projection_n the_o concurrent_a circle_n meet_v in_o the_o pole_n a_o and_o b_o be_v meridian_n those_o meridian_n be_v 180_o in_o number_n and_o divide_v the_o equator_fw-la c_o d_o into_o 360._o degree_n because_o every_o one_o of_o they_o cut_v it_o twice_o that_o be_v once_o in_o each_o hemisphere_n by_o these_o be_v number_v the_o right_a ascension_n of_o the_o star_n and_o planet_n and_o the_o hour_n and_o minute_n of_o day_n and_o night_n for_o every_o 15_o of_o these_o meridian_n number_v from_o the_o limb_n be_v a_o hour_n circle_n as_o have_v be_v show_v book_n 1.6_o they_o be_v number_v from_o d_o to_z c_z that_o be_v from_o septentrio_fw-la to_o meridies_n 1.2.3_o etc._n etc._n for_o the_o morning_n hour_n and_o back_o again_o from_o c_z to_z d_o in_o like_a manner_n for_o the_o afternoon_n the_o axletree_n line_n a_o b_o fall_v out_o to_o be_v the_o six_o a_o clock_n line_v both_o way_n by_o those_o meridian_n also_o be_v number_v the_o longitude_n of_o town_n and_o country_n in_o geography_n the_o circle_n or_o semicircle_n cross_v these_o meridian_n be_v the_o parallel_n of_o declination_n they_o be_v lesser_a circle_n who_o property_n it_o be_v to_o divide_v the_o sphere_n into_o unequal_a part_n in_o the_o midst_n of_o they_o lie_v the_o equator_fw-la c_o d_o be_v here_o a_o straight_a line_n and_o cut_v the_o axtree-line_n a_o b_o at_o right_a angle_n in_o the_o centre_n e_o the_o parallel_n be_v great_a near_o the_o equator_fw-la and_o from_o thence_o they_o lessen_v towards_o the_o pole_n they_o be_v 180_o in_o number_n i._n e._n 90_o on_o each_o side_n the_o equator_fw-la save_v that_o the_o two_o extreme_a parallel_n be_v reduce_v to_o two_o point_n in_o the_o pole_n by_o these_o parallel_n be_v number_v the_o declination_n of_o the_o star_n in_o astronomy_n and_o the_o latitude_n of_o town_n and_o country_n in_o geography_n and_o this_o name_n and_o use_n have_v the_o circle_n of_o the_o mater_n always_o in_o the_o meridional_a projection_n the_o ecliptic_a always_o stand_v for_o itself_o when_o it_o be_v use_v which_o be_v only_o in_o the_o first_o mode_n of_o this_o projection_n but_o the_o circle_n of_o the_o reet_n have_v divers_a name_n and_o use_n in_o the_o divers_a modes_n of_o this_o projection_n which_o here_o follow_v 1_o the_o first_o mode_n of_o the_o meridional_a projection_n the_o point_n a_o of_o the_o reet_n in_o which_o the_o concurrent_a arch_n meet_v be_v call_v the_o vertex_fw-la of_o the_o reet_n set_a the_o vertex_fw-la of_o the_o reet_n to_o the_o latitude_n of_o your_o place_n so_o shall_v the_o vertex_fw-la be_v zenith_n and_o the_o concurrent_a arch_n there_o meet_v shall_v be_v azimuth_n call_v also_o vertical_a circle_n and_o circle_n of_o position_n pass_v from_o zenith_n to_o nadir_n and_o divide_v the_o horizon_n into_o 360_o degr_n as_o the_o meridian_n on_o the_o mater_n pass_v from_o pole_n to_o pole_n and_o divide_v the_o equinoctial_a the_o semicircle_n cross_v these_o azimuth_n shall_v be_v almicanter_n or_o circle_n of_o altitude_n the_o diameter_n cross_v the_o axletree_n of_o the_o reet_n at_o right_a angle_n shall_v be_v the_o horizon_n or_o finiter_n who_o graduation_n be_v set_v to_o he_o in_o a_o border_n below_o the_o centre_n and_o from_o he_o be_v the_o almicanter_n reckon_v upward_o to_o the_o zenith_n the_o azimuth_n may_v be_v reckon_v from_o the_o north_n or_o south_n semicircle_n of_o the_o meridian_n or_o from_o the_o axtree_n line_n of_o the_o reet_n which_o be_v the_o east_n or_o west_n azimuth_n common_o call_v the_o prime_n vertical_a when_o i_o bid_v you_o set_v the_o vertex_fw-la of_o the_o reet_n to_o the_o latitude_n of_o your_o place_n you_o must_v first_o know_v what_o your_o latitude_n be_v it_o be_v the_o near_a distance_n of_o your_o place_n from_o the_o terrestrial_a equinoctial_a number_v in_o degree_n and_o minute_n of_o a_o great_a circle_n the_o latitude_n of_o london_n be_v 31_o degr_n 32_o min._n north._n the_o latitude_n of_o ecton_n or_o northampton_n be_v 52_o degr_n 15_o minute_n or_o very_o near_o and_o how_o to_o get_v the_o latitude_n of_o those_o or_o any_o other_o place_n shall_v be_v show_v book_n 4.11_o the_o latitude_n have_v number_v the_o degree_n thereof_o upon_o the_o ring_n from_o c_o or_o meridies_n where_o the_o equator_fw-la cut_v the_o meridian_n towards_o a_o or_o oriens_fw-la which_o in_o this_o projection_n be_v the_o north_n pole_n because_o we_o in_o england_n have_v north_n latitude_n at_o the_o end_n of_o this_o number_n see_v for_o london_n 51._o degree_n 32._o minute_n from_o the_o equator_fw-la northward_o set_v the_o vertex_fw-la of_o the_o reet_n so_o this_o vertex_fw-la represent_v the_o zenith_n or_o point_n in_o the_o heaven_n which_o be_v just_a over_o your_o head_n in_o which_o point_n all_o the_o azimuth_n meet_v and_o through_o which_o also_o pass_v the_o meridian_n of_o your_o place_n which_o here_o be_v represent_v by_o the_o outmost_a circle_n of_o the_o mater_n or_o the_o innermost_a circle_n of_o the_o ring_n now_o be_v the_o upper_a semicircle_n of_o your_o meridian_n divide_v into_o four_o notable_a part_n from_o the_o zenith_n southward_o to_o the_o equator_fw-la be_v the_o latitude_n 51._o degree_n 32_o minute_n from_o thence_o to_o the_o horizon_n be_v the_o compliment_n of_o the_o latitude_n 38._o degree_n 28._o minute_n make_v up_o a_o quadrant_n again_o from_o the_o zenith_n northerly_a to_o the_o pole_n be_v the_o compliment_n of_o latitude_n 38._o degr_n 28._o minute_n as_o before_o and_o from_o thence_o to_o the_o north_n of_o the_o horizon_n be_v the_o elevation_n of_o the_o pole_n above_o your_o horizon_n which_o be_v always_o equal_a to_o the_o latitude_n of_o your_o place_n for_o where_o in_o a_o right_a sphere_n the_o poles_o in_o the_o horizon_n and_o have_v on_o elevation_n there_o the_o equator_fw-la pass_v through_o the_o zenith_n and_o if_o you_o go_v from_o such_o a_o country_n northward_o till_o the_o pole_n be_v elevate_v one_o degree_n the_o equator_fw-la shall_v there_o decline_v from_o your_o zenith_n one_o degree_n southward_o because_o the_o equator_fw-la keep_v always_o the_o distance_n of_o 90_o degree_n from_o the_o pole_n and_o this_o distance_n of_o the_o zenith_n of_o your_o place_n from_o the_o equator_fw-la be_v call_v by_o geographer_n latitude_n and_o be_v always_o equal_a to_o the_o elevation_n of_o your_o pole_n so_o that_o it_o be_v all_o one_o whether_o you_o set_v the_o vertex_fw-la 51._o degree_n 32._o min._n above_o the_o equator_fw-la or_o set_v the_o north_n point_n of_o the_o horizon_n 51._o degree_n 32._o minute_n below_o the_o north_n pole_n now_o the_o vertex_fw-la of_o the_o reet_n set_v to_o the_o latitude_n and_o consequent_o the_o pole_n mount_v to_o his_o due_a elevation_n your_o planisphear_n be_v in_o a_o right_a mode_n and_o posture_n speedy_o to_o resolve_v all_o question_n concern_v the_o diurnal_a motion_n as_o the_o sun_n longitude_n declination_n right_a ascension_n the_o ascensionall_a difference_n with_o the_o semidiurnall_a arch_n or_o length_n of_o the_o day_n the_o sun_n altitude_n azimuth_n and_o amplitude_n the_o hour_n and_o minute_n of_o the_o day_n the_o beginning_n end_n and_o duration_n of_o twilight_n and_o such_o like_a and_o that_o with_o so_o great_a facility_n that_o have_v only_o the_o longitude_n of_o the_o sun_n with_o the_o ephemeris_fw-la on_o the_o ring_n shall_v give_v you_o for_o ask_v and_o therewith_o either_o the_o altitude_n azimuth_n or_o hour_n one_o of_o they_o you_o may_v see_v all_o the_o rest_n at_o the_o first_o view_n without_o change_v the_o posture_n of_o your_o instrument_n as_o shall_v appear_v in_o the_o four_o book_n 2_o the_o second_o mode_n of_o the_o meridional_a projection_n set_a the_o zenith_n or_o vertex_fw-la of_o the_o reet_n to_o the_o north_n pole_n of_o the_o ecliptic_a or_o which_o be_v all_o one_o set_v the_o horizon_n line_n of_o the_o reet_n in_o the_o ecliptic_a line_n of_o the_o mater_n so_o the_o azimuth_n shall_v in_o this_o posture_n become_v circle_n of_o longitude_n and_o the_o almicanters_n circle_n of_o latitude_n and_o in_o this_o mode_n your_o planisphear_n be_v fit_v to_o resolve_v all_o question_n of_o the_o longitude_n latitude_n right_a ascension_n and_o declination_n of_o the_o star_n 3_o the_o three_o mode_n of_o the_o meridional_a projection_n number_v the_o altitude_n of_o culmen_fw-la caeli_fw-la that_o be_v the_o sothe_v point_n of_o the_o ecliptic_a in_o the_o ring_n from_o the_o north_n pole_n towards_o meridies_n if_o the_o ascendant_n be_v a_o north_n sign_n or_o towards_o septentrio_fw-la if_o the_o ascendant_n be_v a_o south_n sign_n to_o the_o end_n of_o this_o numeration_n place_n the_o finiter_fw-la reckon_v also_o upon_o the_o finiter_n from_o the_o centre_n towards_o septentrie_n the_o amplitude_n of_o the_o ascendant_n the_o meridian_n cut_v there_o give_v you_o
recline_a decline_a dyal_n another_o way_n have_v find_v the_o arch_n and_o angle_n requisite_a by_o chapter_n 16._o and_o plait_v down_o your_o horizontal_n and_o vertical_a line_n and_o place_v the_o noon_n line_n above_o oâ—_n below_o the_o horizontal_n line_n according_a as_o the_o arch_n of_o his_o oblique_a ascension_n or_o descension_n require_v and_o have_v place_v also_o the_o sub-style_n in_o his_o due_a situation_n as_o be_v above_o teach_v you_o may_v easy_o find_v the_o distance_n of_o the_o several_a hour_n from_o the_o sub-style_n as_o you_o find_v they_o in_o the_o former_a chapter_n for_o the_o decline_a horizontal_n dyal_n for_o when_o you_o have_v set_v the_o finitor_n to_o the_o latitude_n of_o your_o plain_n as_o there_o you_o do_v the_o limb_n be_v sub-stylar_a and_o if_o you_o number_v thence_o in_o the_o finitor_n the_o declination_n of_o the_o gnomon_n there_o shall_v meet_v you_o the_o meridian_n of_o the_o place_n here_o you_o shall_v begin_v and_o take_v every_o 15_o meridian_n forward_o and_o backward_o for_o a_o hour_n line_n and_o observe_v how_o many_o degree_n be_v in_o the_o finitor_n between_o the_o limb_n and_o every_o one_o of_o these_o hour_n line_n so_o many_o degree_n shall_v you_o place_v that_o hour_n line_n from_o the_o sub-style_n in_o the_o plain_a if_o you_o understand_v the_o former_a chapter_n this_o will_v need_v no_o example_n chap._n xxiii_o to_o draw_v the_o proper_a hour_n of_o any_o decline_a dyal_n every_o decline_a plain_n whether_o it_o recline_v or_o not_o have_v two_o great_a meridian_n much_a speak_v of_o 1._o the_o meridian_n of_o the_o plain_a which_o be_v the_o proper_a meridian_n of_o that_o country_n to_o who_o horizon_n the_o plain_n h_v parallel_v 2._o the_o meridian_n of_o the_o place_n which_o be_v the_o meridian_n of_o your_o country_n in_o which_o you_o set_v up_o this_o decline_a plain_n to_o show_v the_o hour_n and_o so_o either_o of_o these_o meridian_n dial_n may_v be_v conform_v how_o to_o draw_v the_o hour_n of_o our_o country_n on_o such_o a_o plain_a be_v the_o hard_a work_n because_o the_o plain_n be_v irregular_a to_o our_o horiz_n on_o yet_o i_o suppose_v i_o have_v make_v the_o way_n very_o easy_a in_o the_o former_a chapter_n but_o to_o draw_v the_o hour_n of_o the_o country_n to_o which_o the_o plain_a belong_v be_v most_o easy_a for_o if_o you_o take_v the_o sub-stylar_a for_o the_o noon-line_n and_o the_o elevation_n of_o the_o pole_n above_o the_o plain_a for_o the_o latitude_n you_o may_v make_v this_o dyal_n in_o all_o point_n like_o the_o vertical_a dyal_n after_o the_o precept_n of_o the_o 9_o chapter_n chap._n xxiv_o to_o know_v in_o what_o country_n any_o decline_a dyal_n shall_v serve_v for_o a_o vertical_a dyal_n if_o the_o dyal_n decline_v east_n add_v the_o difference_n of_o longitude_n find_v as_o above_o chapter_n 21._o to_o the_o longitude_n of_o your_o place_n and_o the_o sum_n or_o the_o excess_n above_o 360_o be_v the_o number_n of_o the_o longitude_n seek_v if_o the_o dyal_n decline_v west_n subtract_v the_o say_a difference_n of_o longitude_n out_o of_o the_o longitude_n of_o your_o place_n and_o the_o difference_n be_v the_o longitude_n inquire_v but_o when_o the_o longitude_n of_o your_o place_n happen_v to_o be_v less_o than_o the_o difference_n of_o longitude_n you_o must_v add_v to_o it_o 360._o before_o you_o subtract_v the_o difference_n of_o longitude_n the_o elevation_n of_o the_o pole_n above_o the_o plain_n be_v the_o latitude_n of_o the_o place_n inquire_v example_n the_o decline_a plain_n of_o chapter_n 12._o will_v be_v a_o vertical_a plain_n in_o the_o longitude_n 61._o degree_n and_o north_n latitude_n 32._o degree_n that_o be_v in_o the_o mediterranean_a sea_n between_o alexandria_n and_o the_o isle_n of_o crect_n and_o the_o decline_a recline_a plain_n of_o chapter_n 16_o 17_o 18._o be_v parallel_n to_o the_o horizon_n of_o those_o that_o sail_n in_o longitude_n 359._o degree_n and_o north_n latitude_n 29._o degree_n that_o be_v as_o terrestrial_a globe_n and_o map_n show_v i_o between_o the_o azore_n and_o hesperides_n chap._n xxv_o to_o set_v a_o plain_a parallel_n to_o the_o horizon_n of_o any_o country_n propose_v if_o you_o can_v get_v the_o declination_n and_o reclination_n of_o such_o a_o plain_a you_o have_v enough_o to_o place_v he_o in_o his_o true_a situation_n and_o those_o may_v be_v find_v by_o the_o difference_n of_o longitude_n and_o the_o latitude_n of_o the_o strange_a country_n which_o be_v in_o this_o problem_n suppose_v to_o be_v give_v even_o as_o in_o chapter_n 16._o you_o find_v both_o those_o by_o the_o declination_n and_o reclination_n give_v example_n i_o will_v set_v a_o plain_a parallel_n to_o the_o horizon_n of_o jerusalem_n to_o show_v i_o what_o time_n the_o sun_n rise_v and_o set_v there_o any_o day_n of_o the_o year_n and_o what_o hour_n pass_v at_o jerusalem_n at_o any_o time_n of_o our_o day_n first_o i_o seek_v by_o geographical_a table_n or_o map_n the_o longitude_n and_o latitude_n of_o jerusalem_n and_o i_o find_v that_o jerusalem_n be_v remove_v eastward_o from_o london_n in_o longitude_n 47_o degree_n and_o that_o the_o latitude_n there_o be_v 32_o degree_n or_o thereabouts_o therefore_o in_o the_o rectangled_a triangle_n p_o r_o o_o of_o chapter_n 16._o i_o have_v the_o angle_n p_o 47_o degree_n difference_n of_o longitude_n also_o the_o side_n p_o r_o the_o latitude_n of_o jerusalem_n 32_o degree_n and_o hence_o by_o the_o 4_o problem_n of_o rectangled_a triangle_n book_n 3.6_o i_o get_v p_o o_o 42.30_o minute_n and_o by_o consequence_n o_o n_n 9.45_o minute_n because_o p_o n_n be_v our_o latitude_n and_o i_o get_v also_o the_o angle_n o_o 51.40_o minute_n and_o these_o have_v i_o get_v by_o the_o same_o problem_n in_o the_o adjoin_a triangle_n o_o n_n d_o both_z d_o n_z 12.05_o degree_n the_o compliment_n of_o the_o declination_n inquire_v and_o the_o angle_n d_o 39.23_o compliment_n of_o the_o reclination_n inquire_v wherefore_o i_o conclude_v that_o a_o plain_a which_o shall_v represent_v here_o the_o horizonof_n jerusalem_n must_v decline_v eastward_o 77.55_o minute_n and_o recline_v northward_o 50.37_o minute_n draw_v upon_o this_o plain_a the_o proper_a hour_n of_o jerusalem_n by_o chapter_n 23._o and_o know_v that_o when_o the_o sun_n leave_v this_o plain_a cease_v to_o inlighten_v the_o upper_a part_n of_o it_o than_o he_o set_v at_o jerusalem_n and_o look_v how_o many_o hour_n and_o minute_n the_o sun_n set_v after_o noon_n in_o any_o country_n so_o many_o hour_n and_o minute_n he_o rise_v before_o noon_n chap._n xxvi_o how_o other_o circle_n of_o the_o sphere_n beside_o the_o meridian_n may_v be_v project_v upon_o dial_n the_o projection_n of_o some_o other_o circle_n of_o the_o sphere_n beside_o the_o meridian_n though_o it_o be_v not_o necessary_a for_o find_v the_o hour_n yet_o may_v be_v both_o a_o ornament_n to_o dial_n and_o useful_a also_o for_o find_v the_o meridian_n and_o place_v the_o dyal_n in_o his_o due_a situation_n if_o it_o be_v make_v upon_o a_o movable_a body_n as_o shall_v be_v show_v chapter_n 33._o the_o circle_n fit_a to_o be_v project_v in_o all_o dial_n for_o those_o purpose_n be_v the_o equator_fw-la with_o the_o tropique_n and_o other_o his_o parallel_n which_o may_v be_v account_v parallel_n of_o declination_n as_o they_o pass_v through_o equal_a degree_n as_o every_o 5_o or_o 10_o of_o declination_n or_o parallel_n of_o the_o sign_n as_o they_o pass_v through_o such_o degree_n of_o declination_n as_o the_o sun_n decline_v when_o he_o enter_v into_o any_o sign_n or_o any_o notable_a degree_n thereof_o or_o parallel_n of_o the_o length_n of_o the_o day_n as_o they_o pass_v through_o such_o degree_n of_o declination_n wherein_o the_o sun_n increase_v or_o decrease_v the_o length_n of_o the_o day_n by_o hour_n or_o half-hour_n also_o the_o horizon_n with_o his_o azimuth_n and_o almicantars_n be_v a_o ornament_n to_o horizontal_n and_o vertical_a dial_n and_o be_v likewise_o use_v full_a for_o project_v the_o equator_fw-la and_o his_o parallel_n in_o all_o dial_n my_o purpose_n be_v to_o be_v brief_a in_o this_o treatise_n of_o the_o tumiture_n here_o follow_v because_o i_o hasten_v to_o a_o end_n i_o shall_v therefore_o think_v it_o sufficient_a if_o i_o show_v you_o one_o way_n to_o furnish_v any_o dyal_n with_o the_o circle_n of_o the_o sphere_n leave_v you_o to_o devise_v other_o which_o i_o can_v have_v show_v chap._n xxvii_o how_o to_o describe_v on_o any_o dyal_n the_o proper_a azimuth_n and_o almicantars_n of_o the_o plain_a from_o any_o point_n of_o the_o gnomon_n take_v at_o pleasure_n let_v fall_v a_o perpendicular_a upon_o the_o sub-style_n that_o perpendicular_a shall_v be_v part_n of_o the_o axis_n of_o the_o plain_a and_o shall_v be_v repute_v radius_fw-la to_o the_o horizon_n of_o your_o
and_o mars_n in_o twain_o set_v forward_o and_o come_v round_o again_o then_o in_o one_o year_n the_o sun_n display_v three_o hundred_o sixty_o and_o five_o day_n and_o near_o a_o quarter_n which_o in_o four_o encompassing_n make_v one_o day_n more_o between_o the_o sun_n and_o we_o there_o fly_v fair_a venus_n and_o swift_a mercury_n these_o always_o near_o the_o sun_n we_o find_v not_o far_o before_o nor_o far_o behind_o the_o moon_n be_v the_o low_a who_o in_o seven_o and_o twenty_o day_n go_v round_o the_o heaven_n and_o above_o two_o day_n more_o do_v run_v before_o she_o overtake_v the_o sun_n so_o twenty_o nine_o and_o a_o half_a in_o all_o do_v make_v a_o month_n synodical_a these_o planet_n make_v their_o course_n to_o the_o east_n though_o they_o be_v fast_o hurl_v west_n and_o six_o degree_n the_o rest_n may_v stray_v beside_o the_o sun_n ecliptic_a way_n the_o circle_n of_o the_o sphere_n fix_v great_a circle_n mark_v you_o shall_v which_o equal_o divide_v this_o ball._n just_o in_o the_o midst_n between_o the_o pole_n from_o east_n to_o west_n the_o equator_fw-la roll_n the_o ecliptic_a cut_v he_o and_o do_v slide_v scarce_o twenty_o four_o degree_n aside_o horizon_n even_o with_o the_o ground_n from_o star_n below_o our_o sight_n do_v bind_v meridian_n upright_o do_v rise_v part_v the_o east_n and_o western_a sky_n two_o colour_n through_o the_o pole_n do_v run_v quarr_v the_o circle_n of_o the_o sun_n one_o where_o the_o spring_n and_o fall_v begin_v the_o other_o where_o long_a day_n come_v in_o four_z lesser_a circle_n mark_v they_o well_o be_v to_o the_o equator_fw-la parallel_n two_o tropique_n bind_v the_o sun_n high_a way_n show_v the_o long_a and_o short_a day_n the_o arctique_a circle_n cur_n the_o bear_n the_o antarctique_a opposite_a appear_v meridian_n half_n twenty_o four_o for_o hour_n and_o for_o degree_n ninescore_o through_o both_o the_o pole_n of_o the_o world_n do_v pass_v and_o the_o equinoctial_a down_o right_a cross_n and_o ninescore_o parallel_n have_v that_o line_n by_o which_o star_n north_n and_o south_n decline_v the_o ecliptic_a have_v his_o longitude_n and_o parallel_n of_o latitude_n for_o star_n but_o in_o geography_n the_o town_n beside_o the_o equator_fw-la lie_n over_o our_o head_n and_o under_o foot_n the_o ninescore_o azimuth_n do_v meet_v and_o here_o as_o many_o parallel_n of_o altitude_n horizon_n tell_v longitude_n and_o meridian_n all_o and_o azimuth_n great_a circle_n call_v but_o all_o their_o parallel_n in_o heaven_n be_v lesser_a cut_v the_o globe_n uneven_a degree_n three_o hundred_o and_o threescore_o have_v every_o circle_n and_o no_o more_o when_o i_o consider_v thy_o heaven_n the_o work_n of_o thy_o finger_n the_o moon_n and_o the_o star_n which_o thou_o have_v ordain_v what_o be_v man_n that_o thou_o be_v mindful_a of_o he_o or_o the_o son_n of_o man_n that_o thou_o visite_a he_o ps_n 8._o errata_fw-la some_o fault_n have_v be_v commit_v between_o the_o writer_n and_o the_o printer_n the_o chief_n whereof_o the_o reader_n be_v desire_v to_o amend_v as_o follow_v pag._n and_o line_n fault_n amendment_n 2_o 3_o 4._o etc._n etc._n to_o pag._n 30._o in_o the_o title_n the_o first_o book_n of_o the_o fabric_n of_o the_o planisphere_n the_o first_o book_n of_o the_o fabric_n of_o the_o planisphear_n 31_o and_o 32._o in_o the_o title_n the_o second_o book_n of_o the_o projection_n of_o the_o sphere_n the_o second_o book_n of_o the_o projection_n of_o the_o sphere_n 1._o 13._o mossy_a massy_a 2._o 7._o declination_n delineation_n 3._o ant_n declination_n delineation_n 4._o 16._o look_v up_o look_v upon_o 4._o 36._o eye_n beam_n eye-beame_n 5._o 13._o euclid_n 4_o 5._o euclid_n 4.5_o 22._o require_v of_o your_o compass_n over_o reach_n require_v if_o your_o compass_n reach_v short_a 5._o 23._o if_o it_o reach_v short_a if_o it_o overreach_v 6._o 39_o structure_n structure_n 8._o secant_fw-la 67._o 25693._o 25593._o  _fw-fr the_n 5._o last_o tangent_n want_v a_o place_n you_o must_v add_v a_o cypher_n to_o each_o of_o they_o 9_o 16._o two_o so_o 12._o 18._o all_o but_o all_o but_o 13._o 07._o work_v it_o work_v it_o 16._o 19_o four_o few_o 17._o 18._o alamath_n alamach_n 21._o henerichus_n heniochus_n 17._o antop_n little_a rain_n little_a wain_n 18._o 8._o brow_n crown_n 18._o 30._o praecepe_o praesepe_v 19_o 16._o bedalgieure_fw-fr bedalgieuze_fw-fr 23._o alhaber_n alhabor_n 20._o 6._o round_o the_o inner_a circle_n or_o edge_n of_o this_o ring_n it_o must_v round_o the_o inner_a circle_n or_o edge_n of_o this_o ring_n must_v 20._o 14._o nail_n screw_v male_a screw_n 17._o small_a screw_n female_a screw_n 19_o bare_a bear_v 22._o 30._o be_v make_v and_o go_v for_o that_o year_n your_o scale_n be_v make_v and_o so_o for_o that_o year_n your_o scale_n 24._o 9_o but_o one_o degree_n but_o for_o one_o degree_n 25._o 7._o  _fw-fr put_v out_o the_o mark_n of_o parenthesis_n 26._o 8_o year_n henr._n 3._o year_n of_o henr_n 3_o 23._o periodus_fw-la periodus_fw-la 28._o always_o upon_o always_o upon_o 35._o thus_o set_v thus_o set_v 28._o 1._o and_o 5._o grostons_n graston_n 30._o 3_o second_o meridional_a second_o or_o the_o meridional_a 33_o 6._o set_v for_o london_n namely_o for_o london_n 33._o â—1_n on_o elevation_n no_o elevation_n 34._o â—â—_o 〈◊〉_d the_o which_o the_o 9_o azimuth_n azimuthe_n 37._o 6._o the_o eye_n place_v the_o eye_n be_v place_v 41._o 3._o centre_n b_o a_o centre_n b_o a_o 48._o 4._o either_o way_n either_o way_n 22._o a_o c_o c_o a_o 50._o 16._o zenith_n of_o zenith_n of_o 32._o zenith_n and_o b_o zenith_n a_n and_o b_o 53._o 12._o 12_o and_o 13_o number_n 12_o and_o 13_o number_v 56._o 8._o these_o side_n the_o side_n 20._o subâ—endeth_v a_o which_o subâ—endeth_v a_o 62._o 17._o fall_n fall_v 63._o 7_o 9_o way_n ray_n ult_n of_o deleatur_fw-la 64._o 10._o min._n at_o 70_o min._n and_o at_o 70_o 11._o between_o 8_o degr_n 34._o min._n between_o 18_o and_o 24_o min._n 12._o here_o refraction_n be_v as_o the_o sun_n her_o refraction_n be_v as_o the_o sun_n be_v 65_o 1._o your_o meridian_n your_o meridian_n 66._o 30._o require_v inquire_v 67._o 3._o michal_n michael_n 68_o 39_o long_o long_o 73._o 6_o chap._n two_o chap_n xi_o 74._o 20._o alrucabe_n alrucaba_n 75._o 8._o alrucabe_n alrucaba_n 75._o 12._o first_o make_v first_o mode_n 76._o 29._o prick_v here_o prick_v here_o 8â—_n 16_o 17._o by_o declin_n by_o their_o declin_n 82._o 12._o her_o declin_n his_o declin_n antep_n sta_fw-la star_n 86._o 16_o 17_o 18_o 19_o pleyade_n rise_v set_v pleiades_n rise_v set_v 86._o 30._o to_o be_v least_o to_o be_v lose_v 87._o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 88_o 4._o can_v happen_v can_v not_o happen_v â—_o 14._o note_n know_v 17._o asera_n asera_n 91._o â—1_n duet_n deut._n 99_o 21._o 23_o degree_n 23_o degree_n 102._o 6_o and_o 30._o eniph_n alph._n eniph_n alph._n 23._o 35_o â…“_n 56_o â…“_n 105._o 8._o star_n i_o star_n i_o â—_o caeti_fw-la ceti_fw-la 19_o 120_o deg_fw-la 125_o degr_n 110._o pen._n by_o oblique_a problem_n by_o probl_n 2_o obliqu_n 111._o 25._o in_o 39_o ½_n in_o all_o 39_o ½_n 114._o 17._o agree_v set_v agree_v set_v 11._o house_n also_o house_n also_o 31._o 49_o 30_o 50_o 51._o 118._o 6_o 7._o 49_o 50_o 50_o 51._o 24._o and_o so_o and_o to_o 119._o 1_o astrologer_n astrology_n 17._o futurus_fw-la futurus_fw-la 122._o 29._o no_o man_n no_o man_n 123._o 3._o princeps_fw-la nero_n princeps_fw-la nero_n 4._o citherae_fw-la citharae_fw-la 10._o dereliquit_fw-la nero_n dereliquit_fw-la nero_n 12._o persuesum_fw-la persuasum_fw-la 27._o se_z nore_z temerè_fw-la 128._o 26._o as_o by_o and_o by_o 29._o set_v go_v set_v therefore_o 130._o 34._o jupiter_n in_o that_o meridian_n jupiter_n in_o that_o meridian_n 139._o 6._o christ_n time_n christ_n time_n 17._o ticius_n tacitus_n 141._o 6._o 4_o 5._o 11._o 4._o 5_o 11._o 145._o 13._o sun_n dial_n sun_n dial_n 147._o 5._o or_o equinoctial_a deleatur_fw-la 19_o so_o the_o hour_n line_n to_o the_o hour-line_n 154._o in_o the_o scheam_n the_o letter_n i_o be_v want_v at_o the_o low_a end_n of_o the_o hour-line_n of_o 11._o  _fw-fr 157._o 17._o with_o a_o extension_n with_o any_o extension_n 174._o 32._o precrucem_fw-la per_fw-la crucem_fw-la 176._o 11._o by_o the_o arch_n by_o r_n t_o the_o arch_n 180._o 9_o declination_n plain_a decline_v plain_a 181._o 20._o pray_fw-mi per_fw-la 184._o 27._o the_o vertical_a of_o my_o dial_n and_o also_o deleatur_fw-la 185._o 28._o and_o so_o and_o to_o 188._o 9_o tumiture_fw-fr furniture_n 190._o 7._o you_o use_v you_o may_v use_v 192._o in_o the_o scheme_n the_o prick_a line_n last_o save_o one_o shall_v be_v put_v out_o  _fw-fr 193._o of_o it_o a_o vertical_a plain_n a_o vertical_a or_o a_o south_n horizontal_n
both_o the_o scheme_n of_o the_o former_a chapt._n now_o i_o tell_v you_o book_n 3.2_o that_o if_o any_o two_o part_n of_o a_o rectangled_a triangle_n be_v give_v with_o the_o right_a angle_n the_o rest_n may_v be_v easy_o find_v observe_v then_o your_o triangle_n a_o b_o c_o in_o the_o first_o scheme_n of_o the_o former_a chapter_n and_o likewise_o in_o the_o meridional_a projection_n of_o your_o planisphere_n you_o shall_v see_v the_o very_a same_o for_o the_o finitor_n be_v set_v to_o the_o latitude_n c_o shall_v be_v where_o the_o tropic_a of_o cancer_n cut_v the_o finiter_n the_o arch_n of_o the_o meridian_n between_o c_o and_z the_o equator_fw-la be_v c_o a_n and_o the_o declination_n thence_o in_o the_o equator_fw-la to_o the_o centre_n be_v a_o b_o the_o base_a and_o the_o ascensional_a difference_n b_o c_o in_o the_o horizon_n be_v the_o amplitude_n b_o be_v the_o compliment_n of_o latitude_n a_o be_v 90_o degr_n c_o be_v unknown_a and_o we_o need_v it_o not_o else_o if_o you_o have_v read_v the_o three_o book_n i_o hope_v you_o can_v find_v he_o here_o be_v six_o case_n 1._o admit_v now_o that_o the_o declination_n and_o amplitude_n be_v give_v put_v the_o term_n of_o the_o amplitude_n i_o mean_v the_o point_n where_o it_o end_v count_v from_o the_o centre_n upon_o the_o parallel_n of_o the_o declination_n and_o your_o triangle_n be_v form_v and_o thereby_o the_o ascensional_a difference_n and_o the_o compliment_n of_o latitude_n be_v discover_v 2._o or_o if_o the_o declination_n and_o ascensional_a difference_n be_v give_v number_n the_o ascensional_a difference_n from_o the_o centre_n downward_o in_o the_o equator_fw-la then_o go_v up_o in_o a_o meridian_n as_o many_o degree_n as_o the_o declination_n come_v to_o and_o to_o the_o point_n where_o you_o end_v which_o be_v c_z set_v the_o finiter_n so_o he_o be_v place_v to_o your_o latitude_n and_o the_o amplitude_n also_o be_v show_v 3._o or_o if_o the_o declination_n and_o latitude_n be_v give_v the_o finiter_n be_v set_v to_o the_o latitude_n follow_v the_o parallel_n of_o declination_n to_o the_o finiter_n there_o be_v c_o thence_o go_v down_o by_o a_o meridian_n to_o a_o in_o the_o equator_fw-la thence_o in_o the_o equator_fw-la to_o bat_n the_o centre_n thence_o turn_v by_o the_o finiter_n to_z c_o and_o you_o have_v compass_v your_o triangle_n and_o therefore_o have_v all_o know_v but_o c._n 4._o if_o the_o latitude_n and_o ascensional_a difference_n be_v give_v the_o finiter_n be_v set_v to_o the_o latitude_n count_v from_o the_o centre_n in_o the_o equator_fw-la to_o the_o end_n of_o the_o ascensional_a difference_n there_o be_v a_o go_v up_o thence_o in_o a_o meridian_n to_o the_o finiter_n there_o be_v c_o go_v thence_o in_o the_o finiter_fw-la to_o the_o centre_n there_o be_v b._n 5._o if_o the_o latitude_n and_o amplitude_n be_v give_v the_o finiter_n be_v set_v to_o the_o latitude_n count_v from_o the_o centre_n b_o in_o the_o finiter_fw-la to_o the_o end_n of_o the_o amplitude_n where_o shall_v be_v c_z go_v down_o thence_o in_o a_o meridian_n to_o the_o equator_fw-la where_o be_v a_o thence_o in_o the_o equator_fw-la return_n to_o the_o centre_n b._n 6._o if_o the_o amplitude_n and_o ascensional_a difference_n be_v give_v prick_v the_o end_n of_o the_o amplitude_n number_v in_o the_o finiter_fw-la from_o the_o centre_n and_o prick_v the_o end_n of_o the_o ascensional_a difference_n number_v in_o the_o equator_fw-la from_o the_o centre_n then_o turn_v about_o the_o reet_n till_o some_o one_o of_o the_o meridian_n cut_n both_o these_o prick_n and_o that_o shall_v make_v up_o the_o triangle_n note_v that_o for_o south_n star_n or_o the_o sun_n in_o south_n sign_n this_o triangle_n lie_v on_o the_o southside_n the_o centre_n and_o above_o the_o finiter_n but_o for_o north_n sign_n it_o lie_v north_n of_o the_o centre_n and_o below_o the_o finiter_n chap._n xvi_o to_o do_v the_o same_o in_o the_o equinoctial_a projection_n here_o serve_v the_o second_o figure_n of_o the_o horizontal_n triangle_n in_o chap._n 14._o where_o b_o at_fw-fr be_v the_o ascensional_a difference_n c_o he_o the_o declination_n b_o c_o the_o amplitude_n b_o compliment_n of_o the_o latitude_n if_o the_o latitude_n and_o declination_n be_v give_v number_n the_o declination_n on_o the_o label_n inward_o and_o at_o the_o end_n make_v a_o prick_n turn_v this_o prick_n to_o the_o horizon_n of_o the_o mater_n and_o so_o shall_v the_o outward_a arch_n of_o the_o label_n be_v c_o a_o the_o short_a arch_n of_o that_o horizon_n b_o c_o and_o a_o arch_n of_o the_o limb_n b_o a_o of_o your_o triangle_n if_o the_o latitude_n and_o amplitude_n be_v give_v do_v as_o in_o this_o example_n i_o observe_v sirius_n to_o rise_v 27_o ¼_n from_o the_o east_n southward_o my_o latitude_n be_v 52_o degr_n ¼_n i_o go_v to_o the_o 52_o ¼_n meridian_n on_o the_o mater_n reckon_v from_o the_o centre_n on_o the_o southside_n because_o the_o star_n be_v southern_a as_o his_o rise_a show_n this_o 52_o ¼_n meridian_n be_v my_o horizon_n as_o book_n 2.2_o i_o number_n in_o he_o the_o amplitude_n of_o sirius_n from_o oriens_fw-la towards_o meridies_n 27_o ¼_n and_o thereto_o i_o lay_v the_o label_n and_o i_o see_v my_o horizon_n cut_v the_o label_n in_o 16¼_n that_o be_v c_o a_o the_o south_n decimation_n of_o sirius_n and_o between_o the_o label_n and_o oriens_fw-la in_o the_o limb_n i_o have_v b_o a_o 22_o ¼_n his_o ascensional_a difference_n if_o you_o can_v do_v these_o two_o you_o may_v resolve_v the_o four_o other_o case_n of_o this_o chapter_n with_o like_a facility_n view_v but_o the_o scheam_n in_o the_o book_n and_o in_o your_o planisphear_n and_o that_o alone_o will_v instruct_v you_o chap._n xvii_o to_o find_v the_o semi-diurnal_a and_o semi-nocturnal_a arch_n of_o the_o sun_n or_o star_n the_o time_n of_o their_o rise_n and_o set_v and_o the_o length_n of_o their_o day_n and_o night_n by_o declination_n and_o the_o latitude_n of_o the_o place_n set_v the_o finiter_n to_o the_o latitude_n asin_a the_o first_o mode_n of_o the_o meridional_a projection_n then_o seek_v the_o parallel_n of_o the_o declination_n of_o the_o sun_n or_o star_n north_n or_o south_n as_o it_o happen_v to_o be_v that_o parallel_n shall_v be_v divide_v by_o the_o finiter_n into_o two_o arch_n the_o arch_n above_o the_o finiter_n be_v the_o semi-diurnal_a arch_n in_o which_o you_o may_v count_v the_o time_n of_o rise_v and_o set_v and_o the_o length_n of_o the_o day_n that_o below_o be_v the_o semi-nocturnal_a arch_n in_o which_o you_o may_v reckon_v the_o length_n of_o the_o night_n or_o if_o your_o question_n be_v of_o a_o star_n the_o time_n he_o spend_v under_o the_o horizon_n example_n in_o the_o first_o scheme_n of_o the_o 14_o chapter_n d_o e_z be_v the_o tropic_a of_o cancer_n that_o be_v the_o 23_o ½_n parallel_v of_o north_n declination_n c_o e_z be_v the_o semi-diurnal_a arch_n c_o d_o the_o semi-nocturnal_a and_o you_o shall_v find_v in_o the_o meridional_a projection_n of_o your_o planisphear_n those_o arch_n be_v divide_v by_o the_o meridian_n and_o the_o arch_n c_o e_o contain_v 124_o degr_n 10_o min._n which_o turn_v into_o hour_n and_o minute_n account_v every_o degree_n 4_o minute_n of_o time_n and_o every_o 15_o degree_n a_o hour_n be_v 8_o hour_n 16_o min._n 40_o sec_fw-la half_n the_o length_n of_o our_o long_a day_n and_o the_o arch_n c_o d_o contain_v 55._o deg_fw-la 50_o min._n that_o be_v three_o hour_n 43_o min._n 20_o sec_fw-la half_n the_o length_n of_o our_o short_a night_n therefore_o at_o three_o hour_n 43_o min._n after_o midnight_n the_o sun_n rise_v in_o the_o tropic_a and_o set_v so_o much_o before_o midnight_n that_o be_v at_o eight_o hour_n 16_o min._n 40_o sec_fw-la and_o so_o may_v you_o find_v your_o desire_n in_o any_o other_o parallel_n example_n 2._o i_o observe_v that_o fomahant_n his_o meridian_n altitude_n be_v but_o 6.30_o min._n therefore_o by_o chap._n 13_o he_o decline_v southward_o 31¼_n i_o will_v know_v how_o long_o he_o shine_v with_o we_o and_o i_o present_o see_v in_o the_o meridional_a projection_n of_o my_o planisphear_n that_o his_o parallel_n have_v but_o 38_o degr_n above_o the_o horizon_n that_o be_v he_o will_v set_v two_o hour_n 32_o min._n after_o he_o be_v south_n and_o the_o whole_a time_n he_o shine_v in_o our_o horizon_n be_v five_o hour_n four_o minute_n example_n 3._o lyra_n her_o declination_n be_v 38.30_o min._n north_n and_o i_o see_v his_o parallel_n come_v within_o 45_o min._n of_o the_o horizon_n in_o the_o north_n part_n of_o the_o meridian_n but_o never_o touch_v it_o therefore_o i_o conclude_v that_o lyra_n never_o set_v with_o we_o at_o all_o chap._n xviii_o to_o find_v the_o same_o in_o the_o equinoctial_a projection_n turn_v about_o the_o
pleyade_n in_o our_o lat_fw-mi cosmical_o set_v ☉_o in_o â™_o 29_o ½_n nou._n 11._o at_o athens_n cosmical_o rise_v ☉_o in_o ♉_o 19_o ½_n april_n 30._o at_o athens_n cosmical_o set_v ☉_o in_o â™_o 27_o ½_n novem._n 9_o arcturus_n in_o our_o lat._n cosmical_o ri._n ☉_o in_o ♎_o 0_o sep._n 13._o arcturus_n in_o our_o lat._n cosmical_o set._n ☉_o in_o ♋_o 4_o june_n 15._o at_o athens_n cosmical_o rise_v ☉_o in_o ♎_o 10_o ½_n sept._n 23._o at_o athens_n cosmical_o set_v ☉_o in_o ♊_o 6._o may_v 17._o chap._n xxi_o to_o find_v the_o time_n when_o any_o star_n rise_v or_o set_v acronycal_o by_o his_o declination_n and_o right_a ascension_n and_o the_o latitude_n of_o the_o place_n when_o a_o star_n rise_v just_a at_o sunsetting_a he_o be_v say_v to_o rise_v acronical_o to_o find_v the_o time_n turn_v the_o star_n to_o the_o east_n part_n of_o the_o horizon_n in_o the_o equinoctial_a projection_n and_o mark_v what_o degree_n of_o the_o ecliptic_a descend_v in_o the_o west_n for_o when_o the_o sun_n come_v to_o that_o degree_n the_o star_n shall_v rise_v acronical_o example_n when_o sirius_n touch_v the_o south_n east_n quarter_n of_o our_o horizon_n i_o see_v â™’_o 18._o set_v therefore_o when_o the_o sun_n be_v in_o â™’_o 18._o sirius_n rise_v acronical_o a_o star_n set_v acronical_o when_o he_o set_v with_o the_o sun_n to_o find_v the_o time_n place_v the_o star_n set_v in_o the_o west-part_n of_o the_o horizon_n and_o see_v what_o degree_n of_o the_o ecliptic_a set_v with_o he_o for_o when_o the_o sun_n be_v in_o that_o degree_n the_o star_n shall_v set_v acronical_o thus_o in_o our_o latitude_n sirius_n acronical_o rise_v ☉_o in_o â™’_o 18._o jan._n 27._o sirius_n acronical_o seat_v ☉_o in_o ♉_o 23._o may_v 3_o at_o athens_n sirius_n acronical_o ri._n ☉_o in_o â™’_o 4._o janu._n 13._o at_o athens_n sirius_n acronical_o set._n ☉_o in_o ♊_o 9_o may_v 20._o pleiades_n acronical_o rise_v ☉_o in_o â™_o 13._o octo._n 26._o pleiades_n acronical_o seat_v ☉_o in_o ♉_o 29_o ½_n may_v 10._o at_o athens_n pleiades_n acroni_n rise_v ☉_o in_o â™_o 19_o ½_n nou._n 1._o at_o athens_n pleiades_n acroni_n seat_v ☉_o in_o ♉_o 27_o ½_n may_v 8._o arcturus_n acronical_o rise_v ☉_o in_o ♈_o 0._o march_n 10._o arcturus_n acronical_o seat_v ☉_o in_o ♑_o 4_o dec._n 15._o at_o athens_n arcturus_n acroni_n rise_v ☉_o in_o ♈_o 10._o ½_n mar._n 20._o at_o athens_n arcturus_n acroni_n seat_v ☉_o in_o â™_o 6._o nove._n 18._o chap._n xxii_o to_o find_v when_o a_o star_n rise_v or_o set_v heliacal_o astar_n rise_v heliacal_o when_o he_o gete_v out_o of_o the_o beam_n of_o the_o sun_n and_o begin_v to_o be_v see_v in_o the_o east_n a_o little_a before_o sun_n rise_v and_o a_o star_n be_v say_v to_o set_v heliacal_o when_o he_o get_v into_o the_o beam_n of_o the_o sun_n and_o begin_v to_o be_v least_o in_o the_o evening_n by_o reason_n of_o the_o sun_n opproach_v to_o he_o those_o star_n which_o you_o see_v near_a the_o east_n horizon_n in_o the_o morning_n twilight_n be_v heliacall_a riser_n and_o those_o which_o you_o see_v near_a the_o westpart_n of_o the_o horizon_n in_o the_o evening_n twilight_n be_v heliacall_a setter_n for_o this_o no_o exact_a rule_n can_v be_v give_v for_o all_o man_n have_v not_o like_a quickness_n of_o sight_n nor_o all_o star_n like_o brightness_n nor_o all_o climate_n country_n and_o day_n of_o the_o year_n the_o same_o clearness_n of_o air._n and_o the_o moon_n oft_o time_n augment_v the_o twilight_n when_o she_o be_v within_o a_o few_o day_n of_o the_o change_n and_o keep_v the_o star_n long_o combust_v common_o about_o twenty_o day_n before_o their_o acronical_a set_n they_o come_v within_o the_o sun_n beam_n and_o so_o set_v heliacal_o and_o they_o appear_v again_o that_o be_v rise_v heliacal_o about_o twenty_o day_n after_o their_o cosmical_a rise_n but_o if_o they_o be_v great_a star_n the_o air_n clear_a your_o sight_n good_a the_o angle_n make_v between_o the_o ecliptic_a and_o the_o horizon_n great_a they_o may_v appear_v soon_o and_o late_a in_o the_o contrary_a case_n according_a to_o this_o rule_n the_o pleyade_n set_v heliacal_o now_o at_o athens_n ☉_o in_o ♉_o 7._o and_o rise_v heliacally_a ☉_o in_o ♊_o 9_o so_o they_o shall_v be_v combust_v there_o 32_o day_n but_o because_o they_o be_v star_n of_o less_o magnitude_n we_o may_v perhaps_o allow_v they_o 40_o day_n as_o hesiod_n do_v in_o his_o time_n in_o the_o begin_n of_o his_o second_o book_n of_o week_n and_o day_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d chap._n xxiii_o to_o find_v the_o age_n when_o any_o astrologer_n live_v and_o what_o time_n of_o the_o solar_a year_n the_o season_n happen_v in_o his_o country_n by_o know_v his_o latitude_n and_o the_o rise_n of_o any_o star_n in_o his_o time_n the_o old_a grecian_n and_o after_o they_o the_o latin_n before_o julius_n caesar_n especial_o design_v the_o season_n of_o the_o year_n by_o the_o rise_n and_o set_v of_o some_o notable_a star_n hesiod_n begin_v his_o second_o book_n of_o week_n and_o day_n with_o this_o georgical_a canon_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d that_o be_v when_o the_o pleyade_n rise_v begin_v to_o mow_v and_o to_o plough_v when_o they_o set_v and_o in_o the_o same_o book_n verse_n 182._o he_o say_v 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d that_o be_v 60_o day_n after_o the_o winter_n tropic_n arcturus_n rise_v acronical_o and_o then_o appear_v the_o swallow_n the_o spring_n be_v then_o new_o begin_v these_o and_o the_o like_a rule_n be_v the_o husbandman_n almanac_n by_o which_o they_o measure_v the_o solar_a year_n and_o the_o return_n of_o the_o season_n for_o in_o their_o civil_a year_n consist_v of_o lunar_a month_n by_o reason_n of_o a_o intercalary_n month_n which_o be_v add_v every_o three_o year_n and_o somewhat_o oft_o the_o season_n can_v happen_v upon_o the_o same_o day_n of_o the_o month_n yearly_a but_o sometime_o 2_o or_o 3_o week_n soon_o or_o late_a as_o our_o movable_a feast_n do_v the_o rise_n and_o set_v of_o the_o fix_a star_n keep_v the_o same_o distance_n yearly_o from_o the_o equinoctial_a and_o solstitial_a point_n for_o a_o man_n age_n near_o enough_o but_o long_o those_o rule_n can_v last_v without_o some_o perceivable_a error_n for_o in_o 100_o year_n the_o star_n go_v forward_o in_o longitude_n according_a to_o tycho_n 1_o degree_n 25_o minute_n by_o reason_n whereof_o the_o rise_n and_o setting_n of_o the_o star_n happen_v late_a in_o the_o year_n about_o a_o day_n and_o half_a every_o 100_o year_n in_o the_o same_o latitude_n now_o if_o you_o will_v note_v in_o what_o age_n a_o star_n have_v such_o a_o rise_n or_o set_v in_o such_o a_o latitude_n as_o for_o example_n in_o what_o age_n arcturus_n rise_v 60_o day_n after_o midwinter_n in_o the_o latitude_n of_o asera_n in_o boeotia_n near_o athens_n who_o latitude_n be_v 37_o ¼_n and_o consequent_o how_o long_o since_o hesiod_n live_v in_o who_o day_n arcturus_n have_v such_o rise_n you_o shall_v reason_v thus_o 60._o day_n after_o the_o winter_n tropic_n the_o sun_n be_v in_o ♓_o 1_o degree_n by_o the_o ephemeris_fw-la for_o in_fw-la those_o 60_o day_n near_o his_o perigium_n he_o go_v about_o 61_o degree_n i_o be_o therefore_o to_o seek_v when_o arcturus_n do_v rise_v at_o athens_n with_o the_o opposite_a degree_n of_o the_o ecliptic_a â™_o 1_o degree_n the_o sun_n be_v in_o ♓_o 1_o degree_n then_o set_v over_o against_o it_o i_o seek_v the_o longitude_n and_o latitude_n of_o arcturus_n and_o find_v in_o tycho'es_n table_n that_o anno_fw-la domi._n 1600._o arcturus_n have_v longitude_n ♎_o 18._o 39_o minute_n latitude_n b._n 31.02_o minute_n then_o i_o will_v suppose_v that_o hesiod_n live_v 830._o year_n before_o christ_n for_o there_o some_o chronologer_n place_v he_o but_o without_o any_o good_a proof_n that_o i_o find_v that_o be_v 2430_o year_n before_o anno_fw-la domi._n 1600._o in_o which_o space_n of_o time_n arcturus_n must_v have_v increase_v his_o longitude_n by_o tycho_n '_o hypothesis_n 34_o degree_n 25_o minute_n which_o be_v subduct_v out_o of_o the_o longitude_n which_o arcturus_n have_v anno_fw-la domi._n 1600._o leaf_n his_o longitude_n for_o the_o year_n before_o christ_n 830._o â™_o 14._o degree_n 14._o minute_n his_o latitude_n be_v then_o and_o ever_o 31.02_o minute_n now_o from_o this_o longitude_n and_o latitude_n i_o get_v his_o right_a ascension_n and_o declination_n by_o chap._n 34._o of_o this_o book_n where_o i_o find_v ascension_n 180._o degree_n declination_n north_n 34._o degree_n 15_o minute_n those_o have_v i_o
the_o moon_n age_n example_n january_n 20._o 1656._o according_a to_o the_o account_n of_o the_o church_n of_o england_n who_o begin_v the_o year_n with_o march_n 25._o which_o be_v the_o equinoctial_a day_n about_o christ_n time_n the_o epact_n be_v 14._o january_n be_v the_o 11_o month_n and_o the_o 20_o day_n be_v propose_v now_o add_v 14_o 11_o and_o 20._o together_o they_o make_v 45._o out_o of_o which_o i_o take_v 30._o and_o there_o remain_v 15._o the_o moon_n age_n this_o rule_n be_v of_o good_a use_n not_o only_o to_o find_v the_o age_n of_o the_o moon_n and_o so_o her_o change_n to_o a_o day_n but_o also_o for_o examine_v of_o chronologie_n where_o the_o time_n be_v most_o certain_o reckon_v by_o eclipse_n but_o you_o must_v note_v that_o if_o you_o apply_v this_o rule_n to_o the_o year_n pass_v before_o anno_fw-la dom_fw-la 1600._o then_o for_o every_o 312._o year_n that_o the_o year_n propose_v precede_v anno_fw-la dom._n 1600._o you_o must_v subtract_v one_o day_n out_o of_o the_o age_n of_o the_o moon_n find_v by_o this_o rule_n example_n â—icius_fw-la lib._n 1._o report_n that_o in_o the_o begin_n of_o tiberius_n caesar_n reign_n there_o be_v a_o eclipse_n of_o the_o moon_n and_o temporarius_n say_v that_o whereas_o augustus_n die_v aug._n 29._o i_o think_v he_o shall_v say_v 19_o this_o eclipse_n happen_v sep._n 27._o i_o will_v know_v whether_o it_o be_v possible_a for_o a_o eclipse_n to_o happen_v that_o day_n suppose_v the_o beginning_n of_o tiberius_n to_o be_v in_o august_n anno_fw-la dom._n 14._o and_o anno_fw-la periodi_fw-la julianae_n 4727._o the_o prime_n for_o that_o year_n be_v 15_o and_o the_o epact_n 15._o by_o book_n 1._o 11._o add_v now_o to_o the_o epact_n for_o september_n 7._o and_o for_o the_o day_n of_o the_o month_n 27._o and_o the_o sum_n be_v 49._o out_o of_o which_o subduct_v 30._o i_o leave_v the_o moon_n age_n 19_o but_o because_o anno_fw-la dom._n 14._o precede_v anno_fw-la dom._n 1600._o 5._o time_n 312._o year_n therefore_o out_o of_o 19_o i_o subduct_v 5._o and_o there_o remain_v 14._o the_o age_n of_o the_o moon_n correct_v for_o september_n 27._o anno_fw-la dom._n 14._o therefore_o it_o be_v about_o the_o full_a moon_n and_o it_o be_v possible_a the_o moon_n may_v be_v eclipse_v then_o as_o temporarius_n say_v but_o it_o can_v not_o be_v eclipse_v september_n 27._o anno_fw-la dom._n 13._o for_o then_o the_o epact_n be_v 4._o the_o age_n of_o the_o moon_n by_o the_o same_o rule_n be_v 3._o neither_o can_v it_o happen_v sep._n 27._o anno_fw-la dom._n 15._o for_o then_o by_o the_o same_o rule_n the_o age_n of_o the_o moon_n be_v 25._o at_o what_o age_n the_o moon_n be_v far_o from_o her_o opposition_n to_o the_o sun_n and_o therefore_o can_v not_o be_v eclipse_v chap._n lxviii_o to_o find_v in_o what_o parallel_n and_o climate_n a_o place_n be_v by_o the_o latitude_n give_v parallel_n in_o geography_n be_v lesser_a circle_n parallel_v to_o the_o equator_fw-la and_o pass_v through_o the_o zenith_n of_o a_o place_n and_o succeed_v one_o another_o at_o such_o distance_n that_o at_o every_o parallel_n the_o length_n of_o the_o day_n be_v vary_a a_o quarter_n of_o a_o hour_n a_o climate_n be_v such_o a_o parallel_n as_o alter_v the_o length_n of_o the_o day_n half_a a_o hour_n the_o parallel_n and_o climate_n begin_v from_o the_o equator_fw-la under_o which_o the_o day_n be_v always_o equal_a to_o the_o night_n and_o each_o 12_o hour_n long_o hence_o they_o count_v the_o parallel_n and_o climate_n northward_o and_o southward_o but_o because_o the_o earth_n be_v not_o so_o far_o know_v to_o ptolemy_n and_o the_o ancient_a geographer_n as_o it_o have_v be_v to_o those_o of_o late_a time_n therefore_o there_o be_v great_a difference_n between_o the_o ancient_n and_o late_a geographer_n about_o the_o number_n and_o quantity_n of_o the_o space_n contain_v by_o they_o as_o among_o other_o kerkerman_n sy_v geography_n lib._n 1._o have_v show_v yet_o may_v they_o easy_o be_v find_v to_o every_o man_n mind_n by_o the_o planisphear_n in_o the_o meridional_a projection_n thus_o find_v by_o 4._o 17._o what_o be_v the_o semi-diurnal_a arch_n of_o the_o sun_n in_o ♋_o out_z of_o which_o take_v 6_o hour_n and_o look_v how_o many_o quarter_n of_o a_o hour_n the_o double_a of_o the_o residue_n contain_v so_o many_o geographical_a parallel_n be_v the_o place_n remove_v from_o the_o equator_fw-la and_o half_a so_o many_o climate_n example_n i_o find_v the_o semi-diurnal_a arch_n in_o our_o latitude_n to_o be_v 8_o hour_n 16_o minute_n in_o the_o tropic_n of_o cancer_n out_o of_o which_o taking_n 6._o and_o double_v the_o residue_n i_o have_v 4._o 33._o which_o be_v more_o than_o 9_o half_a hour_n or_o more_o than_o 18._o quarter_n so_o much_o our_o long_a day_n exceed_v 12_o hour_n therefore_o we_o shall_v be_v pass_v the_o 18_o parallel_n and_o 9_o climate_n viz._n in_o the_o begin_n of_o the_o 10_o climate_n and_o 19_o parallel_n chap._n lxix_o the_o longitude_n and_o latitude_n of_o two_o place_n give_v to_o find_v their_o distance_n what_o longitude_n and_o latitude_n in_o geography_n be_v and_o how_o they_o differ_v from_o longitude_n and_o latitude_n in_o astronomy_n have_v be_v show_v book_n 4_o 5.11_o if_o the_o place_n differ_v only_o in_o latitude_n and_o have_v one_o longitude_n bear_v full_a north_n or_o south_n one_o from_o another_o then_o take_v their_o difference_n of_o latitude_n by_o subduct_v the_o less_o out_o of_o the_o great_a if_o the_o place_n have_v both_o north_n latitude_n or_o both_o south_n latitude_n or_o take_v the_o sum_n of_o their_o latitude_n if_o one_o be_v north_n and_o the_o other_o south_n then_o for_o every_o degree_n of_o this_o difference_n or_o aggregate_v number_n you_o may_v reckon_v 69_o ½_n english_a mile_n of_o the_o statute_n which_o ordain_v 1760._o yard_n to_o be_v a_o mile_n but_o of_o english_a mile_n measure_v by_o common_a estimation_n there_o go_v not_o above_o 60._o to_o a_o degree_n so_o that_o every_o such_o mile_n that_o you_o travel_v north_n or_o south_n shall_v alter_v your_o latitude_n about_o one_o minute_n if_o they_o differ_v in_o longitude_n only_o and_o have_v no_o latitude_n but_o be_v both_o under_o the_o equator_fw-la you_o shall_v reckon_v in_o like_a manner_n for_o every_o degree_n they_o differ_v in_o longitude_n 69_o ½_n miles_n of_o distance_n in_o all_o other_o case_n you_o have_v a_o triangle_n soluble_a by_o the_o second_o problem_n of_o obliquangled_a triangle_n of_o which_o triangle_n the_o compliment_n of_o latitude_n make_v the_o two_o comprehend_v side_n and_o the_o difference_n of_o the_o longitude_n of_o the_o place_n be_v the_o angle_n comprehend_v between_o they_o and_o the_o three_o side_n be_v the_o arch_n of_o the_o distance_n of_o the_o place_n which_o when_o you_o have_v find_v in_o degree_n and_o minute_n of_o a_o great_a circle_n you_o may_v turn_v into_o miles_n as_o before_o mark_v how_o the_o distance_n of_o two_o star_n be_v find_v by_o their_o longitude_n and_o latitude_n give_v chapter_n 37._o in_o the_o same_o manner_n may_v you_o find_v the_o distance_n of_o two_o city_n or_o to_n example_n i_o will_v know_v the_o distance_n of_o london_n from_o jerusalem_n the_o compliment_n of_o the_o latitude_n of_o london_n be_v 38._o 28_o minute_n the_o compliment_n of_o the_o latitude_n of_o jerusalem_n be_v 58._o 05_o minute_n the_o difference_n of_o their_o longitude_n 46._o 0_o minute_n i_o set_v the_o zenith_n to_o the_o latitude_n of_o london_n in_o the_o limb_n that_o be_v 38._o 28_o minute_n from_o the_o pole_n so_o the_o limb_n be_v the_o circle_n of_o longitude_n in_o which_o london_n stand_v than_o i_o seek_v the_o 46_o meridian_n from_o that_o side_n of_o the_o limb_n where_o zenith_n be_v set_v for_o london_n for_o that_o 46_o méridian_n be_v the_o circle_n of_o jerusalem_n longitude_n because_o the_o difference_n of_o longitude_n be_v 46._o now_o because_o jerusalem_n latitude_n be_v 31._o 55._o and_o the_o compliment_n thereof_o or_o distance_n from_o the_o pole_n 58._o 5_o minute_n i_o walk_v on_o in_o the_o 46_o meridian_n till_o i_o come_v where_o the_o 58th_o parallel_n from_o the_o pole_n cross_v he_o and_o there_o be_v the_o place_n of_o jerusalem_n the_o azimuth_n that_o go_v hence_o to_o the_o zenith_n be_v the_o near_a way_n from_o jerusalem_n to_o london_n what_o azimuth_n this_o be_v i_o regard_v not_o for_o i_o inquire_v not_o the_o angle_n at_o london_n but_o i_o observe_v by_o the_o parallel_n how_o many_o degree_n there_o be_v in_o he_o between_o the_o place_n of_o jerusalem_n and_o the_o zenith_n and_o i_o find_v 38_o degree_n 20_o minute_n which_o be_v resolve_v into_o miles_n be_v 2300._o mile_n of_o common_a estimation_n but_o miles_n of_o the_o statute_n 2664._o the_o distance_n of_o
the_o arch_n of_o the_o ecliptic_a from_o the_o ascendant_n to_o the_o midheaven_n and_o his_o match_n take_v so_o many_o degree_n on_o the_o other_o side_n the_o centre_n give_v the_o other_o arch_n of_o the_o ecliptic_a from_o the_o midheaven_n to_o the_o descendant_n the_o rest_n of_o the_o meridian_n and_o the_o parallel_n be_v in_o this_o mode_n of_o no_o use_n the_o almicanter_n and_o azimuth_n of_o the_o reet_n here_o show_v you_o the_o altitude_n and_o azimuth_n of_o every_o degree_n of_o the_o ecliptic_a at_o one_o view_n chap._n two_o of_o the_o equinoctial_a projection_n show_v the_o northern_a or_o southern_a hemisphear_n the_o equinoctial_a projection_n represent_v the_o northern_a or_o southern_a hemisphere_n project_v upon_o the_o plain_a of_o the_o equator_fw-la here_o the_o limb_n or_o outmost_a circle_n of_o the_o mater_n and_o reet_n be_v equator_fw-la the_o eye-point_n be_v the_o north_n or_o south_n pole_n which_o you_o will_v by_o turn_n which_o pole_n be_v here_o express_v on_o the_o centre_n of_o the_o equator_fw-la because_o the_o sphere_n be_v picture_v on_o a_o plain_a or_o flat_a the_o axtree_n line_n of_o the_o mater_n a_o b_o be_v colurus_n equinoctiorum_fw-la the_o diameter_n c_o d_o cross_v he_o be_v colurus_n solstitiorum_fw-la but_o contrary_a on_o the_o reet_a the_o axletree_n be_v colurus_n solstitiorum_fw-la and_o the_o finiter_n colurus_n equinoctiorum_fw-la the_o colurus_n solstitiorum_fw-la on_o the_o mater_n be_v also_o the_o meridian_n of_o your_o place_n and_o therefore_o be_v mark_v with_o septentrio_fw-la and_o meridies_n and_o the_o end_n of_o the_o axtree_n with_o oriens_fw-la and_o occidens_fw-la the_o rest_n of_o the_o meridian_n be_v all_o straight_a line_n meet_v in_o the_o pole_n or_o centre_n be_v easy_o supply_v by_o the_o label_n and_o so_o may_v the_o parallel_n also_o be_v concentric_a with_o the_o equator_fw-la for_o if_o you_o lay_v the_o label_n on_o the_o 15._o degree_n in_o the_o limb_n from_o meridies_n 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about_o the_o label_n with_o the_o point_n it_o shall_v describe_v a_o circle_n which_o will_v serve_v for_o both_o the_o tropic_n and_o so_o may_v you_o make_v any_o other_o of_o the_o parallel_n i_o do_v not_o advise_v you_o to_o draw_v the_o meridian_n and_o parallel_n in_o this_o form_n lest_o you_o cumber_v your_o instrument_n but_o i_o show_v you_o how_o you_o may_v represent_v any_o of_o they_o in_o a_o moment_n when_o occasion_n require_v the_o meridian_n of_o the_o mater_n that_o be_v so_o call_v in_o the_o meridional_a projection_n be_v here_o turn_v into_o the_o several_a orison_n of_o the_o world_n and_o the_o parallel_n here_o serve_v only_o to_o graduate_v those_o orison_n out_o of_o these_o orison_n choose_v your_o own_o horizon_n and_o distinguish_v he_o if_o you_o will_v that_o you_o may_v ready_o find_v he_o when_o you_o shall_v look_v for_o he_o your_o horizon_n be_v thus_o inquire_v because_o the_o elevation_n of_o the_o pole_n at_o northampton_n be_v 52._o degree_n 15._o minute_n therefore_o from_o the_o centre_n now_o north_n pole_n number_n in_o the_o meridian_n line_n northward_o 52._o degree_n 15._o minute_n and_o there_o cut_v the_o the_o north_n semicircle_n of_o our_o horizon_n or_o there_o you_o may_v imagine_v he_o between_o the_o 52_o and_o 53_o orison_n and_o the_o southern_a semicircle_n thereof_o lie_v 52_o degree_n 15_o minute_n on_o the_o other_o side_n the_o centre_n towards_o meridies_n this_o may_v seem_v strange_a that_o the_o north_n and_o south_n point_v of_o the_o horizon_n which_o in_o the_o sphere_n be_v unequal_o distant_a from_o the_o north_n pole_n viz._n the_o one_o but_o 51._o degree_n 15._o minute_n and_o the_o other_o 127._o degree_n 45._o minute_n the_o supplement_n thereof_o shall_v be_v equal_o distant_a in_o this_o projection_n but_o the_o reason_n be_v because_o the_o centre_n be_v both_o north_n and_o south_n pole_n here_o at_o pleasure_n and_o the_o northern_a and_o southern_a hemisphear_n be_v both_o here_o represent_v by_o turn_n carry_v this_o in_o your_o head_n and_o then_o lie_v the_o eabel_n upon_o the_o south_n part_n of_o the_o meridian_n and_o number_n thereon_o from_o the_o centre_n now_o north_n pole_n outward_a to_o the_o equator_fw-la at_o the_o limb_n 90._o degree_n thence_o number_n backward_o towards_o the_o centre_n now_o the_o south_n pole_n the_o elevation_n of_o the_o equator_fw-la which_o be_v always_o compliment_n of_o the_o elevation_n of_o the_o pole_n and_o be_v here_o 37._o degree_n 45_o minute_n there_o be_v the_o southern_a point_n of_o the_o horizon_n and_o be_v distant_a from_o the_o centre_n now_o south_n pole_n only_a 52_o degree_n 15_o minute_n but_o from_o the_o centre_n be_v north_n pole_n 127._o degree_n 45._o minute_n and_o from_o the_o northern_a point_n of_o the_o horizon_n before_o find_v just_a 180._o degree_n as_o it_o be_v in_o the_o sphere_n have_v find_v the_o north_n arch_n of_o your_o horizon_n 52._o degr_n 15._o min._n behind_o the_o centre_n count_v as_o many_o degree_n and_o minute_n forward_o in_o the_o meridian_n before_o the_o centre_n towards_o meridies_n and_o the_o arch_n cross_v there_o shall_v be_v his_o match_n to_o make_v up_o the_o whole_a circle_n and_o so_o may_v you_o find_v your_o whole_a horizon_n upon_o the_o mater_n whatsoever_o your_o latitude_n be_v here_o you_o must_v remember_v that_o star_n which_o have_v northern_a declination_n rise_v and_o set_v upon_o the_o northern_a arch_n of_o the_o horizon_n and_o those_o which_o have_v southern_a declination_n upon_o the_o southern_a arch_n remember_v also_o that_o many_o star_n between_o the_o tropic_n which_o have_v northern_a latitude_n have_v nevertheless_o southern_a declination_n and_o contrary_a many_o which_o have_v southern_a latitude_n have_v northern_a declination_n the_o lineament_n of_o the_o reet_n serve_v you_o in_o this_o projection_n be_v only_o the_o ecliptic_a and_o the_o fix_a star_n the_o almicanter_n and_o azimuth_n here_o be_v of_o no_o use_n the_o meridian_n and_o parallel_n be_v supply_v by_o the_o label_n for_o the_o reet_n as_o well_o as_o for_o the_o mater_n and_o whereas_o the_o ecliptic_a here_o seem_v to_o be_v irregular_a see_v the_o solstitial_a point_n of_o cancer_n and_o caprcorn_n be_v not_o distant_a 180_o degree_n as_o they_o shall_v be_v you_o must_v imagine_v that_o the_o southern_a arch_n of_o the_o ecliptic_a be_v project_v by_o the_o eye_n place_v in_o the_o north_n pole_n and_o for_o the_o northern_a arch_n the_o eye_n place_n in_o the_o south_n pole_n and_o the_o centre_n serve_v for_o both_o the_o pole_n alike_o as_o have_v be_v show_v number_n therefore_o as_o you_o be_v teach_v for_o the_o horizon_n in_o this_o projection_n for_o the_o reason_n of_o the_o draught_n of_o the_o horizon_n and_o of_o the_o ecliptic_a in_o this_o projection_n be_v the_o same_o chap._n iii_o of_o the_o nonagesimal_n projection_n show_v the_o eastern_a and_o western_a part_n of_o the_o sphere_n be_v divide_v by_o the_o azimuth_n of_o the_o nonagesimus_fw-la gradus_fw-la number_n in_o the_o limb_n from_o the_o equinoctial_a line_n towards_o the_o pole_n the_o altitude_n of_o the_o nonagesimus_fw-la gradus_fw-la which_o be_v the_o high_a degree_n of_o the_o ecliptic_a and_o thereto_o set_v the_o finitor_n turn_v the_o almicanter_n either_o to_o the_o north_n or_o to_o the_o south_n as_o your_o work_n propose_v shall_v require_v now_o be_v the_o finiter_n ecliptic_a his_o point_n at_o the_o limbis_a nonagesimus_fw-la gradus_fw-la the_o centre_n of_o the_o planisphear_n be_v ascendant_n and_o descendant_n the_o east_n and_o west_n point_v of_o the_o horizon_n be_v here_o distant_a from_o the_o centre_n as_o much_o as_o the_o amplitude_n of_o the_o ascendant_n come_v to_o to_o be_v count_v from_o the_o centre_n upon_o the_o eqinoctial_a line_n of_o the_o mater_n which_o here_o stand_v for_o horizon_n the_o meridian_n and_o parallel_n of_o the_o mater_n be_v here_o
meridian_n 3._o a_o three_o way_n when_o the_o great_a wain_n be_v see_v under_o cynosura_n the_o pole_n star_n observe_v with_o your_o eye_n the_o distance_n of_o the_o thill-horse_n call_v alioth_n from_o the_o next_o wheel_n of_o the_o wain_n and_o set_v that_o distance_n by_o aim_n in_o 5_o part_n observe_v by_o a_o plumbline_n when_o alioth_n draw_v near_o to_o be_v in_o the_o same_o perpendicular_a with_o the_o pole_n star_n for_o when_o he_o want_v but_o one_o of_o those_o 5_o part_n to_o come_v into_o the_o perpendicular_a then_o be_v the_o polestar_n in_o the_o meridian_n over_o the_o pole_n in_o our_o age_n at_o other_o time_n of_o the_o night_n the_o polestar_n may_v be_v 4_o degree_n wide_a and_o in_o one_o hour_n near_o the_o meridian_n he_o change_v his_o azimuth_n above_o one_o degree_n 4._o a_o four_o way_n because_o the_o distance_n of_o the_o polestar_n from_o the_o pole_n be_v now_o 2_o degree_n 30_o minute_n and_o the_o pole_n be_v in_o the_o circle_n or_o line_n which_o pass_v from_o the_o polestar_n near_o alioth_n as_o before_o you_o may_v by_o guess_v cut_v off_o from_o that_o line_n 2_o degree_n 30_o min._n and_o in_o that_o section_n you_o have_v the_o pole_n at_o any_o time_n this_o way_n may_v be_v use_v abroad_o in_o the_o field_n where_o you_o can_v stand_v upon_o exactness_n and_o herein_o you_o shall_v miss_v very_o little_a if_o you_o accustom_v yourself_o to_o observe_v the_o distance_n of_o the_o star_n about_o the_o pole_n chap._n four_o to_o observe_v the_o azimuth_n of_o the_o sun_n or_o star_n lay_v your_o planisphear_n upon_o a_o horizontal_n plain_a or_o level_n and_o his_o meridian_n on_o the_o meridian_n line_n of_o your_o place_n find_v by_o the_o last_o chapter_n then_o turn_v your_o label_n that_o the_o sun_n may_v cast_v the_o shadow_n of_o one_o sight_n upon_o the_o other_o or_o direct_o towards_o it_o or_o till_o the_o shadow_n of_o a_o plumb_n line_n cut_v both_o the_o sight_n alike_o then_o do_v the_o label_n show_v the_o azimuth_n in_o the_o limb._n for_o the_o star_n you_o must_v so_o direct_v the_o sight_n by_o your_o eye_n that_o their_o edge_n may_v touch_v the_o visual_a line_n that_o come_v from_o the_o star_n to_o your_o eye_n and_o if_o your_o long_a sight_n prove_v too_o short_a turn_v he_o towards_o your_o eye_n and_o enlighten_v the_o short_a sight_n by_o a_o candle_n hold_v behind_o you_o mark_v where_o the_o edge_n of_o the_o long_a sight_n cut_v both_o the_o edge_n of_o the_o short_a sight_n and_o the_o star_n for_o there_o be_v your_o label_n in_o the_o azimuth_n of_o the_o star_n which_o you_o may_v count_v on_o the_o limb._n note_v that_o if_o you_o seek_v the_o azimuth_n to_o get_v the_o hour_n you_o shall_v find_v it_o most_o easy_o when_o the_o sun_n or_o star_n be_v near_o the_o horizon_n and_o then_o you_o shall_v not_o be_v trouble_v with_o their_o refraction_n but_o there_o be_v most_o use_n of_o observe_v azimuth_n near_o the_o meridian_n because_o there_o the_o azimuth_n change_v apace_o the_o altitude_n very_o slow_o yet_o if_o you_o may_v choose_v choose_v to_o take_v altitude_n rather_o than_o azimuth_n so_o you_o come_v not_o within_o 2_o or_o 3_o hour_n of_o the_o meridian_n because_o the_o sight_n serve_v all_o altitude_n with_o like_a facility_n and_o you_o may_v soon_o have_v a_o true_a plumb_n line_v any_o where_n than_o a_o true_a horizontall_a plain_n and_o a_o true_a meridian_n line_n caap._n v._o to_o find_v the_o sun_n longitude_n the_o longitude_n of_o the_o sun_n be_v the_o arch_n of_o his_o distance_n from_o ♈_o 0_o in_o the_o ecliptic_a or_o it_o be_v the_o angle_n make_v at_o the_o pole_n of_o the_o ecliptic_a comprehend_v between_o the_o circle_n of_o longitude_n pass_v through_o ♈_o 0_o and_o another_o circle_n of_o longitude_n pass_v through_o the_o centre_n of_o the_o sun_n for_o the_o say_a arch_n of_o the_o ecliptic_a be_v always_o the_o proper_a measure_n of_o this_o angle_n and_o because_o the_o sun_n centre_n 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the_o meridian_n of_o the_o place_n and_o this_o angle_n have_v his_o measure_n in_o the_o equator_fw-la chap._n vi_o the_o sun_n longitude_n declination_n right_a ascension_n any_o one_o of_o they_o give_v to_o find_v the_o rest_n in_o the_o first_o projection_n what_o the_o sun_n longitude_n be_v have_v be_v show_v chap._n 5._o his_o declination_n be_v his_o distance_n from_o the_o near_a point_n of_o the_o equator_fw-la and_o therefore_o be_v always_o measure_v in_o a_o arch_n of_o that_o meridian_n which_o happen_v to_o pass_v through_o the_o centre_n of_o the_o sun_n and_o always_o cut_v the_o equator_fw-la at_o right_a angle_n as_o do_v all_o the_o meridian_n the_o right_a ascension_n of_o the_o sun_n be_v the_o angle_n at_o the_o pole_n of_o the_o world_n comprehend_v between_o that_o side_n of_o the_o colurus_n equinoctiorum_fw-la which_o cut_v the_o intersection_n of_o the_o ecliptic_a with_o the_o equator_fw-la in_fw-la ♈_o 0_o and_o the_o arch_n of_o another_o meridian_n which_o pass_v through_o the_o centre_n of_o the_o sun_n and_o note_v that_o this_o angle_n may_v increase_v above_o 180_o degree_n even_o to_o 360_o degree_n though_o every_o angle_n proper_o so_o call_v be_v less_o than_o 180_o degree_n and_o never_o more_o than_o 90_o degree_n come_v into_o the_o triangle_n for_o if_o you_o number_v backward_o or_o forward_o from_o either_o of_o the_o equinoctial_a point_n you_o shall_v have_v like_o arch_n of_o right_a ascension_n answer_v to_o like_a arhce_n of_o longitude_n and_o declination_n so_o that_o have_v find_v the_o right_a ascension_n in_o any_o one_o quadrant_n or_o the_o compliment_n thereof_o you_o shall_v find_v the_o whole_a right_a ascension_n from_o ♈_o 0_o by_o add_v one_o two_o or_o three_o whole_a quadrant_n to_o the_o right_a ascension_n find_v or_o to_o the_o compliment_n thereof_o as_o by_o the_o view_n of_o your_o planisphear_n you_o shall_v present_o know_v how_o to_o do_v better_a than_o by_o more_o word_n otherwise_o 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meridian_n and_o the_o meridian_n do_v limit_v it_o in_o all_o part_n and_o posture_n of_o the_o equator_fw-la without_o any_o respect_n to_o the_o horizon_n at_o all_o but_o the_o old_a term_n have_v so_o long_o enure_v that_o i_o believe_v it_o will_v not_o be_v change_v without_o better_a authority_n these_o definition_n premise_v you_o shall_v know_v that_o these_o three_o arch_n viz._n of_o longitude_n in_o the_o ecliptic_a of_o right_a ascension_n in_o the_o equator_fw-la and_o of_o declination_n in_o a_o meridian_n do_v make_v up_o a_o notable_a rectangled-triangle_n in_o the_o sphere_n triangle_n the_o elliptical_a triangle_n like_v unto_o that_o which_o be_v make_v the_o common_a example_n in_o all_o the_o five_o problem_n of_o rectangled-triangle_n book_n 3_o 3._o etc._n etc._n but_o to_o see_v your_o triangle_n and_o resolve_v
place_v arcturus_n in_o my_o reet_n according_a to_o that_o right_a ascension_n and_o declination_n as_o be_v teach_v book_n 1_o 7._o and_o book_n 4.18_o and_o by_o chapter_n 21._o i_o find_v â™_o 4_o rising_z with_o he_o and_o at_o the_o same_o time_n ♓_o 4._o set_v in_o the_o same_o herizon_n of_o athens_n but_o i_o ought_v to_o find_v ♓_o 1_o degree_n set_v in_o hesieds_fw-fr time_n therefore_o i_o will_v suppose_v again_o that_o hesiod_n live_v 1130_o year_n before_o christ_n and_o proceed_v as_o upon_o the_o former_a supposition_n i_o find_v that_o then_o â™’_o 29._o degree_n do_v set_v at_o his_o acronical_a rise_n but_o i_o ought_v to_o find_v ♓_o 1_o degree_n rise_v and_o see_v it_o be_v hereby_o find_v that_o in_o 300_o year_n his_o acronical_a set_n vary_v 5._o degree_n or_o day_n i_o take_v the_o proportional_a part_n of_o that_o time_n and_o lay_v that_o in_o the_o year_n 1010._o before_o christ_n arcturus_n do_v set_v acronical_o 60._o day_n after_o the_o winter_n trepique_n and_o then_o live_v hosiod_n or_o soon_o after_o for_o be_v a_o astrologer_n himself_o as_o pliny_n tell_v we_o lib._n 18.25_o say_n huâ—us_fw-la quaque_fw-la nomine_fw-la extat_fw-la astrologia_fw-la it_o be_v likely_a he_o will_v not_o use_v a_o antiquate_a rule_n arcturus_n therefore_o rise_v acronical_o at_o athens_n in_o hesiod_n time_n ☉_o in_o ♓_o 1_o degree_n that_o be_v about_o febr._n 9_o of_o our_o julian_n year_n as_o it_o now_o go_v then_o the_o swallow_v use_v to_o come_v to_o athens_n but_o in_o our_o age_n he_o rise_v acronical_o at_o athens_n ☉_o in_o ♈_o 10_o ½_n that_o be_v mar._n 20._o and_o at_o ecton_n or_o northampton_n ☉_o ♈_o 0._o that_o be_v mar._n 10._o by_o this_o you_o may_v see_v that_o the_o old_a astrological_a rule_n concern_v the_o rise_n and_o set_v of_o the_o star_n leave_v we_o by_o hesiod_n cato_n aratus_n varro_n palladius_n virgil_n ovid_n pliny_n columella_n ptolemy_n and_o other_o ancient_a author_n can_v serve_v for_o our_o age_n nor_o for_o every_o latitude_n and_o the_o best_a use_n we_o can_v make_v of_o they_o be_v to_o find_v the_o age_n when_o they_o live_v pliny_n lib._n 18.26_o say_v that_o in_o caesur_n calender_n octavo_fw-la calend_n martij_fw-la be_v hirundinis_fw-la adventus_fw-la &_o jostero_fw-la die_fw-la arcturi_fw-la exor_fw-la us_o vespertimus_n which_o agree_v not_o to_o caesar_n time_n also_o lib._n 2.47_o he_o say_v ardentissimo_fw-la aestatis_fw-la tempore_fw-la exoritur_fw-la caniculae_fw-la fidus_fw-la sole_fw-la primem_fw-la partem_fw-la leonis_fw-la ingrediente_fw-la qui_fw-la dies_fw-la est_fw-la 15._o ante_fw-la caelend_n augusti_fw-la that_o be_v july_n 18_o rome_n be_v in_o latitude_n 42_o degree_n pliny_n live_v about_o 70._o year_n after_o christ_n then_o be_v canicula_fw-la that_o be_v sarius_fw-la in_o ♊_o 17._o degree_n latitude_n 39_o ½_n right_a ascension_n 79_o ½_n declination_n south_n 16_o â…”_n and_o do_v rise_v at_o rome_n cosmical_o decimo_fw-la quinto_fw-la calend._n augusti_fw-la or_o july_n 18._o as_o thus_o far_o he_o report_v true_o but_o the_o sun_n be_v not_o then_o in_o ♌_o 1_o deg_fw-la as_o pliny_n say_v but_o in_o ♋_o 23_o degree_n for_o the_o sun_n enter_v ♌_o in_o his_o time_n not_o decimo_fw-la quinto_fw-la calend_n augusti_n but_o octavo_fw-la calend._n augusti_fw-la the_o sun_n in_o those_o day_n enter_v the_o several_a sign_n most_o on_o the_o 5_o day_n of_o the_o several_a month_n as_o in_o our_o age_n about_o the_o 11_o day_n as_o astronomer_n well_o know_v pliny_n seem_v to_o have_v take_v his_o astrology_n upon_o trust_n and_o i_o can_v devise_v what_o shall_v lead_v he_o to_o suppose_v that_o howsoever_o the_o equinox_n and_o solstice_n in_o his_o time_n happen_v octavo_fw-la calend._n as_o he_o deny_v not_o yet_o the_o sun_n enter_v into_o a_o new_a sign_n about_o the_o ides_n of_o every_o month_n and_o that_o the_o equinoctial_a and_o soistitial_a point_n be_v in_o octavis_fw-la partibus_fw-la signorum_fw-la as_o if_o the_o sun_n come_v not_o to_o the_o equinoctial_a till_o he_o come_v to_o the_o 8_o degree_n of_o aries_n see_v pliny_n book_n 18._o chapter_n 25_o 26_o 27_o 28._o he_o seem_v to_o distrust_v the_o julian_n calender_n and_o to_o adhear_v more_o to_o the_o account_n use_v by_o varro_n de_fw-fr rerusticâ_fw-la lib._n 1.27_o but_o either_o he_o understand_v neither_o of_o they_o well_o or_o i_o do_v not_o well_o understand_v he_o now_o sirius_n rise_v in_o our_o horizon_n with_o ♌_o 18½_n about_o august_n 1_o in_o the_o declination_n of_o the_o heat_n who_o in_o plinye_n time_n rise_v ardentissimo_fw-la astatis_fw-la tempore_fw-la and_o our_o dog-day_n if_o we_o follow_v the_o dog_n rise_v will_v be_v every_o age_n cold_a and_o cold_a and_o at_o length_n fall_v in_o winter_n it_o be_v better_a to_o reduce_v they_o to_o the_o sun_n entrance_n into_o leo_n or_o to_o cancer_n 23_o rather_o as_o they_o be_v in_o plinye_n time_n and_o to_o count_v the_o ardentissimum_fw-la tempus_fw-la a_o fortnight_n before_o and_o a_o fortnight_n after_o for_o sirius_n be_v not_o by_o the_o ancient_n suppose_v the_o cause_n of_o the_o sultry_a heat_n of_o summer_n but_o a_o concomitant_a sign_n of_o that_o season_n whereof_o the_o sun_n continuance_n in_o the_o north-signe_n be_v the_o cause_n will_v you_o know_v also_o when_o they_o begin_v to_o blow_n and_o to_o mow_v in_o greece_n in_o hesiod_n time_n he_o say_v when_o the_o pleyade_n rise_v begin_v to_o mow_v and_o to_o plough_v when_o they_o set_v the_o pleyade_n i_o mean_v the_o bright_a of_o they_o 1010_o year_n before_o christ_n be_v in_o ♈_o 17.25_o minute_n latitude_n 4_o degree_n north._n declination_n therefore_o by_o chapter_n 34_o 11_o degree_n right_a ascension_n 14½_n degree_n therefore_o they_o rise_v cosmical_o at_o athens_n or_o ascra_n hesiod_n birth_n place_n ☉_o in_o ♈_o 10_o â…“_n that_o be_v as_o our_o julian_n year_n now_o go_v about_o march_n 20._o the_o heliacall_a rise_n be_v about_o 20._o day_n after_o the_o cosmical_a chapter_n 22._o that_o be_v about_o april_n 9_o therefore_o either_o march_v 20._o at_o the_o cosmical_a rise_n or_o april_n 9_o at_o the_o heliacall_a rise_n they_o begin_v to_o mow_v and_o i_o think_v he_o mean_v the_o cosmical_a the_o acronical_a rise_n be_v there_o in_o his_o age_n ☉_o in_o ♎_o 10._o â…“_n about_o sep._n 23._o which_o be_v too_o late_o beyond_o reason_n now_o that_o they_o shall_v begin_v mow_v in_o greece_n within_o 10_o day_n after_o the_o equinoctial_a be_v not_o strange_a see_v the_o first_o fruit_n of_o ripe_a corn_n be_v offer_v at_o jerusalem_n yearly_a at_o easter_n which_o fall_v ordinary_o 15._o day_n after_o the_o equinoctial_a or_o thereabouts_o duet_n 16._o and_o in_o egypt_n cum_fw-la falce_fw-la arva_fw-la visunt_fw-la paulo_n ante_fw-la calendas_fw-la apriles_fw-la mossis_fw-la autem_fw-la peragitur_fw-la maio_n say_v pliny_n 18.18_o viz._n harvest_n begin_v in_o egypt_n a_o little_a before_o april_n and_o april_n then_o begin_v 8_o day_n after_o the_o equinoctial_a only_o the_o cosmical_a set_n of_o the_o plaiade_n at_o athens_n in_o hesiod_n time_n 1010._o year_n before_o christ_n be_v ☉_o in_o ♎_o 18._o degree_n octob._n 1._o then_o begin_v they_o to_o blow_n and_o sow_n the_o egyptian_n begin_v novembri_fw-la mense_fw-la incipiente_fw-la pliny_n 18.18_o but_o if_o hesiod_n be_v now_o alive_a at_o ascra_n he_o will_v find_v the_o plaiade_n rise_v cosmical_o with_o ♉_o 19_o ½_n alpril_n 30._o and_o set_v cosmical_o ☉_o in_o â™_o 27_o ½_n nou._n 9_o so_o much_o be_v his_o georgique_n rule_v now_o antiquate_v and_o serve_v for_o little_a else_o but_o to_o show_v how_o many_o age_n ago_o he_o live_v and_o how_o the_o season_n happen_v in_o his_o age._n chap._n xxiv_o the_o latitude_n of_o your_o place_n the_o declination_n altitude_n azimuth_n and_o hour_n of_o the_o sun_n or_o star_n any_o three_o of_o these_o be_v give_v so_o find_v the_o other_o two_o set_v your_o planisphear_n in_o the_o first_o mode_n of_o the_o meridional_a projection_n triangle_n the_o complimental_a triangle_n and_o you_o shall_v find_v all_o these_o five_o in_o one_o oblique-angled_n triangle_n which_o i_o use_v to_o call_v the_o complimental_a triangle_n because_o it_o consist_v of_o three_o side_n which_o be_v all_o compliment_n other_o may_z call_v it_o as_o they_o please_v a_o b_o in_o the_o limb_n between_o the_o pole_n and_o zenith_n compliment_n of_o latitude_n a_o c_o in_o a_o meridian_n compliment_n of_o the_o declination_n or_o the_o supplement_n of_o that_o compliment_n b_o c_o in_o a_o azimuth_n compliment_n of_o the_o altitude_n a_o at_o the_o pole_n be_v the_o angle_n of_o horary_a distance_n from_o the_o meridian_n who_o full_a measure_n be_v in_o the_o equinoctial_a line_n but_o because_o every_o parallel_n be_v divide_v by_o the_o meridian_n into_o 180._o degree_n as_o the_o equator_fw-la be_v and_o every_o 5_o and_o 15_o meridian_n
triangle_n the_o parallactical_a triangle_n which_o may_v be_v call_v the_o parallactical_a triangle_n and_o the_o leg_n which_o have_v the_o parallax_n of_o longitude_n be_v a_o segment_n of_o the_o ecliptic_a or_o of_o a_o parallel_n near_o it_o and_o the_o leg_n which_o have_v the_o parallax_n of_o latitude_n be_v a_o segment_n of_o a_o circle_n of_o longitude_n pass_v through_o the_o apparent_a place_n of_o the_o planet_n and_o through_o the_o pole_n of_o the_o ecliptic_a and_o cut_v the_o ecliptic_a or_o his_o say_a parallel_n at_o right_a angle_n as_o in_o the_o figure_n c_o be_v the_o apparent_a place_n of_o the_o planet_n b_o be_v his_o true_a place_n in_o which_o he_o must_v be_v see_v from_o the_o centre_n a_o b_o c_o be_v the_o parallactique_a angle_n b_o c_o be_v the_o parallax_n of_o altitude_n b_o a_o the_o parallax_n of_o longitude_n c_o a_o the_o parallax_n of_o latitude_n wherefore_o by_o the_o three_o problem_n of_o rectangled_a triangle_n book_n 3._o 5._o you_o may_v present_o get_v both_o the_o leg_n example_n the_o parallactical_a angle_n b_o be_v find_v chapter_n 62._o to_o be_v 86._o 41_o minute_n and_o the_o parallax_n of_o the_o moon_n altitude_n chapter_n 63._o to_o be_v 46_o ½_n minute_n for_o the_o same_o time_n here_o therefore_o have_v lay_v the_o label_n to_o 86._o 41_o minute_n from_o the_o equinoctial_a i_o number_n in_o the_o label_n from_o the_o centre_n 46_o degree_n and_o a_o half_a in_o stead_n of_o 46_o minute_n and_o a_o half_a the_o parallax_n of_o altitude_n and_o i_o find_v that_o the_o 46_o ⅓_n parallel_n cut_v the_o say_v 46_o ½_n degree_n of_o the_o label_n by_o which_o i_o know_v that_o the_o leg_n c_o a_o for_o the_o parallax_n of_o latitude_n be_v 46_o ⅓_n very_o near_o for_o the_o ☽_o hear_v be_v near_o the_o nonagesimus_fw-la gradus_fw-la all_fw-mi her_o parallax_n almost_o go_v into_o longitude_n but_o b_o a_o of_o my_o triangle_n be_v cover_v by_o the_o head_n of_o my_o label_n nevertheless_o i_o may_v see_v his_o 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cut_v also_o the_o meridian_n 0_o ⅔_n show_v i_o that_o the_o side_n b_o a_o parallax_n of_o longitude_n be_v almost_o 7_o second_n the_o sun_n therefore_o though_o he_o never_o have_v latitude_n by_o reason_n of_o his_o parallax_n appear_v in_o the_o middle_n of_o this_o eclipse_n to_o have_v south_n latitude_n 1_o ½_n minute_n the_o moon_n true_a latitude_n be_v then_o by_o lantsbergius_n his_o table_n 45_o minute_n 24_o second_o north_n so_o that_o by_o this_o account_n the_o sun_n and_o moon_n centre_n be_v distant_a in_o latitude_n 46_o minute_n 54_o second_n but_o when_o out_o of_o this_o distance_n you_o have_v subtract_v 46_o ⅓_n for_o the_o moon_n parallax_n of_o latitude_n there_o remain_v 34_o second_n for_o the_o apparent_a distance_n of_o the_o centre_n of_o the_o sun_n and_o moon_n but_o by_o observation_n i_o find_v they_o distant_a 1_o minute_n 48_o second_n for_o the_o digit_n eclipse_v at_o ecton_n be_v 11._o 22_o ½_n minute_n and_o so_o perhaps_o may_v i_o have_v find_v by_o my_o planisphear_n or_o some_o what_o near_o have_v it_o be_v large_a enough_o and_o have_v i_o regard_v every_o minute_n and_o second_v precise_o in_o set_v down_o this_o example_n which_o be_v more_o than_o need_v for_o my_o purpose_n in_o this_o place_n chap._n lxv_o to_o find_v the_o moon_n latitude_n by_o her_o distance_n from_o either_o of_o the_o nodi_fw-la call_v caput_n and_o caudi_fw-la draconis_fw-la as_o the_o ecliptic_a cross_v the_o equator_fw-la with_o a_o angle_n of_o 23._o 30_o minute_n for_o our_o age_n so_o the_o orbite_n or_o circle_n in_o which_o the_o moon_n move_v cross_v the_o ecliptic_a but_o the_o angle_n of_o inclination_n be_v not_o always_o nor_o long_v the_o same_o for_o in_o the_o conjunction_n of_o the_o sun_n and_o moon_n the_o angle_n be_v ever_o 5_o 00_o minute_n and_o increase_v to_o the_o time_n of_o the_o quadrature_n when_o it_o be_v find_v 5_o degree_n 16_o minute_n thence_o it_o decrease_v to_o the_o opposition_n where_o it_o be_v again_o but_o 5_o degree_n as_o in_o the_o conjunction_n thence_o it_o increase_v again_o to_o 5_o degree_n 16_o minute_n in_o the_o latter_a □_o and_o again_o thence_o decrease_v to_o 5_o degree_n in_o the_o ☌_o get_v by_o the_o astronomical_a table_n the_o quantity_n of_o the_o angle_n make_v between_o the_o ecliptic_a and_o the_o orbite_n of_o the_o moon_n which_o in_o all_o conjunction_n and_o opposition_n and_o therefore_o in_o all_o eclipse_n be_v 5_o degree_n as_o be_v now_o say_v and_o get_v also_o by_o the_o like_a table_n the_o moon_n distance_n from_o the_o near_a of_o the_o nodes_fw-la then_o may_v you_o find_v the_o moon_n latitude_n by_o the_o problem_n 3_o rectangled_a triangle_n book_n 3._o 5._o just_a as_o you_o use_v to_o find_v the_o sun_n declination_n by_o his_o longitude_n and_o great_a declination_n example_n the_o ☽_o in_o the_o former_a case_n be_v distant_a from_o caput_fw-la draconis_fw-la by_o lantsbergius_n table_n 8_o degree_n 43_o minute_n i_o lay_v the_o label_n from_o the_o equinoctial_a line_n to_o 5_o degree_n in_o the_o limb_n and_o count_v in_o the_o label_n from_o the_o centre_n 8._o 43._o i_o see_v there_o the_o parallel_n of_o 0_o ¾_n that_o be_v 45_o minute_n or_o 46_o minute_n cross_v for_o the_o moon_n latitude_n chap._n lxvi_o to_o find_v the_o dominical_a letter_n the_o prime_n epact_n easter_n day_n and_o the_o rest_n of_o the_o movable_a feast_n for_o ever_o by_o the_o calendar_n describe_v book_n 1._o 11._o a_o example_n shall_v serve_v here_o instead_o of_o a_o rule_n for_o the_o year_n 1657._o i_o will_v know_v all_o these_o wherefore_o i_o seek_v the_o year_n 1657._o in_o the_o table_n of_o the_o sun_n cycle_n and_o over_o against_o it_o i_o find_v 14._o for_o the_o year_n of_o the_o cycle_n of_o the_o sun_n and_o d_o for_o the_o dominical_a letter_n and_o note_v here_o that_o every_o leap-year_n have_v 2_o dominical_a letter_n as_o 1660._o have_v a_o g_z and_o the_o first_o viz._n a_o serve_v that_o year_n till_o february_n 25_o and_o the_o second_o g_z for_o the_o rest_n of_o the_o year_n and_o note_v that_o these_o letter_n go_v always_o backward_o when_o you_o count_v forward_o as_o b_o a_o then_z g_z f_o etc._n etc._n not_o f_o g_z and_z then_z a_o b_o as_o you_o may_v see_v by_o the_o table_n then_o in_o the_o table_n of_o the_o cycle_n of_o the_o moon_n i_o have_v for_o the_o year_n 1657._o the_o prime_n 5._o the_o epact_n 25._o those_o have_v i_o go_v to_o the_o table_n for_o easter_n and_o seek_v there_o in_o the_o first_o rank_n the_o prime_n 5._o and_o under_o it_o in_o the_o middle_a rank_n stand_v e_z that_o be_v not_o my_o dominical_a letter_n therefore_o i_o seek_v not_o backward_o but_o always_o forward_o in_o the_o middle_a rank_n till_o i_o come_v to_o my_o dominical_a letter_n d._n and_o under_o it_o i_o find_v in_o the_o three_o rank_n march_v 29._o upon_o which_o easter_n day_n fall_v this_o year_n 1657._o the_o rest_n of_o the_o movable_a feast_n may_v be_v have_v by_o their_o distance_n from_o easter_n which_o be_v always_o the_o same_o only_o for_o advent_v sunday_n remember_v that_o the_o next_o sunday_n after_o november_n 26_o be_v advent_fw-fr sunday_n read_v book_n 1._o 11._o and_o that_o will_v sufficient_o instruct_v you_o with_o this_o example_n chap._n lxvii_o to_o find_v the_o age_n of_o the_o moon_n by_o the_o epact_n remember_v first_o that_o the_o epact_n begin_v with_o march_n which_o must_v be_v here_o account_v the_o first_o month_n then_o if_o you_o add_v to_o the_o epact_n the_o number_n of_o the_o month_n current_n and_o the_o number_n of_o the_o day_n of_o the_o month_n current_n the_o sum_n or_o the_o excess_n above_o 30_o be_v
12._o 52._o n._n 3._o lyra_n 276._o 27._o 38._o 30._o n._n 1._o in_o ariadne_n brow_n mumir_n 230._o 12._o 27._o 51._o n._n 2._o the_o swan_n bill_n 289._o 23._o 27._o 18._o n._n 3._o the_o eagle_n heart_n 293._o 41._o 08._o 03._o n_o 2._o tail_n 282._o 36._o 13._o 25._o n_o 3_o the_o dolphin_n tail_n 304._o 24._o 10._o 14._o n_o 3_o pegasus_n his_o mouth_n eniph_n 322._o 03._o 8._o 24._o n_o 3_o head_n 328._o 24._o 4_o 38._o n._n 4._o neck_n 336._o 21._o 9_o 08._o n._n 3._o right_o shoulder_n sheet_n 341._o 59_o 26._o 18._o n._n 2._o first_o in_o the_o wing_n marcab_n 342._o 07._o 13._o 28._o n._n 2_o last_o in_o the_o wing_n 359._o 08._o 13._o 22._o n._n 2._o the_o ram_n head_n 27._o 12._o 21._o 54._o n._n 3._o horn_n 23._o 54._o 17._o 40._o n_o 4._o horn_n 24._o 08._o 19_o 12._o n._n 4._o the_o bull_n north_n eye_n 62._o 23._o 18._o 26._o n._n 3._o south_n eye_n aldebaran_n 64._o 17._o 15._o 48._o n_o 1._o bright_a of_o the_o pleyade_n 52._o 00._o 23._o 03._o n_o 3_o gemini_fw-la head_n of_o apollo_n 108._o 24_o 32._o 33._o n._n 2._o head_n of_o hercules_n 111._o 19_o 28._o 46._o n._n 2._o the_o first_o foot_n 88_o 48._o 22._o 33._o n_o 4._o the_o first_o foot_n 90._o 48_o 22._o 38._o n._n 3._o the_o three_o foot_n 94._o 41_o 16_o 38._o n._n 2._o cancer_n praecepe_v 125._o 22._o 20._o 48._o n_o ne_fw-la leo_fw-la the_o lion_n neck_n 150._o 26._o 21._o 29._o n._n 2._o heart_n regulus_n 147._o 43._o 13._o 33._o n_o 1._o back_o 164._o 08._o 22._o 20._o n_o 2._o tail_n 173._o 04._o 16._o 25._o n._n 1._o virgo_fw-la spica_fw-la â™_o azimech_v 196._o 56._o 9_o 31._o s._n 1._o libra_n south_n balance_n 218._o 13._o 14._o 37._o s._n 2._o north_n balance_n 224._o 52._o 8._o 07._o s._n  _fw-fr scorpio_n in_o his_o forehead_n the_o low_a 234._o 50._o 25._o 06._o s._n 3._o midst_n 235._o 15._o 21._o 38._o s._n 3._o high_a 236._o 36._o 18._o 51._o s._n 3._o heart_n antare_n 242._o 23._o 25._o 37._o s._n 1._o sagittaries_n head_n the_o midst_n 281._o 18._o 22._o 07._o s._n 4_o capricom_n horn_n the_o high_a 299._o 58._o 13._o 29._o s._n 3._o tail_n 320._o 29._o 18._o 02._o s._n 3._o tail_n 322._o 15._o 17._o 32._o s._n 3._o aquarius_n right_a shoulder_n 327._o 16._o 1._o 52._o s._n 3._o leave_v shoulder_n 318._o 07._o 6._o 56½_n s_o 3_o right_o leg_n scheat_n 339._o 22._o 17._o 31._o s._n 3._o end_v of_o the_o flood_n fomahant_n 339._o 46._o 31._o 17._o s._n 1._o the_o whale_n mandibula_fw-la 41._o 21._o 2._o 48._o n_o 2._o mouth_n the_o midst_n 36._o 36._o 1._o 50._o n_o 3_o check_v 35._o 44._o 1._o 07._o s._n 3._o belly_n baten_v kaito_n 23._o 52._o 11._o 54._o s._n 3._o tail_n northern_a 0._o 43._o 10._o 37._o s._n 3._o tail_n southern_a 6._o 45._o 19_o 48._o s._n 2._o orion_n right_o shoulder_n bedalgieure_fw-fr 84._o 23._o 07._o 18._o n_o 1._o leave_v shoulder_n bellatrix_fw-la 76._o 54._o 06._o 01._o n_o 2._o girdle_n the_o first_o 78._o 52._o 0._o 35._o s._n 2._o second_o 79._o 55._o 1._o 26._o s._n 2._o three_o 81._o 04._o 2._o 09._o s._n 2._o leave_v foot_n rigel_n 74._o 44._o 8._o 37._o s._n 1._o right_o foot_n 83._o 03._o 9_o 49._o s._n 3._o thegreat_a dog_n mouth_n alhaber_n sirius_n 97._o 42._o 16._o 14½_n s._n 1._o foremost_a foot_n 92._o 08._o 17._o 49._o s._n 2._o the_o little_a dog_n neck_n 107._o 22._o 8._o 54._o n_o 3_o thigh_n procyon_n 110._o 34._o 6._o 03._o n_o 2._o hydra_n the_o heart_n alphard_n 137._o 54._o 7._o 15._o s._n 2._o corvus_n in_o his_o beak_n the_o first_o of_o the_o â–¡_o 177._o 50._o 22._o 54_o s._n 4._o second_o of_o the_o â–¡_o 179._o 49._o 15._o 39_o s._n 3._o three_o of_o the_o â–¡_o 183._o 16._o 14._o 39_o s._n 3._o four_o â–¡_o 184._o 20._o 21._o 33._o s._n 3._o chap._n viii_o of_o the_o ring_n or_o limb_n of_o the_o mater_n the_o three_o part_n of_o this_o instrument_n be_v the_o ring_n or_o limb_n which_o be_v nothing_o else_o but_o the_o skirt_n of_o a_o circular_a plate_n equal_a with_o the_o mater_n who_o middle_a be_v cut_v out_o by_o a_o lesser_a concentrique_fw-la circle_n it_o be_v bound_v with_o two_o parallel_n circle_n the_o outmost_a must_v touch_v the_o edge_n of_o the_o mater_n round_o the_o inner_a circle_n or_o edge_n of_o this_o ring_n it_o must_v be_v a_o little_a less_o than_o the_o limb_n of_o the_o reet_n that_o it_o may_v take_v hold_n of_o the_o reet_n to_o keep_v it_o flat_a and_o safe_a from_o harm_n this_o ring_n have_v need_n be_v thick_a than_o the_o reet_n but_o not_o so_o thick_a as_o the_o mater_n and_o for_o breadth_n about_o 1_o 10_o part_n of_o the_o diameter_n it_o must_v be_v pin_v or_o screw_v on_o to_o the_o mater_n with_o 6_o or_o 8_o pin_n or_o screw_n that_o so_o you_o may_v take_v your_o plate_n asunder_o when_o need_n be_v to_o cleanse_v they_o from_o any_o stain_n or_o dust_n that_o may_v get_v between_o let_v the_o pin_n that_o carry_v the_o naile-screws_a be_v rivert_v in_o the_o ring_n and_o chair_n head_n so_o file_v down_o and_o polish_a that_o they_o be_v not_o see_v to_o check_v the_o label_n and_o hole_n be_v make_v in_o the_o mater_fw-la for_o the_o pin_n to_o pass_v through_o you_o shall_v have_v small_a screw_n of_o what_o fashion_n you_o like_o best_a to_o turn_v upon_o they_o on_o the_o backside_n these_o screw_n will_v be_v make_v all_o of_o a_o length_n and_o may_v serve_v as_o foot_n to_o bare_v up_o the_o instrument_n about_o a_o three_o part_n of_o a_o inch_n from_o the_o ground_n that_o it_o be_v not_o scratch_v and_o be_v ready_a to_o take_v up_o and_o that_o the_o reet_n may_v turn_v more_o pleasant_o under_o the_o ring_n and_o lie_v as_o near_o as_o may_v be_v in_o the_o same_o plain_a with_o the_o ring_n you_o shall_v abate_v half_o the_o thickness_n of_o the_o upper_a edge_n of_o the_o reet_n about_o a_o barly-corn's_a breadth_n round_o about_o so_o far_o as_o he_o shall_v run_v under_o the_o ring_n and_o likewise_o aba_fw-la e_fw-la half_o the_o thickness_n of_o the_o inner_a edge_n of_o the_o ring_n on_o the_o low_a side_n where_o he_o clasp_v down_o the_o reet_n which_o a_o good_a turner_n know_v now_o to_o do_v or_o you_o may_v make_v a_o shift_n to_o do_v it_o with_o a_o beam-compass_n if_o you_o make_v your_o run_a point_n like_o a_o narrow_a chesill_n your_o ring_n thus_o fit_v to_o the_o mater_n you_o shall_v set_v one_o foot_n of_o your_o compass_n in_o the_o centre_n of_o the_o mater_n and_o with_o the_o other_o draw_v near_o the_o inner_a edge_n of_o the_o limb_n a_o circle_n about_o 8_o 100_o of_o a_o inch_n distant_a from_o the_o edge_n also_o open_v your_o compass_n about_o â…™_n of_o a_o inch_n more_o you_o shall_v draw_v another_o parallel_n circle_n and_o lay_v your_o ruler_n or_o label_n from_o the_o centre_n to_o the_o several_a degree_n of_o the_o fundamental_a circle_n of_o the_o mater_n you_o shall_v draw_v short_a line_n for_o every_o degree_n from_o the_o inner_a edge_n of_o the_o ring_n to_o the_o first_o circle_n and_o every_o ten_o degree_n you_o shall_v prolong_v to_o the_o second_o circle_n and_o let_v every_o five_o be_v 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space_n enough_o leave_v upon_o the_o ring_n without_o the_o circle_n of_o the_o degree_n and_o hour_n you_o may_v fill_v it_o up_o with_o the_o ephemeris_fw-la of_o the_o sun_n in_o this_o manner_n the_o former_a scale_n on_o the_o inner_a edge_n of_o the_o ring_n shall_v serve_v you_o to_o this_o purpose_n for_o a_o ecliptic_a and_o you_o may_v set_v to_o he_o the_o character_n of_o the_o sign_n if_o you_o will_v at_o every_o thirty_o degree_n beginning_n at_o oriens_fw-la and_o there_o set_v ♈_o and_o
♋_o at_o meridies_n and_o the_o rest_n in_o like_a order_n then_o draw_v another_o scale_n without_o this_o upon_o the_o ring_n consist_v of_o two_o space_n in_o the_o inner_a space_n shall_v be_v the_o day_n of_o the_o year_n in_o the_o outer_a space_n which_o must_v be_v a_o little_o large_a shall_v be_v the_o name_n of_o the_o month_n in_o their_o order_n and_o to_o divide_v this_o scale_n right_o you_o shall_v do_v thus_o go_v to_o some_o eshemeris_fw-la for_o the_o leap_v year_n that_o next_o come_v viz._n 1660_o or_o rather_o for_o some_o leap_v year_n about_o 20_o year_n hence_o that_o your_o scale_n may_v serve_v without_o any_o prosthapheresis_fw-la for_o 40_o year_n to_o come_v without_o sensible_a error_n and_o begin_v your_o year_n with_o march_n look_v where_o the_o sun_n be_v on_o the_o 29_o of_o february_n at_o noon_n which_o you_o shall_v find_v to_o be_v ♓_o 20_o degr_n 47_o min_fw-mi for_o the_o year_n 1660._o therefore_o lay_v the_o label_n or_o a_o ruler_n from_o 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that_o the_o space_n for_o the_o last_o day_n of_o the_o year_n febr._n 28_o will_v fall_v out_o to_o be_v less_o by_o a_o four_o part_n then_o the_o rest_n by_o reason_n that_o the_o sun_n want_v almost_o 6_o hour_n to_o finish_v his_o circle_n which_o he_o finish_v in_o day_n 365_o 5_o hour_n 48_o minute_n and_o for_o this_o cause_n these_o scale_n will_v serve_v you_o to_o find_v the_o sun_n place_n at_o noon_n for_o any_o day_n in_o a_o like_a year_n that_o be_v every_o four_o year_n account_v hence_o either_o backward_o or_o forward_o which_o year_n shall_v evermore_o be_v account_v to_o begin_v from_o febr._n 29._o and_o may_v be_v account_v the_o first_o year_n after_o leap_n year_n because_o the_o intercalation_n be_v february_n 25_o next_o before_o then_o for_o the_o year_n next_o follow_v viz_o 1661._o beginning_n march_v 1_o and_o be_v second_o from_o the_o bissextile_a or_o leap_v year_n these_o scale_n shall_v give_v you_o the_o place_n of_o the_o sun_n at_o six_o hour_n after_o noon_n and_o the_o three_o year_n from_o bissextile_a 1662._o beginning_n as_o before_z march_z 1_o these_o scale_n shall_v give_v you_o the_o sun_n place_n 12_o hour_n after_o noon_n or_o the_o midnight_n follow_v and_o the_o four_o year_n 1663._o be_v bissextile_a these_o scale_n show_v the_o place_n of_o the_o sun_n at_o 18_o hour_n after_o noon_n the_o next_o year_n 1664_o be_v the_o first_o after_o bissextile_a and_o beginning_n as_o aforesaid_a march_v 1_o be_v the_o very_a same_o year_n for_o which_o your_o scale_n be_v make_v and_o go_v for_o that_o year_n your_o scale_n show_v the_o sun_n place_n at_o noon_n again_o but_o because_o the_o julian_n year_n be_v big_a than_o the_o true_a solar_a year_n by_o almost_o 12_o mi._n of_o time_n that_o be_v near_o a_o quarter_n of_o a_o hour_n in_o which_o time_n the_o sun_n move_v 27_o sec_fw-la 13_o three_o 37_o fourth_n therefore_o when_o you_o have_v find_v the_o sun_n place_n by_o the_o former_a scale_n any_o year_n after_o 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quadrant_n who_o semediameter_n be_v equal_a to_o the_o diameter_n of_o your_o planisphear_n but_o if_o the_o altitude_n exceed_v 30_o or_o 40._o degree_n then_o will_v the_o plumb-line_n cut_v the_o limb_n too_o slope_n and_o have_v too_o much_o play_v to_o your_o trouble_n for_o remedy_n whereof_o you_o shall_v remove_v the_o sight_n at_o d_o towards_o a_o some_o degree_n as_o for_o example_n 60_o degree_n by_o which_o mean_v you_o shall_v abate_v the_o sun_n altitude_n 30_o degree_n which_o 30_o degree_n must_v be_v add_v to_o the_o altitude_n observe_v as_o for_o example_n the_o sight_n be_v place_v one_o at_o c_o the_o other_o 60_o degree_n above_o d_o towards_o a_o and_o the_o