plain_o distinguish_v from_o the_o rest_n in_o the_o fabric_n of_o this_o instrument_n therefore_o you_o may_v easy_o count_v the_o angle_n of_o the_o hour_n in_o any_o parallel_n b_o at_o the_o zenith_n be_v the_o angle_n of_o the_o azimuth_n account_v from_o the_o north_n part_n of_o the_o meridian_n his_o full_a measure_n be_v in_o the_o finiterline_v of_o the_o reet_n but_o you_o may_v number_v it_o in_o any_o almicanter_n because_o every_o 5_o and_o 15_o azimuth_n be_v distinguish_v on_o the_o reet_n as_o the_o meridian_n be_v on_o the_o mater_n c_o the_o place_n of_o the_o sun_n or_o star_n in_o the_o meeting_n of_o the_o meridian_n and_o azimuth_n be_v the_o three_o angle_n which_o common_o be_v neither_o know_v nor_o inquire_v but_o it_o may_v be_v find_v when_o you_o please_v by_o turn_v the_o triangle_n as_o have_v be_v often_o show_v now_o if_o you_o be_v verse_v in_o the_o 8_o last_o chapter_n of_o the_o three_o book_n you_o may_v easy_o find_v any_o of_o the_o requisite_n of_o this_o chapter_n without_o any_o more_o direction_n nevertheless_o for_o the_o learner_n sake_n i_o shall_v exemplify_v this_o general_a problem_n in_o the_o 4_o next_o chapter_n and_o also_o further_o in_o the_o 31_o 32_o and_o 33._o chapter_n hereafter_o follow_v see_v the_o scheam_n chap._n 26._o chap._n xxv_o to_o find_v the_o altitude_n and_o azimuth_n of_o the_o sun_n or_o star_n at_o any_o time_n propose_v the_o latitude_n and_o declination_n be_v know_v your_o planisphear_n set_v in_o the_o first_o mode_n of_o the_o meridional_a projection_n as_o in_o the_o former_a chapter_n go_v to_o the_o parallel_n of_o the_o declination_n of_o the_o sun_n or_o star_n and_o follow_v he_o through_o all_o the_o meridian_n from_o the_o finiter_fw-la to_o the_o limb_n which_o be_v the_o meridian_n of_o your_o place_n and_o thence_o back_o again_o to_o the_o finiter_n and_o you_o shall_v find_v at_o the_o first_o sight_n what_o almicanter_n and_o azimuth_n cross_v the_o parallel_n in_o any_o point_n propose_v and_o so_o have_v you_o the_o altitude_n and_o azimuth_n thereof_o example_n june_n 10._o the_o sun_n be_v in_o the_o tropic_n of_o cancer_n and_o so_o make_v his_o diurnal_a revolution_n in_o the_o 23_o ½_n parallel_v of_o declination_n i_o follow_v this_o parallel_n the_o tropic_n from_o the_o horizon_n upward_o and_o have_v go_v 4_o degree_n i_o meet_v the_o ragged_a arch_n or_o hour_n line_n of_o 4._o which_o be_v the_o 120th_o meridian_n from_o the_o south_n there_o cross_v the_o second_o almicantar_n and_o the_o three_o and_o fifty_o azimuth_n from_o the_o north_n whereby_o i_o learn_v that_o at_o 4._o in_o the_o morning_n june_n 10_o the_o sun_n be_v 2_o degree_n high_a and_o in_o azimuth_n from_o the_o north_n 53._o thence_o go_v on_o 15_o degree_n i_o come_v to_o the_o hour_n circle_n of_o 5._o where_o cut_v the_o 10_o almicantar_n almost_o and_o azimuth_n 64_o degree_n and_o better_o go_v 15_o degree_n further_o i_o come_v to_o the_o axtree-line_n which_o be_v the_o hour_n circle_n of_o 6._o and_o there_o i_o find_v the_o sun_n altitude_n 18_o degree_n and_o his_o azimuth_n from_o the_o north_n 75_o degree_n etc._n etc._n and_o look_v what_o altitude_n and_o azimuth_n i_o find_v at_o 4_o 5_o 6._o &c_n &c_n in_o the_o morning_n the_o same_o i_o find_v at_o the_o afternoon_n hour_n that_o have_v like_o distance_n from_o noon_n because_o the_o eastern_a and_o western_a hemisphear_n be_v alike_o and_o the_o same_o line_n serve_v they_o both_o thus_o you_o may_v do_v in_o any_o other_o parallel_n and_o for_o any_o star_n as_o well_o as_o the_o sun_n have_v his_o declination_n give_v and_o so_o you_o may_v make_v table_n of_o the_o sun_n altitude_n and_o azimuth_n at_o every_o hour_n and_o quarter_n of_o a_o hour_n if_o you_o please_v for_o every_o day_n throughout_o the_o year_n and_o that_o as_o fast_o as_o you_o can_v write_v they_o without_o change_v the_o posture_n of_o the_o planisphear_n at_o all_o chap._n xxvi_o the_o latitude_n altitude_n and_o azimuth_n give_v to_o find_v the_o declination_n and_o the_o hour_n example_n have_v observe_v the_o sun_n altitude_n 13._o degree_n and_o his_o azimuth_n from_o the_o south_n westward_n 28_o ½_n in_o our_o latitude_n 52_o ¼_n my_o planisphear_n set_v in_o the_o same_o manner_n as_o chapter_n 25._o i_o seek_v out_o the_o 13_o almicantar_n at_o the_o limb_n of_o my_o reet_n and_o follow_v he_o inward_o till_o i_o come_v between_o azimuth_n 28_o and_o 29_o there_o i_o meet_v the_o 30_o meridian_n and_o the_o 20_o ¼_n parallel_v of_o declination_n by_o which_o i_o gather_v that_o it_o be_v 2_o of_o the_o clock_n after_o noon_n and_o that_o the_o sun_n decline_v southward_o 20_o degree_n ¼_n note_v here_o that_o the_o hour_n of_o a_o star_n thus_o find_v be_v not_o the_o hour_n of_o the_o night_n unless_o the_o star_n happen_v to_o be_v opposite_a to_o the_o sun_n but_o it_o be_v the_o time_n the_o star_n lack_v to_o come_v to_o the_o south_n or_o the_o time_n of_o his_o course_n from_o the_o south_n chap._n xxvii_o the_o latitude_n declination_n and_o altitude_n give_v to_o find_v the_o hour_n and_o azimuth_n here_o the_o three_o side_n of_o the_o complimental_a triangle_n be_v give_v and_o the_o angle_n a_o and_o b_o seek_v example_n march_v the_o 10_o in_o the_o morning_n the_o sun_n be_v in_o the_o equinoctial_a i_o observe_v his_o altitude_n 32_o degree_n the_o finiter_n be_v set_v to_o my_o latitude_n 52_o ¼_n as_o before_o i_o go_v to_o the_o 32._o almicantar_n in_o the_o reet_n and_o where_o i_o find_v he_o cross_v the_o equinoctial_a line_n of_o the_o mater_n there_o i_o conclude_v be_v the_o place_n of_o the_o sun_n at_o the_o time_n of_o my_o observation_n and_o the_o angle_n c_o of_o my_o triangle_n there_o the_o 30_o ½_n meridian_n pass_v show_v i_o that_o the_o angle_n a_o at_o the_o pole_n be_v 30_o ½_n or_o that_o it_o want_v half_a a_o degree_n that_o be_v 2_o minute_n of_o time_n of_o ten_o of_o the_o clock_n and_o there_o also_o the_o azimuth_n 36_o â…”_n from_o the_o south_n or_o from_o the_o north_n 143_o â…“_n show_v i_o that_o the_o angle_n b_o at_o the_o zenith_n be_v 143_o â…“_n the_o azimuth_n from_o the_o north_n and_o his_o supplement_n 36_o â…”_n the_o azimuth_n from_o the_o south_n chap._n xxviii_o the_o declination_n altitude_n and_o azimuth_n of_o the_o sun_n give_v to_o find_v the_o hour_n and_o latitude_n in_o the_o meridional_a projection_n look_v in_o the_o reet_n where_o the_o almicantar_n for_o the_o altitude_n give_v and_o the_o azimuth_n give_v do_v cross_a and_o turn_v the_o point_n of_o the_o reet_n where_o they_o cross_v to_o the_o parallel_n of_o the_o sun_n declination_n upon_o the_o mater_n the_o meridian_n that_o cut_v there_o show_v the_o hour_n and_o between_o the_o finiter_n and_o the_o pole_n or_o between_o the_o equator_fw-la and_o the_o zenith_n you_o have_v the_o latitude_n in_o the_o limb._n chap._n xxix_o to_o find_v the_o hour_n of_o the_o night_n by_o the_o northing_n or_o sothe_v rise_v or_o set_v of_o any_o star_n use_v for_o this_o the_o equinoctial_a projection_n and_o if_o the_o star_n be_v in_o your_o reet_n turn_v he_o to_o the_o north_n or_o south_n of_o the_o meridian_n line_n or_o to_o the_o east_n or_o west_n part_n of_o the_o horizon_n in_o your_o planisphear_n as_o you_o see_v he_o in_o the_o heaven_n then_o turn_v the_o label_n to_o the_o sun_n place_n in_o the_o ecliptic_a of_o the_o reet_n and_o it_o shall_v show_v the_o hour_n in_o the_o limb_n but_o if_o the_o star_n be_v not_o in_o the_o reet_n you_o shall_v supply_v he_o by_o the_o shift_n use_v chap._n 18._o example_n march_n 10_o i_o see_v sirius_n set_v in_o the_o south-west_n and_o have_v turn_v he_o to_o the_o same_o place_n in_o my_o planisphear_n i_o lay_v the_o label_n to_o ♈_o 0._o which_o be_v the_o sun_n place_n for_o that_o day_n and_o it_o cut_v in_o the_o limb_n 11._o hour_n 3_o minute_n past_o noon_n again_o december_n 1_o see_v lucida_n pleiadum_fw-la in_o the_o meridian_n i_o turn_v the_o star_n till_o he_o touch_v the_o meridian_n line_n of_o the_o mater_n then_o lay_v the_o label_n to_o â™_o 19_o the_o place_n of_o the_o sun_n i_o find_v it_o be_v 10._o hour_n 17._o minute_n at_o night_n the_o same_o night_n i_o see_v ras_n aben_n or_o the_o bright_a in_o the_o dragon_n head_n under_o the_o pole_n in_o the_o north_n part_n of_o the_o meridian_n wherefore_o i_o place_v he_o on_o the_o meridian_n line_n between_o the_o centre_n and_o septentrio_fw-la and_o the_o label_n lay_v to_o â™_o 19_o show_v i_o it_o be_v 12._o 36._o minute_n that_o be_v more_o than_o half_a a_o hour_n past_o midnight_n chap._n xxx_o the_o time_n of_o day_n or_o night_n
♋_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 the_o centre_n to_o ♓_o 20_o degr_n 47_o min._n in_o the_o inner_a scale_n strike_v a_o long_a stroke_n through_o your_o outward_a scale_n and_o from_o thence_o begin_v your_o year_n write_v from_o thence_o towards_o the_o right_a hand_n march_v 1660._o then_o lay_v the_o label_n to_o ♓_o 21_o degr_n 47_o min_fw-mi which_o be_v the_o sun_n place_n on_o the_o first_o day_n of_o march_n at_o noon_n the_o same_o year_n and_o where_o it_o cut_v the_o outer_a scale_n mark_v the_o first_o day_n of_o march_n and_o so_o the_o rest_n in_o order_n and_o to_o the_o first_o day_n of_o every_o month_n you_o shall_v set_v his_o proper_a letter_n which_o belong_v to_o he_o in_o the_o calendar_n as_o to_o the_o first_o of_o march_v you_o shall_v set_v d_o and_o to_o the_o first_o of_o april_n g_z etc._n etc._n and_o when_o you_o have_v do_v december_n you_o must_v take_v the_o sun_n place_n for_o january_n and_o february_n out_o of_o the_o next_o year_n ephemeris_fw-la viz._n 1661._o and_o note_n 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 1660_o look_v how_o many_o year_n be_v pass_v since_o 1660_o and_o so_o many_o time_n you_o must_v add_v 27_o sec_fw-la 13_o three_o 37_o fourth_n that_o be_v almost_o half_a a_o minute_n to_o the_o sun_n place_n find_v and_o for_o year_n past_o â—ou_n must_v subtract_v as_o much_o that_o you_o may_v find_v the_o sun_n place_n exact_o this_o prosthapheresis_fw-la in_o 2_o or_o 3_o year_n be_v scarce_o considerable_a in_o a_o instrument_n but_o in_o 10_o year_n there_o will_v be_v 4_o minute_n 32._o second_o and_o in_o 20_o year_n 9_o minute_n 5._o second_o to_o be_v add_v after_o 1660._o and_o as_o much_o to_o be_v subtract_v in_o like_a number_n of_o year_n precede_v the_o year_n 1660._o to_o which_o this_o scale_n be_v suppose_v to_o be_v frame_v this_o ephemeris_fw-la or_o calender_n m._n blagrave_n will_v have_v on_o the_o backside_n where_o he_o will_v also_o have_v a_o ruler_n with_o sight_n to_o take_v the_o altitude_n of_o the_o sun_n or_o star_n but_o this_o will_v be_v find_v incommodious_a in_o many_o respect_n both_o in_o the_o frame_n and_o in_o the_o use_n and_o therefore_o i_o advise_v that_o nothing_o be_v set_v on_o the_o backside_n but_o the_o table_n of_o the_o prime_n epact_n and_o cycle_n of_o the_o sun_n thereby_o to_o find_v the_o age_n of_o the_o moon_n her_o conjunction_n and_o opposition_n and_o the_o movable_a feast_n for_o ever_o of_o which_o see_v chap._n 11._o chap._n x._o of_o the_o label_n and_o sight_n the_o label_n be_v a_o ruler_n slit_v in_o the_o midst_n and_o the_o half_a of_o it_o cut_v away_o to_o the_o head_n where_o it_o be_v pin_v to_o turn_v upon_o the_o centre_n and_o reach_v to_o the_o outside_n of_o the_o limb._n the_o fiducial_a edge_n thereof_o which_o point_v upon_o the_o centre_n must_v be_v graduate_v like_a to_o the_o semidiameter_n of_o the_o mater_n and_o reet_n into_o 90_o degree_n to_o be_v number_v either_o inward_a or_o outward_a the_o fashion_n of_o it_o may_v be_v understand_v by_o the_o figure_n without_o more_o word_n to_o this_o label_n you_o may_v fit_a sight_n either_o fix_v or_o movable_a as_o you_o like_v best_a for_o observe_v altitude_n and_o azimuth_n but_o for_o take_v azimuth_n you_o have_v need_n have_v one_o tall_a sight_n at_o least_o half_a as_o long_o as_o the_o label_n and_o then_o it_o have_v need_n be_v movable_a to_o take_v off_o at_o pleasure_n for_o take_v the_o altitude_n of_o the_o sun_n i_o have_v make_v a_o pair_n of_o movable_a sight_n to_o slip_v up_o and_o down_o upon_o the_o edge_n of_o the_o planisphear_n have_v on_o the_o backside_n spring_v plate_n of_o brass_n to_o pintch_n they_o close_o and_o make_v they_o stick_v where_o you_o set_v they_o these_o be_v common_o to_o be_v set_v at_o c_o and_o d_o the_o end_n of_o the_o equinoctial_a line_n at_o a_o in_o the_o limb_n and_o in_o the_o circle_n next_o unto_o the_o inner_a edge_n which_o bound_v the_o stroke_n of_o the_o several_a degree_n you_o shall_v drill_v a_o small_a hole_n through_o which_o you_o may_v put_v a_o thread_n to_o hang_v a_o plummet_n on_o the_o sun_n then_o shine_v through_o the_o sight_n place_v at_o c_o and_o d_o the_o plumbline_n shall_v show_v his_o altitude_n in_o the_o semicircle_n b_o c_o a_o you_o beginning_n to_o number_n from_o b_o and_o observe_v where_o the_o plumbline_n cross_v the_o circle_n in_o which_o the_o hole_n for_o hang_v the_o plumbline_n be_v make_v and_o here_o you_o must_v remember_v that_o because_o the_o plumbline_n fall_v not_o from_o the_o centre_n of_o the_o planisphear_n but_o from_o a_o point_n in_o the_o circumference_n about_o a_o therefore_o the_o space_n of_o two_o degree_n must_v be_v take_v but_o one_o degree_n so_o that_o if_o the_o plumb-line_n fall_v 20_o degr_n below_z b_o toward_z c_z the_o sun_n altitude_n be_v 10_o degree_n as_o you_o may_v see_v demonstrate_v euclid_n 3.20_o and_o pitisc_n trigonem_fw-la 1.53_o and_o thus_o you_o may_v observe_v the_o sun_n altitude_n near_o the_o horizon_n as_o exact_o as_o by_o a_o 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
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
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
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
plumb-line_n cut_v 10_o degree_n from_o b_o towards_o c_o i_o say_v then_o be_v the_o sun_n 5_o degree_n high_a and_o 30_o degree_n more_o in_o all_o 35_o degree_n in_o like_a manner_n you_o may_v place_v the_o sight_n at_o any_o other_o number_n of_o degree_n from_o d_o towards_o a_o as_o you_o shall_v find_v most_o convenient_a for_o the_o present_a altitude_n remember_v always_o that_o how_o many_o degree_n soever_o you_o remove_v the_o sight_n half_o so_o many_o be_v to_o be_v add_v to_o the_o altitude_n find_v but_o if_o your_o reet_n happen_v to_o run_v so_o far_o under_o the_o limb_n that_o you_o can_v make_v a_o center-hole_n for_o the_o plumbet_n through_o the_o limb_n and_o mater_n without_o hinder_v the_o reet_n motion_n then_o may_v you_o have_v a_o small_a plate_n of_o sheet_n brass_n in_o fashion_n of_o a_o arm_n or_o tongue_n in_o the_o point_n whereof_o you_o shall_v have_v a_o center-hole_n drill_v and_o this_o plate_n shall_v be_v so_o join_v with_o a_o sluice_n or_o screw_v about_o the_o limb_n near_o a_o that_o the_o center-hole_n make_v in_o this_o plate_n may_v lie_v close_o to_o the_o point_n where_o the_o centre_n shall_v have_v be_v bore_v in_o the_o limb_n in_o the_o line_n a_o b_o and_o thus_o you_o may_v put_v it_o on_o and_o take_v it_o off_o at_o pleasure_n that_o it_o hinder_v not_o the_o motion_n of_o the_o reet_n or_o label_n of_o the_o fashion_n of_o the_o sight_n see_v more_o book_n 4.2_o chap._n xi_o of_o the_o perpetual_a calendar_n on_o the_o backside_n on_o the_o backside_n of_o your_o planisphear_n you_o may_v set_v the_o calendar_n follow_v which_o consist_v of_o three_o table_n gather_v round_o the_o long_a will_v be_v set_v outtermost_a the_o first_o be_v the_o table_n of_o the_o cycle_n of_o the_o sun_n that_o be_v of_o the_o sunday_n letter_n this_o be_v here_o place_v in_o the_o middle_n it_o be_v a_o cycle_n of_o 28._o year_n in_o which_o time_n the_o dominical_a letter_n run_v all_o his_o change_n cause_v by_o the_o one_o odd_a day_n above_o 52_o week_n in_o every_o common_a year_n and_o two_o odd_a day_n which_o run_v over_o the_o even_a week_n in_o the_o leap_v year_n to_o find_v the_o begin_n of_o this_o cycle_n add_v to_o the_o year_n of_o our_o lord_n 9_o because_o the_o first_o year_n of_o our_o lord_n as_o we_o common_o acount_v be_v the_o 10_o of_o this_o cycle_n and_o divide_v the_o sum_n by_o 28._o the_o remainder_n be_v the_o year_n of_o the_o cycle_n run_v and_o if_o nothing_o remain_v than_o it_o be_v the_o 28._o or_o last_o year_n so_o you_o shall_v find_v that_o the_o cycle_n now_o run_v shall_v end_v with_o the_o julian_n year_n 1671_o as_o in_o the_o table_n and_o shall_v begin_v again_o with_o the_o year_n of_o our_o lord_n 1672._o thus_o may_v you_o renew_v the_o table_n when_o it_o be_v expire_v or_o make_v this_o very_a table_n serve_v you_o for_o ever_o example_n enter_v this_o table_n with_o the_o year_n of_o our_o lord_n 1656._o now_o run_v and_o you_o shaall_v find_v over_o against_o this_o year_n in_o the_o next_o space_n inward_o 13._o show_v you_o that_o it_o be_v the_o 13_o year_n of_o the_o sun_n cycle_n so_o shall_v the_o 28_o year_n forward_o viz._n 1684_o be_v again_o the_o 13_o year_n of_o the_o cycle_n next_o come_v in_o the_o next_o space_n within_o you_o have_v the_o dominical_a letter_n f_o and_o e_o because_o it_o be_v leap_v year_n f_o shall_v be_v the_o dominical_a letter_n till_o you_o come_v pass_v the_o intercalary_n day_n which_o be_v the_o day_n follow_v the_o 24_o of_o february_n and_o for_o the_o rest_n of_o this_o year_n the_o dominical_a letter_n shall_v be_v e_z for_o the_o letter_n always_o change_v backward_o also_o you_o shall_v note_v here_o that_o the_o day_n insert_v in_o every_o four_o year_n be_v not_o february_n 29_o but_o february_n 25._o for_o february_n 24._o be_v 6_o cal._n martij_fw-la be_v repeat_v again_o in_o the_o leap_n year_n and_o they_o write_v again_o february_n 25.6_o cal._n martij_fw-la and_o the_o 25_o of_o february_n in_o the_o leap_n year_n be_v mark_v with_o the_o same_o letter_n f_o wherewith_o the_o 24_o of_o february_n happen_v always_o to_o be_v mark_v hence_o the_o leap_n year_n be_v call_v annus_fw-la bissextilis_fw-la and_o note_v that_o by_o the_o eclesiasticall_a law_n s._n mathias_n day_n which_o be_v february_n 24_o in_o common_a year_n in_o the_o bissextile_a year_n be_v to_o be_v observe_v on_o february_n 25._o nevertheless_o in_o our_o secular_a law_n not_o the_o 24_o and_o 25_o of_o february_n but_o the_o 28_o and_o 29_o in_o the_o leap_n year_n be_v ordain_v to_o be_v one_o day_n in_o the_o account_n of_o law_n as_o by_o statutum_n de_fw-fr anno_fw-la bissextili_fw-la make_v in_o 21_o year_n henry_n 3_o may_v appear_v the_o second_o table_n be_v of_o the_o cycle_n of_o the_o moon_n consist_v of_o the_o prime_n or_o golden_a number_n and_o the_o epact_n this_o table_n contain_v 19_o year_n which_o be_v the_o annus_fw-la metonicus_fw-la in_o which_o space_n of_o time_n meton_n a_o astronomer_n about_o 430_o year_n before_o christ_n observe_v the_o moon_n to_o finish_v all_o her_o variation_n so_o that_o every_o 19_o year_n the_o mean_a conjunction_n or_o change_n shall_v happen_v upon_o the_o same_o day_n of_o the_o month_n that_o they_o do_v happen_v upon_o 19_o year_n before_o only_o a_o hour_n and_o half_a soon_o yet_o because_o every_o 19_o year_n contain_v not_o the_o same_o number_n of_o leap_v year_n but_o sometime_o there_o come_v five_o leap_n year_n in_o 19_o year_n and_o sometime_o but_o four_o therefore_o there_o may_v happen_v in_o this_o period_n of_o meton_n a_o error_n of_o a_o whole_a day_n beside_o the_o hour_n and_o half_o above_o mention_v for_o remedy_v whereof_o calippus_n about_o the_o 330_o year_n before_o christ_n devise_v to_o quadruple_a this_o period_n of_o meton_n make_v periodâ—s_v calippica_fw-la of_o 76_o year_n which_o contain_v just_a 19_o quaternion_n of_o year_n so_o contain_v always_o the_o same_o number_n of_o leap_v year_n and_o day_n this_o period_n be_v therefore_o more_o perfect_a than_o metons_n for_o after_o this_o period_n of_o 76_o year_n the_o moon_n run_v over_o the_o same_o course_n for_o her_o conjunction_n and_o opposition_n change_v in_o the_o same_o year_n of_o the_o period_n always_o upon_o the_o same_o day_n of_o the_o month_n save_v only_o that_o she_o change_v soon_o by_o six_o hour_n in_o the_o latter_a period_n then_o in_o the_o former_a but_o the_o church_n still_o retain_v the_o period_n of_o meton_n call_v the_o prime_n or_o golden_a number_n because_o it_o use_v to_o be_v set_v in_o golden_a letter_n in_o the_o calendar_n in_o a_o certain_a artificial_a order_n throughout_o every_o month_n to_o guide_v you_o to_o the_o day_n of_o the_o moon_n prime_a or_o change_a so_o may_v you_o find_v it_o in_o red_a letter_n thus_o set_v to_o the_o calendar_n print_v in_o large_a folio_n with_o the_o book_n of_o common_a prayer_n in_o the_o time_n of_o the_o late_a queen_n elizabeth_n to_o find_v the_o year_n of_o the_o prime_n add_v to_o the_o year_n of_o our_o lord_n 1_o and_o divide_v the_o sum_n by_o 19_o the_o remainder_n be_v the_o year_n of_o the_o prime_n or_o if_o nothing_o remain_v it_o be_v the_o 19_o or_o last_o year_n thus_o you_o may_v find_v the_o present_a year_n 1656_o to_o be_v the_o four_o year_n of_o the_o prime_n and_o so_o you_o find_v it_o in_o the_o table_n the_o cycle_n or_o period_n now_o run_v end_v with_o 1671._o and_o begin_v again_o with_o the_o year_n follow_v the_o epact_n or_o concurrent_a be_v set_v against_o the_o prime_n in_o the_o next_o space_n inward_o and_o finish_v his_o cycle_n in_o the_o same_o time_n it_o be_v devise_v to_o find_v more_o ready_o the_o day_n of_o the_o change_n and_o age_n of_o the_o moon_n the_o way_n to_o find_v it_o be_v this_o multiply_v the_o golden_a number_n serve_v for_o your_o year_n by_o 11_o and_o divide_v the_o product_n by_o 30_o the_o residue_n be_v the_o epact_n for_o your_o year_n or_o have_v the_o epact_n know_v for_o any_o year_n you_o may_v make_v it_o from_o year_n to_o year_n by_o add_v 11_o to_o the_o epact_n of_o the_o year_n forego_v and_o cast_v away_o 30_o when_o the_o sum_n exceed_v 30._o the_o reason_n whereof_o be_v that_o the_o moon_n change_v 12_o time_n in_o 354._o day_n that_o be_v 11_o day_n before_o the_o sun_n have_v go_v his_o round_n for_o which_o cause_n the_o change_n must_v needs_o happen_v every_o year_n 11_o day_n soon_o observe_v here_o that_o the_o prime_n change_v every_o year_n the_o first_o day_n of_o january_n the_o epact_n not_o till_o the_o first_o of_o march_n the_o dominical_a letter_n change_v upon_o the_o
give_v to_o find_v in_o what_o coast_n any_o star_n be_v and_o how_o much_o he_o be_v distant_a from_o the_o horizon_n or_o meridian_n lay_v the_o sun_n place_n to_o the_o hour_n give_v in_o the_o equinoctial_a projection_n then_o may_v you_o present_o see_v all_o the_o star_n of_o the_o reet_n in_o what_o coast_n they_o be_v whether_o under_o the_o horizon_n or_o above_o and_o how_o many_o hour_n they_o lack_v or_o be_v past_o either_o the_o horizon_n or_o meridian_n example_n sit_v within_o door_n at_o seven_o of_o the_o clock_n on_o christmas_n day_n at_o night_n i_o desire_v to_o know_v what_o star_n be_v rise_v and_o what_o near_o the_o meridian_n wherefore_o lay_v ♑_o 14._o to_o 7._o of_o the_o clock_n afternoon_n i_o see_v in_o the_o reet_a the_o ram_n horn_n a_o little_a past_a south_n the_o plaiade_n want_v 1._o hour_n 28._o minute_n of_o south_n as_o the_o label_n show_v i_o in_o the_o limb_n ♌_o be_v rise_v but_o cor_n ♌_o not_o yet_o up_o i_o will_v know_v now_o what_o he_o want_v of_o rise_v therefore_o i_o turn_v forward_o the_o reet_n till_o cor_n ♌_o come_n to_o the_o horizon_n and_o observe_v how_o many_o degree_n of_o the_o reet_n pass_v under_o the_o label_n or_o by_o any_o point_n of_o the_o limb_n while_o the_o reet_n turn_v and_o i_o find_v that_o ♈_o 0_o and_o so_o any_o other_o point_n move_v on_o in_o the_o limb_n 10_o degree_n in_o the_o while_n that_o cor_n ♌_o be_v come_v to_o the_o horizon_n whereupon_o i_o understand_v that_o he_o will_v rise_v 40_o minute_n after_o chap._n xxxi_o the_o time_n and_o latitude_n give_v to_o find_v the_o altitude_n and_o azimuth_n of_o any_o star_n and_o thereby_o to_o get_v the_o knowledge_n of_o the_o star_n find_v the_o hour_n of_o the_o star_n by_o the_o former_a chapter_n and_o by_o the_o label_n observe_v his_o declination_n then_o set_v your_o planisphear_n in_o the_o meridional_a projection_n and_o in_o the_o parallel_n of_o the_o star_n declination_n number_n his_o hour-distance_n from_o the_o south_n where_o the_o number_n end_v set_v a_o needle_n point_n there_o be_v the_o place_n of_o the_o star_n and_o the_o almicantar_n and_o azimuth_n that_o cut_v he_o there_o show_v your_o desire_n example_n i_o will_v know_v the_o cloudy_a star_n praesepe_v in_o the_o breast_n of_o cancer_n which_o indeed_o be_v a_o glimmer_a light_n make_v up_o of_o five_o small_a and_o bright_a star_n as_o by_o the_o telescope_n appearech_v this_o praesepe_n i_o find_v by_o the_o last_o chapter_n to_o want_v 6._o hour_n 21._o min._n of_o south_n his_o declination_n find_v by_o the_o label_n be_v 21._o degree_n north._n therefore_o set_v the_o finiter_n to_o our_o latitude_n 52_o ¼_n i_o follow_v the_o 21._o parallel_v of_o north_n declination_n from_o the_o meridian_n till_o i_o come_v 5_o degree_n 15_o minute_n past_o the_o axletree_n because_o i_o find_v he_o 6_o hour_n 21_o minute_n before_o the_o meridian_n there_o the_o 17_o azimuth_n from_o the_o east_n northward_o cut_v the_o parallel_n of_o praesepe_n and_o there_o cut_v he_o also_o the_o 13_o almicantar_n now_o to_o find_v he_o out_o i_o lay_v my_o planisphear_n horizontal_o set_v the_o meridian_n of_o my_o planisphear_n in_o the_o meridian_n of_o the_o place_n by_o chap._n 3_o and_o 4._o and_o i_o turn_v my_o label_n and_o sight_n to_o the_o azimuth_n of_o praesepe_n 17_o degree_n from_o the_o east_n northward_o and_o before_o my_o sight_n i_o hang_v up_o a_o plumb-line_n upon_o a_o pole_n to_o keep_v the_o azimuth_n then_o keep_v my_o station_n i_o set_v my_o planisphear_n upon_o his_o edge_n or_o hang_v he_o upon_o a_o staff_n with_o a_o socket_n in_o the_o azimuth_n of_o the_o star_n so_o that_o the_o plumbet_n show_v altitude_n 13_o degree_n by_o chap._n 1_o then_o do_v the_o sight_n point_v just_a upon_o praesepe_n and_o will_v teach_v i_o the_o star_n if_o i_o do_v not_o know_v he_o before_o chap._n xxxii_o the_o latitude_n of_o the_o place_n the_o declination_n of_o a_o star_n with_o his_o altitude_n or_o azimuth_n give_v to_o find_v both_o the_o hour_n of_o the_o star_n and_o the_o hour_n of_o the_o night_n by_o this_o chapter_n you_o may_v find_v the_o time_n of_o night_n at_o any_o time_n by_o any_o star_n if_o he_o be_v visible_a above_o the_o horizon_n use_v the_o first_o mode_n of_o the_o meridional_a projection_n and_o have_v observe_v the_o altitude_n or_o azimuth_n of_o the_o star_n look_v where_o that_o altitude_n or_o azimuth_n cut_v the_o parallel_n of_o the_o star_n declination_n there_o cut_v also_o a_o meridian_n which_o show_v the_o hour_n of_o the_o star_n that_o be_v the_o distance_n of_o a_o star_n from_o the_o meridian_n in_o hour_n and_o minute_n and_o by_o this_o hour_n of_o the_o star_n to_o get_v the_o hour_n of_o the_o night_n you_o shall_v place_v the_o star_n at_o the_o hour_n find_v in_o the_o equinoctial_a projection_n which_o do_v the_o label_n lay_v to_o the_o place_n of_o the_o sun_n shall_v show_v the_o hour_n of_o the_o night_n in_o the_o limb._n example_n december_n 25._o i_o observe_v procyon_n to_o be_v full_a east_n his_o declination_n north_n be_v 6_o degree_n 3_o minute_n in_o the_o meridional_a projection_n i_o look_v where_o the_o axis_n of_o the_o reet_n which_o be_v the_o east_n azimuth_n cut_v the_o six_o of_o the_o north_n parallel_n and_o i_o find_v the_o intersection_n 1_o degree_n southward_o from_o the_o axtree_n of_o the_o mater_n or_o hour-line_n of_o six_o there_o also_o cut_v the_o 5_o ½_n almicantar_n which_o show_v more_o than_o i_o seek_v that_o procyon_n be_v 5_o degree_n 30_o minute_n above_o the_o horizon_n now_o have_v the_o hour_n of_o the_o star_n 6_o hour_n 4_o minute_n before_o the_o meridian_n i_o take_v the_o equinoctial_a projection_n and_o have_v lay_v the_o label_n one_o degree_n from_o oriens_fw-la southward_o in_o the_o limb_n i_o turn_v procyon_n to_o the_o label_n which_o show_v his_o hour_n 6_o hour_n 4_o minute_n and_o leave_v he_o there_o i_o turn_v away_o the_o label_n to_o ♑_o 14_o the_o sun_n place_n and_o it_o show_v i_o in_o the_o limb_n the_o time_n of_o night_n 6_o hour_n 26_o min._n past_o noon_n and_o the_o same_o i_o may_v have_v find_v if_o instead_o of_o his_o azimuth_n i_o have_v observe_v his_o altitude_n 5_o degree_n ½_n the_o cross_v of_o that_o almicantar_n which_o the_o 6_o parallel_n will_v have_v give_v i_o the_o same_o hour_n of_o the_o star_n and_o further_o his_o azimuth_n undesired_a chap._n xxxiii_o your_o latitude_n know_v and_o the_o altitude_n and_o azimuth_n of_o any_o star_n planet_n or_o comet_n observe_v and_o the_o time_n of_o night_n how_o to_o find_v his_o right_a ascension_n and_o declination_n this_o case_n differ_v little_a from_o the_o case_n of_o chapter_n 26._o where_o from_o the_o same_o thing_n give_v the_o declination_n and_o hour_n be_v require_v for_o the_o hour_n and_o right_a ascension_n be_v in_o a_o sort_n the_o same_o thing_n only_o the_o account_n of_o the_o right_a ascension_n begin_v always_o at_o ♈_o 0._o and_o be_v make_v in_o degree_n and_o minute_n of_o a_o degree_n the_o account_n of_o the_o hour_n begin_v at_o the_o meridian_n and_o be_v make_v in_o hour_n and_o minute_n of_o a_o hour_n fifteen_o whole_a degree_n make_v a_o hour_n and_o consequent_o 15_o minute_n of_o a_o degree_n make_v one_o minute_n of_o time_n for_o in_o every_o minute_n of_o time_n there_o pass_v the_o meridian_n a_o quarter_n of_o a_o degree_n of_o the_o equinoctial_a the_o time_n of_o night_n be_v here_o further_o require_v to_o be_v give_v which_o may_v be_v have_v by_o chap_n 29._o or_o 32._o the_o rule_n when_o you_o observe_v the_o altitude_n and_o azimuth_n of_o the_o star_n observe_v also_o the_o time_n of_o night_n by_o chapter_n 29._o or_o 32._o and_o to_o save_v you_o labour_v herein_o you_o shall_v do_v best_a to_o observe_v your_o altitude_n and_o azimuth_n when_o some_o know_a star_n be_v see_v just_a in_o the_o meridian_n then_o with_o your_o latitude_n and_o the_o altitude_n and_o azimuth_n of_o the_o star_n get_v by_o chapter_n 26._o the_o declination_n and_o hour_n of_o the_o star_n then_o in_o the_o equinoctial_a projection_n lay_v the_o degree_n of_o the_o sun_n to_o the_o hour_n of_o the_o night_n thence_o turn_v the_o label_n to_o the_o hour_n of_o the_o star_n and_o you_o have_v his_o right_a ascension_n in_o the_o limb_n of_o the_o reet_n between_o ♈_o 0_o and_o the_o label_n example_n put_v case_n i_o will_v find_v the_o declination_n and_o right_a ascension_n of_o lucida_n pleiadum_fw-la the_o sun_n be_v in_o sagittarius_fw-la 20._o december_n 2._o i_o observe_v that_o when_o australis_fw-la caudae_fw-la caeti_fw-la be_v full_a south_n lucida_n pleiadum_fw-la be_v near_o southeast_n viz._n in_o the_o azimuth_n
problem_n and_o to_o make_v all_o sort_n of_o sun_a dial_n very_o easy_o by_o the_o planisphear_n chap._n i._n the_o preface_n of_o the_o kind_n of_o dial_n although_o gnomonique_n pertain_v to_o astronomy_n yet_o i_o think_v it_o not_o amiss_o for_o the_o ease_n of_o the_o reader_n in_o find_v they_o to_o place_v the_o gnomonical_a problem_n in_o a_o distinct_a book_n by_o themselves_o sun_n dial_n may_v be_v reduce_v to_o two_o sort_n some_o show_v the_o hour_n by_o the_o altitude_n of_o the_o sun_n as_o quadrant_n ring_n cylinder_n etc._n etc._n for_o the_o make_n whereof_o you_o must_v know_v the_o sun_n altitude_n for_o every_o day_n or_o at_o least_o every_o 10_o day_n of_o the_o year_n and_o for_o every_o hour_n of_o those_o day_n which_o altitude_n you_o may_v find_v immediate_o upon_o this_o planisphear_n as_o in_o a_o table_n make_v to_o your_o hand_n for_o any_o latitude_n by_o book_n 3.25_o and_o so_o make_v they_o of_o any_o shape_n according_a to_o your_o mind_n the_o other_o sort_n show_v the_o hour_n by_o the_o shadow_n of_o a_o gnomon_n or_o style_n parallel_n to_o the_o axis_n of_o the_o world_n and_o of_o those_o i_o treat_v chief_o in_o this_o book_n those_o be_v all_o projection_n of_o the_o sphere_n upon_o a_o plain_a which_o lie_v parallel_n to_o some_o horizon_n or_o other_o in_o the_o world_n and_o if_o upon_o such_o a_o plain_a the_o meridian_n only_a be_v project_v they_o shall_v suffice_v to_o show_v the_o hour_n without_o project_v the_o other_o circle_n as_o the_o ecliptic_a the_o equator_fw-la with_o his_o parallel_n of_o declination_n the_o horizon_n with_o his_o almicantars_n and_o azimuth_n which_o be_v sometime_o draw_v upon_o dial_n more_o for_o ornament_n than_o for-necessity_n chap._n ii_o theorem_n premise_v for_o the_o better_a understanding_n of_o the_o reason_n of_o dial_n these_o theorem_n will_v be_v know_v 1._o that_o every_o plain_a whereupon_o any_o dyal_n be_v draw_v be_v part_n of_o the_o plain_a of_o great_a circle_n of_o the_o heaven_n which_o circle_n be_v a_o horizon_n to_o some_o country_n or_o other_o that_o the_o centre_n of_o the_o dyal_n represent_v the_o centre_n of_o the_o earth_n and_o world_n and_o the_o gnomon_n which_o cast_v the_o shade_n represent_v the_o axis_n and_o aught_o to_o point_v direct_o to_o the_o two_o pole_n and_o if_o upon_o the_o centre_n of_o the_o dyal_n you_o fasten_v a_o label_n with_o sight_n of_o equal_a altitude_n and_o keep_v your_o eye_n in_o the_o line_n of_o the_o sight_n turn_v this_o label_n round_o you_o shall_v thereby_o describe_v in_o the_o heaven_n that_o great_a circle_n wherein_o your_o dyal-plain_a lie_n and_o see_v where_o it_o cut_v our_o horizon_n and_o how_o much_o it_o be_v elevate_v above_o it_o on_o one_o side_n and_o depress_v on_o the_o other_o 2._o that_o those_o dyal-plain_n geometrical_o be_v not_o in_o the_o very_a plain_n of_o great_a circle_n for_o than_o they_o shall_v have_v their_o centre_n in_o the_o centre_n of_o the_o earth_n from_o which_o they_o be_v remove_v almost_o 4000_o miles_n and_o in_o truth_n they_o lie_v in_o the_o plain_n of_o circle_n parallel_v to_o the_o say_a orison_n but_o so_o near_o they_o that_o optical_o they_o seem_v to_o be_v the_o plain_n of_o those_o orison_n because_o the_o semidiameter_n of_o the_o earth_n bear_v so_o small_a proportion_n to_o the_o sun_n distance_n that_o the_o whole_a earth_n may_v be_v take_v for_o one_o point_n or_o centre_n without_o any_o perceivable_a error_n 3._o that_o as_o all_o great_a circle_n of_o the_o sphere_n so_o every_o dyal-plain_a have_v his_o axis_n which_o be_v a_o straight_a line_n pass_v through_o the_o centre_n of_o the_o plain_a and_o make_v right_a angle_n with_o it_o and_o at_o the_o end_n of_o the_o axis_n be_v the_o two_o pole_n of_o the_o plain_a whereof_o that_o above_o our_o horizon_n be_v call_v the_o pole_n zenith_n and_o the_o other_o the_o pole_n nadir_n of_o the_o dyal_n 4._o that_o every_o dyal-plain_a have_v two_o face_n or_o side_n and_o look_v what_o respect_n or_o situation_n the_o north_n pole_n of_o the_o world_n have_v to_o the_o one_o side_n the_o same_o have_v the_o south_n pole_n to_o the_o other_o and_o these_o two_o side_n will_v always_o receive_v 24_o hour_n so_o that_o what_o one_o side_n want_v the_o other_o side_n shall_v have_v and_o the_o one_o be_v describe_v in_o all_o thing_n as_o the_o other_o 5._o that_o as_o orison_n so_o dyal-plain_n be_v with_o respect_n to_o the_o equator_fw-la divide_v into_o 1._o parallel_n or_o equinoctial_a 2._o right_o 3._o oblique_a 6._o a_o parallel_n or_o polar_a dyal-plain_a make_v no_o angle_n with_o the_o equator_fw-la but_o lie_v in_o the_o plain_a of_o it_o or_o parallel_v to_o it_o such_o dial_n be_v scioterica_fw-la orthognomonica_n that_o be_v have_v the_o gnomon_n erect_v on_o the_o plain_a at_o right_a angle_n as_o the_o axis_n of_o the_o world_n be_v upon_o the_o plain_a of_o the_o equator_fw-la because_o the_o axis_n and_o pole_n of_o the_o dyal_n be_v here_o all_o one_o with_o the_o axis_n and_o pole_n of_o the_o world_n and_o the_o hour_n line_n here_o meet_v all_o at_o the_o centre_n make_v equal_a angle_n and_o divide_v the_o dyal_n circle_n into_o 24._o equal_a part_n as_o the_o meridian_n do_v the_o equator_fw-la in_o who_o plain_n the_o dyal_n lie_v 7._o a_o right_a horizon_n or_o dyal-plain_a cut_v the_o equator_fw-la at_o right_a angle_n and_o so_o cut_v through_o both_o the_o pole_n of_o the_o world_n therefore_o such_o dial_n be_v paralielognomonical_a that_o be_v have_v the_o gnomon_n parallel_n to_o the_o plain_a and_o so_o the_o hour_n line_n and_o the_o hour_n line_n all_o parallel_n one_o to_o another_o because_o their_o plain_n though_o infinite_o extend_v will_v never_o cut_v the_o axis_n of_o the_o world_n yet_o have_v those_o dial_n a_o centre_n though_o not_o for_o the_o meeting_n of_o the_o hour_n line_n viz._n through_o which_o the_o axis_n of_o the_o dyal_n circle_n pass_v cut_v the_o plain_a at_o right_a angle_n and_o cut_v also_o near_o enough_o for_o the_o project_v of_o a_o dyal_n the_o centre_n of_o the_o world_n 8._o a_o oblique_a horizon_n or_o dyal-plain_a cut_v the_o equator_fw-la at_o oblique_a angle_n such_o dial_n be_v scalenognomonical_a that_o be_v have_v for_o their_o gnomon_n the_o side_n of_o a_o triangle_n who_o angle_n vary_v according_a to_o the_o more_o or_o less_o obliquity_n of_o the_o say_a horizon_n and_o the_o gnomon_n shall_v always_o make_v a_o angle_n with_o the_o plain_a of_o so_o many_o degree_n as_o the_o axis_n of_o the_o world_n make_v with_o the_o plain_a or_o as_o either_o of_o the_o pole_n of_o the_o world_n be_v elevate_v above_o the_o plain_a 9_o every_o oblique_a horizon_n be_v divide_v by_o the_o meridian_n or_o hour_n circle_n of_o the_o sphere_n into_o 24._o unequal_a part_n which_o part_n be_v always_o lesser_a as_o they_o be_v scare_o to_o the_o meridian_n of_o that_o horizon_n or_o plain_n and_o great_a as_o they_o be_v further_o off_o and_o on_o both_o side_n the_o meridian_n of_o the_o plain_a the_o hour_n circle_n which_o be_v equal_o distant_a in_o time_n be_v also_o equal_o distant_a in_o space_n whence_o it_o be_v that_o the_o division_n of_o one_o quadrant_n of_o your_o dyal_n plain_o be_v know_v the_o division_n of_o the_o whole_a circle_n be_v likewise_o know_v 10._o the_o hour-line_n in_o a_o oblique_a dyal_n be_v the_o section_n of_o the_o plain_n of_o the_o hour-circle_n of_o the_o sphere_n with_o the_o dial_n plain_a and_o because_o the_o plain_n of_o great_a circle_n do_v always_o cut_v one_o another_o in_o half_n by_o diameter_n which_o be_v straight_o line_n pass_v through_o the_o common_a centre_n therefore_o line_n draw_v from_o the_o centre_n of_o the_o dyal_n to_o the_o intersection_n of_o the_o hour-circle_n with_o the_o great_a circle_n of_o the_o plain_a shall_v be_v those_o very_a section_n and_o the_o very_a hour-line_n of_o the_o dyal_n 11._o every_o dyal-plain_a be_v a_o horizon_n to_o some_o place_n in_o the_o earth_n as_o be_v say_v theorem_fw-la 1_o have_v his_o proper_a meridian_n which_o be_v the_o meridian_n cut_v through_o the_o â—oles_n of_o the_o plain_a and_o make_v right_a angle_n with_o the_o plain_a if_o the_o pole_n of_o the_o dyal-plain_a lie_n in_o the_o meridian_n of_o our_o place_n then_o be_v the_o meridian_n of_o the_o plain_a all_o one_o with_o the_o meridian_n of_o the_o place_n and_o the_o gnomon_n or_o style_n shall_v stand_v erect_v upon_o the_o noon-line_n or_o line_n of_o 12_o a_o clock_n as_o in_o all_o direct_a dial_n but_o if_o the_o plain_a decline_n then_o shall_v the_o substylar_n or_o line_n wherein_o the_o gnomon_n stand_v which_o be_v the_o meridian_n of_o the_o plain_a vary_v from_o the_o noon-line_n which_o be_v the_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
fol._n 93_o chap._n 27._o the_o latitude_n declination_n and_o altitude_n give_v to_o find_v the_o hour_n and_o azimuth_n fol._n 94_o chap._n 28._o the_o declination_n altitude_n and_o azimuth_n of_o the_o sun_n give_v to_o find_v the_o hour_n and_o latitude_n fol._n 95_o chap._n 29._o to_o find_v the_o hour_n of_o the_o night_n by_o the_o northing_n or_o sothe_v rise_v or_o set_v of_o any_o star_n fol._n 95_o chap._n 30._o the_o time_n of_o day_n or_o night_n give_v to_o find_v in_o what_o coast_n any_o star_n be_v and_o how_o much_o he_o be_v distant_a from_o the_o horizon_n or_o meridian_n fol._n 96_o chap._n 31._o the_o time_n and_o latitude_n give_v to_o find_v the_o altitude_n and_o azimuth_n of_o any_o star_n and_o thereby_o to_o get_v the_o knowledge_n of_o the_o star_n fol._n 96_o chap._n 32._o the_o latitude_n of_o the_o place_n the_o declination_n of_o a_o star_n with_o his_o altitude_n or_o azimuth_n give_v to_o find_v both_o the_o hour_n of_o the_o star_n and_o the_o hour_n of_o the_o night_n fol._n 97_o chap._n 33._o your_o latitude_n know_v and_o the_o altitude_n and_o azimuth_n of_o any_o star_n planet_n or_o comet_n observea_o and_o the_o time_n of_o night_n how_o to_o find_v his_o right_a ascension_n and_o declination_n fol._n 98_o chap._n 34._o the_o declination_n and_o right_a ascension_n of_o any_o star_n give_v to_o find_v his_o longitude_n and_o latitude_n fol._n 100_o chap._n 35._o the_o longitude_n and_o latitude_n of_o any_o star_n give_v to_o find_v his_o right_a ascension_n and_o declination_n and_o to_o place_v the_o star_n in_o the_o mater_fw-la fol._n 101_o chap._n 36._o the_o latitude_n and_o declination_n of_o a_o star_n give_v to_o find_v his_o longitude_n and_o right_a ascension_n fol._n 103_o chap._n 37._o the_o longitude_n and_o latitude_n of_o two_o star_n give_v to_o find_v their_o distance_n fol._n 103_o chap._n 38._o the_o declination_n and_o right_a ascension_n of_o any_o two_o star_n give_v to_o find_v their_o distance_n fol._n 104_o chap._n 39_o the_o declination_n of_o a_o star_n or_o planet_n and_o his_o distance_n from_o a_o know_a star_n give_v to_o find_v his_o right_a ascension_n fol._n 104_o chap._n 40._o the_o latitude_n of_o a_o star_n or_o planet_n and_o his_o distance_n from_o a_o know_a star_n give_v to_o find_v his_o longitude_n fol._n 106_o chap._n 41._o to_o find_v the_o distance_n of_o two_o star_n by_o their_o altitude_n and_o their_o difference_n of_o azimuth_n observe_v at_o the_o same_o time_n fol._n 106_o chap._n 42._o to_o find_v the_o angle_n of_o station_n which_o any_o two_o star_n make_v with_o the_o pole_n by_o their_o right_a ascension_n and_o declination_n or_o with_o the_o pole_n of_o the_o ecliptic_a by_o their_o longitude_n and_o latitude_n or_o with_o the_o zenith_n by_o their_o altitude_n and_o azimuth_n fol._n 106_o chap._n 43._o to_o find_v whether_o three_o star_n be_v in_o one_o great_a circle_n by_o have_v their_o longitude_n and_o latitude_n or_o their_o right_a ascension_n and_o declination_n or_o their_o azimuth_n and_o altitude_n know_v fol._n 107_o chap._n 44._o if_o a_o comet_n or_o star_n unknown_a be_v see_v in_o a_o straight_a line_n with_o two_o other_o know_v star_n and_o his_o distance_n from_o one_o of_o the_o know_a star_n be_v observe_v how_o to_o find_v the_o true_a place_n of_o the_o comet_n or_o star_n unknown_a fol._n 108_o chap._n 45._o the_o distance_n of_o a_o planet_n from_o two_o know_a star_n be_v observe_v to_o find_v his_o longitude_n and_o latitude_n fol._n 109_o chap._n 46._o to_o find_v the_o culmen_fw-la caeli_fw-la and_o the_o altitude_n thereof_o at_o any_o time_n propose_v fol._n 111_o chap._n 47._o to_o find_v the_o ascendent_n or_o horoscope_n and_o the_o other_o three_o principal_a house_n for_o any_o time_n propose_v fol._n 111_o chap._n 48._o to_o find_v the_o beginning_n of_o the_o other_o eight_o house_n fol._n 112_o chap._n 49._o to_o know_v what_o degree_n of_o the_o ecliptic_a be_v in_o the_o begin_n of_o every_o house_n fol._n 114_o chap._n 50._o another_o way_n to_o find_v what_o degree_n of_o the_o ecliptic_a be_v in_o the_o begin_n of_o every_o house_n and_o thereby_o to_o set_v a_o figure_n more_o easy_o then_o by_o the_o former_a chapter_n fol._n 114_o chap._n 51._o a_o three_o way_n to_o set_v a_o figure_n with_o less_o labour_n fol._n 116_o chap._n 52._o how_o to_o place_v any_o star_n or_o planet_n in_o his_o proper_a house_n fol._n 117_o chap._n 53._o to_o find_v the_o division_n of_o the_o house_n according_a to_o campanus_n fol._n 118_o chap._n 54._o how_o to_o direct_v a_o figure_n fol._n 118_o appendix_n concern_v judiciarie_n astrologer_n fol._n 119_o chap._n 55._o to_o find_v the_o angle_n of_o the_o ascendent_n or_o the_o angle_n of_o the_o ecliptic_a with_o the_o horizon_n and_o the_o altitude_n of_o the_o nonagesimus_fw-la gradus_fw-la at_o any_o time_n fol._n 124_o chap._n 56._o the_o ascendent_n and_o his_o amplitude_n and_o the_o altitude_n of_o culmen_fw-la caeli_fw-la give_v so_o to_o represent_v the_o ecliptic_a that_o you_o may_v present_o find_v not_o only_o the_o altitude_n of_o the_o nonagesimus_fw-la gradus_fw-la but_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 fol._n 125_o chap._n 57_o to_o do_v the_o same_o another_o way_n by_o the_o horizontal_n projection_n very_o plain_o fol._n 126_o chap._n 58._o to_o do_v the_o same_o by_o the_o nonagesimal_n projection_n if_o the_o altitude_n of_o nonagesimus_fw-la gradus_fw-la be_v first_o give_v in_o stead_n of_o the_o altitude_n of_o culmen_fw-la caeli_fw-la fol._n 127_o chap._n 59_o the_o nonagesimus_fw-la gradus_fw-la and_o his_o altitude_n and_o azimuth_n give_v as_o in_o the_o former_a chapter_n how_o in_o the_o same_o projection_n to_o get_v the_o altitude_n and_o azimuth_n of_o any_o planet_n or_o star_n by_o his_o longitude_n and_o latitude_n fol._n 129_o chap._n 60._o the_o altitude_n and_o azimuth_n of_o any_o star_n take_v and_o either_o the_o alcendent_a nonagesimus_fw-la gradus_fw-la or_o culmen_fw-la caeli_fw-la know_v how_o by_o the_o same_o nonagesimal_a projection_n to_o find_v the_o star_n longitude_n and_o latitude_n fol._n 129_o chap._n 61._o the_o latitude_n and_o azimuth_n of_o a_o star_n and_o either_o the_o ascendent_n nonagesimus_fw-la gradus_fw-la or_o the_o culmination_n give_v to_o find_v his_o longitude_n fol._n 131_o chap._n 62._o to_o find_v the_o parallactical_a angle_n that_o be_v what_o angle_n the_o azimuth_n make_v with_o any_o point_n of_o the_o ecliptic_a by_o the_o altitude_n of_o that_o point_n and_o of_o the_o nonagesimus_fw-la gradus_fw-la fol._n 131_o chap._n 63._o to_o find_v the_o parallax_n of_o altitude_n of_o the_o sun_n or_o moon_n fol._n 133_o chap._n 64._o the_o parallactique_a angle_n and_o the_o parallax_n of_o altitude_n give_v to_o find_v the_o parallax_n of_o longitude_n and_o latitude_n fol._n 135_o chap._n 65._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 fol._n 137_o chap._n 66._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 1.11_o fol._n 138_o chap._n 67._o to_o find_v the_o age_n of_o the_o moon_n by_o the_o epact_n fol._n 138_o chap._n 68_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 fol._n 140_o chap._n 69._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 fol._n 141_o chap._n 70._o the_o latitude_n and_o distance_n of_o two_o place_n give_v to_o find_v the_o difference_n of_o longitude_n fol._n 142_o chap._n 71._o to_o find_v what_o degree_n of_o the_o ecliptic_a culminate_v in_o another_o country_n at_o any_o time_n propose_v if_o the_o difference_n of_o longitude_n be_v know_v fol._n 143_o chap._n 72._o to_o find_v what_o a_o clock_n it_o be_v in_o another_o country_n by_o know_v the_o hour_n at_o home_n and_o the_o difference_n of_o longitude_n fol._n 144_o chap._n 73._o the_o longitude_n and_o latitude_n of_o one_o place_v know_v and_o the_o rumb_n and_o distance_n of_o a_o second_o place_n to_o find_v both_o the_o longitude_n and_o latitude_n of_o the_o second_o place_n fol._n 144_o chap._n 74._o the_o latitude_n and_o distance_n of_o two_o place_n give_v to_o find_v the_o rumb_n and_o the_o difference_n of_o longitude_n fol._n 144_o the_o content_n of_o the_o five_o book_n chap._n 1._o the_o preface_n of_o the_o kind_n of_o dial_n fol._n 145_o chap._n 2._o theorem_n premise_v fol._n 146_o chap._n 3._o how_o to_o draw_v a_o horizontal_n or_o vertical_a line_n upon_o any_o plain_a fol._n 149_o chap._n 4._o how_o to_o make_v the_o polar_a dyal_n and_o how_o to_o place_v it_o fol._n 150_o chap._n