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35_o second_n the_o difference_n of_o the_o declination_n in_o 24_o hour_n at_o that_o time_n 22_o minute_n 13_o seconds_z now_o as_o 360_o be_v to_o 22_o minute_n 13_o second_o so_o be_v 90_o degree_n to_o 5_o minute_n 33_o second_n the_o part_n proportional_a or_o equation_n desire_v which_o because_o the_o declination_n increase_v and_o the_o bay_n of_o mexico_n be_v also_o westward_o from_o the_o meridian_n of_o london_n must_v be_v add_v to_o the_o declination_n before_o find_v in_o the_o table_n and_o so_o shall_v you_o have_v the_o true_a declination_n of_o the_o sun_n that_o day_n at_o noon_n for_o that_o place_n 7_o degr_n 45_o min._n 8_o sec._n but_o admit_v you_o have_v sail_v eastward_n and_o be_v in_o the_o east_n indian_a ocean_n sea_n differ_v likewise_o in_o longitude_n from_o london_n about_o 90_o deg_n therefore_o the_o difference_n of_o declination_n and_o the_o part_n proportional_a thereof_o or_o equation_n of_o the_o declination_n shall_v be_v the_o same_o they_o 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right_a side_n 41_o 38_o 2_o 56_o 2_o the_o goat_n or_o wagoner_n leave_v shoulder_n 44_o 30_o 4_o 49_o 1_o the_o wagoner_n right_a shoulder_n 45_o 11_o 5_o 30_o 2_o the_o first_o in_o the_o great_a bear_v forefoot_n 40_o 30_o 8_o 24_o 3_o the_o second_o in_o the_o same_o foot_n 41_o 28_o 8_o 32_o 3_o in_o her_o former_a left_a knee_n 36_o 37_o 8_o 58_o 3_o the_o great_a bear_v side_n 31_o 26_o 10_o 58_o 2_o the_o great_a bear_n back_o 26_o 05_o 10_o 40_o 2_o the_o end_n of_o the_o dragon_n tail_n 18_o 26_o 11_o 08_o 3_o the_o great_a bear_v thigh_n 34_o 03_o 11_o 32_o 2_o the_o great_a bear_v rump_n 30_o 41_o 11_o 54_o 2_o the_o next_o to_o the_o end_n of_o the_o dragon_n tail_n 17_o 57_o 12_o 14_o 3_o the_o first_o in_o the_o great_a bear_v tail_n next_o her_o rump_n 31_o 49_o 12_o 32_o 2_o the_o middlemost_a in_o her_o tail_n 32_o 55_o 13_o 06_o 2_o in_o the_o end_n of_o her_o tail_n 38_o 37_o 13_o 32_o 2_o the_o next_o before_o the_o turn_n of_o the_o dragon_n tail_n 23_o 40_o 13_o 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the_o meridian_n to_o this_o end_n there_o be_v table_n publish_v and_o almost_o in_o every_o mariner_n hand_n pretend_v to_o show_v at_o what_o hour_n and_o minute_n every_o star_n in_o the_o first_o of_o these_o two_o former_a table_n come_v to_o the_o meridian_n for_o the_o beginning_n and_o midst_n of_o every_o month_n in_o the_o year_n agree_v likewise_o in_o every_o error_n one_o with_o another_o but_o because_o these_o error_n breed_v not_o at_o any_o time_n great_a danger_n or_o damage_n to_o the_o mariner_n that_o be_v ware_n of_o they_o then_o to_o make_v he_o watch_v for_o their_o come_n to_o the_o meridian_n a_o quarter_n or_o half_o a_o hour_n long_o than_o otherwise_o he_o need_v this_o inconvenience_n only_o provide_v for_o those_o table_n may_v serve_v the_o turn_n well_o enough_o for_o they_o that_o list_v not_o trouble_v themselves_o to_o learn_v a_o better_a way_n but_o for_o they_o that_o be_v desirous_a of_o a_o more_o true_a and_o general_a way_n i_o have_v also_o 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you_o will_v observe_v the_o star_n about_o the_o pole_n which_o never_o set_v to_o know_v the_o time_n of_o their_o come_n to_o the_o nether_a part_n of_o the_o meridian_n which_o may_v easy_o be_v do_v only_o by_o add_v 12_o hour_n to_o the_o time_n of_o their_o come_n to_o the_o upper_a part_n of_o the_o meridian_n if_o it_o be_v less_o than_o 12_o hour_n or_o by_o subtract_v as_o much_o if_o it_o be_v more_o suppose_v for_o example_n the_o 25_o of_o february_n 1599_o i_o will_v know_v the_o time_n of_o the_o great_a dog_n come_v to_o the_o meridian_n first_o therefore_o in_o the_o next_o table_n follow_v the_o column_n descend_v from_o february_n downward_o and_o the_o line_n proceed_v from_o the_o 25_o day_n towards_o the_o right_a hand_n in_o the_o common_a meeting_n of_o they_o both_o i_o find_v 23_o hour_n 10_o min._n the_o sun_n right_a ascension_n that_o day_n at_o noon_n then_o in_o the_o first_o table_n of_o fix_a star_n i_o find_v the_o great_a dog_n right_a ascension_n 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right_a ascension_n add_v 24_o hour_n and_o from_o the_o sum_n 38_o hour_n 24_o min._n subtract_v the_o sun_n right_a ascension_n 18_o hour_n 36_o min_fw-mi so_fw-mi there_o shall_v remain_v 20_o hour_n 18_o min._n the_o time_n of_o the_o foremost_a guard_n come_v to_o the_o upper_a part_n of_o the_o meridian_n from_o which_o subtract_v 12_o so_o you_o have_v the_o time_n when_o it_o come_v to_o the_o nether_a part_n of_o the_o meridian_n 8_o hour_n 18_o min._n after_o noon_n a_o table_n of_o the_o sun_n right_a ascension_n in_o hour_n and_o minute_n for_o every_o day_n of_o the_o year_n  _fw-fr january_n february_n march_v april_n may_v june_n d._n h._n m._n h._n m._n h._n m._n h._n m._n h._n m._n h._n m._n 1_o 19_o 30_o 21_o 39_o 23_o 25_o 1_o 18_o 3_o 11_o 5_o 15_o 2_o 19_o 34_o 21_o 43_o 23_o 28_o 1_o 22_o 3_o 15_o 5_o 19_o 3_o 19_o 39_o 21_o 47_o 23_o 32_o 1_o 26_o 3_o 19_o 5_o 25_o 4_o 19_o 43_o 21_o 50_o 23_o 36_o 1_o 29_o 3_o 23_o 5_o 27_o 5_o 19_o 47_o 21_o 54_o 23_o 40_o 1_o 33_o 3_o 27_o 5_o 31_o 6_o 19_o 52_o 21_o 58_o 23_o 44_o 1_o 36_o 3_o 30_o 5_o 36_o 7_o 19_o 56_o 22_o 02_o 23_o 47_o 1_o 40_o 3_o 34_o 5_o 40_o 8_o 20_o 00_o 22_o 06_o 23_o 51_o 1_o 43_o 3_o 38_o 5_o 45_o 9_o 20_o 04_o 22_o 09_o 23_o 55_o 1_o 47_o 3_o 42_o 5_o 49_o 10_o 20_o 08_o 22_o 14_o 23_o 58_o 1_o 51_o 3_o 46_o 5_o 53_o 11_o 20_o 13_o 22_o 18_o 0_o 02_o 1_o 55_o 3_o 50_o 5_o 57_o 12_o 20_o 17_o
excuse_v for_o find_v a_o fault_n herein_o and_o not_o amend_v it_o at_o this_o time_n and_o that_o so_o much_o the_o rather_o because_o that_o according_a to_o promise_v make_v in_o the_o first_o edition_n of_o this_o book_n i_o will_v now_o show_v the_o mean_n how_o by_o observation_n of_o the_o polestar_n and_o guard_n to_o find_v present_o the_o height_n of_o the_o pole_n not_o only_a when_o the_o fore-guard_n be_v in_o some_o one_o of_o those_o eight_o principal_a position_n beforementioned_a as_o the_o manner_n have_v be_v hitherto_o but_o in_o any_o other_o position_n also_o and_o at_o any_o time_n of_o the_o night_n when_o the_o polestar_n and_o guard_n may_v be_v see_v and_o that_o without_o any_o allowance_n or_o abatement_n give_v or_o take_v by_o addition_n or_o subtraction_n of_o any_o equation_n in_o regard_n of_o the_o pole-star_n be_v high_o or_o low_a than_o the_o pole_n all_o which_o beside_o divers_a other_o pleasant_a and_o profitable_a conclusion_n may_v easy_o 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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
clavius_n his_o gross_a demonstration_n hereof_o 90_o a_o more_o exact_a demonst_a with_o the_o practice_n thereof_o 92_o the_o angle_n of_o dip_v for_o any_o height_n of_o the_o eye_n 96_o 3_o error_n by_o the_o parallax_n of_o the_o sun_n correct_v 96_o 4_o error_n in_o observe_v by_o the_o refraction_n of_o the_o sun_n or_o star_n correct_v 97_o chap._n 16·_a fault_n amend_v in_o the_o table_n of_o the_o sun_n declination_n common_o call_v the_o regiment_n of_o the_o sun_n 97_o chap._n 17._o of_o the_o table_n of_o declination_n of_o every_o minute_n of_o the_o ecliptic_a in_o degree_n min._n and_o sec._n make_v according_a to_o the_o great_a obliquity_n of_o the_o zodiac_n this_o present_a age_n which_o by_o exact_a observation_n be_v find_v to_o be_v 23_o degree_n 31_o min._n and_o a_o half_a 98_o a_o table_n of_o the_o declination_n of_o every_o minute_n of_o the_o ecliptic_a in_o degree_n min._n and_o sec._n 101_o chap._n 18._o the_o use_n of_o the_o former_a table_n of_o declination_n 116_o chap._n 19_o the_o description_n and_o use_n of_o a_o great_a quadrant_n for_o observation_n of_o the_o sun_n on_o land_n 120_o a_o table_n of_o observation_n of_o the_o sun_n meridian_n altitude_n take_v by_o the_o foresay_a quadrant_n in_o the_o year_n 1594_o 1595_o 1596_o 1597_o at_o london_n  _fw-fr chap._n 20._o the_o find_n of_o the_o sun_n apogeum_n and_o eccentricity_n out_o of_o the_o former_a observation_n 142_o to_o know_v the_o time_n of_o the_o sun_n come_v to_o any_o point_n of_o the_o ecliptic_a 142_o chap._n 21._o the_o middle_a motion_n of_o the_o sun_n correct_v out_o of_o the_o former_a observation_n 150_o a_o table_n of_o the_o sun_n middle_a motion_n 152_o chap._n 22._o a_o new_a theoric_n of_o the_o sun_n for_o the_o make_n of_o the_o table_n of_o the_o sun_n prosthaphaereses_n 154_o a_o table_n of_o the_o sun_n prosthaphaereses_n 157_o chap._n 23._o the_o make_n of_o the_o ephemerides_n of_o the_o sun_n 159_o chap._n 24._o how_o to_o reduce_v the_o apparent_a time_n to_o the_o equal_a time_n answer_v thereto_o 162_o a_o table_n of_o the_o aequation_n of_o natural_a day_n 162_o chap._n 25._o a_o table_n of_o aequation_n of_o the_o sun_n ephemerides_n to_o make_v they_o serve_v for_o many_o year_n 163_o ephemerides_n of_o the_o sun_n 164_o chap._n 26._o the_o use_n of_o these_o ephemerides_n 169_o chap._n 27._o the_o make_n of_o the_o table_n of_o the_o sun_n declination_n 170_o prosthaphaereses_n of_o the_o sun_n declination_n 172_o a_o table_n of_o the_o sun_n declination_n 173_o chap._n 28·_a the_o use_n of_o the_o former_a table_n of_o declination_n or_o regiment_n of_o the_o sun_n 181_o chap._n 29_o the_o declination_n of_o the_o principal_a fix_a star_n about_o the_o equinoctial_a correct_v by_o observation_n 183_o a_o table_n of_o fix_a star_n about_o the_o equinoctial_a 198_o chap._n 30._o the_o use_n of_o the_o former_a table_n 199_o chap._n 31._o the_o true_a distance_n of_o certain_a principal_a fix_a star_n from_o the_o north_n pole_n find_v by_o late_a observation_n 199_o chap._n 32._o to_o know_v at_o what_o time_n any_o of_o the_o foresay_a fix_a star_n come_v to_o the_o meridian_n for_o any_o day_n of_o the_o year_n 202_o a_o table_n of_o the_o sun_n right_a ascension_n in_o hour_n and_o minute_n for_o every_o day_n of_o the_o year_n 204_o chap._n 33._o by_o the_o former_a table_n of_o fix_a star_n and_o the_o sun_n right_a ascension_n to_o know_v the_o hour_n of_o the_o night_n at_o any_o time_n of_o the_o year_n 206_o chap._n 34._o of_o find_v the_o elevation_n of_o the_o pole_n by_o observation_n of_o the_o pole_n star_n and_o guard_n 207_o chap._n 35._o the_o description_n and_o part_n of_o the_o sea_n quadrant_n 208_o chap._n 36._o the_o description_n of_o the_o nocturnal_a or_o night_n dial_n 210_o chap._n 37._o the_o use_n of_o the_o sea_n quadrant_n first_o in_o observe_v the_o height_n of_o the_o sun_n look_v only_o to_o the_o horizon_n at_o sea_n 211_o chap._n 38._o how_o with_o this_o quadrant_n to_o observe_v the_o height_n of_o the_o sun_n with_o â—our_n back_o turn_v towards_o the_o sun_n 211_o chap._n 39_o how_o to_o observe_v with_o this_o quadrant_n the_o height_n of_o the_o sun_n or_o star_n look_v both_o to_o the_o sun_n or_o star_n and_o to_o the_o horizon_n 212_o chap_n 40._o how_o to_o find_v the_o height_n of_o the_o pole_n by_o observation_n of_o the_o polestar_n and_o guard_n without_o give_v or_o take_v any_o allowance_n or_o abatement_n at_o any_o time_n when_o the_o polestar_n the_o guard_n and_o horizon_n may_v be_v see_v 213_o to_o know_v the_o hour_n of_o the_o night_n by_o the_o nocturnal_a 213_o a_o answer_n to_o simon_n stevin_n show_v his_o erorr_v in_o blame_v i_o of_o error_n in_o my_o table_n of_o rumb_n 214_o the_o content_n of_o the_o treatise_n of_o the_o art_n of_o navigation_n the_o division_n of_o the_o whole_a art_n of_o navigation_n pag._n 1_o chap._n 1._o the_o definition_n of_o the_o sphere_n 2_o 2._o that_o the_o whole_a world_n be_v a_o sphere_n 2_o 3._o of_o the_o division_n of_o the_o sphere_n 2_o 4._o of_o the_o motion_n of_o the_o heaven_n 4_o 5._o of_o the_o figure_n of_o the_o heaven_n 4_o 6._o that_o the_o earth_n and_o water_n make_v one_o perfect_a globe_n 5_o 7._o that_o the_o earth_n be_v in_o the_o centre_n of_o the_o world_n 5_o 8._o the_o whole_a quantity_n of_o the_o earth_n 5_o 9_o of_o the_o equinoctial_a circle_n 6_o 10._o of_o the_o pole_n of_o the_o world_n 6_o 11._o of_o the_o ecliptic_a line_n 7_o 12._o of_o the_o declination_n of_o the_o sun_n 7_o 13._o of_o the_o colour_n 8_o 14._o of_o the_o meridian_n circle_n 8_o 15._o of_o the_o horizon_n 9_o 16._o of_o the_o 32_o wind_n 10_o 17._o of_o the_o two_o tropic_n 12_o 18._o of_o the_o parallel_n 13_o 19_o of_o the_o degree_n 13_o 20._o what_o be_v mean_v by_o longitude_n and_o latitude_n 14_o the_o second_o part_n of_o the_o art_n of_o navigation_n wherein_o be_v handle_v the_o practic_n part_n show_v the_o make_n and_o use_n of_o the_o principal_a instrument_n belong_v to_o this_o art_n chap._n 1._o the_o make_n of_o the_o astrolabe_n pag._n 15_o chap._n 2._o of_o the_o height_n of_o the_o sun_n pag._n 17_o 3._o of_o the_o shadow_n 18_o 4._o of_o the_o regiment_n and_o rule_n of_o the_o sun_n 19_o 5._o of_o the_o declination_n of_o the_o sun_n and_o of_o the_o table_n thereof_o 20_o how_o the_o declination_n of_o the_o sun_n may_v be_v find_v out_o 21_o 6._o the_o equation_n of_o the_o sun_n declination_n 22_o 7._o four_o example_n for_o the_o plain_a declaration_n of_o that_o which_o be_v say_v before_o 22_o 8._o another_o manner_n of_o account_v by_o the_o sun_n as_o they_o use_v in_o portugal_n 25_o 9_o how_o the_o height_n of_o the_o sun_n may_v be_v know_v in_o any_o place_n whatsoever_o without_o a_o astrolabe_n first_o know_v your_o distance_n from_o the_o equinoctial_a 25_o 10._o the_o rule_n or_o regiment_n of_o the_o north-star_n for_o the_o knowledge_n of_o the_o height_n of_o the_o pole_n 26_o 11._o the_o make_n of_o the_o crosse-staffe_n 27_o 12._o of_o the_o position_n of_o the_o north-star_n and_o the_o guard_n 28_o 13._o of_o the_o height_n of_o the_o star_n take_v with_o the_o crosse-staffe_n 30_o 14._o the_o regiment_n or_o rule_n of_o the_o north_n star_n 30_o 15._o other_o thing_n to_o be_v note_v in_o observe_v the_o height_n of_o the_o pole_n 32_o 16._o of_o the_o crosier_n 34_o 17._o of_o the_o sea-compasse_n 34_o 18._o how_o the_o variation_n of_o the_o compass_n may_v be_v find_v 37_o the_o find_v of_o the_o meridian_n line_n 37_o 19_o of_o the_o sea-chart_n 38_o 20._o of_o the_o point_n of_o imagination_n 41_o 21._o of_o the_o traverse_n or_o geometrical_a point_n 42_o 22._o of_o the_o amend_v of_o the_o point_n of_o imagination_n 42_o the_o amend_v of_o the_o point_n of_o imagination_n by_o the_o traverse_n point_n 43_o the_o amendment_n of_o the_o point_n of_o imagination_n by_o north_n south_n east_n west_n 43_o 23._o the_o point_n by_o imagination_n and_o the_o height_n 44_o 24._o what_o it_o be_v to_o increase_v or_o diminish_v in_o height_n 45_o 25._o how_o you_o may_v cast_v a_o traverse_n point_n without_o compass_n 46_o 26._o of_o another_o kind_n of_o cast_v a_o point_n by_o traverse_n 46_o 27._o of_o the_o league_n which_o in_o navigation_n answer_v to_o each_o degree_n of_o latitude_n in_o every_o rumb_n 47_o chap._n 28._o how_o you_o may_v come_v to_o know_v the_o longitude_n or_o the_o course_n from_o east_n to_o west_n pag_n 48_o 29._o how_o you_o may_v set_v down_o in_o your_o chart_n a_o new_a land_n never_o before_o discover_v 50_o 30._o see_v two_o know_a point_n or_o cape_n of_o land_n as_o you_o sail_v along_o
0_o 0_o 56_o 15_o about_o midway_n betwixt_o lisbon_n and_o saint_n micâ—â—â—ls_v even_o 0_o 0_o 61_o 40_o wnw_n 0_o 0_o 73_o 7_o betwixt_o s._n michael_n &_o tercaera_n e_o by_o n_o â…•_n n_o 2_o 0_o 70_o 52_o about_o 3._o leag_n from_o tercaera_n ssw_n e_o by_o n_o ¼_n n_o 2_o 30_o 70_o 53_o at_o saint_n cruz_n in_o flores_n  _fw-fr 29_o 25_o 83_o 30_o these_o observation_n make_v in_o the_o town_n of_o fayal_n and_o the_o former_a also_o at_o s._n cruz_n in_o flores_n be_v take_v by_o m._n william_n borowe_n instrument_n of_o variation_n publish_v in_o his_o book_n of_o the_o variation_n of_o the_o compass_n and_o by_o a_o quadrant_n who_o semidiameter_n be_v almost_o three_o foot_n  _fw-fr 18_o 0_o 73_o 0_o  _fw-fr 16_o 36_o 74_o 40_o  _fw-fr 20_o 30_o 62_o 20_o  _fw-fr 20_o 0_o 62_o 54_o  _fw-fr 19_o 20_o 63_o 35_o  _fw-fr 18_o 16_o 64_o 45_o  _fw-fr 30_o 41_o 57_o 15_o  _fw-fr 46_o 13_o 17_o 53_o  _fw-fr 46_o 18_o 16_o 36_o  _fw-fr 40_o 42_o 32_o 45_o or_o 4_o league_n from_o tercaera_n see_fw-la ease_n ¼_n e_o 0_o 0_o 75_o 50_o from_o s._n mary_n w_n by_o saint_n 6_o league_n wsw_n 13_o 0_o 61_o 50_o from_o s._n mary_n w_n by_o saint_n 6_o league_n w_n by_o saint_n ½_o 0_o 0_o 67_o 25_o from_o s._n mary_n south_n 5._o league_n ease_n ½_o s_o 0_o 0_o 69_o 30_o from_o saint_n mary_n 16_o league_n ease_n ¼_n e_o 0_o 0_o 75_o 50_o nw_n by_o w_n northerly_a ease_n 2_o 30_o 73_o 7_o ½_o from_o s._n george_n se_n by_o e_z 3_o leag_fw-mi ease_n ¼_n e_o 0_o 0_o 75_o 50_o from_o the_o east_n part_n of_o s._n michael_n wsw_n ¼_n s_o 0_o 0_o 59_o 0_o ne_fw-fr by_o n_o about_z 15_o or_o 20_o leag_n ease_n ¼_n e_o 0_o 0_o 70_o 23_o from_o the_o rock_n w_n about_o 66_o leag_n see_fw-la by_o saint_n â…™_n s_o 26_o  _fw-fr 37_o 30_o from_o c._n finisterre_n n_o easterly_a ease_n ½_o s_o 0_o  _fw-fr 67_o 30_o ease_n â…”_n s_o 2_o  _fw-fr 65_o 37_o sweet_z 11_o  _fw-fr 39_o 22_o the_o time_n of_o observation_n the_o latitude_n of_o the_o place_n of_o observation_n the_o declination_n of_o the_o sun_n the_o true_a azimuth_n of_o the_o sun_n the_o variation_n of_o the_o compass_n the_o middle_a variation_n the_o part_n of_o variation_n  _fw-fr  _fw-fr de._n mi_fw-mi de._n mi_fw-mi de._n mi_fw-mi de._n mi_fw-mi de._n min._n  _fw-fr jul._n 9_o a_fw-la 39_o 50_o 20_o 53_o 62_o 0_o 7_o 30_o  _fw-fr  _fw-fr eastward_o 12_o bn_n 39_o 0_o 20_o 25_o 63_o 20_o 6_o 45_o  _fw-fr  _fw-fr eastward_o 23_o bn_n 38_o 0_o 17_o 55_o 67_o 0_o 5_o 20_o 5_o 38_o eastward_o 23_o a_o 38_o 0_o 17_o 46_o 67_o 10_o 5_o 57_o eastward_o aug_n 8_o b_o n_o 38_o 20_o 13_o 13_o 74_o 10_o 3_o 18_o  _fw-fr  _fw-fr eastward_o 9_o bn_n 38_o 20_o 12_o 54_o 75_o 0_o 4_o 7_o  _fw-fr  _fw-fr eastward_o 14_o a_o 39_o 50_o 11_o 5_o 79_o 30_o 4_o 0_o  _fw-fr  _fw-fr westward_a se._n 13_o a_fw-la 38_o 54_o 0_o 8_o 74_o 35_o 1_o 35_o 3_o 5_o eastward_o 13_o a_o 38_o 54_o 0_o 9_o 76_o 0_o 1_o 20_o eastward_o 22_o a_o 38_o 54_o 3_o 39_o 67_o 10_o 4_o 50_o eastward_o 22_o a_o 38_o 54_o 3_o 39_o 67_o 30_o 4_o 36_o eastward_o 22_o a_o 38_o 54_o 3_o 30_o 68_o 15_o 4_o 40_o eastward_o 22_o a_o 38_o 54_o 3_o 40_o 69_o 20_o 4_o 35_o eastward_o 23_o bn_n 38_o 54_o 3_o 53_o 54_o 20_o 2_o 55_o eastward_o 23_o bn_n 38_o 54_o 3_o 54_o 14_o 0_o 3_o 53_o eastward_o 23_o bn_n 38_o 54_o 3_o 54_o 13_o 30_o 3_o 6_o eastward_o 23_o a_o 38_o 54_o 4_o 0_o 35_o 15_o 2_o 30_o eastward_o oc._n 18_o bn_n 38_o 20_o 13_o 5_o 73_o 0_o 2_o 5_o  _fw-fr  _fw-fr eastward_o 23_o a_o 37_o 0_o 14_o 50_o 60_o 0_o 1_o 50_o 0_o 55_o westward_n 23_o a_fw-la 37_o 0_o 14_o 51_o 71_o 5_o 3_o 40_o eastward_o 24_o bn_n 37_o 0_o 15_o 2_o 70_o 50_o 3_o 20_o westward_n 26_o bn_n 37_o 30_o 15_o 38_o 69_o 50_o 6_o 0_o 5_o 34_o eastward_o 26_o bn_n 37_o 30_o 15_o 39_o 68_o 0_o 5_o 7_o eastward_o 28_o bn_n 38_o 40_o 16_o 16_o 68_o 45_o 7_o 5_o  _fw-fr  _fw-fr eastward_o no._n 1_o a_fw-la 38_o 40_o 17_o 30_o 67_o 10_o 8_o 10_o  _fw-fr  _fw-fr eastward_o 2_o bn_n 38_o 40_o 17_o 41_o 66_o 50_o 3_o 33_o  _fw-fr  _fw-fr eastward_o 6_o bn_n 38_o 35_o 18_o 43_o 31_o 0_o 6_o 30_o  _fw-fr  _fw-fr eastward_o 12_o bn_n 44_o 25_o 20_o 5_o 61_o 0_o 6_o 30_o 7_o 4_o eastward_o 12_o bn_n 44_o 25_o 20_o 5_o 58_o 0_o 7_o 37_o eastward_o 12_o a_o 44_o 30_o 20_o 11_o 46_o 15_o 6_o 52_o eastward_o notwithstanding_o there_o be_v much_o difference_n betwixt_o some_o of_o these_o variation_n take_v at_o the_o same_o place_n with_o the_o same_o instrument_n yet_o we_o use_v with_o what_o diligence_n we_o can_v such_o instrument_n as_o then_o we_o have_v prepare_v for_o that_o purpose_n which_o i_o speak_v that_o other_o that_o shall_v go_v about_o hereafter_o to_o observe_v the_o variation_n at_o sea_n especial_o may_v be_v the_o more_o circumspect_a to_o foresee_v and_o prevent_v all_o cause_n of_o error_n herein_o exact_a truth_n among_o the_o unconstant_a wave_n of_o the_o sea_n be_v not_o to_o be_v look_v for_o though_o good_a instrument_n be_v never_o so_o well_o apply_v to_o their_o use_n yet_o with_o heedful_a diligence_n we_o may_v come_v so_o near_o the_o truth_n as_o the_o nature_n of_o the_o sea_n and_o of_o our_o sight_n and_o instrument_n will_v give_v we_o leave_v neither_o if_o there_o be_v some_o disagreement_n betwixt_o observation_n be_v they_o all_o by_o and_o by_o to_o be_v reject_v but_o as_o when_o many_o arrow_n be_v shoot_v at_o a_o mark_n and_o the_o mark_n afterward_o take_v away_o he_o may_v be_v think_v to_o work_v according_a to_o reason_n who_o to_o find_v the_o place_n where_o the_o mark_n stand_v shall_v seek_v out_o the_o middle_a place_n among_o all_o the_o arrow_n so_o among_o many_o different_a observation_n the_o middlemost_a be_v like_a to_o come_v near_o the_o truth_n cause_n of_o error_n herein_o some_o can_v be_v avoid_v as_o the_o unsteadinesse_n of_o the_o ship_n the_o imperfection_n of_o the_o sense_n and_o instrument_n the_o weak_a respective_a force_n of_o the_o needle_n or_o wire_n be_v they_o never_o so_o well_o touch_v other_o may_v be_v eschew_v as_o that_o there_o be_v no_o iron_n near_o the_o compass_n in_o the_o time_n of_o observation_n that_o the_o wire_n be_v keep_v clean_o from_o rust_n and_o that_o they_o be_v not_o keep_v too_o long_o untouched_a from_o the_o stone_n that_o such_o instrument_n be_v use_v for_o observation_n as_o need_v least_o work_n afterward_o for_o find_v out_o the_o variation_n wherein_o the_o instrument_n heretofore_o publish_v for_o this_o purpose_n be_v faulty_a be_v such_o as_o serve_v for_o observation_n only_a oâ—_n land_n as_o also_o require_v many_o work_n afterward_o unfit_a for_o mariner_n before_o the_o matter_n can_v come_v to_o issue_n wherein_o be_v as_o many_o lurk_a hole_n of_o error_n without_o great_a diligence_n i_o have_v therefore_o here_o set_v down_o the_o make_n and_o use_n of_o a_o certain_a instrument_n whereby_o the_o variation_n of_o the_o compass_n and_o time_n of_o the_o day_n be_v present_o give_v together_o with_o the_o observation_n the_o latitude_n of_o the_o place_n be_v know_v and_o that_o universal_o throughout_o the_o world_n both_o at_o sea_n and_o land_n as_o also_o the_o variation_n be_v give_v the_o height_n of_o the_o pole_n and_o hour_n of_o the_o day_n may_v thereby_o be_v know_v without_o those_o inconvenience_n wherewith_o martin_n curtis_n his_o instrument_n chap._n 11._o part_n 3._o of_o the_o art_n of_o navigation_n and_o michael_n coignet_n his_o nautical_a hemisphere_n be_v much_o encumber_v to_o omit_v the_o observation_n of_o the_o height_n of_o the_o sun_n which_o as_o i_o have_v oft_o make_v trial_n at_o sea_n may_v thereby_o be_v more_o exact_o perform_v then_o have_v be_v hitherto_o by_o staff_n ring_n or_o astrolabe_n as_o they_o be_v common_o use_v the_o make_n of_o the_o searing_n the_o figure_n of_o the_o searings_a upon_o the_o concave_a side_n of_o the_o innermost_a ring_n let_v be_v describe_v the_o degree_n of_o the_o sun_n declination_n for_o the_o right_n place_v of_o the_o little_a bead_n upon_o the_o thread_n according_a to_o the_o time_n of_o the_o year_n which_o may_v easy_a be_v do_v after_o this_o manner_n the_o bead_n be_v thus_o right_o place_v put_v aside_o the_o equinoctial_a ring_n from_o the_o brass_n pointer_n represent_v the_o pole_n actick_a that_o it_o may_v cross_v the_o meridian_n at_o right_a angle_n which_o it_o shall_v precise_o do_v if_o you_o bring_v the_o prick_n or_o little_a hole_n upon_o the_o outside_n of_o the_o
41_o 12_o 49_o 53_o 26_o 11_o 36_o 26_o 5_o 0_o 6_o 36_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 3_o 36_o 9_o 9_o ♎_o 3_o 26_o 8_o ♎_o 57_o 0_o 6_o 26_o 6_o 42_o 5_o 16_o 59_o 57_o 16_o 51_o 0_o 8_o 57_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 8_o 57_o 54_o 22_o 58_o 13_o 22_o 48_o 0_o 10_o 13_o 11_o 8_o 15_o 28_o 56_o 34_o 28_o 46_o 0_o 10_o 34_o 11_o 50_o 55_o 0_o â™_o 57_o 28_o 0_o â™_o 45_o 0_o 12_o 28_o 15_o 12_o 37_o 11_o 5_o 41_o 10_o 46_o 0_o 19_o 41_o 16_o 17_o 10_o 14_o 4_o 23_o 13_o 46_o 0_o 18_o 23_o 16_o 43_o 19_o 16_o 7_o 30_o 15_o 47_o 0_o 20_o 30_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 8_o 5_o 58_o 21_o 6_o 26_o 20_o 48_o 0_o 18_o 26_o 16_o 9_o 0_o 25_o 16_o 16_o 24_o 50_o 0_o 26_o 16_o 22_o 7_o 55_o 10_o â™_o 42_o 36_o 10_o â™_o 1_o 0_o 41_o 36_o chap._n xx._n the_o find_n of_o the_o sun_n apogeum_n and_o eccentricitie_n out_o of_o the_o former_a observation_n now_o by_o the_o whole_a course_n of_o these_o observation_n it_o manifest_o appear_v that_o the_o declination_n set_v down_o in_o the_o regiment_n of_o the_o sun_n that_o be_v and_o have_v be_v hitherto_o ordinary_o use_v by_o our_o seaman_n do_v for_o the_o most_o part_n notable_o err_v from_o the_o truth_n of_o the_o heaven_n which_o error_n as_o they_o may_v most_o true_o be_v correct_v by_o observation_n only_o in_o those_o day_n wherein_o certain_a observation_n be_v make_v so_o for_o find_v out_o the_o declination_n of_o the_o middle_a day_n between_o the_o observation_n i_o think_v it_o the_o best_a way_n first_o to_o make_v the_o ephemerides_n of_o the_o sun_n hereafter_o follow_v agreeable_a to_o the_o former_a observation_n and_o then_o to_o find_v out_o the_o declination_n answerable_a to_o the_o place_n of_o the_o sun_n for_o every_o day_n of_o four_o year_n together_o because_o that_o after_o that_o number_n of_o year_n the_o same_o place_n of_o the_o sun_n and_o the_o same_o declination_n return_v again_o without_o sensible_a error_n which_o also_o by_o a_o certain_a equation_n may_v be_v correct_v and_o for_o the_o easy_a find_v out_o of_o this_o equation_n i_o have_v continue_v these_o table_n for_o one_o year_n more_o make_v they_o for_o five_o year_n and_o so_o include_v two_o leap_v year_n by_o the_o difference_n of_o which_o year_n we_o may_v easy_o find_v the_o say_a equation_n by_o mean_n whereof_o these_o table_n may_v be_v make_v serviceable_a for_o many_o year_n first_o therefore_o for_o make_v these_o ephemerides_n it_o be_v needful_a to_o know_v the_o time_n of_o the_o sun_n entrance_n into_o certain_a principal_a point_n of_o the_o zodiac_n as_o also_o the_o time_n of_o the_o sun_n continuance_n in_o the_o arch_n of_o the_o zodiac_n contain_v between_o those_o point_n whereby_o the_o proportion_n of_o the_o sun_n motion_n may_v geometrical_o be_v find_v out_o his_o eccentricitie_n and_o place_n of_o his_o apogeum_n be_v hereby_o know_v to_o know_v the_o time_n of_o the_o sun_n commnig_v to_o any_o point_n of_o the_o ecliptic_a ecliptick·_n it_o be_v best_o to_o observe_v exact_o the_o meridian_n altitude_n of_o the_o sun_n not_o only_o the_o same_o day_n wherein_o he_o be_v like_a to_o enter_v into_o the_o point_n desire_v but_o every_o day_n also_o for_o two_o or_o three_o day_n together_o both_o before_o and_o after_o that_o day_n that_o both_o by_o the_o testimony_n of_o so_o many_o observation_n compare_v together_o you_o may_v have_v the_o more_o assure_a truth_n as_o also_o that_o if_o the_o day_n you_o most_o desire_n fall_v not_o out_o to_o be_v so_o clear_a as_o you_o will_v wish_v you_o may_v notwithstanding_o by_o the_o observation_n of_o the_o day_n go_v before_o and_o follow_v after_o or_o either_o of_o they_o obtain_v your_o desire_n have_v thus_o observe_v the_o meridian_n altitude_n of_o the_o sun_n and_o thereby_o also_o find_v his_o declination_n for_o every_o one_o of_o those_o day_n wherein_o you_o observe_v you_o shall_v easy_o know_v also_o the_o true_a place_n of_o the_o sun_n in_o every_o each_o one_o of_o the_o same_o day_n with_o help_n of_o the_o former_a table_n of_o the_o declination_n of_o every_o minute_n of_o the_o ecliptic_a in_o such_o sort_n as_o before_o be_v declare_v when_o i_o show_v the_o use_n of_o that_o table_n now_o if_o it_o fall_v out_o so_o happy_o that_o both_o the_o day_n be_v clear_a when_o the_o sun_n enter_v into_o the_o desire_a point_n of_o the_o ecliptic_a and_o that_o the_o place_n of_o the_o sun_n answerable_a to_o the_o declination_n of_o that_o day_n be_v all_o one_o with_o the_o point_n desire_v you_o have_v already_o that_o you_o seek_v for_o without_o any_o more_o ado_n viz._n that_o the_o sun_n enter_v that_o day_n at_o noon_n into_o the_o point_n desire_v otherwise_o subtract_v the_o observe_v place_n of_o the_o sun_n next_o before_o the_o point_n desire_v out_o of_o the_o observe_v place_n of_o the_o sun_n next_o follow_v that_o point_n and_o the_o remainder_n shall_v show_v you_o the_o true_a motion_n of_o the_o sun_n answerable_a to_o the_o time_n between_o those_o observation_n subtract_v also_o the_o former_a place_n of_o the_o sun_n from_o his_o place_n in_o the_o point_n desire_v and_o note_v the_o difference_n for_o as_o the_o former_a remainder_n that_o be_v the_o apparent_a motion_n of_o the_o sun_n between_o the_o observation_n be_v to_o the_o time_n between_o those_o observation_n so_o be_v this_o difference_n to_o the_o time_n between_o the_o first_o observation_n and_o the_o sun_n entrance_n into_o the_o point_n desire_v example_n of_o the_o first_o i_o desire_v to_o know_v the_o time_n of_o the_o sun_n entrance_n into_o 17_o degree_n 0_o min._n of_o ♌_o in_o the_o year_n 1595._o i_o observe_v therefore_o at_o london_n the_o apparent_a height_n of_o the_o sun_n at_o noon_n the_o 31_o of_o july_n the_o same_o year_n and_o find_v it_o to_o be_v 54_o degree_n 14_o minute_n out_o of_o which_o his_o true_a height_n correct_v by_o his_o parallax_n be_v find_v to_o be_v 54_o degr_n 15_o min._n 46_o sec._n whereby_o his_o declination_n be_v gather_v to_o be_v 15._o degree_n 47_o minute_n 46_o sec._n and_o consequent_o his_o place_n in_o 17_o degree_n 0_o minute_n of_o ♌_o that_o day_n at_o noon_n example_n of_o the_o second_o admit_v the_o year_n follow_v 1596_o you_o will_v know_v the_o time_n of_o the_o sun_n entrance_n into_o the_o midst_n of_o taurus_n have_v therefore_o to_o this_o end_n observe_v the_o apparent_a meridian_n altitude_n of_o the_o sun_n the_o 24_o 25_o and_o 26._o day_n of_o april_n in_o that_o year_n within_o the_o space_n of_o which_o day_n i_o be_o sure_a the_o sun_n must_v needs_o be_v in_o that_o point_n to_o be_v 54_o degree_n 35_o minute_n 54_o degree_n 51_o min._n ½_o 55_o degree_n 8_o min._n ½_o and_o consequent_o the_o true_a height_n 54_o degr_n 36_o min._n 44_o sec._n 54_o degr_n 53_o min._n 13_o sec._n 55_o degree_n 10_o min._n 13_o sec_fw-la and_o out_o of_o these_o the_o true_a declination_n 16_o degr_n 8_o min._n 44_o sec._n 16_o degr_n 25_o min._n 13_o sec._n 16._o degr_n 52_o min._n 13._o sec._n hereby_o i_o find_v the_o true_a place_n of_o the_o sun_n the_o same_o day_n to_o be_v 14_o degr_n 9_o min._n 40_o sec._n of_o taurus_n 15_o degr_n 5_o min._n 20_o sec._n of_o taurus_n 16_o degr_n 3_o min._n 42_o sec._n of_o taurus_n subtract_v therefore_o 14_o degr_n 9_o min_fw-mi 40_o sec._n of_o taurus_n that_o be_v the_o place_n of_o the_o sun_n the_o 24_o day_n out_o of_o 15_o degr_n 5_o min._n 20_o sec._n of_o taurus_n the_o place_n of_o the_o sun_n the_o 25_o day_n the_o remainder_n shall_v be_v 55_o min._n 40_o sec._n which_o be_v the_o true_a motion_n of_o the_o sun_n between_o the_o 24_o and_o 25._o day_n at_o noon_n that_o be_v the_o diurn_n motion_n of_o the_o sun_n at_o that_o time_n subtract_v also_o 14_o degr_n 9_o min._n 40_o sec._n of_o taurus_n out_o of_o 15_o degr_v 0_o min._n of_o taurus_n the_o difference_n be_v 50_o min._n 20_o sec._n now_o as_o 55_o min._n 40_o sec_fw-la be_v to_o 50_o min._n 20_o sec._n so_o be_v 24_o hour_n to_o 21_o hour_n 42_o min._n and_o 2_o sec_fw-la it_o appear_v therefore_o by_o subtract_v 21_o hour_n 42_o min._n 2_o sec._n out_o of_o 24_o hour_n that_o the_o sun_n shall_v enter_v into_o the_o midst_n of_o taurus_n the_o 25_o day_n about_o two_o hour_n and_o almost_o 18_o min._n before_o noon_n that_o be_v at_o nine_o a_o clock_n and_o 42_o minute_n now_o suppose_v i_o have_v not_o or_o can_v not_o have_v observe_v the_o
25_o day_n i_o may_v notwithstanding_o find_v the_o time_n of_o the_o sun_n entrance_n into_o the_o midst_n of_o taurus_n by_o the_o observation_n of_o the_o 24_o and_o 26_o day_n after_o this_o manner_n subtract_v 14_o degr_n 9_o min._n 40_o sec._n of_o taurus_n out_o of_o 16_o degr_n 3_o min._n 42_o sec._n of_o taurus_n the_o remainder_n will_v be_v one_o degr_n 54_o min._n 2_o sec._n that_o be_v the_o motion_n of_o the_o sun_n for_o two_o day_n between_o the_o 24_o and_o 26_o day_n at_o noon_n therefore_o as_o 1_o degr_n 54_o min._n be_v to_o 48_o hour_n so_o be_v 50_o min._n 20_o sec._n that_o be_v the_o difference_n of_o the_o place_n of_o the_o sun_n the_o 24_o day_n from_o the_o midst_n of_o taurus_n find_v out_o as_o before_o to_o 21_o hour_n and_o 12._o min._n almost_o so_o as_o hereby_o it_o seem_v the_o sun_n shall_v enter_v into_o the_o midst_n of_o taurus_n the_o 25_o day_n about_o two_o hour_n and_o 48_o minute_n before_o noon_n that_o be_v at_o nine_o of_o the_o clock_n and_o 12_o minute_n but_o if_o it_o so_o fall_v out_o that_o you_o do_v not_o or_o can_v observe_v both_o before_o and_o after_o the_o time_n of_o the_o sun_n come_v to_o the_o point_n desire_v as_o suppose_v i_o can_v not_o have_v observe_v the_o 24_o day_n but_o only_o the_o 25_o and_o 26_o day_n in_o both_o which_o day_n the_o sun_n be_v go_v past_o the_o point_n desire_v notwithstanding_o you_o may_v obtain_v your_o desire_n thus_o subtract_v 15_o degr_n 5_o min._n 20_o sec_fw-la taurus_n the_o place_n of_o the_o sun_n the_o 25_o day_n out_o of_o 16_o degr_n 3_o min._n 42_o sec._n taurus_n the_o place_n of_o the_o sun_n the_o 26_o day_n there_o will_v remain_v 58_o min._n 22_o sec._n the_o diurn_n motion_n of_o the_o sun_n between_o the_o noon-tide_n of_o the_o 25_o and_o 26_o day_n now_o because_o that_o on_o the_o 25_o day_n at_o noon_n the_o sun_n be_v go_v 5_o min._n 20_o sec._n past_o the_o point_n desire_v therefore_o as_o 58._o min._n 20_o sec._n be_v to_o 24_o hour_n so_o be_v 5_o min._n 20_o sec._n to_o 2_o hour_n 12_o min._n almost_o by_o this_o account_n then_o the_o sun_n shall_v enter_v into_o the_o midst_n of_o taurus_n the_o 25_o day_n 2_o hour_n and_o about_o 12_o min._n before_o noon_n that_o be_v at_o nine_o of_o the_o clock_n and_o 48_o minute_n neither_o ought_v that_o small_a difference_n that_o appear_v between_o these_o account_n to_o be_v great_o regard_v which_o amount_v not_o to_o so_o much_o as_o half_a a_o hour_n in_o which_o time_n the_o motion_n of_o the_o sun_n be_v little_a above_o a_o minute_n and_o the_o declination_n of_o the_o sun_n in_o that_o part_n of_o the_o zodiac_n can_v alter_v so_o much_o as_o â…“_n of_o a_o minute_n which_o be_v so_o small_a as_o can_v by_o sense_n very_o hardly_o be_v observe_v or_o discern_v neither_o yet_o ought_v that_o little_a difference_n of_o a_o minute_n or_o two_o that_o appear_v between_o the_o diurn_n motion_n of_o the_o sun_n find_v by_o observation_n great_o move_v any_o man_n in_o that_o by_o the_o first_o and_o second_o observation_n the_o diurn_n motion_n shall_v be_v almost_o 56_o min._n by_o the_o first_o and_o three_o 57_o min._n by_o the_o second_o and_o three_o 58_o min._n and_o more_o the_o great_a of_o which_o difference_n may_v almost_o arise_v by_o err_v but_o one_o half_a minute_n only_o in_o take_v the_o height_n of_o the_o sun_n which_o error_n be_v in_o a_o manner_n altogether_o insensible_a and_o will_v be_v easy_o pardon_v by_o they_o that_o have_v or_o shall_v accustom_v themselves_o to_o make_v the_o like_a observation_n when_o beside_o their_o own_o experience_n they_o shall_v find_v that_o they_o which_o have_v most_o excel_v in_o this_o art_n as_o tycho_n brahe_n de_fw-fr recentiorâ—b_fw-la aetherei_fw-la mundi_fw-la phaenom_fw-la lib_n 2_o cap._n 10._o part_n 1._o copern_n revol_fw-it libr._n 4._o cap._n 21._o and_o ptoleme_a himself_o in_o all_o his_o catalogue_n of_o the_o fix_a star_n almage_a lib._n 7._o cap._n 5._o when_o they_o shall_v find_v i_o say_v that_o even_o these_o prince_n in_o astronomy_n so_o great_o exercise_v in_o observation_n have_v account_v a_o whole_a minute_n or_o two_o hardly_o sensible_a ptoleme_a also_o in_o his_o almage_a content_v himself_o for_o the_o most_o part_n to_o have_v set_v down_o the_o place_n of_o the_o fix_a star_n to_o six_o part_n of_o degree_n and_o very_o seldom_o come_v to_o twelve_o part_n think_v it_o sufficient_a as_o it_o may_v seem_v by_o the_o perpetual_a course_n of_o that_o catalogue_n to_o come_v within_o five_o or_o ten_o minute_n of_o the_o truth_n but_o to_o return_v again_o to_o that_o from_o whence_o we_o have_v a_o little_a digress_v after_o this_o manner_n now_o show_v we_o find_v the_o time_n of_o the_o sun_n entrance_n into_o the_o beginning_n of_o ♈_o and_o ♎_o and_o into_o the_o midst_n of_o ♉_o ♌_o â™_o and_o â™’_o as_o into_o place_n serve_v most_o fit_o for_o find_v out_o of_o the_o sun_n eccentricitie_n and_o apogeum_n follow_v also_o herein_o the_o example_n of_o copernicus_n lib._n 3._o cap._n 16._o revol_fw-it who_o well_o perceive_v how_o hard_o yea_o rather_o impossible_a a_o thing_n it_o be_v to_o find_v by_o observation_n the_o time_n of_o the_o sun_n entrance_n into_o the_o solstitial_a point_n where_o the_o meridian_n altitude_n and_o declination_n of_o the_o sun_n continue_v almost_o the_o same_o without_o any_o sensible_a difference_n for_o two_o or_o three_o day_n together_o choose_v rather_o the_o part_n of_o the_o zodiac_n already_o mention_v where_o the_o place_n of_o the_o sun_n may_v more_o true_o be_v know_v by_o reason_n of_o the_o quick_a alter_n of_o his_o declination_n the_o difference_n thereof_o in_o the_o space_n of_o 24_o hour_n amount_v to_o more_o than_o 17_o min._n the_o time_n therefore_o of_o the_o sun_n come_v to_o the_o foresay_a point_n in_o the_o year_n 1594_o 1595_o 1596_o 1597._o we_o find_v to_o be_v such_o as_o be_v set_v down_o in_o the_o table_n follow_v  _fw-fr 1594_o 1595_o 1596_o 1597_o  _fw-fr  _fw-fr  _fw-fr da._n ho._n mi._n da._n ho._n mi._n da._n ho._n mi._n da._n ho._n mi._n sig._n de._n jan._n  _fw-fr  _fw-fr  _fw-fr 24_o 17_o 35_o 25_o 0_o 7_o 24_o 5_o 54_o â™’_o 15_o mar._n  _fw-fr  _fw-fr  _fw-fr 10_o 13_o 26_o 9_o 18_o 43_o 10_o 0_o 37_o ♈_o 0_o april_n  _fw-fr  _fw-fr  _fw-fr 25_o 16_o 50_o 24_o 21_o 47_o 25_o 3_o 54_o ♉_o 15_o july_n 28_o 15_o 35_o 28_o 20_o 4_o 28_o 1_o 43_o 28_o 9_o 56_o ♌_o 15_o sept._n 13_o 2_o 45_o 13_o 7_o 39_o 12_o 13_o 48_o 12_o 19_o 15_o ♎_o 0_o octob._n 28_o 5_o 46_o 28_o 9_o 36_o 27_o 15_o 23_o 272_o 1_o 50_o â™_o 15_o hereby_o the_o time_n of_o the_o sun_n continuance_n in_o the_o ark_n of_o the_o zodiac_n betwixt_o those_o point_n as_o also_o the_o ark_n of_o the_o eccentrick_a answerable_a to_o those_o time_n be_v more_o easy_o find_v then_o that_o it_o shall_v now_o be_v needful_a for_o i_o to_o be_v further_a tedious_a in_o set_v down_o the_o manner_n of_o find_v the_o same_o wherein_o notwithstanding_o there_o may_v some_o difference_n of_o a_o hour_n or_o two_o sometime_o appear_v by_o compare_v together_o those_o time_n in_o several_a year_n yet_o this_o error_n be_v such_o as_o may_v arise_v by_o miss_v little_a more_o than_o one_o minute_n in_o one_o observation_n or_o little_o more_o than_o half_a a_o minute_n in_o two_o observation_n of_o the_o meridian_n altitude_n of_o the_o sun_n one_o observation_n be_v make_v when_o the_o sun_n be_v about_o the_o begin_n of_o the_o ark_n the_o other_o when_o he_o be_v about_o the_o end_n thereof_o i_o make_v no_o doubt_n but_o that_o it_o will_v at_o the_o least_o be_v favourable_o censure_v by_o they_o that_o have_v acquaint_v themselves_o with_o some_o practice_n of_o observe_v wherein_o he_o shall_v in_o my_o opinion_n quit_v himself_o meet_o well_o who_o neither_o through_o imperfection_n of_o sense_n either_o in_o make_v or_o divide_v or_o in_o rectify_v or_o in_o use_v his_o instrument_n and_o every_o part_n thereof_o nor_o through_o the_o difficulty_n of_o note_v precise_o the_o edge_n of_o the_o shadow_n of_o the_o upper_a sight_n fall_v upon_o the_o nether_a the_o limit_n or_o bound_n of_o which_o shadow_n be_v but_o a_o confuse_a mixture_n as_o it_o be_v of_o light_n and_o darkness_n or_o else_o a_o mean_a equal_o compound_v of_o they_o both_o which_o can_v no_o better_o be_v discern_v then_o by_o guess_v nor_o yet_o by_o rrefraction_n of_o the_o sun_n beam_n through_o the_o thickness_n of_o the_o air_n especial_o when_o the_o sun_n be_v in_o the_o southerly_a semicircle_n of_o the_o zodiac_n which_o refraction_n admit_v some_o alteration_n according_a to_o the_o diversity_n
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
the_o very_a degree_n of_o the_o compass_n upon_o which_o the_o sun_n rise_v or_o set_v then_o the_o horizon_n be_v set_v fast_o as_o we_o have_v show_v in_o the_o former_a chapter_n mark_v in_o the_o instrument_n by_o which_o part_n or_o degree_n of_o those_o upon_o the_o horizon_n the_o parallel_n of_o the_o sun_n declination_n that_o day_n do_v cross_v the_o same_o count_v in_o the_o number_n of_o the_o horizon_n from_o the_o centre_n towards_o the_o north_n pole_n if_o it_o be_v from_o the_o 11_o of_o march_n to_o the_o 13_o of_o september_n or_o towards_o the_o south_n pole_n the_o other_o half_o of_o the_o year_n and_o mark_v also_o whether_o this_o cross_n be_v so_o many_o deg_n distant_a from_o the_o division_n of_o the_o equinoctial_a of_o your_o instrument_n as_o the_o sun_n in_o his_o rise_n be_v distant_a from_o the_o east_n of_o the_o compass_n or_o at_o his_o go_v down_o be_v distant_a from_o the_o west_n thereof_o for_o than_o you_o may_v say_v that_o the_o compass_n have_v no_o variation_n at_o all_o but_o if_o it_o be_v not_o so_o mark_v the_o rule_n follow_v 1_o when_o the_o sun_n rise_v by_o the_o same_o rumb_n of_o the_o compass_n which_o the_o instrument_n do_v show_v the_o compass_n have_v no_o variation_n at_o all_o 2_o when_o the_o sun_n rise_v more_o to_o the_o north_n of_o the_o compass_n or_o go_v down_o more_o to_o the_o south_n then_o be_v show_v by_o the_o instrument_n all_o the_o difference_n between_o the_o instrument_n and_o the_o compass_n be_v the_o north-easting_a or_o variation_n thereof_o to_o the_o eastward_o 3_o if_o the_o sun_n rise_v more_o to_o the_o south_n of_o the_o compass_n or_o seat_v more_o to_o the_o north_n than_o the_o instrument_n show_v all_o the_o difference_n between_o the_o instrument_n and_o the_o compass_n be_v the_o north-westing_a or_o westerly_a variation_n thereof_o chap._n xxxviii_o at_o what_o hour_n the_o sun_n rise_v and_o set_v every_o day_n in_o all_o part_n of_o the_o world_n the_o height_n of_o the_o pole_n in_o that_o part_n where_o you_o desire_v to_o know_v this_o be_v know_v place_v the_o horizon_n in_o such_o sort_n as_o be_v show_v in_o the_o 36_o chapter_n and_o find_v by_o the_o table_n of_o the_o sun_n declination_n the_o declination_n which_o the_o sun_n have_v that_o day_n count_v the_o same_o from_o the_o equinoctial_a of_o the_o instrument_n towards_o that_o part_n whither_o the_o sun_n decline_v among_o the_o parallel_n and_o then_o mark_v the_o parallel_n whereat_o your_o account_n end_v in_o what_o hour_n and_o in_o what_o part_n of_o the_o hour_n it_o cut_v the_o horizon_n note_v that_o every_o hour_n have_v two_o number_n one_o afternoon_n which_o be_v the_o hour_n of_o the_o sun_n set_v and_o another_o before_o noon_n which_o be_v that_o wherein_o the_o sun_n rise_v chap._n thirty-nine_o of_o the_o length_n of_o the_o day_n and_o of_o the_o night_n the_o hour_n of_o the_o sun_n go_v down_o be_v know_v double_v it_o and_o the_o double_a number_n of_o hour_n will_v show_v you_o the_o length_n of_o the_o day_n also_o the_o hour_n of_o the_o sun_n rise_v be_v know_v and_o double_v will_v manifest_v unto_o you_o the_o length_n of_o the_o night_n in_o that_o part_n of_o the_o year_n when_o you_o desire_v to_o know_v the_o same_o chap._n xl._o of_o a_o night-diall_n by_o the_o north._n that_o be_v know_v which_o be_v before_o declare_v of_o the_o situation_n of_o the_o north_n star_n and_o of_o the_o guard_n we_o may_v easy_o know_v in_o the_o night_n what_o a_o clock_n it_o be_v wheresoever_o we_o can_v see_v the_o north_n star_n presuppose_v that_o upon_o the_o 15_o of_o april_n at_o the_o very_a point_n of_o midnight_n the_o former_a guard_n go_v a-head_n in_o respect_n of_o the_o north_n star_n and_o because_o by_o this_o account_n of_o the_o hour_n of_o the_o night_n we_o must_v take_v for_o a_o beginning_n the_o very_a instant_n when_o the_o former_a guard_n make_v midnight_n the_o rule_n follow_v be_v to_o be_v observe_v the_o 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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
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to_o the_o midst_n of_o taurus_n 46._o day_n and_o about_o three_o hour_n and_o four_o minute_n and_o consequent_o the_o arch_n of_o the_o sun_n eccentrick_a answerable_a to_o that_o time_n and_o arch_n of_o the_o ecliptic_a 45._o degr_n 27_o min._n 56._o sec._n i_o find_v hereby_o the_o sun_n eccentricitie_n and_o place_n of_o his_o apogeum_n as_o follow_v past_o this_o upon_o the_o margin_n of_o letter_n z._n fol._n 148_o so_o as_o it_o may_v lie_v open_a all_o the_o while_n the_o follow_a matter_n of_o the_o 20_o and_o 21_o chap_n be_v read_v which_o may_v yet_o also_o be_v more_o easy_o find_v by_o the_o tetragonical_a table_n or_o table_n of_o root_n and_o square_n for_o take_v ao_o and_o ob_fw-la to_o be_v 2290_o and_o 2757_o their_o square_n will_v be_v 5,244,100_o and_o 7,601,049_o which_o add_v together_o make_v 12,845,149_o the_o square_a root_n or_o side_n whereof_o be_v 3584._o the_o sun_n eccentricitie_n in_o such_o part_n whereof_o the_o semidiameter_n of_o the_o 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right_o angle_a triangle_n adb_n 356,892_o to_o ab_fw-la the_o eccentricitie_n of_o the_o sun_n 358,414_o which_o have_v not_o any_o sensible_a difference_n from_o that_o we_o find_v before_o but_o the_o place_n of_o the_o sun_n apogeum_n find_v by_o the_o foresay_a observation_n differ_v from_o tycho_n twenty_o minute_n if_o we_o add_v â—o_o his_o place_n of_o the_o apogeum_n of_o the_o sun_n 7_o minute_n for_o the_o moâ—â—on_n of_o the_o sun_n apogeum_n in_o the_o ten_o year_n space_n betwixt_o his_o observation_n and_o i_o all_o which_o difference_n notwithstanding_o may_v arise_v by_o err_v little_a more_o than_o half_a a_o quarter_n of_o a_o minute_n in_o observe_v the_o the_o sun_n height_n about_o the_o midst_n of_o tarus_n which_o error_n although_o it_o be_v so_o small_a that_o it_o may_v worthy_o be_v neglect_v for_o whether_o of_o they_o soever_o you_o follow_v either_o his_o apogeum_n or_o i_o for_o the_o make_n of_o the_o ephemerides_n and_o table_n ensue_v there_o can_v 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48._o sec._n of_o aries_n his_o middle_a motion_n from_o the_o begin_n of_o aries_n be_v also_o easy_o find_v after_o this_o manner_n let_v a_o be_v the_o place_n of_o the_o sun_n in_o his_o eccentrick_a b_o the_o sun_n true_a place_n in_o the_o zodiac_n b_o a_o a_o line_n draw_v from_o the_o centre_n of_o the_o eccentrick_a to_o the_o centre_n of_o the_o sun_n a_o d_o a_o line_n draw_v from_o the_o centre_n of_o the_o ecliptic_a parallel_n to_o b_o a_o show_v the_o middle_a place_n of_o the_o sun_n in_o the_o zodiac_n ab_fw-la a_o line_n draw_v from_o the_o centre_n of_o the_o ecliptic_a by_o the_o centre_n of_o the_o sun_n to_o the_o zodiac_n show_v the_o true_a place_n of_o the_o sun_n therefore_o the_o angle_n bid_v be_v 5._o degr_n 37._o min._n and_o consequent_o the_o angle_n bajazet_n 95._o degr_n
2_o 30_o 39_o  _fw-fr 21_o 6_o 9_o 5_o 43_o  _fw-fr 8_o 6_o 18_o 57_o 40_o 14_o 45_o 6_o  _fw-fr 25_o 53_o 2_o 4_o 7_o 2_o 7_o 18_o  _fw-fr 22_o 7_o 9_o 27_o 51_o 21_o 58_o 7_o 19_o 12_o 25_o 14_o 23_o 7_o  _fw-fr 27_o 57_o 1_o 45_o 8_o 1_o 43_o 56_o  _fw-fr 27_o 8_o 9_o 49_o 49_o  _fw-fr 52_o 8_o 19_o 26_o 48_o 14_o 1_o 8_o  _fw-fr 29_o 32_o 1_o 8_o 9_o 1_o 20_o 29_o  _fw-fr 27_o 9_o 10_o 11_o 41_o  _fw-fr 42_o 9_o 19_o 40_o 49_o 13_o 40_o 9_o  _fw-fr 30_o 40_o 0_o 39_o 10_o 0_o 57_o 2_o  _fw-fr 29_o 10_o 10_o 33_o 23_o  _fw-fr 33_o 10_o 19_o 54_o 29_o 13_o 18_o 10_o  _fw-fr 31_o 19_o 0_o 11_o 11_o 0_o 33_o 33_o  _fw-fr 31_o 11_o 10_o 54_o 56_o 21_o 23_o 11_o 20_o 7_o 47_o 12_o 55_o 11_o  _fw-fr 31_o 30_o 0_o 18_o 12_o 0_o 10_o 2_o  _fw-fr 32_o 12_o 11_o 16_o 19_o  _fw-fr 13_o 12_o 20_o 20_o 42_o 12_o 34_o 12_o  _fw-fr 31_o 12_o 0_o 48_o 13_o 0_o 13_o 30_o  _fw-fr 33_o 13_o 11_o 37_o 32_o  _fw-fr 2_o 13_o 20_o 33_o 16_o 12_o 9_o 13_o  _fw-fr 30_o 24_o 1_o 14_o 14_o 0_o 37_o 3_o  _fw-fr 32_o 14_o 11_o 58_o 34_o 20_o 51_o 14_o 20_o 45_o 25_o 11_o 48_o 14_o  _fw-fr 29_o 10_o 1_o 44_o 15_o 1_o 0_o 35_o 23_o 34_o 15_o 12_o 19_o 25_o  _fw-fr 39_o 15_o 20_o 57_o 12_o 11_o 23_o 15_o  _fw-fr 27_o 26_o 2_o 13_o 16_o 1_o 24_o 9_o  _fw-fr 32_o 16_o 12_o 40_o 4_o  _fw-fr 28_o 16_o 21_o 8_o 35_o 10_o 59_o 16_o  _fw-fr 25_o 13_o 2_o 40_o 17_o 1_o 47_o 41_o  _fw-fr 31_o 17_o 13_o 0_o 32_o  _fw-fr 16_o 17_o 21_o 19_o 34_o 10_o 34_o 17_o  _fw-fr 22_o 33_o 3_o 9_o 18_o 2_o 11_o 12_o  _fw-fr 31_o 18_o 13_o 20_o 48_o 20_o 3_o 18_o 21_o 30_o 8_o 10_o 9_o 18_o  _fw-fr 19_o 24_o 3_o 37_o 19_o 2_o 34_o 43_o  _fw-fr 29_o 19_o 13_o 40_o 51_o 19_o 49_o 19_o 21_o 40_o 17_o 9_o 46_o 19_o  _fw-fr 15_o 47_o 4_o 5_o 20_o 2_o 58_o 12_o  _fw-fr 28_o 20_o 14_o 0_o 40_o 19_o 36_o 20_o 21_o 50_o 3_o 9_o 19_o 20_o  _fw-fr 11_o 42_o 4_o 34_o 21_o 3_o 21_o 40_o  _fw-fr 26_o 21_o 14_o 20_o 16_o 19_o 23_o 21_o 21_o 59_o 22_o 8_o 53_o 21_o  _fw-fr 7_o 8_o 5_o 0_o 22_o 3_o 45_o 6_o  _fw-fr 22_o 22_o 14_o 39_o 39_o 19_o 8_o 22_o 22_o 8_o 15_o 8_o 28_o 22_o  _fw-fr 2_o 8_o 5_o 29_o 23_o 4_o 8_o 28_o  _fw-fr 19_o 23_o 14_o 58_o 47_o 18_o 53_o 23_o 22_o 16_o 43_o 8_o 2_o 23_o 22_o 56_o 39_o 5_o 56_o 24_o 4_o 31_o 47_o  _fw-fr 17_o 24_o 15_o 17_o 40_o 18_o 38_o 24_o  _fw-fr 24_o 45_o 7_o 36_o 24_o  _fw-fr 50_o 43_o 6_o 23_o 25_o 4_o 55_o 4_o  _fw-fr 12_o 25_o 15_o 36_o 18_o 18_o 22_o 25_o  _fw-fr 32_o 21_o 7_o 9_o 25_o  _fw-fr 44_o 20_o 6_o 51_o 26_o 5_o 18_o 16_o  _fw-fr 9_o 26_o 15_o 54_o 40_o 18_o 7_o 26_o  _fw-fr 39_o 30_o 6_o 42_o 26_o  _fw-fr 37_o 29_o 7_o 10_o 27_o 5_o 41_o 25_o 23_o 5_o 27_o 16_o 12_o 47_o 17_o 50_o 27_o  _fw-fr 46_o 12_o 6_o 15_o 27_o  _fw-fr 30_o 19_o 7_o 52_o 28_o 6_o 4_o 30_o  _fw-fr 0_o 28_o 16_o 30_o 37_o 17_o 33_o 28_o  _fw-fr 52_o 27_o 5_o 48_o 28_o  _fw-fr 22_o 27_o 8_o 11_o 29_o 6_o 27_o 30_o 22_o 54_o 29_o 16_o 48_o 10_o 17_o 16_o 29_o  _fw-fr 58_o 15_o 5_o 20_o 29_o  _fw-fr 14_o 16_o 8_o 36_o 30_o 6_o 50_o 24_o 22_o 49_o 30_o 17_o 5_o 26_o 16_o 58_o 30_o 23_o 3_o 35_o 4_o 53_o 30_o  _fw-fr 5_o 40_o 9_o 3_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 31_o 17_o 22_o 24_o 16_o 41_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 31_o 21_o 56_o 37_o 9_o 26_o chap._n xxviii_o the_o use_n of_o the_o former_a table_n or_o regiment_n of_o the_o sun_n this_o table_n of_o the_o sun_n declination_n as_o it_o differ_v nothing_o in_o form_n from_o other_o that_o have_v be_v publish_v heretofore_o so_o likewise_o the_o manner_n of_o use_v it_o be_v altogether_o the_o same_o that_o have_v be_v accustom_v in_o former_a table_n of_o this_o kind_n save_v that_o i_o must_v give_v warning_n of_o one_o error_n that_o have_v be_v commit_v herein_o which_o be_v as_o i_o have_v observe_v that_o some_o of_o our_o seaman_n do_v take_v the_o sun_n declination_n out_o of_o their_o regiment_n without_o any_o aequation_n by_o addition_n or_o subtraction_n of_o the_o part_n proportional_a agreeable_a to_o the_o difference_n of_o longitude_n of_o the_o place_n where_o they_o be_v as_o if_o they_o be_v always_o at_o the_o same_o place_n or_o under_o the_o same_o meridian_n for_o which_o their_o regiment_n be_v make_v for_o which_o cause_n alone_o though_o they_o avoid_v all_o other_o error_n it_o may_v so_o fall_v out_o that_o they_o may_v be_v deceive_v sometime_o 10_o or_o 12._o minute_n or_o more_o in_o a_o long_a voyage_n in_o take_v the_o sun_n declination_n for_o there_o be_v not_o any_o table_n of_o the_o sun_n declination_n but_o that_o it_o must_v needs_o be_v make_v for_o some_o one_o meridian_n as_o this_o former_a table_n be_v make_v for_o the_o meridian_n of_o london_n and_o therefore_o can_v be_v true_o use_v in_o any_o other_o without_o some_o equation_n answerable_a to_o the_o distance_n of_o the_o meridians_fw-la or_o difference_n of_o longitude_n to_o avoid_v this_o error_n therefore_o first_o learn_v how_o much_o you_o differ_v in_o longitude_n from_o the_o place_n for_o which_o your_o table_n be_v make_v and_o though_o you_o miss_v half_a a_o dozen_o or_o half_o a_o score_n degree_n herein_o it_o can_v in_o this_o point_n breed_v any_o sensible_a error_n second_o take_v out_o the_o difference_n of_o the_o sun_n declination_n agreeable_a to_o the_o space_n of_o 24._o hour_n about_o the_o time_n of_o your_o observation_n three_o as_o 360._o be_v to_o this_o difference_n of_o declination_n so_o be_v the_o difference_n of_o longitude_n to_o the_o part_n proportional_a or_o equation_n of_o the_o declination_n which_o equation_n be_v to_o be_v add_v to_o the_o declination_n of_o the_o day_n of_o observation_n if_o the_o declination_n of_o the_o sun_n be_v either_o increase_a and_o the_o place_n of_o observation_n westward_o or_o else_o decrease_v and_o the_o place_n of_o observation_n eastward_n from_o the_o place_n for_o which_o your_o table_n of_o declination_n be_v make_v otherwise_o this_o equation_n be_v to_o be_v subtract_v from_o the_o declination_n of_o your_o day_n of_o observation_n that_o you_o may_v have_v the_o true_a declination_n of_o the_o sun_n for_o the_o time_n and_o place_n of_o your_o observation_n but_o if_o the_o time_n of_o your_o observation_n be_v the_o noontide_a immediate_o before_o or_o after_o the_o sun_n entrance_n into_o either_o of_o the_o aequinoctial_a point_n you_o must_v follow_v another_o rule_n and_o that_o be_v this_o divide_v the_o difference_n of_o longitude_n by_o 15_o mark_v how_o many_o unite_v the_o quotient_n contain_v and_o so_o many_o minute_n add_v to_o the_o declination_n find_v in_o the_o former_a table_n if_o you_o be_v either_o eastward_o from_o the_o meridian_n of_o london_n and_o observe_v the_o noontide_n before_o the_o equinoctium_n or_o if_o you_o be_v westward_o from_o that_o meridian_n and_o observe_v the_o noontide_n after_o the_o equinoctium_n for_o the_o sum_n shall_v be_v the_o declination_n desire_v otherwise_o if_o you_o be_v either_o westward_n from_o the_o meridian_n of_o london_n and_o observe_v the_o noontide_n next_o before_o the_o equinoctium_n or_o eastward_o from_o that_o meridian_n and_o observe_v the_o day_n immediate_o after_o the_o equinoctium_n compare_v the_o declination_n find_v in_o the_o table_n with_o the_o foresay_a quotient_n and_o subtract_v the_o lesser_a out_o of_o the_o great_a for_o that_o remain_v be_v the_o declination_n desire_v which_o declination_n have_v the_o same_o denomination_n of_o north_n or_o south_n that_o the_o table_n show_v if_o the_o quotient_a be_v less_o than_o the_o declination_n find_v in_o the_o table_n but_o if_o the_o quotient_a be_v great_a the_o denomination_n must_v be_v alter_v from_o north_n to_o south_n or_o from_o south_n to_o north_n contrary_a to_o that_o the_o table_n show_v if_o the_o quotient_n be_v equal_a to_o the_o declination_n find_v in_o the_o former_a table_n the_o sun_n be_v in_o the_o very_a equinoctial_a point_n and_o have_v no_o declination_n at_o all_o a_o few_o example_n will_v make_v these_o rule_v more_o plain_a suppose_v therefore_o the_o 30_o of_o march_n 1610._o you_o be_v sail_v in_o the_o bay_n of_o mexico_n differ_v in_o longitude_n to_o the_o westward_n from_o the_o meridian_n of_o london_n about_o 90_o degree_n by_o estimation_n the_o declination_n of_o the_o sun_n for_o that_o day_n find_v in_o the_o former_a table_n be_v 7_o degree_n 39_o minute_n
22_o 21_o 0_o 06_o 1_o 58_o 3_o 54_o 6_o 01_o 13_o 20_o 22_o 22_o 25_o 0_o 09_o 2_o 02_o 3_o 58_o 6_o 05_o 14_o 20_o 26_o 22_o 29_o 0_o 12_o 2_o 06_o 4_o 03_o 6_o 09_o 15_o 20_o 30_o 22_o 32_o 0_o 16_o 2_o 10_o 4_o 07_o 6_o 13_o 16_o 20_o 34_o 22_o 36_o 0_o 20_o 2_o 14_o 4_o 11_o 6_o 18_o 17_o 20_o 38_o 22_o 40_o 0_o 23_o 2_o 18_o 4_o 15_o 6_o 22_o 18_o 20_o 42_o 22_o 44_o 0_o 27_o 2_o 22_o 4_o 19_o 6_o 26_o 19_o 20_o 46_o 22_o 48_o 0_o 31_o 2_o 26_o 4_o 23_o 6_o 30_o 20_o 20_o 50_o 22_o 52_o 0_o 35_o 2_o 30_o 4_o 27_o 6_o 34_o 21_o 20_o 54_o 22_o 56_o 0_o 38_o 2_o 33_o 4_o 31_o 6_o 38_o 22_o 20_o 58_o 22_o 59_o 0_o 42_o 2_o 37_o 4_o 35_o 6_o 42_o 23_o 21_o 03_o 23_o 03_o 0_o 46_o 2_o 41_o 4_o 39_o 6_o 46_o 24_o 21_o 07_o 23_o 07_o 0_o 49_o 2_o 44_o 4_o 43_o 6_o 51_o 25_o 21_o 11_o 23_o 10_o 0_o 53_o 2_o 48_o 4_o 47_o 6_o 55_o 26_o 21_o 15_o 23_o 14_o 0_o 57_o 2_o 52_o 4_o 51_o 6_o 59_o 27_o 21_o 19_o 23_o 18_o 1_o 00_o 2_o 56_o 4_o 56_o 7_o 03_o 28_o 21_o 23_o 23_o 22_o 1_o 03_o 3_o 00_o 5_o 00_o 7_o 07_o 29_o 21_o 27_o  _fw-fr  _fw-fr 1_o 07_o 3_o 04_o 5_o 03_o 7_o 11_o 30_o 21_o 31_o  _fw-fr  _fw-fr 1_o 11_o 3_o 07_o 5_o 07_o 7_o 15_o 31_o 21_o 35_o  _fw-fr  _fw-fr 1_o 15_o  _fw-fr  _fw-fr 5_o 11_o  _fw-fr  _fw-fr  _fw-fr july_n august_n septemb_n october_n novemb_n decemb_v d._n h._n m._n h._n m._n h._n m._n h._n m._n h._n m._n h._n m._n 1_o 7_o 19_o 9_o 22_o 11_o 16_o 13_o 05_o 15_o 05_o 17_o 12_o 2_o 7_o 23_o 9_o 26_o 11_o 20_o 13_o 08_o 15_o 09_o 17_o 17_o 3_o 7_o 27_o 9_o 30_o 11_o 23_o 13_o 12_o 15_o 13_o 17_o 21_o 4_o 7_o 31_o 9_o 33_o 11_o 27_o 13_o 16_o 15_o 17_o 17_o 25_o 5_o 7_o 35_o 9_o 36_o 11_o 30_o 13_o 19_o 15_o 21_o 17_o 30_o 6_o 7_o 40_o 9_o 40_o 11_o 33_o 13_o 23_o 15_o 25_o 17_o 34_o 7_o 7_o 44_o 9_o 44_o 11_o 37_o 13_o 27_o 15_o 29_o 17_o 39_o 8_o 7_o 48_o 9_o 48_o 11_o 41_o 13_o 31_o 15_o 33_o 17_o 43_o 9_o 7_o 52_o 9_o 52_o 11_o 44_o 13_o 34_o 15_o 37_o 17_o 47_o 10_o 7_o 56_o 9_o 56_o 11_o 48_o 13_o 38_o 15_o 42_o 17_o 52_o 11_o 8_o 00_o 9_o 59_o 11_o 52_o 13_o 42_o 15_o 46_o 17_o 56_o 12_o 8_o 04_o 10_o 03_o 11_o 55_o 13_o 45_o 15_o 50_o 18_o 00_o 13_o 8_o 08_o 10_o 07_o 11_o 59_o 13_o 49_o 15_o 54_o 18_o 05_o 14_o 8_o 12_o 10_o 11_o 12_o 03_o 13_o 53_o 15_o 58_o 18_o 10_o 15_o 8_o 16_o 10_o 15_o 12_o 07_o 13_o 57_o 16_o 03_o 18_o 14_o 16_o 8_o 20_o 10_o 18_o 12_o 11_o 14_o 01_o 16_o 07_o 18_o 18_o 17_o 8_o 24_o 10_o 22_o 12_o 14_o 14_o 05_o 16_o 11_o 18_o 23_o 18_o 8_o 28_o 10_o 26_o 12_o 18_o 14_o 09_o 16_o 16_o 18_o 27_o 19_o 8_o 31_o 10_o 29_o 12_o 22_o 14_o 13_o 16_o 20_o 18_o 32_o 20_o 8_o 35_o 10_o 33_o 12_o 25_o 14_o 17_o 16_o 24_o 18_o 36_o 21_o 8_o 39_o 10_o 36_o 12_o 29_o 14_o 20_o 16_o 28_o 18_o 41_o 22_o 8_o 43_o 10_o 40_o 12_o 32_o 14_o 24_o 16_o 33_o 18_o 45_o 23_o 8_o 47_o 10_o 44_o 12_o 36_o 14_o 28_o 16_o 37_o 18_o 50_o 24_o 8_o 52_o 10_o 47_o 12_o 40_o 14_o 32_o 16_o 41_o 18_o 55_o 25_o 8_o 55_o 10_o 51_o 12_o 43_o 14_o 36_o 16_o 46_o 18_o 59_o 26_o 8_o 59_o 10_o 54_o 12_o 47_o 14_o 40_o 16_o 50_o 19_o 03_o 27_o 9_o 03_o 10_o 58_o 12_o 51_o 14_o 44_o 16_o 55_o 19_o 07_o 28_o 9_o 07_o 11_o 02_o 12_o 54_o 14_o 48_o 16_o 59_o 19_o 12_o 29_o 9_o 11_o 11_o 06_o 12_o 58_o 14_o 53_o 17_o 03_o 19_o 16_o 30_o 9_o 15_o 11_o 09_o 13_o 02_o 14_o 57_o 17_o 08_o 19_o 21_o 31_o 9_o 19_o 11_o 13_o  _fw-fr  _fw-fr 15_o 01_o  _fw-fr  _fw-fr 19_o 25_o chap._n xxxiii_o by_o the_o former_a table_n of_o the_o fix_a star_n and_o the_o sun_n right_a ascension_n to_o know_v the_o hour_n of_o the_o night_n at_o any_o time_n of_o the_o year_n by_o these_o table_n of_o fix_a star_n and_o right_a ascension_n of_o the_o sun_n you_o may_v easy_o know_v also_o the_o hour_n of_o the_o night_n at_o any_o time_n of_o the_o year_n after_o this_o manner_n look_v which_o of_o those_o star_n be_v at_o the_o meridian_n which_o may_v easy_o be_v know_v by_o a_o needle-dial_n or_o compass_n or_o if_o you_o will_v observe_v the_o north_n star_n that_o never_o set_v which_o indeed_o be_v fit_a for_o this_o purpose_n especial_o when_o they_o come_v to_o the_o meridian_n under_o the_o pole_n you_o shall_v first_o find_v the_o place_n of_o the_o pole_n in_o the_o heaven_n so_o near_o as_o you_o can_v by_o estimation_n for_o a_o little_a error_n herein_o break_v no_o square_a which_o may_v be_v do_v thus_o from_o the_o polestar_n direct_o towards_o the_o first_o star_n next_o the_o rump_n in_o the_o great_a bear_n tail_n imagine_v almost_o so_o much_o space_n as_o the_o guard_n be_v distant_a asunder_o for_o near_o thereabouts_o be_v the_o place_n of_o the_o pole_n now_o betwixt_o your_o eye_n and_o this_o place_n of_o the_o pole_n hold_v a_o plumbline_n hang_v as_o perpendicular_o and_o steadfast_o as_o you_o may_v and_o mark_v withal_o if_o that_o plumbline_n come_v betwixt_o your_o sight_n and_o any_o of_o the_o star_n note_v in_o the_o table_n of_o fix_a star_n about_o the_o pole_n for_o that_o star_n be_v at_o the_o meridian_n then_o learn_v as_o before_o be_v show_v at_o what_o time_n that_o star_n come_v to_o the_o meridian_n and_o so_o you_o shall_v have_v the_o hour_n of_o the_o night_n suppose_v for_o example_n the_o 10_o of_o february_n you_o find_v after_o this_o manner_n the_o swan_n tail_n at_o the_o meridian_n under_o the_o pole_n desire_v hereby_o to_o know_v the_o hour_n of_o the_o night_n at_o that_o time_n the_o right_a ascension_n of_o the_o sun_n for_o that_o day_n you_o shall_v find_v as_o before_o to_o be_v 22_o hour_n 14_o minute_n whereto_o you_o may_v add_v a_o minute_n or_o two_o more_o because_o that_o star_n will_v come_v to_o the_o meridian_n very_o late_o in_o the_o evening_n so_o make_v the_o sun_n right_a ascension_n 22_o hour_n 16_o minute_n the_o right_a ascension_n of_o that_o star_n in_o the_o second_o table_n of_o fix_a star_n you_o shall_v find_v to_o be_v 20_o hour_n 30_o minute_n from_o which_o because_o now_o you_o desire_v to_o know_v the_o time_n of_o that_o star_n come_v to_o the_o nether_a part_n of_o the_o meridian_n you_o may_v subtract_v 12_o hour_n and_o there_o shall_v remain_v 8_o hour_n 30_o minute_n to_o this_o remainder_n because_o it_o be_v less_o than_o then_o the_o sun_n right_a ascension_n add_v 24_o hour_n and_o from_o the_o sum_n 32_o hour_n 30_o minute_n subtract_v the_o right_a ascension_n of_o the_o sun_n 22_o hour_n 16_o minute_n so_o there_o shall_v remain_v 10_o hour_n 14_o minute_n the_o time_n of_o the_o night_n desire_v chap._n xxxiv_o of_o find_v the_o elevation_n of_o the_o pole_n by_o observation_n of_o the_o polestar_n and_o guard_n beside_o the_o way_n already_o speak_v of_o to_o find_v the_o elevation_n of_o the_o pole_n by_o the_o meridian_n altitude_n and_o declination_n of_o the_o sun_n and_o fix_a star_n in_o general_a there_o have_v be_v also_o use_v another_o way_n more_o special_a by_o the_o height_n of_o the_o polestar_n when_o the_o fore-guard_n be_v situate_a from_o it_o either_o towards_o the_o east_n west_n north_n or_o south_n or_o else_o upon_o the_o middle_a point_n betwixt_o these_o principal_n as_o upon_o the_o north-east_n northwest_o southeast_n and_o southwest_n point_v of_o which_o way_n as_o it_o have_v be_v hitherto_o publish_v and_o use_v i_o must_v for_o the_o present_a only_o give_v the_o mariner_n warning_n that_o he_o trust_v not_o to_o it_o be_v very_o erroneous_a and_o ground_v upon_o two_o false_a position_n the_o one_o be_v that_o the_o distance_n of_o the_o polestar_n from_o the_o pole_n be_v 3_o degree_n 30_o minute_n which_o by_o often_o and_o exact_a observation_n be_v find_v to_o be_v at_o this_o time_n not_o above_o 2_o degree_n 48_o minute_n the_o other_o be_v that_o the_o equation_n or_o allowance_n to_o be_v add_v to_o or_o subtract_v from_o the_o height_n of_o the_o polestar_n to_o find_v thereby_o the_o height_n of_o the_o pole_n be_v make_v the_o same_o for_o all_o latitude_n but_o have_v already_o show_v sufficient_o how_o to_o know_v the_o latitude_n almost_o at_o any_o time_n of_o the_o night_n by_o the_o fix_a star_n in_o the_o former_a table_n i_o hope_v to_o be_v the_o easy_o
come_v from_o the_o say_a edge_n of_o the_o sight_n fall_v for_o that_o edge_n of_o the_o shadow_n upon_o the_o hollow_a side_n of_o the_o arch_n of_o the_o quadrant_n show_v the_o height_n of_o the_o upper_a edge_n of_o the_o sun_n from_o this_o therefore_o subtract_v 16_o minute_n and_o so_o much_o also_o as_o be_v answerable_a to_o the_o height_n of_o your_o eye_n above_o the_o water_n in_o such_o sort_n as_o i_o have_v show_v in_o the_o use_n of_o the_o crosse-staff_n in_o the_o 15_o chapter_n of_o this_o book_n and_o so_o you_o shall_v have_v the_o apparent_a height_n of_o the_o sun_n above_o the_o true_a horizon_n chap._n xxxviii_o how_o with_o this_o quadrant_n to_o observe_v the_o height_n of_o the_o sun_n with_o your_o back_n turn_v towards_o the_o sun_n set_v the_o edge_n of_o one_o of_o the_o broad_a movable_a sight_n or_o vane_n even_o with_o that_o end_n of_o the_o quadrant_n where_o the_o little_a sight_n be_v fix_v then_o look_v through_o the_o slit_n which_o be_v make_v through_o the_o midst_n of_o the_o middle_a sight_n that_o be_v fasten_v to_o the_o double_a box_n or_o socket_n turn_v your_o back_n towards_o the_o sun_n and_o lay_v the_o edge_n of_o the_o vane_n at_o the_o centre_n even_o with_o the_o horizon_n lift_v up_o or_o put_v down_o the_o arch_n of_o the_o quadrant_n till_o the_o upper_a edge_n of_o the_o shadow_n of_o the_o broad_a movable_a sight_n place_v even_o with_o the_o upper_a end_n of_o the_o arch_n of_o the_o quadrant_n agree_v just_o with_o the_o edge_n of_o the_o sight_n or_o vane_n place_v at_o the_o centre_n then_o reckon_v from_o the_o upper_a end_n of_o the_o arch_n of_o the_o quadrant_n downward_o see_v what_o number_n of_o degree_n and_o minute_n you_o find_v at_o the_o upper_a edge_n or_o end_n of_o the_o socket_n through_o which_o the_o quadrant_n move_v add_v always_o thereto_o two_o degree_n for_o so_o shall_v you_o have_v the_o height_n of_o the_o sun_n if_o you_o abate_v from_o hence_o 16_o min_fw-mi for_o the_o sun_n semidiameter_n and_o the_o surplusage_n answerable_a to_o the_o height_n of_o the_o eye_n above_o the_o water_n as_o before_o be_v show_v in_o the_o former_a chapter_n chap._n thirty-nine_o how_o to_o observe_v with_o this_o quadrant_n the_o height_n of_o the_o sun_n or_o star_n look_v both_o to_o the_o sun_n or_o star_n and_o to_o the_o horizon_n set_v the_o upper_a edge_n of_o the_o uppermost_a movable_a sight_n of_o the_o quadrant_n at_o some_o even_a number_n of_o degree_n as_o at_o 10_o 20_o or_o 30_o etc._n etc._n and_o set_v the_o end_n of_o the_o semidiameter_n of_o the_o quadrant_n where_o the_o centre_n be_v to_o the_o corner_n of_o the_o eye_n as_o you_o do_v when_o you_o observe_v with_o the_o crosse-staffe_n lay_v that_o edge_n of_o the_o sight_n even_o with_o the_o upper_a edge_n of_o the_o sun_n and_o move_v the_o nether_a movable_a sight_n up_o or_o down_o till_o the_o upper_a edge_n thereof_o lie_v even_o with_o the_o horizon_n then_o see_v how_o many_o degree_n and_o minute_n be_v contain_v between_o the_o upper_a edge_n of_o both_o sight_n from_o which_o abate_v as_o before_o 16_o minute_n for_o the_o sun_n semidiameter_n and_o the_o surplus_n answerable_a to_o the_o height_n of_o your_o eye_n above_o the_o water_n so_o shall_v you_o have_v the_o apparent_a height_n of_o the_o sun_n above_o the_o true_a horizon_n but_o when_o you_o observe_v the_o height_n of_o any_o star_n lay_v the_o upper_a edge_n of_o the_o upper_a sight_n even_o with_o the_o midst_n of_o the_o star_n and_o from_o the_o number_n of_o degree_n and_o minute_n contain_v between_o the_o upper_a edge_n of_o both_o sight_n abate_v only_o the_o surplus_n answerable_a to_o the_o height_n of_o your_o eye_n above_o the_o water_n and_o so_o you_o shall_v have_v the_o true_a height_n of_o the_o star_n but_o here_o iâ—_n must_v be_v remember_v that_o before_o you_o observe_v the_o sun_n or_o star_n after_o this_o manner_n you_o must_v find_v out_o the_o eccentricity_n of_o your_o eye_n in_o such_o sort_n as_o i_o have_v show_v in_o the_o 15_o chapter_n of_o this_o book_n which_o eccentricity_n you_o must_v add_v to_o the_o distance_n of_o the_o centre_n oâ—_n the_o quadrant_n from_o the_o end_n of_o the_o semidiameter_n where_o you_o seâ—_n your_o eye_n for_o so_o much_o as_o the_o sum_n of_o this_o distance_n and_o eccentriâ—city_n amount_v unto_o so_o much_o must_v you_o thrust_v forward_o the_o foreâ—end_n of_o the_o semidiameter_n of_o the_o quadrant_n beyond_o the_o further_a end_n of_o the_o square_a socket_n through_o which_o it_o be_v put_v that_o so_o the_o centre_n oâ—_n your_o eye_n may_v be_v bring_v to_o the_o centre_n of_o the_o quadrant_n chap._n xl._o how_o to_o find_v the_o height_n of_o the_o pole_n by_o observation_n of_o the_o polestar_n and_o guard_n without_o give_v or_o take_v any_o allowance_n or_o abatement_n at_o any_o time_n when_o the_o polestar_n the_o guard_n and_o horizon_n may_v be_v see_v the_o long_a index_n of_o the_o nocturnal_a which_o i_o call_v the_o guard_n index_n be_v fix_v upon_o the_o place_n of_o the_o middle_a guard_n in_o the_o day-circle_n and_o the_o nocturnal_a be_v put_v upon_o the_o end_n of_o the_o arch_n of_o the_o quadrant_n place_v also_o the_o end_n of_o the_o semidiamter_n to_o your_o eye_n as_o before_z and_o hold_v the_o quadrant_n upright_o with_o the_o nocturnal_a towards_o the_o polestar_n till_o the_o diameter_n of_o the_o semicircular_a hole_n of_o the_o polestar_n circle_v lie_v by_o estimation_n aequidistant_a from_o the_o horizon_n both_o end_n of_o the_o diameter_n be_v level_a or_o of_o like_a height_n one_o with_o another_o and_o so_o keep_v the_o polestar_n so_o near_o as_o you_o can_v guess_v upon_o the_o midst_n of_o that_o diameter_n and_o the_o fiducial_a line_n of_o the_o guard-index_n upon_o the_o guard_n move_z one_o of_o the_o movable_a sight_n of_o the_o quadrant_n up_o or_o down_o till_o the_o edge_n thereof_o lie_v even_o with_o the_o horizon_n thus_o therefore_o the_o polestar_n lie_v upon_o the_o midst_n of_o the_o diameter_n that_o be_v upon_o the_o centre_n of_o the_o polestar_n circle_n and_o the_o fiducial_a line_n of_o the_o guard_n index_n upon_o the_o guard_n and_o the_o edge_n of_o the_o sight_n even_o with_o the_o horizon_n the_o number_n of_o degree_n and_o minute_n from_o the_o end_n of_o the_o quadrant_n where_o the_o nocturnal_a be_v place_v to_o the_o edge_n of_o the_o sight_n add_v thereto_o five_o degree_n that_o be_v the_o distance_n of_o the_o centre_n of_o the_o nocturnal_a from_o the_o end_n of_o the_o quadrant_n shall_v be_v the_o height_n of_o the_o pole_n save_v that_o you_o must_v abate_v as_o before_o so_o much_o as_o be_v answerable_a to_o the_o height_n of_o your_o eye_n above_o the_o water_n to_o know_v the_o hour_n of_o the_o night_n by_o the_o nocturnal_a and_o the_o point_n of_o the_o short_a index_n which_o we_o call_v the_o day-index_n be_v first_o set_v to_o the_o day_n of_o the_o month_n show_v in_o the_o hour-circle_n the_o hour_n of_o the_o night_n at_o the_o time_n of_o your_o observation_n simon_n stevin_n his_o error_n in_o blame_v i_o of_o error_n in_o my_o table_n of_o rumb_n wherein_o also_o i_o be_o the_o more_o confirm_v by_o the_o like_a trial_n i_o have_v make_v of_o the_o first_o rumb_n count_v from_o the_o meridian_n though_o simon_n stevin_n in_o his_o solemn_a demonstration_n continue_v almost_o in_o three_o whole_a page_n in_o folio_n wherein_o he_o profess_v that_o the_o scope_n or_o mark_n he_o aim_v at_o 155._o be_v to_o demonstrate_v that_o my_o table_n of_o rumb_n be_v erroneous_a will_v make_v the_o world_n believe_v that_o my_o table_n err_v above_o two_o minute_n in_o the_o latitude_n of_o that_o rumb_n before_o i_o come_v to_o so_o little_a as_o two_o degree_n of_o longitude_n but_o the_o truth_n be_v he_o much_o mistake_v the_o matter_n the_o error_n be_v indeed_o in_o his_o own_o gross_a manner_n of_o trial_n much_o more_o than_o in_o my_o table_n for_o work_v after_o his_o own_o way_n by_o whole_a degree_n as_o he_o do_v it_o fall_v out_o even_o so_o as_o he_o say_v that_o the_o latitude_n of_o that_o rumb_n for_o two_o degree_n of_o longitude_n will_v be_v above_o 2_o minute_n great_a than_o my_o table_n have_v but_o if_o he_o work_v the_o very_a same_o way_n by_o six_o part_n of_o degree_n or_o ten_o of_o minute_n he_o shall_v find_v but_o little_a above_o half_a a_o minute_n more_o than_o be_v in_o my_o table_n of_o rumb_n nay_o moreover_o if_o it_o shall_v please_v he_o at_o his_o leisure_n to_o take_v the_o pain_n to_o make_v trial_n hereof_o to_o every_o single_a minute_n he_o shall_v not_o find_v so_o much_o as_o one_o second_o more_o than_o my_o account_n give_v for_o
with_o the_o regiment_n of_o the_o sun_n and_o of_o the_o star_n the_o rule_n of_o the_o moon_n and_o of_o the_o tide_n the_o declaration_n of_o the_o sea-chart_n and_o other_o thing_n appertain_v hereunto_o chap._n i._n the_o definition_n of_o the_o sphere_n a_o sphere_n be_v a_o solid_a or_o massy_a body_n without_o hollowness_n and_o perfect_o round_a in_o the_o midst_n whereof_o there_o be_v a_o prick_n call_v the_o centre_n by_o which_o there_o pass_v a_o right_a line_n name_v the_o axtree_n and_o the_o point_n where_o this_o line_n end_v upon_o the_o superficies_n of_o the_o whole_a body_n be_v call_v pole_n because_o upon_o they_o the_o sphere_n be_v move_v chap._n ii_o that_o the_o whole_a world_n be_v a_o sphere_n and_o so_o it_o be_v evident_a that_o the_o whole_a frame_n of_o the_o world_n wherein_o we_o live_v be_v a_o sphere_n be_v as_o it_o be_v solid_a so_o that_o in_o the_o whole_a world_n there_o be_v no_o empty_a place_n also_o it_o be_v perfect_o round_a upon_o the_o upper_a superficies_n of_o the_o high_a heaven_n and_o it_o have_v in_o the_o very_a midst_n a_o certain_a point_n to_o wit_n the_o centre_n of_o the_o earth_n by_o which_o we_o do_v imagine_v a_o right_a line_n or_o axtree_n to_o pass_v from_o one_o pole_n to_o another_o upon_o which_o the_o world_n be_v move_v about_o from_o east_n to_o west_n chap._n iii_o of_o the_o division_n of_o the_o sphere_n the_o whole_a sphere_n of_o the_o world_n be_v divide_v into_o two_o part_n or_o region_n the_o elementary_a and_o celestial_a the_o elementary_a part_n or_o region_n have_v four_o part_n the_o first_o whereof_o be_v the_o earth_n which_o together_o with_o the_o element_n of_o water_n which_o be_v the_o second_o make_v one_o perfect_a globe_n and_o round_o about_o both_o these_o be_v two_o other_o element_n namely_o the_o air_n and_o above_o that_o the_o fire_n which_o fill_v the_o space_n between_o the_o air_n and_o the_o sphere_n of_o the_o moon_n of_o which_o element_n by_o virtue_n of_o the_o heat_n of_o the_o heaven_n be_v make_v and_o compound_v all_o corruptible_a thing_n in_o the_o world_n the_o celestial_a region_n consist_v of_o other_o ten_o part_n the_o first_o whereof_o be_v the_o sphere_n of_o the_o moon_n the_o second_o the_o sphere_n of_o mercury_n the_o three_o of_o venus_n the_o four_o be_v the_o sphere_n of_o the_o sun_n the_o five_o of_o mars_n the_o six_o of_o jupiter_n the_o seven_o of_o saturn_n the_o eight_o be_v the_o sphere_n of_o the_o fix_a star_n which_o be_v call_v the_o firmament_n the_o nine_o be_v the_o crystalline_a heaven_n and_o last_o the_o ten_o and_o high_a be_v the_o sphere_n call_v the_o primum_fw-la mobile_a that_o be_v the_o first_o or_o high_a movable_a heaven_n that_o which_o remain_v call_v the_o empyreal_a heaven_n because_o it_o have_v no_o motion_n come_v not_o to_o be_v consider_v on_o in_o the_o art_n of_o navigation_n a_o figure_n wherein_o may_v be_v see_v the_o composition_n of_o the_o whole_a sphere_n of_o the_o world_n chap._n iu._n of_o the_o motion_n of_o the_o heaven_n the_o number_n of_o the_o heaven_n be_v know_v by_o the_o motion_n observe_v in_o they_o which_o be_v ten_o distinct_a one_o from_o another_o for_o the_o moon_n move_v her_o proper_a and_o peculiar_a motion_n in_o 27_o day_n and_o 8_o hour_n which_o be_v one_o revolution_n mercury_n venus_n and_o the_o sun_n finish_v their_o motion_n in_o one_o year_n which_o contain_v 365_o day_n and_o almost_o a_o quarter_n of_o a_o day_n mars_n run_v his_o course_n in_o two_o year_n jupiter_n in_o twelve_o year_n saturn_n in_o thirty_o year_n the_o eight_o sphere_n according_a to_o the_o opinion_n of_o some_o in_o seven_o thousand_o year_n the_o nine_o in_o five_o and_o twenty_o thousand_o and_o eight_o hundred_o year_n and_o the_o ten_o in_o four_o and_o twenty_o hour_n almost_o which_o ten_o motion_n be_v reduce_v unto_o three_o principal_a the_o first_o be_v that_o of_o the_o first_o movable_a upon_o the_o two_o end_n of_o the_o axletree_n which_o be_v call_v the_o pole_n of_o the_o world_n from_o east_n to_o west_n turn_v about_o again_o unto_o the_o east_n in_o 24_o hour_n and_o this_o sphere_n by_o the_o force_n of_o his_o motion_n carry_v about_o with_o it_o all_o the_o other_o low_a sphere_n in_o the_o space_n of_o 24_o hour_n howbeit_o they_o move_v also_o the_o contrary_a way_n with_o a_o second_o motion_n which_o be_v from_o west_n to_o east_n upon_o two_o other_o pole_n distant_a from_o the_o first_o about_o three_o and_o twenty_o and_o a_o half_a such_o part_n whereof_o the_o whole_a compass_n of_o heaven_n contain_v three_o hundred_o and_o sixty_o and_o this_o second_o motion_n be_v accomplish_v in_o each_o of_o the_o low_a heaven_n in_o divers_a space_n of_o time_n as_o be_v before_o say_v the_o three_o motion_n be_v proper_a to_o the_o eight_o heaven_n wherein_o the_o fix_a star_n be_v place_v which_o motion_n be_v the_o cause_n that_o the_o distance_n of_o the_o pole_n of_o the_o first_o motion_n from_o they_o of_o the_o second_o motion_n do_v vary_v be_v sometime_o great_a and_o sometime_o less_o chap._n v._o of_o the_o figure_n of_o the_o heaven_n that_o the_o heaven_n be_v round_o it_o be_v prove_v because_o roundness_n be_v the_o most_o perfect_a figure_n of_o all_o other_o be_v whole_a and_o entire_a have_v no_o need_n of_o any_o joint_n be_v also_o of_o the_o great_a capacity_n of_o all_o figure_n that_o have_v the_o same_o compass_n and_o in_o that_o respect_n most_o fit_a to_o contain_v all_o other_o thing_n also_o the_o principal_a body_n of_o the_o world_n as_o the_o sun_n the_o moon_n and_o the_o star_n be_v of_o this_o figure_n and_o we_o see_v the_o same_o likewise_o in_o those_o thing_n which_o be_v bound_v by_o themselves_o as_o it_o be_v manifest_a in_o drop_n of_o water_n and_o all_o other_o liquid_a thing_n chap._n vi_o that_o the_o earth_n and_o water_n make_v one_o perfect_a globe_n there_o be_v nothing_o that_o show_v more_o clear_o that_o the_o earth_n and_o water_n make_v one_o round_a globe_n than_o the_o shadow_n which_o they_o make_v in_o the_o eclipse_n of_o the_o moon_n which_o shadow_n we_o always_o see_v to_o be_v a_o part_n of_o a_o circle_n for_o if_o the_o body_n which_o be_v the_o cause_n of_o the_o same_o shadow_n be_v threesquare_a or_o foursquare_a the_o shadow_n itself_o also_o will_v appear_v in_o the_o same_o fashion_n wherefore_o the_o shadow_n of_o these_o two_o body_n together_o be_v round_o it_o be_v manifest_a that_o they_o be_v round_o also_o chap._n vii_o that_o the_o earth_n be_v in_o the_o centre_n of_o the_o world_n one_o sign_n we_o have_v to_o be_v assure_v that_o the_o earth_n be_v in_o the_o midst_n and_o centre_n of_o the_o world_n namely_o that_o wheresoever_o we_o be_v upon_o the_o face_n of_o the_o earth_n we_o always_o see_v one_o half_a of_o the_o heaven_n the_o other_o half_o be_v hide_v out_o of_o our_o sight_n moreover_o the_o star_n in_o what_o part_n of_o the_o heaven_n soever_o they_o be_v either_o in_o the_o east_n west_n or_o south_n we_o see_v that_o they_o be_v always_o of_o the_o very_a same_o bigness_n whereby_o we_o may_v easy_o perceive_v that_o they_o be_v always_o equal_o distant_a from_o our_o sight_n and_o whereas_o they_o move_v round_o about_o it_o it_o follow_v that_o we_o be_v upon_o the_o centre_n of_o that_o body_n on_o who_o superficies_n the_o say_a star_n describe_v their_o circle_n chap._n viii_o the_o whole_a quantity_n of_o the_o earth_n and_o albeit_o the_o globe_n of_o the_o earth_n and_o water_n compare_v with_o the_o sphere_n of_o the_o star_n be_v as_o it_o be_v a_o centre_n or_o prick_n yet_o be_v consider_v by_o itself_o it_o contain_v in_o the_o great_a circle_n thereof_o 6300_o common_a spanish_a league_n which_o a_o man_n may_v easy_o perceive_v by_o take_v two_o such_o point_n or_o headland_n of_o the_o earth_n as_o be_v under_o the_o same_o meridian_n and_o which_o differ_v in_o distance_n one_o from_o another_o so_o much_o as_o one_o of_o those_o part_n be_v whereof_o the_o compass_n of_o the_o whole_a world_n contain_v 360_o and_o it_o be_v find_v both_o by_o navigation_n at_o sea_n and_o also_o by_o travel_n on_o land_n that_o the_o two_o foresay_a point_n be_v distant_a each_o from_o other_o 17_o league_n and_o a_o half_a of_o which_o league_n each_o one_o contain_v 4000_o pace_n every_o pace_n 5_o foot_n every_o foot_n 16_o finger_n and_o every_o finger_n 4_o grain_n of_o barley_n chap._n ix_o of_o the_o equinoctial_a circle_n be_v to_o treat_v of_o the_o circle_n of_o the_o sphere_n of_o the_o world_n the_o first_o which_o offer_v itself_o to_o be_v speak_v of_o be_v the_o equinoctial_a circle_n by_o mean_n whereof_o we_o do_v know_v in_o
what_o part_n of_o the_o world_n we_o be_v and_o in_o it_o in_o the_o sea-chart_n be_v place_v all_o these_o point_n or_o degree_n of_o longitude_n and_o from_o it_o the_o latitude_n be_v account_v so_o that_o the_o equinoctial_a be_v a_o circle_n which_o divide_v the_o world_n into_o two_o equal_a portion_n and_o be_v equal_o distant_a every_o where_o from_o either_o of_o the_o pole_n and_o it_o be_v call_v the_o equinoctial_a circle_n because_o that_o when_o the_o sun_n pass_v under_o it_o upon_o the_o 11_o of_o march_n and_o the_o 13_o of_o september_n it_o make_v the_o day_n equal_a to_o the_o night_n the_o knowledge_n of_o this_o circle_n in_o the_o art_n of_o navigation_n do_v help_v we_o to_o find_v the_o latitude_n or_o distance_n from_o the_o line_n and_o from_o this_o circle_n be_v reckon_v the_o declination_n of_o the_o sun_n in_o the_o regiment_n thereof_o and_o always_o those_o chart_n of_o navigation_n which_o be_v either_o universal_a or_o half_a universal_a have_v this_o equinoctial_a circle_n draw_v with_o a_o great_a red_a line_n which_o pass_v by_o the_o begin_n of_o the_o account_n of_o the_o degree_n of_o latitude_n chap._n x._o of_o the_o pole_n of_o the_o world_n and_o here_o it_o be_v to_o be_v note_v that_o one_o of_o those_o two_o pole_n from_o which_o the_o equinoctial_a be_v equal_o distant_a which_o be_v always_o in_o our_o sight_n because_o it_o be_v continual_o above_o our_o horizon_n be_v call_v the_o pole-artick_a the_o septentrional_a or_o north_n pole_n but_o the_o other_o opposite_a pole_n which_o we_o never_o see_v because_o it_o be_v under_o our_o horizon_n be_v call_v the_o pole-antartick_a and_o the_o meridional_a or_o south_n pole_n and_o so_o that_o part_n of_o the_o world_n which_o be_v between_o the_o equinoctial_a and_o the_o north_n pole_n be_v call_v the_o north_n part_n and_o that_o which_o be_v from_o the_o equinoctial_a to_o the_o south_n pole_n be_v call_v the_o south_n part_n chap_n xi_o of_o the_o ecliptic_a line_n the_o equinoctial_a circle_n be_v divide_v into_o equal_a part_n by_o another_o circle_n call_v the_o ecliptic_a whereof_o one_o half_a be_v between_o the_o equinoctial_a and_o the_o north_n pole_n and_o the_o other_o half_a between_o the_o equinoctial_a and_o the_o south_n pole_n and_o that_o part_v thereof_o which_o be_v further_a distant_a from_o the_o equinoctial_a be_v distant_a from_o the_o same_o about_o 23_o degree_n and_o a_o half_a and_o because_o the_o sun_n move_v in_o this_o circle_n without_o depart_v from_o it_o hereof_o proceed_v the_o declination_n thereof_o and_o this_o circle_n in_o all_o part_n be_v equal_o distant_a from_o the_o pole_n of_o the_o second_o motion_n which_o be_v call_v the_o pole_n of_o the_o ecliptic_a and_o through_o this_o circle_n the_o sun_n be_v continual_o move_v by_o his_o proper_a motion_n from_o east_n to_o west_n by_o mean_n of_o which_o motion_n sometime_o he_o pass_v under_o the_o equinoctial_a and_o at_o other_o time_n depart_v from_o it_o both_o towards_o the_o north_n and_o towards_o the_o south_n and_o the_o quantity_n of_o his_o great_a distance_n be_v about_o 23_o degree_n and_o a_o half_a and_o so_o much_o be_v the_o distance_n of_o the_o pole_n of_o the_o ecliptic_a from_o the_o pole_n of_o the_o equinoctial_a and_o albeit_o this_o circle_n be_v not_o draw_v in_o the_o sea_n chartley_n yet_o be_v it_o in_o some_o sort_n represent_v in_o the_o table_n of_o the_o sun_n declination_n which_o be_v gather_v from_o the_o motion_n which_o the_o sun_n make_v under_o the_o ecliptic_a chap._n xii_o of_o the_o declination_n of_o the_o sun_n the_o motion_n of_o the_o sun_n under_o the_o ecliptic_a be_v the_o cause_n of_o his_o declination_n which_o be_v nothing_o else_o but_o the_o daily_a swarve_n or_o decline_a of_o the_o sun_n from_o the_o equinoctial_a line_n and_o this_o declination_n when_o the_o sun_n be_v under_o the_o equinoctial_a upon_o the_o eleven_o of_o march_n and_o thirteen_o of_o september_n be_v nothing_o at_o all_o so_o likewise_o upon_o the_o twelve_o of_o june_n and_o twelve_o of_o december_n the_o declination_n be_v at_o the_o great_a and_o albeit_o this_o great_a declination_n be_v now_o in_o our_o time_n about_o three_o and_o twenty_o degree_n and_o a_o half_a yet_o have_v it_o at_o other_o time_n be_v find_v otherwise_o by_o reason_n of_o a_o three_o motion_n proper_a to_o the_o eight_o heaven_n but_o it_o always_o keep_v between_o 23_o degree_n 28_o minute_n and_o 23_o degree_n 53_o minute_n from_o hence_o therefore_o we_o do_v infer_v that_o at_o divers_a time_n it_o be_v meet_v to_o make_v new_a and_o divers_a table_n of_o the_o declination_n of_o the_o sun_n chap._n xiii_o of_o the_o colour_n there_o be_v two_o circle_n of_o the_o sphere_n either_o of_o which_o divide_v in_o into_o two_o equal_a part_n and_o they_o be_v call_v colour_n because_o that_o in_o the_o revolution_n which_o they_o make_v by_o force_n of_o the_o primum_fw-la mobile_a they_o do_v not_o show_v themselves_o whole_o unto_o we_o so_o as_o we_o may_v see_v all_o part_n of_o they_o one_o of_o they_o be_v call_v the_o equinoctial_a colour_n because_o it_o pass_v by_o the_o pole_n of_o the_o world_n and_o the_o point_n where_o the_o ecliptic_a cut_v the_o equinoctial_a and_o when_o the_o sun_n by_o his_o own_o proper_a motion_n come_v unto_o it_o he_o make_v the_o day_n and_o the_o night_n equal_a and_o divide_v the_o winter_n from_o the_o spring_n by_o the_o one_o part_n and_o by_o the_o other_o summer_n from_o autumn_n at_o which_o time_n the_o sun_n have_v no_o declination_n at_o all_o the_o other_o be_v call_v the_o solstitial_a colour_n because_o it_o pass_v by_o the_o pole_n of_o the_o world_n and_o of_o the_o ecliptic_a and_o by_o the_o point_n where_o the_o ecliptic_a be_v further_a distant_a from_o the_o equinoctial_a and_o when_o the_o sun_n by_o his_o proper_a motion_n come_v unto_o it_o in_o the_o one_o part_v it_o make_v the_o long_a day_n and_o the_o short_a night_n and_o divide_v the_o spring_n from_o the_o summer_n and_o have_v his_o great_a declination_n towards_o the_o north_n and_o be_v in_o the_o other_o part_n the_o sun_n make_v the_o long_a night_n and_o short_a day_n and_o divide_v winter_n from_o autumn_n and_o be_v in_o his_o great_a southerly_a declination_n these_o two_o colour_n be_v note_v in_o the_o table_n of_o the_o sun_n declination_n because_o the_o equinoctial_a colour_n pass_v by_o the_o two_o point_n where_o there_o be_v no_o declination_n at_o all_o because_o the_o sun_n be_v under_o the_o very_a equinoctial_a circle_n and_o the_o solstitial_a colour_n pass_v by_o that_o place_n where_o the_o sun_n have_v his_o great_a declination_n which_o be_v in_o 23_o degree_n and_o a_o half_a or_o thereabouts_o chap._n fourteen_o of_o the_o meridian_n circle_n the_o meridian_n be_v a_o circle_n draw_v by_o the_o pole_n of_o the_o world_n which_o be_v all_o one_o with_o the_o pole_n of_o the_o equinoctial_a and_o and_o by_o the_o point_n direct_o over_o our_o head_n call_v the_o zenith_n and_o it_o be_v call_v the_o meridian_n because_o that_o when_o the_o sun_n by_o the_o motion_n of_o the_o primum_fw-la mobile_a come_v unto_o this_o circle_n it_o make_v midday_n and_o then_o he_o have_v be_v run_v his_o course_n from_o his_o rise_n till_o he_o come_v thither_o just_o so_o long_a time_n as_o he_o shall_v be_v run_v from_o thence_o to_o the_o place_n of_o his_o set_n the_o zenith_n be_v a_o point_n in_o the_o firmament_n place_v direct_o over_o our_o head_n and_o it_o be_v to_o be_v note_v that_o when_o the_o sun_n be_v in_o that_o circle_n it_o have_v the_o great_a altitude_n above_o our_o horizon_n that_o it_o can_v possible_o have_v the_o same_o day_n by_o this_o and_o the_o declination_n we_o come_v to_o know_v how_o far_o we_o be_v distant_a from_o the_o equinoctial_a either_o towards_o the_o north_n or_o towards_o the_o south_n and_o hence_o it_o be_v that_o the_o height_n of_o the_o sun_n in_o navigation_n be_v understand_v only_o for_o that_o height_n which_o the_o sun_n have_v when_o he_o be_v in_o this_o circle_n and_o so_o the_o height_n of_o the_o sun_n shall_v be_v that_o part_n of_o the_o meridian_n which_o be_v contain_v between_o the_o sun_n and_o our_o horizon_n this_o circle_n in_o the_o sea-chart_n be_v represent_v by_o all_o those_o line_n which_o be_v draw_v from_o north_n to_o south_n chap._n xv._n of_o the_o horizon_n the_o horizon_n be_v a_o circle_n which_o divide_v that_o part_n of_o the_o heaven_n which_o we_o see_v from_o the_o residue_n which_o we_o do_v not_o see_v and_o it_o be_v proper_o that_o circle_n by_o which_o according_a to_o our_o sight_n the_o heaven_n seem_v to_o be_v join_v with_o the_o water_n when_o we_o be_v at_o sea_n without_o sight_n of_o
rule_n of_o the_o declination_n of_o the_o sun_n we_o be_v to_o note_v that_o the_o year_n which_o be_v the_o time_n of_o the_o sun_n motion_n from_o any_o point_n of_o the_o ecliptic_a till_o he_o return_v again_o to_o the_o same_o point_n consist_v not_o always_o of_o a_o equal_a number_n of_o day_n for_o beside_o 365_o day_n it_o contain_v almost_o one_o quarter_n of_o a_o day_n but_o the_o year_n which_o we_o common_o account_n contain_v 365_o day_n in_o common_a year_n and_o in_o leap_v year_n 366._o it_o be_v therefore_o needful_a to_o make_v four_o table_n of_o twelve_o month_n apiece_o whereof_o the_o three_o first_o contain_v 365_o day_n and_o the_o four_o 366_o and_o in_o such_o sort_n to_o distribute_v the_o declination_n of_o the_o sun_n among_o they_o that_o you_o may_v make_v account_n of_o the_o declination_n which_o be_v want_v to_o the_o sun_n at_o the_o end_n of_o 365_o day_n for_o lack_v of_o those_o six_o hour_n almost_o which_o the_o sun_n want_v to_o come_v unto_o the_o point_n from_o which_o it_o depart_v at_o the_o begin_n of_o the_o year_n and_o also_o of_o the_o declination_n which_o result_v in_o the_o four_o year_n because_o it_o consist_v of_o 366_o day_n at_o what_o time_n it_o come_v to_o recover_v that_o which_o in_o the_o three_o former_a year_n it_o have_v lose_v therefore_o to_o know_v at_o all_o time_n which_o of_o the_o four_o table_n we_o ought_v to_o make_v use_n of_o i_o will_v set_v down_o a_o rule_n whereby_o you_o may_v know_v whether_o the_o present_a year_n be_v leap_v year_n or_o whether_o it_o be_v the_o first_o second_o or_o three_o year_n after_o the_o leap_n year_n and_o the_o rule_n be_v this_o that_o take_v from_o the_o year_n of_o our_o lord_n which_o run_v in_o our_o common_a account_n the_o number_n of_o 1600_o if_o the_o remainder_n thereof_o be_v a_o even_a number_n and_o half_a of_o the_o remainder_n and_o even_a number_n than_o that_o year_n be_v leap_v year_n and_o if_o the_o remainder_n be_v even_o and_o the_o half_a thereof_o odd_a than_o that_o year_n be_v the_o second_o year_n after_o the_o leap_n year_n but_o if_o the_o remainder_n of_o the_o year_n number_v be_v odd_a we_o must_v try_v the_o year_n next_o go_v before_o to_o see_v whether_o the_o remainder_n thereof_o and_o half_o the_o remainder_n be_v even_a number_n for_o then_o the_o present_a year_n be_v the_o first_o after_o the_o leap_n year_n and_o if_o the_o remainder_n of_o the_o year_n go_v before_o be_v even_o and_o the_o half_a thereof_o odd_a than_o the_o present_a year_n be_v the_o three_o year_n after_o the_o leap_n year_n how_o the_o declination_n of_o the_o sun_n may_v be_v find_v out_o now_o to_o know_v the_o sun_n declination_n every_o day_n we_o must_v look_v in_o that_o table_n which_o answer_v to_o the_o present_a year_n and_o seek_v the_o month_n in_o the_o upper_a part_n of_o the_o page_n and_o the_o day_n of_o the_o month_n wherein_o we_o will_v know_v the_o declination_n in_o the_o column_n which_o defend_v towards_o the_o left_a hand_n right_o over_o against_o the_o say_a day_n and_o under_o the_o title_n of_o our_o month_n we_o shall_v find_v two_o number_n one_o of_o degree_n and_o the_o other_o of_o minute_n which_o be_v the_o declination_n of_o the_o sun_n that_o day_n towards_o that_o part_n of_o the_o world_n which_o the_o first_o rule_n of_o the_o sun_n do_v teach_v chap._n vi_o the_o equation_n of_o the_o sun_n declination_n they_o which_o sail_n in_o the_o month_n of_o june_n and_o december_n need_v not_o much_o to_o make_v any_o equation_n in_o the_o table_n of_o the_o sun_n declination_n because_o that_o in_o those_o month_n the_o declination_n of_o one_o day_n differ_v very_o little_a from_o the_o declination_n of_o another_o but_o at_o all_o other_o time_n of_o the_o year_n we_o ought_v to_o make_v some_o kind_n of_o equation_n to_o know_v precise_o our_o height_n or_o our_o distance_n from_o the_o equinoctial_a this_o equation_n be_v to_o be_v make_v after_o this_o manner_n you_o must_v subtract_v the_o declination_n of_o the_o sun_n for_o the_o present_a day_n from_o the_o declination_n of_o the_o day_n follow_v or_o contrariwise_o subtract_v always_o the_o less_o out_o oâ—_n the_o great_a and_o the_o difference_n or_o remainder_n shall_v be_v multiply_v by_o the_o league_n which_o our_o ship_n have_v sail_v from_o the_o meridian_n of_o london_n and_o the_o product_n of_o the_o multiplication_n must_v be_v divide_v by_o desire_v 7200_o league_n which_o be_v contain_v in_o the_o compass_n of_o the_o whole_a earth_n then_o if_o you_o have_v sail_v westward_o the_o quotient_n must_v be_v add_v to_o the_o declination_n of_o the_o sun_n that_o day_n if_o it_o be_v from_o the_o 11_o of_o march_n to_o the_o 12_o of_o june_n or_o from_o the_o 13_o of_o september_n to_o the_o 12_o of_o december_n or_o it_o must_v if_o the_o ship_n also_o have_v sail_v westward_o be_v subtract_v if_o you_o find_v it_o in_o any_o other_o time_n of_o the_o year_n except_o in_o the_o day_n of_o the_o equinoctium_n for_o then_o this_o difference_n be_v know_v by_o take_v the_o declination_n of_o the_o present_a day_n with_o that_o of_o the_o day_n follow_v but_o if_o you_o be_v to_o the_o eastward_o from_o the_o meridian_n of_o london_n you_o must_v do_v contrariwise_o subtract_v the_o say_a squation_n where_o before_o you_o add_v it_o in_o stead_n of_o the_o table_n of_o the_o sun_n declination_n here_o insert_v by_o roderigo_n samorano_n use_v the_o table_n before_o set_v down_o from_o the_o 174_o page_n to_o the_o 180_o page_n chap._n vii_o four_o example_n for_o the_o plain_a declaration_n of_o that_o which_o be_v say_v before_o a_o example_n of_o the_o second_o rule_n in_o the_o year_n 1608_o the_o 15_o of_o april_n suppose_v i_o be_v sail_v and_o take_v the_o height_n of_o the_o sun_n with_o my_o astrolabe_n at_o noon_n and_o find_v the_o height_n thereof_o to_o be_v just_a 90_o degree_n first_o therefore_o i_o take_v from_o 1608._o the_o number_n of_o 1600._o and_o their_z remain_z 8_o whicâ—_n remainder_n be_v a_o even_a number_n and_o four_o the_o half_a thereof_o be_v even_o also_o i_o say_v the_o year_n 1608_o be_v the_o leap_v year_n and_o so_o i_o go_v unto_o the_o four_o year_n in_o the_o table_n of_o the_o sun_n declination_n which_o be_v leap_v year_n and_o under_o the_o month_n of_o april_n over_o against_o the_o 15_o day_n i_o find_v 13_o degree_n and_o 25_o minute_n 41_o second_o i_o say_v therefore_o that_o i_o be_o distant_a from_o the_o equinoctial_a towards_o the_o north_n 13_o degree_n and_o 26_o minute_n almost_o because_o it_o be_v between_o the_o 11_o of_o march_n and_o the_o 13_o of_o september_n in_o which_o space_n fall_v the_o 15_o day_n of_o april_n the_o second_o example_n of_o the_o three_o rule_n in_o the_o year_n 1602_o upon_o the_o 13_o day_n of_o september_n admit_v i_o take_v the_o height_n of_o the_o sun_n and_o find_v it_o in_o my_o astrolabe_n to_o be_v 70_o degree_n and_o a_o half_a and_o that_o in_o the_o table_n of_o declination_n belong_v to_o the_o same_o year_n upon_o the_o foresay_a day_n of_o september_n i_o find_v that_o the_o sun_n have_v no_o declination_n but_o that_o it_o be_v under_o the_o very_a equinoctial_a line_n now_o because_o the_o degree_n of_o the_o height_n which_o the_o sun_n want_v of_o 90_o be_v 19_o and_o a_o half_a i_o say_v that_o i_o be_o so_o much_o distant_a from_o the_o equinoctial_a towards_o that_o part_n of_o the_o world_n unto_o which_o the_o shadow_n fall_v example_n of_o the_o four_o rule_n upon_o the_o 13_o of_o may_n 1609_o suppose_v i_o take_v the_o height_n of_o the_o sun_n at_o noon_n in_o my_o astrolabe_n and_o find_v it_o to_o be_v 85_o degree_n and_o three_o quarter_n now_o because_o 1609_o be_v a_o odd_a number_n i_o go_v back_o to_o the_o former_a year_n of_o 1608._o and_o i_o find_v according_a to_o the_o rule_n of_o leap_n year_n that_o the_o year_n 1608_o be_v leap_v year_n and_o hence_o i_o judge_v that_o the_o year_n 1609_o be_v the_o year_n next_o follow_v the_o leap_n year_n then_o i_o go_v to_o the_o table_n of_o declination_n belong_v to_o the_o first_o year_n after_o the_o leap_n year_n and_o under_o the_o month_n of_o may_n against_o the_o 13_o day_n the_o sun_n declination_n be_v find_v to_o be_v 20_o degree_n 41_o minute_n 15_o second_o and_o because_o that_o from_o the_o 11_o of_o march_n to_o the_o 13_o of_o september_n the_o sun_n keep_v his_o course_n to_o the_o northwards_o of_o the_o equinoctial_a have_v mark_v the_o shadow_n at_o midday_n i_o see_v that_o the_o low_a vain_a of_o my_o astrolabe_n look_v to_o the_o north_n of_o the_o compass_n and_o so_o i_o say_v that_o
the_o quarter_n a_o example_n whereby_o the_o foresay_a rule_n be_v make_v more_o plain_a suppose_v a_o fleet_n of_o ship_n lie_v within_o the_o heaven_n of_o san_n lucar_n de_fw-fr barrameda_fw-la expect_v a_o fit_a time_n to_o pass_v over_o the_o bar_n towards_o the_o indies_n it_o be_v evident_a that_o if_o the_o ship_n be_v great_a they_o have_v need_n of_o much_o water_n to_o pass_v the_o bank_n or_o the_o bar_n which_o quantity_n of_o water_n be_v only_o in_o the_o springtide_n and_o because_o they_o be_v twice_o in_o one_o month_n namely_o in_o the_o conjunction_n and_o in_o the_o full_a of_o the_o moon_n i_o desire_v to_o know_v when_o the_o springtide_n and_o neap-tide_n of_o the_o month_n of_o june_n in_o the_o year_n 1588._o be_v to_o be_v expect_v in_o which_o month_n i_o presuppose_v the_o fleet_n be_v to_o depart_v first_o therefore_o i_o cast_v away_o 1500_o and_o cut_v of_o the_o 88_o remain_v i_o take_v from_o each_o 20._o one_o which_o make_v four_o in_o all_o which_o be_v add_v to_o the_o 8_o that_o surmount_v 80._o they_o make_v the_o golden_a number_n to_o be_v 12_o according_a to_o the_o first_o rule_n i_o divide_v these_o twelve_o by_o three_o and_o the_o quotient_n be_v four_o and_o nothing_o remain_v and_o because_o there_o be_v no_o remainder_n i_o will_v take_v two_o more_o of_o the_o concurrent_a thâ—n_n of_o the_o golden_a number_n and_o there_o shall_v be_v two_o of_o the_o concurrent_a cast_v away_o thirty_o by_o the_o second_o rule_n add_v these_o two_o to_o the_o four_o month_n which_o be_v from_o the_o begin_n of_o march_n pass_v till_o this_o present_a month_n of_o june_n england_n i_o find_v that_o they_o make_v six_o and_o because_o six_o want_n twenty_o four_o to_o make_v up_o thirty_o i_o say_v that_o in_o the_o year_n 1588._o we_o have_v a_o conjunction_n of_o the_o moon_n upon_o the_o 24_o of_o june_n by_o the_o three_o rule_n and_o add_v seven_o unto_o the_o day_n of_o this_o conjunction_n you_o have_v the_o first_o day_n of_o july_n which_o be_v the_o day_n of_o the_o first_o quarter_n and_o take_v away_o 15_o from_o 24_o be_v the_o number_n of_o the_o conjunction_n day_n there_o remain_v nine_o and_o upon_o that_o day_n of_o the_o month_n you_o have_v the_o full_a moon_n and_o add_v other_o seven_o unto_o the_o nine_o day_n of_o the_o full_a moon_n you_o have_v the_o last_o quarter_n upon_o the_o sixteen_o of_o june_n by_o the_o four_o rule_n i_o say_v therefore_o that_o the_o springtide_n or_o great_a water_n of_o the_o month_n of_o june_n be_v in_o that_o year_n upon_o the_o nine_o and_o four_o and_o twenty_o day_n of_o june_n and_o the_o neap-tide_n or_o less_o water_n be_v upon_o the_o sixteenth-day_n of_o june_n and_o the_o first_o of_o july_n by_o the_o five_o rule_n chap._n xxxii_o of_o the_o daily_a tide_n now_o that_o we_o know_v the_o rule_n of_o the_o springtide_n and_o neap-tide_n let_v we_o say_v somewhat_o of_o the_o tide_n that_o happen_v every_o day_n which_o depend_v upon_o another_o swift_a motion_n of_o the_o moon_n whereby_o turn_v round_o about_o the_o world_n from_o east_n to_o west_n it_o pass_v every_o day_n by_o the_o 32_o point_n of_o the_o compass_n and_o this_o daily_a motion_n of_o the_o sea_n fall_v not_o every_o day_n at_o the_o same_o hour_n because_o the_o moon_n do_v not_o always_o keep_v one_o and_o the_o same_o distance_n from_o the_o sun_n for_o the_o moon_n move_v almost_o thirteen_o degree_n of_o her_o proper_a motion_n in_o one_o natural_a day_n whereas_o the_o sun_n move_v scarce_o one_o and_o so_o one_o be_v take_v from_o thirteen_o there_o remain_v 12._o and_o because_o the_o sun_n do_v give_v and_o mark_v out_o unto_o we_o hour_n and_o the_o moon_n tide_n it_o come_v to_o pass_v that_o a_o hour_n be_v that_o space_n of_o time_n wherein_o fifteen_o degree_n of_o the_o equinoctial_a pass_n by_o every_o point_n of_o the_o compass_n the_o part_n by_o which_o the_o moon_n be_v distant_a from_o the_o sun_n shall_v be_v twelve_o degree_n which_o twelve_o be_v â…˜_n of_o fifteen_o degree_n contain_v in_o each_o hour_n insomuch_o that_o the_o moon_n by_o her_o middle_a motion_n be_v every_o day_n distant_a from_o the_o sun_n about_o twelve_o degree_n which_o be_v reduce_v into_o time_n do_v make_v â…˜_n part_n of_o a_o hour_n whereby_o the_o moon_n be_v every_o day_n slow_a than_o the_o sun_n in_o come_v to_o each_o point_n of_o the_o heaven_n by_o the_o motion_n from_o east_n to_o west_n in_o regard_n of_o that_o which_o she_o have_v borrow_v for_o she_o own_o proper_a motion_n from_o west_n to_o east_n whereof_o it_o come_v to_o pass_v that_o so_o many_o day_n as_o the_o moon_n be_v old_a so_o many_o time_n â…˜_n part_n of_o a_o hour_n it_o be_v slow_a than_o the_o sun_n in_o pass_v by_o each_o rumb_n until_o the_o day_n of_o their_o conjunction_n when_o as_o they_o pass_v both_o by_o the_o same_o rumb_n in_o one_o and_o the_o same_o hour_n and_o so_o according_o because_o we_o be_v to_o set_v down_o the_o certain_a hour_n of_o every_o day_n wherein_o the_o tide_n happen_v we_o must_v diligent_o observe_v the_o rule_n follow_v the_o first_o rule_n in_o divers_a part_n of_o the_o sea_n coast_n the_o moon_n make_v a_o full_a sea_n every_o day_n be_v in_o divers_a rumb_n according_a to_o the_o disposition_n of_o the_o land_n but_o upon_o all_o the_o coast_n of_o spain_n in_o the_o ocean_n it_o be_v full_a sea_n when_o the_o moon_n be_v in_o the_o north-east_n and_o south-west_n the_o second_o rule_n upon_o the_o day_n of_o the_o conjunction_n and_o full_a moon_n you_o have_v a_o full_a sea_n at_o three_o a_o clock_n in_o the_o morning_n and_o at_o three_o in_o the_o after_o noon_n for_o at_o those_o hour_n the_o moon_n go_v with_o the_o sun_n at_o the_o north-east_n and_o at_o the_o south-west_n but_o upon_o other_o day_n of_o the_o moon_n the_o full_a sea_n fall_v out_o at_o the_o same_o hour_n when_o the_o moon_n come_v to_o those_o two_o point_n which_o be_v know_v by_o count_v the_o age_n of_o the_o moon_n the_o three_o rule_n that_o you_o may_v know_v at_o all_o time_n how_o many_o day_n old_a the_o moon_n be_v you_o must_v add_v three_o number_n together_o to_o wit_n the_o concurrent_a and_o the_o month_n from_o the_o begin_n of_o march_n to_o the_o month_n present_a and_o the_o day_n of_o the_o month_n wherein_o you_o will_v know_v this_o and_o if_o the_o whole_a product_n exceed_v not_o thirty_o it_o contain_v just_a the_o day_n of_o the_o moon_n but_o if_o it_o do_v exceed_v thirty_o the_o surplusage_n show_v the_o day_n of_o the_o moon_n age_n the_o four_o rule_n multiply_v the_o day_n of_o the_o moon_n age_n by_o four_o and_o divide_v the_o product_n by_o five_o and_o the_o remainder_n after_o division_n contain_v the_o hour_n whereby_o the_o moon_n come_v more_o slow_o than_o the_o sun_n to_o the_o north-east_n or_o south-west_n or_o to_o that_o rumb_n wherein_o it_o make_v a_o full_a sea_n which_o hour_n shall_v be_v add_v to_o the_o three_o hour_n of_o the_o morning_n and_o then_o you_o have_v the_o hour_n of_o the_o first_o tide_n or_o of_o the_o full_a and_o swell_a sea_n and_o six_o hour_n and_o almost_o a_o quarter_n after_o come_v the_o first_o ebb_n or_o low_a water_n and_o 12_o hour_n and_o â…•_n after_o the_o first_o full_a sea_n come_v the_o second_o tide_n and_o other_o six_o hour_n and_o â…•_n after_o the_o second_o tide_n come_v the_o second_o ebb_n the_o five_o rule_n when_o the_o day_n of_o the_o moon_n age_n be_v less_o than_o fifteen_o we_o may_v make_v by_o they_o our_o account_n for_o the_o tide_n but_o if_o they_o exceed_v fifteen_o we_o must_v make_v our_o account_n by_o the_o surplusage_n a_o example_n of_o the_o say_a rule_n upon_o the_o 29_o of_o july_n 1588._o i_o desire_v to_o know_v the_o hour_n of_o the_o full_a sea_n and_o of_o the_o ebb_n to_o make_v choice_n of_o that_o which_o may_v seem_v most_o expedient_a for_o my_o voyage_n by_o the_o forme_a example_n i_o find_v that_o the_o golden_a number_n of_o this_o year_n be_v 12_o and_o the_o concurrent_a 2_o according_a to_o the_o correction_n of_o the_o year_n by_o pope_n gregory_n the_o 13._o then_o i_o add_v this_o number_n of_o 2_o to_o the_o number_n of_o 5_o month_n which_o have_v pass_v from_o the_o begin_n of_o march_n and_o the_o 29_o day_n of_o the_o month_n of_o july_n all_o which_o 3_o number_n make_v 36_o then_o i_o cast_v away_o 30_o and_o there_o remain_v six_o day_n for_o the_o age_n of_o the_o moon_n and_o because_o they_o exceed_v not_o fifteen_o i_o multiply_v they_o by_o â…˜_n of_o a_o hour_n according_a to_o the_o four_o rule_n and_o they_o may_v make_v 24_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