Selected quad for the lemma: day_n

Word A Word B Word C Word D Occurrence Frequency Band MI MI Band Prominent
day_n eclipse_n hour_n minute_n 17,598 5 14.3206 5 true
View all documents for the selected quad

Text snippets containing the quad

ID Title Author Corrected Date of Publication (TCP Date of Publication) STC Words Pages
A15751 The description and vse of the sphaere· Deuided into three principall parts. Whereof the first intreateth especially of the circles of the vppermost moueable sphære, and of the manifold vses of euery one of them seuerally. The second sheweth the plentifull vse of the vppermost sphære, and of the circles thereof joyntly. The third contayneth the description of the orbes whereof the sphæres of the sunne and moone haue been supposed to bee made, with their motions and vses. By Edvvard Wright. The contents of each part are more particularly set downe in the table. Wright, Edward, 1558?-1615. 1627 (1627) STC 26022; ESTC S120334 50,441 102

There are 11 snippets containing the selected quad. | View original text

centre_n than_o the_o centre_n of_o the_o earth_n and_o therefore_o that_o the_o circle_n or_o orb_n wherein_o the_o sun_n be_v move_v be_v a_o eccentricke_a chap._n vii_o of_o the_o use_n of_o the_o sun_n eccentrical_a orb_n therefore_o the_o use_n of_o the_o sun_n eccentricke_a may_v be_v these_o 1._o first_o to_o show_v the_o reason_n of_o the_o apparent_a inequality_n which_o seem_v to_o be_v in_o the_o motion_n of_o the_o sun_n for_o although_o the_o sun_n mo●e_n equal_o in_o his_o own_o obbe_n and_o about_o his_o own_o centre_n yet_o to_o they_o that_o be_v at_o the_o centre_n of_o the_o world_n or_o upon_o the_o earth_n he_o shall_v seem_v to_o move_v unequal_o that_o be_v swift_o when_o he_o be_v in_o that_o part_n of_o his_o eccentricke_a which_o be_v near_a unto_o the_o earth_n and_o slow_o when_o he_o be_v far_o from_o the_o earth_n and_o therefore_o in_o summer_n when_o the_o sun_n be_v about_o his_o apogaeum_n and_o in_o his_o great_a distance_n from_o the_o earth_n he_o seem_v to_o move_v little_a above_o 57_o min._n in_o one_o day_n but_o in_o winter_n be_v about_o his_o perigaeum_n and_o near_a unto_o the_o earth_n he_o seem_v to_o move_v more_o than_o 16._o minute_n whereas_o notwithstanding_o he_o move_v equal_o in_o his_o eccentricke_a every_o day_n about_o nine_o and_o fifty_o minute_n and_o 8._o second_n and_o so_o finish_v his_o revolution_n in_o 365._o day_n and_o six_o hour_n almost_o 2._o the_o second_o use_n of_o the_o sun_n eccentricke_a may_v be_v to_o show_v the_o reason_n why_o the_o sun_n appear_v great_a at_o one_o time_n then_o at_o another_o for_o the_o sun_n be_v in_o those_o part_n of_o the_o eccentrick_a that_o be_v near_a unto_o we_o seem_v great_a and_o when_o he_o be_v in_o those_o part_n of_o his_o eccentrick_a that_o be_v further_a from_o we_o he_o appear_v to_o be_v least_o 3._o and_o last_o the_o inequality_n of_o the_o sun_n distance_n from_o the_o earth_n cause_v by_o his_o eccentrick_a be_v one_o especial_a cause_n of_o the_o inequality_n of_o the_o eclipse_n both_o of_o the_o sun_n and_o moon_n chap._n viii_o the_o definition_n of_o certain_a astronomical_a word_n of_o art_n for_o the_o better_a understanding_n of_o the_o theoric_n of_o the_o sun_n 1._o what_o the_o aux_fw-fr or_o apogaeum_n of_o the_o sun_n be_v it_o have_v be_v partly_o show_v already_o that_o ●●mely_o it_o be_v that_o part_n or_o rather_o point_n of_o the_o orb_n carry_v the_o sun_n apogaeum_n wherein_o the_o say_a orb_n be_v thin_a or_o narrow_a or_o it_o be_v that_o point_n of_o the_o eccentrick_a which_o be_v further_a distant_a from_o the_o earth_n and_o be_v always_o show_v by_o a_o right_a line_n understand_v to_o be_v draw_v from_o the_o centre_n of_o the_o world_n by_o the_o centre_n of_o the_o eccentrick_a unto_o the_o orb_n carry_v the_o sun_n apogaeum_n which_o line_n be_v therefore_o call_v the_o line_n of_o the_o sun_n his_o aux_fw-fr or_o the_o line_n of_o the_o sun_n apogaeum_n 2._o the_o motion_n of_o the_o aux_fw-fr or_o of_o the_o apogaeum_n of_o the_o sun_n which_o be_v also_o call_v the_o sun_n aux_fw-fr in_o the_o second_o signification_n be_v nothing_o else_o but_o the_o arch_n of_o the_o ecliptic_a contain_v between_o the_o beginning_n of_o aries_n and_o the_o line_n of_o the_o sun_n apogaeum_n draw_v forth_o to_o the_o zodiac_n where_o this_o line_n also_o show_v the_o place_n of_o the_o sun_n apogaeum_n 3._o the_o middle_a or_o mean_a place_n of_o the_o sun_n in_o the_o zodiac_n be_v show_v by_o a_o line_n draw_v from_o the_o centre_n of_o the_o world_n unto_o the_o zodiac_n equidistant_a from_o the_o centre_n of_o the_o eccentricke_a and_o of_o the_o sun_n 4._o this_o line_n be_v therefore_o call_v the_o line_n of_o the_o mean_a or_o middle_a place_n of_o the_o sun_n 5._o the_o middle_a or_o mean_a motion_n of_o the_o sun_n be_v the_o arch_n of_o the_o ecliptic_n between_o the_o beginning_n of_o aries_n and_o the_o middle_a place_n of_o the_o sun_n 6._o the_o true_a place_n of_o the_o sun_n be_v show_v by_o a_o straight_a line_n draw_v from_o the_o centre_n of_o the_o earth_n by_o the_o centre_n of_o the_o sun_n unto_o the_o zodiac_n which_o line_n be_v therefore_o call_v the_o line_n of_o the_o true_a place_n of_o the_o sun_n 7._o the_o true_a motion_n of_o the_o sun_n be_v the_o arch_n of_o the_o ecliptic_n from_o the_o begin_n of_o aries_n unto_o the_o true_a place_n of_o the_o sun_n 8._o the_o argument_n of_o the_o sun_n at_o the_o 〈◊〉_d ●erme_v it_o or_o the_o motion_n of_o the_o sun_n anomaly_n as_o copernicus_n call_v it_o be_v the_o arch_n of_o the_o ecliptic_n contain_v between_o the_o place_n of_o the_o sun_n apogaeum_n and_o the_o middle_a place_n of_o the_o sun_n according_a to_o the_o order_n and_o succession_n of_o the_o sign_n this_o arch_n be_v call_v the_o argument_n or_o motion_n of_o the_o sun_n anomaly_n or_o irregularity_n because_o that_o by_o it_o be_v always_o find_v how_o much_o the_o sun_n true_a motion_n which_o be_v unequal_a and_o irregular_a differ_v from_o his_o middle_a motion_n which_o difference_n they_o call_v the_o sun_n equation_n or_o prosthapheresis_fw-la 9_o the_o equation_n or_o prosthapheresis_fw-la of_o the_o sun_n be_v nothing_o else_o but_o the_o arch_n of_o the_o ecliptic_n contain_v between_o the_o true_a and_o middle_a place_n of_o the_o sun_n this_o arch_n be_v call_v the_o sun_n equation_n because_o it_o make_v the_o sun_n middle_a motion_n equal_a to_o his_o true_a motion_n be_v add_v to_o it_o or_o subtract_v from_o it_o as_o occasion_n require_v for_o which_o cause_n it_o be_v more_o significant_o and_o fit_o call_v prosthaphaeresis_fw-la that_o be_v as_o much_o to_o say_v as_o that_o which_o be_v to_o be_v add_v to_o or_o subtract_v from_o the_o middle_a motion_n that_o so_o we_o may_v have_v the_o true_a motion_n for_o so_o long_o as_o the_o sun_n be_v in_o the_o semicircle_n of_o his_o eccentrick_a descend_v from_o his_o apogaeum_n to_o his_o ●●●gaeum_n so_o long_o this_o prosthapheresis_fw-la be_v to_o be_v subtract_v from_o the_o middle_a motion_n but_o the_o sun_n be_v in_o the_o other_o half_n of_o his_o eccentrick_a ascend_n the_o prosthapheresis_fw-la or_o equation_n of_o the_o sun_n must_v be_v add_v to_o the_o middle_a motion_n that_o 〈…〉_z motion_n and_o place_n of_o the_o sun_n may_v be_v find_v because_o that_o in_o the_o first_o semicircle_n of_o the_o eccentricke_a descend_v the_o middle_a place_n of_o the_o sun_n go_v before_o the_o 〈◊〉_d and_o the_o middle_a motion_n be_v 〈…〉_z great_a 〈…〉_z the_o sun_n and_o therefore_o the_o difference_n of_o these_o 〈◊〉_d motion_n that_o be_v to_o say_v the_o 〈◊〉_d or_o prosthaphaeresis_fw-la must_v be_v subtract_v to_o find_v 〈…〉_z for_o the_o true_a place_n of_o the_o sun_n go_v always_o 〈…〉_z motion_n and_o place_n of_o the_o same_o chap._n ix_o of_o the_o uppermost_a orb_n of_o the_o sphere_n of_o the_o moon_n carry_v the_o dragon_n head_n and_o tail_n next_o within_o the_o orb_n of_o the_o sun_n in_o this_o sphere_n be_v contain_v the_o orb_n of_o the_o sphere_n of_o the_o moon_n which_o 〈…〉_z in_o number_n the_o uppermost_a of_o they_o which_o in_o this_o sphere_n be_v next_o under_o the_o orb_n that_o carry_v the_o sun_n perigaeum_n and_o be_v colour_v with_o red_a be_v call_v the_o caryer_n of_o the_o dragon_n head_n and_o tail_n or_o 〈…〉_z which_o be_v as_o much_o to_o say_v as_o the_o caryer_n of_o the_o knot_n that_o be_v of_o the_o two_o intersection_n or_o point_n wherein_o the_o rest_n of_o the_o orb_n of_o the_o moon_n do_v cross_v overthwart_a this_o orb_n this_o orb_n be_v divide_v into_o four_o ninety_n of_o degree_n for_o the_o easy_a reckon_n of_o the_o motion_n and_o place_n of_o the_o dragon_n head_n or_o tail_n in_o this_o sphere_n and_o it_o be_v move_v about_o in_o 18._o julian_n year_n 224._o day_n 3._o hour_n and_o 5._o minute_n almost_o from_o the_o east_n westward_n under_o the_o ecliptic_n by_o reason_n of_o this_o motion_n it_o come_v to_o pass_v that_o the_o eclipse_n or_o rather_o the_o place_n wherein_o the_o eclipse_n of_o the_o sun_n or_o moon_n do_v happen_v in_o the_o heaven_n be_v remove_v continual_o more_o backward_o in_o the_o zodiac_n contrary_a to_o the_o order_n and_o succession_n of_o the_o sign_n as_o for_o example_n the_o eclipse_n of_o the_o moon_n happen_v this_o present_a year_n 1600._o the_o 20._o of_o januarie_n near_o unto_o the_o dragon_n tail_n about_o the_o 9_o degree_n and_o 40._o min._n of_o leo_n the_o next_o eclipse_n that_o shall_v happen_v near_o the_o same_o intersection_n of_o the_o dragon_n tail_n in_o the_o year_n 1601._o the_o 29._o of_o november_n shall_v be_v in_o 17._o degree_n and_o a_o half_a of_o
that_o degree_n and_o the_o equinoctial_a to_o be_v 14._o degree_n and_o about_o 51._o minute_n prop._n four_o to_o know_v the_o right_a ascension_n of_o the_o sun_n etc._n etc._n bring_v that_o point_n as_o before_o to_o the_o meridian_n and_o see_v then_o how_o many_o degree_n and_o minute_n of_o the_o equinoctial_a be_v contain_v between_o the_o beginning_n of_o aries_n and_o the_o meridian_n for_o that_o be_v the_o right_a ascension_n of_o that_o point_n so_o you_o shall_v find_v the_o right_a ascension_n of_o the_o 10._o degr_n of_o taurus_n to_o be_v 37._o degr_n 35._o min._n for_o if_o you_o bring_v that_o degree_n of_o taurus_n to_o the_o meridian_n you_o shall_v find_v so_o many_o degree_n and_o min._n between_o the_o begin_n of_o aries_n and_o the_o meridian_n prop._n v._o to_o know_v the_o oblique_a ascension_n of_o the_o sun_n etc._n etc._n set_v the_o sphere_n to_o the_o elevation_n of_o the_o place_n for_o which_o you_o desire_v to_o know_v the_o oblique_a ascension_n then_o bring_v the_o sun_n star_n or_o point_n who_o oblique_a ascension_n you_o will_v know_v unto_o the_o east_n semicircle_n of_o the_o horizon_n and_o look_v how_o many_o degree_n and_o minute_n of_o the_o equinoctial_a circle_n be_v contain_v between_o the_o east_n point_n of_o the_o horizon_n and_o the_o beginning_n of_o aries_n for_o so_o much_o be_v the_o oblique_a ascension_n desire_v as_o for_o example_n if_o you_o see_v the_o sphere_n to_o the_o latitude_n of_o london_n 51._o degr_n 32._o min._n and_o then_o bring_v the_o 10._o degree_n of_o taurus_n to_o the_o east_n part_n of_o the_o horizon_n you_o shall_v find_v about_o 19_o degree_n and_o a_o half_a of_o the_o equinoctial_a at_o the_o same_o east_n part_n of_o the_o horizon_n which_o be_v the_o oblique_a ascension_n of_o that_o degree_n of_o taurus_n for_o the_o latitude_n of_o the_o city_n of_o london_n prop._n vi_o to_o find_v the_o difference_n of_o ascension_n compare_v the_o right_a and_o oblique_a ascension_n of_o the_o sun_n or_o of_o any_o point_n of_o the_o zodiac_n together_o and_o subtract_v the_o less_o from_o the_o great_a for_o the_o remainder_n shall_v be_v the_o difference_n of_o ascension_n as_o for_o example_n the_o right_a ascension_n of_o the_o 10._o degree_n of_o taurus_n be_v find_v by_o the_o 4._o propo._n to_o be_v 37._o degree_n 35._o min._n and_o the_o oblique_a ascension_n of_o the_o same_o degree_n at_o london_n by_o the_o 5._o prop._n 19_o degree_n 30._o min._n by_o subtraction_n of_o the_o less_o out_o of_o the_o great_a the_o difference_n shall_v be_v find_v to_o be_v 18._o degr_n and_o 5._o minute_n which_o be_v the_o difference_n of_o ascension_n seek_v for_o prop._n vii_o to_o find_v at_o what_o time_n the_o sun_n rise_v or_o set_v reduce_v the_o difference_n of_o ascension_n into_o hour_n and_o minute_n take_v for_o every_o 15_o degree_n 1._o hour_n and_o for_o every_o one_o degree_n that_o remain_v 4._o minute_n and_o for_o every_o minute_n of_o a_o degree_n 4_o second_n for_o these_o hour_n minute_n and_o second_n be_v add_v to_o 6._o hour_n if_o the_o sun_n be_v in_o any_o of_o the_o south_n sign_n or_o subtract_v if_o he_o be_v in_o the_o north_n sign_n show_v the_o time_n of_o the_o sunrising_n and_o contrariwise_o the_o same_o hour_n and_o minute_n subtract_v from_o six_o hour_n when_o the_o sun_n be_v in_o the_o south_n sign_n or_o add_v when_o he_o be_v in_o the_o north_n sign_n show_v the_o the_o time_n of_o the_o sunne-setting_a as_o for_o example_n the_o sun_n be_v in_o the_o 10._o degree_n of_o taurus_n which_o happen_v about_o the_o 20._o or_o 21._o day_n of_o april_n i_o will_v know_v at_o what_o hour_n and_o minute_n the_o sun_n rise_v and_o set_v at_o london_n have_v therefore_o find_v by_o the_o former_a proposition_n the_o difference_n of_o ascension_n to_o be_v 18._o degr_n and_o 5._o minute_n i_o take_v for_o 15._o degree_n thereof_o one_o hour_n and_o for_o the_o three_o degr_n remain_v 12._o minute_n of_o a_o hour_n and_o for_o the_o 5._o minute_n 20._o second_n of_o a_o hour_n which_o hour_n minute_n and_o second_n be_v subtract_v out_o of_o 6._o hour_n because_o the_o sun_n be_v in_o a_o north_n sign_n there_o remain_v the_o time_n of_o the_o sun_n rise_v at_o 4._o a_o clock_n 47._o minute_n 40._o second_n and_o add_v the_o same_o hour_n min._n and_o second_o to_o 6._o hour_n you_o have_v the_o time_n of_o the_o sunsetting_a that_o day_n at_o 7._o a_o clock_n 12._o min._n and_o 20._o second_n prop._n viii_o to_o find_v the_o length_n of_o the_o artificial_a day_n or_o night_n the_o artificial_a day_n be_v the_o time_n contain_v between_o the_o sunrising_n and_o the_o sunsetting_a and_o the_o artificial_a night_n be_v the_o time_n between_o sunne-setting_a and_o sunrising_n the_o length_n of_o both_o these_o be_v find_v after_o this_o manner_n have_v find_v the_o difference_n of_o ascension_n and_o reduce_v it_o into_o hour_n and_o minute_n as_o in_o the_o former_a proposition_n double_v th●se_a hour_n and_o minute_n and_o add_v they_o to_o 12._o hour_n if_o the_o sun_n be_v in_o the_o north_n sign_n or_o subtract_v they_o from_o 12._o hour_n if_o the_o sun_n be_v in_o the_o south_n sign_n for_o so_o shall_v you_o have_v the_o length_n of_o the_o day_n but_o contrariwise_o subtract_v the_o same_o hour_n and_o minute_n be_v double_v from_o 12._o hour_n the_o sun_n be_v in_o the_o north_n sign_n and_o add_v they_o to_o 12._o hour_n when_o he_o be_v in_o the_o south-signe_n so_o have_v you_o the_o length_n of_o the_o night_n or_o else_o double_v the_o time_n of_o the_o sunsetting_a so_o have_v you_o the_o length_n of_o the_o day_n and_o double_v the_o time_n of_o the_o sunrising_n so_o have_v you_o the_o length_n of_o the_o right_n as_o the_o time_n of_o the_o sunrising_n be_v find_v by_o the_o former_a proposition_n to_o be_v 4_o hour_n 48._o minute_n after_o mignight_n at_o london_n the_o sun_n be_v in_o the_o 10._o degr_n of_o taurus_n by_o double_v the_o time_n of_o the_o sunrising_n the_o length_n of_o the_o night_n shall_v be_v find_v to_o be_v 9_o hour_n and_o 36._o minute_n and_o double_v the_o time_n of_o the_o sunset_n that_o be_v 7._o hour_n and_o 12._o minute_n you_o have_v the_o length_n of_o the_o day_n 14._o hour_n and_o 24._o minute_n prop._n ix_o to_o know_v the_o time_n of_o the_o sun_n rise_v and_o sun_n set_v the_o place_n of_o the_o sun_n be_v find_v by_o the_o 2._o proposition_n bring_v the_o same_o to_o the_o meridian_n and_o withal_o set_v the_o point_n of_o the_o index_n of_o the_o hour_n circle_n to_o the_o 12._o hour_n in_o the_o same_o circle_n then_o bring_v the_o place_n of_o the_o sun_n to_o the_o horizon_n eastward_n and_o the_o point_n of_o the_o hour_n index_n shall_v show_v you_o in_o the_o hour_n circle_n the_o time_n of_o the_o sunrising_n but_o if_o you_o bring_v the_o place_n of_o the_o sun_n to_o the_o horizon_n westward_n the_o point_n of_o the_o index_n will_v show_v in_o the_o hour_n circle_v the_o time_n of_o the_o sunsetting_a as_o for_o example_n the_o sun_n be_v in_o the_o 10._o degree_n of_o taurus_n bring_v the_o same_o degree_n to_o the_o meridian_n and_o bring_v the_o point_n of_o the_o hour_n index_n also_o to_o the_o meridian_n then_o the_o sphere_n be_v set_v to_o the_o latitude_n of_o london_n bring_v the_o same_o 10._o degree_n of_o taurus_n to_o the_o east_n part_n of_o the_o horizon_n for_o then_o the_o hour_n index_n will_v show_v you_o in_o the_o hour_n circle_n that_o the_o sun_n rise_v at_o 4._o of_o the_o clock_n and_o 48._o minute_n and_o bring_v the_o same_o degree_n to_o the_o west_n semicircle_n of_o the_o horizon_n the_o same_o index_n will_v show_v the_o time_n of_o the_o sunsetting_a to_o be_v 7._o hour_n and_o 12._o min._n after_o noon_n prop._n x._o to_o find_v the_o length_n of_o the_o artificial_a day_n or_o night_n bring_v the_o place_n of_o the_o sun_n be_v find_v as_o before_o to_o the_o east_n semicircle_n of_o the_o horizon_n set_v the_o hour_n index_n 12._o a_o clock_n in_o the_o hour_n circle_n turn_v about_o the_o sphere_n from_o the_o east_n westward_n till_o the_o place_n of_o the_o sun_n come_v to_o the_o horizon_n and_o mark_v how_o many_o hour_n the_o index_n have_v run_v over_o upon_o the_o hour_n circle_n in_o the_o mean_a time_n for_o so_o much_o be_v the_o length_n of_o the_o day_n and_o to_o find_v the_o length_n of_o the_o night_n bring_v the_o place_n of_o the_o sun_n to_o the_o west_n semicircle_n of_o the_o horizon_n and_o set_v the_o index_n to_o 12._o a_o clock_n as_o before_o then_o turn_v forward_o the_o sphere_n from_o east_n westward_o till_o the_o place_n of_o the_o sun_n come_v to_o
the_o sun_n turn_v the_o sphere_n westward_n till_o you_o can_v but_o only_o touch_v the_o horizon_n with_o the_o other_o foot_n for_o then_o the_o index_n show_v in_o the_o hour_n circle_n at_o what_o time_n the_o day_n break_v so_o the_o 21._o of_o april_n the_o sun_n be_v in_o the_o 10_o degr_n of_o taurus_n you_o shall_v find_v that_o the_o day_n break_v about_o half_a a_o hour_n past_o 2._o of_o the_o clock_n in_o the_o morning_n prop._n xviii_o to_o find_v how_o long_o the_o twilight_n continue_v find_v out_o by_o the_o former_a prop._n at_o what_o time_n the_o day_n break_v and_o learn_v also_o at_o what_o time_n the_o sun_n rise_v by_o the_o 7._o or_o 9_o prop._n then_o subtract_v the_o lesser_a from_o the_o great_a and_o there_o shall_v remain_v the_o length_n of_o the_o twilight_n or_o else_o thus_o have_v bring_v the_o point_n that_o be_v opposite_a to_o the_o place_n of_o the_o sun_n to_o be_v 17._o degree_n above_o the_o horizon_n westward_n in_o such_o sort_n as_o be_v show_v in_o the_o former_a proposition_n and_o keep_v the_o sphere_n in_o that_o position_n bring_v about_o the_o point_n of_o the_o hour_n index_n unto_o 12._o a_o clock_n upon_o the_o hour_n circle_n then_o tune_v the_o sphere_n westward_n until_o the_o degree_n or_o point_n of_o the_o ecliptic_a that_o be_v opposite_a to_o the_o place_n of_o the_o sun_n come_v to_o the_o horizon_n and_o see_v how_o many_o hour_n the_o point_n of_o the_o index_n have_v run_v over_o in_o the_o mean_a time_n upon_o the_o hour_n circle_n for_o so_o many_o hour_n continue_v the_o twilight_n by_o either_o of_o these_o way_n the_o sun_n be_v in_o the_o 10._o degr_n of_o taurus_n you_o shall_v find_v that_o the_o twilight_n that_o be_v the_o time_n from_o the_o break_n of_o the_o day_n till_o sun-rise_n be_v about_o 2._o hour_n and_o 20._o minute_n prop._n xix_o to_o find_v how_o much_o the_o declination_n of_o the_o sun_n must_v alter_v at_o any_o time_n of_o the_o year_n to_o make_v the_o day_n a_o hour_n long_o or_o short_a bring_v the_o place_n of_o the_o sun_n find_v by_o the_o second_o prop._n to_o the_o east_n semicircle_n of_o the_o horizon_n and_o mark_v what_o degree_n or_o point_n of_o the_o horizon_n it_o fall_v upon_o bring_v one_o of_o the_o colour_n to_o the_o same_o degree_n or_o point_n and_o there_o make_v a_o prick_n in_o that_o colour_n and_o hold_v the_o sphere_n immovable_a mark_v withal_o what_o degree_n of_o the_o equinoctial_a or_o of_o either_o of_o the_o tropicke_n be_v then_o at_o the_o horizon_n then_o turn_v the_o sphere_n 7._o degree_n and_o a_o half_a forward_o towards_o the_o west_n if_o the_o day_n shorten_v but_o contrariwise_o if_o the_o day_n lengthen_v and_o hold_v the_o sphere_n there_o immovable_a make_v another_o prick_n in_o the_o colour_n at_o the_o horizon_n for_o the_o distance_n of_o these_o two_o prick_v in_o the_o colour_n take_v with_o the_o compass_n and_o bring_v to_o the_o ecliptic_a or_o equinoctial_a show_v how_o much_o the_o sun_n declination_n must_v alter_v to_o make_v the_o day_n a_o hour_n long_o if_o the_o day_n increase_n or_o short_a if_o they_o decrease_v after_o this_o manner_n you_o shall_v find_v that_o the_o sun_n be_v in_o the_o 10._o degree_n of_o taurus_n his_o declination_n must_v increase_v about_o 5._o degree_n or_o little_o more_o to_o make_v the_o day_n a_o hour_n long_o but_o when_o the_o sun_n be_v in_o the_o 20._o degree_n of_o pisces_fw-la his_o declination_n or_o rather_o his_o meridian_n altitude_n must_v increase_v about_o 6._o degree_n to_o make_v the_o day_n a_o hour_n long_o and_o when_o he_o be_v in_o the_o begin_n of_o capricorn_n his_o declination_n decrease_v scarce_o 5._o degree_n to_o make_v the_o day_n a_o hour_n long_o prop._n xx._n to_o find_v how_o many_o day_n it_o be_v ere_o the_o day_n lengthen_v or_o shorten_v a_o hour_n bring_v the_o foresay_a prick_v make_v in_o the_o colour_n by_o the_o former_a proposition_n unto_o the_o meridian_n and_o there_o make_v two_o mark_n just_o answerable_a unto_o those_o prick_v in_o the_o colour_n turn_v about_o the_o sphere_n till_o the_o ecliptic_a line_n come_v just_a under_o one_o of_o those_o mark_n and_o there_o make_v a_o prick_n in_o the_o ecliptic_a then_o again_o turn_v the_o sphere_n till_o the_o ecliptic_a come_v just_a under_o the_o other_o mark_v make_v in_o the_o meridian_n and_o there_o make_v another_o prick_n in_o the_o ecliptic_a but_o here_o it_o be_v to_o be_v note_v that_o whereas_o the_o ecliptic_a may_v be_v bring_v under_o that_o mark_n whether_o way_n soever_o you_o turn_v the_o sphere_n it_o must_v i_o say_v be_v note_v that_o the_o sphere_n must_v be_v turn_v that_o way_n which_o may_v soon_o bring_v the_o ecliptic_a under_o that_o mark_n last_o find_v out_o among_o the_o sign_n and_o degree_n describe_v upon_o the_o horizon_n the_o like_a arch_n to_o this_o that_o be_v contain_v between_o these_o prick_v in_o the_o ecliptic_a for_o the_o number_n of_o day_n answerable_a to_o this_o arch_n in_o the_o horizon_n be_v the_o time_n wherein_o the_o day_n grow_v a_o hour_n long_o or_o short_a thus_o shall_v you_o find_v that_o when_o the_o sun_n be_v in_o the_o begin_n of_o aries_n it_o will_v be_v about_o 18._o day_n after_o ere_o the_o day_n be_v one_o hour_n long_o but_o when_o the_o sun_n be_v in_o the_o begin_n of_o capricorn_n you_o shall_v find_v that_o it_o will_v be_v almost_o twice_o so_o much_o that_o be_v near_o 34._o day_n before_o the_o day_n will_v be_v a_o hour_n long_o hereby_o therefore_o the_o error_n of_o they_o manifest_o appear_v which_o think_v that_o in_o every_o 15._o day_n the_o day_n be_v lengthen_v or_o shorten_v a_o hour_n whereas_o indeed_o the_o lengthen_v or_o shorten_v of_o the_o day_n keep_v no_o such_o rule_n for_o when_o the_o sun_n be_v about_o the_o equinoctial_a point_n the_o day_n lenghthen_v or_o shorten_v very_o fast_o but_o when_o he_o be_v near_o the_o tropical_a point_n they_o grow_v long_o or_o short_a very_o slow_o prop._n xxi_o to_o make_v a_o horizontall_a dial_n set_v the_o sphere_n to_o the_o elevation_n of_o the_o place_n for_o which_o you_o will_v make_v the_o dial_n turn_v about_o the_o sphere_n till_o the_o solstitial_a colour_n be_v 15._o degree_n measure_v in_o the_o equinoctial_a from_o the_o meridian_n and_o where_o the_o colour_n cross_v the_o horizon_n there_o make_v a_o prick_n then_o turn_v the_o colour_n yet_o 15._o degr_n further_o that_o be_v 30._o degree_n from_o the_o meridian_n and_o where_o the_o colour_n cross_v the_o horizon_n there_o make_v a_o other_o prick_n again_o turn_v the_o colour_n forward_o yet_o 15._o deg_n more_o that_o be_v 45._o degree_n from_o the_o meridian_n and_o at_o the_o common_a meeting_n of_o the_o colour_n and_o horizon_n make_v the_o three_o prick_n in_o the_o horizon_n and_o so_o proceed_v with_o the_o rest_n till_o you_o have_v make_v so_o many_o prick_n on_o that_o side_n of_o the_o horizon_n as_o there_o be_v hour_n in_o halse_a the_o long_a day_n then_o look_v how_o many_o degree_n the_o first_o second_o three_o four_o prick_v etc._n etc._n be_v from_o the_o meridian_n for_o so_o many_o degree_n must_v the_o hour_n line_n of_o 11._o a_o clock_n and_o one_o a_o clock_n of_o 10._o and_o 2_o of_o 9_o and_o 3._o of_o 8._o and_o 4._o etc._n etc._n be_v from_o the_o 12._o a_o clock_n line_n in_o the_o horizontall_a dial_n after_o this_o manner_n in_o a_o horizontall_a dial_n make_v for_o the_o latitude_n of_o london_n which_o be_v 51._o degr_n and_o 32._o minute_n you_o shall_v find_v the_o distance_n of_o all_o the_o rest_n of_o the_o houre-line_n from_o the_o 12._o a_o clock_n line_n as_o follow_v betwixt_o twelve_o and_o 11._o and_o twelve_o and_o 1._o be_v conceyn_v 12._o degree_n almost_o between_o 12._o and_o 10._o and_o 12._o and_o 2._o there_o be_v contain_v 14._o degr_n and_o a_o half_a between_o 12._o and_o 9_o and_o 12._o and_o 3._o 38._o degr_n between_o 12._o and_o 8._o and_o 12._o and_o 4._o 53._o degr_n between_o 12._o and_o 7._o and_o 12._o and_o 5._o 70._o degree_n and_o a_o half_a between_o 12._o and_o 6._o both_o before_o and_o after_o noon_n 90._o degr_n the_o other_o hour_n space_n before_o 6._o in_o the_o morning_n and_o after_o 6._o in_o the_o evening_n be_v equal_a to_o the_o hour_n space_n after_o six_o in_o the_o morning_n and_o before_o 6._o in_o the_o afternoon_n prop._n xxii_o how_o to_o make_v a_o direct_a mural_a dial_n set_v the_o pole_n arctic_a of_o the_o sphere_n so_o much_o under_o the_o horizon_n as_o be_v the_o compliment_n of_o the_o pole_n elevation_n the_o horizon_n therefore_o be_v thus_o set_v as_o it_o be_v to_o the_o zenith_n of_o the_o sphere_n and_o
27._o day_n of_o may_n it_o our_o latitude_n of_o london_n the_o bull_n eye_n rise_v cosmical_o and_o the_o star_n in_o serpentarius_n his_o right_a foot_n set_v cosmical_o you_o may_v see_v also_o that_o the_o same_o day_n the_o star_n in_o the_o bull_n south_n horn_n set_v achronycal_o and_o the_o northermost_a star_n in_o serpentarius_n his_o right_a foot_n rise_v achronycal_o and_o last_o you_o may_v find_v that_o about_o the_o same_o time_n the_o pleiade_n and_o the_o star_n in_o the_o bull_n north_n home_o rise_v heliacal_o and_o that_o the_o same_o star_n also_o and_o the_o former_a twin_n foot_n set_v heliacal_o prop._n xxx_o to_o find_v the_o four_o principal_a or_o cardinal_a point_n of_o heaven_n as_o the_o astrologian_n call_v they_o at_o any_o time_n these_o four_o cardinal_n point_n be_v nothing_o else_o but_o four_o point_n of_o the_o ecliptic_a whereof_o one_o be_v at_o the_o east_n part_n of_o the_o horizon_n ascend_v and_o be_v therefore_o call_v the_o ascendent_n another_o be_v at_o the_o upper_a part_n of_o the_o meridian_n above_o the_o horizon_n and_o be_v call_v the_o midst_n of_o heaven_n and_o the_o hart_n of_o heaven_n the_o three_o be_v at_o the_o west_n part_n of_o the_o horizon_n descend_v and_o may_v be_v therefore_o call_v the_o descendent_a the_o four_o point_n be_v that_o which_o be_v at_o the_o nether_a part_n of_o the_o meridian_n under_o the_o horizon_n which_o four_o point_n be_v the_o beginning_n of_o the_o first_o ten_o seven_o and_o four_o house_n therefore_o to_o find_v these_o point_n at_o any_o time_n by_o the_o sphere_n bring_v the_o place_n of_o the_o sun_n be_v find_v for_o that_o time_n by_o the_o 2._o proposition_n to_o the_o meridian_n and_o the_o index_n to_o 12._o a_o clock_n then_o turn_v the_o sphere_n till_o the_o index_n come_v to_o that_o hour_n at_o which_o you_o desire_v to_o know_v those_o four_o point_n and_o there_o hold_v the_o sphere_n that_o it_o move_v not_o and_o look_v withal_o what_o point_v of_o the_o ecliptic_a be_v at_o the_o east_n and_o west_n semicircle_n of_o the_o horizon_n and_o at_o the_o upper_a and_o nether_a part_n of_o the_o meridian_n for_o those_o be_v the_o four_o principal_a or_o cardinal_n point_v you_o seek_v for_o take_v for_o example_n the_o time_n of_o the_o sun_n entrance_n into_o aries_n this_o present_a year_n 1600._o which_o be_v upon_o the_o ten_o day_n of_o march_n about_o eight_o of_o the_o clock_n in_o the_o morning_n or_o little_o after_o with_o we_o here_o at_o london_n have_v therefore_o bring_v the_o beginning_n of_o aries_n together_o with_o the_o hour_n index_n to_o the_o meridian_n and_o then_o turn_v back_o the_o whole_a sphere_n till_o the_o index_n come_v to_o 8._o of_o the_o clock_n upon_o the_o hour_n circle_n you_o shall_v find_v the_o ascendent_n at_o that_o time_n to_o be_v the_o 27._o degree_n of_o taurus_n the_o midst_n or_o hart_n of_o heaven_n the_o 27._o of_o capricorn_n the_o descendent_a the_o 27._o deg_n of_o scorpio_n and_o the_o low_a part_n of_o heaven_n the_o 27._o degree_n of_o cancer_n prop._n xxxi_o to_o find_v out_o the_o breadth_n of_o any_o climate_n etc._n etc._n lift_v up_o or_o put_v down_o the_o pole_n of_o the_o sphere_n till_o you_o find_v that_o there_o be_v 7._o deg_n and_o a_o half_a of_o the_o tropic_a of_o cancer_n more_o or_o less_o above_o the_o horizon_n than_o there_o be_v before_o and_o mark_v with_o all_o how_o much_o the_o pole_n of_o the_o sphere_n be_v raise_v or_o let_v fall_v in_o the_o mean_a time_n more_o than_o it_o be_v before_o for_o so_o much_o be_v the_o breadth_n of_o that_o climate_n as_o far_o example_n have_v set_v the_o sphere_n to_o our_o latitude_n of_o london_n of_o 51._o deg_n and_o a_o half_a with_o the_o point_n of_o your_o compass_n hold_v and_o guide_v some_o point_n of_o the_o tropic_a of_o cancer_n right_n under_o the_o horizon_n then_o lift_v up_o the_o pole_n till_o you_o find_v 7._o degree_n and_o a_o half_n more_o above_o the_o horizon_n than_o be_v before_o you_o shall_v find_v the_o pole_n elevate_v about_o 2._o degr_n and_o a_o half_n more_o than_o it_o be_v before_o likewise_o if_o you_o put_v down_o the_o pole_n till_o there_o be_v 7._o degree_n and_o a_o half_a of_o the_o tropic_n of_o cancer_n few_o above_o the_o horizon_n than_o be_v before_o you_o shall_v find_v the_o elevation_n of_o the_o pole_n to_o be_v about_o 3._o degree_n less_o than_o before_o prop._n xxxii_o the_o reason_n of_o the_o inequality_n of_o natural_a day_n etc._n etc._n the_o reason_n hereof_o be_v show_v partly_o by_o the_o inequality_n of_o the_o difference_n of_o right_a ascension_n answerable_a to_o equal_a arck_n of_o the_o zodiac_n and_o partly_o by_o the_o unequal_a apparent_a motion_n of_o the_o sun_n for_o the_o first_o the_o difference_n of_o right_a ascension_n answerable_a to_o the_o part_n of_o the_o ecliptic_a about_o the_o tropical_a point_n of_o cancer_n and_o capricorn_n be_v much_o great_a than_o about_o the_o equinoctial_a point_n of_o aries_n and_o libra_n in_o so_o much_o that_o whereas_o the_o difference_n of_o right_a ascension_n answerable_a to_o one_o sign_n or_o 30._o degree_n take_v about_o those_o tropical_a point_n be_v more_o than_o 32._o degree_n and_o a_o half_a about_o the_o equinoctial_a point_n it_o be_v little_o more_o than_o 27._o degree_n and_o a_o half_a as_o it_o may_v appear_v by_o the_o sphere_n so_o as_o you_o may_v hereby_o gather_v that_o the_o difference_n of_o ascension_n answerable_a to_o one_o degree_n which_o about_o the_o begin_n of_o capricorn_n be_v one_o degree_n and_o about_o 6._o minute_n about_o the_o begin_n of_o aries_n or_o libra_n be_v only_o 55_o minute_n second_o the_o apparent_a motion_n of_o the_o sun_n be_v much_o swift_a about_o his_o parig●●●_n in_o the_o sign_n of_o capricorn_n then_o about_o his_o apogaeum_n in_o cancer_n or_o in_o other_o part_n of_o the_o zodiac_n so_o that_o whereas_o the_o sun_n be_v in_o capricorn_n move_v 61._o minute_n and_o something_o more_o in_o a_o day_n in_o aries_n or_o libra_n he_o move_v but_o 59_o min._n or_o very_o little_a more_o in_o the_o same_o time_n therefore_o see_v the_o natural_a day_n be_v nothing_o else_o but_o the_o time_n wherein_o the_o sun_n move_v from_o the_o meridian_n about_o till_o it_o return_v again_o to_o the_o same_o part_n of_o the_o meridian_n it_o must_v needs_o be_v that_o always_o in_o one_o natural_a day_n there_o be_v make_v one_o whole_a revolution_n of_o the_o equinoctial_a circle_n and_o so_o much_o more_o as_o be_v the_o difference_n of_o right_a ascension_n answerable_a to_o the_o apparent_a motion_n of_o the_o sun_n in_o the_o mean_a time_n which_o difference_n of_o ascension_n because_o they_o be_v unequal_a for_o the_o two_o cause_n before_o allege_v the_o natural_a day_n must_v needs_o also_o be_v unequal_a the_o motion_n of_o the_o equinoctial_a circle_n about_o his_o own_o centre_n be_v as_o it_o have_v be_v always_o suppose_v to_o be_v equal_a that_o be_v move_v always_o a_o equal_a space_n in_o equal_a time_n which_o by_o this_o example_n may_v most_o plain_o appear_v the_o sun_n be_v in_o capricorn_n move_v 61._o minute_n in_o a_o natural_a day_n difference_n of_o ascension_n agreeable_a thereto_o be_v 67._o minute_n or_o something_o more_o therefore_o at_o that_o time_n in_o the_o space_n of_o one_o natural_a day_n the_o equinoctial_a circle_n must_v make_v one_o full_a revolution_n and_o 67._o minute_n more_o but_o when_o the_o sun_n be_v in_o aries_n move_v only_o 59_o minute_n in_o a_o day_n and_o the_o difference_n of_o right_a ascension_n answerable_a thereto_o scarce_o 54._o minute_n more_o than_o one_o revolution_n of_o the_o equinoctial_a circle_n there_o shall_v pass_v only_o 54._o minute_n more_o in_o a_o natural_a day_n so_o as_o here_o the_o equinoctial_a circle_n move_v not_o about_o so_o much_o in_o one_o day_n as_o before_o by_o 13._o minute_n see_v then_o that_o 15._o degr_n or_o little_o more_o of_o the_o equinoctial_a circle_n do_v pass_v the_o meridian_n in_o every_o hour_n and_o consequent_o one_o degree_n of_o the_o equinoctial_a pass_v the_o meridian_n in_o 4._o minute_n of_o a_o hour_n and_o one_o minute_n of_o a_o degree_n in_o 4._o second_n of_o a_o hour_n therefore_o 13._o minute_n of_o the_o equinoctial_a shall_v pass_v the_o meridian_n in_o 52._o second_n that_o be_v almost_o in_o one_o minute_n of_o a_o hour_n whereby_o it_o manifest_o appear_v that_o the_o natural_a day_n that_o be_v to_o say_v the_o space_n of_o 24._o hour_n which_o be_v the_o time_n wherein_o the_o sun_n move_v from_o the_o noonestead_n to_o the_o same_o noonestead_n again_o be_v in_o our_o age_n great_a almost_o by_o one_o minute_n of_o a_o hour_n when_o the_o sun_n be_v in_o capricorn_n then_o
gemini_fw-la and_o that_o eclipse_n which_o shall_v be_v the_o next_o year_n after_o near_a the_o same_o intersection_n the_o 19_o of_o november_n in_o the_o morning_n shall_v be_v about_o the_o 6._o degree_n and_o 40._o minute_n of_o gemini_fw-la etc._n etc._n all_o this_o remove_n of_o the_o eclipse_n backward_o come_v to_o pass_v by_o reason_n of_o the_o motion_n of_o this_o orb_n carry_v the_o dragon_n head_n and_o tail_n contrary_a to_o the_o course_n and_o order_n of_o the_o sign_n this_o orb_n continue_v always_o right_a under_o tail_n and_o even_o with_o the_o orb_n of_o the_o sphere_n of_o the_o sun_n which_o abide_v always_o in_o all_o part_n just_a under_o the_o ecliptic_a line_n and_o have_v his_o centre_n agree_v and_o all_o one_o with_o the_o centre_n of_o the_o world_n and_o of_o the_o ecliptic_n and_o therefore_o the_o pole_n and_o axtree_n about_o which_o this_o orb_n be_v turn_v agree_v just_o with_o the_o axtree_n of_o the_o ecliptic_a the_o rest_n of_o the_o orb_n of_o the_o moon_n orb_n that_o be_v contain_v within_o this_o have_v all_o their_o plain_n agree_v in_o one_o and_o lie_v even_o one_o with_o another_o but_o the_o one_o half_a of_o all_o their_o plain_n arise_v above_o the_o plain_n of_o the_o former_a orb_n and_o of_o the_o ecliptic_a towards_o the_o north_n pole_n of_o the_o zodiac_n and_o the_o other_o half_o descend_v beneath_o the_o plain_n of_o the_o ecliptic_n towards_o the_o south_n pole_n even_o as_o the_o one_o half_a of_o the_o zodiac_n arise_v above_o the_o equinoctial_a circle_n towards_o the_o north_n and_o the_o other_o half_o descend_v towards_o the_o south_n and_o as_o the_o angle_n of_o intersection_n or_o obliquity_n of_o the_o ecliptic_n with_o the_o equinoctial_a circle_n be_v 23._o degr_n and_o a_o half_a or_o little_o more_o so_o the_o angle_n of_o intersection_n or_o obliquity_n of_o the_o plain_n of_o these_o orb_n of_o the_o moon_n from_o the_o plain_a of_o the_o ecliptic_a and_o of_o the_o former_a orb_n carry_v the_o dragon_n head_n and_o tail_n be_v 5._o degree_n or_o according_a to_o tig●●_n brahe_n his_o observation_n 5._o degr_n and_o a_o quarter_n almost_o sometime_o and_o sometime_o less_o than_o 5._o degr_n that_o point_n or_o intersection_n of_o these_o orb_n with_o the_o former_a from_o which_o they_o begin_v to_o arise_v about_o the_o plain_n of_o the_o ecliptic_n towards_o the_o north_n proceed_v east-ward_n be_v call_v the_o dragon_n head_n and_o be_v signify_v by_o this_o character_n ☊_o and_o the_o other_o point_n or_o intersection_n diametral_o opposite_a unto_o this_o be_v call_v the_o dragon_n tail_n which_o be_v also_o signify_v by_o the_o former_a character_n turn_v up_o side_n down_o after_o this_o manner_n ☋_o the_o two_o point_n of_o these_o orb_n that_o be_v further_a distant_a from_o the_o plain_a of_o the_o 〈◊〉_d be_v call_v the_o bound_n or_o limit_n of_o the_o moon_n latitude_n and_o they_o be_v 90._o deg_n from_o the_o dragon_n head_n and_o tail_n and_o 5._o deg_n and_o a_o quarter_n almost_o from_o the_o plain_n of_o the_o ecliptic_a according_a to_o the_o obliquity_n or_o great_a declination_n of_o the_o plain_n of_o these_o orb_n from_o the_o plain_n of_o the_o ecliptic_n of_o these_o two_o point_n that_o which_o be_v in_o the_o north_n side_n of_o the_o ecliptic_n be_v call_v the_o north_n limit_n or_o bind_v of_o the_o moon_n latitude_n and_o contrariwise_o the_o other_o point_n opposite_a to_o this_o on_o the_o south_n side_n of_o the_o ecliptic_a be_v call_v the_o south_n limit_v of_o the_o moon_n latitude_n and_o when_o the_o moon_n come_v to_o either_o of_o these_o two_o point_n she_o have_v her_o great_a latitude_n chap._n x._o of_o the_o orb_n carry_v the_o moon_n apogaeum_n and_o perigaeum_n next_o within_o the_o orb_n carry_v the_o dragon_n head_n and_o tail_n be_v contain_v the_o orb_n call_v deferens_fw-la apogaeum_n lunae_fw-la which_o be_v the_o point_n wherein_o the_o moon_n be_v further_a distant_a from_o the_o earth_n and_o under_o this_o orb_n be_v place_v the_o moon_n eccentrick_a which_o be_v also_o call_v deferens_fw-la epiculum_fw-la lunae_fw-la that_o be_v the_o orb_n carry_v the_o moon_n epicycle_n again_o within_o this_o eccentrick_a of_o the_o moon_n be_v contain_v the_o least_o and_o low_a orb_n of_o all_o that_o be_v in_o this_o sphere_n which_o they_o call_v diferens_n perigaeum_n lunae_fw-la that_o be_v the_o orb_n carry_v the_o moon_n perigaeum_n which_o be_v the_o point_n wherein_o the_o moon_n come_v near_a to_o the_o earth_n the_o uppermost_a and_o nethermost_a of_o these_o three_o orb_n that_o be_v to_o say_v the_o orb_n carry_v the_o moon_n apogaeum_n and_o perigaeum_n both_o which_o orb_n in_o this_o sphere_n be_v colour_v with_o blue_a be_v always_o place_v in_o such_o sort_n that_o the_o nar●●west_a part_n of_o the_o one_o be_v continual_o answerable_a to_o the_o broad_a part_n of_o the_o other_o whereby_o it_o come_v to_o pass_v that_o the_o sphere_n of_o the_o moon_n be_v make_v concentricall_a that_o be_v to_o say_v to_o have_v the_o same_o centre_n with_o the_o world_n which_o also_o be_v one_o especial_a use_n why_o these_o orb_n be_v divide_v another_o use_n of_o these_o orb_n be_v to_o show_v the_o reason_n of_o the_o motion_n of_o the_o moon_n apogaeum_n and_o perigaeum_n therefore_o both_o these_o orb_n be_v move_v together_o with_o one_o motion_n equal_o about_o the_o centre_n of_o the_o world_n in_o the_o same_o time_n from_o the_o east_n westward_n in_o the_o space_n of_o 32._o day_n 3._o hour_n and_o 5._o minute_n almost_o so_o move_v in_o one_o day_n 11._o deg_n 12._o min._n and_o 1._o three_o part_n almost_o the_o axtree_n about_o which_o these_o orb_n be_v move_v equal_o pass_v through_o the_o centre_n of_o the_o world_n and_o of_o the_o ecliptic_n but_o the_o pole_n of_o these_o orb_n differ_v from_o the_o pole_n of_o the_o ecliptic_a and_o of_o the_o orb_n carry_v the_o dragon_n head_n and_o tail_n by_o the_o space_n of_o 5._o degr_n and_o a_o quarter_n or_o thereabouts_o which_o pole_n be_v carry_v about_o the_o pole_n of_o the_o orb_n carry_v the_o dragon_n head_n and_o tail_n with_o the_o motion_n of_o the_o same_o orb_n in_o the_o space_n of_o 19_o year_n almost_o whereby_o it_o come_v to_o pass_v that_o the_o pole_n of_o the_o orb_n carry_v the_o apogaeum_n and_o perigaeum_n of_o the_o moon_n describe_v certain_a little_a circle_n about_o the_o pole_n of_o the_o orb_n that_o carry_v the_o dragon_n head_n and_o tail_n even_o as_o the_o arctic_a and_o antarctick_a circle_n in_o the_o ordinary_a sphere_n be_v describe_v by_o the_o motion_n of_o the_o pole_n of_o the_o ecliptic_a carry_v about_o daily_o with_o the_o motion_n of_o the_o first_o and_o high_a movable_a sphere_n in_o the_o space_n of_o 24._o hour_n almost_o chap._n xi_o of_o the_o eccentricke_a of_o the_o moon_n the_o eccentrick_a of_o the_o moon_n contain_v between_o the_o two_o former_a orb_n and_o colour_a with_o a_o sad_a yellow_a colour_n in_o this_o sphere_n be_v move_v equal_o about_o the_o centre_n of_o the_o same_o orb_n from_o the_o west_n towards_o the_o east_n finish_v his_o motion_n under_o the_o zodiac_n in_o the_o space_n of_o 27._o day_n and_o 8._o hour_n almost_o and_o with_o this_o motion_n it_o carry_v about_o the_o moon_n epicycle_n equal_o under_o the_o zodiac_n therefore_o the_o motion_n of_o this_o orb_n about_o his_o own_o centre_n must_v needs_o be_v unequal_a that_o be_v to_o say_v swift_a in_o those_o part_n that_o be_v about_o the_o apogaeum_n and_o slow_a in_o the_o low_a part_n about_o the_o perigaeum_n because_o that_o great_a arch_n of_o the_o eccentrick_a do_v answer_n to_o equal_a arch_n of_o the_o zodiac_n about_o the_o apogaeum_n then_o about_o the_o perigaeum_n of_o the_o eccentrick_a the_o axtree_n about_o which_o this_o orb_n be_v move_v be_v always_o in_o all_o place_n equidistant_a from_o the_o axtree_n of_o the_o orb_n carry_v the_o apogaeum_n of_o the_o moon_n and_o the_o pole_n of_o the_o axtree_n of_o the_o moon_n eccentrick_a be_v fasten_v in_o the_o orb_n carry_v the_o moon_n apogaeum_n equidistant_o from_o the_o pole_n of_o the_o same_o orb_n therefore_o these_o pole_n together_o with_o the_o whole_a axtree_n of_o the_o eccentrick_a be_v carry_v and_o equal_o move_v about_o the_o pole_n and_o axtree_n of_o the_o orb_n carry_v the_o apogaeum_n from_o the_o east_n towards_o the_o west_n with_o this_o motion_n therefore_o the_o pole_n and_o centre_n of_o the_o eccentrick_a describe_v certain_a little_a circle_n of_o equal_a bigness_n about_o the_o pole_n and_o centre_n of_o the_o orb_n carry_v the_o apogaeum_n from_o the_o east_n westward_n and_o therefore_o also_o the_o apogaeum_n of_o the_o eccentrick_a be_v move_v about_o equal_o under_o the_o ecliptic_n contrary_a to_o the_o
order_n of_o sign_n from_o the_o east_n westward_n whereby_o it_o come_v to_o pass_v that_o both_o the_o apogaeum_n and_o centre_n of_o the_o eccentricke_a be_v sometime_o under_o the_o ecliptic_a that_o be_v when_o they_o be_v under_o the_o dragon_n head_n or_o tail_n but_o for_o the_o most_o part_n they_o be_v beside_o the_o plain_a of_o the_o ecliptic_n either_o towards_o the_o north_n or_o else_o towards_o the_o south_n hereby_o also_o it_o appear_v that_o the_o plain_a of_o the_o ecliptic_a do_v not_o always_o divide_v the_o plain_a of_o the_o eccentricke_a into_o epqall_a part_n or_o half_n but_o then_o only_o when_o the_o centre_n and_o apogaeum_n of_o the_o eccentrick_a be_v right_o under_o the_o dragon_n head_n or_o tail_n for_o then_o only_a the_o plain_a of_o the_o ecliptic_a devide_v the_o plain_a of_o the_o eccentrick_a by_o the_o centre_n thereof_o and_o consequent_o devide_v it_o precise_o into_o two_o half_n otherwise_o if_o the_o apogaeum_n of_o the_o eccentrick_a be_v not_o under_o the_o dragon_n head_n or_o tail_n look_v on_o which_o side_n of_o the_o plain_a of_o the_o ecliptic_a the_o apogaeum_n be_v for_o on_o the_o same_o side_n of_o the_o ecliptic_n be_v the_o great_a part_n of_o the_o eccentrick_a chap._n xii_o in_o what_o proportion_n the_o moon_n eccentrick_a and_o orb_n carry_v her_o apogaeum_n be_v move_v now_o the_o eccentrick_a of_o the_o moon_n and_o the_o orb_n carry_v her_o apogaeum_n be_v move_v in_o such_o sort_n that_o the_o middle_a place_n of_o the_o sun_n be_v always_o right_a in_o the_o midst_n between_o the_o centre_n of_o the_o epicycle_n carry_v in_o the_o eccentrick_a and_o the_o apogaeum_n of_o the_o eccentrick_a except_o it_o be_v when_o the_o centre_n of_o the_o epicycle_n be_v in_o conjunction_n or_o opposition_n to_o the_o middle_a place_n of_o of_o the_o sun_n for_o in_o every_o middle_a conjunction_n and_o opposition_n of_o the_o sun_n and_o moon_n the_o centre_n of_o the_o epicycle_n and_o the_o apogaeum_n of_o the_o eccentrick_a be_v unite_v together_o but_o in_o the_o conjunction_n they_o be_v both_o conjoin_v with_o the_o middle_a place_n of_o the_o sun_n and_o in_o the_o opposition_n they_o be_v both_o together_o opposite_a to_o the_o same_o whereof_o it_o follow_v that_o in_o the_o first_o and_o last_o quarter_n of_o the_o moon_n the_o centre_n of_o her_o epicycle_n be_v diametral_o opposite_a to_o the_o apogaeum_n of_o her_o eccentrick_a hereof_o it_o come_v to_o pass_v that_o although_o the_o moon_n have_v the_o same_o position_n in_o her_o epicycle_n at_o the_o time_n of_o the_o new_a and_o full_a moon_n and_o of_o the_o first_o and_o last_o quarter_n yet_o the_o equation_n or_o prosthaphaeresis_fw-la of_o the_o moon_n argument_n as_o they_o call_v it_o that_o be_v the_o difference_n between_o the_o true_a and_o middle_a place_n of_o the_o moon_n be_v always_o great_a in_o the_o first_o and_o last_o quarter_n then_o in_o the_o full_a and_o new_a moon_n hereby_o likewise_o it_o appear_v that_o in_o the_o time_n contain_v between_o new_a moon_n and_o new_a moon_n which_o they_o call_v mensem_fw-la synodicum_fw-la that_o be_v the_o month_n coniunctional_a or_o the_o time_n from_o conjunction_n to_o conjunction_n the_o centre_n of_o the_o epicycle_n make_v two_o complete_a revolution_n under_o the_o orb_n carry_v the_o apogaeum_n of_o the_o moon_n eccentrick_a and_o therefore_o in_o every_o month_n the_o centre_n of_o the_o epicycle_n come_v twice_o to_o the_o apogaeum_n and_o twice_o to_o the_o perigaeum_n of_o the_o eccentrick_a and_o so_o the_o monthly_a motion_n of_o the_o centre_n of_o the_o epicycle_n describe_v a_o oval_a figure_n the_o end_n whereof_o be_v always_o towards_o the_o place_n of_o the_o full_a and_o new_a moon_n and_o the_o ●ides_n towards_o the_o place_n of_o the_o first_o and_o last_o quarter_n by_o this_o that_o have_v be_v speak_v it_o be_v also_o manifest_a that_o if_o the_o middle_a motion_n of_o the_o sun_n be_v subtract_v out_o of_o the_o middle_a motion_n of_o the_o moon_n there_o remain_v the_o middle_a motion_n of_o the_o moon_n longitude_n from_o the_o sun_n and_o that_o if_o this_o longitude_n again_o be_v double_v you_o shall_v have_v the_o motion_n of_o the_o centre_n of_o the_o moon_n epicycle_n from_o the_o apogaeum_n of_o her_o eccentrick_a which_o motion_n they_o call_v the_o centre_n of_o the_o moon_n chap._n xiii_o of_o the_o epicycle_n of_o the_o moon_n and_o how_o it_o be_v move_v the_o little_a orb_n place_v in_o the_o eccentrick_a be_v call_v the_o epicycle_n of_o the_o moon_n in_o the_o circumference_n whereof_o be_v also_o place_v the_o body_n of_o the_o moon_n represent_v by_o the_o round_a beade_n set_v into_o the_o moon_n epicycle_n in_o this_o sphere_n the_o plain_a superficies_n of_o this_o epicycle_n agree_v even_o with_o the_o plain_a of_o the_o eccentrick_a and_o the_o axtree_n about_o which_o it_o be_v move_v be_v perpendicular_a to_o the_o plain_a of_o the_o eccentrick_a this_o epicycle_n be_v move_v equal_o from_o his_o middle_a apogaeum_n about_o his_o own_o centre_n and_o axtree_n from_o the_o east_n westward_n contrary_a to_o the_o motion_n of_o the_o eccentrick_a carry_v forward_o the_o body_n of_o the_o moon_n with_o this_o motion_n 13._o degree_n and_o almost_o 4._o min._n every_o day_n and_o finish_v his_o revolution_n in_o 27._o day_n 13._o hour_n and_o 19_o minute_n almost_o the_o middle_a apogaeum_n of_o the_o epicycle_n be_v show_v by_o a_o right_a line_n imagine_v to_o be_v draw_v from_o that_o point_n of_o the_o little_a circle_n describe_v by_o the_o motion_n of_o the_o centre_n of_o the_o moon_n eccentrick_a which_o be_v opposite_a to_o the_o centre_n of_o the_o eccentrick_a by_o the_o centre_n of_o the_o epicycle_n unto_o the_o upper_a part_n of_o the_o epicycle_n but_o the_o true_a apogaeum_n of_o the_o epicycle_n be_v show_v by_o a_o right_a line_n understand_v to_o be_v draw_v from_o the_o centre_n of_o the_o earth_n by_o the_o centre_n of_o the_o epicycle_n unto_o the_o upper_a part_n of_o the_o circumference_n thereof_o by_o the_o motion_n of_o this_o epicycle_n it_o may_v easy_o be_v conceive_v why_o the_o moon_n seem_v to_o move_v sometime_o swift_o and_o somteimes_o slow_a slow_a for_o see_v that_o the_o upper_a part_n of_o the_o epicycle_n move_v contrary_a to_o the_o motion_n of_o the_o eccentrick_a from_o the_o east_n westward_n when_o the_o moon_n come_v in_o that_o part_n she_o must_v needs_o seem_v to_o move_v more_o slow_o to_o they_o that_o be_v at_o the_o centre_n of_o the_o world_n but_o when_o the_o moon_n come_v in_o the_o nether_a part_n of_o the_o epicycle_n the_o eccentrick_a carry_v the_o epicycle_n and_o the_o epicycle_n carry_v the_o body_n of_o the_o moon_n both_o one_o way_n that_o be_v from_o the_o west_n east-ward_n and_o therefore_o at_o that_o time_n the_o moon_n seem_v to_o move_v more_o swift_o according_a as_o you_o may_v see_v in_o ephemerides_n the_o d●●●ne_a motion_n of_o the_o moon_n to_o be_v sometime_o little_o more_o than_o 11._o degree_n and_o sometime_o again_o little_o less_o than_o 15._o degree_n the_o true_a motion_n of_o the_o moon_n seem_v then_o to_o be_v swift_a when_o the_o moon_n be_v in_o the_o perigaeum_n of_o her_o epicycle_n and_o the_o epicycle_n in_o the_o perigaeum_n of_o the_o eccentrick_a because_o than_o she_o be_v not_o only_o carry_v forward_o the_o same_o way_n both_o by_o her_o epicycle_n and_o eccentrick_a but_o she_o be_v also_o at_o that_o time_n near_o unto_o we_o for_o which_o cause_n her_o motion_n shall_v seem_v swift_a than_o when_o the_o epicycle_n be_v in_o other_o part_n of_o the_o eccentrick_a 〈…〉_z chap._n xiiii_o the_o definition_n of_o certain_a astronomical_a word_n of_o art_n for_o the_o better_a understanding_n of_o the_o theoric_n of_o the_o moon_n 1._o the_o line_n of_o the_o moon_n middle_a motion_n be_v a_o line_n understand_v to_o be_v draw_v from_o the_o centre_n of_o the_o earth_n by_o the_o centre_n of_o the_o moon_n epicycle_n unto_o the_o zodiac_n 2._o this_o line_n show_v the_o middle_a place_n of_o the_o moon_n in_o the_o zodiac_n 3._o and_o the_o middle_a motion_n of_o the_o moon_n be_v the_o arch_n of_o the_o zodiac_n from_o the_o begin_n of_o aries_n unto_o the_o same_o line_n 4._o so_o likewise_o the_o line_n of_o the_o true_a motion_n or_o of_o the_o true_a place_n of_o the_o moon_n be_v draw_v from_o the_o centre_n of_o the_o world_n by_o the_o centre_n of_o the_o moon_n to_o the_o zodiac_n 5._o this_o line_n therefore_o show_v the_o true_a place_n of_o the_o moon_n in_o the_o zodiac_n 6._o and_o the_o true_a motion_n of_o the_o moon_n be_v the_o arch_n of_o the_o zodiac_n from_o the_o begin_n of_o aries_n unto_o the_o true_a place_n of_o the_o moon_n 7._o the_o middle_a longitude_n of_o the_o moon_n from_o the_o sun_n
begin_n of_o any_o year_n from_o this_o present_a year_n 1600._o till_o the_o year_n 1620._o the_o second_o part_n show_v how_o much_o the_o dragon_n head_n move_v in_o any_o number_n of_o month_n of_o the_o year_n the_o three_o part_n give_v you_o the_o motion_n of_o the_o dragon_n head_n in_o any_o number_n of_o day_n of_o the_o month_n the_o place_n of_o the_o dragon_n head_n  _fw-fr year_n sign_n deg._n mt._n month_n complete_a de._n mi._n da._n de._n mi._n 1600_o aquarius_n 0_o 45_o january_n 1_o 38_o 1_o 0_o 3_o 1601_o capricorn_n 11_o 21_o february_n 3_o 8_o 2_o 0_o 6_o 1602_o sagittar_n 22_o 2_o march_n 4_o 46_o 3_o 0_o 10_o 1603_o sagittar_n 2_o 42_o april_n 6_o 22_o 4_o 0_o 13_o 1604_o scorpio_n 13_o 22_o may_n 8_o 0_o 5_o 0_o 16_o 1605_o libra_n 23_o 59_o june_n 9_o 36_o 6_o 0_o 19_o 1606_o libra_n 4_o 39_o july_n 11_o 14_o 7_o 0_o 22_o 1607_o virgo_fw-la 15_o 19_o august_n 12_o 53_o 8_o 0_o 25_o 1608_o leo_fw-la 25_o 59_o septemb_n 14_o 28_o 9_o 0_o 29_o 1609_o leo_fw-la 6_o 35_o october_n 16_o 7_o 10_o 0_o 32_o 1610_o cancer_n 17_o 15_o novemb._n 17_o 42_o 11_o 0_o 35_o ●●rd_n 1611_o gemini_fw-la 27_o 55_o decemb._n 19_o 21_o 12_o 0_o 38_o 1612_o gemini_fw-la 8_o 35_o  _fw-fr  _fw-fr 13_o 0_o 41_o 1613_o taurus_n 19_o 12_o  _fw-fr  _fw-fr 14_o 0_o 44_o 1614_o aries_n 29_o 52_o  _fw-fr  _fw-fr 15_o 0_o 48_o 1615_o aries_n 10_o 32_o  _fw-fr  _fw-fr 16_o 0_o 51_o 1616_o pisces_fw-la 21_o 12_o  _fw-fr  _fw-fr 17_o 0_o 54_o 1617._o pisces_fw-la 1_o 49_o  _fw-fr  _fw-fr 18_o 0_o 57_o 1618._o aquarius_n 12_o 29_o  _fw-fr  _fw-fr 19_o 1_o 0_o 1619_o capricorn_n 23_o 9_o  _fw-fr  _fw-fr 20_o 1_o 4_o 1620_o capricorn_n 3_o 49_o  _fw-fr  _fw-fr 21_o 1_o 7_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 22_o 1_o 10_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 23_o 1_o 13_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 24_o 1_o 16_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 25_o 1_o 19_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 26_o 1_o 13_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 27_o 1_o 26_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 28_o 1_o 29_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 29_o 1_o 32_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 30_o 1_o 35_o chap._n xxi_o to_o find_v the_o place_n of_o the_o dragon_n head_n or_o tail_n by_o the_o former_a table_n find_v out_o in_o the_o former_a table_n the_o month_n next_o go_v before_o the_o month_n give_v find_v out_o also_o the_o day_n of_o the_o month_n add_v together_o the_o number_n of_o degree_n and_o minute_n answerable_a to_o that_o month_n and_o day_n of_o the_o month_n and_o subtract_v the_o same_o out_o of_o the_o place_n of_o the_o dragon_n head_n at_o the_o begin_n of_o the_o year_n add_v thereto_o 30._o degr_n ●●at_n be_v the_o whole_a sign_n next_o go_v before_o resolve_v in_o to_o degr_v if_o the_o sun_n aforesaid_a be_v great_a than_o the_o number_n of_o degr_n show_v the_o place_n of_o the_o dragon_n head_n at_o the_o begin_n of_o the_o year_n so_o shall_v you_o have_v the_o place_n of_o the_o dragon_n head_n for_o the_o time_n give_v and_o the_o point_n of_o the_o zodiac_n opposite_a to_o this_o be_v the_o place_n of_o the_o dragon_n tail_n take_v for_o example_n the_o 29._o of_o november_n 1601._o i_o find_v therefore_o against_o october_n the_o month_n go_v next_o before_o november_n 16._o degree_n 7._o minute_n and_o against_o the_o 29._o day_n 1._o degree_n 32._o minute_n the_o sum_n of_o both_o these_o add_v together_o be_v 17._o degree_n 39_o min._n the_o place_n of_o the_o dragon_n head_n for_o the_o begin_n of_o the_o year_n 1601._o be_v 11._o deg_n 21._o min._n of_o capricorn_n which_o because_o they_o be_v less_o than_o 17._o deg_n 39_o min._n i_o add_v unto_o they_o 30._o deg_n that_o be_v the_o whole_a sign_n of_o sagittarie_n and_o the_o sum_n of_o both_o be_v 41._o deg_n 12._o min._n out_o of_o which_o subtract_v 17._o deg_n 39_o min._n and_o there_o shall_v remain_v 23._o deg_n 42._o minute_n of_o sagittarie_n the_o place_n of_o the_o dragon_n head_n at_o that_o time_n and_o the_o point_n of_o the_o zodiac_n which_o be_v opposite_a hereto_o that_o be_v the_o 2d_o 〈◊〉_d 42._o minute_n of_o gemini_fw-la be_v the_o place_n of_o the_o 〈◊〉_d tail_n chap._n xxii_o to_o know_v at_o what_o time_n there_o shall_v be_v a_o eclipse_n of_o the_o moon_n the_o place_n of_o the_o dragon_n head_n be_v thus_o know_v find_v out_o the_o same_o place_n upon_o the_o horizon_n of_o the_o sphere_n and_o see_v what_o day_n and_o month_n answer_v thereto_o find_v out_o also_o the_o place_n of_o the_o full_a moon_n which_o happen_v next_o before_o or_o after_o that_o day_n which_o place_n if_o it_o chance_v to_o be_v within_o 11._o or_o 12._o deg_n either_o before_o or_o after_o that_o point_n of_o the_o zodiac_n which_o be_v opposite_a to_o the_o dragon_n head_n there_o must_v needs_o be_v for_o the_o most_o part_n in_o eclipse_n of_o the_o moon_n likewise_o if_o you_o find_v what_o day_n and_o month_n be_v answerable_a to_o the_o place_n of_o the_o dragon_n tail_n upon_o the_o horizon_n of_o the_o sphere_n if_o the_o place_n of_o the_o full_a moon_n which_o happen_v next_o before_o or_o after_o that_o day_n chance_v to_o be_v within_o 11._o or_o 12._o degree_n of_o the_o dragon_n head_n for_o the_o most_o part_n there_o shall_v be_v a_o eclipse_n of_o the_o moon_n as_o for_o example_n the_o 20._o of_o januarie_n last_o this_o present_a year_n 1600._o the_o place_n of_o the_o dragon_n head_n be_v find_v by_o the_o former_a chapter_n to_o have_v be_v in_o 29._o deg_n 41._o min._n of_o capricorn_n whereto_o there_o answer_v in_o the_o horizon_n the_o 10._o day_n of_o januarie_n the_o place_n of_o the_o full_a moon_n happen_v next_o after_o upon_o the_o 20._o of_o the_o same_o month_n in_o the_o morning_n must_v needs_o be_v in_o the_o place_n opposite_a to_o the_o place_n of_o the_o sun_n the_o same_o 20._o 〈◊〉_d therefore_o because_o 〈◊〉_d sun_n that_o day_n be_v in_o 9_o deg_n 〈◊〉_d one_o half_a of_o aquarius_n therefore_o the_o place_n why_o this_o circle_n be_v call_v the_o equinoctial_a or_o equator_fw-la the_o situation_n of_o the_o orb_n carry_v the_o dragon_n head_n and_o tail_n the_o situation_n of_o the_o rest_n of_o the_o orb_n why_o the_o moon_n seem_v sometime_o to_o move_v swift_a sometime_o slow_a to_o find_v the_o moon_n proportional_a minute_n what_o the_o proportional_a minute_n of_o the_o moon_n be_v ●t_z the_o begin_n of_o the_o 〈◊〉_d of_o our_o ●●rd_n
much_o be_v the_o pole_n of_o the_o ecliptic_a distant_a from_o the_o pole_n of_o the_o world_n chap._n xvi_o use_v of_o the_o polar_a circle_n 1._o the_o polar_a circle_n show_v the_o pole_n of_o the_o zodiac_n and_o show_v their_o distance_n from_o the_o pole_n of_o the_o equinoctial_a 2._o the_o temperate_a zone_n be_v bound_v by_o these_o polar_n circle_n for_o the_o arctic_a circle_n bound_v the_o north_n side_n of_o the_o north_n temperate_a zone_n and_o the_o antarctic_a circle_n bound_v out_o the_o south_n side_n of_o the_o south_n temperate_a zone_n 3._o the_o polar_a circle_n separate_v the_o temperate_a zone_n from_o the_o cold_a zone_n which_o they_o compass_v round_o about_o and_o enclose_v within_o they_o therefore_o the_o four_o lesser_a circle_n that_o be_v the_o two_o polar_a circle_n and_o the_o tropic_n divide_v heaven_n and_o earth_n into_o five_o zone_n chap._n xvii_o of_o the_o zone_n a_o zone_n be_v a_o space_n of_o heaven_n or_o earth_n contain_v between_o two_o of_o the_o small_a circle_n or_o enclose_v within_o the_o compass_n of_o either_o polar_a circle_n they_o be_v call_v zone_n that_o be_v as_o much_o to_o say_v as_o girdle_n because_o they_o compass_v about_o heaven_n or_o earth_n like_o a_o girdle_n the_o zone_n be_v divide_v by_o ancient_a writer_n into_o two_o kind_n that_o be_v into_o temperate_a and_o untemperate_a zone_n a_o temperate_a zone_n be_v the_o space_n of_o heaven_n or_o earth_n contain_v between_o either_o of_o the_o tropic_n and_o the_o next_o polar_a circle_n there_o be_v two_o temperate_a zone_n the_o one_o north_n the_o other_o south_n the_o north_n temperate_a zone_n be_v contain_v between_o the_o tropic_n of_o cancer_n and_o the_o arctic_a polar_n circle_n the_o south_n temperate_a zone_n be_v that_o which_o be_v contain_v between_o the_o tropic_n of_o capricorn_n and_o the_o antarctic_a polar_n circle_n they_o be_v call_v temperate_a zone_n because_o they_o have_v a_o better_a temperature_n of_o the_o air_n for_o the_o most_o part_n and_o more_o mere_a for_o habitation_n than_o the_o untemperate_a zone_n the_o breadth_n of_o either_o temperate_a zone_n be_v always_o equal_a to_o the_o compliment_n of_o the_o distance_n of_o the_o tropic_n and_o therefore_o in_o this_o age_n be_v about_o 43._o degree_n that_o be_v 2580._o english_a mile_n there_o be_v two_o kind_n of_o untemperate_a zone_n the_o one_o exceed_v in_o heat_n the_o other_o in_o cold_a for_o the_o most_o part_n the_o hot_a untemperate_a zone_n call_v also_o the_o torrid_a that_o be_v the_o burn_a or_o broil_v zone_n be_v that_o space_n of_o heaven_n or_o earth_n which_o be_v contain_v between_o the_o tropick_n it_o be_v call_v the_o burn_a zone_n because_o that_o by_o reason_n of_o the_o sun_n continual_a go_v over_o that_o zone_n and_o cast_v his_o beam_n direct_o down_o thereupon_o it_o be_v scorch_v with_o overmuch_a heat_n and_o be_v not_o so_o meet_v to_o be_v inhabit_v as_o the_o temperate_a zone_n the_o breadth_n of_o this_o zone_n be_v always_o equal_a to_o the_o obliquity_n of_o the_o zodiac_n or_o great_a declination_n of_o the_o sun_n double_v which_o in_o our_o time_n be_v about_o 47._o degree_n that_o be_v 2820._o english_a mile_n the_o cold_a or_o freeze_a zone_n be_v the_o space_n of_o heaven_n or_o earth_n contain_v within_o the_o polar_a circle_n there_o be_v two_o cold_a zone_n the_o one_o north_n contain_v within_o the_o compass_n of_o the_o arctic_a circle_n the_o other_o south_n contain_v within_o the_o compass_n of_o the_o antarctic_a polar_a circle_n these_o zone_n exceed_v in_o cold_a because_o they_o want_v the_o sight_n of_o the_o sun_n for_o a_o great_a part_n of_o the_o year_n and_o when_o the_o sun_n appear_v unto_o they_o his_o beam_n fall_v so_o oblique_o upon_o they_o that_o they_o can_v in_o all_o likelihood_n receive_v but_o small_a heat_n thereby_o for_o the_o most_o part_n the_o breadth_n of_o these_o zone_n be_v measure_v from_o the_o pole_n of_o the_o world_n to_o the_o polar_a circle_n and_o therefore_o must_v always_o be_v so_o much_o as_o the_o polar_a circle_n be_v distant_a from_o the_o pole_n that_o be_v in_o our_o age_n about_o 23._o degree_n and_o a_o half_a which_o make_v 1410._o english_a mile_n chap._n xviii_o the_o difference_n of_o shadow_n that_o the_o sun_n make_v in_o these_o zone_n they_o that_o dwell_v in_o the_o torride_a zone_n do_v cast_v their_o shadow_n which_o the_o sun_n make_v at_o noon_n which_o we_o may_v therefore_o call_v their_o noon_n shadow_n both_o towards_o the_o north_n and_o towards_o the_o south_n towards_o the_o north_n when_o the_o sun_n be_v betwixt_o their_o zenith_n and_o the_o south_n point_n of_o the_o horizon_n and_o towards_o the_o south_n where_o the_o sun_n be_v between_o their_o zenith_n and_o the_o north._n for_o see_v the_o zenith_n of_o they_o that_o dwell_v in_o that_o zone_n be_v between_o the_o tropic_n the_o sun_n must_v needs_o be_v sometime_o northwards_o from_o their_o zenith_n and_o so_o make_v a_o south_n shadow_n and_o sometime_o southwards_o and_o then_o make_v a_o north_n shadow_n for_o which_o cause_n they_o that_o inhabit_v this_o zone_n be_v call_v amphiscij_fw-la that_o be_v such_o as_o cast_v their_o noon_n shadow_n on_o both_o side_n but_o they_o that_o dwell_v in_o the_o temperate_a zone_n be_v call_v heteroscij_fw-la that_o be_v such_o as_o cast_v their_o shadow_n at_o noon_n one_o way_n only_o for_o they_o that_o dwell_v in_o the_o north_n temperate_a zone_n have_v the_o sun_n always_o at_o noon_n from_o their_o zenith_n southwards_o and_o therefore_o must_v needs_o always_o cast_v their_o noon_n shadow_n northwards_o whereas_o contrariwise_o they_o that_o inhabit_v the_o south_n temperate_a zone_n have_v the_o sun_n at_o noon_n always_o northwards_o from_o their_o zenith_n must_v needs_o have_v their_o shadow_n at_o noon_n always_o towards_o the_o south_n and_o they_o that_o be_v in_o the_o cold_a zone_n be_v call_v periscij_fw-la that_o be_v such_o as_o cast_v their_o shadow_n round_o about_o they_o for_o see_v the_o sun_n continue_v every_o year_n for_o certain_a day_n together_o always_o above_o their_o horizon_n and_o therefore_o move_v round_o about_o they_o without_o set_v it_o must_v needs_o be_v that_o their_o shadow_n also_o be_v carry_v round_o about_o they_o fall_v towards_o all_o part_n of_o the_o world_n in_o the_o space_n of_o 24._o hour_n *_o ⁎_o *_o the_o second_o part_n of_o the_o use_n of_o the_o uppermost_a sphere_n and_o of_o the_o circle_n thereof_o joint_o prop._n i._o to_o rectify_v the_o sphere_n to_o the_o latitude_n etc._n etc._n first_o find_v by_o observation_n or_o otherwise_o the_o height_n of_o the_o pole_n or_o latitude_n of_o that_o place_n for_o which_o you_o will_v rectify_v the_o sphere_n then_o by_o turn_v about_o the_o meridian_n of_o the_o sphere_n lift_v up_o or_o put_v down_o the_o north_n pole_n of_o the_o sphere_n about_o which_o the_o hour_n circle_n be_v fasten_v till_o the_o arch_n of_o the_o meridian_n from_o the_o north_n part_n of_o the_o horizon_n upward_o unto_o the_o pole_n be_v just_a so_o many_o degree_n as_o the_o elevation_n of_o the_o pole_n or_o latitude_n of_o the_o place_n be_v find_v to_o be_v for_o so_o have_v you_o the_o sphere_n due_o rectify_v as_o for_o example_n the_o latitude_n of_o the_o city_n of_o london_n be_v 51._o degree_n and_o 32._o minute_n therefore_o if_o you_o lift_v up_o the_o north_n pole_n of_o the_o sphere_n above_o the_o north_n part_n of_o the_o horizon_n so_o many_o degree_n and_o minute_n you_o shall_v have_v your_o sphere_n rectify_v for_o that_o place_n prop._n ii_o to_o know_v the_o place_n of_o the_o sun_n etc._n etc._n look_v the_o day_n of_o the_o month_n for_o which_o you_o desire_v to_o know_v the_o place_n of_o the_o sun_n in_o the_o horizon_n and_o see_v what_o sign_n and_o degree_n of_o the_o zodiac_n upon_o the_o horizon_n answer_v thereto_o for_o there_o have_v you_o the_o place_n of_o the_o sun_n take_v for_o example_n the_o 25._o of_o december_n look_v this_o day_n therefore_o in_o the_o horizon_n and_o you_o shall_v find_v answerable_a thereto_o 13._o degree_n and_o about_o 40._o minute_n of_o capricorn_n which_o be_v the_o place_n of_o the_o sun_n at_o that_o time_n prop._n iii_o to_o know_v the_o declination_n of_o the_o sun_n etc._n etc._n bring_v the_o point_n who_o declination_n you_o desire_v to_o know_v unto_o the_o meridian_n of_o the_o sphere_n and_o look_v what_o number_n of_o degree_n and_o minute_n of_o the_o meridian_n be_v contain_v between_o that_o point_n and_o the_o equinoctial_a for_o so_o much_o be_v the_o declination_n as_o if_o you_o will_v know_v the_o declination_n of_o the_o 10._o degree_n of_o taurus_n bring_v that_o degree_n to_o the_o meridian_n and_o you_o shall_v find_v the_o arch_n of_o the_o meridian_n between_o
the_o east_n semicircle_n of_o the_o horizon_n see_v how_o many_o hour_n the_o index_n pass_v over_o in_o the_o houre-circle_n for_o so_o many_o hour_n long_o be_v the_o night_n as_o for_o example_n suppose_v the_o sun_n to_o be_v as_o before_o in_o the_o 10._o degree_n of_o taurus_n bring_v the_o same_o degree_n to_o the_o east_n part_n of_o the_o horizon_n and_o the_o point_n of_o the_o index_n to_o the_o meridian_n then_o turn_v about_o the_o sphere_n till_o the_o same_o degree_n come_v to_o the_o west_n part_n of_o the_o horizon_n you_o shall_v find_v that_o in_o the_o mean_a time_n the_o point_n of_o the_o index_n shall_v pass_v over_o 14._o hour_n and_o 24._o minute_n which_o be_v the_o length_n of_o the_o day_n likewise_o if_o you_o bring_v the_o same_o 10._o degr_n of_o taurus_n to_o the_o west_n part_n of_o the_o horizon_n and_o the_o index_n to_o the_o meridian_n and_o turn_v about_o the_o sphere_n till_o that_o degree_n come_v to_o the_o east_n semicircle_n of_o the_o horizon_n the_o number_n of_o hour_n that_o the_o index_n run_v over_o in_o the_o mean_a time_n upon_o the_o hour_n circle_n shall_v be_v find_v to_o be_v 9_o degree_n and_o 36._o minute_n prop._n xi_o to_o know_v the_o meridian_n altitude_n or_o the_o height_n of_o the_o sun_n at_o noon_n for_o any_o time_n and_o place_n set_v the_o sphere_n to_o the_o latitude_n of_o the_o place_n where_o you_o desire_v to_o know_v the_o sun_n height_n at_o noon_n bring_v the_o place_n of_o the_o sun_n be_v find_v as_o before_o by_o the_o 2._o prop._n to_o the_o meridian_n then_o see_v how_o many_o degree_n of_o the_o meridian_n be_v contain_v between_o the_o horizon_n and_o the_o place_n of_o the_o sun_n for_o so_o much_o be_v the_o height_n of_o the_o sun_n at_o noon_n in_o like_a sort_n it_o may_v be_v know_v how_o much_o the_o sun_n be_v under_o the_o horizon_n at_o midnight_n after_o this_o manner_n bring_v the_o place_n of_o the_o sun_n in_o the_o zodiac_n to_o the_o meridian_n under_o the_o horizon_n and_o see_v how_o many_o degree_n of_o the_o meridian_n be_v contain_v between_o the_o upperside_n of_o the_o horizon_n and_o the_o place_n of_o the_o sun_n downward_o and_o so_o shall_v you_o have_v that_o you_o seek_v for_o or_o else_o if_o you_o can_v well_o come_v to_o the_o meridian_n under_o the_o horizon_n bring_v that_o point_n of_o the_o ecliptic_a which_o be_v opposite_a to_o the_o place_n of_o the_o sun_n unto_o the_o meridian_n above_o the_o horizon_n for_o the_o arch_n of_o the_o meridian_n or_o the_o number_n of_o degree_n and_o minute_n of_o the_o meridian_n between_o that_o point_n and_o the_o horizon_n show_v how_o much_o the_o sun_n be_v under_o the_o horizon_n at_o midnight_n after_o this_o manner_n the_o sun_n be_v in_o the_o 10._o degr_n of_o taurus_n you_o shall_v find_v that_o his_o meridian_n altitude_n at_o london_n be_v 53._o degree_n and_o about_o one_o half_a as_o also_o that_o he_o be_v under_o the_o horizon_n at_o midnight_n about_o 23._o degree_n and_o a_o half_a at_o london_n prop._n xii_o to_o know_v how_o high_a the_o sun_n be_v above_o the_o horizon_n at_o any_o time_n of_o the_o day_n bring_v the_o place_n of_o the_o sun_n find_v by_o the_o 2._o prop._n to_o the_o meridian_n set_v the_o hour_n index_n to_o 12._o a_o clock_n upon_o the_o hour_n circle_n turn_v the_o sphere_n about_o till_o the_o index_n come_v to_o the_o hour_n at_o which_o you_o desire_v to_o know_v the_o height_n of_o the_o sun_n above_o the_o horizon_n take_v the_o distance_n of_o the_o place_n of_o the_o sun_n from_o the_o horizon_n with_o a_o large_a pair_n of_o compass_n then_o set_v both_o foot_n of_o the_o compass_n in_o the_o ecliptic_a and_o look_v how_o many_o degree_n be_v contain_v between_o they_o for_o so_o much_o be_v the_o height_n of_o the_o sun_n thus_o may_v you_o find_v by_o the_o sphere_n that_o when_o the_o sun_n be_v in_o the_o ten_o degree_n of_o taurus_n his_o height_n at_o 10._o of_o the_o clock_n in_o the_o forenoon_n the_o sphere_n be_v due_o rectify_v by_o the_o first_o proposition_n shall_v be_v about_o 45._o degree_n and_o a_o half_a at_o london_n prop._n xiii_o to_o find_v the_o hour_n of_o the_o day_n by_o the_o height_n of_o the_o sun_n etc._n etc._n set_v the_o pole_n arctic_a of_o the_o sphere_n to_o his_o elevation_n for_o that_o place_n where_o you_o desire_v to_o know_v the_o hour_n of_o the_o day_n bring_v the_o place_n of_o the_o sun_n in_o the_o zodiac_n to_o the_o meridian_n and_o the_o hour_n index_n to_o 12._o a_o clock_n of_o the_o hour_n circle_n take_v so_o many_o degree_n of_o the_o ecliptic_a between_o the_o foot_n of_o your_o compass_n as_o the_o height_n of_o the_o sun_n amount_v unto_o then_o set_v one_o foot_n of_o your_o compass_n in_o the_o place_n of_o the_o sun_n and_o turn_v the_o sphere_n about_o eastward_n if_o it_o be_v in_o the_o forenoon_n or_o westward_n if_o in_o the_o afternoon_n till_o you_o can_v but_o only_o touch_v the_o horizon_n with_o the_o other_o foot_n of_o your_o compass_n for_o then_o the_o index_n point_v out_o the_o hour_n of_o the_o day_n in_o the_o hour_n circle_n as_o suppose_v you_o observe_v the_o height_n of_o the_o sun_n be_v in_o the_o 10._o degr_n of_o taurus_n and_o find_v he_o to_o be_v 30._o degree_n high_a in_o the_o forenoon_n you_o shall_v find_v follow_v the_o direction_n prescribe_v in_o this_o proposition_n that_o it_o shall_v then_o be_v about_o 8._o of_o the_o clock_n in_o the_o morning_n prop._n xiiii_o to_o find_v the_o amplitude_n or_o breadth_n of_o the_o sun_n rise_v or_o set_v etc._n etc._n the_o pole_n of_o the_o sphere_n be_v set_v to_o his_o elevation_n and_o the_o place_n of_o the_o sun_n to_o the_o east_n semicircle_n of_o the_o horizon_n see_v how_o many_o degree_n of_o the_o horizon_n be_v contain_v between_o the_o place_n of_o the_o sun_n and_o the_o true_a east_n point_n for_o so_o you_o shall_v have_v the_o breadth_n of_o the_o sun_n rise_n thus_o the_o sun_n be_v in_o the_o 10._o degree_n of_o taurus_n you_o shall_v find_v by_o the_o sphere_n that_o for_o the_o latitude_n of_o london_n he_o rise_v about_o 23._o degr_n and_o a_o half_a northwards_o from_o the_o true_a east_n point_n and_o that_o he_o set_v as_o many_o degree_n towards_o the_o north_n from_o the_o true_a west_n point_n prop._n xv._n to_o find_v the_o place_n of_o the_o sun_n etc._n etc._n the_o quarter_n of_o the_o year_n be_v know_v bring_v the_o quarter_n of_o the_o ecliptic_a that_o be_v answerable_a thereto_o under_o the_o meridian_n and_o turn_v the_o sphere_n to_o or_o fro_o till_o there_o be_v so_o many_o degree_n and_o minute_n of_o the_o meridian_n contain_v between_o the_o ecliptic_a and_o the_o equator_fw-la as_o the_o declination_n come_v to_o then_o look_v what_o degree_n of_o the_o ecliptic_a be_v under_o the_o meridian_n for_o that_o be_v the_o place_n of_o the_o sun_n as_o suppose_v the_o declination_n of_o the_o sun_n in_o some_o day_n of_o the_o springtime_n of_o the_o year_n be_v find_v to_o be_v 14._o degr_n 51._o min._n turn_v therefore_o the_o sphere_n to_o and_o fro_o till_o some_o part_n of_o the_o spring_n quarter_n of_o the_o ecliptic_a come_v right_a under_o that_o degree_n and_o minute_n of_o declination_n in_o the_o meridian_n you_o may_v find_v that_o the_o sun_n be_v then_o in_o the_o ten_o degree_n of_o taurus_n prop._n xvi_o to_o find_v what_o day_n of_o the_o month_n it_o be_v etc._n etc._n the_o place_n of_o the_o sun_n be_v find_v by_o his_o declination_n as_o be_v already_o show_v seek_v the_o place_n of_o the_o sun_n in_o the_o horizon_n of_o the_o sphere_n and_o look_v what_o day_n be_v answerable_a thereto_o for_o that_o be_v the_o day_n of_o the_o month_n which_o be_v seek_v for_o as_o the_o place_n of_o the_o sun_n be_v find_v by_o his_o declination_n as_o be_v show_v in_o the_o former_a proposition_n to_o be_v in_o the_o 10._o degree_n of_o taurus_n the_o day_n of_o the_o month_n shall_v thus_o be_v find_v to_o be_v the_o 21._o of_o april_n prop._n xvii_o the_o day_n of_o the_o month_n be_v know_v to_o find_v at_o what_o time_n the_o day_n break_v find_v the_o place_n of_o the_o sun_n by_o the_o 2._o prop._n and_o bring_v it_o to_o the_o meridian_n then_o bring_v the_o hour_n index_n to_o 12._o a_o clock_n upon_o the_o hour_n circle_n find_v out_o also_o the_o point_n of_o the_o ecliptic_a that_o be_v right_o over_o against_o the_o place_n of_o the_o sun_n then_o take_v between_o the_o foot_n of_o your_o compass_n 17._o degree_n of_o the_o ecliptic_a and_o set_v one_o foot_n of_o the_o compass_n in_o the_o point_n opposite_a to_o the_o place_n of_o
when_o he_o be_v in_o aries_n or_o libra_n prop._n xxxiii_o to_o find_v by_o the_o sphere_n how_o much_o the_o natural_a day_n be_v long_o at_o one_o time_n of_o the_o year_n then_o at_o another_o for_o this_o purpose_n it_o will_v be_v best_a to_o take_v a_o good_a number_n of_o day_n together_o as_o for_o example_n take_v the_o whole_a month_n of_o december_n and_o the_o whole_a month_n of_o march_n both_o which_o month_n consist_v of_o the_o same_o number_n of_o 31._o natural_a day_n find_v the_o place_n of_o the_o sun_n for_o the_o beginning_n and_o end_v of_o both_o month_n which_o you_o may_v find_v by_o the_o second_o proposition_n to_o be_v for_o the_o begin_n of_o march_n this_o present_a year_n 1600._o about_o 20._o degree_n and_o 13._o minute_n of_o pisces_fw-la and_o for_o the_o end_n about_o 20._o degr_n 48._o minute_n of_o aries_n also_o for_o the_o begin_n of_o december_n the_o same_o year_n 18._o degr_n 46._o minute_n of_o s●gitarie_a and_o for_o the_o end_n 20._o degree_n 24._o minute_n of_o capricorn_n then_o seek_v out_o the_o right_a ascension_n of_o the_o same_o place_n of_o the_o sun_n for_o the_o beginning_n and_o end_n of_o both_o those_o month_n by_o the_o four_o proposition_n and_o the_o difference_n of_o ascension_n answerable_a to_o the_o motion_n of_o the_o sun_n in_o each_o month_n by_o the_o six_o proposition_n which_o you_o may_v find_v by_o the_o sphere_n to_o be_v about_o 33._o degree_n 24_o minute_n for_o december_n and_o 28._o degree_n 39_o minute_n for_o march._n last_o find_v out_o the_o difference_n of_o these_o difference_n of_o ascension_n by_o substract_v the_o lesser_a out_o of_o the_o great_a which_o in_o this_o example_n be_v 4._o degree_n 45._o minute_n which_o resolve_v into_o minute_n of_o a_o hour_n by_o take_v for_o every_o degree_n 4._o minute_n of_o a_o hour_n and_o for_o every_o 15._o minute_n of_o a_o degree_n one_o minute_n of_o a_o hour_n shall_v amount_v to_o 19_o minute_n of_o a_o hour_n that_o be_v a_o quarter_n of_o a_o hour_n and_o 4._o minute_n and_o so_o much_o be_v the_o month_n of_o december_n long_a than_o the_o month_n of_o march_n notwithstanding_o both_o of_o they_o consist_v of_o the_o same_o number_n of_o 31._o natural_a day_n the_o three_o part._n of_o the_o orb_n whereof_o the_o sphere_n of_o the_o sun_n and_o moon_n have_v be_v imagine_v to_o be_v make_v and_o of_o their_o motion_n and_o use_v chap._n i._o of_o the_o orb_n whereof_o the_o sphere_n of_o the_o sun_n be_v make_v within_o the_o sphere_n or_o orb_n contain_v all_o the_o circle_n that_o we_o have_v hitherto_o speak_v of_o and_o represent_v unto_o we_o the_o primum_fw-la mobile_a that_o be_v the_o first_o and_o high_a movable_a heaven_n that_o have_v be_v imagine_v by_o the_o astronomer_n to_o show_v the_o reason_n of_o that_o daily_a motion_n which_o appear_v to_o be_v in_o all_o the_o heaven_n and_o of_o all_o the_o apparence_n that_o follow_v thereupon_o be_v include_v the_o sphere_n and_o orb_n of_o the_o sun_n and_o moon_n the_o sphere_n of_o the_o sun_n contain_v three_o orb_n the_o uppermost_a of_o they_o which_o in_o this_o sphere_n be_v signify_v by_o the_o yellow_a circle_n that_o come_v next_o within_o the_o compass_n of_o the_o zodiac_n be_v call_v deferens_fw-la apogaeum_fw-la solis_fw-la that_o be_v the_o orb_n which_o carry_v about_o that_o point_n wherein_o the_o sun_n be_v further_a distant_a from_o the_o earth_n next_o within_o this_o orb_n be_v place_v the_o eccentrick_a carry_v about_o the_o body_n of_o the_o sun_n which_o in_o this_o sphere_n be_v represent_v by_o the_o green_a colour_a circle_n that_o come_v next_o under_o the_o deferens_fw-la apogaeum_fw-la again_o within_o this_o eccentrick_a be_v include_v the_o three_o orb_n of_o the_o sphere_n of_o the_o sun_n call_v deferens_fw-la perigaeum_n solis_fw-la that_o be_v the_o orb_n carry_v about_o that_o point_n wherein_o the_o sun_n be_v near_a to_o the_o earth_n this_o be_v the_o nethermost_a of_o the_o three_o orb_n of_o the_o sun_n and_o in_o this_o sphere_n be_v represent_v unto_o you_o by_o the_o yellow_a colour_a circle_n next_o under_o the_o sun_n eccentricke_a chap._n ii_o of_o the_o uppermost_a and_o nethermost_a orb_n of_o the_o sphere_n of_o the_o sun_n more_o particular_o in_o the_o uppermost_a and_o nethermost_a of_o these_o three_o orb_n there_o be_v 4._o point_n especial_o to_o be_v consider_v that_o be_v the_o point_n where_o they_o be_v narrow_a and_o where_o they_o be_v broad_a and_o where_o they_o be_v of_o a_o mean_a breadth_n betwixt_o the_o narrow_a and_o broad_a for_o at_o the_o narrow_a part_n of_o the_o uppermost_a orb_n where_o you_o may_v see_v write_v aux_fw-fr solis_fw-la and_o the_o broad_a part_n of_o the_o nethermost_a orb_n be_v the_o place_n of_o the_o sun_n apogaeum_n so_o that_o whensoever_o the_o sun_n come_v there_o he_o be_v further_a distant_a from_o the_o earth_n as_o you_o may_v easy_o try_v if_o with_o a_o pair_n of_o compass_n or_o otherwise_o you_o take_v the_o distance_n betwixt_o the_o earth_n and_o the_o sun_n be_v bring_v about_o to_o that_o place_n and_o compare_v the_o same_o with_o the_o distance_n that_o the_o sun_n have_v from_o the_o earth_n in_o other_o place_n this_o point_n be_v call_v aux_fw-fr solis_fw-la and_o longitude_n longior_fw-la that_o be_v the_o point_n of_o the_o sun_n further_a distance_n from_o the_o earth_n but_o under_o the_o broad_a part_n of_o the_o uppermost_a and_o uttermost_a orb_n where_o you_o see_v print_v perigaeum_n and_o right_a above_o the_o narrow_a part_n of_o the_o nethermost_a orb_n be_v the_o place_n where_o the_o sun_n come_v near_a to_o the_o earth_n as_o you_o may_v easy_o find_v with_o your_o compass_n or_o otherwise_o in_o like_a sort_n as_o before_o be_v show_v the_o point_n where_o the_o sun_n come_v near_a to_o the_o earth_n be_v call_v oppositum_fw-la a●gis_fw-la and_o longitudo_fw-la propior_fw-la that_o be_v the_o point_n opposite_a to_o the_o apogaeum_n and_o the_o near_a distance_n and_o at_o those_o part_n of_o this_o orb_n which_o be_v in_o the_o midst_n between_o the_o former_a the_o sun_n have_v a_o mean_a distance_n from_o the_o earth_n a_o mean_a i_o say_v between_o the_o least_o and_o great_a distance_n the_o very_a point_n wherein_o this_o mean_a or_o middle_a distance_n happen_v be_v show_v by_o the_o point_n that_o be_v just_a in_o the_o midst_n between_o the_o short_a line_n ab_fw-la and_o ik_fw-mi which_o be_v draw_v overthwart_o on_o either_o side_n of_o this_o orb_n these_o point_n be_v call_v longitudines_fw-la media_fw-la that_o be_v the_o mean_a distance_n of_o the_o sun_n because_o the_o sun_n come_v to_o these_o point_n have_v a_o mean_a distance_n between_o the_o least_o and_o the_o great_a about_o these_o point_n also_o the_o true_a motion_n of_o the_o sun_n be_v as_o it_o be_v in_o a_o mean_a between_o the_o slow_a which_o happen_v the_o sun_n be_v about_o the_o apogaeum_n and_o the_o swift_a which_o happen_v about_o his_o perigaeum_n moreover_o the_o line_n a_o and_o k_o show_v the_o place_n wherein_o there_o be_v the_o great_a prosthaphaerisis_n or_o equation_n of_o the_o sun_n that_o be_v the_o great_a difference_n between_o the_o true_a and_o middle_a or_o mean_a place_n of_o the_o sun_n last_o the_o distance_n between_o the_o line_n i_o and_o k_o or_o a_o and_o b_o show_v how_o much_o the_o eccentricitie_n of_o the_o sun_n eccentricke_a be_v that_o be_v how_o far_o the_o centre_n of_o the_o eccentricke_a be_v distant_a from_o the_o centre_n of_o earth_n chap._n iii_o to_o find_v how_o much_o the_o sun_n be_v near_a or_o further_o from_o the_o earth_n at_o one_o time_n then_o at_o another_o by_o mean_n of_o this_o circle_n you_o may_v easy_o find_v with_o your_o compass_n how_o much_o the_o sun_n be_v near_a to_o or_o further_o from_o the_o earth_n at_o one_o time_n then_o at_o another_o for_o have_v set_v one_o foot_n of_o the_o compass_n upon_o the_o utmost_a edge_n of_o the_o deferens_fw-la apogaeum_n under_o the_o place_n of_o the_o sun_n in_o the_o zodiac_n find_v by_o the_o second_o prop._n stretch_v out_o the_o other_o foot_n to_o the_o innermost_a edge_n of_o the_o same_o orb_n for_o then_o if_o you_o set_v one_o foot_n of_o your_o compass_n upon_o the_o utmost_a edge_n of_o this_o orb_n at_o the_o apogaeum_n the_o other_o foot_n turn_v inward_o towards_o the_o centre_n of_o the_o sphere_n will_v show_v you_o how_o much_o the_o sun_n be_v near_a to_o the_o earth_n at_o that_o time_n then_o when_o he_o be_v in_o his_o apogaeum_n for_o so_o much_o as_o that_o foot_n reach_v within_o the_o inner_a edge_n of_o the_o orb_n so_o much_o be_v the_o sun_n near_o likewise_o if_o you_o set_v one_o foot_n of_o your_o compass_n upon_o the_o
the_o sixty_v part_n of_o the_o diversity_n of_o diameter_n or_o of_o the_o excess_n wherewith_o the_o equation_n of_o the_o argument_n or_o prostaphaeresis_fw-la of_o the_o epicycle_n be_v to_o be_v augment_v when_o the_o epicycle_n be_v any_o other_o part_n of_o the_o eccentrick_a then_o in_o the_o apogaeum_n otherwise_o also_o these_o proportional_a min._n may_v be_v define_v to_o be_v sixty_v part_n of_o the_o excess_n wherewith_o the_o line_n draw_v from_o the_o centre_n of_o the_o earth_n to_o the_o apogaeum_n of_o the_o moon_n eccentrick_a exceed_v the_o line_n draw_v from_o the_o same_o centre_n to_o the_o perigaeum_n of_o the_o eccentrick_a for_o these_o sixty_v part_n also_o may_v not_o unfit_o be_v call_v proportional_a min._n because_o that_o always_o look_v how_o many_o of_o these_o part_n there_o be_v leave_v without_o the_o circumference_n of_o the_o eccentrick_a or_o beyond_o the_o centre_n of_o the_o epicycle_n so_o many_o of_o the_o former_a sixty_v part_n of_o the_o diversity_n of_o diameter_n or_o of_o the_o excess_n of_o the_o prostaphaerse_n of_o the_o epicycle_n must_v be_v add_v to_o the_o equation_n of_o the_o argument_n that_o the_o true_a equation_n of_o the_o argument_n may_v be_v have_v for_o that_o position_n or_o situation_n of_o the_o epicycle_n in_o the_o eccentrick_a chap._n xvii_o the_o reason_n of_o the_o eclipse_n of_o the_o sun_n and_o moon_n etc._n etc._n now_o by_o this_o sphere_n it_o may_v easy_o be_v conceive_v why_o there_o be_v not_o a_o eclipse_n in_o every_o conjunction_n or_o opposition_n of_o the_o sun_n and_o moon_n for_o see_v that_o the_o moon_n have_v for_o the_o most_o part_n a_o great_a apparent_a latitude_n than_o the_o visible_a or_o apparent_a conjoin_a semediameter_n of_o the_o sun_n and_o moon_n in_o the_o conjunction_n and_o because_o the_o true_a latitude_n of_o the_o moon_n be_v also_o for_o the_o most_o part_n great_a than_o the_o apparent_a semediameter_n of_o the_o moon_n and_o shadow_n of_o the_o earth_n at_o that_o place_n where_o the_o moon_n shall_v pass_v through_o that_o shadow_n in_o the_o oppossition_n to_o make_v a_o eclipse_n it_o come_v to_o pass_v that_o in_o most_o conjunction_n and_o opposition_n of_o the_o sun_n and_o moon_n there_o be_v no_o eclipse_n and_o the_o reason_n hereof_o be_v this_o because_o that_o the_o moon_n come_v under_o the_o way_n of_o the_o sun_n which_o we_o call_v the_o ecliptic_a line_n only_a twice_o in_o a_o month_n and_o those_o 2._o point_n wherein_o the_o way_n of_o the_o sun_n and_o moon_n across_o each_o other_o only_a twice_o in_o a_o synodical_a month_n which_o two_o point_n we_o call_v the_o dragon_n head_n and_o tail_n whereof_o we_o have_v also_o speak_v before_o wherefore_o see_v the_o sun_n go_v but_o once_o only_a through_o the_o compass_n of_o the_o ecliptic_a in_o a_o year_n can_v come_v but_o once_o in_o a_o year_n to_o either_o of_o those_o point_n the_o moon_n for_o the_o most_o part_n when_o she_o come_v to_o be_v in_o opposition_n or_o conjunction_n with_o the_o sun_n must_v needs_o be_v for_n far_o wide_a from_o the_o ecliptic_a line_n or_o way_n of_o the_o sun_n either_o towards_o the_o north_n or_o south_n that_o she_o can_v neither_o come_v betwixt_o we_o and_o the_o sun_n in_o the_o conjunction_n nor_o yet_o within_o the_o compass_n of_o the_o shadow_n of_o the_o earth_n in_o the_o opposition_n but_o when_o the_o sun_n come_v near_o either_o of_o those_o point_n which_o happen_v once_o in_o six_o month_n there_o must_v needs_o for_o the_o most_o part_n be_v some_o eclipse_n either_o of_o the_o sun_n or_o moon_n or_o both_o chap._n xviii_o of_o the_o diversity_n of_o the_o bound_n or_o space_n within_o which_o a_o eclipse_n may_v happen_v and_o the_o reason_n of_o that_o diversity_n the_o bound_n or_o distance_n from_o the_o dragon_n head_n or_o tail_n within_o which_o there_o may_v happen_v a_o eclipse_n of_o the_o moon_n be_v sometime_o great_a and_o sometime_o less_o by_o reason_n of_o the_o diverse_a distance_n of_o the_o sun_n or_o moon_n or_o both_o of_o they_o from_o the_o earth_n for_o see_v the_o body_n of_o the_o sun_n be_v great_a than_o the_o globe_n of_o the_o whole_a earth_n as_o it_o be_v manifest_o demonstrate_v by_o ptolemee_n and_o copernicus_n it_o must_v needs_o be_v that_o the_o great_a distance_n the_o sun_n have_v from_o the_o earth_n the_o great_a shadow_n must_v the_o earth_n have_v and_o the_o near_o the_o sun_n be_v to_o the_o earth_n the_o less_o shadow_n shall_v the_o earth_n have_v at_o the_o place_n of_o the_o moon_n passage_n through_o the_o shadow_n at_o equal_a distance_n from_o the_o earth_n contrariwise_o the_o further_a that_o the_o moon_n be_v from_o the_o earth_n the_o less_o shall_v the_o shadow_n of_o the_o earth_n be_v and_o the_o near_o the_o moon_n be_v to_o the_o earth_n the_o great_a shall_v the_o shadow_n be_v at_o the_o place_n where_o the_o moon_n be_v to_o pass_v through_o the_o shadow_n the_o great_a distance_n therefore_o from_o the_o dragon_n head_n or_o tail_n wherein_o there_o can_v at_o any_o time_n happen_v any_o eclipse_n of_o the_o moon_n be_v about_o 13._o degree_n and_o the_o least_o distance_n at_o which_o it_o be_v possible_a for_o the_o moon_n to_o avoid_v a_o eclipse_n be_v about_o 10._o degr_n and_o one_o three_o part_n of_o a_o degree_n which_o happen_v when_o the_o moon_n be_v in_o the_o apogaeum_n of_o her_o epicycle_n in_o her_o great_a distance_n from_o the_o earth_n and_o the_o sun_n in_o his_o perigaeum_n in_o the_o time_n of_o his_o great_a eccentricity_n for_o then_o the_o sun_n come_v near_a to_o the_o earth_n and_o make_v the_o least_o shadow_n as_o contrariwise_o at_o the_o same_o time_n of_o his_o great_a eccentricity_n be_v in_o his_o apogaeum_n he_o have_v his_o great_a distance_n from_o the_o earth_n and_o so_o make_v the_o earth_n cast_v forth_o her_o great_a shadow_n at_o which_o time_n if_o the_o moon_n also_o chance_v to_o be_v in_o the_o perigaeum_n of_o her_o epicycle_n and_o so_o in_o her_o near_a distance_n from_o the_o earth_n she_o may_v be_v something_o eclipse_v although_o she_o be_v full_a 13._o degree_n or_o something_o more_o from_o the_o dragon_n head_n or_o tail_n chap._n xix_o how_o to_o find_v the_o place_n of_o the_o dragon_n head_n and_o tail_n for_o any_o time_n now_o the_o place_n and_o time_n of_o the_o full_a moon_n be_v easy_o know_v by_o some_o almanac_n or_o prognostication_n it_o shall_v not_o be_v hard_a to_o give_v a_o reasonable_a near_o estimate_n and_o to_o foretell_v both_o the_o time_n and_o quantity_n of_o the_o eclipse_n of_o the_o moon_n the_o place_n of_o the_o dragon_n head_n and_o tail_n be_v first_o know_v after_o this_o manner_n the_o place_n of_o the_o dragan_o head_n be_v first_o give_v for_o any_o time_n for_o every_o year_n before_o the_o same_o time_n add_v to_o the_o same_o place_n and_o for_o every_o year_n after_o the_o same_o time_n subtract_v 19_o degree_n and_o one_o three_o part_n of_o a_o degree_n and_o for_o every_o month_n a_o degree_n and_o a_o half_a and_o a_o ten_o part_n of_o a_o degree_n and_o for_o every_o day_n 3._o minute_n and_o the_o remainder_n shall_v show_v you_o the_o place_n of_o the_o dragon_n head_n after_o the_o same_o time_n or_o the_o sum_n before_o that_o time_n without_o any_o great_a error_n as_o for_o example_n the_o 30._o of_o june_n this_o present_a year_n 1600._o suppose_v you_o will_v know_v the_o place_n of_o the_o dragon_n head_n the_o place_n therefore_o of_o the_o dragon_n head_n be_v first_o give_v for_o the_o begin_n of_o the_o same_o year_n in_o 0._o degree_n 45._o minute_n of_o aquarius_n and_o six_o month_n only_o of_o that_o year_n be_v pass_v i_o take_v for_o those_o six_o month_n 6._o degree_n and_o 6._o half_a degree_n that_o be_v 9_o degree_n and_o sixteen_o part_n of_o a_o degree_n that_o be_v 36._o min._n the_o sum_n of_o all_o which_o be_v 9_o degree_n and_o 36._o minute_n which_o be_v subtract_v out_o of_o 0._o degree_n 45._o minute_n of_o aquarius_n there_o remain_v 21._o degree_n 9_o min._n of_o capricorn_n for_o the_o place_n of_o the_o dragon_n head_n at_o that_o time_n chap._n xx._n a_o table_n for_o find_v the_o place_n of_o the_o dragon_n head_n and_o tail_n more_o exact_o and_o the_o declaration_n thereof_o but_o if_o you_o will_v have_v the_o place_n of_o the_o dragon_n head_n more_o exact_o you_o may_v find_v the_o same_o most_o easy_o by_o mean_n of_o the_o table_n follow_v for_o any_o time_n within_o the_o space_n of_o these_o 20._o year_n yet_o to_o come_v this_o table_n contain_v three_o principal_a part_n or_o column_n the_o first_o part_n show_v you_o in_o what_o sign_n degr_n and_o min._n the_o dragon_n head_n be_v at_o the_o