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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pass_v over_o the_o south_n sea_n come_v the_o 12_o of_o september_n to_o the_o philippinas_fw-la differ_v in_o longitude_n from_o london_n westward_n about_o 210_o degree_n in_o this_o example_n because_o the_o sun_n be_v near_o the_o equinoctial_a point_n alter_v his_o declination_n about_o 24_o min._n in_o 24_o hour_n that_o be_v for_o every_o hour_n one_o minute_n therefore_o divide_v 210._o the_o difference_n of_o longitude_n by_o 15_o the_o number_n of_o degree_n contain_v in_o one_o hour_n the_o quotient_n will_v be_v 14_o minute_n the_o difference_n of_o declination_n answerable_a to_o that_o difference_n of_o longitude_n the_o declination_n find_v in_o the_o table_n for_o that_o day_n be_v 10_o minute_n 2_o second_n northerly_a which_o declination_n because_o it_o decrease_v the_o sun_n not_o be_v yet_o come_v to_o the_o equinoctial_a must_v be_v subtract_v out_o of_o 14._o and_o there_o shall_v remain_v 3_o min._n 58_o sec._n the_o declination_n of_o the_o sun_n that_o day_n at_o noon_n for_o that_o place_n but_o this_o declination_n be_v southerly_a because_o the_o quotient_a 14_o min._n be_v great_a than_o 10_o min._n 2_o sec._n the_o declination_n find_v in_o the_o table_n it_o will_v be_v at_o this_o time_n too_o tedious_a for_o i_o further_o to_o exemplify_v every_o particularity_n specify_v in_o the_o former_a rule_n which_o may_v cause_v some_o small_a diversity_n in_o the_o use_n of_o the_o sun_n declination_n have_v already_o give_v example_n of_o the_o hard_a case_n that_o may_v befall_v herein_o which_o if_o they_o be_v well_o consider_v and_o especial_o compare_v with_o the_o globe_n or_o sphere_n wherein_o the_o whole_a manner_n of_o the_o sun_n motion_n and_o declination_n may_v most_o easy_o not_o only_o be_v see_v but_o also_o feel_v as_o it_o be_v with_o the_o finger_n end_n the_o reason_n and_o demonstration_n of_o all_o those_o rule_n and_o of_o all_o the_o diversity_n of_o work_v therein_o specify_v may_v most_o plain_o appear_v to_o he_o that_o be_v but_o of_o a_o mean_a capacity_n chap._n xxix_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 but_o because_o the_o declination_n of_o the_o sun_n be_v then_o only_o of_o good_a use_n for_o know_v the_o latitude_n at_o sea_n when_o his_o meridian_n altitude_n may_v be_v observe_v so_o as_o although_o all_o the_o rest_n of_o the_o day_n and_o night_n be_v fair_a and_o clear_a if_o a_o cloud_n cover_v the_o sun_n but_o one_o quarter_n of_o a_o hour_n only_o about_o noon_n your_o table_n of_o the_o sun_n declination_n will_v stand_v you_o in_o no_o stead_n there_o have_v be_v therefore_o other_o mean_n divise_v for_o attain_v to_o the_o knowledge_n of_o the_o height_n of_o the_o pole_n not_o only_o in_o particular_a by_o observation_n of_o the_o polestar_n and_o guard_n but_o also_o in_o general_a by_o the_o meridian_n altitude_n and_o declination_n of_o any_o notable_a fix_a star_n whatsoever_o so_o as_o not_o in_o the_o day_n time_n alone_o and_o that_o only_a at_o noon_n but_o almost_o at_o any_o time_n of_o the_o night_n if_o any_o small_a portion_n of_o the_o heaven_n towards_o the_o north_n or_o south_n appear_v but_o a_o small_a time_n clear_a through_o the_o rake_n cloud_n the_o latitude_n of_o the_o place_n where_o you_o be_v may_v hereby_o be_v more_o easy_o know_v then_o by_o observation_n of_o the_o sun_n meridian_n altitude_n for_o to_o omit_v the_o change_n of_o the_o sun_n declination_n from_o north_n to_o south_n and_o from_o south_n to_o north_n twice_o in_o every_o year_n which_o notwithstanding_o breed_v some_o diversity_n of_o work_v by_o neglect_n whereof_o some_o have_v grosâ—y_o err_v the_o sun_n by_o reason_n of_o his_o swiftness_n of_o motion_n increase_v or_o diminish_v his_o declination_n daily_o yea_o hourly_o and_o that_o very_o sensible_o many_o time_n whereof_o there_o must_v needs_o arise_v many_o several_a consideration_n to_o be_v have_v of_o the_o right_a use_n and_o application_n of_o the_o sun_n declination_n find_v in_o the_o table_n as_o well_o in_o respect_n of_o the_o part_n of_o declination_n whether_o it_o be_v north_n or_o south_n as_o also_o in_o regard_n of_o the_o difference_n of_o longitude_n between_o the_o place_n for_o which_o the_o table_n of_o the_o sun_n declination_n be_v make_v and_o the_o place_n of_o observation_n whether_o it_o be_v easterly_a or_o westerly_a from_o thence_o beside_o many_o other_o particularity_n late_o relate_v and_o needless_a here_o to_o be_v repeat_v but_o the_o fix_a star_n move_a so_o exceed_o slow_o that_o in_o more_o than_o 70_o year_n they_o go_v not_o so_o much_o as_o one_o degree_n in_o there_o proper_a motion_n from_o the_o west_n eastward_n keep_v not_o only_o the_o same_o part_n of_o the_o north_n or_o south_n but_o almost_o the_o same_o point_n and_o minute_n of_o declination_n for_o many_o year_n together_o i_o mean_v those_o star_n especial_o that_o be_v place_v in_o the_o sign_n of_o gemini_fw-la cancer_n sagittarie_n or_o capricorn_n near_o the_o solstitial_a colour_n which_o in_o a_o hundred_o year_n or_o two_o can_v alter_v their_o declination_n scarce_o one_o minute_n whereas_o those_o star_n that_o be_v in_o pisces_fw-la aries_n virgo_fw-la or_o libra_n especial_o if_o they_o be_v near_o the_o equinoctial_a colour_n may_v differ_v in_o there_o declination_n about_o one_o minute_n in_o 3_o year_n which_o difference_n though_o it_o be_v something_o yet_o for_o a_o dozen_o or_o twenty_o year_n will_v hardly_o be_v so_o much_o as_o can_v at_o sea_n be_v observe_v by_o any_o instrument_n hitherto_o have_v in_o use_n there_o for_o these_o two_o cause_n therefore_o that_o be_v for_o the_o more_o easy_a and_o general_a use_n of_o the_o declination_n of_o the_o fix_a star_n then_o of_o the_o sun_n i_o wish_v they_o be_v more_o general_o know_v and_o observe_v by_o our_o seaman_n then_o they_o be_v as_o whereby_o they_o may_v not_o only_o most_o easy_o know_v the_o elevation_n of_o the_o pole_n at_o any_o time_n of_o the_o night_n but_o also_o in_o any_o place_n of_o the_o world_n much_o more_o commodious_o than_o otherwise_o they_o can_v because_o that_o in_o what_o latitude_n and_o how_o far_o soever_o they_o shall_v come_v either_o northwards_o or_o southwards_o they_o may_v always_o have_v their_o choice_n of_o divers_a fix_a star_n near_o the_o meridian_n both_o towards_o the_o north_n and_o south_n of_o a_o convenient_a height_n to_o be_v observe_v but_o herewith_o it_o be_v also_o to_o be_v wish_v that_o the_o table_n of_o the_o fix_a star_n declination_n which_o be_v most_o common_a among_o english_a mariner_n have_v be_v more_o free_a from_o error_n than_o they_o be_v i_o mean_v especial_o the_o table_n publish_v in_o bourn_n regiment_n and_o norman_n new_a attractive_a which_o table_n agree_v almost_o in_o
6_o 0_o 48_o 45_o 1_o 54_o 28_o 3_o 2_o 3_o 3_o 0_o 4_o 1_o 44_o 17_o 1_o 8_o 0_o 56_o 49_o 1_o 56_o 27_o 4_o 2_o 2_o 58_o 0_o 5_o 1_o 43_o 7_o 1_o 10_o 0_o 94_o 52_o 1_o 57_o 26_o 5_o 2_o 2_o 50_o 0_o 8_o 1_o 41_o 54_o 1_o 13_o 0_o 52_o 55_o 1_o 57_o 25_o 6_o 2_o 2_o 40_o 0_o 10_o 1_o 40_o 40_o 1_o 14_o 0_o 50_o 56_o 1_o 59_o 24_o 7_o 2_o 2_o 28_o 0_o 12_o 1_o 39_o 24_o 1_o 16_o 0_o 48_o 56_o 2_o 0_o 23_o 8_o 2_o 2_o 13_o 0_o 15_o 1_o 38_o 7_o 1_o 17_o 0_o 46_o 55_o 2_o 1_o 22_o 9_o 2_o 1_o 56_o 0_o 17_o 1_o 36_o 47_o 1_o 20_o 0_o 44_o 53_o 2_o 2_o 21_o 10_o 2_o 1_o 37_o 0_o 19_o 1_o 35_o 25_o 1_o 22_o 0_o 42_o 51_o 2_o 2_o 20_o 11_o 2_o 1_o 16_o 0_o 21_o 1_o 34_o 2_o 1_o 23_o 0_o 40_o 47_o 2_o 4_o 19_o 12_o 2_o 0_o 52_o 0_o 24_o 1_o 32_o 37_o 1_o 25_o 0_o 38_o 43_o 2_o 4_o 18_o 13_o 2_o 0_o 27_o 0_o 25_o 1_o 31_o 10_o 1_o 27_o 0_o 36_o 38_o 2_o 5_o 17_o 14_o 1_o 59_o 59_o 0_o 28_o 1_o 29_o 42_o 1_o 28_o 0_o 34_o 33_o 2_o 5_o 16_o 15_o 1_o 59_o 28_o 0_o 31_o 1_o 28_o 11_o 1_o 31_o 0_o 32_o 26_o 2_o 7_o 15_o 16_o 1_o 58_o 56_o 0_o 32_o 1_o 26_o 39_o 1_o 32_o 0_o 30_o 19_o 2_o 7_o 14_o 17_o 1_o 58_o 21_o 0_o 35_o 1_o 25_o 6_o 1_o 33_o 0_o 28_o 12_o 2_o 7_o 13_o 18_o 1_o 57_o 44_o 0_o 37_o 1_o 23_o 30_o 1_o 36_o 0_o 26_o 4_o 2_o 8_o 12_o 19_o 1_o 57_o 5_o 0_o 39_o 1_o 21_o 54_o 1_o 36_o 0_o 23_o 55_o 2_o 9_o 11_o 20_o 1_o 56_o 24_o 0_o 41_o 1_o 20_o 15_o 1_o 39_o 0_o 21_o 46_o 2_o 9_o 10_o 21_o 1_o 55_o 41_o 0_o 43_o 1_o 18_o 43_o 1_o 40_o 0_o 19_o 37_o 2_o 9_o 9_o 22_o 1_o 54_o 55_o 0_o 46_o 1_o 16_o 54_o 1_o 41_o 0_o 17_o 27_o 2_o 10_o 8_o 23_o 1_o 54_o 8_o 0_o 47_o 1_o 15_o 11_o 1_o 43_o 0_o 15_o 17_o 2_o 10_o 7_o 24_o 1_o 53_o 18_o 0_o 50_o 1_o 13_o 27_o 1_o 44_o 0_o 13_o 6_o 2_o 11_o 6_o 25_o 1_o 52_o 26_o 0_o 52_o 1_o 11_o 41_o 1_o 46_o 0_o 10_o 56_o 2_o 10_o 5_o 26_o 1_o 51_o 32_o 0_o 54_o 1_o 9_o 54_o 1_o 47_o 0_o 8_o 45_o 2_o 11_o 4_o 27_o 1_o 50_o 36_o 0_o 56_o 1_o 8_o 6_o 1_o 48_o 0_o 6_o 34_o 2_o 11_o 3_o 28_o 1_o 49_o 38_o 0_o 58_o 1_o 6_o 16_o 1_o 50_o 0_o 4_o 23_o 2_o 11_o 2_o 29_o 1_o 48_o 38_o 1_o 0_o 1_o 4_o 25_o 1_o 51_o 0_o 2_o 11_o 2_o 12_o 1_o 30_o 1_o 47_o 35_o 1_o 3_o 1_o 2_o 33_o 1_o 52_o 0_o 0_o 0_o 2_o 11_o 0_o  _fw-fr 8_o add._n dif_a ad_fw-la 7_o add._n dif_a ad_fw-la 6._o add._n dif_a ad_fw-la  _fw-fr chap._n xxiii_o the_o make_n of_o the_o ephemerides_n of_o the_o sun_n here_o follow_v with_o help_v of_o the_o two_o former_a table_n of_o the_o sun_n middle_a motion_n and_o of_o his_o prosthaphaerese_n the_o sun_n true_a place_n may_v be_v ready_o find_v and_o so_o the_o ephemerides_n follow_v easy_o make_v after_o this_o manner_n reduce_v the_o apparent_a time_n give_v to_o the_o equal_a time_n answer_v thereto_o with_o help_n of_o tycho_n brahe_n his_o table_n of_o equation_n of_o natural_a day_n and_o for_o that_o time_n so_o reduce_v add_v together_o the_o sun_n middle_a motion_n of_o longitude_n in_o year_n month_n day_n hour_n and_o minute_n out_o of_o the_o sum_n subtract_v the_o place_n of_o the_o sun_n apogaeum_n the_o remainder_n shall_v be_v the_o sun_n motion_n of_o anomaly_n or_o his_o distance_n from_o his_o apogaeum_n now_o if_o this_o anomaly_n be_v less_o than_o a_o semicircle_n look_v the_o sign_n thereof_o in_o the_o head_n of_o the_o table_n of_o the_o sun_n prostaphaerese_n and_o the_o degree_n in_o the_o first_o column_n towards_o the_o left_a hand_n descend_v and_o proceed_v in_o the_o same_o line_n towards_o the_o right_a hand_n till_o you_o come_v under_o the_o foresay_a sign_n of_o the_o sun_n anomaly_n for_o there_o shall_v you_o have_v the_o sun_n prostaphaeresis_fw-la for_o that_o tâ—me_n remember_v this_o withal_o that_o if_o there_o be_v any_o minute_n adhere_v to_o those_o degree_n of_o anomaly_n that_o prostaphaeresis_fw-la must_v be_v correct_v by_o the_o part_n of_o the_o adjacent_a difference_n proportional_a to_o those_o minute_n add_v or_o subtract_v the_o same_o hereto_o according_a as_o you_o be_v direct_v in_o the_o head_n of_o the_o column_n wherein_o that_o difference_n be_v set_v down_o but_o if_o the_o sun_n anomaly_n be_v more_o than_o a_o semicircle_n you_o must_v find_v the_o sign_n thereof_o in_o the_o foot_n of_o the_o table_n and_o the_o degree_n in_o the_o last_o column_n next_o the_o right_a hand_n ascend_v and_o in_o the_o common_a meeting_n of_o the_o line_n wherein_o you_o find_v this_o degree_n and_o of_o the_o column_n of_o the_o say_a sign_n of_o the_o sun_n anomaly_n you_o shall_v find_v the_o sun_n prostaphaeresis_fw-la as_o before_o which_o if_o there_o be_v any_o minute_n adherent_a to_o the_o sun_n anomaly_n must_v be_v correct_v by_o the_o part_n proportional_a of_o the_o disterence_n adjoin_v as_o before_o add_v or_o subtract_v the_o same_o according_a as_o you_o find_v your_o direction_n in_o the_o foot_n of_o the_o column_n contain_v that_o difference_n as_o for_o example_n suppose_v you_o will_v know_v the_o sun_n true_a place_n the_o 6_o of_o may_n at_o noon_n that_o be_v the_o 5_o of_o may_n complete_a according_a to_o astronomical_a account_n in_o the_o year_n 1608_o which_o time_n reduce_v to_o equality_n by_o the_o foresay_a table_n shall_v be_v the_o 4_o of_o may_v complete_v 23_o hour_n 48_o minute_n for_o the_o sun_n be_v at_o that_o time_n about_o the_o 26_o degree_n of_o taurus_n that_o table_n show_v you_o that_o 12_o minute_n be_v to_o be_v subtract_v from_o the_o apparent_a time_n to_o make_v it_o equal_a for_o this_o time_n therefore_o let_v the_o middle_a motion_n of_o the_o sun_n be_v gather_v together_o in_o this_o manner_n the_o sun_n middle_a motion_n of_o longitude_n for_o  _fw-fr si._n d._n m._n se._n the_o year_n of_o christ_n 1607_o complete_a 9_o 20_o 15_o 56_o four_o month_n of_o the_o leap_n year_n 3_o 29_o 15_o 48_o four_o day_n  _fw-fr 3_o 56_o 33_o 23_o hour_n  _fw-fr  _fw-fr 56_o 40_o 48_o minute_n  _fw-fr  _fw-fr 1_o 58_o  _fw-fr si._n d._n m_o s_o the_o sum_n of_o all_o these_o be_v the_o sun_n middle_a motion_n of_o longitude_n for_o the_o time_n aforesaid_a 1_o 24_o 26_o 55_o the_o place_n of_o the_o sun_n apogaeum_n for_o the_o year_n of_o christ_n 1607_o complete_a be_v 3_o 5_o 45_o 0_o the_o motion_n thereof_o in_o the_o month_n day_n hour_n etc._n etc._n remain_v be_v  _fw-fr  _fw-fr  _fw-fr 15_o which_o put_v together_o make_v the_o place_n of_o the_o sun_n apogaeum_n for_o the_o time_n aforesaid_a 3_o 5_o 45_o 15_o this_o be_v subduct_v out_o of_o the_o sun_n middle_a motion_n 1_o 24_o 26_o 55_o there_o shall_v remain_v the_o sun_n motion_n of_o anomaly_n 10_o 18_o 41_o 40_o the_o prosthaphaeresis_fw-la answerable_a to_o 10_o sign_n 18_o degr_n you_o shall_v find_v in_o the_o table_n of_o prosthaphaeresis_fw-la  _fw-fr 1_o 21_o 19_o with_o the_o difference_n answer_v thereto_o  _fw-fr  _fw-fr 1_o 36_o the_o part_n proportional_a whereof_o answer_a to_o 41_o min._n 40_o second_n you_o shall_v find_v to_o be_v  _fw-fr  _fw-fr 1_o 7_o which_o subtract_v out_o of_o the_o prosthaphaeresis_fw-la answer_v to_o 10_o sig_n 18_o de_fw-la  _fw-fr 1_o 21_o 19_o there_o remain_v the_o prosthaphaeresis_fw-la correct_v  _fw-fr 1_o 20_o 12_o which_o be_v add_v to_o the_o sun_n middle_a motion_n of_o longitude_n for_o the_o time_n aforesaid_a 1_o 24_o 26_o 25_o you_o shall_v have_v the_o sun_n true_a place_n for_o that_o time_n 1_o 25_o 47_o 7_o agree_v just_o with_o the_o ephemerides_n follow_v where_o you_o shall_v find_v the_o sun_n at_o that_o time_n to_o be_v in_o 25_o degr_n 47_o min_fw-mi 7_o sec._n of_o taurus_n admit_v also_o i_o will_v know_v the_o true_a place_n of_o the_o sun_n the_o 27._o of_o october_n 1609._o at_o noon_n as_o we_o common_o account_v that_o be_v for_o the_o 26._o of_o october_n complete_a by_o the_o foresay_a account_n astronomical_a which_o reduce_v to_o the_o equal_a time_n will_v make_v 25._o day_n 23._o hour_n 36._o min._n the_o sun_n middle_a motion_n therefore_o together_o with_o the_o rest_n of_o the_o account_n for_o find_v the_o sun_n true_a place_n for_o that_o time_n may_v be_v short_o gather_v after_o this_o manner_n the_o sun_n middle_a motion_n of_o longitude_n for_o  _fw-fr si._n d._n m_o see_v the_o year_n of_o christ_n 1608_o complete_a 9_o 21_o 0_o 45_o september_n
of_o the_o common_a year_n complete_a 8_o 29_o 4_o 54_o five_o and_o twenty_o day_n  _fw-fr 24_o 38_o 28_o twenty_o three_o hour_n  _fw-fr  _fw-fr 56_o 40_o thirty_o six_o minute_n  _fw-fr  _fw-fr 1_o 29_o the_o sum_n of_o these_o be_v the_o sun_n middle_a motion_n of_o longitude_n for_o that_o time_n 7_o 15_o 42_o 14_o from_o whence_o subtract_v the_o place_n of_o the_o sun_n apogaeum_n 3_o 5_o 46_o 18_o there_o remain_v the_o sun_n anomaly_n 4_o 9_o 55_o 56_o whereby_o be_v find_v the_o sun_n prosthaphaeresis_fw-la  _fw-fr 1_o 35_o 31_o and_o by_o subtraction_n hereof_o his_o true_a longitude_n 7_o 14_o 6_o 45_o agree_v likewise_o just_o with_o the_o emphemeride_n follow_v after_o which_o manner_n also_o they_o may_v be_v whole_o make_v notwithstanding_o it_o be_v sufficient_a to_o make_v some_o convenient_a part_n of_o they_o in_o this_o manner_n and_o for_o spare_a time_n and_o labour_n to_o supply_v the_o rest_n by_o convenient_a part_n proportional_a whereof_o there_o may_v sometime_o arise_v some_o small_a difference_n of_o a_o few_o second_o which_o may_v worthy_o be_v neglect_v see_v they_o can_v breed_v no_o sensible_a error_n in_o this_o business_n chap._n xxiv_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 notwithstanding_o the_o great_a difference_n between_o the_o apparent_a and_o equal_a time_n to_o be_v small_a that_o by_o neglect_n thereof_o there_o can_v scarce_o at_o any_o time_n arise_v thereof_o so_o much_o as_o one_o minute_n error_n in_o the_o place_n of_o the_o sun_n and_o consequent_o not_o so_o much_o as_o half_a a_o minute_n error_n in_o his_o declination_n yet_o because_o the_o rule_n and_o ground_n of_o art_n ought_v so_o much_o as_o may_v be_v to_o be_v free_a from_o all_o error_n i_o have_v therefore_o think_v it_o better_o here_o to_o set_v down_o the_o foresay_a table_n of_o equation_n of_o natural_a day_n rather_o than_o to_o leave_v the_o reader_n to_o seek_v any_o further_a for_o 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5_o 7_o 4_o 1_o 9_o ½_o 11_o 6_o 2_o 7_o 17_o 24_o 20_o 6_o 6_o 7_o 6_o 1_o 10_o 11_o 5_o ½_o 2_o 7_o 18_o 24_o 19_o ½_o 5_o 6_o 7_o 8_o 2_o 10_o 11_o 5_o 2_o 8_o 18_o 24_o ½_o 19_o 4_o 6_o ½_o 6_o ½_o 10_o 3_o 11_o 11_o 5_o 2_o 9_o 19_o 24_o 18_o 3_o ½_o 7_o 6_o 12_o 3_o 11_o 10_o 4_o 2_o 9_o 20_o 24_o 17_o 2_o ½_o 7_o 6_o 14_o 4_o 11_o 10_o 4_o 3_o 10_o 20_o 24_o 16_o 2_o 7_o ½_o 5_o 16_o 5_o 11_o 10_o 3_o ½_o 3_o 11_o 21_o 24_o 15_o 1_o 8_o 5_o 18_o 5_o 11_o ½_o 9_o 3_o 3_o 11_o ½_o 21_o 24_o 14_o 0_o 8_o 4_o 20_o 6_o 12_o 9_o 3_o 3_o 12_o 22_o 23_o ½_o 13_o ½_o a_o 1_o 8_o 4_o 22_o 6_o 12_o 8_o ½_o 3_o 4_o 13_o 22_o 23_o 12_o 1_o â—_o 2_o 8_o 3_o 24_o 7_o 12_o 8_o 2_o ½_o 4_o 13_o ½_o 23_o 23_o 11_o ½_o 3_o 8_o 2_o ½_o 26_o 7_o ½_o 12_o 8_o 2_o 5_o 14_o 23_o 22_o 10_o ½_o 3_o 8_o 2_o 28_o 8_o 12_o 7_o 2_o 5_o 15_o 23_o 22_o 9_o ½_o 4_o 8_o 1_o 30_o 8_o ½_o 12_o 7_o 2_o 6_o 16_o 24_o 21_o 8_o ½_o 5_o 7_o ½_o 0_o ½_o this_o table_n must_v be_v thus_o use_v with_o the_o sign_n and_o degree_n of_o the_o sun_n true_a place_n take_v out_o in_o the_o common_a meeting_n the_o minute_n of_o time_n which_o according_a to_o the_o letter_n a_o saint_n in_o the_o head_n of_o the_o table_n must_v be_v add_v to_o or_o subtract_v from_o the_o apparent_a time_n to_o make_v it_o equal_a remember_v to_o do_v contrariwise_o if_o the_o equal_a time_n must_v be_v change_v into_o the_o apparent_a chap._n xxv_o a_o table_n of_o equation_n of_o the_o sun_n ephemerides_n  _fw-fr january_n febr._n march_n april_n may._n june_n day_n mi._n se_fw-la mi._n se_fw-la mi._n se_fw-la mi._n se_fw-la mi._n se_fw-la mi._n se_fw-la 3_o 1_o 53_o 1_o 51_o 1_o 49_o 1_o 47_o 1_o 46_o 1_o 45_o 6_o 1_o 52_o 1_o 50_o 1_o 49_o 1_o 47_o 1_o 46_o 1_o 45_o 9_o 1_o 52_o 1_o 50_o 1_o 49_o 1_o 47_o 1_o 45_o 1_o 45_o 12_o 1_o 52_o 1_o 51_o 1_o 48_o 1_o 46_o 1_o 46_o 1_o 44_o 15_o 1_o 52_o 1_o 50_o 1_o 49_o 1_o 47_o 1_o 45_o 1_o 45_o 18_o 1_o 52_o 1_o 50_o 1_o 48_o 1_o 46_o 1_o 45_o 1_o 45_o 21_o 1_o 51_o 1_o 50_o 1_o 48_o 1_o 46_o 1_o 45_o 1_o 45_o 24_o 1_o 52_o 1_o 50_o 1_o 48_o 1_o 46_o 1_o 45_o 1_o 44_o 27_o 1_o 51_o 1_o 50_o 1_o 48_o 1_o 46_o 1_o 45_o 1_o 45_o 30_o 1_o 52_o  _fw-fr  _fw-fr 1_o 47_o 1_o 46_o 1_o 45_o 1_o 45_o  _fw-fr july_n august_n sept._n octob_n novem_n decem._n day_n mi._n se_fw-la mi._n se._n mi._n se._n mi._n se._n mi._n se._n mi._n se._n 3_o 1_o 45_o 1_o 45_o 1_o 48_o 1_o 49_o 1_o 51_o 1_o 52_o 6_o 1_o 45_o 1_o 46_o 1_o 48_o 1_o 50_o 1_o 52_o 1_o 52_o 9_o 1_o 45_o 1_o 46_o 1_o 48_o 1_o 50_o 1_o 52_o 1_o 52_o 12_o 1_o 45_o 1_o 46_o 1_o 48_o 1_o 50_o 1_o 52_o 1_o 53_o 15_o 1_o 45_o 1_o 47_o 1_o 49_o 1_o 50_o 1_o 52_o 1_o 52_o 18_o 1_o 45_o 1_o 47_o 1_o 48_o 1_o 51_o 1_o 52_o 1_o 52_o 21_o 1_o 45_o 1_o 47_o 1_o 49_o 1_o 50_o 1_o 52_o 1_o 52_o 24_o 1_o 46_o 1_o 47_o 1_o 49_o 1_o 51_o 1_o 52_o 1_o 53_o 27_o 1_o 46_o 1_o 47_o 1_o 49_o 1_o 51_o 1_o 52_o 1_o 52_o 30_o 1_o 45_o 1_o 47_o 1_o 49_o 1_o 52_o 1_o 53_o 1_o 52_o by_o mean_n of_o this_o table_n and_o these_o ephemerides_n the_o true_a place_n of_o the_o sun_n may_v most_o easy_o be_v find_v for_o many_o year_n either_o past_a or_o to_o come_v as_o shall_v hereafter_o be_v show_v in_o the_o next_o chapter_n ephemerides_n the_o sun_n 1608._o leap_v year_n  _fw-fr january_n  _fw-fr februar_n  _fw-fr march._n  _fw-fr april_n  _fw-fr may._n  _fw-fr june_n d_o gr_n mi._n sec_fw-la d_o gr_fw-fr mi._n se._n d_o gr_n mi._n se._n d_o gr_n mi_fw-mi se_fw-mi d_o gr_n mi._n sec_fw-la d_o gr_fw-fr mi._n sec_fw-la 1_o 20_o 47_o 21_o 1_o 22_o 17_o 51_o 1_o 21_o 23_o 9_o 1_o 21_o 56_o 7_o 1_o 20_o 59_o 3_o 1_o 20_o 37_o 23_o 2_o 21_o 48_o 38_o 2_o 23_o 18_o 28_o 2_o 22_o 22_o 49_o 2_o 22_o 54_o 41_o 2_o 21_o 56_o 43_o 2_o 21_o 34_o 31_o 3_o 22_o 49_o 52_o 3_o 24_o 19_o 3_o 3_o 23_o 22_o 27_o 3_o 23_o 53_o 13_o 3_o 22_o 54_o 21_o 3_o 22_o 31_o 38_o 4_o 23_o 51_o 6_o 4_o 25_o 19_o 37_o 4_o 24_o 22_o 2_o 4_o 24_o 51_o 42_o 4_o 23_o 51_o 58_o 4_o 23_o 28_o 46_o 5_o 24_o 52_o 18_o 5_o 26_o 20_o 8_o 5_o 25_o 21_o 36_o 5_o 25_o 50_o 10_o 5_o 24_o 49_o 33_o 5_o 24_o 25_o 52_o 6_o 25_o 53_o 30_o 6_o 27_o 20_o 39_o 6_o 26_o 21_o 7_o 6_o 26_o 48_o 35_o 6_o 25_o 47_o 7_o 6_o 25_o 22_o 58_o 7_o 26_o 54_o 40_o 7_o 28_o 21_o 7_o 7_o 27_o 20_o 37_o 7_o 27_o 46_o 58_o 7_o 26_o 44_o 40_o 7_o 26_o 20_o 4_o 8_o 27_o 55_o 49_o 8_o 29_o 21_o 34_o 8_o 28_o 20_o 4_o 8_o 28_o 45_o 19_o 8_o 27_o 42_o 11_o 8_o 27_o 17_o 10_o 9_o 28_o 56_o 57_o 9_o ♓_o 21_o 59_o 9_o 29_o 19_o 28_o 9_o 29_o 43_o 37_o 9_o 28_o 39_o 41_o 9_o 28_o 14_o 15_o 10_o 29_o 58_o 5_o 10_o 1_o 22_o 22_o 10_o ♈_o 18_o 51_o 10_o ♉_o 41_o 55_o 10_o 29_o 37_o 9_o 10_o 29_o 11_o 20_o 11_o â™’_o 59_o 11_o 11_o 2_o 22_o 43_o 11_o 1_o 18_o 12_o 11_o 1_o 40_o 10_o 11_o ♊_o 34_o 36_o 11_o ♋_o 8_o 24_o 12_o 2_o 0_o 16_o 12_o 3_o 23_o 2_o 12_o 2_o 17_o 31_o 12_o 2_o 38_o 24_o 12_o 1_o 32_o 2_o 12_o 1_o 5_o 29_o 13_o 3_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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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
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
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
year_n which_o be_v also_o leap_v year_n themselves_o under_o every_o one_o of_o these_o rank_n of_o year_n there_o be_v two_o column_n the_o first_o whereof_o contain_v the_o degree_n and_o min._n of_o the_o sun_n declination_n answerable_a to_o every_o day_n of_o the_o month_n superscribe_v in_o each_o of_o those_o year_n without_o sensible_a error_n in_o the_o second_o column_n be_v set_v down_o the_o minute_n of_o the_o difference_n of_o the_o sun_n declination_n for_o every_o one_o of_o those_o day_n for_o the_o ready_a find_v of_o the_o part_n proportional_a of_o this_o difference_n answer_v to_o any_o difference_n of_o longitude_n from_o london_n whereof_o you_o may_v read_v more_o pag._n 181_o etc._n etc._n in_o the_o first_o column_n of_o each_o of_o these_o table_n next_o the_o left_a hand_n be_v place_v the_o number_n of_o the_o day_n of_o the_o month_n that_o be_v set_v down_o in_o the_o head_n thereof_o the_o use_n of_o this_o table_n for_o know_v the_o declination_n of_o the_o sun_n at_o any_o time_n be_v thus_o table_n look_v the_o month_n and_o year_n wherein_o you_o will_v know_v the_o same_o in_o the_o head_n of_o the_o table_n and_o the_o day_n of_o the_o month_n in_o the_o first_o column_n next_o the_o left_a hand_n then_o proceed_v from_o that_o day_n direct_o in_o the_o same_o line_n towards_o the_o right_a hand_n till_o you_o come_v right_a under_o the_o same_o year_n you_o shall_v there_o find_v the_o declination_n you_o seek_v for_o take_v for_o example_n the_o 24_o day_n of_o february_n in_o the_o year_n 1610._o find_v therefore_o that_o month_n and_o year_n in_o the_o head_n of_o the_o table_n and_o the_o 24_o day_n in_o the_o first_o column_n in_o the_o same_o line_n proceed_v towards_o the_o right_a hand_n till_o you_o come_v right_a under_o that_o year_n you_o have_v there_o the_o sun_n declination_n for_o that_o time_n 5_o degree_n 34_o minute_n towards_o the_o south_n january_n  _fw-fr 1_o 2_o 3_o 4_o day_n 1609_o 1610_o 1611_o 1612_o 1613_o 1614_o 1615_o 1616_o 1617._o 1618._o 1619_o 1620_o deg_n mi._n di_fw-it deg_n mi._n di_fw-it deg_n mi._n di_fw-it deg_n mi._n di_fw-it 1_o 21_o 47_o  _fw-fr 21_o 50_o  _fw-fr 21_o 52_o  _fw-fr 21_o 54_o  _fw-fr 2_o 21_o 37_o 10_o 21_o 40_o 10_o 21_o 42_o 10_o 21_o 45_o 9_o 3_o 21_o 27_o 10_o 21_o 30_o 10_o 21_o 32_o 10_o 21_o 35_o 10_o 4_o 21_o 17_o 10_o 21_o 19_o 11_o 21_o 22_o 10_o 21_o 24_o 11_o 5_o 21_o 6_o 11_o 21_o 8_o 11_o 21_o 11_o 11_o 21_o 13_o 11_o 6_o 20_o 54_o 12_o 20_o 57_o 11_o 21_o 0_o 11_o 21_o 2_o 11_o 7_o 20_o 42_o 12_o 20_o 45_o 12_o 20_o 48_o 12_o 20_o 51_o 11_o 8_o 20_o 30_o 12_o 20_o 33_o 12_o 20_o 36_o 12_o 20_o 39_o 12_o 9_o 20_o 17_o 13_o 20_o 20_o 13_o 20_o 23_o 13_o 20_o 26_o 13_o 10_o 20_o 4_o 13_o 20_o 7_o 13_o 20_o 10_o 13_o 20_o 13_o 13_o 11_o 19_o 50_o 14_o 19_o 54_o 13_o 19_o 57_o 13_o 20_o 0_o 13_o 12_o 19_o 36_o 14_o 19_o 40_o 14_o 19_o 43_o 14_o 19_o 47_o 13_o 13_o 19_o 22_o 14_o 19_o 26_o 14_o 19_o 29_o 14_o 19_o 33_o 14_o 14_o 19_o 8_o 14_o 19_o 11_o 15_o 19_o 15_o 14_o 19_o 18_o 15_o 15_o 18_o 53_o 15_o 18_o 56_o 15_o 19_o 0_o 15_o 19_o 4_o 14_o 16_o 18_o 38_o 15_o 18_o 41_o 15_o 18_o 45_o 15_o 18_o 49_o 15_o 17_o 18_o 22_o 16_o 18_o 26_o 15_o 18_o 30_o 15_o 18_o 33_o 16_o 18_o 18_o 6_o 16_o 18_o 10_o 16_o 18_o 14_o 16_o 18_o 18_o 15_o 19_o 17_o 50_o 16_o 17_o 54_o 16_o 17_o 58_o 16_o 18_o 2_o 16_o 20_o 17_o 33_o 17_o 17_o 37_o 17_o 17_o 41_o 17_o 17_o 45_o 17_o 21_o 17_o 16_o 17_o 17_o 21_o 16_o 17_o 25_o 16_o 17_o 29_o 16_o 22_o 16_o 59_o 17_o 17_o 4_o 17_o 17_o 8_o 17_o 17_o 12_o 17_o 23_o 16_o 42_o 17_o 16_o 46_o 18_o 16_o 50_o 18_o 16_o 55_o 17_o 24_o 16_o 24_o 18_o 16_o 29_o 17_o 16_o 33_o 17_o 16_o 37_o 18_o 25_o 16_o 6_o 18_o 16_o 11_o 18_o 16_o 15_o 18_o 16_o 19_o 18_o 26_o 15_o 48_o 18_o 15_o 52_o 19_o 15_o 57_o 18_o 16_o 1_o 18_o 27_o 15_o 29_o 19_o 15_o 34_o 18_o 15_o 38_o 19_o 15_o 43_o 18_o 28_o 15_o 10_o 19_o 15_o 15_o 19_o 15_o 20_o 18_o 15_o 24_o 19_o 29_o 14_o 51_o 19_o 14_o 56_o 19_o 15_o 1_o 19_o 15_o 5_o 19_o 30_o 14_o 32_o 19_o 14_o 37_o 19_o 14_o 41_o 20_o 14_o 46_o 19_o 31_o 14_o 13_o 19_o 14_o 17_o 20_o 14_o 22_o 19_o 14_o 27_o 19_o february_n  _fw-fr 1_o 2_o 3_o 4_o day_n 1609_o 1610_o 1611_o 1612_o 1613_o 1614_o 1615_o 1616_o 1617._o 1618._o 1619_o 1620_o deg_n mi._n di_fw-it deg_n mi._n di_fw-it deg_n mi._n di_fw-it deg_n mi._n di_fw-it 1_o 13_o 53_o  _fw-fr 13_o 58_o  _fw-fr 14_o 2_o  _fw-fr 14_o 7_o  _fw-fr 2_o 13_o 33_o 20_o 13_o 38_o 20_o 13_o 42_o 20_o 13_o 47_o 20_o 3_o 13_o 12_o 21_o 13_o 17_o 21_o 13_o 22_o 20_o 13_o 27_o 20_o 4_o 12_o 52_o 20_o 12_o 57_o 20_o 13_o 2_o 20_o 13_o 6_o 21_o 5_o 12_o 31_o 21_o 12_o 36_o 21_o 12_o 41_o 21_o 12_o 46_o 20_o 6_o 12_o 10_o 21_o 12_o 16_o 20_o 12_o 21_o 20_o 12_o 26_o 20_o 7_o 11_o 49_o 21_o 11_o 55_o 21_o 12_o 0_o 21_o 12_o 5_o 21_o 8_o 11_o 28_o 21_o 11_o 33_o 22_o 11_o 38_o 22_o 11_o 44_o 21_o 9_o 11_o 7_o 21_o 11_o 12_o 21_o 11_o 17_o 21_o 11_o 22_o 22_o 10_o 10_o 45_o 22_o 10_o 50_o 22_o 10_o 56_o 21_o 11_o 1_o 21_o 11_o 10_o 23_o 22_o 10_o 28_o 22_o 10_o 34_o 22_o 10_o 39_o 22_o 12_o 10_o 1_o 22_o 10_o 7_o 21_o 10_o 12_o 22_o 10_o 17_o 22_o 13_o 9_o 39_o 22_o 9_o 45_o 22_o 9_o 50_o 22_o 9_o 55_o 22_o 14_o 9_o 17_o 22_o 9_o 23_o 22_o 9_o 28_o 22_o 9_o 33_o 22_o 15_o 8_o 55_o 22_o 9_o 0_o 23_o 9_o 6_o 22_o 9_o 11_o 22_o 16_o 8_o 32_o 23_o 8_o 38_o 22_o 8_o 43_o 23_o 8_o 49_o 22_o 17_o 8_o 10_o 22_o 8_o 15_o 23_o 8_o 21_o 22_o 8_o 26_o 23_o 18_o 7_o 47_o 23_o 7_o 53_o 22_o 7_o 58_o 23_o 8_o 4_o 22_o 19_o 7_o 24_o 23_o 7_o 30_o 23_o 7_o 35_o 23_o 7_o 41_o 23_o 20_o 7_o 1_o 23_o 7_o 7_o 23_o 7_o 12_o 23_o 7_o 18_o 23_o 21_o 6_o 38_o 23_o 6_o 44_o 23_o 6_o 49_o 23_o 6_o 55_o 23_o 22_o 6_o 15_o 23_o 6_o 21_o 23_o 6_o 26_o 23_o 6_o 32_o 23_o 23_o 5_o 52_o 23_o 5_o 58_o 23_o 6_o 3_o 23_o 6_o 9_o 23_o 24_o 5_o 29_o 23_o 5_o 34_o 24_o 5_o 40_o 23_o 5_o 46_o 23_o 25_o 5_o 5_o 24_o 5_o 11_o 23_o 5_o 17_o 23_o 5_o 22_o 24_o 26_o 4_o 42_o 23_o 4_o 48_o 23_o 4_o 53_o 24_o 4_o 59_o 23_o 27_o 4_o 18_o 24_o 4_o 24_o 24_o 4_o 30_o 23_o 4_o 36_o 23_o 28_o 3_o 55_o 23_o 4_o 1_o 23_o 4_o 6_o 24_o 4_o 12_o 24_o 29_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 3_o 49_o 23_o march_v  _fw-fr 1_o 2_o 3_o 4_o day_n 1609_o 1610_o 1611_o 1612_o 1613_o 1614_o 1615_o 1616_o 1617._o 1618._o 1619_o 1620_o degr_n mi_fw-mi di_fw-mi deg._n m_o the_z de._n mi._n di_fw-it deg._n m_o di_o 1_o 3_o 31_o  _fw-fr 3_o 37_o  _fw-fr 3_o 43_o  _fw-fr 3_o 23_o  _fw-fr 2_o 3_o 8_o 23_o 3_o 13_o 24_o 3_o 19_o 24_o 3_o 1_o 24_o 3_o 2_o 44_o 24_o 2_o 50_o 23_o 2_o 56_o 23_o 2_o 37_o 24_o 4_o 2_o 20_o 24_o 2_o 26_o 24_o 2_o 32_o 24_o 2_o 14_o 23_o 5_o 1_o 57_o 23_o 2_o 3_o 23_o 2_o 8_o 24_o 1_o 50_o 24_o 6_o 1_o 33_o 24_o 1_o 39_o 24_o 1_o 45_o 23_o 1_o 27_o 23_o 7_o 1_o 9_o 24_o 1_o 15_o 24_o 1_o 21_o 24_o 1_o 3_o 24_o 8_o 0_o 46_o 23_o 0_o 51_o 24_o 0_o 57_o 24_o 0_o 39_o 24_o 9_o 0_o 22_o 24_o 0_o 28_o 23_o 0_o 33_o 24_o 0_o 15_o 24_o  _fw-fr  _fw-fr  _fw-fr 24_o 0_o 4_o 24_o 0_o 10_o 23_o  _fw-fr  _fw-fr 23_o equinoctal_n 10_o 0_o 2_o 23_o  _fw-fr  _fw-fr 24_o  _fw-fr  _fw-fr 24_o 0_o 8_o 24_o 11_o 0_o 25_o 24_o 0_o 20_o 23_o 0_o 14_o 24_o 0_o 32_o 24_o 12_o 0_o 49_o 24_o 0_o 43_o 24_o 0_o 38_o 23_o 0_o 56_o 23_o 13_o 1_o 13_o 23_o 1_o 7_o 24_o 1_o 1_o 24_o 1_o 19_o 24_o 14_o 1_o 36_o 24_o 1_o 31_o 23_o 1_o 25_o 24_o 1_o 43_o 23_o 15_o 2_o 0_o 24_o 1_o 54_o 24_o 1_o 49_o 23_o 2_o 6_o 24_o 16_o 2_o 24_o 23_o 2_o 18_o 23_o 2_o 12_o 24_o 2_o 30_o 23_o 17_o 2_o 47_o 23_o 2_o 41_o 24_o 2_o 36_o 23_o 2_o 53_o 24_o 18_o 3_o 10_o 24_o 3_o 5_o 23_o 2_o 59_o 23_o 3_o 17_o 23_o 19_o 3_o 34_o 23_o 3_o 28_o 23_o 3_o 22_o 24_o 3_o 40_o 23_o 20_o 3_o 57_o 23_o 3_o 51_o 24_o 3_o 46_o 23_o
second_n  _fw-fr a_o four_o cause_n of_o error_n be_v the_o refraction_n of_o the_o beam_n of_o the_o sun_n or_o star_n which_o we_o observe_v by_o reason_n of_o the_o vaporous_a thickness_n of_o the_o air_n that_o be_v betwixt_o we_o and_o they_o especial_o when_o they_o be_v near_o the_o horizon_n for_o the_o find_n whereof_o not_o have_v hitherto_o have_v sufficient_a mean_n by_o my_o own_o observation_n for_o my_o full_a satisfaction_n herein_o i_o have_v therefore_o think_v good_a to_o adjoyne_v these_o table_n of_o the_o sun_n and_o fix_a star_n refraction_n out_o of_o tycho_n brahe_n which_o differ_v little_a from_o such_o observation_n as_o i_o have_v make_v for_o trial_n hereof_o the_o use_n whereof_o be_v this_o in_o the_o first_o column_n seek_v the_o altitude_n or_o height_n of_o the_o sun_n or_o fix_a star_n and_o in_o the_o second_o you_o shall_v have_v the_o refraction_n answer_v thereto_o which_o be_v subtract_v out_o of_o the_o observe_v height_n you_o shall_v have_v the_o height_n of_o the_o sun_n or_o star_n remain_v without_o refraction_n chap._n xvi_o 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 notwithstanding_o the_o sun_n and_o star_n be_v at_o sea_n the_o most_o certain_a mark_n and_o guide_v the_o navigator_n have_v whereby_o he_o may_v direct_v himself_o to_o rectify_v his_o course_n and_o know_v where_o he_o be_v after_o many_o turn_n and_o traversing_n this_o way_n and_o that_o way_n especial_o in_o long_a voyage_n wherein_o he_o may_v be_v force_v many_o time_n by_o contrary_a wind_n and_o calm_n to_o sing_v with_o the_o poet_n for_o many_o week_n and_o month_n together_o coelum_fw-la undique_fw-la &_o undique_fw-la pontus_n and_o nihil_fw-la est_fw-la nisi_fw-la pontus_n &_o aether_n yet_o the_o table_n of_o declination_n of_o the_o sun_n and_o fix_a star_n hitherto_o publish_v which_o i_o have_v compare_v together_o and_o examine_v by_o observation_n be_v oft_o time_n very_o faulty_a the_o declination_n of_o the_o sun_n in_o they_o set_v down_o be_v many_o time_n less_o than_o truth_n by_o 10_o 11_o or_o 12_o minute_n especial_o in_o the_o month_n of_o february_n and_o march_n and_o some_o of_o the_o principal_a fix_a star_n that_o be_v of_o most_o use_n in_o navigation_n differ_v in_o declination_n from_o that_o be_v set_v down_o in_o the_o table_n more_o than_o one_o whole_a degree_n as_o i_o have_v find_v by_o many_o observation_n for_o the_o easy_a mend_n of_o these_o fault_n in_o the_o table_n of_o the_o sun_n declination_n i_o think_v it_o meet_v first_o to_o set_v down_o the_o table_n follow_v which_o show_v the_o declination_n of_o every_o minute_n of_o the_o ecliptik_a in_o degree_n minute_n and_o second_o whereby_o the_o place_n of_o the_o sun_n be_v present_o know_v his_o declination_n be_v first_o give_v by_o observation_n and_o consequent_o his_o eccentricity_n and_o apogeum_n be_v easy_o find_v and_o the_o theoric_n of_o the_o sun_n correct_v out_o of_o which_o the_o ephemerides_n hereafter_o follow_v be_v calculate_v show_v the_o true_a place_n of_o the_o sun_n for_o every_o day_n of_o five_o year_n agreeable_a without_o notable_a error_n to_o the_o truth_n of_o the_o heaven_n and_o out_o of_o these_o with_o help_n of_o this_o table_n of_o declination_n a_o new_a regiment_n or_o table_n of_o the_o sun_n declination_n for_o every_o day_n of_o five_o year_n be_v most_o easy_o make_v free_a from_o such_o error_n wherewith_o the_o table_n hitherto_o publish_v and_o common_o use_v have_v be_v too_o much_o pester_v as_o by_o comparison_n of_o this_o and_o those_o table_n with_o the_o observation_n hereafter_o follow_v may_v evident_o appear_v chap._n xvii_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 minute_n and_o second_n made_n 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 bo_z 23_o degree_n 31_o minute_n and_o a_o halfe·_a because_o the_o table_n of_o declination_n here_o follow_v do_v differ_v something_o from_o the_o table_n heretofore_o publish_v by_o other_o whereof_o some_o make_v the_o great_a declination_n of_o the_o sun_n to_o be_v 23_o degr_n and_o 28_o minute_n only_o as_o copernicus_n and_o his_o follower_n according_a to_o which_o the_o table_n of_o declination_n and_o regiment_n of_o the_o sun_n that_o have_v be_v use_v for_o the_o most_o part_n by_o our_o english_a mariner_n be_v make_v whereas_o other_o of_o late_a as_o that_o noble_a astronomer_n thyco_n brahe_n in_o his_o second_o book_n de_fw-fr recentioribus_fw-la aetherei_fw-la mundi_fw-la phoenomenis_fw-la find_v the_o same_o to_o be_v by_o his_o observation_n 23_o degr_n 27_o mi._n pag._n 38._o 23_o degr_n 31_o mi._n pag._n 386._o 23_o degr_n 31_o mi._n 30_o sec._n pag._n 217._o according_a to_o which_o there_o be_v a_o table_n of_o declination_n already_o publish_v by_o maginus_fw-la and_o that_o excellent_a geometrician_n regiomontanus_n who_o petrus_n nonius_n compare_v by_o ramus_n to_o archimedes_n and_o clavius_n choose_v rather_o to_o follow_v make_v it_o to_o be_v but_o 23_o degr_n 30_o min._n i_o think_v it_o therefore_o needful_a to_o show_v what_o reason_n move_v i_o to_o make_v choice_n of_o the_o great_a of_o all_o the_o declination_n before_o recite_v be_v thereunto_o induce_v not_o only_o by_o the_o authority_n of_o that_o famous_a astronomer_n of_o our_o time_n tycho_n brahe_n but_o rest_v also_o upon_o many_o and_o diligent_a observation_n of_o my_o own_o take_v by_o a_o quadrant_a of_o more_o than_o six_o foot_n semidiameter_n so_o exact_o make_v and_o divide_v into_o minute_n and_o half_a minute_n as_o i_o can_v and_o as_o heedful_o use_v and_o true_o rectify_v by_o plumbline_n every_o time_n i_o observe_v as_o my_o sight_n can_v discern_v all_o which_o observation_n do_v prove_v with_o one_o consent_n that_o the_o great_a declination_n of_o the_o sun_n in_o this_o our_o age_n be_v 23_o degree_n 31_o minute_n and_o a_o half_a as_o thus_o it_o may_v appear_v in_o the_o year_n 1594_o the_o 11_o and_o 12_o day_n of_o june_n the_o apparent_a meridian_n altitude_n of_o the_o sun_n be_v observe_v to_o be_v 61_o degr_n 58_o min._n whereto_o the_o observation_n of_o the_o 8_o 9_o 10_o 13_o 14_o and_o 15_o day_n of_o the_o same_o month_n do_v well_o agree_v wherein_o the_o apparent_a meridian_n altitude_n of_o the_o sun_n be_v 61_o degr_n 55_o ½_o mi._n 61_o degr_n 56_o ½_o mi._n 61_o degr_n 57_o mi._n 61_o degr_n 57_o ½_o mi._n 61_o degr_n 57_o mi._n 61_o degr_n 56_o mi._n almost_o as_o also_o the_o observation_n of_o the_o 9_o 11_o 12_o and_o 13_o day_n of_o june_n in_o the_o year_n 1597_o in_o which_o day_n the_o apparent_a meridian_n altitude_n of_o the_o sun_n be_v 61_o degr_n 57_o mi._n 61_o degr_n 58_o ½_o mi._n almost_o 61_o degr_n 58_o mi._n 61_o degr_n 57_o ½_o mi._n by_o all_o which_o observation_n it_o may_v be_v certain_o conclude_v that_o the_o great_a apparent_a height_n of_o the_o sun_n here_o at_o london_n be_v 61_o degr_n and_o 58_o minute_n moreover_o by_o many_o and_o heedful_a observation_n of_o the_o polestar_n take_v about_o the_o year_n 1593._o and_o 1594_o i_o find_v the_o great_a height_n thereof_o at_o that_o time_n here_o in_o london_n to_o be_v 54_o degree_n 24_o minute_n and_o a_o half_a and_o the_o least_o height_n 48_o degr_n 39_o ½_o minute_n the_o difference_n of_o which_o height_n be_v 5_o degree_n 45_o minute_n the_o half_a whereof_o be_v 2_o degree_n 52_o ½_o min._n that_o be_v the_o distance_n of_o the_o polestar_n from_o the_o pole_n at_o that_o time_n add_v to_o the_o low_a height_n of_o the_o polestar_n show_v the_o height_n of_o the_o pole_n at_o london_n to_o be_v 51_o degree_n 32_o minute_n the_o compliment_n whereof_o 38_o degree_n 28_o minute_n be_v the_o height_n of_o the_o equinoctial_a which_o substract_v out_o of_o the_o great_a apparent_a height_n of_o the_o sun_n 61_o degree_n 58_o minute_n there_o remain_v the_o great_a apparent_a declination_n of_o the_o sun_n 23_o degree_n 30_o minute_n whereto_o if_o we_o add_v 1_o minute_n 22_o second_o that_o be_v the_o parallax_n of_o the_o sun_n answerable_a to_o that_o height_n we_o shall_v have_v the_o great_a true_a height_n of_o the_o sun_n 61_o degree_n 59_o minute_n 22_o second_n and_o consequent_o the_o great_a true_a declination_n of_o the_o sun_n for_o our_o time_n 23_o degree_n 31_o minute_n 22_o second_n differ_v but_o half_o a_o quarter_n of_o one_o minute_n from_o the_o great_a declination_n final_o determine_v and_o resolve_o set_v down_o by_o tycho_n brahe_n for_o this_o our_o age_n 23_o degree_n 31_o minute_n and_o one_o half_a aries_n libra_n  _fw-fr degr._fw-la 0_o di_o degr._fw-la 1_o di_fw-fr degr._fw-la 2_o
exact_a observation_n take_v by_o a_o quadrant_n of_o six_o foot_n and_o a_o quarter_n semidiameter_n in_o the_o year_n 1594._o 1595._o 1596._o 1597._o find_v therefore_o taurus_n and_o the_o 20_o degree_n in_o the_o upper_a part_n of_o this_o table_n and_o 45_o minute_n in_o the_o first_o column_n i_o have_v in_o the_o common_a meeting_n of_o the_o column_n descend_v from_o 20._o and_o of_o the_o line_n proceed_v from_o 45._o minute_n towards_o the_o right_a hand_n 18._o degree_n 0_o minute_n 18._o second_o the_o declination_n of_o the_o sun_n the_o same_o day_n at_o noon_n here_o at_o london_n example_n of_o the_o second_o the_o 15._o of_o august_n the_o same_o year_n by_o the_o same_o ephemerides_n the_o sun_n be_v in_o 2_o degr_n 2._o minute_n of_o virgo_fw-la therefore_o i_o seek_v virgo_fw-la and_o 2._o in_o the_o nether_a part_n of_o this_o table_n and_o 50._o minute_n in_o the_o last_o column_n towards_o the_o right_a hand_n ascend_v upward_o then_o follow_v the_o line_n of_o 2_o minute_n leftwards_o and_o the_o column_n of_o 2._o degree_n upward_o in_o the_o common_a meeting_n of_o the_o line_n and_o column_n i_o find_v ten_o degree_n 47._o minute_n 19_o sec._n the_o declination_n of_o the_o sun_n the_o same_o day_n at_o noon_n for_o the_o meridian_n of_o london_n but_o the_o declination_n of_o the_o sun_n be_v first_o know_v by_o observation_n or_o otherwise_o the_o place_n of_o the_o sun_n shall_v most_o easy_o be_v find_v out_o by_o this_o table_n after_o this_o manner_n seek_v the_o sun_n declination_n in_o the_o area_n of_o the_o table_n then_o if_o the_o sign_n wherein_o the_o sun_n be_v which_o you_o may_v for_o the_o most_o part_n easy_o know_v by_o estimation_n be_v in_o the_o head_n of_o the_o table_n ascend_v upward_o to_o the_o top_n of_o the_o same_o column_n in_o which_o you_o find_v the_o declination_n give_v for_o there_o you_o shall_v have_v the_o degree_n of_o the_o sun_n follow_v also_o the_o line_n wherein_o you_o find_v the_o give_v declination_n towards_o the_o left_a hand_n till_o you_o come_v to_o the_o first_o column_n leftwards_o and_o there_o you_o shall_v have_v the_o minute_n also_o but_o if_o the_o name_n of_o the_o sign_n wherein_o the_o sun_n be_v be_v in_o the_o nether_a part_n of_o the_o table_n you_o must_v do_v all_o thing_n contrariwise_o descend_v from_o the_o declination_n find_v in_o the_o area_n of_o this_o table_n in_o the_o same_o column_n till_o you_o come_v to_o the_o low_a part_n thereof_o where_o you_o shall_v find_v the_o degree_n of_o the_o sun_n and_o proceed_v from_o the_o declination_n towards_o the_o right_a hand_n in_o the_o same_o line_n till_o you_o come_v to_o the_o last_o column_n where_o you_o shall_v find_v the_o minute_n to_o be_v adjoin_v that_o you_o may_v have_v the_o true_a place_n of_o the_o sun_n this_o way_n of_o find_v out_o the_o place_n of_o the_o sun_n by_o his_o declination_n first_o know_v by_o observation_n be_v then_o of_o especial_a use_n and_o truth_n when_o the_o sun_n be_v near_o the_o equinoctial_a point_n for_o there_o his_o declination_n alter_v quick_a increase_v or_o decrease_v about_o 24_o min._n in_o 24._o hour_n but_o when_o the_o sun_n be_v near_o either_o of_o the_o tropic_n the_o miss_v of_o one_o minute_n yea_o or_o half_o a_o minute_n in_o observe_v the_o declination_n may_v cause_v you_o err_v a_o whole_a degree_n and_o more_o in_o the_o place_n of_o the_o sun_n he_o therefore_o that_o list_v try_v how_o well_o the_o ephemerides_n and_o astronomical_a table_n hitherto_o publish_v agree_v with_o the_o truth_n of_o the_o heaven_n have_v best_o make_v observation_n when_o the_o sun_n be_v in_o pisces_n aries_n virgo_fw-la and_o libra_n where_o mise_v one_o whole_a minute_n in_o observe_v the_o declination_n will_v cause_v you_o miss_v not_o past_o two_o minute_n and_o a_o half_a in_o the_o true_a place_n of_o the_o sun_n when_o the_o sun_n be_v near_o either_o of_o the_o equinoctial_a point_n there_o may_v sometime_o be_v some_o small_a difficulty_n in_o find_v out_o what_o sign_n the_o sun_n be_v in_o which_o may_v easy_o be_v avoid_v thus_o the_o meridian_n altitude_n of_o the_o sun_n increase_v as_o in_o winter_n and_o spring_n time_n if_o the_o height_n of_o the_o sun_n be_v less_o than_o the_o compliment_n of_o the_o pole_n elevation_n the_o sun_n be_v in_o pisces_fw-la otherwise_o in_o aries_n but_o if_o the_o meridian_n altitude_n of_o the_o sun_n be_v every_o day_n less_o than_o other_o as_o in_o summer_n and_o autumn_n and_o the_o height_n of_o the_o sun_n at_o noon_n great_a than_o the_o height_n of_o the_o equinoctial_a the_o sun_n be_v in_o virgo_fw-la otherwise_o in_o libra_n there_o may_v likewise_o be_v some_o doubt_n in_o what_o sign_n the_o sun_n be_v be_v near_o either_o of_o the_o tropic_n which_o may_v be_v resolve_v thus_o the_o sun_n have_v south_n declination_n increase_v be_v in_o sagittarie_n but_o if_o the_o declination_n of_o the_o sun_n be_v southerly_a and_o decrease_a he_o be_v in_o capricorn_n contrariwise_o the_o declination_n of_o the_o sun_n be_v northerly_a and_o increase_a he_o be_v in_o gemini_fw-la if_o decrease_v he_o be_v cancer_n now_o whether_o the_o declination_n of_o the_o sun_n increase_v or_o decrease_v you_o may_v know_v by_o compare_v the_o declination_n of_o two_o day_n together_o for_o if_o the_o declination_n answerable_a to_o the_o second_o day_n be_v great_a the_o declination_n increase_v otherwise_o it_o decrease_v if_o both_o day_n have_v equal_a declination_n the_o first_o day_n the_o sun_n be_v in_o gemini_fw-la the_o second_o in_o cancer_n if_o his_o declination_n be_v northerly_a if_o southerly_a the_o first_o day_n he_o be_v in_o sagittarie_n the_o second_o in_o capricorn_n a_o example_n or_o two_o will_v make_v all_o plain_a the_o eight_o day_n of_o april_n 1597._o the_o declination_n of_o the_o sun_n be_v find_v by_o observation_n to_o be_v 10._o degree_n 55._o minute_n 27._o second_n which_o i_o seek_v out_o in_o the_o area_n of_o this_o table_n and_o in_o the_o head_n of_o the_o same_o column_n in_o which_o i_o find_v the_o declination_n that_o come_v near_a unto_o this_o that_o be_v 10_o degr_n 55._o min._n 33._o sec._n i_o see_v 28._o degree_n of_o aries_n for_o in_o april_n the_o sun_n can_v be_v in_o libra_n and_o in_o the_o same_o line_n wherein_o i_o find_v this_o declination_n in_o the_o further_a column_n towards_o the_o left_a hand_n i_o find_v 21._o minute_n out_o of_o which_o abate_v 17._o second_n that_o be_v the_o part_n proportional_a answerable_a to_o 6._o sec._n which_o be_v the_o excess_n of_o 10_o degr_n 55._o minute_n 33._o sec._n the_o declination_n find_v in_o the_o table_n above_o 10._o degr_n 55._o min_fw-mi 27._o sec._n the_o declination_n find_v by_o observation_n and_o there_o shall_v remain_v the_o true_a place_n of_o the_o sun_n the_o same_o year_n and_o day_n 28._o degr_n 20._o min._n 43._o sec._n of_o aries_n which_o maginus_fw-la follow_v copernicus_n and_o the_o prutenical_a table_n as_o he_o profess_v make_v to_o be_v the_o 27._o degr_n 57_o minute_n of_o aries_n almost_o that_o be_v 24._o minute_n less_o than_o truth_n that_o equation_n also_o be_v abate_v which_o be_v answerable_a to_o the_o difference_n of_o longitude_n betwixt_o london_n and_o venice_n the_o 11._o of_o march_n the_o same_o year_n at_o london_n whereby_o many_o and_o diligent_a observation_n by_o large_a and_o several_a instrument_n the_o height_n of_o the_o pole_n be_v find_v to_o be_v 51_o degree_n 32_o minute_n the_o apparent_a meridian_n altitude_n of_o the_o sun_n be_v exact_o observe_v to_o be_v 38_o degree_n 49_o minute_n but_o be_v correct_v by_o the_o parallax_n and_o refraction_n of_o the_o sun_n answerable_a to_o that_o height_n his_o true_a height_n shall_v be_v 38_o degr_n 51_o min._n 4_o sec._n whereby_o it_o appear_v that_o his_o true_a declination_n the_o same_o day_n at_o noon_n be_v 0_o degr_n 23_o min_fw-mi 4_o sec._n and_o that_o northerly_a because_o the_o height_n of_o the_o sun_n be_v great_a than_o the_o height_n of_o the_o equinoctial_a it_o be_v plain_a therefore_o that_o at_o that_o time_n the_o sun_n be_v enter_v into_o aries_n but_o now_o to_o know_v how_o far_o he_o be_v enter_v seek_v out_o 0_o degr_n 23_o min._n 4_o sec._n or_o the_o number_n next_o to_o it_o which_o be_v 0_o degr_n 23_o min._n 9_o sec._n in_o the_o area_n of_o this_o table_n wherewith_o you_o shall_v also_o find_v in_o the_o same_o line_n in_o the_o column_n next_o the_o left_a hand_n 58_o minute_n and_o in_o the_o top_n of_o the_o column_n right_a over_o this_o declination_n you_o shall_v have_v 0_o degr_n therefore_o it_o be_v manifest_a that_o at_o that_o time_n the_o sun_n be_v in_o 0_o degr_n 58_o min._n of_o aries_n almost_o for_o there_o want_v
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
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 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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 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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 sun_n and_o the_o shadow_n be_v both_o one_o way_n then_o i_o look_v for_o the_o height_n which_o be_v 85_o degree_n and_o three_o quarter_n so_o that_o it_o lack_v of_o 90_o degree_n four_o degree_n and_o one_o quarter_n which_o be_v fifteen_o minute_n these_o four_o degree_n and_o fifteen_o minute_n be_v add_v to_o the_o declination_n which_o be_v twenty_o degree_n and_o 41_o minute_n amount_v in_o all_o to_o 24_o degree_n and_o 56_o minute_n and_o so_o much_o be_o i_o distant_a from_o the_o equinoctial_a towards_o the_o north_n which_o be_v the_o part_n of_o the_o sun_n and_o of_o the_o shadow_n a_o example_n of_o the_o five_o rule_n upon_o the_o 17_o of_o october_n 1609_o which_o be_v the_o first_o year_n after_o the_o leap_n year_n the_o sun_n now_o go_v his_o course_n towards_o the_o south_n suppose_v i_o take_v his_o altitude_n in_o 50_o degree_n and_o one_o three_o and_o when_o i_o take_v it_o the_o low_a vain_a of_o my_o astrolabe_n decline_v towards_o the_o north_n of_o my_o compass_n wherefore_o i_o say_v that_o the_o sun_n and_o the_o shadow_n be_v different_a and_o so_o add_v 05_o degree_n and_o 20_o minute_n which_o be_v one_o three_o part_n of_o a_o degree_n with_o 12_o degree_n and_o 55_o minute_n which_o upon_o that_o day_n be_v the_o sun_n declination_n they_o amount_v in_o all_o to_o 63_o degree_n and_o 15_o minute_n which_o be_v less_o than_o 90_o degree_n by_o 26_o degree_n and_o 45_o minute_n and_o so_o far_o i_o be_o distant_a from_o the_o equinoctial_a to_o the_o part_n of_o the_o shadow_n that_o be_v to_o the_o north_n for_o the_o sun_n and_o shadow_n be_v different_a the_o height_n and_o declination_n come_v not_o to_o 90_o degr_n a_o second_o example_n of_o the_o five_o rule_n the_o same_o day_n and_o year_n suppose_v that_o some_o man_n find_v the_o sun_n in_o 77_o degree_n and_o five_o minute_n of_o height_n the_o sun_n itself_o decline_v to_o the_o south_n and_o the_o shadow_n fall_v to_o the_o north_n which_o be_v add_v to_o 12_o degree_n and_o 55_o minute_n of_o declination_n amount_v in_o all_o to_o 90_o degree_n just_a whereby_o i_o know_v that_o the_o ship_n wherein_o this_o altitude_n be_v take_v be_v under_o the_o equinoctial_a because_o the_o sun_n and_o shadow_n be_v different_a the_o height_n and_o declination_n make_v just_a 90_o degree_n the_o three_o example_n of_o the_o five_o rule_n upon_o the_o 20_o of_o may_v 1608_o suppose_v a_o certain_a man_n find_v the_o sun_n height_n to_o be_v 88_o degree_n and_o two_o three_o part_n the_o sun_n and_o shadow_n be_v different_a which_o be_v add_v to_o 21_o degr_n 54_o minute_n the_o sun_n declination_n that_o day_n amount_v to_o 110_o degree_n 34_o minute_n which_o exceed_v 90_o by_o 20_o degree_n and_o 34_o minute_n i_o say_v therefore_o that_o this_o man_n be_v 20_o degree_n 34_o minute_n distant_a from_o the_o equinoctial_a towards_o the_o part_n of_o the_o sun_n which_o be_v to_o the_o north_n because_o the_o sun_n and_o the_o shadow_n be_v diffeâ—rent_a the_o height_n of_o the_o sun_n and_o the_o declination_n be_v add_v together_o exceed_v 90_o degree_n chap._n viii_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 some_o astrolabe_fw-la there_o be_v who_o account_n begin_v not_o from_o the_o horizon_n but_o from_o the_o zenith_n and_o end_v with_o 90_o degr_n in_o the_o horizon_n and_o the_o height_n take_v by_o they_o be_v nothing_o else_o but_o the_o distance_n of_o the_o sun_n from_o our_o zenith_n and_o to_o make_v a_o account_n of_o the_o sun_n according_a to_o the_o altitude_n take_v with_o such_o astrolabe_fw-la there_o be_v these_o rule_n follow_v to_o be_v observe_v 1._o when_o the_o sun_n and_o the_o shadow_n be_v both_o one_o way_n add_v the_o height_n unto_o the_o declination_n and_o the_o product_n will_v show_v how_o far_o you_o be_v distant_a from_o the_o line_n towards_o the_o part_n of_o the_o sun_n and_o shadow_n 2._o if_o the_o sun_n and_o the_o shadow_n be_v differ_v subduct_v the_o declination_n from_o the_o height_n or_o the_o height_n from_o the_o declination_n the_o lesser_a from_o the_o great_a and_o the_o remainder_n will_v show_v how_o far_o you_o be_v from_o the_o line_n towards_o the_o part_n of_o that_o which_o be_v great_a and_o if_o the_o height_n be_v great_a then_o be_v you_o on_o the_o part_n of_o the_o shadow_n 3._o when_o the_o sun_n be_v in_o the_o line_n and_o have_v no_o declination_n so_o much_o altitude_n as_o you_o shall_v find_v so_o far_o be_v you_o distant_a from_o the_o equinoctial_a towards_o the_o part_n of_o the_o shadow_n 4._o when_o you_o shall_v take_v the_o sun_n in_o your_o zenith_n have_v then_o no_o altitude_n his_o declination_n will_v show_v you_o how_o far_o you_o be_v distant_a from_o the_o line_n towards_o the_o part_n of_o the_o sun_n these_o rule_n because_o they_o be_v so_o easy_a and_o plain_a need_v no_o example_n chap._n ix_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 some_o pilot_n for_o their_o curiosity_n sake_n desire_v to_o know_v the_o height_n of_o the_o sun_n for_o any_o day_n without_o a_o astrolabe_n for_o the_o performance_n whereof_o it_o be_v expedient_a that_o they_o know_v three_o thing_n that_o be_v to_o say_v the_o declination_n of_o the_o sun_n the_o distance_n of_o the_o place_n from_o the_o equinoctial_a and_o the_o part_n whereunto_o the_o shadow_n do_v incline_v at_o midday_n these_o three_o thing_n be_v know_v you_o shall_v come_v to_o the_o knowledge_n of_o the_o sun_n height_n by_o four_o rule_n 1_o when_o you_o and_o the_o sun_n be_v both_o on_o one_o side_n of_o the_o equinoctial_a if_o your_o distance_n from_o the_o line_n be_v equal_a to_o the_o sun_n declination_n you_o shall_v find_v the_o sun_n in_o your_o zenith_n in_o 90_o degr_n and_o shall_v have_v no_o shadow_n 2_o when_o the_o sun_n have_v no_o 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which_o the_o remainder_n shall_v want_v of_o 90_o deg_n shall_v be_v the_o height_n of_o the_o sun_n chap._n x._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 the_o zenith_n be_v the_o pole_n of_o the_o horizon_n because_o it_o be_v every_o where_o distant_a from_o it_o just_a 90_o deg_n and_o hence_o it_o be_v that_o the_o pole_n of_o the_o world_n be_v so_o much_o elevate_v above_o our_o horizon_n as_o our_o zenith_n be_v distant_a from_o the_o equinoctial_a which_o be_v very_o manifest_a for_o have_v 90_o deg_n of_o the_o meridian_n from_o our_o zenith_n by_o the_o pole_n of_o the_o world_n to_o the_o horizon_n and_o other_o 90_o deg_n of_o the_o meridian_n from_o the_o pole_n of_o the_o world_n by_o our_o zenith_n to_o the_o equinoctial_a because_o they_o be_v two_o quadrant_n of_o one_o and_o the_o same_o circle_n they_o must_v needs_o be_v of_o equal_a quantity_n from_o both_o which_o that_o part_n be_v take_v away_o which_o be_v common_a to_o both_o that_o be_v the_o whole_a distance_n from_o the_o pole_n of_o the_o world_n to_o our_o zenith_n that_o which_o remain_v on_o both_o part_n shall_v be_v equal_a and_o so_o that_o space_n from_o our_o zenith_n to_o the_o equinoctial_a which_o be_v call_v the_o distance_n from_o the_o line_n be_v equal_a â—o_o the_o distance_n that_o be_v between_o the_o pole_n of_o the_o world_n and_o the_o horizon_n which_o be_v call_v the_o height_n of_o the_o pole_n whereby_o it_o be_v manifest_a that_o the_o height_n of_o the_o pole_n be_v so_o much_o as_o our_o distance_n from_o the_o line_n be_v and_o although_o they_o be_v two_o different_a thing_n yet_o the_o one_o be_v take_v for_o the_o other_o
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 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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 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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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west_n and_o six_o to_o the_o foot_n it_o may_v be_v say_v that_o the_o former_a guard_n go_v two_o hour_n before_o the_o foot_n towards_o the_o south-west_n that_o it_o be_v midnight_n which_o shall_v come_v to_o pass_v when_o the_o former_a guard_n go_v a_o hour_n before_o from_o the_o south-west_n this_o be_v thus_o presuppose_v when_o i_o will_v know_v in_o the_o night_n what_o a_o clock_n it_o be_v i_o must_v note_v two_o thing_n the_o one_o be_v in_o what_o part_n the_o former_a guard_n make_v midnight_n the_o same_o night_n the_o second_o be_v in_o what_o part_n the_o say_a guard_n be_v at_o the_o same_o instant_n when_o i_o will_v know_v the_o time_n of_o the_o night_n which_o be_v understand_v i_o will_v make_v my_o account_n from_o that_o which_o the_o guard_n want_v of_o be_v come_v to_o the_o place_n where_o that_o day_n it_o make_v midnight_n or_o from_o so_o much_o as_o it_o have_v pass_v the_o same_o place_n make_v my_o account_n that_o one_o three_o part_n of_o four_o point_n of_o the_o compass_n be_v a_o hour_n and_o that_o which_o it_o want_v of_o be_v come_v or_o which_o it_o have_v pass_v forward_o be_v the_o hour_n before_o midnight_n if_o it_o be_v not_o come_v to_o the_o place_n or_o after_o midnight_n if_o it_o have_v go_v beyond_o as_o for_o example_n i_o see_v the_o former_a guard_n in_o the_o northwest_o upon_o the_o 15_o of_o july_n because_o that_o upon_o the_o 15_o of_o july_n by_o the_o account_n before_o mention_v the_o former_a guard_n make_v midnight_n in_o the_o west_n and_o from_o the_o north_n or_o head_n to_o the_o west_n be_v six_o hour_n and_o from_o the_o northwest_o where_o i_o see_v the_o guard_n to_o the_o west_n where_o it_o make_v midnight_n be_v three_o hour_n i_o say_v therefore_o that_o it_o be_v three_o hour_n before_o midnight_n that_o be_v to_o say_v nine_o of_o the_o clock_n at_o night_n finis_fw-la because_o the_o table_n of_o the_o sun_n declination_n that_o have_v be_v most_o in_o use_n among_o english_a seaman_n do_v both_o in_o fashion_n and_o manner_n of_o use_v something_o differ_v from_o those_o before_o set_v down_o pag._n 173_o 174_o etc._n etc._n lest_o any_o therefore_o of_o the_o meanner_n sort_n may_v be_v mistake_v or_o shall_v not_o right_o conceive_v the_o manner_n of_o use_v these_o table_n i_o think_v good_a to_o adjoyn_v these_o also_o here_o follow_v bear_v in_o a_o manner_n the_o same_o form_n and_o shape_n and_o therefore_o also_o to_o be_v use_v altogether_o almost_o in_o the_o same_o sort_n that_o those_o table_n have_v be_v which_o for_o these_o many_o year_n have_v be_v most_o use_v by_o english_a mariner_n this_o table_n of_o the_o sun_n declination_n contain_v twelve_o particular_a table_n show_v the_o declination_n of_o the_o sun_n for_o every_o day_n of_o the_o twelve_o month_n of_o the_o year_n for_o four_o year_n together_o from_o leap_z year_n to_o leap_v year_n in_o the_o head_n of_o every_o one_o of_o these_o table_n be_v first_o set_v down_o the_o month_n for_o which_o that_o table_n be_v make_v under_o this_o be_v place_v the_o year_n of_o our_o lord_n for_o which_o those_o table_n may_v serve_v which_o year_n be_v divide_v into_o four_o rank_n signify_v by_o the_o four_o arithmetical_a character_n 1_o 2_o 3_o 4_o that_o be_v set_v over_o they_o the_o first_o rank_n contain_v the_o first_o year_n immediate_o follow_v after_o the_o leap_n year_n the_o next_o rank_n contain_v the_o second_o year_n after_o the_o leap_n year_n in_o the_o three_o rank_n be_v set_v down_o the_o year_n that_o follow_v three_o year_n after_o the_o leap_n year_n and_o in_o the_o four_o and_o last_o rank_n be_v the_o four_o year_n after_o the_o precedent_n leap_v
sake_n have_v need_n to_o note_v and_o when_o he_o have_v expect_v afternoon_n till_o the_o sun_n descend_v by_o the_o same_o instrument_n be_v find_v place_v in_o the_o same_o 25._o degr_v of_o altitude_n than_o the_o box_n itself_o must_v again_o be_v turn_v this_o way_n or_o that_o way_n until_o the_o sun_n again_o shine_v through_o the_o sight_n the_o magnetical_a needle_n do_v point_n to_o the_o begin_n of_o the_o circle_n which_o thing_n be_v thus_o dispatch_v the_o middle_a point_n of_o the_o arch_n in_o the_o horizontall_a plain_a between_o the_o first_o and_o second_o experiment_n be_v the_o north_n point_n and_o how_o much_o the_o needle_n decline_v from_o that_o point_n so_o much_o be_v the_o variation_n seek_v for_o as_o before_o we_o have_v show_v in_o the_o first_o example_n more_o at_o large_a whatsoever_o we_o have_v affirm_v to_o be_v available_a in_o the_o day_n time_n in_o these_o experiment_n of_o the_o sun_n the_o same_o may_v be_v understand_v and_o do_v in_o 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