the_o perpendicular_o or_o sin_n of_o their_o latitude_n of_o and_o it_o be_v make_v fx_n equal_a to_o f_n the_o distance_n of_o those_o sin_n and_o ay_o equal_a to_o st_n the_o sine_fw-la of_o cuscoes_n latitude_n take_v the_o distance_n xy_n between_o the_o foot_n of_o the_o compass_n and_o set_v they_o both_o in_o the_o circumference_n of_o the_o circle_n as_o in_o the_o first_o example_n so_o shall_v you_o find_v that_o there_o be_v betwixt_o london_n and_o cusco_n almost_o 97_o degree_n of_o a_o great_a circle_n that_o be_v 1940_o league_n or_o 5820_o mile_n if_o you_o have_v rather_o keep_v within_o the_o compass_n of_o the_o circle_n make_v the_o perpendicular_a xz_n equal_a to_o st_n and_o proceed_v with_o ez_n as_o you_o do_v before_o with_o xy_n paste_n this_o 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 there_o be_v between_o the_o top_n of_o the_o sin_n of_o hierusalems_n and_o london_n latitude_n in_o the_o globe_n last_o fx_n be_v equal_a to_o f_n the_o distance_n of_o the_o sin_n of_o latitude_n of_o london_n and_o cusco_n in_o peru_n and_o xz_n perpendicular_a to_o fx_v and_o equal_a to_o st_n the_o sine_fw-la of_o cuscoes_n latitude_n as_o of_o be_v the_o sine_fw-la of_o london_n latitude_n and_o perpendicular_a to_o the_o same_o line_n xf_n ez_n to_o which_o xy_n be_v equal_a by_o the_o 6._o c._n 12._o e_fw-la 5_o ram._n 33._o pr._n 1._o eucl._n you_o be_v equal_a and_o parallel_n to_o xz_n must_v needs_o be_v equal_a to_o a_o straight_a line_n extend_v within_o the_o globe_n between_o the_o point_n of_o latitude_n of_o cusco_n and_o london_n now_o out_o of_o this_o demonstration_n it_o be_v a_o easy_a matter_n if_o any_o list_v take_v the_o pain_n to_o be_v so_o curious_a to_o find_v out_o the_o distance_n of_o any_o two_o place_n arithmetical_o by_o the_o doctrine_n of_o 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
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 sun_n on_o land_n the_o instrument_n therefore_o wherewith_o i_o take_v those_o observation_n be_v a_o quadrant_n of_o more_o than_o six_o foot_n and_o a_o quarter_n semidiameter_n for_o the_o room_n wherein_o i_o be_v to_o use_v it_o can_v not_o well_o admit_v a_o great_a quantity_n which_o by_o reason_n of_o his_o largeness_n be_v so_o exact_o make_v and_o divide_v that_o both_o minute_n and_o half_a minute_n may_v therein_o be_v easy_o discern_v the_o limb_n and_o side_n of_o the_o quadrant_n be_v about_o two_o inch_n and_o a_o quarter_n in_o thickness_n the_o breadth_n of_o the_o limb_n about_o four_o inch_n the_o breadth_n of_o the_o side_n about_o two_o inch_n and_o a_o half_a in_o the_o midst_n of_o the_o end_n of_o one_o side_n of_o this_o quadrant_n be_v two_o round_a hole_n make_v in_o either_o end_n one_o whereby_o the_o quadrant_n be_v hang_v like_o a_o gate_n on_o his_o hinge_n upon_o two_o round_a pin_n fit_v to_o those_o hole_n and_o fix_v in_o the_o end_n of_o a_o 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