as_o you_o sail_v along_o how_o you_o may_v know_v the_o distance_n of_o your_o ship_n from_o they_o it_o be_v the_o custom_n of_o passenger_n when_o they_o first_o descry_v that_o land_n which_o they_o will_v arrive_v at_o to_o ask_v the_o pilot_n how_o far_o they_o be_v from_o land_n unto_o which_o question_n he_o may_v well_o answer_v if_o he_o know_v two_o cape_n or_o point_n or_o notable_a place_n thereupon_o which_o place_n the_o further_o they_o be_v asunder_o one_o from_o another_o the_o more_o certain_o may_v he_o answer_v to_o that_o question_n let_v he_o pitch_v therefore_o one_o foot_n of_o one_o pair_n of_o compass_n upon_o one_o of_o the_o two_o foresay_a cape_n and_o the_o other_o foot_n upon_o the_o rumb_n which_o in_o his_o compass_n point_v towards_o that_o cape_n and_o in_o like_a manner_n shall_v he_o do_v with_o another_o pair_n of_o compass_n place_v one_o foot_n thereof_o upon_o the_o other_o know_v cape_n and_o the_o other_o foot_n upon_o the_o rumb_n which_o stretch_v towards_o the_o say_v second_o cape_n and_o move_v the_o two_o compass_n so_o open_v by_o their_o two_o rumb_n off_o from_o the_o land_n the_o very_a same_o point_n where_o the_o two_o foot_n which_o come_v from_o the_o two_o cape_n do_v meet_v you_o may_v affirm_v to_o be_v the_o very_a point_n where_o your_o ship_n be_v and_o then_o take_v measure_n by_o the_o scale_n of_o league_n you_o may_v see_v what_o distance_n there_o be_v from_o the_o say_a point_n to_o either_o of_o the_o foresay_a cape_n or_o to_o any_o other_o place_n which_o you_o think_v good_a for_o it_o be_v a_o very_a easy_a matter_n if_o you_o know_v the_o point_n where_o your_o ship_n be_v chap._n xxxi_o of_o the_o account_n of_o the_o moon_n the_o account_n of_o the_o moon_n and_o of_o the_o tide_n be_v most_o necessary_a to_o be_v know_v of_o mariner_n to_o enter_v and_o depart_v from_o any_o havens_n rivers_n or_o bar_n and_o to_o pass_v by_o some_o bank_n and_o shoald_n a_o tide_n be_v a_o regular_a motion_n of_o the_o sea_n whereby_o at_o some_o time_n it_o seem_v more_o increase_v then_o at_o other_o and_o these_o tide_n be_v of_o two_o sort_n for_o some_o be_v such_o as_o we_o call_v springtide_n and_o neap-tide_n and_o the_o course_n of_o this_o motion_n happen_v from_o one_o half_a month_n to_o another_o half_a month_n other_o be_v those_o which_o we_o call_v more_o proper_o by_o the_o name_n of_o tide_n to_o wit_n a_o full_a sea_n and_o a_o low_a sea_n a_o swell_a and_o a_o fall_a sea_n and_o these_o be_v from_o the_o one_o half_a lunar_a day_n to_o the_o other_o half_a which_o tide_n as_o well_o the_o first_o as_o the_o second_o have_v their_o course_n and_o move_a from_o the_o motion_n of_o the_o moon_n which_o be_v of_o two_o sort_n one_o proper_a from_o west_n to_o east_n by_o mean_n whereof_o in_o thirty_o day_n almost_o it_o be_v in_o conjunction_n with_o the_o sun_n which_o we_o call_v the_o new_a moon_n and_o in_o opposition_n which_o we_o call_v the_o full_a of_o the_o moon_n and_o those_o we_o name_v the_o quarter_n when_o it_o shine_v half_a unto_o we_o the_o other_o motion_n be_v from_o east_n to_o west_n by_o the_o force_n of_o the_o primum_fw-la mobile_a or_o the_o first_o movable_a heaven_n whereby_o in_o one_o lunar_a day_n the_o moon_n pass_v over_o all_o the_o two_o and_o thirty_o point_n of_o the_o compass_n or_o to_o speak_v more_o plain_o it_o rise_v and_o set_v and_o return_v again_o to_o arise_v which_o two_o motion_n of_o the_o moon_n be_v know_v we_o may_v easy_o discern_v the_o manner_n of_o both_o kind_n of_o the_o foresay_a tide_n and_o because_o that_o to_o the_o knowledge_n hereof_o it_o be_v requisite_a that_o we_o know_v the_o middle_a motion_n of_o the_o moon_n i_o will_v first_o set_v down_o how_o it_o may_v be_v know_v and_o then_o how_o thereby_o we_o may_v discern_v the_o season_n of_o the_o tide_n for_o which_o purpose_n we_o be_v to_o note_v that_o the_o golden_a number_n as_o it_o be_v common_o call_v be_v a_o certain_a number_n of_o year_n wherein_o the_o moon_n have_v all_o the_o diversity_n of_o aspect_n with_o the_o sun_n that_o can_v happen_v between_o they_o which_o be_v do_v in_o every_o nineteen_o year_n almost_o as_o for_o example_n if_o in_o the_o year_n 1588._o there_o be_v a_o conjunction_n of_o the_o sun_n and_o moon_n upon_o the_o 26_o of_o april_n or_o a_o opposition_n upon_o the_o 11_o of_o april_n i_o say_v that_o there_o shall_v not_o happen_v a_o conjunction_n of_o the_o sun_n and_o moon_n upon_o the_o 26_o of_o april_n nor_o a_o opposition_n upon_o the_o 11_o of_o april_n till_o 19_o year_n be_v expire_v which_o will_v be_v in_o the_o year_n of_o our_o lord_n 1607._o and_o so_o be_v we_o to_o conceive_v likewise_o of_o the_o quarter_n and_o other_o aspect_n the_o second_o thing_n to_o be_v note_v be_v that_o from_o this_o golden_a number_n spring_v another_o which_o be_v call_v the_o concurrent_a be_v the_o day_n of_o the_o moon_n at_o the_o begin_n of_o the_o year_n which_o year_n according_a to_o that_o account_n begin_v from_o the_o last_o of_o february_n about_o twelve_o a_o clock_n at_o night_n which_o be_v the_o begin_n of_o march._n and_o the_o day_n of_o the_o moon_n which_o then_o remain_v beside_o all_o the_o whole_a lunare_fw-la month_n of_o the_o year_n past_a be_v call_v by_o calculator_n the_o concurrent_n because_o they_o serve_v to_o know_v the_o account_n of_o the_o moon_n throughout_o the_o whole_a year_n that_o be_v to_o come_v and_o they_o concur_v with_o other_o number_n to_o know_v the_o age_n of_o the_o moon_n now_o by_o these_o two_o number_n to_o be_v able_a to_o discern_v the_o day_n of_o the_o moon_n or_o the_o distance_n thereof_o from_o the_o sun_n you_o be_v to_o note_v the_o rule_n follow_v the_o first_o rule_n of_o the_o golden_a number_n from_o the_o present_a year_n of_o our_o lord_n you_o must_v deduct_v 1500._o and_o out_o of_o the_o remainder_n take_v one_o in_o every_o twenty_o we_o shall_v find_v the_o 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conjunction_n the_o number_n of_o the_o concurent_fw-fr being_n know_v you_o must_v add_v it_o unto_o the_o number_n of_o month_n which_o have_v pass_v from_o the_o begin_n of_o march_n last_o pass_v till_o the_o end_n of_o that_o month_n wherein_o you_o will_v know_v the_o same_o and_o if_o the_o whole_a product_n amount_v not_o to_o thirty_o mark_v how_o much_o it_o want_v of_o thirty_o and_o if_o it_o exceed_v thirty_o see_v what_o it_o lack_v of_o sixty_o and_o that_o which_o it_o want_v either_o of_o thirty_o or_o sixty_o be_v the_o number_n of_o the_o day_n of_o such_o a_o month_n wherein_o the_o conjunction_n happen_v the_o four_o rule_n of_o the_o full_a and_o quarter_n of_o the_o moon_n if_o the_o day_n of_o the_o conjunction_n be_v before_o the_o 15_o day_n of_o the_o month_n add_v 15_o unto_o the_o day_n of_o the_o conjunction_n and_o you_o shall_v find_v the_o day_n of_o the_o full_a moon_n and_o if_o the_o conjunction_n happen_v after_o the_o 15_o day_n take_v away_o 15_o from_o the_o number_n of_o the_o day_n of_o the_o conjunction_n and_o you_o shall_v have_v the_o full_a moon_n of_o that_o month_n the_o first_o quarter_n be_v seven_o day_n after_o the_o conjunction_n and_o the_o last_o quarter_n seven_o day_n after_o the_o full_a moon_n the_o five_o rule_n of_o the_o springtide_n and_o neap-tide_n upon_o the_o day_n of_o the_o conjunction_n and_o of_o the_o full_a moon_n be_v the_o springtide_n and_o upon_o the_o two_o quarter_n day_n be_v the_o neap-tide_n and_o so_o much_o the_o more_o do_v the_o water_n increase_v as_o the_o conjunction_n or_o full_a moon_n be_v near_o and_o so_o much_o the_o more_o they_o decrease_v also_o the_o near_a they_o come_v unto_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 thân_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
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
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 tâme_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
50_o 28_o 15_o 22_o 30_o 28_o 15_o 23_o 46_o 28_o 16_o 51_o 58_o 28_o 17_o 30_o 35_o 29_o 15_o 56_o 12_o 29_o 15_o 53_o 16_o 29_o 16_o 22_o 3_o 29_o 16_o 24_o 19_o 29_o 17_o 53_o 10_o 29_o 18_o 31_o 51_o 30_o 16_o 53_o 46_o 30_o 16_o 51_o 44_o 30_o 17_o 21_o 37_o 30_o 17_o 24_o 53_o 30_o 18_o 54_o 23_o 30_o 19_o 33_o 7_o 31_o 17_o 51_o 21_o 31_o 17_o 50_o 14_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 31_o 18_o 25_o 29_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 31_o 20_o 34_o 22_o chap._n xxvi_o the_o use_n of_o these_o ephemerides_n of_o the_o use_n of_o these_o ephemerides_n because_o they_o be_v altogether_o of_o the_o same_o form_n that_o other_o general_o be_v and_o have_v be_v heretofore_o and_o to_o be_v use_v also_o in_o all_o point_n after_o the_o same_o manner_n for_o find_v out_o by_o they_o the_o true_a place_n of_o the_o sun_n at_o any_o time_n desire_v for_o so_o many_o year_n as_o they_o serve_v i_o think_v it_o needless_a for_o i_o in_o this_o place_n to_o make_v any_o further_a mention_n it_o be_v my_o purpose_n in_o this_o book_n rather_o to_o make_v supply_n of_o that_o be_v want_v in_o other_o then_o to_o meddle_v with_o that_o which_o be_v by_o they_o sufficient_o handle_v and_o already_o publish_v this_o notwithstanding_o i_o think_v good_a to_o advertise_v the_o reader_n that_o these_o ephemerides_n though_o thây_v be_v make_v for_o five_o year_n only_o yet_o may_v profitable_o serve_v for_o many_o year_n to_o come_v after_o this_o manner_n subtract_v 1612_o out_o of_o the_o year_n of_o christ_n give_v divide_v that_o remain_v by_o four_o if_o any_o thing_n remain_v after_o division_n make_v it_o show_v which_o of_o the_o three_o common_a year_n in_o these_o ephemerides_n answer_v to_o the_o year_n give_v if_o nothing_o remain_v the_o four_o year_n be_v answerable_a to_o the_o year_n give_v then_o seek_v out_o the_o month_n and_o day_n of_o the_o time_n give_v both_o in_o these_o ephemerides_n for_o that_o year_n and_o in_o the_o table_n of_o their_o equation_n and_o out_o of_o they_o take_v both_o the_o place_n of_o the_o sun_n and_o the_o equation_n answerable_a to_o that_o month_n and_o day_n for_o the_o product_n of_o this_o equation_n by_o the_o quotient_a add_v to_o the_o say_a place_n of_o the_o sun_n if_o the_o number_n of_o the_o year_n give_v be_v more_o than_o 1612_o or_o subtract_v if_o it_o be_v less_o shall_v give_v you_o the_o true_a place_n of_o the_o sun_n for_o the_o time_n give_v as_o for_o example_n the_o 1_o of_o july_n 1620_o suppose_v you_o will_v know_v the_o place_n of_o the_o sun_n subtract_v therefore_o 1612_o out_o of_o 1620_o the_o remainder_n be_v 8_o which_o be_v divide_v by_o 4_o the_o quotient_n be_v 2_o and_o nothing_o remain_v which_o show_v that_o the_o four_o year_n viz._n 1612_o answer_v to_o the_o year_n give_v also_o the_o say_a month_n and_o day_n seek_v out_o in_o these_o ephemerides_n and_o in_o the_o table_n of_o their_o equation_n give_v you_o the_o place_n of_o the_o sun_n 19_o degr_n 11_o min._n 45_o sec._n of_o cancer_n and_o the_o equation_n 1_o min._n 45_o second_n which_o multiply_v by_o the_o quotient_a 2_o make_v 3_o min._n 30_o sec._n and_o this_o add_v to_o the_o say_a place_n of_o the_o sun_n the_o 1_o of_o july_n 1612_o show_v you_o the_o true_a place_n of_o the_o sun_n for_o the_o time_n give_v to_o be_v 19_o degr_n 15_o min._n and_o 15_o sec._n of_o cancer_n chap_n xxvii_o the_o make_n of_o the_o table_n of_o the_o sun_n declination_n the_o place_n of_o the_o sun_n be_v thus_o easy_o know_v by_o these_o ephemerides_n for_o every_o day_n of_o five_o year_n the_o declination_n of_o the_o sun_n for_o every_o day_n of_o the_o same_o year_n be_v easy_o find_v out_o 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 be_v show_v in_o the_o use_n of_o that_o table_n before_o set_v down_o chap._n 18._o pag._n 116._o and_o 117_o and_o so_o be_v make_v with_o no_o less_o facility_n the_o table_n follow_v 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the_o declination_n contain_v in_o this_o table_n the_o true_a declination_n of_o the_o sun_n for_o any_o day_n though_o many_o year_n hence_o may_v easy_o be_v find_v and_o that_o after_o this_o manner_n out_o of_o the_o number_n of_o the_o year_n of_o christ_n give_v subtract_v 1612_o divide_v the_o remainder_n by_o four_o and_o set_v aside_o the_o quotient_a if_o any_o thing_n remain_v that_o remainder_n show_v in_o which_o of_o the_o 3_o common_a year_n you_o be_v to_o seek_v the_o sun_n declination_n if_o nothing_o remain_v you_o must_v look_v the_o sun_n declination_n in_o the_o four_o and_o last_o year_n which_o be_v leap_v year_n then_o seek_v the_o month_n and_o day_n of_o the_o time_n give_v both_o in_o that_o year_n so_o find_v in_o the_o table_n of_o the_o sun_n declination_n and_o also_o in_o this_o little_a table_n of_o prosthaphaereses_n of_o the_o sun_n declination_n here_o immediate_o follow_v take_v out_o of_o that_o the_o sun_n declination_n and_o out_o of_o this_o little_a table_n the_o equation_n of_o that_o declination_n for_o four_o year_n which_o equation_n you_o shall_v multiply_v by_o the_o say_v quotient_a and_o add_v the_o product_n to_o the_o declination_n find_v in_o the_o table_n in_o the_o spring_n and_o autumn_n that_o be_v if_o the_o sun_n be_v in_o aries_n taurus_n gemini_fw-la libra_n scorpio_n or_o sagittarie_a or_o subtract_v it_o in_o summer_n and_o winter_n viz._n the_o sun_n be_v in_o cancer_n leo_n virgo_fw-la capricorn_n aquarie_n or_o pisces_fw-la for_o so_o shall_v you_o have_v the_o sun_n true_a declination_n for_o the_o time_n give_v take_v for_o example_n the_o 15_o of_o march_n in_o the_o year_n of_o christ_n 1630_o out_o of_o this_o subtract_v 1612_o the_o remainder_n be_v 18_o which_o be_v divide_v by_o 4_o the_o quotient_n be_v also_o 4_o and_o 2_o remain_z which_o show_v that_o you_o must_v seek_v the_o sun_n declination_n in_o the_o second_o year_n after_o the_o leap_n year_n for_o the_o month_n and_o day_n 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of_o which_o if_o you_o subtract_v 1612_o there_o shall_v remain_v 47_o which_o be_v divide_v by_o 4_o the_o quotient_n will_v be_v 11_o and_o 3_o remain_v i_o find_v therefore_o in_o the_o table_n of_o the_o sun_n declination_n in_o the_o three_o year_n for_o the_o month_n and_o day_n aforesaid_a the_o sun_n declination_n 5_o degr_v 29_o min._n â5_n sec._n also_o in_o this_o little_a table_n of_o prosthaphaereses_n of_o the_o sun_n declination_n i_o find_v for_o the_o same_o month_n and_o day_n the_o difference_n of_o the_o declination_n of_o the_o sun_n for_o 4_o year_n to_o be_v 42_o sec._n which_o multiply_v by_o the_o quotient_a 11_o make_v the_o product_n 7_o min._n 42_o sec._n which_o subtract_v out_o of_o the_o declination_n aforesaid_a 5_o degr_n 29_o min._n 35_o second_n shall_v leave_v you_o the_o sun_n true_a declination_n for_o the_o 30_o of_o august_n 1659._o 5_o degr_n 21_o min._n 53_o sec._n prosthaphereses_n of_o the_o sun_n declination_n  _fw-fr ja_n fe._n m_o a._n m_o ju_n ju_n a._n se._n o._n n_o d._n day_n se._n se._n se._n se._n se._n se._n se_fw-la se._n se._n se._n se._n se._n 1_o 17_o 36_o 42_o 40_o 28_o 8_o 15_o 33_o 42_o 41_o 30_o 9_o 2_o 18_o 37_o 43_o 39_o 28_o 7_o 15_o 34_o 43_o 42_o 29_o 8_o 3_o 19_o 37_o 43_o 40_o 27_o 6_o 16_o 35_o 43_o 42_o 29_o 7_o 4_o 20_o 38_o 44_o 40_o 27_o 5_o 17_o 35_o 43_o 42_o 28_o 6_o 5_o 20_o 37_o 44_o 39_o 26_o 4_o 18_o 34_o 43_o 41_o 28_o 5_o 6_o 21_o 37_o 43_o 39_o 25_o 4_o 19_o 35_o 43_o 41_o 28_o 4_o 7_o 21_o 38_o 43_o 38_o 25_o 3_o 19_o 35_o 44_o 41_o 27_o 3_o 8_o 22_o 39_o 43_o 38_o 24_o 2_o 19_o 35_o 43_o 40_o 26_o 2_o 9_o 24_o 38_o 44_o 38_o 23_o 2_o 20_o 36_o 44_o 40_o 25_o 1_o 10_o 24_o 39_o 45_o 37_o 23_o 1_o 21_o 36_o 43_o 40_o 24_o 1_o 11_o 25_o 39_o 44_o 37_o 22_o 0_o 21_o 37_o 43_o 40_o 24_o 0_o 12_o 25_o 40_o 44_o 37_o 22_o 1_o 22_o 38_o 43_o 39_o 23_o 0_o 13_o 26_o 41_o 43_o 37_o 21_o 1_o 22_o 38_o 43_o 39_o 22_o 1_o 14_o 26_o 40_o 44_o 37_o 20_o 2_o 23_o 38_o 44_o 38_o 21_o 2_o 15_o 27_o 41_o 44_o 35_o 20_o 3_o 23_o 38_o 43_o 38_o 21_o 3_o 16_o 28_o 42_o 43_o 35_o 19_o 4_o 24_o 39_o 44_o 37_o 20_o 4_o 17_o 28_o 41_o 42_o 35_o 19_o 4_o 25_o 39_o 43_o 38_o 20_o 5_o 18_o 29_o 41_o 43_o 35_o 18_o 5_o 26_o 39_o 43_o 37_o 19_o 6_o 19_o 30_o 41_o 43_o 34_o 17_o 6_o 26_o 39_o 43_o 37_o 18_o 7_o 20_o 31_o 42_o 42_o 34_o 17_o 7_o 27_o 40_o 43_o 36_o 17_o 8_o 21_o 31_o 42_o 43_o 33_o 16_o 8_o 27_o 40_o 43_o 36_o 16_o 9_o 22_o 32_o 42_o 43_o 33_o 15_o 8_o 28_o 41_o 44_o 35_o 16_o 10_o 23_o 32_o 43_o 43_o 32_o 14_o 9_o 29_o 40_o 43_o 35_o 15_o 11_o 24_o 32_o 43_o 42_o 32_o 14_o 10_o 29_o 41_o 42_o 34_o 14_o 12_o 25_o 33_o 44_o 42_o 31_o 12_o 11_o 30_o 41_o 43_o 34_o 13_o 12_o 26_o 33_o 44_o 41_o 31_o 12_o 12_o 30_o 41_o 42_o 33_o 13_o 13_o 27_o 34_o 43_o 41_o 30_o 11_o 13_o 30_o 41_o 42_o 34_o 12_o 14_o 28_o 35_o 43_o 41_o 29_o 11_o 13_o 31_o 42_o 42_o 33_o 11_o 15_o 29_o 35_o 43_o 41_o 29_o 9_o 14_o 31_o 41_o 43_o 32_o 11_o 16_o 30_o 35_o  _fw-fr 41_o 29_o 9_o 14_o 32_o 42_o 42_o 32_o 10_o 16_o 31_o 36_o  _fw-fr 41_o  _fw-fr 8_o  _fw-fr 33_o 42_o  _fw-fr 31_o  _fw-fr 17_o a_o table_n of_o the_o sun_n declination_n 1608._o leap_v year_n  _fw-fr jan._n decl_n differ_v  _fw-fr feb._n decl_n differ_v  _fw-fr mar._n decl_n differ_v  _fw-fr apr._n decl_n differ_v d_o gr_n mi._n s._n mi._n se_fw-fr d_o gr_n mi._n s_o mi._n se_fw-fr d_o gr_n mi_fw-mi se._n mi._n se_fw-fr d_o gr_fw-fr mi._n se._n mi._n se_fw-la 1_o 21_o 54_o 39_o 9_o 35_o 1_o 14_o 7_o 44_o 20_o 11_o 1_o 3_o 25_o 38_o 23_o 36_o 1_o 8_o 34_o 21_o 21_o 52_o 2_o 21_o 45_o 4_o 9_o 59_o 2_o 13_o 47_o 33_o 19_o 45_o 2_o 3_o 2_o 2_o 23_o 38_o 2_o 8_o 56_o 23_o 21_o 42_o 3_o 21_o 35_o 5_o 10_o 24_o 3_o 13_o 27_o 48_o 21_o 18_o 3_o 2_o 38_o 24_o 23_o 41_o 3_o 9_o 18_o 5_o 21_o 33_o 4_o 21_o 24_o 41_o 10_o 54_o 4_o 13_o 6_o 30_o 20_o 52_o 4_o 2_o 14_o 43_o 23_o 41_o 4_o 9_o 39_o 38_o 21_o 25_o 5_o 21_o 13_o 45_o 11_o 7_o 5_o 12_o 46_o 38_o 20_o 23_o 5_o 1_o 51_o 2_o 23_o 43_o 5_o 10_o 1_o 3_o 21_o 14_o 6_o 21_o 2_o 38_o 11_o 37_o 6_o 12_o 26_o 15_o 20_o 54_o 6_o 1_o 27_o 19_o 23_o 43_o 6_o 10_o 22_o 17_o 21_o 4_o 7_o 20_o 51_o 1_o 12_o 2_o 7_o 12_o 5_o 21_o 21_o 6_o 7_o 1_o 3_o 36_o 23_o 43_o 7_o 10_o 43_o 21_o 20_o 53_o 8_o 20_o 38_o 59_o 12_o 24_o 8_o 11_o 44_o 15_o 21_o 18_o 8_o 0_o 39_o 53_o 23_o 42_o 8_o 11_o 4_o 14_o 20_o 36_o 9_o 20_o 26_o 35_o 12_o 48_o 9_o 11_o 22_o 57_o 21_o 27_o 9_o 0_o 16_o 11_o 23_o 42_o 9_o 11_o 24_o 50_o 20_o 38_o 10_o 20_o 13_o 47_o 13_o 10_o 10_o 11_o 1_o 30_o 21_o 39_o 10_o 0_o 7_o 31_o 23_o 42_o 10_o 11_o 45_o 28_o 20_o 20_o 11_o 20_o 0_o 37_o 13_o 34_o 11_o 10_o 39_o 51_o 21_o 47_o 11_o 0_o 31_o 13_o 23_o 39_o 11_o 12_o 5_o 48_o 20_o 8_o 12_o 19_o 47_o 3_o 13_o 54_o 12_o 10_o 18_o 4_o 21_o 56_o 12_o 0_o 54_o 52_o 23_o 39_o 12_o 12_o 25_o 56_o 19_o 56_o 13_o 19_o 33_o 9_o 14_o 17_o 13_o 9_o 56_o 8_o 22_o 7_o 13_o 1_o 18_o 31_o 23_o 36_o 13_o 12_o 45_o 52_o 18_o 43_o 14_o 19_o 18_o 52_o 14_o 24_o 14_o 9_o 34_o 1_o 22_o 14_o 14_o 1_o 42_o 7_o 23_o 34_o 14_o 13_o 4_o 35_o 20_o 31_o 15_o 19_o 4_o 28_o 15_o 12_o 15_o 9_o 11_o 47_o 22_o 22_o 15_o 2_o 5_o 41_o 23_o 31_o 15_o 13_o 25_o 6_o 19_o 18_o 16_o 18_o 49_o 16_o 15_o 33_o 61_o 8_o 49_o 25_o 22_o 31_o 16_o 2_o 29_o 12_o 23_o 28_o 16_o 13_o 44_o 24_o 19_o 4_o 17_o 18_o 33_o 43_o 15_o 26_o 17_o 8_o 26_o 54_o 22_o 37_o 17_o 2_o 52_o 40_o 23_o 24_o 17_o 14_o 3_o 2d_o 18_o 50_o 18_o 18_o 18_o 17_o 15_o 59_o 18_o 8_o 4_o 17_o 22_o 45_o 18_o 3_o 16_o 4_o 23_o 20_o 18_o 14_o 22_o 18_o 18_o 37_o 19_o 18_o 2_o 18_o 16_o 18_o 19_o 7_o 41_o 32_o 22_o 50_o 19_o 3_o 39_o 24_o 23_o 16_o 19_o 14_o 40_o 55_o 18_o 22_o 20_o 17_o 46_o 0_o 16_o 38_o 20_o 7_o 18_o 42_o 22_o 58_o 20_o 4_o 2_o 40_o 23_o 12_o 20_o 14_o 59_o 17_o 18_o 9_o 21_o 17_o 29_o 22_o 16_o 55_o 21_o 6_o 55_o 44_o 23_o 3_o 21_o 4_o 25_o 52_o 23_o 7_o 21_o 15_o 17_o 26_o 17_o 50_o 22_o 17_o 12_o 27_o 17_o 14_o 22_o 6_o 32_o 41_o 23_o 8_o 22_o 4_o 48_o 59_o 23_o 2_o 22_o 15_o 35_o 16_o 17_o 38_o 23_o 16_o 55_o 13_o 17_o 31_o 23_o 6_o 9_o 33_o 23_o 13_o 23_o 5_o 12_o 1_o 22_o 58_o 23_o 15_o 52_o 54_o 17_o 20_o 24_o 16_o 37_o 42_o 17_o 49_o 24_o 5_o 46_o 20_o 23_o 17_o 24_o 5_o 34_o 59_o 22_o 50_o 24_o 16_o 10_o 14_o 17_o 6_o 25_o 16_o 19_o 53_o 18_o 6_o 25_o 5_o 23_o 3_o 23_o 22_o 25_o 5_o 57_o 49_o 22_o 45_o 25_o 16_o 27_o 20_o 16_o 49_o 26_o 16_o 1_o 47_o 18_o 21_o 26_o 4_o 59_o 41_o 23_o 27_o 26_o 6_o 20_o 34_o 22_o 37_o 26_o 16_o 44_o 9_o 16_o 33_o 27_o 15_o 43_o 26_o 18_o 38_o 27_o 4_o 36_o 14_o 23_o 28_o 27_o 6_o 43_o 11_o 22_o 31_o 27_o 17_o 0_o 42_o 16_o 16_o 28_o 15_o 24_o 48_o 18_o 54_o 28_o 4_o 12_o 46_o 23_o 32_o 28_o 7_o 5_o 42_o 22_o 24_o 28_o 17_o 16_o 58_o 15_o 58_o 29_o 15_o 5_o 54_o 19_o 9_o 29_o 3_o 49_o 14_o 23_o 36_o 29_o 7_o 28_o 6_o 22_o 16_o 29_o 17_o 32_o 56_o 15_o 41_o 30_o 14_o 46_o 45_o 19_o 23_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 30_o 7_o 50_o 22_o 22_o 8_o 30_o 17_o 48_o 37_o 15_o 24_o 31_o 14_o 27_o 22_o 19_o 38_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 31_o 8_o 12_o 30_o 22_o 1_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr ma._n decl_n differ_v  _fw-fr ju_n decl_n diff._n  _fw-fr ju_n decl_n diff._n  _fw-fr au_n decl_n diff._n d_o gr_n mi._n se._n mi_fw-mi se_fw-mi d_o gr_n m._n se_fw-la mi._n se_fw-fr d_o gr_n mi._n se_fw-la mi._n se_fw-fr d_o gr_n mi_fw-mi se._n mi._n s_o 1_o 18_o 4_o 1_o 15_o 5_o 1_o 23_o 11_o 32_o 3_o 50_o 1_o 22_o 8_o 57_o 8_o 16_o 1_o 15_o 14_o 50_o 18_o 3_o 2_o 18_o 19_o 6_o 14_o 48_o 2_o 23_o 15_o 22_o 3_o 26_o 2_o 22_o 0_o 42_o 8_o 39_o 2_o 14_o
right_a side_n 41_o 38_o 2_o 56_o 2_o the_o goat_n or_o wagoner_n leave_v shoulder_n 44_o 30_o 4_o 49_o 1_o the_o wagoner_n right_a shoulder_n 45_o 11_o 5_o 30_o 2_o the_o first_o in_o the_o great_a bear_v forefoot_n 40_o 30_o 8_o 24_o 3_o the_o second_o in_o the_o same_o foot_n 41_o 28_o 8_o 32_o 3_o in_o her_o former_a left_a knee_n 36_o 37_o 8_o 58_o 3_o the_o great_a bear_v side_n 31_o 26_o 10_o 58_o 2_o the_o great_a bear_n back_o 26_o 05_o 10_o 40_o 2_o the_o end_n of_o the_o dragon_n tail_n 18_o 26_o 11_o 08_o 3_o the_o great_a bear_v thigh_n 34_o 03_o 11_o 32_o 2_o the_o great_a bear_v rump_n 30_o 41_o 11_o 54_o 2_o the_o next_o to_o the_o end_n of_o the_o dragon_n tail_n 17_o 57_o 12_o 14_o 3_o the_o first_o in_o the_o great_a bear_v tail_n next_o her_o rump_n 31_o 49_o 12_o 32_o 2_o the_o middlemost_a in_o her_o tail_n 32_o 55_o 13_o 06_o 2_o in_o the_o end_n of_o her_o tail_n 38_o 37_o 13_o 32_o 2_o the_o next_o before_o the_o turn_n of_o the_o dragon_n tail_n 23_o 40_o 13_o 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the_o half_a thereof_o odd_a than_o that_o year_n be_v the_o second_o year_n after_o the_o leap_n year_n but_o if_o the_o remainder_n of_o the_o year_n number_v be_v odd_a we_o must_v try_v the_o year_n next_o go_v before_o to_o see_v whether_o the_o remainder_n thereof_o and_o half_o the_o remainder_n be_v even_a number_n for_o then_o the_o present_a year_n be_v the_o first_o after_o the_o leap_n year_n and_o if_o the_o remainder_n of_o the_o year_n go_v before_o be_v even_o and_o the_o half_a thereof_o odd_a than_o the_o present_a year_n be_v the_o three_o year_n after_o the_o leap_n year_n how_o the_o declination_n of_o the_o sun_n may_v be_v find_v out_o now_o to_o know_v the_o sun_n declination_n every_o day_n we_o must_v look_v in_o that_o table_n which_o answer_v to_o the_o present_a year_n and_o seek_v the_o month_n in_o the_o upper_a part_n of_o the_o page_n and_o the_o day_n of_o the_o month_n wherein_o we_o will_v know_v the_o declination_n in_o the_o column_n which_o defend_v towards_o the_o left_a hand_n right_o over_o against_o the_o say_a day_n and_o under_o the_o title_n of_o our_o month_n we_o shall_v find_v two_o number_n one_o of_o degree_n and_o the_o other_o of_o minute_n which_o be_v the_o declination_n of_o the_o sun_n that_o day_n towards_o that_o part_n of_o the_o world_n which_o the_o first_o rule_n of_o the_o sun_n do_v teach_v chap._n vi_o the_o equation_n of_o the_o sun_n declination_n they_o which_o sail_n in_o the_o month_n of_o june_n and_o december_n need_v not_o much_o to_o make_v any_o equation_n in_o the_o table_n of_o the_o sun_n declination_n because_o that_o in_o those_o month_n the_o declination_n of_o one_o day_n differ_v very_o little_a from_o the_o declination_n of_o another_o but_o at_o all_o other_o time_n of_o the_o year_n we_o ought_v to_o make_v some_o kind_n of_o equation_n to_o know_v precise_o our_o height_n or_o our_o distance_n from_o the_o equinoctial_a this_o equation_n be_v to_o be_v make_v after_o this_o manner_n you_o must_v subtract_v the_o declination_n of_o the_o sun_n for_o the_o present_a day_n from_o the_o declination_n of_o the_o day_n follow_v or_o contrariwise_o subtract_v always_o the_o less_o out_o oâ_n the_o great_a and_o the_o difference_n or_o remainder_n shall_v be_v multiply_v by_o the_o league_n which_o our_o ship_n have_v sail_v from_o the_o meridian_n of_o london_n and_o the_o product_n of_o the_o multiplication_n must_v be_v divide_v by_o desire_v 7200_o league_n which_o be_v contain_v in_o the_o compass_n of_o the_o whole_a earth_n then_o if_o you_o have_v sail_v westward_o the_o quotient_n must_v be_v add_v to_o the_o declination_n of_o the_o sun_n that_o day_n if_o it_o be_v from_o the_o 11_o of_o march_n to_o the_o 12_o of_o june_n or_o from_o the_o 13_o of_o september_n to_o the_o 12_o of_o december_n or_o it_o must_v if_o the_o ship_n also_o have_v sail_v westward_o be_v subtract_v if_o you_o find_v it_o in_o any_o other_o time_n of_o the_o year_n except_o in_o the_o day_n of_o the_o equinoctium_n for_o then_o this_o difference_n be_v know_v by_o take_v the_o declination_n of_o the_o present_a day_n with_o that_o of_o the_o day_n follow_v but_o if_o you_o be_v to_o the_o eastward_o from_o the_o meridian_n of_o london_n you_o must_v do_v contrariwise_o subtract_v the_o say_a squation_n where_o before_o you_o add_v it_o in_o stead_n of_o the_o table_n of_o the_o sun_n declination_n here_o insert_v by_o roderigo_n samorano_n use_v the_o table_n before_o set_v down_o from_o the_o 174_o page_n to_o the_o 180_o page_n chap._n vii_o four_o example_n for_o the_o plain_a declaration_n of_o that_o which_o be_v say_v before_o a_o example_n of_o the_o second_o rule_n in_o the_o year_n 1608_o the_o 15_o of_o april_n suppose_v i_o be_v sail_v and_o take_v the_o height_n of_o the_o sun_n with_o my_o astrolabe_n at_o noon_n and_o find_v the_o height_n thereof_o to_o be_v just_a 90_o degree_n first_o therefore_o i_o take_v from_o 1608._o the_o number_n of_o 1600._o and_o their_z remain_z 8_o whicâ_n remainder_n be_v a_o even_a number_n and_o four_o the_o half_a thereof_o be_v even_o also_o i_o say_v the_o year_n 1608_o be_v the_o leap_v year_n and_o so_o i_o go_v unto_o the_o four_o year_n in_o the_o table_n of_o the_o sun_n declination_n which_o be_v leap_v year_n and_o under_o the_o month_n of_o april_n over_o against_o the_o 15_o day_n i_o find_v 13_o degree_n and_o 25_o minute_n 41_o second_o i_o say_v therefore_o that_o i_o be_o distant_a from_o the_o equinoctial_a towards_o the_o north_n 13_o degree_n and_o 26_o minute_n almost_o because_o it_o be_v between_o the_o 11_o of_o march_n and_o the_o 13_o of_o september_n in_o which_o space_n fall_v the_o 15_o day_n of_o april_n the_o second_o example_n of_o the_o three_o rule_n in_o the_o year_n 1602_o upon_o the_o 13_o day_n of_o september_n admit_v i_o take_v the_o height_n of_o the_o sun_n and_o find_v it_o in_o my_o astrolabe_n to_o be_v 70_o degree_n and_o a_o half_a and_o that_o in_o the_o table_n of_o declination_n belong_v to_o the_o same_o year_n upon_o the_o foresay_a day_n of_o september_n i_o find_v that_o the_o sun_n have_v no_o declination_n but_o that_o it_o be_v under_o the_o very_a equinoctial_a line_n now_o because_o the_o degree_n of_o the_o height_n which_o the_o sun_n want_v of_o 90_o be_v 19_o and_o a_o half_a i_o say_v that_o i_o be_o so_o much_o distant_a from_o the_o equinoctial_a towards_o that_o part_n of_o the_o world_n unto_o which_o the_o shadow_n fall_v example_n of_o the_o four_o rule_n upon_o the_o 13_o of_o may_n 1609_o suppose_v i_o take_v the_o height_n of_o the_o sun_n at_o noon_n in_o my_o astrolabe_n and_o find_v it_o to_o be_v 85_o degree_n and_o three_o quarter_n now_o because_o 1609_o be_v a_o odd_a number_n i_o go_v back_o to_o the_o former_a year_n of_o 1608._o and_o i_o find_v according_a to_o the_o rule_n of_o leap_n year_n that_o the_o year_n 1608_o be_v leap_v year_n and_o hence_o i_o judge_v that_o the_o year_n 1609_o be_v the_o year_n next_o follow_v the_o leap_n year_n then_o i_o go_v to_o the_o table_n of_o declination_n belong_v to_o the_o first_o year_n after_o the_o leap_n year_n and_o under_o the_o month_n of_o may_n against_o the_o 13_o day_n the_o sun_n declination_n be_v find_v to_o be_v 20_o degree_n 41_o minute_n 15_o second_o and_o because_o that_o from_o the_o 11_o of_o march_n to_o the_o 13_o of_o september_n the_o sun_n keep_v his_o course_n to_o the_o northwards_o of_o the_o equinoctial_a have_v mark_v the_o shadow_n at_o midday_n i_o see_v that_o the_o low_a vain_a of_o my_o astrolabe_n look_v to_o the_o north_n of_o the_o compass_n and_o so_o i_o say_v that_o
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
seven_o hundred_o but_o for_o as_o much_o as_o the_o charge_n though_o not_o great_a to_o speak_v of_o of_o provide_v meet_a mean_n for_o supply_v of_o these_o want_n in_o the_o course_n and_o longitude_n but_o chief_o in_o the_o latter_a exceed_v the_o mean_a ability_n of_o the_o most_o part_n of_o they_o that_o be_v most_o addict_v to_o these_o ungainful_a study_n i_o must_v not_o say_v ungrateful_a although_o in_o these_o day_n they_o prove_v most_o unprofitable_a to_o their_o great_a lover_n therefore_o they_o be_v for_o my_o part_n like_a to_o rest_v as_o hitherto_o they_o have_v do_v untouched_a and_o only_o commend_v unto_o a_o certain_a kind_n of_o hope_n whether_o vain_a or_o no_o i_o know_v not_o of_o some_o maecenas_n at_o length_n of_o manificent_a spirit_n to_o be_v stir_v up_o to_o have_v some_o due_a consideration_n both_o of_o these_o and_o other_o such_o want_n and_o imperfection_n as_o yet_o remain_v in_o so_o excellent_a a_o art_n as_o this_o of_o navigation_n be_v 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innermost_a circle_n to_o the_o end_n of_o the_o foresay_a brass_n pointer_n so_o as_o the_o end_n thereof_o may_v enter_v thereinto_o then_o set_v the_o line_n that_o be_v draw_v from_o the_o end_n of_o the_o brass_n pointer_n to_o the_o elevation_n of_o the_o pole_n at_o the_o place_n of_o your_o observation_n and_o so_o have_v you_o all_o part_n of_o your_o instrument_n right_o place_v for_o observation_n now_o when_o you_o will_v make_v observation_n with_o this_o instrument_n instrument_n hang_v the_o same_o by_o this_o ring_n upon_o your_o finger_n as_o you_o do_v when_o you_o observe_v the_o height_n of_o the_o sun_n with_o the_o astrolabe_n turn_v the_o foresay_a brass_n pointer_n northwards_o till_o you_o find_v the_o midst_n of_o the_o shadow_n of_o the_o bead_n to_o fall_v upon_o the_o peripherie_n draw_v round_o about_o through_o the_o midst_n of_o the_o concavitie_n of_o the_o equinoctial_a ring_n which_o peripherie_n we_o call_v the_o parallel_n of_o the_o sun_n and_o 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come_v to_o the_o say_v perpendicular_a this_o arch_n resolve_v into_o degree_n shall_v give_v you_o the_o true_a azimuth_n of_o the_o sun_n chap._n xiiii_o to_o find_v the_o inclination_n or_o dip_v of_o the_o magnetical_a needle_n under_o the_o horizon_n first_o the_o angle_n oar_n be_v give_v because_o of_o the_o arch_n obr_n measure_v the_o same_o 150_o degree_n and_o consequent_o the_o angle_n at_o r_o 15_o degree_n be_v equal_a to_o the_o equal_a side_v angle_n at_o o_o both_o which_o together_o be_v 30_o degree_n because_o they_o be_v the_o compliment_n of_o the_o angle_n oar_n 150_o degree_n to_o a_o semicircle_n or_o 180_o degree_n second_o in_o the_o triangle_n ars_n all_o the_o side_n be_v give_v be_v the_o radius_fw-la or_o semidiameter_n 10,000,000_o r_n equal_a to_o ro_n the_o subtense_n of_o 150_o degree_n 19,318,516_o and_o as_o equal_a to_o ad_fw-la triple_a in_o power_n to_o ab_fw-la because_o it_o be_v equal_a in_o power_n to_o ab_fw-la and_o bd_o that_o be_v boy_n which_o be_v double_a in_o power_n to_o ab_fw-la or_o else_o thus_o the_o arch_n ob_fw-la being_n 90_o degree_n the_o subtense_n thereof_o ob_fw-la that_o be_v the_o tangent_fw-la bd_o be_v 14,142,126_o which_o seek_v in_o the_o table_n of_o tangent_n shall_v give_v you_o the_o angle_n bid_v 54_o degree_n 44_o minute_n 8_o second_o the_o secant_fw-la whereof_o be_v the_o line_n ad_fw-la that_o be_v as_o 17,320,508_o now_o then_o by_o 4_o axiom_n of_o the_o 2_o book_n of_o ptisc_n as_o the_o base_a or_o great_a side_n sir_n 19,318,516_o be_v to_o the_o sum_n of_o the_o other_o two_o side_n sa_o and_o ar_n 27,320,508_o so_o be_v the_o difference_n of_o they_o sx_v 7,320,508_o to_o the_o segment_n of_o the_o great_a side_n sy_n 10,352,762_o which_o be_v take_v out_o of_o sir_n 19,318,516_o there_o remain_v your_o 8,965,754_o the_o half_a whereof_o rz_n 4,482,877_o be_v the_o sine_fw-la of_o the_o angle_n raz_n 26_o degree_n 38_o minute_n 2_o second_o the_o compliment_n whereof_o 63_o degree_n 21_o minute_n 58_o second_n be_v the_o angle_n arz_n which_o add_v to_o the_o angle_n aro_n 15_o degree_n make_v the_o whole_a angle_n orseolo_n 78_o degree_n â1_n minute_n 58_o second_o whereof_o 60_o 90_o make_v 52_o degree_n 14_o minute_n 38_o second_n which_o take_v out_o of_o arz_n 63_o degree_n 21_o minute_n 58_o second_n there_o remain_v the_o angle_n tra_n 11_o degree_n 7_o minute_n 20_o second_o the_o compliment_n whereof_o be_v the_o inclination_n seek_v for_o 78_o degree_n 52_o minute_n 40_o second_n the_o sum_n and_o difference_n of_o the_o side_n sa_o and_o be_v be_v always_o the_o same_o viz._n 27,320,508_o and_o 7,320,508_o inclination_n the_o product_n of_o they_o shall_v likewise_o be_v always_o the_o same_o viz._n 199,999,997,378.064_o to_o be_v divide_v by_o the_o side_n sir_n that_o be_v ro_n the_o subtense_n of_o rbo._n therefore_o there_o may_v be_v some_o labour_n save_v in_o make_v the_o table_n of_o magnetical_a inclination_n if_o in_o stead_n of_o the_o say_v product_v you_o take_v continual_o but_o the_o half_a thereof_o that_o be_v 99,999,998,689,032_o and_o so_o divide_v it_o by_o half_a the_o subtense_n ro_n that_o be_v by_o the_o sine_fw-la of_o half_a the_o arch_n obr_n or_o rather_o thus_o as_o half_a the_o base_a r_n that_o be_v as_o the_o sine_z of_o half_a the_o arch_n obr_n be_v to_o half_a the_o sum_n of_o the_o other_o two_o side_n sa_o and_o ar_n 13,660,254_o so_o be_v half_a the_o difference_n of_o they_o 3,660,254_o to_o half_a of_o the_o segment_n sy_n which_o take_v out_o of_o half_a the_o base_a there_o remain_v rz_n the_o sine_fw-la of_o raz_n the_o table_n of_o magnetical_a inclination_n first_o col_fw-fr second_o col_fw-fr first_o col·_fw-la second_o col_fw-fr first_o col_fw-fr second_n col_fw-fr height_n of_o the_o pole_n magnetical_a inclination_n height_n of_o the_o pole_n magnetical_a inclination_n height_n of_o the_o pole_n magnetical_a inclination·_n degree_n degr._fw-la min._n degree_n degr._fw-la min_n degree_n degr._fw-la min._n 1_o 2_o 11_o 31_o 52_o 27_o 61_o 79_o 29_o 2_o 4_o 20_o 32_o 53_o 41_o 62_o 80_o 4_o 3_o 6_o 27_o 33_o 54_o 53_o 63_o 80_o 38_o 4_o 8_o 31_o 34_o 56_o 4_o 64_o 81_o 11_o 5_o 10_o 34_o 35_o 57_o 13_o 65_o 81_o 43_o 6_o 12_o 34_o 36_o 58_o 21_o 66_o 82_o 13_o 7_o 14_o 32_o 37_o 59_o 28_o 67_o 82_o 43_o 8_o 16_o 28_o 38_o 60_o 33_o 68_o 83_o 12_o 9_o 18_o 22_o 39_o 61_o 37_o 69_o 83_o 40_o 10_o 20_o 14_o 40_o 62_o 39_o 70_o 84_o 7_o 11_o 22_o 4_o 41_o 63_o 40_o 71_o 84_o 32_o 12_o 24_o 52_o 42_o 64_o 39_o 72_o 84_o 57_o 13_o 25_o 38_o 43_o 65_o 38_o 73_o 85_o 21_o 14_o 27_o 22_o 44_o 66_o 35_o 74_o 85_o 44_o 15_o 29_o 4_o 45_o 67_o 30_o 75_o 86_o 7_o 16_o 30_o 45_o 46_o 68_o 24_o 76_o 86_o 28_o 17_o 32_o
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 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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 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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 â_o 3_o 26_o 8_o â_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 â_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 â_o that_o day_n at_o noon_n example_n of_o the_o second_o admit_v the_o year_n follow_v 1596_o you_o will_v know_v the_o time_n of_o the_o sun_n entrance_n into_o the_o midst_n of_o taurus_n have_v therefore_o to_o this_o end_n observe_v the_o apparent_a meridian_n altitude_n of_o the_o sun_n the_o 24_o 25_o and_o 26._o day_n of_o april_n in_o that_o year_n within_o the_o space_n of_o which_o day_n i_o be_o sure_a the_o sun_n must_v needs_o be_v in_o that_o point_n to_o be_v 54_o degree_n 35_o minute_n 54_o degree_n 51_o min._n ½_o 55_o degree_n 8_o min._n ½_o and_o consequent_o the_o true_a height_n 54_o degr_n 36_o min._n 44_o sec._n 54_o degr_n 53_o min._n 13_o sec._n 55_o degree_n 10_o min._n 13_o sec_fw-la and_o out_o of_o these_o the_o true_a declination_n 16_o degr_n 8_o min._n 44_o sec._n 16_o degr_n 25_o min._n 13_o sec._n 16._o degr_n 52_o min._n 13._o sec._n hereby_o i_o find_v the_o true_a place_n of_o the_o sun_n the_o same_o day_n to_o be_v 14_o degr_n 9_o min._n 40_o sec._n of_o taurus_n 15_o degr_n 5_o min._n 20_o sec._n of_o taurus_n 16_o degr_n 3_o min._n 42_o sec._n of_o taurus_n subtract_v therefore_o 14_o degr_n 9_o min_fw-mi 40_o sec._n of_o taurus_n that_o be_v the_o place_n of_o the_o sun_n the_o 24_o day_n out_o of_o 15_o degr_n 5_o min._n 20_o sec._n of_o taurus_n the_o place_n of_o the_o sun_n the_o 25_o day_n the_o remainder_n shall_v be_v 55_o min._n 40_o sec._n which_o be_v the_o true_a motion_n of_o the_o sun_n between_o the_o 24_o and_o 25._o day_n at_o noon_n that_o be_v the_o diurn_n motion_n of_o the_o sun_n at_o that_o time_n subtract_v also_o 14_o degr_n 9_o min._n 40_o sec._n of_o taurus_n out_o of_o 15_o degr_v 0_o min._n of_o taurus_n the_o difference_n be_v 50_o min._n 20_o sec._n now_o as_o 55_o min._n 40_o sec_fw-la be_v to_o 50_o min._n 20_o sec._n so_o be_v 24_o hour_n to_o 21_o hour_n 42_o min._n and_o 2_o sec_fw-la it_o appear_v therefore_o by_o subtract_v 21_o hour_n 42_o min._n 2_o sec._n out_o of_o 24_o hour_n that_o the_o sun_n shall_v enter_v into_o the_o midst_n of_o taurus_n the_o 25_o day_n about_o two_o hour_n and_o almost_o 18_o min._n before_o noon_n that_o be_v at_o nine_o a_o clock_n and_o 42_o minute_n now_o suppose_v i_o have_v not_o or_o can_v not_o have_v observe_v the_o
25_o day_n i_o may_v notwithstanding_o find_v the_o time_n of_o the_o sun_n entrance_n into_o the_o midst_n of_o taurus_n by_o the_o observation_n of_o the_o 24_o and_o 26_o day_n after_o this_o manner_n subtract_v 14_o degr_n 9_o min._n 40_o sec._n of_o taurus_n out_o of_o 16_o degr_n 3_o min._n 42_o sec._n of_o taurus_n the_o remainder_n will_v be_v one_o degr_n 54_o min._n 2_o sec._n that_o be_v the_o motion_n of_o the_o sun_n for_o two_o day_n between_o the_o 24_o and_o 26_o day_n at_o noon_n therefore_o as_o 1_o degr_n 54_o min._n be_v to_o 48_o hour_n so_o be_v 50_o min._n 20_o sec._n that_o be_v the_o difference_n of_o the_o place_n of_o the_o sun_n the_o 24_o day_n from_o the_o midst_n of_o taurus_n find_v out_o as_o before_o to_o 21_o hour_n and_o 12._o min._n almost_o so_o as_o hereby_o it_o seem_v the_o sun_n shall_v enter_v into_o the_o midst_n of_o taurus_n the_o 25_o day_n about_o two_o hour_n and_o 48_o minute_n before_o noon_n that_o be_v at_o nine_o of_o the_o clock_n and_o 12_o minute_n but_o if_o it_o so_o fall_v out_o that_o you_o do_v not_o or_o can_v observe_v both_o before_o and_o after_o the_o time_n of_o the_o sun_n come_v to_o the_o point_n desire_v as_o suppose_v i_o can_v not_o have_v observe_v the_o 24_o day_n but_o only_o the_o 25_o and_o 26_o day_n in_o both_o which_o day_n the_o sun_n be_v go_v past_o the_o point_n desire_v notwithstanding_o you_o may_v obtain_v your_o desire_n thus_o subtract_v 15_o degr_n 5_o min._n 20_o sec_fw-la taurus_n the_o place_n of_o the_o sun_n the_o 25_o day_n out_o of_o 16_o degr_n 3_o min._n 42_o sec._n taurus_n the_o place_n of_o the_o sun_n the_o 26_o day_n there_o will_v remain_v 58_o min._n 22_o sec._n the_o diurn_n motion_n of_o the_o sun_n between_o the_o noon-tide_n of_o the_o 25_o and_o 26_o day_n now_o because_o that_o on_o the_o 25_o day_n at_o noon_n the_o sun_n be_v go_v 5_o min._n 20_o sec._n past_o the_o point_n desire_v therefore_o as_o 58._o min._n 20_o sec._n be_v to_o 24_o hour_n so_o be_v 5_o min._n 20_o sec._n to_o 2_o hour_n 12_o min._n almost_o by_o this_o account_n then_o the_o sun_n shall_v enter_v into_o the_o midst_n of_o taurus_n the_o 25_o day_n 2_o hour_n and_o about_o 12_o min._n before_o noon_n that_o be_v at_o nine_o of_o the_o clock_n and_o 48_o minute_n neither_o ought_v that_o small_a difference_n that_o appear_v between_o these_o account_n to_o be_v great_o regard_v which_o amount_v not_o to_o so_o much_o as_o half_a a_o hour_n in_o which_o time_n the_o motion_n of_o the_o sun_n be_v little_a above_o a_o minute_n and_o the_o declination_n of_o the_o sun_n in_o that_o part_n of_o the_o zodiac_n can_v alter_v so_o much_o as_o â
_n of_o a_o minute_n which_o be_v so_o small_a as_o can_v by_o sense_n very_o hardly_o be_v observe_v or_o discern_v neither_o yet_o ought_v that_o little_a difference_n of_o a_o minute_n or_o two_o that_o appear_v between_o the_o diurn_n motion_n of_o the_o sun_n find_v by_o observation_n great_o move_v any_o man_n in_o that_o by_o the_o first_o and_o second_o observation_n the_o diurn_n motion_n shall_v be_v almost_o 56_o min._n by_o the_o first_o and_o three_o 57_o min._n by_o the_o second_o and_o three_o 58_o min._n and_o more_o the_o great_a of_o which_o difference_n may_v almost_o arise_v by_o err_v but_o one_o half_a minute_n only_o in_o take_v the_o height_n of_o the_o sun_n which_o error_n be_v in_o a_o manner_n altogether_o insensible_a and_o will_v be_v easy_o pardon_v by_o they_o that_o have_v or_o shall_v accustom_v themselves_o to_o make_v the_o like_a observation_n when_o beside_o their_o own_o experience_n they_o shall_v find_v that_o they_o which_o have_v most_o excel_v in_o this_o art_n as_o tycho_n brahe_n de_fw-fr recentiorâb_fw-la aetherei_fw-la mundi_fw-la phaenom_fw-la lib_n 2_o cap._n 10._o part_n 1._o copern_n revol_fw-it libr._n 4._o cap._n 21._o and_o ptoleme_a himself_o in_o all_o his_o catalogue_n of_o the_o fix_a star_n almage_a lib._n 7._o cap._n 5._o when_o they_o shall_v find_v i_o say_v that_o even_o these_o prince_n in_o astronomy_n so_o great_o exercise_v in_o observation_n have_v account_v a_o whole_a minute_n or_o two_o hardly_o sensible_a ptoleme_a also_o in_o his_o almage_a content_v himself_o for_o the_o most_o part_n to_o have_v set_v down_o the_o place_n of_o the_o fix_a star_n to_o six_o part_n of_o degree_n and_o very_o seldom_o come_v to_o twelve_o part_n think_v it_o sufficient_a as_o it_o may_v seem_v by_o the_o perpetual_a course_n of_o that_o catalogue_n to_o come_v within_o five_o or_o ten_o minute_n of_o the_o truth_n but_o to_o return_v again_o to_o that_o from_o whence_o we_o have_v a_o little_a digress_v 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themselves_o with_o some_o practice_n of_o observe_v wherein_o he_o shall_v in_o my_o opinion_n quit_v himself_o meet_o well_o who_o neither_o through_o imperfection_n of_o sense_n either_o in_o make_v or_o divide_v or_o in_o rectify_v or_o in_o use_v his_o instrument_n and_o every_o part_n thereof_o nor_o through_o the_o difficulty_n of_o note_v precise_o the_o edge_n of_o the_o shadow_n of_o the_o upper_a sight_n fall_v upon_o the_o nether_a the_o limit_n or_o bound_n of_o which_o shadow_n be_v but_o a_o confuse_a mixture_n as_o it_o be_v of_o light_n and_o darkness_n or_o else_o a_o mean_a equal_o compound_v of_o they_o both_o which_o can_v no_o better_o be_v discern_v then_o by_o guess_v nor_o yet_o by_o rrefraction_n of_o the_o sun_n beam_n through_o the_o thickness_n of_o the_o air_n especial_o when_o the_o sun_n be_v in_o the_o southerly_a semicircle_n of_o the_o zodiac_n which_o refraction_n admit_v some_o alteration_n according_a to_o the_o diversity_n
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to_o the_o midst_n of_o taurus_n 46._o day_n and_o about_o three_o hour_n and_o four_o minute_n and_o consequent_o the_o arch_n of_o the_o sun_n eccentrick_a answerable_a to_o that_o time_n and_o arch_n of_o the_o ecliptic_a 45._o degr_n 27_o min._n 56._o sec._n i_o find_v hereby_o the_o sun_n eccentricitie_n and_o place_n of_o his_o apogeum_n as_o follow_v past_o this_o upon_o the_o margin_n of_o letter_n z._n fol._n 148_o so_o as_o it_o may_v lie_v open_a all_o the_o while_n the_o follow_a matter_n of_o the_o 20_o and_o 21_o chap_n be_v read_v which_o may_v yet_o also_o be_v more_o easy_o find_v by_o the_o tetragonical_a table_n or_o table_n of_o root_n and_o square_n for_o take_v ao_o and_o ob_fw-la to_o be_v 2290_o and_o 2757_o their_o square_n will_v be_v 5,244,100_o and_o 7,601,049_o which_o add_v together_o make_v 12,845,149_o the_o square_a root_n or_o side_n whereof_o be_v 3584._o the_o sun_n eccentricitie_n in_o such_o part_n whereof_o the_o semidiameter_n of_o the_o 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right_o angle_a triangle_n adb_n 356,892_o to_o ab_fw-la the_o eccentricitie_n of_o the_o sun_n 358,414_o which_o have_v not_o any_o sensible_a difference_n from_o that_o we_o find_v before_o but_o the_o place_n of_o the_o sun_n apogeum_n find_v by_o the_o foresay_a observation_n differ_v from_o tycho_n twenty_o minute_n if_o we_o add_v âo_o his_o place_n of_o the_o apogeum_n of_o the_o sun_n 7_o minute_n for_o the_o moââon_n of_o the_o sun_n apogeum_n in_o the_o ten_o year_n space_n betwixt_o his_o observation_n and_o i_o all_o which_o difference_n notwithstanding_o may_v arise_v by_o err_v little_a more_o than_o half_a a_o quarter_n of_o a_o minute_n in_o observe_v the_o the_o sun_n height_n about_o the_o midst_n of_o tarus_n which_o error_n although_o it_o be_v so_o small_a that_o it_o may_v worthy_o be_v neglect_v for_o whether_o of_o they_o soever_o you_o follow_v either_o his_o apogeum_n or_o i_o for_o the_o make_n of_o the_o ephemerides_n and_o table_n ensue_v there_o can_v hereof_o arise_v any_o such_o disagreement_n as_o can_v by_o sight_n be_v disern_v yet_o in_o that_o small_a difference_n that_o be_v though_o insensible_a i_o shall_v not_o unwilling_o yield_v unto_o he_o consider_v with_o how_o great_a preparation_n cost_n skill_n diligence_n and_o circumspection_n every_o way_n he_o go_v about_o this_o business_n as_o all_o they_o that_o have_v any_o judgement_n and_o use_n of_o observation_n will_v easy_o grant_v i_o say_v therefore_o not_o build_v only_o upon_o his_o authority_n though_o in_o this_o kind_n it_o be_v great_a than_o any_o other_o yet_o know_v to_o the_o world_n that_o follow_v the_o ordinary_a receive_v hypothesis_n of_o a_o eccentrick_a for_o salve_v the_o sun_n apparent_a inequality_n of_o motion_n the_o sun_n eccentricitie_n and_o place_n of_o his_o apogeum_n set_v down_o by_o tycho_n as_o before_o we_o have_v show_v be_v in_o this_o our_o age_n very_o agreeable_a to_o truth_n and_o without_o all_o such_o error_n as_o can_v by_o sense_n be_v discern_v and_o as_o for_o the_o difference_n that_o seem_v to_o be_v betwixt_o we_o be_v so_o small_a and_o insensible_a so_o far_o ought_v it_o to_o be_v from_o breed_a doubtfulness_n in_o any_o that_o it_o may_v rather_o make_v not_o a_o little_a for_o the_o confirmation_n of_o the_o truth_n both_o of_o he_o and_o my_o observation_n so_o as_o none_o shall_v need_v to_o make_v scruple_n of_o the_o certainty_n and_o infallibility_n of_o those_o table_n of_o the_o sun_n declination_n which_o for_o the_o navigator_n use_n shall_v out_o of_o these_o ground_n be_v gather_v and_o deduce_v chap._n xxi_o the_o middle_a motion_n of_o the_o sun_n correct_v out_o of_o the_o former_a observation_n the_o eccentricitie_n therefore_o and_o apogeum_n of_o the_o sun_n be_v thus_o know_v together_o with_o his_o true_a place_n which_o by_o so_o exact_a observation_n as_o we_o can_v in_o the_o year_n 1597._o the_o 11._o of_o march_n at_o noon_n we_o find_v to_o be_v 0_o degr_n 57_o min._n 48._o sec._n of_o aries_n his_o middle_a motion_n from_o the_o begin_n of_o aries_n be_v also_o easy_o find_v after_o this_o manner_n let_v a_o be_v the_o place_n of_o the_o sun_n in_o his_o eccentrick_a b_o the_o sun_n true_a place_n in_o the_o zodiac_n b_o a_o a_o line_n draw_v from_o the_o centre_n of_o the_o eccentrick_a to_o the_o centre_n of_o the_o sun_n a_o d_o a_o line_n draw_v from_o the_o centre_n of_o the_o ecliptic_a parallel_n to_o b_o a_o show_v the_o middle_a place_n of_o the_o sun_n in_o the_o zodiac_n ab_fw-la a_o line_n draw_v from_o the_o centre_n of_o the_o ecliptic_a by_o the_o centre_n of_o the_o sun_n to_o the_o zodiac_n show_v the_o true_a place_n of_o the_o sun_n therefore_o the_o angle_n bid_v be_v 5._o degr_n 37._o min._n and_o consequent_o the_o angle_n bajazet_n 95._o degr_n
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 so_o small_a a_o matter_n if_o any_o perhaps_o shall_v be_v desirous_a to_o exercise_v himself_o in_o calculate_v the_o sun_n true_a place_n according_a to_o the_o manner_n here_o before_o set_v down_o either_o for_o the_o examine_n of_o the_o sun_n ephemerides_n hear_v follow_v or_o any_o other_o or_o for_o make_v some_o other_o like_a to_o these_o when_o the_o date_n of_o they_o shall_v be_v expire_v wherein_o if_o perhaps_o you_o find_v some_o little_a difference_n of_o a_o few_o second_o from_o your_o calculation_n you_o need_v not_o therewith_o to_o be_v any_o thing_n trouble_v see_v it_o can_v produce_v any_o sensible_a error_n neither_o in_o the_o sun_n declination_n nor_o yet_o in_o his_o place_n a_o table_n of_o equation_n of_o natural_a day_n  _fw-fr â_o â_o â_o â_o â_o â_o â_o â_o â_o â_o â_o â_o  _fw-fr s_o s_o s_o s_o s_o s_o s_o s_o s_o s_o a_o a_o d._n m_o mi_n mi._n m_o m_o mi._n mi._n mi._n mi._n mi._n m_o m_o 2_o 0_o 9_o 12_o 6_o 2_o 6_o 16_o ½_o 24_o 21_o 7_o 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 â_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 â_o 18_o 51_o 10_o â_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 â_o 34_o 36_o 11_o â_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
2_o 30_o 39_o  _fw-fr 21_o 6_o 9_o 5_o 43_o  _fw-fr 8_o 6_o 18_o 57_o 40_o 14_o 45_o 6_o  _fw-fr 25_o 53_o 2_o 4_o 7_o 2_o 7_o 18_o  _fw-fr 22_o 7_o 9_o 27_o 51_o 21_o 58_o 7_o 19_o 12_o 25_o 14_o 23_o 7_o  _fw-fr 27_o 57_o 1_o 45_o 8_o 1_o 43_o 56_o  _fw-fr 27_o 8_o 9_o 49_o 49_o  _fw-fr 52_o 8_o 19_o 26_o 48_o 14_o 1_o 8_o  _fw-fr 29_o 32_o 1_o 8_o 9_o 1_o 20_o 29_o  _fw-fr 27_o 9_o 10_o 11_o 41_o  _fw-fr 42_o 9_o 19_o 40_o 49_o 13_o 40_o 9_o  _fw-fr 30_o 40_o 0_o 39_o 10_o 0_o 57_o 2_o  _fw-fr 29_o 10_o 10_o 33_o 23_o  _fw-fr 33_o 10_o 19_o 54_o 29_o 13_o 18_o 10_o  _fw-fr 31_o 19_o 0_o 11_o 11_o 0_o 33_o 33_o  _fw-fr 31_o 11_o 10_o 54_o 56_o 21_o 23_o 11_o 20_o 7_o 47_o 12_o 55_o 11_o  _fw-fr 31_o 30_o 0_o 18_o 12_o 0_o 10_o 2_o  _fw-fr 32_o 12_o 11_o 16_o 19_o  _fw-fr 13_o 12_o 20_o 20_o 42_o 12_o 34_o 12_o  _fw-fr 31_o 12_o 0_o 48_o 13_o 0_o 13_o 30_o  _fw-fr 33_o 13_o 11_o 37_o 32_o  _fw-fr 2_o 13_o 20_o 33_o 16_o 12_o 9_o 13_o  _fw-fr 30_o 24_o 1_o 14_o 14_o 0_o 37_o 3_o  _fw-fr 32_o 14_o 11_o 58_o 34_o 20_o 51_o 14_o 20_o 45_o 25_o 11_o 48_o 14_o  _fw-fr 29_o 10_o 1_o 44_o 15_o 1_o 0_o 35_o 23_o 34_o 15_o 12_o 19_o 25_o  _fw-fr 39_o 15_o 20_o 57_o 12_o 11_o 23_o 15_o  _fw-fr 27_o 26_o 2_o 13_o 16_o 1_o 24_o 9_o  _fw-fr 32_o 16_o 12_o 40_o 4_o  _fw-fr 28_o 16_o 21_o 8_o 35_o 10_o 59_o 16_o  _fw-fr 25_o 13_o 2_o 40_o 17_o 1_o 47_o 41_o  _fw-fr 31_o 17_o 13_o 0_o 32_o  _fw-fr 16_o 17_o 21_o 19_o 34_o 10_o 34_o 17_o  _fw-fr 22_o 33_o 3_o 9_o 18_o 2_o 11_o 12_o  _fw-fr 31_o 18_o 13_o 20_o 48_o 20_o 3_o 18_o 21_o 30_o 8_o 10_o 9_o 18_o  _fw-fr 19_o 24_o 3_o 37_o 19_o 2_o 34_o 43_o  _fw-fr 29_o 19_o 13_o 40_o 51_o 19_o 49_o 19_o 21_o 40_o 17_o 9_o 46_o 19_o  _fw-fr 15_o 47_o 4_o 5_o 20_o 2_o 58_o 12_o  _fw-fr 28_o 20_o 14_o 0_o 40_o 19_o 36_o 20_o 21_o 50_o 3_o 9_o 19_o 20_o  _fw-fr 11_o 42_o 4_o 34_o 21_o 3_o 21_o 40_o  _fw-fr 26_o 21_o 14_o 20_o 16_o 19_o 23_o 21_o 21_o 59_o 22_o 8_o 53_o 21_o  _fw-fr 7_o 8_o 5_o 0_o 22_o 3_o 45_o 6_o  _fw-fr 22_o 22_o 14_o 39_o 39_o 19_o 8_o 22_o 22_o 8_o 15_o 8_o 28_o 22_o  _fw-fr 2_o 8_o 5_o 29_o 23_o 4_o 8_o 28_o  _fw-fr 19_o 23_o 14_o 58_o 47_o 18_o 53_o 23_o 22_o 16_o 43_o 8_o 2_o 23_o 22_o 56_o 39_o 5_o 56_o 24_o 4_o 31_o 47_o  _fw-fr 17_o 24_o 15_o 17_o 40_o 18_o 38_o 24_o  _fw-fr 24_o 45_o 7_o 36_o 24_o  _fw-fr 50_o 43_o 6_o 23_o 25_o 4_o 55_o 4_o  _fw-fr 12_o 25_o 15_o 36_o 18_o 18_o 22_o 25_o  _fw-fr 32_o 21_o 7_o 9_o 25_o  _fw-fr 44_o 20_o 6_o 51_o 26_o 5_o 18_o 16_o  _fw-fr 9_o 26_o 15_o 54_o 40_o 18_o 7_o 26_o  _fw-fr 39_o 30_o 6_o 42_o 26_o  _fw-fr 37_o 29_o 7_o 10_o 27_o 5_o 41_o 25_o 23_o 5_o 27_o 16_o 12_o 47_o 17_o 50_o 27_o  _fw-fr 46_o 12_o 6_o 15_o 27_o  _fw-fr 30_o 19_o 7_o 52_o 28_o 6_o 4_o 30_o  _fw-fr 0_o 28_o 16_o 30_o 37_o 17_o 33_o 28_o  _fw-fr 52_o 27_o 5_o 48_o 28_o  _fw-fr 22_o 27_o 8_o 11_o 29_o 6_o 27_o 30_o 22_o 54_o 29_o 16_o 48_o 10_o 17_o 16_o 29_o  _fw-fr 58_o 15_o 5_o 20_o 29_o  _fw-fr 14_o 16_o 8_o 36_o 30_o 6_o 50_o 24_o 22_o 49_o 30_o 17_o 5_o 26_o 16_o 58_o 30_o 23_o 3_o 35_o 4_o 53_o 30_o  _fw-fr 5_o 40_o 9_o 3_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 31_o 17_o 22_o 24_o 16_o 41_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 31_o 21_o 56_o 37_o 9_o 26_o chap._n xxviii_o the_o use_n of_o the_o former_a table_n or_o regiment_n of_o the_o sun_n this_o table_n of_o the_o sun_n declination_n as_o it_o differ_v nothing_o in_o form_n from_o other_o that_o have_v be_v publish_v heretofore_o so_o likewise_o the_o manner_n of_o use_v it_o be_v altogether_o the_o same_o that_o have_v be_v accustom_v in_o former_a table_n of_o this_o kind_n save_v that_o i_o must_v give_v warning_n of_o one_o error_n that_o have_v be_v commit_v herein_o which_o be_v as_o i_o have_v observe_v that_o some_o of_o our_o seaman_n do_v take_v the_o sun_n declination_n out_o of_o their_o regiment_n without_o any_o aequation_n by_o addition_n or_o subtraction_n of_o the_o part_n proportional_a agreeable_a to_o the_o difference_n of_o longitude_n of_o the_o place_n where_o they_o be_v as_o if_o they_o be_v always_o at_o the_o same_o place_n or_o under_o the_o same_o meridian_n for_o which_o their_o regiment_n be_v make_v for_o which_o cause_n alone_o though_o they_o avoid_v all_o other_o error_n it_o may_v so_o fall_v out_o that_o they_o may_v be_v deceive_v sometime_o 10_o or_o 12._o minute_n or_o more_o in_o a_o long_a voyage_n in_o take_v the_o sun_n declination_n for_o there_o be_v not_o any_o table_n of_o the_o sun_n declination_n but_o that_o it_o must_v needs_o be_v make_v for_o some_o one_o meridian_n as_o this_o former_a table_n be_v make_v for_o the_o meridian_n of_o london_n and_o therefore_o can_v be_v true_o use_v in_o any_o other_o without_o some_o equation_n answerable_a to_o the_o distance_n of_o the_o meridians_fw-la or_o difference_n of_o longitude_n to_o avoid_v this_o error_n therefore_o first_o learn_v how_o much_o you_o differ_v in_o longitude_n from_o the_o place_n for_o which_o your_o table_n be_v make_v and_o though_o you_o miss_v half_a a_o dozen_o or_o half_o a_o score_n degree_n herein_o it_o can_v in_o this_o point_n breed_v any_o sensible_a error_n second_o take_v out_o the_o difference_n of_o the_o sun_n declination_n agreeable_a to_o the_o space_n of_o 24._o hour_n about_o the_o time_n of_o your_o observation_n three_o as_o 360._o be_v to_o this_o difference_n of_o declination_n so_o be_v the_o difference_n of_o longitude_n to_o the_o part_n proportional_a or_o equation_n of_o the_o declination_n which_o equation_n be_v to_o be_v add_v to_o the_o declination_n of_o the_o day_n of_o observation_n if_o the_o declination_n of_o the_o sun_n be_v either_o increase_a and_o the_o place_n of_o observation_n westward_o or_o else_o decrease_v and_o the_o place_n of_o observation_n eastward_n from_o the_o place_n for_o which_o your_o table_n of_o declination_n be_v make_v otherwise_o this_o equation_n be_v to_o be_v subtract_v from_o the_o declination_n of_o your_o day_n of_o observation_n that_o you_o may_v have_v the_o true_a declination_n of_o the_o sun_n for_o the_o time_n and_o place_n of_o your_o observation_n but_o if_o the_o time_n of_o your_o observation_n be_v the_o noontide_a immediate_o before_o or_o after_o the_o sun_n entrance_n into_o either_o of_o the_o aequinoctial_a point_n you_o must_v follow_v another_o rule_n and_o that_o be_v this_o divide_v the_o difference_n of_o longitude_n by_o 15_o mark_v how_o many_o unite_v the_o quotient_n contain_v and_o so_o many_o minute_n add_v to_o the_o declination_n find_v in_o the_o former_a table_n if_o you_o be_v either_o eastward_o from_o the_o meridian_n of_o london_n and_o observe_v the_o noontide_n before_o the_o equinoctium_n or_o if_o you_o be_v westward_o from_o that_o meridian_n and_o observe_v the_o noontide_n after_o the_o equinoctium_n for_o the_o sum_n shall_v be_v the_o declination_n desire_v otherwise_o if_o you_o be_v either_o westward_n from_o the_o meridian_n of_o london_n and_o observe_v the_o noontide_n next_o before_o the_o equinoctium_n or_o eastward_o from_o that_o meridian_n and_o observe_v the_o day_n immediate_o after_o the_o equinoctium_n compare_v the_o declination_n find_v in_o the_o table_n with_o the_o foresay_a quotient_n and_o subtract_v the_o lesser_a out_o of_o the_o great_a for_o that_o remain_v be_v the_o declination_n desire_v which_o declination_n have_v the_o same_o denomination_n of_o north_n or_o south_n that_o the_o table_n show_v if_o the_o quotient_a be_v less_o than_o the_o declination_n find_v in_o the_o table_n but_o if_o the_o quotient_a be_v great_a the_o denomination_n must_v be_v alter_v from_o north_n to_o south_n or_o from_o south_n to_o north_n contrary_a to_o that_o the_o table_n show_v if_o the_o quotient_n be_v equal_a to_o the_o declination_n find_v in_o the_o former_a table_n the_o sun_n be_v in_o the_o very_a equinoctial_a point_n and_o have_v no_o declination_n at_o all_o a_o few_o example_n will_v make_v these_o rule_v more_o plain_a suppose_v therefore_o the_o 30_o of_o march_n 1610._o you_o be_v sail_v in_o the_o bay_n of_o mexico_n differ_v in_o longitude_n to_o the_o westward_n from_o the_o meridian_n of_o london_n about_o 90_o degree_n by_o estimation_n the_o declination_n of_o the_o sun_n for_o that_o day_n find_v in_o the_o former_a table_n be_v 7_o degree_n 39_o minute_n
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 be_v before_o but_o because_o you_o be_v go_v so_o much_o eastward_n the_o sun_n come_v 6_o hour_n soon_o to_o your_o meridian_n there_o than_o it_o do_v to_o we_o here_o at_o london_n and_o therefore_o because_o the_o declination_n also_o be_v increase_v and_o will_v be_v great_a when_o the_o sun_n come_v to_o our_o meridian_n then_o it_o be_v the_o sun_n be_v under_o the_o meridian_n of_o the_o east_n indy_n that_o equation_n of_o declination_n must_v there_o be_v subtract_v out_o of_o the_o declination_n find_v in_o the_o table_n which_o before_o be_v to_o be_v add_v when_o we_o suppose_v you_o to_o be_v in_o the_o bay_n of_o mexico_n because_o the_o sun_n come_v late_a by_o six_o hour_n to_o the_o meridian_n of_o that_o place_n then_o to_o we_o and_o therefore_o the_o declination_n of_o the_o sun_n increase_v in_o the_o mean_a time_n will_v be_v great_a there_o than_o here_o now_o imagine_v you_o sail_n in_o the_o year_n 1612_o through_o the_o straits_n of_o magellan_n and_o have_v 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 grosây_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
22_o 21_o 0_o 06_o 1_o 58_o 3_o 54_o 6_o 01_o 13_o 20_o 22_o 22_o 25_o 0_o 09_o 2_o 02_o 3_o 58_o 6_o 05_o 14_o 20_o 26_o 22_o 29_o 0_o 12_o 2_o 06_o 4_o 03_o 6_o 09_o 15_o 20_o 30_o 22_o 32_o 0_o 16_o 2_o 10_o 4_o 07_o 6_o 13_o 16_o 20_o 34_o 22_o 36_o 0_o 20_o 2_o 14_o 4_o 11_o 6_o 18_o 17_o 20_o 38_o 22_o 40_o 0_o 23_o 2_o 18_o 4_o 15_o 6_o 22_o 18_o 20_o 42_o 22_o 44_o 0_o 27_o 2_o 22_o 4_o 19_o 6_o 26_o 19_o 20_o 46_o 22_o 48_o 0_o 31_o 2_o 26_o 4_o 23_o 6_o 30_o 20_o 20_o 50_o 22_o 52_o 0_o 35_o 2_o 30_o 4_o 27_o 6_o 34_o 21_o 20_o 54_o 22_o 56_o 0_o 38_o 2_o 33_o 4_o 31_o 6_o 38_o 22_o 20_o 58_o 22_o 59_o 0_o 42_o 2_o 37_o 4_o 35_o 6_o 42_o 23_o 21_o 03_o 23_o 03_o 0_o 46_o 2_o 41_o 4_o 39_o 6_o 46_o 24_o 21_o 07_o 23_o 07_o 0_o 49_o 2_o 44_o 4_o 43_o 6_o 51_o 25_o 21_o 11_o 23_o 10_o 0_o 53_o 2_o 48_o 4_o 47_o 6_o 55_o 26_o 21_o 15_o 23_o 14_o 0_o 57_o 2_o 52_o 4_o 51_o 6_o 59_o 27_o 21_o 19_o 23_o 18_o 1_o 00_o 2_o 56_o 4_o 56_o 7_o 03_o 28_o 21_o 23_o 23_o 22_o 1_o 03_o 3_o 00_o 5_o 00_o 7_o 07_o 29_o 21_o 27_o  _fw-fr  _fw-fr 1_o 07_o 3_o 04_o 5_o 03_o 7_o 11_o 30_o 21_o 31_o  _fw-fr  _fw-fr 1_o 11_o 3_o 07_o 5_o 07_o 7_o 15_o 31_o 21_o 35_o  _fw-fr  _fw-fr 1_o 15_o  _fw-fr  _fw-fr 5_o 11_o  _fw-fr  _fw-fr  _fw-fr july_n august_n septemb_n october_n novemb_n decemb_v d._n h._n m._n h._n m._n h._n m._n h._n m._n h._n m._n h._n m._n 1_o 7_o 19_o 9_o 22_o 11_o 16_o 13_o 05_o 15_o 05_o 17_o 12_o 2_o 7_o 23_o 9_o 26_o 11_o 20_o 13_o 08_o 15_o 09_o 17_o 17_o 3_o 7_o 27_o 9_o 30_o 11_o 23_o 13_o 12_o 15_o 13_o 17_o 21_o 4_o 7_o 31_o 9_o 33_o 11_o 27_o 13_o 16_o 15_o 17_o 17_o 25_o 5_o 7_o 35_o 9_o 36_o 11_o 30_o 13_o 19_o 15_o 21_o 17_o 30_o 6_o 7_o 40_o 9_o 40_o 11_o 33_o 13_o 23_o 15_o 25_o 17_o 34_o 7_o 7_o 44_o 9_o 44_o 11_o 37_o 13_o 27_o 15_o 29_o 17_o 39_o 8_o 7_o 48_o 9_o 48_o 11_o 41_o 13_o 31_o 15_o 33_o 17_o 43_o 9_o 7_o 52_o 9_o 52_o 11_o 44_o 13_o 34_o 15_o 37_o 17_o 47_o 10_o 7_o 56_o 9_o 56_o 11_o 48_o 13_o 38_o 15_o 42_o 17_o 52_o 11_o 8_o 00_o 9_o 59_o 11_o 52_o 13_o 42_o 15_o 46_o 17_o 56_o 12_o 8_o 04_o 10_o 03_o 11_o 55_o 13_o 45_o 15_o 50_o 18_o 00_o 13_o 8_o 08_o 10_o 07_o 11_o 59_o 13_o 49_o 15_o 54_o 18_o 05_o 14_o 8_o 12_o 10_o 11_o 12_o 03_o 13_o 53_o 15_o 58_o 18_o 10_o 15_o 8_o 16_o 10_o 15_o 12_o 07_o 13_o 57_o 16_o 03_o 18_o 14_o 16_o 8_o 20_o 10_o 18_o 12_o 11_o 14_o 01_o 16_o 07_o 18_o 18_o 17_o 8_o 24_o 10_o 22_o 12_o 14_o 14_o 05_o 16_o 11_o 18_o 23_o 18_o 8_o 28_o 10_o 26_o 12_o 18_o 14_o 09_o 16_o 16_o 18_o 27_o 19_o 8_o 31_o 10_o 29_o 12_o 22_o 14_o 13_o 16_o 20_o 18_o 32_o 20_o 8_o 35_o 10_o 33_o 12_o 25_o 14_o 17_o 16_o 24_o 18_o 36_o 21_o 8_o 39_o 10_o 36_o 12_o 29_o 14_o 20_o 16_o 28_o 18_o 41_o 22_o 8_o 43_o 10_o 40_o 12_o 32_o 14_o 24_o 16_o 33_o 18_o 45_o 23_o 8_o 47_o 10_o 44_o 12_o 36_o 14_o 28_o 16_o 37_o 18_o 50_o 24_o 8_o 52_o 10_o 47_o 12_o 40_o 14_o 32_o 16_o 41_o 18_o 55_o 25_o 8_o 55_o 10_o 51_o 12_o 43_o 14_o 36_o 16_o 46_o 18_o 59_o 26_o 8_o 59_o 10_o 54_o 12_o 47_o 14_o 40_o 16_o 50_o 19_o 03_o 27_o 9_o 03_o 10_o 58_o 12_o 51_o 14_o 44_o 16_o 55_o 19_o 07_o 28_o 9_o 07_o 11_o 02_o 12_o 54_o 14_o 48_o 16_o 59_o 19_o 12_o 29_o 9_o 11_o 11_o 06_o 12_o 58_o 14_o 53_o 17_o 03_o 19_o 16_o 30_o 9_o 15_o 11_o 09_o 13_o 02_o 14_o 57_o 17_o 08_o 19_o 21_o 31_o 9_o 19_o 11_o 13_o  _fw-fr  _fw-fr 15_o 01_o  _fw-fr  _fw-fr 19_o 25_o chap._n xxxiii_o by_o the_o former_a table_n of_o the_o fix_a star_n and_o the_o sun_n right_a ascension_n to_o know_v the_o hour_n of_o the_o night_n at_o any_o time_n of_o the_o year_n by_o these_o table_n of_o fix_a star_n and_o right_a ascension_n of_o the_o sun_n you_o may_v easy_o know_v also_o the_o hour_n of_o the_o night_n at_o any_o time_n of_o the_o year_n after_o this_o manner_n look_v which_o of_o those_o star_n be_v at_o the_o meridian_n which_o may_v easy_o be_v know_v by_o a_o needle-dial_n or_o compass_n or_o if_o you_o will_v observe_v the_o north_n star_n that_o never_o set_v which_o indeed_o be_v fit_a for_o this_o purpose_n especial_o when_o they_o come_v to_o the_o meridian_n under_o the_o pole_n you_o shall_v first_o find_v the_o place_n of_o the_o pole_n in_o the_o heaven_n so_o near_o as_o you_o can_v by_o estimation_n for_o a_o little_a error_n herein_o break_v no_o square_a which_o may_v be_v do_v thus_o from_o the_o polestar_n direct_o towards_o the_o first_o star_n next_o the_o rump_n in_o the_o great_a bear_n tail_n imagine_v almost_o so_o much_o space_n as_o the_o guard_n be_v distant_a asunder_o for_o near_o thereabouts_o be_v the_o place_n of_o the_o pole_n now_o betwixt_o your_o eye_n and_o this_o place_n of_o the_o pole_n hold_v a_o plumbline_n hang_v as_o perpendicular_o and_o steadfast_o as_o you_o may_v and_o mark_v withal_o if_o that_o plumbline_n come_v betwixt_o your_o sight_n and_o any_o of_o the_o star_n note_v in_o the_o table_n of_o fix_a star_n about_o the_o pole_n for_o that_o star_n be_v at_o the_o meridian_n then_o learn_v as_o before_o be_v show_v at_o what_o time_n that_o star_n come_v to_o the_o meridian_n and_o so_o you_o shall_v have_v the_o hour_n of_o the_o night_n suppose_v for_o example_n the_o 10_o of_o february_n you_o find_v after_o this_o manner_n the_o swan_n tail_n at_o the_o meridian_n under_o the_o pole_n desire_v hereby_o to_o know_v the_o hour_n of_o the_o night_n at_o that_o time_n the_o right_a ascension_n of_o the_o sun_n for_o that_o day_n you_o shall_v find_v as_o before_o to_o be_v 22_o hour_n 14_o minute_n whereto_o you_o may_v add_v a_o minute_n or_o two_o more_o because_o that_o star_n will_v come_v to_o the_o meridian_n very_o late_o in_o the_o evening_n so_o make_v the_o sun_n right_a ascension_n 22_o hour_n 16_o minute_n the_o right_a ascension_n of_o that_o star_n in_o the_o second_o table_n of_o fix_a star_n you_o shall_v find_v to_o be_v 20_o hour_n 30_o minute_n from_o which_o because_o now_o you_o desire_v to_o know_v the_o time_n of_o that_o star_n come_v to_o the_o nether_a part_n of_o the_o meridian_n you_o may_v subtract_v 12_o hour_n and_o there_o shall_v remain_v 8_o hour_n 30_o minute_n to_o this_o remainder_n because_o it_o be_v less_o than_o then_o the_o sun_n right_a ascension_n add_v 24_o hour_n and_o from_o the_o sum_n 32_o hour_n 30_o minute_n subtract_v the_o right_a ascension_n of_o the_o sun_n 22_o hour_n 16_o minute_n so_o there_o shall_v remain_v 10_o hour_n 14_o minute_n the_o time_n of_o the_o night_n desire_v chap._n xxxiv_o of_o find_v the_o elevation_n of_o the_o pole_n by_o observation_n of_o the_o polestar_n and_o guard_n beside_o the_o way_n already_o speak_v of_o to_o find_v the_o elevation_n of_o the_o pole_n by_o the_o meridian_n altitude_n and_o declination_n of_o the_o sun_n and_o fix_a star_n in_o general_a there_o have_v be_v also_o use_v another_o way_n more_o special_a by_o the_o height_n of_o the_o polestar_n when_o the_o fore-guard_n be_v situate_a from_o it_o either_o towards_o the_o east_n west_n north_n or_o south_n or_o else_o upon_o the_o middle_a point_n betwixt_o these_o principal_n as_o upon_o the_o north-east_n northwest_o southeast_n and_o southwest_n point_v of_o which_o way_n as_o it_o have_v be_v hitherto_o publish_v and_o use_v i_o must_v for_o the_o present_a only_o give_v the_o mariner_n warning_n that_o he_o trust_v not_o to_o it_o be_v very_o erroneous_a and_o ground_v upon_o two_o false_a position_n the_o one_o be_v that_o the_o distance_n of_o the_o polestar_n from_o the_o pole_n be_v 3_o degree_n 30_o minute_n which_o by_o often_o and_o exact_a observation_n be_v find_v to_o be_v at_o this_o time_n not_o above_o 2_o degree_n 48_o minute_n the_o other_o be_v that_o the_o equation_n or_o allowance_n to_o be_v add_v to_o or_o subtract_v from_o the_o height_n of_o the_o polestar_n to_o find_v thereby_o the_o height_n of_o the_o pole_n be_v make_v the_o same_o for_o all_o latitude_n but_o have_v already_o show_v sufficient_o how_o to_o know_v the_o latitude_n almost_o at_o any_o time_n of_o the_o night_n by_o the_o fix_a star_n in_o the_o former_a table_n i_o hope_v to_o be_v the_o easy_o
with_o the_o regiment_n of_o the_o sun_n and_o of_o the_o star_n the_o rule_n of_o the_o moon_n and_o of_o the_o tide_n the_o declaration_n of_o the_o sea-chart_n and_o other_o thing_n appertain_v hereunto_o chap._n i._n the_o definition_n of_o the_o sphere_n a_o sphere_n be_v a_o solid_a or_o massy_a body_n without_o hollowness_n and_o perfect_o round_a in_o the_o midst_n whereof_o there_o be_v a_o prick_n call_v the_o centre_n by_o which_o there_o pass_v a_o right_a line_n name_v the_o axtree_n and_o the_o point_n where_o this_o line_n end_v upon_o the_o superficies_n of_o the_o whole_a body_n be_v call_v pole_n because_o upon_o they_o the_o sphere_n be_v move_v chap._n ii_o that_o the_o whole_a world_n be_v a_o sphere_n and_o so_o it_o be_v evident_a that_o the_o whole_a frame_n of_o the_o world_n wherein_o we_o live_v be_v a_o sphere_n be_v as_o it_o be_v solid_a so_o that_o in_o the_o whole_a world_n there_o be_v no_o empty_a place_n also_o it_o be_v perfect_o round_a upon_o the_o upper_a superficies_n of_o the_o high_a heaven_n and_o it_o have_v in_o the_o very_a midst_n a_o certain_a point_n to_o wit_n the_o centre_n of_o the_o earth_n by_o which_o we_o do_v imagine_v a_o right_a line_n or_o axtree_n to_o pass_v from_o one_o pole_n to_o another_o upon_o which_o the_o world_n be_v move_v about_o from_o east_n to_o west_n chap._n iii_o of_o the_o division_n of_o the_o sphere_n the_o whole_a sphere_n of_o the_o world_n be_v divide_v into_o two_o part_n or_o region_n the_o elementary_a and_o celestial_a the_o elementary_a part_n or_o region_n have_v four_o part_n the_o first_o whereof_o be_v the_o earth_n which_o together_o with_o the_o element_n of_o water_n which_o be_v the_o second_o make_v one_o perfect_a globe_n and_o round_o about_o both_o these_o be_v two_o other_o element_n namely_o the_o air_n and_o above_o that_o the_o fire_n which_o fill_v the_o space_n between_o the_o air_n and_o the_o sphere_n of_o the_o moon_n of_o which_o element_n by_o virtue_n of_o the_o heat_n of_o the_o heaven_n be_v make_v and_o compound_v all_o corruptible_a thing_n in_o the_o world_n the_o celestial_a region_n consist_v of_o other_o ten_o part_n the_o first_o whereof_o be_v the_o sphere_n of_o the_o moon_n the_o second_o the_o sphere_n of_o mercury_n the_o three_o of_o venus_n the_o four_o be_v the_o sphere_n of_o the_o sun_n the_o five_o of_o mars_n the_o six_o of_o jupiter_n the_o seven_o of_o saturn_n the_o eight_o be_v the_o sphere_n of_o the_o fix_a star_n which_o be_v call_v the_o firmament_n the_o nine_o be_v the_o crystalline_a heaven_n and_o last_o the_o ten_o and_o high_a be_v the_o sphere_n call_v the_o primum_fw-la mobile_a that_o be_v the_o first_o or_o high_a movable_a heaven_n that_o which_o remain_v call_v the_o empyreal_a heaven_n because_o it_o have_v no_o motion_n come_v not_o to_o be_v consider_v on_o in_o the_o art_n of_o navigation_n a_o figure_n wherein_o may_v be_v see_v the_o composition_n of_o the_o whole_a sphere_n of_o the_o world_n chap._n iu._n of_o the_o motion_n of_o the_o heaven_n the_o number_n of_o the_o heaven_n be_v know_v by_o the_o motion_n observe_v in_o they_o which_o be_v ten_o distinct_a one_o from_o another_o for_o the_o moon_n move_v her_o proper_a and_o peculiar_a motion_n in_o 27_o day_n and_o 8_o hour_n which_o be_v one_o revolution_n mercury_n venus_n and_o the_o sun_n finish_v their_o motion_n in_o one_o year_n which_o contain_v 365_o day_n and_o almost_o a_o quarter_n of_o a_o day_n mars_n run_v his_o course_n in_o two_o year_n jupiter_n in_o twelve_o year_n saturn_n in_o thirty_o year_n the_o eight_o sphere_n according_a to_o the_o opinion_n of_o some_o in_o seven_o thousand_o year_n the_o nine_o in_o five_o and_o twenty_o thousand_o and_o eight_o hundred_o year_n and_o the_o ten_o in_o four_o and_o twenty_o hour_n almost_o which_o ten_o motion_n be_v reduce_v unto_o three_o principal_a the_o first_o be_v that_o of_o the_o first_o movable_a upon_o the_o two_o end_n of_o the_o axletree_n which_o be_v call_v the_o pole_n of_o the_o world_n from_o east_n to_o west_n turn_v about_o again_o unto_o the_o east_n in_o 24_o hour_n and_o this_o sphere_n by_o the_o force_n of_o his_o motion_n carry_v about_o with_o it_o all_o the_o other_o low_a sphere_n in_o the_o space_n of_o 24_o hour_n howbeit_o they_o move_v also_o the_o contrary_a way_n with_o a_o second_o motion_n which_o be_v from_o west_n to_o east_n upon_o two_o other_o pole_n distant_a from_o the_o first_o about_o three_o and_o twenty_o and_o a_o half_a such_o part_n whereof_o the_o whole_a compass_n of_o heaven_n contain_v three_o hundred_o and_o sixty_o and_o this_o second_o motion_n be_v accomplish_v in_o each_o of_o the_o low_a heaven_n in_o divers_a space_n of_o time_n as_o be_v before_o say_v the_o three_o motion_n be_v proper_a to_o the_o eight_o heaven_n wherein_o the_o fix_a star_n be_v place_v which_o motion_n be_v the_o cause_n that_o the_o distance_n of_o the_o pole_n of_o the_o first_o motion_n from_o they_o of_o the_o second_o motion_n do_v vary_v be_v sometime_o great_a and_o sometime_o less_o chap._n v._o of_o the_o figure_n of_o the_o heaven_n that_o the_o heaven_n be_v round_o it_o be_v prove_v because_o roundness_n be_v the_o most_o perfect_a figure_n of_o all_o other_o be_v whole_a and_o entire_a have_v no_o need_n of_o any_o joint_n be_v also_o of_o the_o great_a capacity_n of_o all_o figure_n that_o have_v the_o same_o compass_n and_o in_o that_o respect_n most_o fit_a to_o contain_v all_o other_o thing_n also_o the_o principal_a body_n of_o the_o world_n as_o the_o sun_n the_o moon_n and_o the_o star_n be_v of_o this_o figure_n and_o we_o see_v the_o same_o likewise_o in_o those_o thing_n which_o be_v bound_v by_o themselves_o as_o it_o be_v manifest_a in_o drop_n of_o water_n and_o all_o other_o liquid_a thing_n chap._n vi_o that_o the_o earth_n and_o water_n make_v one_o perfect_a globe_n there_o be_v nothing_o that_o show_v more_o clear_o that_o the_o earth_n and_o water_n make_v one_o round_a globe_n than_o the_o shadow_n which_o they_o make_v in_o the_o eclipse_n of_o the_o moon_n which_o shadow_n we_o always_o see_v to_o be_v a_o part_n of_o a_o circle_n for_o if_o the_o body_n which_o be_v the_o cause_n of_o the_o same_o shadow_n be_v threesquare_a or_o foursquare_a the_o shadow_n itself_o also_o will_v appear_v in_o the_o same_o fashion_n wherefore_o the_o shadow_n of_o these_o two_o body_n together_o be_v round_o it_o be_v manifest_a that_o they_o be_v round_o also_o chap._n vii_o that_o the_o earth_n be_v in_o the_o centre_n of_o the_o world_n one_o sign_n we_o have_v to_o be_v assure_v that_o the_o earth_n be_v in_o the_o midst_n and_o centre_n of_o the_o world_n namely_o that_o wheresoever_o we_o be_v upon_o the_o face_n of_o the_o earth_n we_o always_o see_v one_o half_a of_o the_o heaven_n the_o other_o half_o be_v hide_v out_o of_o our_o sight_n moreover_o the_o star_n in_o what_o part_n of_o the_o heaven_n soever_o they_o be_v either_o in_o the_o east_n west_n or_o south_n we_o see_v that_o they_o be_v always_o of_o the_o very_a same_o bigness_n whereby_o we_o may_v easy_o perceive_v that_o they_o be_v always_o equal_o distant_a from_o our_o sight_n and_o whereas_o they_o move_v round_o about_o it_o it_o follow_v that_o we_o be_v upon_o the_o centre_n of_o that_o body_n on_o who_o superficies_n the_o say_a star_n describe_v their_o circle_n chap._n viii_o the_o whole_a quantity_n of_o the_o earth_n and_o albeit_o the_o globe_n of_o the_o earth_n and_o water_n compare_v with_o the_o sphere_n of_o the_o star_n be_v as_o it_o be_v a_o centre_n or_o prick_n yet_o be_v consider_v by_o itself_o it_o contain_v in_o the_o great_a circle_n thereof_o 6300_o common_a spanish_a league_n which_o a_o man_n may_v easy_o perceive_v by_o take_v two_o such_o point_n or_o headland_n of_o the_o earth_n as_o be_v under_o the_o same_o meridian_n and_o which_o differ_v in_o distance_n one_o from_o another_o so_o much_o as_o one_o of_o those_o part_n be_v whereof_o the_o compass_n of_o the_o whole_a world_n contain_v 360_o and_o it_o be_v find_v both_o by_o navigation_n at_o sea_n and_o also_o by_o travel_n on_o land_n that_o the_o two_o foresay_a point_n be_v distant_a each_o from_o other_o 17_o league_n and_o a_o half_a of_o which_o league_n each_o one_o contain_v 4000_o pace_n every_o pace_n 5_o foot_n every_o foot_n 16_o finger_n and_o every_o finger_n 4_o grain_n of_o barley_n chap._n ix_o of_o the_o equinoctial_a circle_n be_v to_o treat_v of_o the_o circle_n of_o the_o sphere_n of_o the_o world_n the_o first_o which_o offer_v itself_o to_o be_v speak_v of_o be_v the_o equinoctial_a circle_n by_o mean_n whereof_o we_o do_v know_v in_o
what_o part_n of_o the_o world_n we_o be_v and_o in_o it_o in_o the_o sea-chart_n be_v place_v all_o these_o point_n or_o degree_n of_o longitude_n and_o from_o it_o the_o latitude_n be_v account_v so_o that_o the_o equinoctial_a be_v a_o circle_n which_o divide_v the_o world_n into_o two_o equal_a portion_n and_o be_v equal_o distant_a every_o where_o from_o either_o of_o the_o pole_n and_o it_o be_v call_v the_o equinoctial_a circle_n because_o that_o when_o the_o sun_n pass_v under_o it_o upon_o the_o 11_o of_o march_n and_o the_o 13_o of_o september_n it_o make_v the_o day_n equal_a to_o the_o night_n the_o knowledge_n of_o this_o circle_n in_o the_o art_n of_o navigation_n do_v help_v we_o to_o find_v the_o latitude_n or_o distance_n from_o the_o line_n and_o from_o this_o circle_n be_v reckon_v the_o declination_n of_o the_o sun_n in_o the_o regiment_n thereof_o and_o always_o those_o chart_n of_o navigation_n which_o be_v either_o universal_a or_o half_a universal_a have_v this_o equinoctial_a circle_n draw_v with_o a_o great_a red_a line_n which_o pass_v by_o the_o begin_n of_o the_o account_n of_o the_o degree_n of_o latitude_n chap._n x._o of_o the_o pole_n of_o the_o world_n and_o here_o it_o be_v to_o be_v note_v that_o one_o of_o those_o two_o pole_n from_o which_o the_o equinoctial_a be_v equal_o distant_a which_o be_v always_o in_o our_o sight_n because_o it_o be_v continual_o above_o our_o horizon_n be_v call_v the_o pole-artick_a the_o septentrional_a or_o north_n pole_n but_o the_o other_o opposite_a pole_n which_o we_o never_o see_v because_o it_o be_v under_o our_o horizon_n be_v call_v the_o pole-antartick_a and_o the_o meridional_a or_o south_n pole_n and_o so_o that_o part_n of_o the_o world_n which_o be_v between_o the_o equinoctial_a and_o the_o north_n pole_n be_v call_v the_o north_n part_n and_o that_o which_o be_v from_o the_o equinoctial_a to_o the_o south_n pole_n be_v call_v the_o south_n part_n chap_n xi_o of_o the_o ecliptic_a line_n the_o equinoctial_a circle_n be_v divide_v into_o equal_a part_n by_o another_o circle_n call_v the_o ecliptic_a whereof_o one_o half_a be_v between_o the_o equinoctial_a and_o the_o north_n pole_n and_o the_o other_o half_a between_o the_o equinoctial_a and_o the_o south_n pole_n and_o that_o part_v thereof_o which_o be_v further_a distant_a from_o the_o equinoctial_a be_v distant_a from_o the_o same_o about_o 23_o degree_n and_o a_o half_a and_o because_o the_o sun_n move_v in_o this_o circle_n without_o depart_v from_o it_o hereof_o proceed_v the_o declination_n thereof_o and_o this_o circle_n in_o all_o part_n be_v equal_o distant_a from_o the_o pole_n of_o the_o second_o motion_n which_o be_v call_v the_o pole_n of_o the_o ecliptic_a and_o through_o this_o circle_n the_o sun_n be_v continual_o move_v by_o his_o proper_a motion_n from_o east_n to_o west_n by_o mean_n of_o which_o motion_n sometime_o he_o pass_v under_o the_o equinoctial_a and_o at_o other_o time_n depart_v from_o it_o both_o towards_o the_o north_n and_o towards_o the_o south_n and_o the_o quantity_n of_o his_o great_a distance_n be_v about_o 23_o degree_n and_o a_o half_a and_o so_o much_o be_v the_o distance_n of_o the_o pole_n of_o the_o ecliptic_a from_o the_o pole_n of_o the_o equinoctial_a and_o albeit_o this_o circle_n be_v not_o draw_v in_o the_o sea_n chartley_n yet_o be_v it_o in_o some_o sort_n represent_v in_o the_o table_n of_o the_o sun_n declination_n which_o be_v gather_v from_o the_o motion_n which_o the_o sun_n make_v under_o the_o ecliptic_a chap._n xii_o of_o the_o declination_n of_o the_o sun_n the_o motion_n of_o the_o sun_n under_o the_o ecliptic_a be_v the_o cause_n of_o his_o declination_n which_o be_v nothing_o else_o but_o the_o daily_a swarve_n or_o decline_a of_o the_o sun_n from_o the_o equinoctial_a line_n and_o this_o declination_n when_o the_o sun_n be_v under_o the_o equinoctial_a upon_o the_o eleven_o of_o march_n and_o thirteen_o of_o september_n be_v nothing_o at_o all_o so_o likewise_o upon_o the_o twelve_o of_o june_n and_o twelve_o of_o december_n the_o declination_n be_v at_o the_o great_a and_o albeit_o this_o great_a declination_n be_v now_o in_o our_o time_n about_o three_o and_o twenty_o degree_n and_o a_o half_a yet_o have_v it_o at_o other_o time_n be_v find_v otherwise_o by_o reason_n of_o a_o three_o motion_n proper_a to_o the_o eight_o heaven_n but_o it_o always_o keep_v between_o 23_o degree_n 28_o minute_n and_o 23_o degree_n 53_o minute_n from_o hence_o therefore_o we_o do_v infer_v that_o at_o divers_a time_n it_o be_v meet_v to_o make_v new_a and_o divers_a table_n of_o the_o declination_n of_o the_o sun_n chap._n xiii_o of_o the_o colour_n there_o be_v two_o circle_n of_o the_o sphere_n either_o of_o which_o divide_v in_o into_o two_o equal_a part_n and_o they_o be_v call_v colour_n because_o that_o in_o the_o revolution_n which_o they_o make_v by_o force_n of_o the_o primum_fw-la mobile_a they_o do_v not_o show_v themselves_o whole_o unto_o we_o so_o as_o we_o may_v see_v all_o part_n of_o they_o one_o of_o they_o be_v call_v the_o equinoctial_a colour_n because_o it_o pass_v by_o the_o pole_n of_o the_o world_n and_o the_o point_n where_o the_o ecliptic_a cut_v the_o equinoctial_a and_o when_o the_o sun_n by_o his_o own_o proper_a motion_n come_v unto_o it_o he_o make_v the_o day_n and_o the_o night_n equal_a and_o divide_v the_o winter_n from_o the_o spring_n by_o the_o one_o part_n and_o by_o the_o other_o summer_n from_o autumn_n at_o which_o time_n the_o sun_n have_v no_o declination_n at_o all_o the_o other_o be_v call_v the_o solstitial_a colour_n because_o it_o pass_v by_o the_o pole_n of_o the_o world_n and_o of_o the_o ecliptic_a and_o by_o the_o point_n where_o the_o ecliptic_a be_v further_a distant_a from_o the_o equinoctial_a and_o when_o the_o sun_n by_o his_o proper_a motion_n come_v unto_o it_o in_o the_o one_o part_v it_o make_v the_o long_a day_n and_o the_o short_a night_n and_o divide_v the_o spring_n from_o the_o summer_n and_o have_v his_o great_a declination_n towards_o the_o north_n and_o be_v in_o the_o other_o part_n the_o sun_n make_v the_o long_a night_n and_o short_a day_n and_o divide_v winter_n from_o autumn_n and_o be_v in_o his_o great_a southerly_a declination_n these_o two_o colour_n be_v note_v in_o the_o table_n of_o the_o sun_n declination_n because_o the_o equinoctial_a colour_n pass_v by_o the_o two_o point_n where_o there_o be_v no_o declination_n at_o all_o because_o the_o sun_n be_v under_o the_o very_a equinoctial_a circle_n and_o the_o solstitial_a colour_n pass_v by_o that_o place_n where_o the_o sun_n have_v his_o great_a declination_n which_o be_v in_o 23_o degree_n and_o a_o half_a or_o thereabouts_o chap._n fourteen_o of_o the_o meridian_n circle_n the_o meridian_n be_v a_o circle_n draw_v by_o the_o pole_n of_o the_o world_n which_o be_v all_o one_o with_o the_o pole_n of_o the_o equinoctial_a and_o and_o by_o the_o point_n direct_o over_o our_o head_n call_v the_o zenith_n and_o it_o be_v call_v the_o meridian_n because_o that_o when_o the_o sun_n by_o the_o motion_n of_o the_o primum_fw-la mobile_a come_v unto_o this_o circle_n it_o make_v midday_n and_o then_o he_o have_v be_v run_v his_o course_n from_o his_o rise_n till_o he_o come_v thither_o just_o so_o long_a time_n as_o he_o shall_v be_v run_v from_o thence_o to_o the_o place_n of_o his_o set_n the_o zenith_n be_v a_o point_n in_o the_o firmament_n place_v direct_o over_o our_o head_n and_o it_o be_v to_o be_v note_v that_o when_o the_o sun_n be_v in_o that_o circle_n it_o have_v the_o great_a altitude_n above_o our_o horizon_n that_o it_o can_v possible_o have_v the_o same_o day_n by_o this_o and_o the_o declination_n we_o come_v to_o know_v how_o far_o we_o be_v distant_a from_o the_o equinoctial_a either_o towards_o the_o north_n or_o towards_o the_o south_n and_o hence_o it_o be_v that_o the_o height_n of_o the_o sun_n in_o navigation_n be_v understand_v only_o for_o that_o height_n which_o the_o sun_n have_v when_o he_o be_v in_o this_o circle_n and_o so_o the_o height_n of_o the_o sun_n shall_v be_v that_o part_n of_o the_o meridian_n which_o be_v contain_v between_o the_o sun_n and_o our_o horizon_n this_o circle_n in_o the_o sea-chart_n be_v represent_v by_o all_o those_o line_n which_o be_v draw_v from_o north_n to_o south_n chap._n xv._n of_o the_o horizon_n the_o horizon_n be_v a_o circle_n which_o divide_v that_o part_n of_o the_o heaven_n which_o we_o see_v from_o the_o residue_n which_o we_o do_v not_o see_v and_o it_o be_v proper_o that_o circle_n by_o which_o according_a to_o our_o sight_n the_o heaven_n seem_v to_o be_v join_v with_o the_o water_n when_o we_o be_v at_o sea_n without_o sight_n of_o
any_o land_n this_o horizon_n be_v of_o two_o sort_n namely_o right_a and_o oblique_a the_o right_a horizon_n be_v that_o which_o they_o have_v that_o live_v under_o the_o equinoctial_a which_o pass_v by_o their_o zenith_n and_o therefore_o the_o equinoctial_a line_n or_o circle_n fall_v perpendicular_o and_o right_o across_o with_o their_o horizon_n and_o both_o the_o south_n and_o the_o north_n pole_n be_v in_o their_o horizon_n the_o oblique_a horizon_n be_v that_o which_o they_o have_v that_o live_v not_o direct_o under_o the_o equinoctial_a for_o unto_o they_o the_o equinoctial_a divide_v the_o horizon_n oblique_o and_o not_o right_o across_o and_o one_o pole_n be_v always_o above_o their_o horizon_n and_o the_o other_o be_v beneath_o their_o horizon_n and_o can_v be_v see_v this_o horizon_n be_v represent_v in_o the_o sea-chart_n by_o a_o certain_a imagine_a circle_n who_o centre_n be_v the_o point_n where_o our_o ship_n be_v from_o which_o centre_n be_v imagine_v to_o proceed_v unto_o the_o say_a circle_n 32_o line_n which_o represent_v the_o 32_o wind_n or_o rumb_n which_o always_o be_v draw_v in_o our_o sea-compasse_n which_o likewise_o in_o a_o little_a piece_n of_o paper_n do_v continual_o represent_v unto_o we_o both_o by_o day_n and_o night_n the_o whole_a horizon_n with_o his_o 32_o division_n chap._n xvi_o of_o the_o 32_o wind_n this_o right_a or_o oblique_a horizon_n be_v divide_v into_o 32_o equal_a part_n by_o 16_o line_n which_o they_o call_v rumb_n and_o they_o cut_v themselves_o in_o the_o point_n where_o we_o stand_v of_o which_o rumb_n that_o which_o pass_v by_o the_o point_n where_o the_o equinoctial_a begin_v and_o end_v which_o be_v where_o the_o sun_n rise_v and_o set_v the_o 11_o of_o march_n and_o the_o 13_o of_o september_n be_v call_v east_n and_o west_n and_o that_o which_o cut_v it_o right_o across_o be_v name_v north_n and_o south_n and_o the_o four_o extreme_n or_o end_n of_o these_o two_o line_n be_v distant_a upon_o the_o horizon_n one_o four_o part_n of_o a_o circle_n and_o they_o make_v four_o quarter_n every_o one_o of_o which_o quarter_n be_v divide_v in_o the_o midst_n do_v make_v four_o other_o point_n and_o that_o which_o fall_v between_o the_o north_n and_o the_o east_n be_v call_v north-east_n and_o that_o between_o the_o north_n and_o the_o west_n northwest_n that_o between_o the_o south_n and_o the_o east_n southeast_n and_o that_o between_o the_o south_n and_o the_o west_n south-west_n and_o so_o the_o horizon_n be_v divide_v by_o four_o line_n or_o numb_v into_o eight_o principal_a wind_n note_v in_o the_o sea-chart_n with_o black_a line_n and_o if_o you_o divide_v every_o one_o of_o those_o eight_o part_n in_o the_o midst_n you_o shall_v have_v other_o eight_o line_n and_o other_o four_o rumb_n which_o in_o all_o be_v 16_o wind_n and_o each_o one_o of_o these_o have_v his_o name_n compound_v of_o the_o name_n of_o those_o principal_a wind_n which_o be_v on_o either_o side_n thereof_o as_o for_o example_n that_o half_a wind_n which_o be_v between_o the_o north_n and_o the_o north-east_n be_v call_v north-north-east_n and_o that_o which_o blow_v between_o the_o east_n and_o the_o north-east_n be_v call_v east-north-east_n and_o that_o between_o the_o east_n and_o the_o southeast_n east-south-east_n and_o that_o between_o the_o south_n and_o the_o southeast_n south-south-east_n and_o that_o between_o the_o south-west_n and_o the_o west_n west-south-west_n and_o that_o between_o the_o west_n and_o northwest_n west-north-west_n and_o that_o between_o the_o northwest_n and_o the_o north_n north-north-west_n and_o these_o be_v note_v in_o the_o chart_n with_o green_a line_n final_o if_o you_o divide_v every_o one_o of_o these_o sixteen_o wind_n in_o the_o midst_n they_o will_v yield_v you_o other_o 16_o wind_n and_o will_v amount_v to_o 32_o wind_n in_o all_o which_o 16_o last_v mention_v be_v draw_v in_o the_o sea-chart_n with_o red_a line_n and_o be_v by_o the_o spaniard_n call_v quarter_n of_o the_o eight_o first_o and_o principal_a wind_n and_o every_o one_o of_o these_o be_v call_v by_o the_o name_n of_o that_o principal_a wind_n which_o be_v next_o it_o together_o with_o a_o addition_n of_o the_o word_n by_o and_o the_o name_n of_o another_o principal_a wind_n which_o be_v next_o unto_o it_o as_o for_o example_n of_o the_o two_o quarter-wind_n which_o fall_v next_o the_o rumb_n of_o the_o north_n that_o which_o lie_v towards_o the_o north-east_n be_v call_v north_n and_o by_o east_n and_o that_o which_o fall_v towards_o the_o northwest_n be_v call_v north_n by_o west_n so_o likewise_o of_o those_o two_o wind_n which_o blow_n next_o the_o north-east_n that_o towards_o the_o north_n be_v call_v north-east_n and_o by_o north_n and_o that_o towards_o the_o east_n north-east_n and_o by_o east_n and_o after_o the_o same_o manner_n you_o may_v name_v all_o the_o rest_n the_o figure_n of_o the_o sea-compasse_n and_o of_o the_o horizon_n divide_v into_o 32_o wind_n by_o 16_o rumb_n but_o here_o be_v to_o be_v note_v wind_n that_o there_o be_v difference_n between_o the_o rumb_n and_o the_o wind_n because_o a_o rumb_n be_v one_o direct_v line_n continue_v with_o two_o contrary_a wind_n as_o the_o rumb_n of_o north_n &_o south_n and_o the_o rumb_n of_o east_n and_o west_n and_o so_o when_o we_o will_v name_v the_o lie_v of_o any_o coast_n we_o will_v say_v that_o it_o lie_v north_n and_o south_n or_o north_n and_o by_o east_n and_o south_n and_o by_o west_n but_o the_o wind_n be_v one_o line_n of_o those_o 32_o into_o which_o the_o horizon_n be_v divide_v and_o it_o be_v one_o part_n of_o those_o two_o which_o together_o be_v call_v the_o rumb_n and_o so_o we_o say_v that_o land_n lie_v from_o we_o towards_o the_o south_n and_o towards_o the_o south_n and_o by_o west_n or_o towards_o the_o south-south-west_n etc._n etc._n chap._n xvii_o of_o the_o two_o tropic_n beside_o the_o six_o circle_n abovementioned_a which_o be_v draw_v upon_o the_o superficies_n of_o the_o sphere_n of_o the_o world_n there_o be_v other_o two_o which_o the_o sun_n describe_v with_o the_o motion_n of_o the_o primum_fw-la mobile_n about_o the_o 12_o day_n of_o june_n and_o of_o december_n of_o which_o two_o circle_n that_o which_o the_o sun_n describe_v the_o 12_o of_o june_n from_o the_o time_n of_o his_o rise_n till_o the_o time_n that_o he_o rise_v the_o day_n follow_v be_v call_v the_o tropic_a of_o the_o summer_n sun-standing_a or_o the_o tropic_a of_o cancer_n for_o the_o sun_n have_v depart_v from_o the_o equinoctial_a and_o increase_v his_o declination_n towards_o the_o north_n when_o he_o come_v to_o describe_v that_o circle_n for_o two_o or_o three_o day_n it_o seem_v that_o he_o come_v no_o near_o to_o our_o zenith_n nor_o depart_v from_o the_o equinoctial_a one_o day_n more_o than_o another_o but_o from_o thence_o forward_o he_o go_v back_o diminish_v his_o declination_n till_o he_o come_v to_o the_o equinoctial_a and_o cross_v the_o same_o he_o go_v on_o the_o other_o side_n increase_v his_o declination_n until_o the_o 12_o of_o december_n upon_o which_o day_n from_o the_o time_n of_o his_o rise_n till_o he_o be_v come_v about_o to_o rise_v again_o the_o next_o morning_n he_o describe_v another_o circle_n call_v the_o tropic_a of_o the_o winter_n sun-standing_a or_o the_o tropic_a of_o capricorn_n for_o the_o sun_n be_v depart_v from_o the_o equinoctial_a and_o increase_v his_o declination_n towards_o the_o south_n when_o he_o come_v to_o describe_v that_o circle_n it_o seem_v for_o two_o or_o three_o day_n that_o he_o return_v not_o one_o whit_n towards_o the_o equinoctial_a nor_o go_v further_o from_o our_o zenith_n one_o day_n more_o than_o other_o but_o from_o thence_o forward_o he_o come_v back_o again_o diminish_v his_o declination_n till_o he_o be_v return_v to_o the_o equinoctial_a and_o from_o thence_o towards_o our_o zenith_n these_o two_o circle_n in_o sea-chart_n be_v mark_v with_o two_o great_a red_a line_n draw_v from_o east_n to_o west_n which_o lie_v on_o either_o side_n of_o the_o equinoctial_a be_v distant_a from_o thence_o about_o 23_o deg_n and_o a_o half_a and_o wheresoever_o our_o ship_n be_v in_o any_o place_n between_o these_o two_o circle_n or_o line_n we_o may_v in_o some_o time_n of_o the_o year_n take_v the_o sun_n in_o our_o zenith_n at_o which_o time_n it_o make_v no_o shadow_n at_o all_o be_v then_o just_a 90_o degr_n high_a above_o our_o horizon_n but_o they_o which_o be_v without_o the_o say_v two_o circle_n or_o line_n shall_v never_o have_v the_o sun_n in_o their_o zenith_n because_o it_o can_v come_v to_o the_o height_n of_o 90_o degr_n above_o their_o horizon_n chap._n xviii_o of_o the_o parallel_n the_o parallel_a circle_n be_v those_o which_o be_v in_o all_o part_n equal_o distant_a from_o the_o
of_o the_o ruler_n in_o the_o midst_n stand_v upright_o the_o very_a midst_n of_o both_o vane_n be_v place_v upon_o the_o line_n he_o through_o the_o centre_n of_o which_o two_o vane_n shall_v be_v make_v two_o little_a hole_n both_o which_o must_v stand_v direct_o over_o the_o line_n he_o and_o in_o equal_a distance_n from_o the_o upper_a face_n of_o the_o ruler_n this_o ruler_n by_o a_o hole_n bore_v through_o the_o midst_n thereof_o shall_v be_v fasten_v upon_o the_o say_a astrolabe_n through_o another_o hole_n of_o the_o bigness_n of_o that_o in_o the_o ruler_n at_o the_o very_a centre_n a_o with_o a_o nail_n which_o may_v be_v make_v fast_o with_o a_o little_a pin_n as_o be_v to_o be_v see_v in_o the_o figure_n chap._n ii_o of_o the_o height_n of_o the_o sun_n to_o take_v the_o height_n of_o the_o sun_n you_o must_v hold_v the_o astrolabe_n by_o the_o ring_n or_o knot_n d_o in_o your_o left_a hand_n and_o turn_v your_o right_a side_n to_o the_o sun_n lift_v up_o the_o ruler_n with_o your_o right_a hand_n till_o the_o beam_n of_o the_o sun_n enter_v by_o the_o hole_n of_o the_o uppermost_a vane_n do_v also_o pierce_v through_o the_o hole_n of_o the_o nethermost_a vane_n and_o then_o note_v the_o degree_n and_o part_n of_o the_o degree_n which_o the_o line_n he_o do_v touch_n for_o that_o be_v the_o height_n of_o the_o sun_n above_o the_o horizon_n which_o if_o it_o be_v the_o great_a height_n that_o the_o sun_n have_v that_o day_n it_o will_v teach_v we_o how_o far_o we_o be_v distant_a from_o the_o equinoctial_a this_o great_a height_n be_v to_o be_v take_v at_o midday_n lift_v up_o the_o uppermost_a vane_n till_o we_o be_v assure_v that_o the_o sun_n cease_v to_o rise_v any_o high_a but_o begin_v to_o fall_v again_o then_o note_v that_o great_a height_n and_o keep_v it_o for_o the_o make_n of_o your_o account_n of_o the_o latitude_n by_o the_o sun_n chap._n iii_o of_o the_o shadow_n the_o shadow_n be_v compare_v with_o the_o sun_n may_v be_v of_o three_o sort_n for_o at_o high_a noon_n the_o shadow_n fall_v either_o towards_o that_o part_n of_o the_o world_n âo_o which_o the_o sun_n decline_v or_o towards_o the_o contrary_a part_n or_o else_o we_o make_v no_o shadow_n at_o all_o the_o first_o and_o second_o sort_n be_v when_o the_o height_n of_o the_o sun_n be_v less_o than_o 90_o degree_n and_o the_o three_o be_v when_o it_o be_v just_a 90_o degree_n high_a the_o first_o be_v when_o the_o sun_n keep_v his_o course_n on_o the_o north_n side_n of_o the_o equinoctial_a which_o be_v from_o the_o 1â_n of_o march_n to_o the_o 13_o of_o september_n and_o likewise_o when_o the_o shadow_n fall_v towards_o the_o north_n of_o the_o compass_n or_o when_o the_o sun_n run_v on_o the_o south_n side_n of_o the_o equinoctial_a which_o be_v from_o the_o 14_o of_o september_n to_o the_o 10_o of_o march_n and_o the_o shadow_n likewise_o fall_v towards_o the_o south_n of_o the_o compass_n and_o this_o be_v when_o the_o sun_n and_o the_o shadow_n go_v both_o one_o way_n the_o second_o be_v when_o the_o sun_n come_v towards_o the_o north_n the_o shadow_n be_v cast_v towards_o the_o south_n of_o the_o compass_n or_o when_o the_o sun_n be_v on_o the_o south_n side_n of_o the_o equinoctial_a the_o shadow_n fall_v towards_o the_o north_n and_o this_o be_v when_o the_o sun_n and_o the_o shadow_n be_v differ_v the_o rule_n of_o the_o shadow_n be_v that_o we_o look_v well_o to_o the_o low_a vane_n of_o the_o astrolabe_n when_o we_o be_v take_v the_o height_n of_o the_o sun_n at_o noon_n for_o if_o the_o line_n he_o fall_v direct_o upon_o the_o line_n of_o the_o astrolabe_n de_fw-fr than_o we_o have_v no_o shadow_n because_o the_o sun_n be_v in_o our_o zenith_n 90_o degree_n high_a but_o if_o the_o line_n he_o fall_v not_o upon_o the_o line_n de_fw-fr you_o must_v mark_v towards_o what_o part_n of_o the_o world_n the_o low_a part_n of_o the_o ruler_n do_v decline_v from_o the_o point_n e_o which_o if_o it_o decline_v towards_o the_o north_n of_o the_o compass_n than_o the_o shadow_n fall_v northwards_o but_o if_o it_o decline_v towards_o the_o south_n of_o the_o compass_n than_o the_o shadow_n fall_v southwards_o chap._n four_o of_o the_o regiment_n and_o rule_n of_o the_o sun_n when_o you_o know_v the_o part_n or_o part_n of_o the_o sun_n and_o shadow_n and_o desire_n by_o the_o sun_n to_o know_v how_o far_o you_o be_v distant_a from_o the_o equinoctial_a you_o have_v five_o rule_n the_o first_o whereof_o show_v in_o what_o part_n of_o the_o heaven_n the_o sun_n be_v that_o be_v whether_o he_o be_v north_n or_o south_n from_o the_o equinoctial_a at_o the_o time_n of_o your_o observation_n the_o second_o teach_v what_o account_n we_o be_v to_o take_v of_o the_o sun_n when_o he_o cast_v no_o shadow_n because_o he_o be_v in_o our_o zenith_n and_o be_v find_v in_o the_o astrolabe_n to_o be_v just_a 90_o deg_n high_a the_o three_o be_v of_o the_o account_n to_o be_v make_v by_o the_o sun_n when_o take_v the_o height_n thereof_o in_o less_o than_o 90_o degr_n it_o make_v a_o shadow_n at_o high_a noon_n and_o have_v no_o declination_n because_o it_o be_v under_o the_o equinoctial_a the_o four_o be_v of_o the_o account_n that_o be_v to_o be_v make_v when_o the_o sun_n and_o the_o shadow_n be_v both_o one_o way_n from_o the_o line_n the_o five_o be_v when_o the_o sun_n and_o the_o shadow_n be_v different_a onâ_n be_v towards_o the_o north_n and_o the_o other_o towards_o the_o south_n the_o first_o rule_n of_o the_o sun_n from_o the_o 11_o of_o mârch_n to_o the_o 13_o of_o september_n the_o sun_n run_v on_o the_o north_n side_n of_o the_o equinoctial_a and_o from_o the_o 14_o of_o september_n to_o the_o 10_o of_o march_n he_o go_v on_o the_o south_n side_n thereof_o the_o second_o rule_n of_o the_o sun_n when_o we_o observe_v the_o sun_n in_o 00_o degree_n of_o height_n we_o must_v see_v what_o degree_n and_o minute_n of_o declination_n the_o sun_n have_v the_o same_o day_n and_o then_o we_o may_v say_v that_o we_o be_v so_o much_o distant_a from_o the_o equinoctial_a towards_o that_o part_n of_o the_o world_n to_o which_o the_o sun_n decline_v the_o three_o rule_n of_o the_o sun_n when_o the_o sun_n be_v less_o than_o 90_o degree_n high_a if_o there_o be_v no_o declination_n the_o same_o day_n than_o so_o much_o as_o it_o want_v in_o height_n of_o 90_o degree_n so_o much_o be_v we_o distant_a from_o the_o equinoctial_a towards_o that_o part_n of_o the_o world_n towards_o which_o the_o shadow_n fall_v the_o four_o rule_n of_o the_o sun·_n when_o the_o sun_n and_o the_o shadow_n be_v both_o towards_o the_o same_o part_n of_o the_o world_n we_o must_v note_v how_o much_o the_o sun_n want_v of_o 90_o degree_n in_o height_n and_o that_o which_o it_o want_v be_v add_v to_o the_o declination_n of_o the_o sun_n the_o same_o day_n be_v our_o just_a distance_n from_o the_o equinoctial_a towards_o that_o part_n of_o the_o world_n to_o which_o the_o sun_n and_o shadow_n decline_v the_o five_o rule_n of_o the_o sun_n when_o the_o declination_n of_o the_o sun_n and_o the_o shadow_n be_v different_a we_o must_v add_v the_o height_n of_o the_o sun_n unto_o the_o declination_n which_o it_o have_v the_o same_o day_n and_o if_o the_o sun_n amount_v to_o 90_o degr_n just_a then_o be_v we_o under_o the_o equinoctial_a line_n but_o if_o it_o exceed_v 90_o degree_n we_o be_v so_o much_o distant_a from_o the_o equinoctial_a towards_o that_o part_n of_o the_o world_n wherein_o the_o sun_n be_v as_o that_o excess_n or_o overpluss_n come_v to_o and_o if_o the_o height_n and_o declination_n add_v together_o come_v to_o less_o than_o 90_o look_v how_o many_o degree_n and_o minute_n you_o want_v of_o 90_o so_o many_o be_v you_o distant_a from_o the_o equinoctial_a towards_o that_o part_n to_o which_o the_o shadow_n fall_v and_o here_o be_v to_o be_v note_v that_o we_o must_v likewise_o make_v account_n of_o the_o minute_n because_o they_o may_v be_v both_o in_o declination_n and_o in_o height_n and_o so_o always_o in_o that_o declination_n where_o we_o shall_v find_v 60_o minute_n we_o must_v make_v of_o they_o one_o degree_n and_o if_o in_o take_v the_o height_n we_o find_v half_o a_o degree_n beside_o all_o the_o whole_a degree_n it_o be_v as_o much_o as_o 30_o minute_n and_o one_o three_o part_n of_o a_o degree_n be_v 20_o minute_n one_o four_o 15_o minute_n one_o five_o part_n 12_o minute_n and_o one_o six_o part_n 10_o minute_n chap._n v._o of_o the_o declination_n of_o the_o sun_n and_o of_o his_o table_n that_o we_o may_v know_v what_o use_n to_o make_v of_o the_o five_o foresay_a
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 diffeârent_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 declination_n look_v how_o much_o your_o distance_n from_o the_o equinoctial_a want_v of_o 90_o deg_n for_o so_o much_o be_v height_n of_o the_o sun_n 3_o when_o the_o sun_n and_o the_o shadow_n be_v both_o towards_o one_o part_n subtract_v out_o of_o your_o distance_n from_o the_o equinoctial_a the_o declination_n of_o the_o sun_n that_o day_n and_o that_o 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 4_o when_o the_o sun_n and_o the_o shadow_n be_v different_a if_o the_o equinoctial_a be_v between_o you_o and_o the_o sun_n add_v the_o declination_n of_o the_o sun_n to_o your_o distance_n from_o the_o equinoctial_a and_o that_o which_o these_o two_o number_n add_v together_o shall_v want_v of_o 90_o deg_n shall_v be_v the_o height_n of_o the_o sun_n but_o if_o you_o be_v between_o the_o sun_n and_o the_o line_n you_o must_v subduct_v your_o distance_n from_o the_o line_n out_o of_o the_o sun_n declination_n and_o then_o that_o 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 âo_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
5_o i_o divide_v these_o 24_o by_o 5_o and_o i_o find_v the_o quotient_a to_o be_v four_o and_o the_o remainder_n four_o and_o so_o i_o say_v that_o the_o moon_n come_v to_o the_o north-east_n four_o hour_n and_o â
_n late_a than_o the_o sun_n and_o because_o the_o sun_n come_v to_o the_o north-east_n at_o three_o a_o clock_n in_o the_o morning_n i_o add_v those_o 4_o hour_n and_o â
_n unto_o the_o 3_o hour_n last_o mention_v and_o they_o make_v seven_o hour_n and_o â
_n which_o be_v the_o hour_n of_o the_o morning_n wherein_o the_o tide_n or_o full_a sea_n happen_v and_o add_v unto_o these_o seven_o hour_n and_o â
_n other_o six_o hour_n and_o â
_n they_o make_v in_o all_o fourteen_o hour_n which_o fall_v out_o at_o two_o a_o clock_n in_o the_o afternoon_n which_o be_v the_o hour_n of_o the_o first_o low_a water_n or_o ebb_v and_o add_v unto_o the_o say_a hour_n of_o the_o full_a sea_n twelve_o hour_n and_o â
_n it_o will_v amount_v unto_o eight_o of_o the_o clock_n and_o â
_n part_v of_o a_o hour_n which_o be_v the_o hour_n of_o the_o night_n wherein_o the_o second_o tide_n or_o high_a water_n be_v and_o add_v unto_o this_o second_o tide_n other_o six_o hour_n and_o â
_n and_o they_o make_v two_o of_o the_o clock_n in_o the_o morning_n and_o â
_n at_o which_o time_n there_o come_v the_o second_o ebb_n or_o low_a sea_n chap._n xxxiii_o of_o a_o certain_a instrument_n whereby_o you_o may_v in_o general_a judge_n of_o the_o tide_n because_o the_o tide_n it_o be_v suppose_v that_o in_o all_o place_n they_o proceed_v from_o the_o motion_n of_o the_o moon_n run_v not_o in_o every_o part_n of_o the_o world_n by_o one_o and_o the_o same_o rumb_n as_o it_o be_v manifest_a in_o the_o channel_n of_o flanders_n and_o in_o all_o the_o coast_n of_o the_o northern_a sea_n which_o be_v a_o matter_n of_o great_a confusion_n and_o difficulty_n to_o mariner_n i_o think_v good_a here_o to_o set_v down_o a_o instrument_n whereby_o the_o day_n of_o the_o moon_n and_o the_o rumb_n whereupon_o the_o moon_n cause_v the_o tide_n in_o every_o part_n be_v know_v they_o may_v judge_v of_o the_o ebb_n and_o flood_n with_o great_a facility_n draw_v upon_o a_o sheet_n of_o paper_n or_o upon_o a_o plate_n of_o tinn_n or_o any_o other_o matter_n a_o circle_n as_o big_a as_o the_o palm_n of_o a_o man_n hand_n and_o half_a a_o finger_n breadth_n within_o that_o circle_n draw_v another_o circle_n and_o have_v divide_v they_o both_o into_o 32_o equal_a part_n with_o line_n draw_v from_o the_o centre_n to_o the_o circumference_n of_o the_o great_a circle_n upon_o the_o upper_a end_n of_o one_o of_o those_o line_n place_v a_o flowerdeluis_a and_o the_o number_n of_o 12_o and_o in_o the_o next_o line_n thereunto_o towards_o the_o left_a hand_n set_v down_o 12_o and_o ¾_n and_o in_o the_o three_o line_n 1_o ½_o and_o so_o proceed_v forward_o put_v down_o upon_o every_o line_n follow_v ¾_n of_o a_o hour_n more_o until_o you_o come_v again_o to_o the_o number_n of_o 12_o in_o the_o low_a line_n and_o from_o thence_o forward_o set_v down_o the_o same_o number_n that_o you_o do_v at_o the_o first_o these_o 32_o line_n so_o draw_v do_v represent_v the_o 32_o wind_n whereby_o the_o sun_n and_o moon_n pass_v every_o day_n and_o so_o you_o may_v set_v down_o the_o name_n of_o the_o principal_a wind_n to_o the_o end_n that_o you_o may_v know_v they_o and_o those_o that_o be_v next_o they_o and_o then_o in_o like_a manner_n make_v another_o round_a and_o slender_a table_n as_o big_a as_o the_o innermost_a circle_n of_o those_o two_o which_o you_o draw_v in_o the_o first_o table_n and_o divide_v it_o into_o thirty_o equal_a part_n first_o into_o two_o by_o a_o line_n divide_v it_o in_o the_o midst_n and_o then_o either_o of_o those_o two_o into_o three_o and_o every_o of_o those_o three_o into_o five_o these_o division_n will_v represent_v the_o day_n of_o the_o moon_n and_o leave_v upon_o 1_o of_o those_o part_n a_o index_n or_o small_a point_n which_o may_v reach_v without_o the_o circle_n set_v down_o the_o number_n thereof_o beginning_n with_o 30_o in_o that_o part_n where_o that_o point_n end_v and_o the_o number_n of_o 1_o in_o the_o line_n follow_v towards_o the_o left_a hand_n and_o then_o 2_o etc._n etc._n till_o you_o end_n at_o the_o same_o point_n with_o 30_o this_o be_v do_v fasten_v with_o a_o thread_n or_o nail_n the_o second_o table_n or_o circle_n upon_o the_o centre_n of_o the_o first_o so_o that_o it_o may_v free_o without_o impediment_n turn_v round_o about_o the_o use_n of_o this_o instrument_n the_o use_n of_o this_o instrument_n be_v that_o know_v in_o every_o port_n or_o part_n of_o any_o coast_n the_o rumb_n or_o quarter_n on_o which_o the_o moon_n make_v full_a sea_n or_o high_a water_n you_o must_v note_v upon_o the_o outward_a circle_n of_o the_o wind_n that_o quarter_n or_o rumb_n and_o place_v the_o tooth_n or_o point_n of_o the_o inner_a circle_n be_v the_o number_n of_o 30_o be_v upon_o that_o quarter_n or_o rumb_n make_v it_o there_o fast_o put_v a_o little_a wax_n underneath_o that_o it_o may_v not_o move_v then_o account_v the_o day_n of_o the_o moon_n age_n in_o the_o inner_a circle_n and_o over_o against_o the_o end_n of_o your_o account_n you_o shall_v see_v in_o the_o uttermost_a circle_n the_o hour_n of_o the_o full_a sea_n of_o that_o day_n together_o with_o the_o rumb_n where_o the_o sun_n be_v at_o that_o hour_n and_o at_o the_o same_o hour_n when_o it_o be_v in_o the_o contrary_a part_n it_o will_v make_v a_o full_a sea_n the_o place_n of_o the_o moon_n at_o the_o hour_n of_o the_o tide_n be_v always_o either_o where_o the_o point_n be_v or_o at_o the_o point_n right_o over_o against_o it_o and_o hence_o you_o may_v easy_o find_v both_o ebb_n also_o this_o little_a instrument_n although_o it_o be_v but_o of_o small_a invention_n be_v of_o great_a use_n and_o profit_n for_o the_o navigation_n of_o flanders_n france_n england_n ireland_n and_o all_o the_o northern_a region_n where_o you_o have_v much_o variety_n in_o the_o tide_n chap._n xxxiiii_o of_o the_o make_n of_o a_o universal_a dial_n which_o may_v serve_v general_o all_o the_o world_n over_o draw_v upon_o a_o table_n or_o pastboord_n the_o circle_n abcd_v upon_o the_o centre_n e_o and_o half_o a_o finger_n breadth_n within_o that_o circle_n upon_o the_o same_o centre_n draw_v another_o circle_n and_o about_o the_o breadth_n of_o a_o wheat_n corn_n within_o the_o second_o circle_n draw_v a_o three_o and_o place_v your_o ruler_n upon_o the_o centre_n e_o by_o the_o right_a line_n ac_fw-la divide_v the_o two_o inner_a circle_n in_o the_o midst_n abc_n and_o cda_n in_o the_o point_n bd_o upon_o which_o and_o upon_o the_o centre_n e_o the_o ruler_n be_v place_v you_o may_v draw_v the_o line_n bd_o whereby_o every_o one_o of_o the_o foresay_a circle_n shall_v be_v divide_v into_o four_o equal_a part_n and_o divide_v every_o one_o of_o those_o four_o quadrant_n of_o the_o inner_a circle_n to_o wit_n ab_fw-la bc_n cd_o da_n into_o 90_o part_n as_o the_o manner_n be_v in_o the_o make_n of_o a_o astrolabe_n set_v number_n thereto_o from_o 5_o to_o 5._o begin_n your_o account_n from_o the_o two_o point_n ac_fw-la and_o so_o procede_v both_o way_n till_o you_o end_v your_o account_n in_o 90_o at_o the_o point_n bd_o and_o this_o inner_a circle_n thus_o divide_v represent_v the_o meridian_n and_o the_o point_n c_o be_v the_o north_n a_o the_o south_n and_o the_o point_n b_o d_o be_v those_o where_o the_o equinoctial_a cut_v the_o meridian_n then_o count_v 23_o degree_n and_o a_o half_a from_o the_o point_n b_o to_o f_o and_o to_o g_o on_o both_o side_n and_o so_o much_o account_n also_o from_o the_o point_n d_o to_o h_n and_o to_o i._o and_o then_o draw_v two_o right_a line_n fh_n and_o give_v the_o line_n fh_n shall_v represent_v the_o tropic_a of_o cancer_n and_o give_v the_o tropic_a of_o capricorn_n and_o those_o two_o line_n shall_v cut_v the_o line_n ca_n which_o be_v the_o axtree_n of_o the_o world_n and_o the_o circle_n of_o six_o of_o the_o clock_n in_o the_o morning_n and_o evening_n upon_o the_o point_v lm_o then_o count_v fifteen_o degree_n from_o c_o towards_o b_o and_o other_o fifteeen_n from_o a_o towards_o b_o and_o place_v your_o ruler_n on_o either_o side_n upon_o the_o end_n of_o your_o account_n you_o shall_v cut_v the_o equinoctial_a bd_o upon_o a_o certain_a point_n which_o shall_v represent_v unto_o you_o seven_o a_o clock_n in_o the_o morning_n and_o five_o of_o the_o clock_n at_o evening_n and_o count_v other_o fifteen_o degree_n on_o both_o side_n more_o towards_o the_o point_n b_o and_o place_v
the_o ruler_n as_o before_o you_o shall_v cut_v the_o line_n bd_o in_o another_o point_n which_o shall_v represent_v eight_o of_o the_o clock_n in_o the_o morning_n and_o four_o in_o the_o afternoon_n and_o account_v high_o fifteen_o degree_n more_o one_o both_o side_n and_o place_v your_o ruler_n upon_o the_o end_n of_o your_o account_n it_o will_v divide_v the_o line_n bd_o at_o another_o point_n which_o shall_v be_v nine_o a_o clock_n in_o the_o morning_n and_o three_o in_o the_o afternoon_n and_o so_o you_o shall_v proceed_v from_o fifteen_o to_o fifteen_o degree_n till_o you_o come_v to_o eleven_o of_o the_o clock_n in_o the_o morning_n and_o one_o in_o the_o afternoon_n and_o if_o you_o will_v have_v the_o half_a hour_n also_o you_o must_v account_v from_o seven_o degree_n and_o a_o half_a to_o seven_o and_o a_o half_a and_o do_v as_o you_o do_v with_o the_o fifteen_o degree_n you_o shall_v have_v the_o half_a hour_n also_o then_o place_v your_o compass_n upon_o the_o centre_n e_o and_o upon_o every_o division_n of_o the_o line_n ebb_v you_o shall_v draw_v the_o same_o division_n likewise_o upon_o the_o line_n ed_z which_o be_v do_v draw_z certain_z obscure_a line_n from_o the_o point_n a_o to_o the_o division_n of_o the_o line_n ebb_v and_o draw_v the_o right_a line_n gf_n see_v where_o gf_n be_v cut_v at_o the_o high_a of_o the_o obscure_a line_n which_o must_v be_v at_o the_o point_n n_o from_o whence_o the_o line_n no_o be_v to_o be_v draw_v equal_o distant_a from_o the_o line_n be._n and_o this_o line_n no_o shall_v be_v divide_v proportional_o by_o the_o obscure_a line_n even_o as_o the_o line_n be._n then_o let_v the_o division_n of_o the_o line_n no_o be_v transfer_v into_o the_o line_n mg_n mi_fw-mi lf_n lh_n and_o then_o the_o tropic_n also_o shall_v be_v divide_v then_o by_o every_o three_o point_n answerable_a in_o the_o equinoctial_a and_o the_o two_o tropic_n you_o shall_v draw_v certain_a part_n of_o circle_n seek_v the_o centre_n of_o those_o three_o point_n in_o the_o equinoctial_a line_n extend_v forth_o on_o either_o side_n and_o these_o part_n of_o circle_n represent_v the_o hour_n then_o make_v a_o account_n of_o the_o degr_n of_o declination_n from_o the_o point_n b_o and_o from_o d_o on_o both_o side_n by_o every_o 2_o degr_n and_o draw_v line_n parallel_v to_o the_o equinoctial_a from_o one_o to_o another_o and_o those_o shall_v be_v the_o parallel_n of_o the_o sun_n declination_n moreover_o you_o shall_v make_v a_o horizon_n as_o large_a as_o the_o diameter_n of_o the_o inner_a circle_n which_o shall_v be_v divide_v after_o this_o manner_n count_n from_o the_o point_n ac_fw-la towards_o b_o five_o degree_n and_o put_v your_o ruler_n upon_o the_o end_n of_o the_o account_n of_o both_o part_n see_v where_o it_o cut_v the_o line_n ebb_n and_o there_o make_v a_o mark_n and_o then_o count_v on_o both_o side_n other_o five_o degree_n and_o put_v the_o ruler_n once_o again_o at_o the_o end_n of_o your_o account_n make_v another_o mark_n where_o it_o cut_v the_o line_n ebb_n and_o so_o the_o line_n ebb_n must_v be_v divide_v from_o five_o to_o five_o degree_n which_o division_n shall_v be_v remove_v into_o the_o say_a horizon_n fasten_v it_o to_o the_o centre_n and_o lay_v it_o to_o the_o line_n bd_o and_o divide_v it_o both_o way_n as_o the_o line_n ebb_n be_v divide_v and_o set_v number_n thereinto_o from_o 5_o to_o 5_o which_o may_v begin_v in_o the_o midst_n and_o end_n with_o 90_o at_o the_o end_n of_o the_o horizon_n and_o let_v every_o one_o of_o these_o part_n be_v divide_v into_o five_o other_o part_n or_o degree_n then_o account_v from_o the_o centre_n e_o in_o the_o horizon_n eleven_o degree_n and_o ¼_n you_o shall_v set_v there_o a_o mark_n which_o shall_v be_v the_o seven_o point_n from_o north_n and_o south_n that_o be_v it_o shall_v represent_v the_o point_n which_o be_v next_o to_o the_o east_n and_o west_n in_o the_o compass_n and_o account_v another_o eleven_o degree_n and_o a_o quarter_n and_o make_v there_o a_o mark_n it_o shall_v represent_v the_o six_o point_n from_o north_n and_o south_n and_o so_o you_o must_v do_v with_o the_o other_o point_n and_o then_o your_o instrument_n be_v finish_v chap._n xxxv_o of_o the_o part_n of_o this_o instrument_n in_o this_o instrument_n the_o first_o thing_n be_v a_o circle_n divide_v into_o 360_o degree_n which_o be_v the_o meridian_n and_o the_o line_n of_o twelve_o a_o clock_n the_o second_o be_v the_o right_a line_n of_o which_o that_o in_o the_o midst_n be_v the_o equinoctial_a and_o the_o two_o other_o be_v the_o tropic_n of_o cancer_n and_o capricorn_n and_o the_o other_o line_n between_o those_o be_v the_o parallel_n of_o the_o sun_n declination_n which_o have_v their_o number_n agreeable_a to_o they_o and_o those_o that_o be_v between_o the_o equinoctial_a and_o the_o tropic_a of_o cancer_n do_v serve_v from_o the_o 11_o of_o march_n to_o the_o 13_o of_o september_n and_o the_o other_o for_o the_o residue_n of_o the_o year_n the_o crooked_a line_n which_o cross_v those_o parallel_n be_v the_o hour_n line_n and_o the_o point_n of_o the_o meridian_n which_o in_o 90_o degree_n distant_a from_o the_o equinoctial_a towards_o the_o left_a hand_n be_v the_o north_n pole_n and_o the_o point_n opposite_a to_o that_o be_v the_o south_n pole_n in_o the_o horizon_n there_o be_v first_o the_o degree_n and_o then_o the_o point_n of_o the_o compass_n distinguish_v by_o the_o small_a prick_v line_n chap._n xxxvi_o how_o you_o may_v know_v what_o a_o clock_n it_o be_v by_o this_o instrument_n at_o any_o time_n of_o the_o day_n when_o you_o will_v know_v what_o a_o clock_n it_o be_v take_v the_o height_n of_o the_o sun_n with_o your_o astrolabe_n and_o seek_v the_o table_n of_o the_o sun_n declination_n what_o declination_n it_o have_v the_o same_o day_n and_o the_o height_n of_o the_o pole_n which_o a_o good_a mariner_n know_v at_o all_o time_n because_o he_o must_v direct_v his_o course_n thereby_o this_o be_v know_v place_v the_o horizon_n instrument_n on_o the_o one_o side_n under_o the_o north_n and_o on_o the_o other_o side_n above_o the_o south_n so_o many_o degree_n as_o his_o distance_n from_o the_o equinoctial_a be_v the_o same_o day_n and_o fasten_v it_o there_o with_o a_o little_a wax_n that_o it_o may_v not_o move_v then_o count_v in_o the_o meridian_n on_o either_o side_n from_o the_o horizon_n which_o now_o stand_v firm_a the_o height_n of_o the_o sun_n above_o the_o horizon_n take_v with_o your_o astrolabe_n and_o by_o the_o end_n of_o the_o account_n draw_v a_o line_n or_o thread_n overthwart_o which_o shall_v be_v equal_o distant_a from_o the_o horizon_n then_o reckon_v the_o sun_n declination_n in_o the_o parallel_n begin_v from_o the_o equinoctial_a of_o the_o instrument_n that_o way_n which_o the_o sun_n decline_v and_o mark_v the_o line_n or_o parallel_v at_o which_o the_o account_n of_o the_o declination_n end_v where_o and_o at_o what_o hour_n it_o be_v cross_v by_o the_o thread_n for_o that_o hour_n be_v the_o hour_n of_o the_o day_n but_o note_v this_o that_o if_o the_o cross_n of_o the_o thread_n and_o parallel_n do_v fall_v upon_o the_o division_n of_o the_o parallel_n and_o of_o the_o hour_n it_o be_v a_o just_a hour_n but_o if_o it_o fall_v beside_o the_o common_a meeting_n of_o the_o parallel_n and_o of_o the_o hour-line_n upon_o that_o side_n where_o it_o fall_v see_v how_o much_o more_o there_o be_v then_o a_o hour_n whether_o ¼_n or_o 1_o â_o or_o ½_o etc._n etc._n now_o although_o every_o hour_n line_n have_v two_o number_n one_o of_o the_o morning_n and_o another_o of_o the_o afternoon_n yet_o it_o be_v a_o easy_a matter_n to_o distinguish_v which_o of_o they_o will_v serve_v your_o turn_n if_o you_o know_v whether_o your_o observation_n be_v before_o high_a noon_n or_o after_o which_o be_v to_o be_v know_v by_o your_o astrolabe_n for_o if_o the_o sun_n ascend_v it_o be_v before_o noon_n but_o if_o it_o descend_v it_o be_v afternoon_n chap._n xxxvii_o of_o the_o variation_n of_o the_o compass_n by_o this_o instrument_n if_o you_o will_v know_v by_o this_o instrument_n the_o variation_n of_o the_o compass_n you_o must_v do_v thus_o when_o the_o sun_n rise_v or_o go_v down_o at_o the_o horizon_n observe_v he_o with_o your_o compass_n note_v very_o diligent_o upon_o what_o rumb_n and_o part_n of_o the_o rumb_n he_o rise_v or_o fall_v and_o if_o the_o compass_n be_v divide_v into_o 360_o part_n begin_v to_o reckon_v they_o from_o the_o east_n and_o from_o the_o west_n on_o either_o side_n and_o end_v in_o the_o north_n and_o south_n with_o 90_o degree_n it_o shall_v be_v the_o fit_a for_o this_o purpose_n because_o than_o you_o shall_v see_v
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 rule_n the_o number_n of_o the_o whole_a month_n which_o have_v pass_v since_o the_o 15_o of_o april_n forward_o be_v double_a you_o have_v the_o number_n of_o the_o hour_n wherein_o the_o former_a guard_n make_v midnight_n be_v head-most_a and_o if_o the_o month_n fall_v not_o out_o just_a add_v for_o every_o fifteen_o day_n above_o the_o whole_a month_n one_o day_n and_o for_o every_o day_n four_o minute_n and_o you_o shall_v know_v when_o it_o be_v midnight_n as_o for_o example_n if_o i_o will_v know_v upon_o the_o 15_o of_o november_n where_o the_o former_a guard_n make_v midnight_n i_o account_v the_o whole_a month_n from_o the_o 15_o of_o april_n and_o i_o find_v they_o to_o be_v seven_o which_o be_v double_v make_v fourteen_o i_o say_v therefore_o that_o upon_o the_o 15_o of_o november_n it_o shall_v be_v midnight_n when_o the_o former_a guard_n have_v pass_v before_o the_o north_n or_o head_n fourteen_o hour_n and_o so_o allow_v three_o to_o the_o northwest_n three_o to_o the_o 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
clavius_n his_o gross_a demonstration_n hereof_o 90_o a_o more_o exact_a demonst_a with_o the_o practice_n thereof_o 92_o the_o angle_n of_o dip_v for_o any_o height_n of_o the_o eye_n 96_o 3_o error_n by_o the_o parallax_n of_o the_o sun_n correct_v 96_o 4_o error_n in_o observe_v by_o the_o refraction_n of_o the_o sun_n or_o star_n correct_v 97_o chap._n 16·_a fault_n amend_v in_o the_o table_n of_o the_o sun_n declination_n common_o call_v the_o regiment_n of_o the_o sun_n 97_o chap._n 17._o of_o the_o table_n of_o declination_n of_o every_o minute_n of_o the_o ecliptic_a in_o degree_n min._n and_o sec._n make_v according_a to_o the_o great_a obliquity_n of_o the_o zodiac_n this_o present_a age_n which_o by_o exact_a observation_n be_v find_v to_o be_v 23_o degree_n 31_o min._n and_o a_o half_a 98_o a_o table_n of_o the_o declination_n of_o every_o minute_n of_o the_o ecliptic_a in_o degree_n min._n and_o sec._n 101_o chap._n 18._o the_o use_n of_o the_o former_a table_n of_o declination_n 116_o chap._n 19_o the_o description_n and_o use_n of_o a_o great_a quadrant_n for_o observation_n of_o the_o sun_n on_o land_n 120_o a_o table_n of_o observation_n of_o the_o sun_n meridian_n altitude_n take_v by_o the_o foresay_a quadrant_n in_o the_o year_n 1594_o 1595_o 1596_o 1597_o at_o london_n  _fw-fr chap._n 20._o the_o find_n of_o the_o sun_n apogeum_n and_o eccentricity_n out_o of_o the_o former_a observation_n 142_o to_o know_v the_o time_n of_o the_o sun_n come_v to_o any_o point_n of_o the_o ecliptic_a 142_o chap._n 21._o the_o middle_a motion_n of_o the_o sun_n correct_v out_o of_o the_o former_a observation_n 150_o a_o table_n of_o the_o sun_n middle_a motion_n 152_o chap._n 22._o a_o new_a theoric_n of_o the_o sun_n for_o the_o make_n of_o the_o table_n of_o the_o sun_n prosthaphaereses_n 154_o a_o table_n of_o the_o sun_n prosthaphaereses_n 157_o chap._n 23._o the_o make_n of_o the_o ephemerides_n of_o the_o sun_n 159_o chap._n 24._o how_o to_o reduce_v the_o apparent_a time_n to_o the_o equal_a time_n answer_v thereto_o 162_o a_o table_n of_o the_o aequation_n of_o natural_a day_n 162_o chap._n 25._o a_o table_n of_o aequation_n of_o the_o sun_n ephemerides_n to_o make_v they_o serve_v for_o many_o year_n 163_o ephemerides_n of_o the_o sun_n 164_o chap._n 26._o the_o use_n of_o these_o ephemerides_n 169_o chap._n 27._o the_o make_n of_o the_o table_n of_o the_o sun_n declination_n 170_o prosthaphaereses_n of_o the_o sun_n declination_n 172_o a_o table_n of_o the_o sun_n declination_n 173_o chap._n 28·_a the_o use_n of_o the_o former_a table_n of_o declination_n or_o regiment_n of_o the_o sun_n 181_o chap._n 29_o the_o declination_n of_o the_o principal_a fix_a star_n about_o the_o equinoctial_a correct_v by_o observation_n 183_o a_o table_n of_o fix_a star_n about_o the_o equinoctial_a 198_o chap._n 30._o the_o use_n of_o the_o former_a table_n 199_o chap._n 31._o the_o true_a distance_n of_o certain_a principal_a fix_a star_n from_o the_o north_n pole_n find_v by_o late_a observation_n 199_o chap._n 32._o to_o know_v at_o what_o time_n any_o of_o the_o foresay_a fix_a star_n come_v to_o the_o meridian_n for_o any_o day_n of_o the_o year_n 202_o a_o table_n of_o the_o sun_n right_a ascension_n in_o hour_n and_o minute_n for_o every_o day_n of_o the_o year_n 204_o chap._n 33._o by_o the_o former_a table_n of_o fix_a star_n and_o the_o sun_n right_a ascension_n to_o know_v the_o hour_n of_o the_o night_n at_o any_o time_n of_o the_o year_n 206_o chap._n 34._o of_o find_v the_o elevation_n of_o the_o pole_n by_o observation_n of_o the_o pole_n star_n and_o guard_n 207_o chap._n 35._o the_o description_n and_o part_n of_o the_o sea_n quadrant_n 208_o chap._n 36._o the_o description_n of_o the_o nocturnal_a or_o night_n dial_n 210_o chap._n 37._o the_o use_n of_o the_o sea_n quadrant_n first_o in_o observe_v the_o height_n of_o the_o sun_n look_v only_o to_o the_o horizon_n at_o sea_n 211_o chap._n 38._o how_o with_o this_o quadrant_n to_o observe_v the_o height_n of_o the_o sun_n with_o âour_n back_o turn_v towards_o the_o sun_n 211_o chap._n 39_o how_o to_o observe_v with_o this_o quadrant_n the_o height_n of_o the_o sun_n or_o star_n look_v both_o to_o the_o sun_n or_o star_n and_o to_o the_o horizon_n 212_o chap_n 40._o how_o to_o find_v the_o height_n of_o the_o pole_n by_o observation_n of_o the_o polestar_n and_o guard_n without_o give_v or_o take_v any_o allowance_n or_o abatement_n at_o any_o time_n when_o the_o polestar_n the_o guard_n and_o horizon_n may_v be_v see_v 213_o to_o know_v the_o hour_n of_o the_o night_n by_o the_o nocturnal_a 213_o a_o answer_n to_o simon_n stevin_n show_v his_o erorr_v in_o blame_v i_o of_o error_n in_o my_o table_n of_o rumb_n 214_o the_o content_n of_o the_o treatise_n of_o the_o art_n of_o navigation_n the_o division_n of_o the_o whole_a art_n of_o navigation_n pag._n 1_o chap._n 1._o the_o definition_n of_o the_o sphere_n 2_o 2._o that_o the_o whole_a world_n be_v a_o sphere_n 2_o 3._o of_o the_o division_n of_o the_o sphere_n 2_o 4._o of_o the_o motion_n of_o the_o heaven_n 4_o 5._o of_o the_o figure_n of_o the_o heaven_n 4_o 6._o that_o the_o earth_n and_o water_n make_v one_o perfect_a globe_n 5_o 7._o that_o the_o earth_n be_v in_o the_o centre_n of_o the_o world_n 5_o 8._o the_o whole_a quantity_n of_o the_o earth_n 5_o 9_o of_o the_o equinoctial_a circle_n 6_o 10._o of_o the_o pole_n of_o the_o world_n 6_o 11._o of_o the_o ecliptic_a line_n 7_o 12._o of_o the_o declination_n of_o the_o sun_n 7_o 13._o of_o the_o colour_n 8_o 14._o of_o the_o meridian_n circle_n 8_o 15._o of_o the_o horizon_n 9_o 16._o of_o the_o 32_o wind_n 10_o 17._o of_o the_o two_o tropic_n 12_o 18._o of_o the_o parallel_n 13_o 19_o of_o the_o degree_n 13_o 20._o what_o be_v mean_v by_o longitude_n and_o latitude_n 14_o the_o second_o part_n of_o the_o art_n of_o navigation_n wherein_o be_v handle_v the_o practic_n part_n show_v the_o make_n and_o use_n of_o the_o principal_a instrument_n belong_v to_o this_o art_n chap._n 1._o the_o make_n of_o the_o astrolabe_n pag._n 15_o chap._n 2._o of_o the_o height_n of_o the_o sun_n pag._n 17_o 3._o of_o the_o shadow_n 18_o 4._o of_o the_o regiment_n and_o rule_n of_o the_o sun_n 19_o 5._o of_o the_o declination_n of_o the_o sun_n and_o of_o the_o table_n thereof_o 20_o how_o the_o declination_n of_o the_o sun_n may_v be_v find_v out_o 21_o 6._o the_o equation_n of_o the_o sun_n declination_n 22_o 7._o four_o example_n for_o the_o plain_a declaration_n of_o that_o which_o be_v say_v before_o 22_o 8._o another_o manner_n of_o account_v by_o the_o sun_n as_o they_o use_v in_o portugal_n 25_o 9_o how_o the_o height_n of_o the_o sun_n may_v be_v know_v in_o any_o place_n whatsoever_o without_o a_o astrolabe_n first_o know_v your_o distance_n from_o the_o equinoctial_a 25_o 10._o the_o rule_n or_o regiment_n of_o the_o north-star_n for_o the_o knowledge_n of_o the_o height_n of_o the_o pole_n 26_o 11._o the_o make_n of_o the_o crosse-staffe_n 27_o 12._o of_o the_o position_n of_o the_o north-star_n and_o the_o guard_n 28_o 13._o of_o the_o height_n of_o the_o star_n take_v with_o the_o crosse-staffe_n 30_o 14._o the_o regiment_n or_o rule_n of_o the_o north_n star_n 30_o 15._o other_o thing_n to_o be_v note_v in_o observe_v the_o height_n of_o the_o pole_n 32_o 16._o of_o the_o crosier_n 34_o 17._o of_o the_o sea-compasse_n 34_o 18._o how_o the_o variation_n of_o the_o compass_n may_v be_v find_v 37_o the_o find_v of_o the_o meridian_n line_n 37_o 19_o of_o the_o sea-chart_n 38_o 20._o of_o the_o point_n of_o imagination_n 41_o 21._o of_o the_o traverse_n or_o geometrical_a point_n 42_o 22._o of_o the_o amend_v of_o the_o point_n of_o imagination_n 42_o the_o amend_v of_o the_o point_n of_o imagination_n by_o the_o traverse_n point_n 43_o the_o amendment_n of_o the_o point_n of_o imagination_n by_o north_n south_n east_n west_n 43_o 23._o the_o point_n by_o imagination_n and_o the_o height_n 44_o 24._o what_o it_o be_v to_o increase_v or_o diminish_v in_o height_n 45_o 25._o how_o you_o may_v cast_v a_o traverse_n point_n without_o compass_n 46_o 26._o of_o another_o kind_n of_o cast_v a_o point_n by_o traverse_n 46_o 27._o of_o the_o league_n which_o in_o navigation_n answer_v to_o each_o degree_n of_o latitude_n in_o every_o rumb_n 47_o chap._n 28._o how_o you_o may_v come_v to_o know_v the_o longitude_n or_o the_o course_n from_o east_n to_o west_n pag_n 48_o 29._o how_o you_o may_v set_v down_o in_o your_o chart_n a_o new_a land_n never_o before_o discover_v 50_o 30._o see_v two_o know_a point_n or_o cape_n of_o land_n as_o you_o sail_v along_o
how_o you_o may_v know_v the_o distance_n of_o the_o ship_n from_o they_o 51_o 31._o of_o the_o account_n of_o the_o moon_n 51_o the_o first_o rule_n of_o the_o golden_a number_n 53_o the_o second_o rule_n of_o the_o concurrent_a 53_o the_o three_o rule_n of_o the_o conjunction_n 53_o the_o four_o rule_n of_o the_o full_a and_o quarter_n of_o the_o moon_n 53_o the_o first_o rule_n of_o the_o springtide_n and_o neap-tide_n 54_o a_o example_n whereby_o the_o foresay_a rule_n be_v make_v more_o plain_a 54_o 32._o of_o the_o daily_a tide_n 55_o the_o first_o rule_n 56_o the_o second_o rule_n 56_o the_o three_o rule_n 56_o the_o four_o rule_n 56_o the_o five_o rule_n 57_o a_o example_n of_o the_o say_a rule_n 57_o 33._o of_o a_o certain_a instrument_n whereby_o you_o may_v in_o general_a judge_n of_o the_o tide_n 58_o the_o use_n of_o this_o instrument_n 59_o 34._o of_o the_o make_n of_o a_o universal_a dial_n which_o may_v serve_v general_o all_o the_o world_n over_o 60_o 35._o of_o the_o 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mi._n se_fw-la de._n mi._n se_fw-la de._n mi._n se_fw-la 0_o 34_o 0_o 23_o 3_o 10_o 0_o 30_o 0_o 1_o 26_o 0_o 24_o 2_o 50_o 1_o 21_o 30_o 2_o 20_o 0_o 25_o 2_o 30_o 2_o 15_o 30_o 3_o 17_o 0_o 26_o 2_o 15_o 3_o 12_o 30_o 4_o 15_o 30_o 27_o 2_o 0_o 4_o 11_o 0_o 5_o 14_o 30_o 28_o 1_o 45_o 5_o 10_o 0_o 6_o 13_o 30_o 29_o 1_o 35_o 6_o 9_o 0_o 7_o 12_o 45_o 30_o 1_o 25_o 7_o 8_o 15_o 8_o 11_o 15_o 31_o 1_o 15_o 8_o 6_o 45_o 9_o 10_o 30_o 32_o 1_o 5_o 9_o 6_o 0_o 10_o 10_o 0_o 33_o  _fw-fr 55_o 10_o 5_o 30_o 11_o 9_o 30_o 34_o  _fw-fr 45_o 11_o 5_o 0_o 12_o 9_o 0_o 35_o  _fw-fr 35_o 12_o 4_o 30_o 13_o 8_o 30_o 36_o  _fw-fr 30_o 13_o 4_o 0_o 14_o 8_o 0_o 37_o  _fw-fr 25_o 14_o 3_o 30_o 15_o 7_o 30_o 38_o  _fw-fr 20_o 15_o 3_o 0_o 16_o 7_o 0_o 39_o  _fw-fr 15_o 16_o 2_o 30_o 17_o 6_o 30_o 40_o  _fw-fr 10_o 17_o 2_o 0_o 18_o 5_o 45_o 41_o  _fw-fr 9_o 18_o 1_o 30_o 19_o 5_o 0_o 42_o  _fw-fr 8_o 19_o 1_o 0_o 20_o 4_o 30_o 43_o  _fw-fr 7_o 20_o 0_o 30_o 21_o 4_o 0_o 44_o  _fw-fr 6_o 21_o 0_o 0_o 22_o 3_o 30_o 45_o  _fw-fr 5_o  _fw-fr  _fw-fr  _fw-fr 1597_o to_o know_v the_o time_n of_o the_o sun_n come_v to_o any_o point_n of_o the_o ecliptick·_n pag._n 153._o pag._n 154._o pag._n 155._o by_o whole_a degree_n the_o first_o rumbe_n lon·_n latitu_fw-la gr_n m._n gr_n mi._n se._n 1_o 0_o 5_o 1_o 38_o 2_o 0_o 10_o 2_o 6_o by_o tin_n of_o min._n the_o first_o rumb_n lon·_n latitude_n gr_n m._n gr_n mi._n se._n the_o 0_o 10_o 0_o 50_o 16_o 23_o 0_o 20_o 1_o 40_o 32_o 26_o 0_o 30_o 2_o 30_o 47_o 33_o 0_o 40_o 3_o 21_o 1_o 5_o 0_o 50_o 4_o 11_o 12_o 16_o 1_o 0_o 5_o 1_o 20_o 46_o 1_o 10_o 5_o 51_o 25_o 35_o 1_o 20_o 6_o 41_o 26_o 18_o 1_o 30_o 7_o 31_o 22_o 14_o 1_o 40_o 8_o 21_o 12_o 38_o 1_o 50_o 9_o 10_o 57_o 0_o 2_o 0_o 10_o 0_o 34_o 40_o difference_n between_o the_o rumb_n and_o the_o wind_n the_o equinoctial_a be_v call_v the_o line_n because_o it_o be_v the_o principal_a of_o all_o other_o which_o be_v draw_v in_o the_o chart._n these_o league_n must_v be_v count_v in_o the_o equinoctial_a between_o the_o meridians_fw-la of_o the_o two_o place_n but_o it_o be_v better_a to_o find_v the_o difference_n of_o longitude_n for_o then_o as_o 360_o degree_n be_v to_o that_o difference_n so_o be_v the_o difference_n of_o declination_n to_o the_o equation_n desire_v in_o stead_n of_o all_o these_o rule_n of_o the_o north_n star_n which_o be_v erroneous_a use_v the_o table_n of_o equation_n of_o the_o pole_n star_n height_n set_v down_o in_o the_o latter_a end_n of_o this_o book_n book_n or_o rather_o increase_v proportional_o from_o the_o equinoctial_a line_n towards_o the_o north_n &_o south_n this_o for_o the_o most_o part_n be_v not_o true_a in_o the_o ordinary_a sea-chart_n these_o day_n mention_v in_o this_o example_n be_v to_o be_v understand_v according_a to_o the_o new_a roman_a gregorian_n calendar_n which_o go_v always_o ten_o day_n before_o we_o use_v in_o england_n the_o use_n of_o this_o table_n equinoctal_n equinoctial_a