place_v at_o the_o east_n or_o west_n point_n of_o the_o horizon_n therefore_o when_o you_o will_v find_v what_o circle_n of_o position_n any_o star_n or_o degree_n of_o the_o ecliptic_a be_v in_o rectify_v the_o globe_n and_o quadrant_n of_o altitude_n and_o bring_v the_o low_a end_n of_o the_o quadrant_n of_o altitude_n to_o the_o east_n or_o west_n point_n of_o the_o horizon_n and_o lift_v up_o the_o circle_n of_o position_n till_o it_o come_v to_o the_o star_n or_o degree_n of_o the_o ecliptic_a propose_v and_o the_o number_n of_o degree_n the_o circle_n of_o position_n than_o cut_v in_o the_o quadrant_n of_o altitude_n be_v the_o number_n of_o the_o circle_n of_o position_n that_o the_o star_n or_o degree_n of_o the_o ecliptic_a be_v in_o if_o the_o star_n or_o degree_n of_o the_o ecliptic_a be_v under_o the_o horizon_n turn_v the_o globe_n about_o till_o 180_o degree_n of_o the_o equator_fw-la pass_v through_o the_o meridian_n then_o will_v the_o star_n or_o degree_n of_o the_o ecliptic_a be_v above_o the_o horizon_n lift_v up_o then_o the_o circle_n of_o position_n as_o before_o to_o the_o star_n or_o degree_n of_o the_o ecliptic_a and_o the_o number_n of_o degree_n of_o the_o quadrant_n of_o altitude_n the_o circle_n of_o position_n cut_v on_o the_o east_n side_n be_v the_o number_n of_o circle_n of_o position_n the_o star_n be_v under_o the_o horizon_n on_o the_o west_n side_n or_o so_o many_o degree_n as_o the_o circle_n of_o position_n cut_v on_o the_o quadrant_n of_o altitude_n in_o the_o west_n side_n the_o horizon_n be_v the_o number_n of_o the_o circle_n of_o position_n the_o star_n or_o degree_n of_o the_o ecliptic_a be_v under_o the_o horizon_n on_o the_o east_n side_n prob._n vii_o to_o find_v the_o right_a ascension_n the_o oblique_a ascension_n and_o the_o declination_n of_o the_o planet_n examine_v the_o right_a ascension_n and_o declination_n of_o those_o prick_v make_v to_o represent_v each_o planet_n in_o prob._n 1._o of_o this_o book_n and_o work_v by_o they_o as_o you_o be_v direct_v to_o work_v by_o the_o sun_n in_o prob._n 26_o 27_o 28._o of_o the_o second_o book_n prob._n viii_o how_o to_o direct_v a_o figure_n by_o the_o globe_n to_o direct_v a_o figure_n be_v to_o examine_v how_o many_o degree_n of_o the_o equinoctial_a be_v move_v eastward_n or_o westward_n while_o any_o planet_n or_o star_n in_o one_o house_n come_v to_o the_o cusp_n or_o any_o other_o point_n of_o any_o other_o house_n when_o you_o will_v direct_v any_o promittor_fw-la to_o any_o hylegiacal_a point_n examine_v the_o degree_n of_o the_o equator_fw-la at_o the_o meridian_n then_o turn_v about_o the_o globe_n till_o the_o promittor_fw-la come_v to_o the_o hylegiacal_a point_n and_o examine_v again_o the_o degree_n of_o the_o equator_fw-la at_o the_o meridian_n and_o by_o substract_v the_o lesser_a from_o the_o great_a you_o will_v have_v the_o number_n of_o degree_n that_o pass_v through_o the_o meridian_n while_o the_o place_n of_o the_o promittor_fw-la be_v bring_v to_o the_o hyâ—â—gâ—â—cal_a point_n and_o that_o number_n of_o degree_n shall_v be_v the_o arch_n of_o direction_n example_n i_o will_v direct_v the_o body_n of_o the_o moon_n in_o our_o figure_n aforesaid_a to_o medium_fw-la câ—â—â—_n or_o the_o ten_o house_n i_o find_v by_o the_o globe_n 20â—_n degree_n 30._o minute_n of_o the_o equator_fw-la at_o the_o meridian_n with_o the_o â—eath_n house_n and_o turn_v the_o globe_n till_o the_o prick_n make_v to_o represent_v the_o moon_n come_v to_o the_o meridian_n i_o find_v 227_o degree_n 20_o minute_n of_o the_o equator_fw-la come_v to_o the_o meridian_n with_o it_o therefore_o i_o 〈◊〉_d the_o lesser_a from_o the_o great_a viz._n 2â—3_n degree_n 3_o minute_n from_o 227._o degree_n 2d_o minute_n and_o have_v remain_v 2d_o degree_n 50_o minute_n this_o 〈◊〉_d degree_n 50._o minute_n show_v that_o 23._o year_n 1â—_n month_n must_v expire_v ere_o the_o effect_n promise_v by_o the_o moon_n present_a position_n shall_v opperate_v upon_o the_o signification_n of_o the_o 〈◊〉_d house_n if_o the_o body_n of_o the_o moon_n have_v be_v direct_v to_o any_o other_o point_n theâ—_n 〈◊〉_d meridian_n or_o horizon_n you_o must_v have_v elevate_v the_o circle_n of_o 〈◊〉_d 〈◊〉_d the_o point_n propose_v and_o have_v under-propped_n it_o to_o that_o 〈◊〉_d and_o 〈◊〉_d have_v turn_v about_o the_o globe_n till_o the_o prick_n 〈◊〉_d the_o moon_n have_v come_v to_o the_o circle_n of_o position_n and_o than_o 〈◊〉_d degree_n of_o the_o equator_fw-la that_o shall_v have_v pass_v through_o the_o meridian_n while_o this_o motion_n be_v make_v shall_v be_v the_o number_n of_o degree_n of_o direction_n and_o signify_v in_o time_n as_o aforesaid_a prob._n ix_o of_o revolution_n and_o how_o they_o be_v find_v by_o the_o globe_n by_o revolution_n be_v mean_v the_o annual_a conversion_n of_o the_o sun_n to_o the_o same_o place_n he_o be_v in_o at_o the_o radix_fw-la of_o any_o business_n when_o you_o will_v find_v a_o revolution_n by_o the_o globe_n first_o find_v the_o right_a ascension_n of_o mâ—d_a heaven_n at_o the_o â—â—adix_fw-la of_o the_o business_n as_o by_o prob_n 26._o of_o the_o second_o book_n you_o be_v direct_v to_o find_v the_o right_a ascerâ—â—on_n of_o the_o 〈◊〉_d and_o 〈◊〉_d add_v 87_o degree_n for_o every_o yâ—aâ—_n since_o the_o radix_fw-la then_o subtract_v 360_o so_o oâ—â—_n as_o you_o can_v from_o the_o whole_a and_o the_o râ—mâ—â—â—s_n shall_v be_v the_o right_a ascension_n oâ—_n mid_a heaven_n for_o the_o aâ—â—â—al_a revolution_n iâ—_n yâ—u_o 〈◊〉_d the_o number_n of_o degree_n of_o the_o equator_fw-la contain_v between_o the_o râ—ght_a aâ—cension_n of_o the_o mid_a heaven_n and_o the_o right_a ascension_n of_o the_o sun_n and_o convert_v that_o number_n of_o degree_n 〈◊〉_d time_n by_o allow_v for_o every_o 15._o degree_n 1_o hour_n of_o time_n it_o will_v show_v if_o the_o sun_n place_n be_v on_o the_o western_a side_n of_o the_o meridian_n the_o number_n of_o hour_n and_o minute_n afternoon_n the_o revolution_n shall_v hâ—ppen_v on_o but_o if_o on_o the_o east_n side_n the_o meridian_n the_o number_n of_o hour_n and_o minute_n beforenoon_n the_o revolution_n shall_v happen_v on_o prob._n x._o how_o a_o figure_n of_o heaven_n may_v be_v erect_v by_o the_o revolution_n thus_o find_v seek_v the_o degree_n of_o right_a ascension_n of_o mid_a heaven_n and_o bring_v it_o to_o the_o meridian_n so_o shall_v the_o four_o cardinal_n point_n of_o the_o globe_n be_v the_o same_o with_o the_o four_o cardinal_n point_n in_o heaven_n at_o the_o time_n of_o the_o revolution_n the_o other_o hâ—â—â—ses_n be_v 〈◊〉_d by_o the_o circle_n of_o position_n as_o in_o the_o first_o problem_n of_o this_o book_n the_o end_n of_o the_o four_o book_n the_o five_o book_n show_v the_o practical_a use_n of_o the_o globe_n apply_v they_o tâ—_n the_o solution_n of_o gnomonical_a problem_n preface_n dial_n be_v of_o two_o sort_n pendent_a and_o fix_v pendeâ—_n be_v such_o as_o be_v hang_v by_o the_o hand_n and_o turn_v towards_o the_o sun_n that_o by_o its_o beam_n dart_v through_o small_a pin-hole_n make_v for_o that_o purpose_n the_o hour_n of_o the_o daâ—_n may_v be_v find_v these_o be_v of_o two_o sort_n universal_a and_o particular_a universal_a dial_n be_v those_o common_o call_v equiâ—ocâ—â—â—_n or_o ring-dyals_n they_o be_v use_v by_o seaman_n and_o traveller_n that_o often_o shift_v latitude_n particular_a be_v such_o as_o be_v make_v and_o only_o serve_v for_o particular_a latitude_n of_o these_o sort_n be_v the_o several_a dyaâ—â—_n describe_v on_o quadrant_n cilinder_n etc._n etc._n fix_a dyaâ—s_n shall_v be_v the_o matter_n of_o this_o discourse_n and_o they_o be_v such_o as_o be_v make_v upon_o fix_a plane_n and_o show_v the_o hour_n of_o the_o day_n by_o a_o style_n or_o gnomon_n make_v parallel_v to_o the_o axiâ—_n of_o the_o world_n of_o the_o several_a kind_n of_o dyal_n plains_n and_o how_o you_o may_v know_v they_o a_o plain_a in_o dyall_v be_v that_o flat_a whereon_o a_o dyal_n be_v describe_v there_o be_v some_o disagreement_n among_o old_a and_o late_a author_n in_o the_o name_n of_o plain_n for_o some_o name_n they_o according_a to_o the_o great_a circle_n in_o heaven_n they_o lie_v in_o and_o other_o according_a to_o the_o situation_n of_o the_o pole_n of_o the_o plain_n thus_o they_o which_o name_v they_o according_a to_o the_o great_a circle_n in_o heaven_n their_o plain_n lie_v in_o call_v that_o a_o horizontal_n plain_n which_o other_o call_v a_o vertical_a plain_n those_o vertical_a which_o other_o will_v call_v horizontal_n and_o those_o polar_a which_o other_o call_v equinoctial_a however_o they_o be_v call_v it_o matter_n not_o so_o you_o can_v but_o distinguish_v their_o kind_n which_o with_o a_o little_a consideration_n you_o may_v easy_o learn_v to_o do_v for_o remember_v but_o upon_o what_o ground_n either_o the_o
that_o shadow_n shall_v be_v a_o meridian_n liâ—e_z second_o on_o the_o backside_n the_o clinatory_n describe_v a_o circle_n and_o draw_v a_o line_n through_o the_o centre_n to_o both_o side_n the_o circumference_n across_o this_o line_n with_o a_o other_o line_n at_o râ—ght_a angle_n in_o the_o centre_n so_o shall_v the_o circle_n be_v divide_v into_o four_o equal_a part_n these_o four_o part_n you_o must_v maâ—k_v with_o east_n west_n north_n south_n and_o divide_v each_o of_o they_o into_o 90._o degree_n in_o the_o centre_n of_o this_o plain_n erect_v a_o straight_a wire_n prependicular_o when_o you_o will_v find_v a_o meridian_n line_n examine_v by_o the_o ten_o prob._n of_o the_o second_o book_n the_o amplitude_n of_o the_o sun_n rise_v or_o set_v from_o the_o east_n or_o west_n point_n and_o wait_v the_o just_a rise_n or_o set_v that_o day_n turn_v the_o instrument_n about_o till_o the_o shadow_n of_o the_o wire_n fall_v upon_o the_o same_o degree_n from_o the_o east_n or_o west_n the_o amplitude_n be_v of_o for_o then_o the_o north_n and_o south_n line_n in_o the_o instrument_n will_v be_v the_o same_o with_o the_o north_n and_o south_n line_n in_o heaven_n three_o by_o the_o sun_n azimuth_n find_v the_o azimuth_n of_o the_o sun_n by_o prob._n 22._o of_o the_o second_o book_n and_o at_o the_o same_o instant_n turn_v the_o instrument_n till_o the_o shadow_n of_o the_o wire_n fall_v upon_o the_o degree_n on_o the_o instrument_n opposite_a to_o the_o degree_n of_o the_o sun_n azimuth_n so_o shall_v the_o meridional_a line_n of_o the_o instrument_n agree_v with_o the_o meridional_a line_n in_o heaven_n you_o may_v the_o same_o way_n work_n by_o the_o azimuth_n of_o any_o star_n only_o whereas_o the_o shadow_n of_o the_o wire_n shall_v fall_v upon_o the_o opposite_a degree_n aforesaid_a now_o you_o must_v place_v a_o sight_n or_o perpendicular_a upon_o that_o opposite_a degree_n and_o turn_v the_o instrument_n about_o till_o the_o wire_n at_o the_o centre_n the_o sight_n in_o the_o opposite_a degree_n of_o the_o star_n azimuth_n and_o the_o star_n in_o heaven_n come_v into_o one_o straight_a line_n so_o shall_v the_o meridian_n line_n of_o the_o instrument_n agree_v with_o the_o meridional_a line_n in_o heaven_n four_o it_o may_v be_v find_v by_o any_o star_n observe_v in_o the_o meridian_n if_o two_o perpendicular_o be_v erect_v in_o the_o meridian_n line_n of_o your_o instrument_n for_o then_o by_o turn_v the_o instrument_n till_o the_o two_o perpendicular_o and_o the_o star_n come_v into_o a_o straight_a line_n the_o meridian_n line_n of_o your_o instrument_n will_v be_v the_o same_o with_o the_o meridian_n line_n in_o heaven_n see_v more_o way_n in_o mr._n palmer_n on_o the_o planisphear_n book_n 4._o chap._n 9_o if_o your_o plain_a either_o recline_v or_o incline_v apply_v one_o of_o the_o side_n of_o your_o clinatory_a parallel_n to_o one_o of_o the_o semidiameters_a of_o the_o quadrant_n to_o the_o plain_a in_o such_o sort_n that_o the_o plumb-line_n hang_v at_o liberty_n may_v fall_v upon_o the_o circumference_n of_o the_o quadrant_n for_o then_o the_o number_n of_o degree_n of_o the_o quadrant_n comprehend_v between_o the_o side_n of_o the_o quadrant_n parallel_n to_o the_o plain_a and_o the_o plumb-line_n shall_v be_v the_o number_n of_o degree_n of_o reclination_n if_o thâ—_n centre_n of_o the_o quadrant_n point_v upward_o or_o inclination_n if_o thâ—_n centre_n point_v downward_o if_o your_o recline_a or_o incline_v plain_a decline_v draw_v upon_o it_o a_o line_n parallel_n to_o the_o horizon_n which_o you_o may_v do_v by_o apply_v the_o backside_n of_o the_o clinatory_n and_o raise_v or_o depress_v the_o centre_n of_o the_o quadrant_n till_o the_o plumb-line_n hang_v just_a upon_o one_o of_o the_o semidiameters_a for_o than_o you_o may_v by_o the_o upper_a side_n of_o the_o clinatory_n draw_v a_o horizontal_n line_n if_o the_o plain_n incline_v or_o by_o the_o under_o side_n if_o it_o recline_v if_o it_o neither_o incline_v or_o recline_v you_o may_v drawâ—_n a_o horizontal_n line_n both_o by_o the_o upper_a and_o under_o side_n of_o the_o clinatory_n have_v draw_v the_o horizontal_n line_n apply_v the_o north_n 〈◊〉_d â—_o of_o the_o clinatory_n to_o it_o and_o if_o the_o north_n end_n of_o the_o needle_n 〈◊〉_d direct_o towards_o the_o plain_a it_o be_v then_o a_o south_n plain_a if_o the_o 〈◊〉_d point_n of_o the_o needle_n point_v direct_o from_o the_o plain_a it_o be_v a_o norâ—â—_n plain_a but_o if_o it_o point_v towards_o the_o east_n it_o be_v a_o east_n plain_a if_o towards_o the_o west_n a_o west_n plain_a if_o it_o do_v not_o point_v direct_o 〈◊〉_d east_n west_n north_n or_o south_n than_o so_o many_o degree_n as_o the_o 〈◊〉_d decline_v from_o any_o of_o these_o four_o point_n to_o any_o of_o the_o other_o of_o 〈◊〉_d four_o point_n so_o many_o degree_n be_v the_o declination_n of_o the_o plain_a 〈◊〉_d respect_n as_o aforesaid_a have_v to_o the_o variation_n of_o the_o compass_n or_o if_o you_o find_v the_o azimuth_n of_o the_o sun_n by_o its_o altitude_n observe_v just_a when_o its_o beam_n be_v come_v on_o or_o go_v off_o youâ—_n plain_a that_o azimuth_n shall_v be_v the_o azimuth_n of_o your_o plain_n or_o you_o may_v erect_v a_o wire_n perpendicular_o on_o your_o plain_n and_o wait_v till_o the_o shadow_n of_o that_o wire_n come_v to_o be_v perpendicular_a with_o the_o horizon_n which_o you_o may_v examine_v by_o apply_v a_o plumb-line_n to_o it_o for_o then_o the_o shadow_n of_o the_o plumb-line_n and_o the_o shadow_n of_o the_o perpendicular_a will_v be_v in_o one_o then_o take_v the_o altitude_n of_o the_o sun_n you_o may_v by_o prob._n 22._o of_o the_o second_o book_n find_v its_o azimuth_n and_o thereby_o know_v in_o what_o azimuth_n the_o plain_a of_o your_o dyal_n lie_v for_o the_o azimuth_n your_o plain_n lie_v in_o be_v distant_a from_o the_o azimuth_n of_o the_o sun_n just_a 90._o degree_n prob._n i._n how_o by_o one_o position_n of_o the_o globe_n to_o find_v the_o distance_n of_o the_o hour-line_n on_o all_o manner_n of_o plain_n you_o may_v have_v meridian_n line_n draw_v from_o pole_n to_o pole_n through_o every_o 15._o degree_n of_o the_o equinoctial_a to_o represent_v the_o horary_a motion_n of_o the_o sun_n both_o day_n and_o night_n and_o when_o the_o pole_n of_o the_o globe_n be_v elevate_v to_o the_o height_n of_o the_o pole_n in_o any_o place_n and_o one_o of_o these_o meridian_n line_n be_v bring_v to_o the_o brazen_a meridian_n all_o the_o rest_n of_o the_o meridian_n line_n shall_v cut_v any_o circle_n which_o you_o intend_v shall_v represent_v the_o plain_a of_o a_o dyal_n in_o the_o number_n of_o degree_n on_o the_o same_o circle_n that_o each_o respective_a hour-line_n be_v distant_a from_o the_o noon-line_n point_n in_o the_o same_o circle_n thus_o if_o you_o shall_v inquire_v the_o distance_n of_o the_o hour-line_n upon_o a_o horizontal_n plain_n in_o london_n latitude_n the_o pole_n of_o the_o globe_n as_o aforesaid_a must_v be_v elevate_v 51½_n degree_n and_o one_o of_o the_o meridian_n line_n you_o may_v choose_v the_o vernal_a colour_n be_v bring_v to_o the_o brazen_a meridian_n which_o be_v do_v you_o be_v only_o to_o examine_v in_o the_o horizon_n because_o it_o be_v a_o horizontal_n plain_n at_o what_o distance_n from_o the_o meridian_n which_o in_o horizontals_n be_v the_o noon-line_n the_o several_a meridian_n draw_v on_o the_o globe_n intersect_v the_o horizon_n for_o that_o distance_n in_o degree_n shall_v be_v the_o distance_n on_o a_o circle_n divide_v into_o 360._o degree_n that_o each_o respective_a hour-line_n must_v have_v from_o the_o meridian_n or_o a_o noon_n line_n choose_v in_o the_o same_o circle_n and_o line_n draw_v from_o the_o centre_n of_o that_o circle_n through_o those_o degree_n shall_v be_v the_o hour_n line_n of_o a_o horizontal_n plain_n if_o your_o plain_n be_v not_o direct_v but_o decline_v east_n or_o west_n 〈◊〉_d must_v number_v the_o declination_n eastward_n or_o westward_n respective_o in_o the_o degree_n of_o the_o horizon_n and_o the_o quadrant_n 〈◊〉_d altitude_n screw_v to_o the_o zenith_n as_o aforesaid_a bring_v the_o low_a end_n of_o the_o quadrant_n of_o altitude_n to_o the_o say_a degree_n of_o declination_n and_o the_o number_n of_o degree_n cut_v by_o the_o meridian_n in_o the_o quadrant_n of_o altitude_n number_v downward_o be_v the_o number_n of_o degree_n that_o the_o hour-line_n be_v distant_a from_o the_o noon_n line_n in_o a_o circle_n of_o 360_o degree_n and_o line_n draw_v from_o the_o centre_n of_o that_o circle_n through_o those_o degree_n be_v the_o hour_n line_n of_o half_a the_o day_n and_o if_o you_o turn_v about_o the_o quadrant_n of_o altitude_n upon_o the_o zenith_n point_n till_o the_o low_a end_n of_o it_o come_v to_o the_o degree_n of_o the_o horizon_n
contingence_n elevate_v to_o the_o height_n of_o the_o equinoctial_a draw_v line_n from_o the_o centre_n through_o every_o 15_o degree_n of_o the_o circle_n of_o position_n and_o by_o continue_v they_o intersect_v the_o line_n of_o contingence_n in_o the_o point_n from_o whence_o the_o hour_n line_n of_o a_o east_n or_o west_n dyal_n be_v to_o be_v draw_v example_n but_o because_o in_o our_o latitude_n the_o sun_n rise_v before_o 4._o in_o the_o morning_n therefore_o two_o hour-line_n be_v yet_o want_v viz._n 5_o and_o 4_o which_o i_o may_v find_v either_o by_o apply_v the_o thread_n first_o to_o 15_o and_o next_o to_o 30_o degree_n from_o 0_o towards_o g_o in_o the_o semicircle_n and_o so_o mark_v where_o it_o cut_v the_o contingent_a line_n as_o before_o or_o else_o by_o transfer_v the_o distance_n of_o the_o same_o number_n of_o hour_n line_n from_o the_o 6_o a_o clock_n line_n already_o draw_v on_o the_o side_n e_o 〈◊〉_d to_o the_o side_n e_o g_o as_o in_o prob._n 2._o of_o this_o book_n be_v more_o full_o show_v have_v thus_o mark_v out_o on_o the_o contingent_a line_n the_o distance_n of_o each_o hour_n i_o draw_v a_o line_n parallel_n to_o the_o contingent_a line_n and_o draw_v line_n from_o every_o hour_n mark_v on_o the_o contingent_a to_o cross_v the_o contingent_a line_n at_o right_a angle_n and_o continue_v each_o line_n to_o the_o line_n parallel_n to_o the_o contingent_a and_o these_o line_n shall_v be_v the_o hour_n line_n of_o a_o east_n plane_n to_o these_o hour-line_n i_o set_v figure_n as_o in_o the_o scheam_n may_v be_v see_v the_o style_n d_o k_o of_o this_o dyal_n as_o well_o as_o of_o other_o must_v stand_v parallel_n to_o the_o axis_n of_o the_o world_n it_o must_v be_v also_o parallel_v to_o all_o the_o hour_n line_n and_o stand_v direct_o over_o the_o 6_o a_o clock_n line_n and_o that_o so_o high_a as_o be_v the_o distance_n between_o the_o centre_n of_o the_o semicircle_n of_o position_n and_o the_o point_n where_o the_o 6_o a_o clock_n line_n cut_v the_o contingent_a line_n or_o which_o be_v all_o one_o at_o such_o a_o height_n as_o when_o it_o be_v lay_v flat_o down_o upon_o the_o plane_n it_o may_v just_o reach_v the_o 3_o a_o clock_n line_n prob._n vii_o to_o make_v a_o erect_a direct_a west_n dyal_n a_o erect_a direct_a west_n dyal_n be_v the_o same_o in_o all_o respect_n with_o a_o erect_a direct_a east_n dyal_n only_o as_o the_o east_n show_v the_o forenoon_n hour_n the_o west_n show_v the_o afternoon_n hour_n thus_o if_o you_o shall_v draw_v the_o east_n dyal_n on_o any_o transparent_a plane_n as_o on_o glass_n horn_n or_o a_o oil_v paper_n on_o the_o one_o side_n will_v appear_v a_o east_n dyal_n and_o on_o the_o other_o a_o west_n only_o the_o figure_n as_o be_v say_v before_o must_v be_v change_v for_o that_o which_o in_o the_o east_n dyal_n be_v 11_o in_o the_o west_n must_v be_v 1_o that_o which_o in_o the_o east_n dyal_n be_v 10_o in_o the_o west_n must_v be_v 2_o that_o which_o in_o the_o east_n dyal_n be_v 9_o in_o the_o west_n must_v be_v 3._o etc._n etc._n prob._n viii_o to_o make_v a_o polar_a dyal_n polar_a dial_n be_v horizontal_n dial_n under_o the_o equinoctial_a they_o be_v of_o the_o same_o kind_n with_o east_n and_o west_n dial_n only_o whereas_o east_n and_o west_n dial_n have_v but_o the_o hour_n line_n of_o half_a the_o long_a day_n describe_v on_o they_o these_o have_v all_o the_o hour_n line_n of_o the_o whole_a day_n and_o be_v mark_v on_o both_o side_n the_o noon_n line_n as_o in_o the_o follow_a figure_n the_o style_n of_o this_o dyal_n must_v stand_v over_o the_o noon_n line_n parallel_n to_o the_o plane_n for_o than_o it_o will_v also_o be_v parallel_n to_o the_o axis_n of_o the_o world_n and_o its_o height_n above_o the_o plane_n must_v be_v the_o distance_n between_o the_o centre_n i_o of_o the_o semicircle_n and_o the_o point_n in_o the_o contingent_a line_n cut_v by_o the_o noon-line_n but_o i_o have_v insert_v the_o figure_n which_o alone_o be_v sufficient_a instruction_n prob._n ix_o to_o make_v erect_a south_n dial_n decline_a eastward_n or_o westward_n draw_v on_o your_o plane_n a_o horizontal_n line_n and_o on_o it_o describe_v a_o semicircle_n as_o you_o be_v teach_v in_o prob_n 4._o then_o rectify_v the_o globe_n quadrant_n of_o altitude_n colour_n and_o hour_n index_n as_o by_o the_o same_o problem_n and_o bring_v the_o low_a end_n of_o the_o quadrant_n of_o altitude_n to_o the_o degree_n of_o declination_n from_o the_o east_n or_o west_n point_n according_a be_v your_o declination_n be_v eastward_n or_o westward_n for_o then_o the_o quadrant_n of_o altitude_n shall_v represent_v a_o plane_n decline_v from_o the_o south_n eastward_n or_o westward_n according_o then_o tuâ—n_v the_o globe_n eastward_n till_o the_o index_n of_o the_o hour-circle_n point_v to_o all_o the_o hour_n before_o noon_n and_o examine_v in_o what_o number_n of_o degree_n from_o the_o zenith_n the_o colour_n cut_v the_o quadrant_n of_o altitude_n when_o the_o index_n point_v to_o each_o hour_n for_o a_o line_n draw_v from_o the_o centre_n a_o through_o the_o same_o number_n of_o degree_n reckon_v from_o the_o perpendicular_a a_o b_o which_o be_v the_o 12_o a_o clock_n line_n towards_o con_n the_o plane_n shall_v be_v the_o same_o hour-line_n the_o index_n point_v at_o example_n i_o will_v make_v a_o erect_a dyal_n decline_v from_o the_o south_n towards_o the_o east_n 27._o degree_n the_o globe_n quadrant_n of_o altitude_n vernal_a colour_n and_o hour_n index_n rectify_v as_o before_o i_o bring_v the_o low_a end_n of_o the_o quadrant_n of_o altitude_n to_o 27._o degree_n count_v from_o the_o east_n point_n of_o the_o horizon_n towards_o the_o north_n then_o i_o turn_v the_o globe_n east-ward_n till_o the_o index_n point_v to_o 11_o a_o clock_n or_o till_o 15._o deg_n of_o the_o equator_fw-la pass_v through_o the_o meridian_n and_o find_v the_o colour_n cut_v the_o quadrant_n of_o altitude_n in_o 9.43_o count_v from_o the_o zenith_n 10_o 19.0_o 9_o 25.57_o 8_o 35.10_o 7_o 45.56_o 6_o 60.15_o 5_o 79.45_o and_o these_o be_v the_o distance_n of_o the_o forenoon_n hour-line_n which_o i_o seek_v in_o the_o west_n side_n of_o the_o plane_n viz._n from_o b_o towards_z c_z and_o through_o these_o distance_n i_o draw_v line_n from_o the_o centre_n and_o these_o line_n shall_v be_v the_o forenoon_n hour-line_n now_o herein_o be_v a_o difference_n between_o decline_a dial_n and_o direct_v dial_n for_o have_v find_v the_o distance_n of_o the_o hour_n line_n for_o one_o half_a of_o the_o day_n be_v it_o either_o for_o before_o noon_n or_o after_o noon_n in_o a_o direct_a dyal_n you_o have_v also_o find_v the_o distance_n for_o the_o other_o half_a day_n because_o as_o be_v say_v prob._n 3._o equal_a number_n of_o hour_n have_v equal_a distance_n from_o the_o noon_n line_n but_o in_o decline_a dial_n it_n be_v not_o so_o because_o the_o sun_n remain_v long_o upon_o that_o side_n of_o the_o plane_n which_o it_o decline_v to_o than_o it_o do_v upon_o the_o contrary_a side_n there_o will_v be_v a_o great_a number_n of_o hour_n line_n upon_o it_o and_o by_o consequence_n the_o distance_n of_o the_o hour_n line_n less_o than_o on_o the_o contrary_a side_n of_o the_o plane_n therefore_o for_o find_v the_o after_o noon_n hour_n line_n i_o turn_v about_o the_o quadrant_n of_o altitude_n upon_o the_o zenith_n point_n till_o the_o low_a end_n of_o it_o come_v to_o the_o degree_n of_o the_o horizon_n opposite_a to_o that_o degree_n of_o declination_n that_o the_o quadrant_n of_o altitude_n be_v place_v at_o when_o i_o seek_v the_o before_o noon_n hour_n line_n viz_o to_o 27._o degree_n count_v â—om_n the_o west_n towards_o the_o south_n and_o bring_v the_o verâ—al_a colour_n again_o to_o the_o meridian_n and_o the_o index_n as_o before_o to_o 12._o then_o turn_v the_o globe_n westward_n till_o the_o index_n point_v to_o 1_o a_o clock_n or_o till_o 15_o degr_n of_o the_o equator_fw-la pass_v through_o the_o meridian_n i_o find_v the_o colour_n cut_v the_o quadrant_n of_o altitude_n in_o 11.20_o count_v from_o the_o zenith_n 2_o 26.47_o 3_o 49.20_o 4_o 75.52_o and_o these_o be_v the_o distance_n of_o the_o after_o noon_n hour_n line_n which_o distaâ—â—â—â—_n i_o seek_v in_o the_o east_n side_n of_o the_o plane_n viz._n from_o b_o towards_z d_o as_o before_o and_o so_o draw_v line_n from_o the_o centre_n a_o through_o these_o distance_n i_o have_v all_o the_o afternoon_n hour_n line_n also_o draw_v on_o my_o plane_n you_o may_v note_v that_o this_o plane_n be_v capable_a to_o receive_v no_o more_o hour_n line_n after_o noon_n then_o 4._o for_o when_o the_o colour_n go_v off_o the_o quadrant_n of_o altitude_n the_o sun_n go_v
the_o equinoctial_a under_o the_o meridian_n of_o your_o place_n have_v a_o continual_a sun-dyal_n of_o it_o and_o the_o hour_n of_o the_o day_n give_v on_o it_o at_o once_o in_o two_o place_n one_o by_o the_o part_a the_o enlighten_v hemisphere_n from_o the_o shadow_a on_o the_o eastern_a side_n the_o other_o by_o the_o part_a the_o enlighten_v hemisphere_n from_o the_o shadow_a on_o the_o western_a side_n the_o globe_n much_o more_o may_v be_v say_v on_o this_o problem_n but_o the_o ingenuous_a artist_n may_v of_o himself_o find_v out_o diversity_n of_o speculation_n therefore_o i_o forbear_v prob._n xlvi_o to_o know_v by_o the_o terrestrial_a globe_n in_o the_o zenith_n of_o what_o place_n of_o the_o earth_n the_o sun_n be_v this_o may_v be_v perform_v by_o the_o former_a problem_n in_o the_o day_n time_n if_o the_o sun_n shine_v but_o not_o else_o but_o to_o find_v it_o at_o all_o time_n do_v thus_o bring_v the_o place_n of_o your_o habitation_n to_o the_o meridian_n and_o the_o index_n of_o the_o hour-circle_n to_o 12_o then_o turn_v the_o globe_n eastward_n if_o afternoon_n or_o westward_n if_o before_o noon_n till_o the_o index_n of_o the_o hour-circle_n pass_v by_o so_o many_o hour_n from_o 12._o as_o your_o time_n give_v be_v either_o before_o or_o afternoon_n so_o shall_v the_o sun_n be_v in_o the_o zenith_n of_o that_o place_n where_o the_o meridian_n intersect_v the_o parallel_n of_o the_o sun_n declination_n for_o that_o day_n example_n may_v 10_o at_o ¾_n of_o a_o hour_n past_o 4._o a_o clock_n after_o noon_n i_o will_v know_v in_o what_o place_n of_o the_o earth_n the_o sun_n be_v in_o the_o zenith_n my_o habitation_n be_v london_n therefore_o i_o bring_v london_n to_o the_o meridian_n and_o the_o index_n of_o the_o hour-circle_n to_o 12._o and_o because_o it_o be_v after_o noon_n i_o turn_v the_o globe_n eastward_n till_o the_o index_n pass_v through_o 4_o hour_n and_o 3_o quarter_n or_o which_o be_v all_o one_o till_o 70_o degree_n 15_o minute_n of_o the_o equator_fw-la pass_v through_o the_o meridian_n then_o i_o find_v by_o prob._n 5._o the_o sun_n declination_n be_v 20._o degree_n 5._o minute_n which_o i_o find_v upon_o the_o meridian_n and_o in_o that_o place_n just_a under_o that_o degree_n and_o minute_n on_o the_o globe_n the_o sun_n be_v in_o the_o zenith_n which_o in_o this_o example_n be_v in_o the_o north_n east_n cape_n of_o hispaniola_n have_v thus_o find_v in_o what_o place_n of_o the_o earth_n the_o sun_n be_v in_o the_o zenith_n bring_v that_o place_n to_o the_o meridian_n and_o elevate_v its_o respective_a pole_n according_a to_o its_o respective_a elevation_n so_o shall_v all_o place_n cut_v by_o the_o horizon_n have_v the_o sun_n in_o their_o horizon_n those_o to_o the_o eastward_n shall_v have_v the_o sun_n set_v those_o to_o the_o westward_n shall_v have_v it_o rise_v in_o their_o horizon_n those_o at_o the_o intersection_n of_o the_o meridian_n and_o horizon_n under_o the_o elevate_v pole_n have_v the_o sun_n in_o their_o horizon_n at_o low_a but_o rise_v those_o at_o the_o intersection_n of_o the_o meridian_n and_o horizon_n under_o the_o depress_v pole_n have_v the_o sun_n in_o their_o horizon_n at_o high_a but_o set_v thus_o in_o those_o country_n that_o be_v above_o the_o horizon_n it_o be_v daylight_n and_o in_o those_o but_o 18_o degree_n below_o the_o horizon_n it_o be_v twilight_n but_o in_o those_o country_n further_a below_o the_o horizon_n it_o be_v at_o that_o time_n dark_a night_n and_o those_o country_n within_o the_o parallel_n of_o the_o same_o number_n of_o degree_n from_o the_o elevate_v pole_n that_o the_o sun_n declination_n be_v from_o the_o equinoctial_a have_v the_o sun_n always_o above_o the_o horizon_n till_o the_o sun_n have_v less_o respective_a declination_n than_o the_o elevate_v pole_n and_o those_o within_o the_o same_o parallel_n of_o the_o depress_v pole_n have_v the_o sun_n always_o below_o their_o horizon_n till_o the_o sun_n incline_v more_o towards_o the_o depress_v pole_n as_o you_o may_v see_v by_o turn_v about_o the_o globe_n for_o in_o this_o position_n that_o portion_n of_o the_o globe_n intercept_v between_o the_o elevate_v pole_n and_o the_o parallel_n circle_n of_o 20._o degree_n 5._o minute_n from_o the_o pole_n do_v not_o descend_v below_o the_o horizon_n neither_o do_v that_o portion_n of_o the_o globe_n intercept_v between_o the_o depress_v pole_n and_o the_o parallel_n circle_n within_o 20._o degree_n 5._o minute_n of_o that_o pole_n ascend_v above_o the_o horizon_n prob._n xlvii_o to_o find_v in_o what_o different_a place_n of_o the_o earth_n the_o sun_n have_v the_o same_o altitude_n at_o the_o same_o time_n found_a by_o the_o former_a problem_n in_o what_o place_n of_o the_o earth_n the_o sun_n be_v in_o the_o zenith_n and_o bring_v that_o place_n on_o the_o globe_n to_o the_o zenith_n and_o on_o the_o meridian_n there_o screw_v the_o quadrant_n of_o altitude_n and_o turn_v it_o about_o the_o horizon_n describe_v degree_n of_o almicantars_n thereby_o as_o by_o prob._n 23._o and_o all_o those_o country_n in_o any_o almicantar_n on_o the_o globe_n shall_v have_v the_o sun_n elevate_v the_o same_o number_n of_o degree_n above_o their_o horizon_n thus_o those_o country_n in_o the_o ten_o almicantar_n shall_v have_v the_o sun_n elevate_v 10._o degree_n above_o their_o horizon_n those_o in_o the_o 20_o the_o almicantar_n shall_v have_v the_o sun_n elevate_v 20_o degree_n above_o their_o horizon_n those_o in_o the_o 30_o the_o 30._o degree_n etc._n etc._n so_o that_o you_o may_v see_v when_o the_o sun_n be_v in_o the_o zenith_n of_o any_o place_n all_o the_o country_n or_o city_n in_o any_o almicantar_n have_v the_o sun_n in_o one_o height_n at_o the_o same_o time_n above_o their_o horizon_n but_o to_o find_v in_o what_o different_a place_n the_o sun_n have_v the_o same_o height_n at_o the_o same_o time_n as_o well_o before_o or_o after_o noon_n as_o at_o full_a noon_n and_o that_o in_o country_n that_o have_v great_a latitude_n than_o the_o sun_n great_a declination_n and_o therefore_o can_v have_v the_o sun_n in_o their_o zenith_n require_v another_o operation_n therefore_o elevate_v its_o respective_a pole_n according_a to_o your_o respective_a latitude_n and_o let_v the_o degree_n of_o the_o brazen_a meridian_n which_o be_v in_o the_o zenith_n represent_v your_o habitation_n and_o the_o degree_n of_o the_o ecliptic_a the_o sun_n be_v in_o represent_v the_o sun_n then_o bring_v the_o sun_n to_o the_o meridian_n and_o the_o index_n of_o the_o hour-circle_n to_o 12_o and_o turn_v the_o globe_n eastward_n if_o before_o noon_n or_o westward_n if_o after_o noon_n till_o the_o index_n point_n to_o the_o hour_n of_o the_o day_n then_o place_v the_o low_a end_n of_o the_o quadrant_n of_o altitude_n to_o the_o east_n point_n of_o the_o horizon_n and_o move_v the_o upper_a end_n by_o slide_v the_o nut_n over_o the_o meridian_n till_o the_o edge_n of_o the_o quadrant_n touch_v the_o place_n of_o the_o sun_n then_o see_v at_o what_o degree_n of_o the_o meridian_n the_o upper_a end_n of_o the_o quadrant_n of_o altitude_n touch_v the_o meridian_n and_o subtract_v that_o number_n of_o degree_n from_o the_o latitude_n of_o your_o place_n and_o count_v the_o number_n of_o remain_a degree_n on_o the_o meridian_n on_o the_o contrary_a side_n the_o degree_n of_o the_o meridian_n where_o the_o upper_a end_n of_o the_o quadrant_n of_o altitude_n touch_v the_o meridian_n and_o where_o that_o number_n of_o degree_n end_n on_o the_o meridian_n in_o that_o latitude_n and_o your_o habitation_n longitude_n have_v the_o sun_n the_o same_o height_n at_o the_o same_o time_n example_n may_v 10._o at_o 53._o minute_n past_o 8._o a_o clock_n in_o the_o morning_n i_o will_v know_v in_o what_o place_n the_o sun_n shall_v have_v the_o same_o altitude_n it_o shall_v have_v at_o london_n london_n latitude_n find_v by_o prob._n 1._o be_v 51½_n degree_n northwards_o and_o because_o the_o elevation_n of_o the_o pole_n be_v equal_a to_o the_o latitude_n of_o the_o place_n as_o be_v show_v prob._n 15._o therefore_o i_o elevate_v the_o north_n pole_n 51½_n degree_n so_o shall_v 51½_n degree_n on_o the_o meridian_n be_v in_o the_o zenith_n this_o 51½_n degree_n on_o the_o meridian_n represent_v london_n the_o sun_n place_v find_v by_o prob._n 3._o be_v ♉_o 29._o therefore_o i_o bring_v ♉_o 29_o to_o the_o meridian_n and_o the_o hour_n index_n to_o 12._o on_o the_o hour_n circle_n then_o i_o turn_v the_o globe_n eastward_n because_o it_o be_v before_o noon_n till_o the_o index_n point_n at_o 8._o hour_n 53_o minute_n on_o the_o hour-circle_n and_o place_v the_o low_a end_n of_o the_o quadrant_n of_o altitude_n to_o the_o east_n point_n in_o the_o horizon_n and_o slide_v the_o upper_a end_n either_o north_n or_o southwards_o
in_o the_o zenith_n and_o bring_v the_o first_o point_n of_o ♈_o to_o the_o meridian_n then_o count_v on_o the_o quadrant_n of_o altitude_n to_o the_o degree_n of_o the_o sun_n declination_n and_o bring_v that_o degree_n to_o the_o equinoctial_a and_o the_o degree_n of_o the_o equinoctial_a cut_n by_o that_o degree_n of_o the_o quadrant_n of_o altitude_n be_v the_o degree_n of_o the_o pole_n elevation_n example_n the_o sun_n amplitude_n be_v 33._o degree_n 20._o minute_n his_o declination_n be_v 20_o degree_n 5_o minute_n his_o compliment_n of_o amplitude_n to_o 90._o be_v 56_o degree_n 7_o minute_n therefore_o i_o elevate_v the_o pole_n 56._o degree_n 7_o minute_n above_o the_o horizon_n and_o screw_v the_o quadrant_n of_o altitude_n to_o 56_o degree_n 7_o minute_n which_o be_v in_o the_o zenith_n then_o i_o bring_v the_o first_o point_n of_o ♈_o to_o the_o meridian_n and_o number_n on_o the_o quadrant_n of_o altitude_n upward_o 20._o deg_n 5_o min._n for_o the_o sun_n declination_n this_o 20_o the_o degree_n 5_o minute_n i_o bring_v to_o the_o equinoctial_a and_o find_v it_o cut_v there_o 51_o ½_o degree_n for_o the_o height_n of_o the_o pole_n prob._n iii_o the_o sun_n declination_n and_o hour_n at_o east_n give_v to_o find_v the_o height_n of_o the_o pole_n elevate_v the_o pole_n so_o many_o degree_n as_o the_o sun_n declination_n be_v and_o screw_v the_o quadrant_n of_o altitude_n in_o the_o zenith_n then_o convert_v the_o hour_n or_o minute_n past_o 6._o give_v into_o degree_n by_o allow_v 15_o degree_n for_o every_o hour_n of_o time_n and_o for_o every_o minute_n of_o time_n 15_o minute_n of_o a_o degree_n and_o number_v those_o degree_n or_o minute_n in_o the_o horizon_n from_o the_o east_n southwards_o so_o shall_v the_o degree_n of_o the_o quadrant_n of_o altitude_n cut_v by_o the_o equator_fw-la be_v the_o compliment_n of_o the_o height_n of_o the_o pole_n example_n the_o sun_n declination_n be_v 20_o deg_n 5_o min._n therefore_o i_o elevate_v the_o pole_n 20_o degree_n 5_o minute_n and_o also_o screw_v the_o quadrant_n of_o altitude_n to_o â—0_n degree_n 5_o minute_n which_o be_v in_o the_o zenith_n the_o hour_n the_o sun_n come_v to_o be_v at_o east_n be_v 8_o a_o clock_n 53_o minute_n that_o be_v 1_o hour_n 7_o minute_n after_o 6._o therefore_o i_o convert_v 1_o hour_n 7_o minute_n into_o degree_n as_o before_o and_o it_o give_v 16_o degree_n 50_o minute_n which_o number_n of_o degree_n and_o minute_n i_o count_v from_o the_o east_n point_v southwards_o and_o thither_o i_o bring_v the_o quadrant_n of_o altitude_n then_o i_o look_v in_o what_o degree_n of_o the_o quadrant_n of_o altitude_n the_o equator_fw-la cut_v and_o find_v 38_o ½_o which_o be_v the_o compliment_n of_o the_o pole_n height_n viz._n 51_o ½_o degree_n for_o the_o height_n of_o the_o pole_n in_o this_o problem_n the_o declination_n of_o the_o sun_n and_o elevation_n of_o the_o pole_n bear_v the_o same_o denomination_n of_o either_o north_n or_o south_n for_o when_o the_o declination_n and_o the_o elevation_n be_v different_a the_o sun_n can_v come_v to_o the_o east_n point_fw-fr prob._n four_o the_o declination_n of_o the_o sun_n and_o his_o altitude_n at_o east_n give_v to_o find_v the_o height_n of_o the_o pole_n elevate_v the_o pole_n to_o the_o compliment_n of_o the_o sun_n altitude_n and_o screw_v the_o quadrant_n of_o altitude_n to_o the_o zenith_n then_o bring_v the_o equinoctial_a point_n ♈_o to_o the_o meridian_n and_o number_n on_o the_o quadrant_n of_o altitude_n the_o degree_n of_o the_o sun_n declination_n and_o bring_v that_o degree_n to_o the_o equinoctial_a and_o note_v the_o degree_n it_o cut_v for_o its_o compliment_n to_o 90_o be_v the_o height_n of_o the_o pole_n example_n may_v 10._o the_o sun_n declination_n be_v 20_o degree_n 5_o minute_n his_o altitude_n at_o east_n be_v 25_o degree_n 55_o minute_n here_o at_o london_n i_o inquire_v the_o height_n of_o the_o pole_n therefore_o i_o subtract_v 20._o 5_o min._n from_o â—0_n the_o remain_v be_v 69_o deg_n 55_o min._n for_o its_o compliment_n wherefore_o i_o bring_v 69_o deg_n 55_o min._n of_o the_o meridian_n to_o the_o horizon_n and_o to_o 69_o deg_n 55_o min._n which_o be_v in_o the_o zenith_n i_o screw_v the_o quadrant_n of_o altitude_n than_o i_o bring_v ♈_o to_o the_o meridian_n and_o count_v on_o the_o quadran_n of_o altitude_n upward_o 20_o deg_n 5_o min_fw-mi and_o move_v it_o about_o the_o equinoctial_a till_o those_o 20_o deg_n 5_o min._n touch_v the_o equinoctial_a which_o i_o find_v to_o be_v in_o 38_o ½_o degree_n therefore_o i_o subtract_v those_o 38_o ½_o from_o 90_o and_o the_o remain_v be_v 51_o ½_o degree_n therefore_o i_o say_v the_o pole_n here_o at_o london_n be_v elevate_v 51_o ½_o degree_n the_o declination_n and_o the_o elevation_n be_v always_o the_o same_o either_o north_n or_o south_n for_o when_o they_o alter_v their_o denomina_fw-la lion_z the_o sun_n at_o east_n can_v have_v no_o altitude_n neither_o can_v it_o indeed_o reach_v the_o east_n point_n and_o therefore_o in_o this_o example_n because_o the_o declination_n of_o the_o sun_n be_v north_n it_o be_v the_o north_n pole_n that_o be_v elevate_v here_o at_o london_n to_o perform_v the_o same_o otherwise_o with_o a_o pair_n of_o compass_n take_v off_o with_o your_o compass_n from_o the_o equator_fw-la or_o quadrant_n of_o altitude_n the_o number_n of_o degree_n of_o altitude_n observe_v and_o place_v one_o foot_n at_o the_o begin_n of_o ♈_o on_o the_o inner_a edge_n of_o the_o horizon_n and_o extend_v the_o other_o direct_o upward_o towards_o the_o zenith_n then_o move_v the_o brazen_a meridian_n through_o the_o notch_n of_o the_o horizon_n till_o the_o other_o point_n of_o your_o compass_n respect_v the_o zenith_n reach_v the_o parallel_n of_o the_o sun_n declination_n so_o shall_v the_o number_n of_o degree_n on_o the_o meridian_n be_v the_o number_n of_o degree_n that_o the_o pole_n be_v elevate_v above_o the_o horizon_n and_o be_v either_o north_n or_o south_n according_a as_o the_o sun_n declination_n be_v as_o before_o this_o may_v yet_o otherwise_o be_v perform_v with_o the_o quadrant_n of_o altitude_n by_o take_v the_o nut_n off_o the_o meridian_n and_o lay_v the_o edge_n of_o its_o index_n specify_v in_o chap._n 1._o sect._n 6._o of_o the_o first_o book_n exact_o on_o the_o east_n line_n of_o the_o horizon_n for_o when_o that_o lie_v straight_o between_o the_o point_n of_o east_n on_o the_o outer_a verge_n of_o the_o horizon_n and_o the_o beginning_n of_o ♈_o in_o the_o inner_a verge_n of_o the_o horizon_n then_o shall_v the_o upper_a end_n of_o the_o quadrant_n of_o altitude_n point_n direct_o to_o the_o zenith_n and_o if_o then_o you_o turn_v the_o meridian_n through_o the_o notch_n of_o the_o horizon_n till_o the_o sun_n altitude_n on_o the_o quadrant_n of_o altitude_n cut_v the_o parallel_n of_o declination_n you_o will_v have_v on_o the_o meridian_n the_o height_n of_o the_o pole_n as_o before_o prob._n v._n by_o the_o sun_n declination_n and_o azimuth_n at_o 6._o of_o the_o clock_n give_v to_o find_v the_o height_n of_o the_o pole_n and_o almicantar_n at_o 6._o elevate_v the_o pole_n so_o many_o degree_n as_o the_o sun_n azimuth_n be_v at_o 6._o and_o screw_v the_o quadrant_n of_o altitude_n in_o the_o zenith_n and_o bring_v the_o first_o point_n of_o ♈_o to_o the_o meridian_n then_o number_n on_o the_o quadrant_n of_o altitude_n upward_o the_o compliment_n of_o the_o sun_n declination_n and_o bring_v that_o degree_n to_o the_o equator_fw-la so_o shall_v the_o degree_n of_o the_o horizon_n cut_v by_o the_o quadrant_n of_o altitude_n be_v the_o compliment_n of_o the_o pole_n elevation_n and_o the_o degree_n of_o the_o equator_fw-la cut_v by_o the_o quadrant_n of_o altitude_n shall_v be_v the_o almicantar_n of_o the_o sun_n at_o 6._o of_o the_o clock_n example_n the_o sun_n azimuth_n at_o 6_o be_v 12¾_n degree_n therefore_o i_o elevate_v the_o pole_n 12¾_n and_o screw_v the_o quadrant_n of_o altitude_n to_o 12¾_n degree_n which_o be_v in_o the_o zenith_n then_o i_o bring_v the_o first_o point_n of_o ♈_o to_o the_o meridian_n the_o sun_n declination_n be_v 20_o degree_n 5_o minute_n therefore_o i_o number_n on_o the_o quadrant_n of_o altitude_n 69_o deg_n 55_o min._n which_o be_v the_o compliment_n of_o 20_o deg_n 5_o min._n to_o 90._o this_o 69_o deg_n 55_o min._n on_o the_o quadrant_n of_o altitude_n i_o bring_v to_o cut_v the_o equator_fw-la and_o find_v when_o 69_o deg_n 55_o min_fw-mi cut_v the_o equator_fw-la that_o the_o quadrant_n of_o altitude_n cut_v the_o horizon_n in_o 38½_n deg_n which_o be_v the_o compliment_n of_o the_o pole_n elevation_n and_o at_o the_o same_o time_n the_o quadrant_n of_o altitude_n also_o cut_v the_o equator_fw-la in_o 15½_n degree_n which_o be_v the_o
and_o prolong_v it_o to_o the_o far_a extent_n of_o the_o plane_n from_o this_o gnomon_n or_o style_n i_o let_v fall_v a_o perpendicular_a upon_o the_o noon_n line_n as_o f_o g_o this_o perpendicular_a be_v call_v the_o substile_a and_o this_o perpendicular_a and_o its_o base_a which_o be_v the_o noon_n line_n and_o hypothenusa_n which_o be_v the_o gnomon_n shall_v make_v a_o triangle_n which_o be_v erect_v upon_o the_o base_a so_o as_o the_o substile_n may_v stand_v perpendicular_a to_o the_o plane_n the_o hypothenusa_n a_o f_o shall_v be_v the_o gnomon_n and_o be_v parallel_n to_o the_o axis_n of_o the_o world_n and_o cast_v a_o shadow_n upon_o the_o hour_n of_o the_o day_n prob._n four_o to_o make_v a_o erect_a direct_a south_n dyal_n draw_v on_o your_o plane_n a_o horizontal_n line_n as_o c_o at_fw-fr d_o as_o be_v show_v in_o the_o preface_n in_o the_o middle_n of_o this_o line_n as_o at_o a_o describe_v as_o on_o a_o centre_n the_o semicircle_n c_o b_o d_o from_o the_o centre_n a_o let_v fall_v a_o perpendicular_a which_o shall_v divide_v the_o semicircle_n into_o two_o quadrant_n each_o of_o which_o quadrant_n you_o must_v divide_v into_o 90_o degree_n then_o rectify_v the_o globe_n quadrant_n of_o altitude_n colour_n and_o hour_n index_n thus_o elevate_v the_o pole_n of_o the_o globe_n to_o the_o latitude_n of_o your_o place_n and_o screw_v the_o quadrant_n of_o altitude_n to_o the_o zenith_n then_o bring_v the_o vernal_a colour_n to_o the_o meridian_n and_o the_o index_n of_o the_o hour_n circle_n to_o the_o hour_n of_o 12._o in_o the_o hour_n circle_n so_o shall_v your_o globe_n quadrant_n of_o altitude_n colour_n and_o hour_n index_n be_v rectify_v aâ—d_v â—â—us_o you_o must_v always_o rectify_v they_o for_o the_o make_n of_o most_o sort_n of_o dial_n by_o the_o globe_n then_o to_o make_v a_o erect_a direct_a south_n dyal_n bring_v the_o low_a end_n of_o the_o quadrant_n of_o altitude_n to_o the_o west_n point_n of_o the_o horizon_n and_o turn_v the_o globe_n westward_n till_o the_o index_n point_v to_o all_o the_o hour_n afternoon_n and_o examine_v in_o what_o number_n of_o degree_n from_o the_o zenith_n the_o colare_fw-la cut_v the_o quadrant_n of_o altitude_n when_o the_o index_n point_v to_o each_o hour_n for_o a_o line_n draw_v from_o the_o centre_n a_o through_o the_o same_o number_n of_o degree_n reckon_v from_o the_o perpendicular_a a_o b_o which_o be_v the_o 12_o a_o clock_n line_n towards_o d_o on_o the_o plane_n shall_v be_v the_o same_o hour_n line_n the_o index_n point_v at_o thus_o in_o our_o latitude_n viz._n 51½_n degree_n the_o vernal_a colour_n be_v bring_v to_o the_o meridian_n and_o the_o index_n to_o 12_o if_o you_o turn_v the_o globe_n westward_n till_o the_o index_n point_v to_o 1_o a_o clock_n or_o till_o 15_o deg_n of_o the_o equator_fw-la pass_v through_o the_o meridian_n the_o colour_n will_v cut_v the_o quadrant_n of_o altitude_n in_o 9_o 18_o count_v from_o the_o zenith_n 2_o 19_o 15_o 3_o 32._o 5_o 4_o 48._o 0_o 5_o 67._o 4_o 6_o 90._o and_o these_o be_v the_o distance_n of_o the_o afternoon_n hour_n line_n which_o you_o must_v transfer_v to_o the_o east_n side_n of_o your_o plane_n viz_o from_o b_o towards_z d_o and_o draw_v line_n from_o the_o centre_n a_o through_o these_o distance_n and_o these_o line_n shall_v be_v your_o afternoon_n hour_n line_n note_v once_o for_o all_o when_o the_o colour_n go_v off_o that_o circle_n you_o examine_v the_o hour_n distance_n in_o the_o sun_n will_v shine_v no_o long_o upon_o that_o plane_n as_o in_o this_o example_n the_o colour_n go_v off_o the_o quadrant_n of_o altitude_n at_o 6_o a_o clock_n therefore_o the_o sun_n will_v not_o shine_v long_o then_o till_o 6_o a_o clock_n upon_o this_o plane_n the_o hour_n line_n before_o noon_n have_v the_o same_o distance_n from_o the_o meridian_n that_o the_o afternoon_n hour_n line_n have_v as_o be_v show_v in_o the_o last_o problem_n only_o they_o must_v be_v draw_v on_o the_o west_n side_n the_o noon_n line_n and_o count_v from_o b_o towards_o c._n otherwise_o you_o may_v reduce_v all_o vertical_o into_o horizontal_n if_o you_o elevate_v the_o pole_n of_o the_o globe_n to_o the_o compliment_n of_o the_o latitude_n of_o your_o place_n and_o bring_v the_o vernal_a colour_n to_o the_o meridian_n under_o the_o horizon_n and_o the_o index_n of_o the_o hour_n circle_n to_o 12_o and_o turn_v the_o globe_n westward_n for_o as_o the_o index_n pass_v through_o every_o hour_n on_o the_o hour_n circle_n the_o colour_n show_v in_o the_o horizon_n the_o distance_n of_o the_o several_a afternoon_n hour_n line_n from_o the_o meridian_n or_o 12_o a_o clock_n line_n in_o the_o circle_n on_o your_o plane_n number_v from_o b_o to_z d_o and_o line_n draw_v from_o the_o centre_n through_o these_o distance_n on_o your_o plane_n shall_v be_v the_o afternoon_n hour_n line_n of_o your_o dyal_n example_n london_n latitude_n be_v 51½_n degree_n its_o compliment_n to_o 90._o be_v 38½_n therefore_o i_o elevate_v the_o pole_n 38½_n degree_n above_o the_o horizon_n and_o bring_v the_o vernal_a colour_n to_o the_o meridian_n under_o the_o horizon_n and_o the_o index_n of_o the_o hour_n circle_n to_o 12_o on_o the_o hour_n circle_n then_o turn_v the_o globe_n westward_n till_o the_o index_n of_o the_o hour_n circle_n point_v to_o 1_o a_o clock_n or_o till_o 15_o deg_n of_o the_o equator_fw-la pass_v through_o the_o meridian_n i_o find_v the_o colour_n cut_v the_o horizon_n in_o 9_o 18_o from_o the_o intersection_n of_o the_o meridian_n and_o the_o horizon_n as_o in_o the_o former_a table_n 2_o 19_o 15_o 3_o 32_o 5_o 4_o 48_o 0_o 5_o 67_o 0_o 6_o 90_o and_o these_o be_v the_o distance_n of_o the_o 6_o hour_n line_n from_o the_o merid._n by_o this_o example_n you_o may_v see_v that_o it_o be_v easy_a to_o reduce_v vertical_n into_o horizonâ—als_n and_o horizontal_n into_o vertical_o for_o this_o erect_v direct_a south_n dyal_n be_v a_o horizontal_n dyal_n to_o those_o people_n that_o inhabit_v 90_o degree_n from_o we_o viz._n in_o the_o south_n latitude_n of_o 38½_n degree_n then_o make_v a_o triangle_n whereof_o the_o noon_n line_n shall_v be_v base_a from_o it_o count_v the_o compliment_n of_o the_o pole_n elevation_n viz._n 38½_n degree_n and_o through_o they_o draw_v the_o line_n a_o f_o from_o the_o centre_n a_o which_o shall_v be_v hypotenusa_fw-la then_o â—et_o fall_v a_o perpendicular_a upon_o the_o noon_n line_n a_o b_o so_o be_v your_o triangle_n make_v if_o this_o triangle_n be_v erect_v perpendicular_o upon_o the_o base_a or_o noon_n line_n the_o hypotenusa_fw-la a_o f_o shall_v stand_v parallel_n to_o the_o axis_n of_o the_o world_n and_o cast_v a_o shadow_n upon_o the_o hour_n of_o the_o day_n prob._n v._n to_o make_v a_o erect_a direct_a north_n dyal_n if_o the_o erect_v direct_a south_n dyal_n be_v turn_v towards_o the_o north_n and_o the_o line_n c_o a_o d_o be_v turn_v downward_o and_o the_o line_n mark_v with_o 7_o be_v now_o mark_v with_o 5_o and_o the_o line_n 8_o with_o 4_o the_o line_n 5_o with_o 7_o and_o the_o line_n 4_o with_o 8_o then_o have_v you_o of_o it_o a_o north_n erect_v direct_v dyal_n all_o the_o other_o hour_n line_n in_o this_o dyal_n be_v useless_a because_o the_o sun_n in_o our_o latitude_n shine_v on_o a_o north_n face_n the_o long_a day_n only_o before_o 6_o in_o the_o morning_n and_o after_o 6_o at_o night_n prob._n vi_o to_o make_v a_o erect_a direct_a east_n dyal_n these_o sort_n of_o dial_n may_n better_o be_v demonstrate_v then_o make_v by_o the_o globe_n unless_o the_o axis_n of_o your_o globe_n be_v accessible_a as_o in_o the_o wyer-globe_n specify_v in_o prob._n 1._o therefore_o when_o you_o will_v make_v a_o east_n or_o west_n dyal_n or_o a_o polar_a dyal_n provide_v a_o square_a board_n as_o a_o b_o c_o d_o draw_v the_o straight_a line_n e_o f_o upon_o it_o parallel_n to_o the_o side_n a_o c_o and_o b_o d._n and_o just_a in_o the_o middle_n between_o they_o across_o this_o straight_a line_n at_o right_a angle_n with_o another_o straight_a line_n as_o g_o h_z quite_o through_o the_o board_n upon_o this_o board_n with_o a_o little_a pitch_n or_o wax_n fasten_v the_o semicircle_n of_o position_n so_o as_o both_o the_o pole_n thereof_o may_v lie_v in_o the_o line_n g_o h_o and_o the_o middle_n of_o the_o semicircle_n mark_v co_z may_v lie_v upon_o the_o line_n e_o f_o so_fw-mi shall_v i_o be_v the_o centre_n of_o the_o semicircle_n of_o position_n in_o this_o centre_n make_v a_o small_a hole_n through_o the_o board_n fit_a to_o receive_v a_o wire_n or_o a_o nail_n so_o may_v you_o with_o this_o circle_n of_o position_n thus_o fit_v and_o the_o side_n c_o d_o apply_v to_o a_o line_n of_o
off_o these_o kind_n of_o planes_n to_o these_o hour_n line_n i_o set_v their_o number_n as_o you_o may_v see_v iâ—_n the_o figure_n here_o you_o may_v see_v that_o in_o decline_a dial_n the_o style_n do_v not_o stand_v at_o the_o same_o elevation_n above_o the_o plane_n that_o it_o do_v in_o erect_a direct_a dial_n neither_o do_v it_o stand_v over_o the_o 12_o a_o clock_n line_n but_o swerve_v from_o it_o towards_o the_o quarter_n of_o declination_n prob._n x._o to_o make_v a_o north_n erect_v dyal_n decline_v eastward_n or_o westward_n as_o in_o prob._n 5._o a_o erect_a direct_a north_n dyal_n have_v the_o same_o delineation_n that_o a_o erect_v direct_a south_n dyal_n have_v and_o differ_v only_o in_o the_o place_n the_o figure_n of_o the_o hour_n line_n so_o a_o north_n erect_v dyal_n that_o decline_v eastward_n or_o westward_n differ_v from_o a_o south_n erect_v dyal_n that_o decline_v eastward_n or_o westward_n the_o same_o number_n of_o degree_n only_o in_o place_v the_o hour_n line_n at_o the_o same_o distance_n on_o the_o contrary_a side_n of_o the_o plane_n and_o by_o transpose_v the_o figure_n of_o 11_o for_o 1_o 10_o for_o 2_o 9_o for_o 3._o etc._n etc._n thus_o if_o you_o draw_v upon_o glass_n horn_n or_o a_o oil_v paper_n the_o south_n dyal_n decline_a eastward_n as_o in_o the_o forego_n problem_n and_o place_n it_o to_o its_o due_a situation_n the_o back_n side_n of_o it_o shall_v be_v a_o north_n dyal_n decline_v towards_o the_o west_n so_o many_o degree_n as_o the_o foreside_n decline_v towards_o the_o east_n and_o the_o only_a difference_n in_o it_o will_v be_v the_o figure_n of_o the_o hour_n line_n as_o be_v say_v before_o prob._n xi_o to_o make_v direct_a recline_a or_o incline_v dial_n direct_v recline_a or_o incline_v dial_n be_v the_o same_o with_o erect_a direct_a dial_n that_n be_v make_v for_o the_o latitude_n of_o some_o other_o place_n the_o latitude_n of_o which_o place_n be_v either_o more_o than_o the_o latitude_n of_o your_o own_o place_n if_o the_o plane_n recline_v or_o less_o if_o the_o plane_n incline_v and_o that_o in_o such_o a_o proportion_n as_o the_o arch_n of_o reclination_n or_o inclination_n of_o your_o plane_n be_v thus_o a_o direct_a south_n dyal_n recline_v 10._o degree_n in_o london_n latitude_n viz._n 51½_n degree_n be_v a_o erect_a direct_v dyal_n make_v for_o the_o latitude_n of_o 61½_n degree_n and_o a_o direct_a south_n dyal_n incline_v 10._o degree_n in_o the_o latitude_n 51½_n degree_n be_v a_o erect_a direct_v dyal_n in_o the_o latitude_n of_o 41½_n degree_n and_o be_v to_o be_v make_v according_a to_o the_o direction_n in_o prob._n 4._o prob._n xii_o to_o make_v decline_a reclining_a or_o decline_a incline_v dial_n the_o distance_n of_o the_o hour_n line_n either_o for_o a_o decline_a recline_a plane_n or_o a_o decline_a incline_v plane_n may_v most_o easy_o be_v find_v upon_o the_o plane_n of_o the_o horizon_n that_o be_v as_o some_o author_n call_v it_o by_o the_o horizontal_n dyal_n by_o change_v the_o circle_n of_o the_o globe_n one_o into_o another_o so_o as_o the_o plane_n of_o the_o horizon_n may_v serve_v to_o represent_v the_o dyal_n plane_n yet_o this_o way_n not_o be_v natural_a because_o you_o must_v admit_v one_o circle_n to_o be_v another_o and_o that_o in_o young_a learner_n may_v sometime_o breed_v a_o little_a difficulty_n gemma_fw-la frisius_n metius_n and_o blaew_n have_v prescribe_v a_o thin_a brass_n plate_n to_o be_v make_v equal_a to_o a_o semicircle_n of_o the_o equinoctial_a and_o divide_v from_o the_o middle_a point_n of_o it_o either_o way_n into_o 90_o degree_n which_o may_v not_o unproper_o be_v call_v a_o gnomonical_a semicircle_n this_o semicircle_n must_v be_v bow_v close_o to_o the_o body_n of_o the_o globe_n into_o a_o semicircular_a form_n and_o so_o set_v to_o any_o reclination_n or_o inclination_n and_o then_o it_o will_v represent_v a_o recline_a or_o incline_v plane_n and_o by_o the_o motion_n of_o the_o colour_n through_o the_o several_a degree_n of_o this_o semicircle_n the_o distance_n of_o the_o hour_n line_n may_v be_v find_v thus_o the_o globe_n quadrant_n of_o altitude_n colour_n and_o hour_n index_n rectify_v as_o by_o prob._n 4._o bring_v the_o low_a end_n of_o the_o quadrant_n of_o altitude_n to_o the_o degree_n in_o the_o horizon_n of_o the_o plane_n declination_n if_o your_o plane_n be_v a_o south_n decline_a recliner_n and_o count_v on_o the_o quadrant_n of_o altitude_n from_o the_o zenith_n downward_o the_o number_n of_o degree_n of_o reclination_n or_o inclination_n and_o to_o that_o number_n of_o degree_n bring_v the_o middle_n of_o the_o gnomonical_a semicircle_n and_o let_v the_o end_n of_o â—t_a cut_v the_o horizon_n on_o either_o side_n in_o the_o degree_n of_o the_o plane_n azimuth_n so_o shall_v the_o gnomonical_a semicircle_n represent_v a_o recline_a plane_n and_o so_o oft_o as_o 15._o degree_n of_o the_o equator_fw-la pass_v through_o the_o meridian_n so_o oft_o shall_v you_o inquire_v what_o degree_n of_o the_o gnomonical_a semicircle_n the_o colour_n cut_v for_o so_o many_o degree_n asunder_o must_v the_o several_a respective_a hour_n line_n of_o a_o recline_a decline_a plane_n be_v in_o a_o semicircle_n divide_v into_o 180._o degree_n but_o if_o your_o plane_n be_v a_o south_n decline_a recliner_n or_o a_o north_n decline_a incliner_n bring_v the_o quadrant_n of_o altitude_n to_o the_o degree_n of_o the_o horizon_n opposite_a to_o the_o degree_n of_o the_o plane_n declination_n because_o the_o upper_a side_n of_o the_o plane_n lie_v beyond_o the_o zenith_n count_v from_o the_o south_n point_n in_o the_o south_n recliner_n and_o from_o the_o north_n point_n in_o north_n incliner_n then_o find_v the_o height_n of_o the_o style_n and_o place_n of_o the_o substyle_n thus_o keep_v your_o gnomonical_a semicircle_n in_o its_o position_n but_o turn_v the_o quadrant_n of_o altitude_n about_o on_o the_o zenith_n point_n till_o the_o low_a end_n of_o it_o come_v to_o the_o degree_n of_o the_o horizon_n opposite_a to_o the_o degree_n it_o be_v place_v at_o before_o and_o turn_v about_o the_o globe_n till_o the_o colour_n cut_v the_o quadrant_n of_o altitude_n above_o the_o horizon_n in_o the_o number_n of_o degree_n the_o plane_n recline_v from_o the_o zenith_n so_o shall_v the_o colour_n cut_v the_o gnomonical_a semicircle_n at_o right_a angle_n then_o count_v the_o degree_n contain_v between_o the_o middle_n of_o the_o gnomonical_a semicircle_n and_o the_o colour_n for_o that_o number_n of_o degree_n be_v the_o distance_n of_o the_o substyle_n from_o a_o perpendicular_a line_n in_o the_o middle_n of_o your_o plane_n and_o must_v be_v place_v westward_n of_o the_o say_v perpendicular_a if_o your_o plane_n decline_v from_o the_o south_n east-ward_n or_o eastward_n if_o your_o plane_n decline_v from_o the_o south_n westward_n then_o observe_v how_o many_o degree_n be_v contain_v between_o the_o semicircle_n and_o the_o pole_n for_o that_o number_n of_o degree_n be_v the_o number_n of_o degree_n that_o the_o style_n be_v to_o be_v elevate_v above_o the_o substyle_n example_n here_o at_o london_n i_o will_v make_v a_o dyal_n upon_o a_o plane_n decline_a from_o the_o south_n eastward_n 30._o degree_n and_o recline_v from_o the_o zenith_n 20._o degree_n london_n latitude_n be_v 51½_n degree_n therefore_o have_v on_o the_o plane_n describe_v a_o semi_a circle_n etc._n etc._n as_o be_v direct_v prob._n 4._o i_o rectify_v the_o globe_n quadrant_n of_o altitude_n colour_n and_o hour_n index_n as_o by_o the_o same_o problem_n and_o bring_v the_o low_a end_n of_o the_o quadrant_n of_o altitude_n to_o 30._o degree_n from_o the_o north_n point_n of_o the_o horizon_n towards_o the_o west_n because_o that_o be_v the_o degree_n opposite_a to_o the_o degree_n of_o the_o plane_n declination_n viz_o to_o 30_o degree_n from_o the_o south_n eastward_n and_o i_o bring_v the_o middle_n of_o the_o gnomonical_a semi_a circle_n to_o 20._o degree_n of_o the_o quadrant_n of_o altitude_n count_v from_o the_o zenith_n downward_o towards_o the_o horizon_n and_o the_o end_n of_o the_o gnomonical_a semi_a circle_n to_o the_o degree_n of_o azimuth_n the_o plane_n lie_v in_o in_o the_o horizon_n viz._n to_o 30._o degree_n from_o the_o east_n point_v northwards_o and_o to_o 30._o degree_n from_o the_o west_n point_v southwards_o so_o shall_v 11._o degree_n 10._o minute_n of_o the_o gnomonical_a semi_a circle_n be_v comprehend_v between_o the_o quadrant_n of_o altitude_n and_o the_o brazen_a meridian_n these_o 11._o degree_n 10._o minute_n show_v that_o the_o 12_o a_o clock_n line_n be_v distant_a from_o the_o perpendicular_a a_o b_o 11._o degree_n 10._o minute_n and_o because_o the_o plane_n decline_v to_o the_o eastward_n therefore_o the_o 12_o a_o clock_n line_n must_v stand_v on_o the_o west_n side_n the_o plane_n 11._o degree_n 10_o
stand_v the_o angle_n c_o which_o a_o b_o subtend_v next_o follow_v the_o 142._o degree_n 42._o minute_n of_o azimuth_n which_o make_v b_o c_o of_o your_o triangle_n to_o the_o horizon_n and_o from_o thence_o number_n in_o the_o horizon_n towards_o the_o east_n point_fw-fr 37_o degree_n 18._o minute_n the_o compliment_n of_o the_o angle_n a_o to_o 180._o degree_n and_o number_n yet_o further_o 52._o degree_n 42._o minute_n beyond_o the_o east_n point_n to_o make_v up_o 90_o and_o there_o be_v the_o pole_n of_o the_o arch_n b_o c_o therefore_o there_o shall_v stand_v the_o angle_n a_o which_o b_o c_z subtend_v then_o count_v in_o the_o equator_fw-la from_o the_o first_o meridian_n 90._o degree_n which_o will_v end_v under_o the_o horizon_n and_o there_o make_v a_o prick_n for_o there_o be_v the_o pole_n of_o the_o arch_n or_o side_n a_o c._n therefore_o at_o that_o prick_n shall_v stand_v the_o angle_n b_o which_o a_o c_o subtend_v here_o you_o see_v your_o second_o triangle_n make_v by_o the_o pole_n of_o the_o first_o adjoin_v to_o the_o east_n point_n of_o the_o globe_n only_o the_o side_n a_o b_o be_v want_v to_o get_v that_o make_v a_o prick_n upon_o the_o globe_n against_o the_o 52._o degree_n 42._o minute_n from_o the_o east_n point_n of_o the_o horizon_n find_v before_o to_o represent_v the_o angle_n a_o then_o turn_v about_o the_o globe_n and_o qudrant_n of_o altitude_n till_o that_o prick_n and_o the_o prick_n make_v before_o for_o the_o angle_n b_o be_v both_o at_o once_o cut_v by_o the_o side_n of_o the_o quadrant_n of_o altitude_n and_o you_o will_v find_v 25._o degree_n 24._o minute_n of_o the_o quadrant_n of_o altitude_n comprehend_v between_o the_o two_o prick_n for_o the_o measure_n of_o the_o side_n a_o b_o prob._n xiii_o how_o to_o let_v fall_v a_o perpendicular_a that_o shall_v divide_v any_o oblique_a spherical_a triangle_n into_o two_o right_a angle_a spherical_a triangle_n this_o problem_n be_v much_o use_v when_o a_o oblique_a triangle_n have_v two_o side_n and_o a_o angle_n give_v be_v to_o be_v solve_v by_o the_o cannon_n of_o sines_n and_o tangent_n but_o by_o the_o globe_n it_o may_v be_v solve_v without_o it_o as_o be_v show_v prob_n 8_o 9_o yet_o because_o let_v fall_v a_o perperdicular_a be_v so_o frequent_a in_o all_o author_n that_o treat_v of_o trigonometry_n i_o have_v insert_v this_o problem_n also_o in_o the_o oblique_a triangle_n of_o the_o fromer_fw-ge problem_n there_o be_v give_v the_o side_n a_o b_o 38½_n degree_n and_o b_o c_o 25._o degree_n and_o the_o angle_n c_o 25._o degree_n 24._o minute_n it_o be_v require_v to_o let_v fall_v a_o perpendicular_a as_o b_o a_o from_o the_o angle_n b._n upon_o the_o base_a a_o c_o and_o to_o know_v both_o the_o measure_n of_o this_o perpendicular_a and_o the_o part_n it_o divide_v the_o base_a into_o therefore_o elevate_v the_o pole_n of_o the_o globe_n above_o the_o horizon_n so_o much_o as_o be_v the_o measure_n of_o the_o angle_n c_o which_o in_o this_o example_n be_v 25._o degree_n 24._o minute_n and_o bring_v the_o intersection_n of_o the_o first_o meridian_n with_o the_o equinoctial_a to_o the_o east_n point_n of_o the_o horizon_n so_o shall_v the_o angle_n at_o the_o east_n point_n of_o the_o horizon_n comprehend_v between_o the_o horizon_n and_o the_o first_o meridian_n be_v equal_a to_o the_o angle_n c_o then_o count_v in_o the_o first_o meridian_n from_o the_o east_n point_n of_o the_o horizon_n the_o measure_n of_o the_o side_n b_o c_o 25._o degree_n and_o have_v the_o quadrant_n of_o altitude_n screw_v to_o the_o zenith_n bring_v the_o graduated_a edge_n of_o it_o to_o these_o 25._o degree_n so_o shall_v the_o arch_n of_o the_o horizon_n comprehend_v between_o the_o east_n point_n and_o the_o low_a end_n of_o the_o quadrant_n of_o altitude_n be_v the_o number_n of_o degree_n that_o the_o perpendicular_a fall_n upon_o the_o base_a count_v from_o the_o angle_n c_o to_o a_o which_o in_o this_o example_n be_v 21¾_n degree_n and_o the_o arch_n of_o the_o quadrant_n of_o altitude_n comprehend_v between_o the_o horizon_n and_o the_o first_o meridian_n be_v the_o measure_n of_o the_o perpendicular_a b_o a_fw-fr 11._o degree_n and_o thus_o by_o let_v fall_n this_o perpendicular_a you_o have_v two_o right_o angle_v spherical_a triangle_n make_v the_o one_o b_o a_o c_o wherein_n be_v find_v c_o a_o 21¾_n degree_n b_o c_o 25._o degree_n b_o a_fw-fr 11._o degree_n c_o 25._o degree_n 24._o minute_n and_o a_o the_o right_a angle_n there_o remain_v only_o the_o angle_n b_o unknown_a which_o you_o must_v find_v by_o turn_v the_o triangle_n as_o be_v teach_v prob._n 1._o the_o other_o right_o angle_v spherical_a triangle_n make_v be_v b_o a_o a_o wherein_o be_v find_v a_o a_o compliment_n of_o 21_o 2_o 4_o degree_n to_o 60_o degree_n the_o whole_a base_a before_o give_v 38¼_n degree_n a_o b_o 38._o degree_n 30._o minute_n b_o a_o 11._o degree_n and_o a_o the_o right_a angle_n which_o be_v more_o then_o enough_o to_o find_v the_o anglâ—_n a_o and_o b_o as_o be_v show_v in_o the_o preface_n theorem_fw-la 1._o the_o end_n of_o the_o six_o book_n here_o follow_v the_o ancient_a story_n of_o the_o several_a star_n and_o constellation_n show_v the_o poetical_a reason_n why_o such_o various_a figure_n be_v place_v in_o heaven_n collect_v from_o dr_n hood_n and_o first_o of_o the_o northern_a constellation_n 1._o ursa_fw-la minor_fw-la this_o constellation_n have_v the_o pre-eminence_n because_o it_o be_v near_a of_o all_o the_o rest_n unto_o the_o north_n pole_n and_o be_v call_v of_o the_o greek_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d whereupon_o the_o pole_n be_v call_v the_o pole_n arctic_a for_o that_o it_o be_v near_o unto_o that_o constellation_n it_o be_v also_o call_v helice_n minor_a because_o of_o the_o small_a revolution_n which_o it_o make_v round_o about_o the_o pole_n or_o rather_o of_o elice_n a_o town_n in_o arcadia_n wherein_o calysto_n the_o great_a bear_n and_o mother_n to_o the_o less_o be_v breed_v it_o be_v call_v cynosura_n because_o this_o constellation_n though_o it_o carry_v the_o name_n of_o a_o bear_n yet_o it_o have_v the_o tail_n of_o a_o dog_n last_o of_o all_o it_o be_v term_v phoenicia_n because_o that_o thales_n who_o first_o give_v the_o name_n to_o this_o constellation_n be_v a_o phoenician_n and_o therefore_o the_o phoenician_n be_v teach_v how_o to_o use_v it_o in_o their_o navigation_n do_v call_v it_o by_o the_o name_n of_o the_o country_n wherein_o thales_n be_v bear_v it_o consist_v of_o 7._o star_n which_o the_o latin_n call_v septemtriones_n because_o by_o their_o continual_a motion_n those_o seven_o star_n do_v as_o it_o be_v wear_v the_o heaven_n the_o spaniard_n call_v they_o all_o bosina_n that_o be_v a_o horn_n because_o they_o may_v be_v very_o well_o bring_v into_o that_o form_n whereof_o that_o which_o be_v in_o the_o end_n of_o the_o tail_n be_v call_v the_o polestar_n by_o reason_n of_o the_o neareness_n thereof_o unto_o the_o pole_n of_o the_o world_n for_o it_o be_v distant_a according_a to_o the_o opinion_n of_o most_o from_o the_o true_a pole_n but_o 23._o deg_n 30._o min._n the_o arabian_n call_v it_o alrukaba_n and_o of_o the_o scythian_n it_o be_v say_v to_o be_v a_o iron_n nail_n and_o be_v worship_v by_o they_o as_o a_o god_n the_o two_o star_n that_o be_v in_o the_o shoulder_n of_o the_o bear_n be_v call_v guard_n of_o the_o spanish_a word_n guardare_n which_o be_v to_o behold_v because_o they_o be_v diligent_o to_o be_v look_v unto_o in_o regard_n of_o the_o singular_a use_n which_o they_o have_v in_o navigation_n the_o reason_n why_o this_o constellation_n be_v bring_v into_o the_o heaven_n be_v diverse_o set_v down_o and_o first_o in_o this_o manner_n saturn_n have_v receive_v of_o the_o oracle_n that_o one_o of_o his_o son_n shall_v banish_v he_o out_o of_o his_o kingdom_n determine_v with_o himself_o to_o kill_v all_o the_o man_n child_n that_o he_o shall_v beget_v whereupon_o he_o give_v command_v to_o ops_n his_o wife_n be_v then_o great_a that_o she_o shall_v show_v he_o the_o child_n so_o soon_o as_o ever_o it_o be_v bear_v but_o she_o bring_v forth_o jupiter_n and_o be_v great_o delight_v with_o his_o hair_n give_v the_o child_n unto_o two_o nymph_n of_o crete_n dwell_v in_o the_o mount_n dicte_n whereof_o this_o be_v one_o and_o be_v call_v cynosura_n the_o other_o be_v helice_n jupter_n after_o that_o according_a to_o the_o oracle_n he_o have_v bereave_v his_o father_n of_o the_o kingdom_n in_o recompense_n of_o their_o pain_n and_o courtesy_n translate_v they_o both_o into_o the_o heaven_n and_o make_v of_o they_o two_o constellation_n the_o lesser_a bear_n and_o the_o great_a bear_n othersome_a say_v that_o it_o be_v arcas_n the_o son_n of_o
solsticial_a colour_n to_o the_o meridian_n on_o the_o north_n side_n the_o horizon_n and_o screw_v the_o quadrant_n of_o altitude_n to_o the_o zenith_n which_o will_v be_v in_o 23½_n degree_n from_o the_o pole_n of_o the_o world_n so_o shall_v the_o ecliptic_a lie_n in_o the_o horizon_n and_o the_o pole_n of_o the_o ecliptic_a also_o lie_v under_o the_o centre_n of_o the_o quadrant_n of_o altitude_n as_o be_v show_v prob._n 27._o now_o to_o find_v the_o longitude_n of_o any_o star_n do_v thus_o turn_v the_o quadrant_n of_o altitude_n about_o till_o the_o graduated_a edge_n of_o it_o lie_v on_o the_o star_n and_o the_o degree_n in_o the_o ecliptic_a that_o the_o quadrant_n touch_v be_v the_o longitude_n of_o that_o star_n example_n for_o a_o star_n on_o the_o north_n side_n the_o ecliptic_a i_o will_v know_v the_o longitude_n of_o marchab_n a_o bright_a star_n in_o the_o wing_n of_o pegasus_n i_o find_v it_o on_o the_o north_n side_n the_o ecliptic_a therefore_o i_o elevate_v the_o north_n pole_n and_o place_v ♋_o on_o the_o north_n side_n the_o meridian_n i_o screw_v the_o quadrant_n of_o altitude_n to_o the_o zenith_n as_o aforesaid_a then_o lay_v the_o edge_n of_o the_o quadrant_n of_o altitude_n upon_o that_o star_n i_o find_v that_o the_o end_n of_o it_o reach_v in_o the_o ecliptic_a to_o ♓_o 18._o 56._o therefore_o i_o say_v the_o longitude_n of_o marchab_n be_v ♓_o 18._o 56._o for_o the_o latitude_n of_o a_o star_n the_o degree_n of_o the_o quadrant_n of_o altitude_n that_o touch_v the_o star_n be_v the_o latitude_n of_o the_o star_n example_n the_o globe_n and_o quadrant_n posit_v as_o before_o i_o find_v 19_o deg_n 26._o min._n account_v upward_o on_o the_o quadrant_n to_o touch_v marchab_n aforesaid_a therefore_o i_o say_v the_o latitude_n of_o marchab_n be_v 19_o deg_n 26._o min._n and_o thus_o by_o elevate_a the_o south_n pole_n and_o place_v the_o globe_n and_o quadrant_n of_o altitude_n as_o aforesaid_a i_o shall_v find_v canicula_fw-la have_v 15._o degree_n 57_o min._n south_n latitude_n and_o 21._o degr_n 18._o min_fw-mi in_fw-la ♋_o longitude_n prob._n xxxiii_o to_o find_v the_o distance_n between_o any_o two_o place_n on_o the_o terrestrial_a globe_n this_o may_v be_v perform_v either_o with_o the_o quadrant_n of_o altitude_n or_o with_o a_o pair_n of_o compass_n with_o the_o quadrant_n of_o altitude_n 〈◊〉_d lay_v the_o low_a end_n thereof_o to_o one_o place_n and_o see_v what_o degree_n reach_v the_o other_o place_n for_o that_o be_v the_o number_n of_o degree_n between_o the_o two_o place_n if_o you_o multiply_v that_o number_n of_o degree_n by_o 60_o the_o product_n shall_v be_v the_o number_n of_o english_a mile_n between_o the_o two_o place_n example_n i_o will_v know_v the_o distance_n between_o london_n and_o the_o most_o easterly_a point_n of_o jamaâ—ca_n i_o lay_v the_o low_a end_n of_o the_o quadrant_n of_o altitude_n to_o jamaica_n and_o extend_v the_o other_o end_n towards_o london_n i_o find_v 68½_n deg_n comprehend_v between_o they_o therefore_o i_o say_v 68½_n be_v the_o number_n of_o degree_n comprehend_v between_o london_n and_o jamaica_n if_o you_o will_v find_v the_o distance_n between_o they_o with_o your_o compass_n you_o must_v pitch_v one_o foot_n of_o your_o compass_n in_o the_o east_n point_n of_o jamaica_n and_o open_v your_o compass_n till_o the_o other_o foot_n reach_n london_n and_o keep_v your_o compass_n at_o that_o distance_n apply_v the_o foot_n to_o the_o equinoctial_a line_n and_o you_o will_v find_v 68½_n degree_n comprehend_v between_o they_o as_o before_o if_o you_o multiply_v 68½_n by_o 60_o be_v it_o give_v 4110._o english_a mile_n if_o you_o multiply_v it_o by_o 20_o it_o give_v 1370._o english_a league_n if_o you_o multiply_v it_o by_o 17½_n it_o give_v 1199._o spanish_a league_n if_o you_o multiply_v it_o by_o 15_o it_o give_v 1054_o dutch_a league_n prob._n xxxiv_o to_o find_v by_o the_o terrestrial_a globe_n upon_o what_o point_n of_o the_o compass_n any_o two_o place_n be_v situate_a one_o from_o another_o find_v the_o two_o place_n on_o the_o terrestrial_a globe_n and_o see_v what_o â—umb_n pass_v through_o they_o for_o that_o be_v the_o point_n of_o the_o compass_n they_o bear_v upon_o example_n bristol_n and_o bermudas_n be_v the_o place_n i_o examine_v what_o rhumb_n pass_v through_o they_o both_o and_o because_o i_o find_v no_o rhumb_n to_o pass_v immediate_o through_o they_o both_o therefore_o i_o take_v that_o rhumb_n which_o run_v most_o parallel_n to_o both_o the_o place_n which_o in_o this_o example_n be_v the_o ten_o rhumb_n count_v from_o the_o north_n towards_o the_o left_a hand_n and_o be_v call_v as_o you_o may_v see_v by_o this_o follow_a figure_n west_n south_n west_n therefore_o i_o say_v bermudos_n lie_v situate_a from_o bristol_n west_n south_n west_n and_o by_o contrary_n bristol_n lie_v cituate_a from_o bermuda_n east_n north_n east_n prob._n xxxv_o to_o find_v by_o the_o celestial_a globe_n the_o cosmical_a rise_n and_o set_v of_o the_o star_n when_o any_o star_n rise_v with_o the_o sun_n it_o be_v say_v to_o rise_v cosmical_o and_o when_o any_o star_n set_v when_o the_o sun_n rise_v it_o be_v saâ—d_v to_o set_a cosmical_o to_o find_v these_o rectify_v the_o globe_n to_o the_o latitude_n of_o your_o place_n and_o bring_v the_o place_n of_o the_o sun_n to_o the_o east_n side_n the_o horizon_n and_o the_o star_n then_o cut_v by_o the_o eastern_a semicircle_n of_o the_o horizon_n rise_v cosmical_o and_o those_o star_n cut_v by_o the_o western_a semicircle_n of_o the_o horizon_n set_v cosmical_o example_n novemb_n 9_o i_o will_v know_v what_o star_n rise_v and_o set_v cosmical_o here_o at_o london_n the_o sun_n place_v find_v as_o by_o the_o three_o problem_n be_v 〈◊〉_d 27._o therefore_o i_o bring_v 〈◊〉_d 27._o to_o the_o east_n side_n the_o horizon_n and_o in_o the_o eastern_a semicircle_n i_o find_v rise_v with_o the_o sun_n the_o right_a wing_n of_o cygnus_n the_o star_n in_o the_o end_n of_o aquila_n tail_n serpentarius_n and_o centaurus_n therefore_o these_o constellation_n be_v say_v to_o the_o cosmical_o in_o the_o western_a semicircle_n of_o the_o horizon_n i_o find_v set_v andromeda_n the_o triangle_n taurus_n orion_n anis_fw-la major_n and_o argo_n navis_fw-la therefore_o i_o say_v these_o constellation_n set_v cosmical_o prob._n xxxvi_o to_o find_v by_o the_o celestial_a globe_n the_o acronical_a rise_n and_o set_v of_o the_o star_n the_o star_n that_o rise_v when_o the_o sun_n set_v be_v say_v to_o rise_v acronical_o and_o the_o star_n that_o set_v with_o the_o sun_n be_v say_v to_o set_a acronical_o to_o find_v these_o rectify_v the_o globe_n to_o the_o latitude_n of_o your_o place_n and_o bring_v the_o place_n of_o the_o sun_n to_o the_o west_n side_n the_o horizon_n and_o the_o star_n then_o cut_v by_o the_o eastern_a semicircle_n of_o the_o horizon_n rise_v acronical_o and_o those_o star_n cut_v by_o the_o western_a semicircle_n of_o the_o horizon_n set_v acronical_o example_n november_n 9_o i_o will_v know_v what_o star_n rise_v and_o set_v acronical_o here_o at_o london_n the_o sun_n place_n as_o before_o be_v 〈◊〉_d 27._o therefore_o i_o bring_v 〈◊〉_d 27._o to_o the_o west_n side_n the_o horizon_n and_o in_o the_o eastern_a semicircle_n i_o find_v rise_v the_o southern_a fiâ—h_n fomahant_n ceâ—us_n taurus_n auriga_fw-la and_o the_o feather_n in_o castor_n cap._n therefore_o these_o constellation_n be_v say_v to_o rise_v acronical_o in_o the_o western_a semicircle_n of_o the_o horizon_n i_o find_v set_v the_o lion_n tail_n virgo_fw-la scorpio_n and_o sagittarius_fw-la therefore_o i_o say_v these_o constellation_n set_v acronical_o prob._n xxxvii_o to_o find_v by_o the_o celestial_a globe_n the_o heliacal_a rise_n and_o set_v of_o the_o star_n when_o a_o star_n former_o in_o the_o sun_n beam_n get_v out_o of_o the_o sun_n beam_n it_o be_v say_v to_o rise_v heliacal_o and._n when_o a_o star_n former_o out_o of_o the_o sun_n beam_n get_v into_o the_o sun_n beam_n it_o be_v say_v to_o set_v heliacal_o a_o star_n be_v say_v to_o be_v in_o the_o sun_n beam_n when_o it_o be_v make_v inconspicuous_a by_o reason_n of_o its_o nearness_n to_o the_o sun_n light_n the_o big_a star_n be_v discernible_a more_o near_o the_o sun_n light_n than_o the_o lesser_a be_v for_o star_n of_o the_o first_o magnitude_n may_v according_a to_o the_o receive_a rule_n of_o ancient_a author_n be_v see_v when_o the_o sun_n be_v but_o 12._o degree_n below_o the_o horizon_n but_o star_n of_o second_o magnitude_n can_v be_v see_v unless_o the_o sun_n be_v 13._o degree_n below_o the_o horizon_n star_n of_o the_o three_o magnitude_n require_v the_o sun_n to_o be_v 14._o degree_n below_o the_o horizon_n ere_o they_o can_v be_v see_v of_o the_o four_o magnitude_n 15._o degree_n of_o the_o five_o
the_o meridian_n cut_v the_o degree_n of_o the_o ecliptic_a on_o the_o cusp_n of_o the_o ten_o house_n the_o western_a semicircle_n of_o the_o horizon_n shall_v cut_v the_o degree_n of_o the_o ecliptic_a on_o the_o cusp_n of_o the_o seven_o house_n and_o the_o semicircle_n of_o the_o meridian_n under_o the_o horizon_n shall_v cut_v the_o degree_n of_o the_o ecliptic_a on_o the_o cusp_n of_o the_o four_o house_n if_o you_o have_v the_o day_n of_o the_o month_n you_o may_v by_o prob._n 3._o of_o the_o second_o book_n find_v the_o sun_n place_n and_o if_o you_o have_v the_o hour_n of_o the_o day_n you_o may_v by_o first_o rectify_v the_o globe_n as_o by_o prob._n 2._o of_o the_o same_o book_n turn_v about_o the_o globe_n till_o the_o index_n of_o the_o hour-circle_n point_n to_o the_o same_o hour_n in_o the_o hour-circle_n and_o you_o will_v then_o at_o the_o eastern_a semicircle_n of_o the_o horizon_n have_v the_o degree_n of_o the_o ecliptic_a that_o be_v rise_v and_o by_o consequence_n as_o aforesaid_a all_o the_o cardinal_n point_v in_o their_o respective_a place_n now_o to_o find_v what_o degree_n of_o the_o ecliptic_a occupy_v the_o cusp_n of_o the_o other_o eight_o house_n of_o heaven_n do_v thus_o the_o globe_n rectify_v as_o aforesaid_a move_v the_o semicircle_n of_o position_n upward_o till_o 30_o degree_n of_o the_o equator_fw-la shall_v be_v contain_v between_o it_o and_o the_o eastern_a semicircle_n of_o the_o horizon_n so_o shall_v the_o semicircle_n of_o position_n cut_v in_o the_o ecliptic_a the_o degree_n and_o minute_n of_o the_o ecliptic_a on_o the_o cusp_n of_o the_o twelve_o house_n and_o its_o opposite_a degree_n and_o minute_n in_o the_o ecliptic_a shall_v be_v the_o cusp_n of_o house_n the_o six_o house_n for_o you_o must_v note_v that_o if_o you_o have_v but_o the_o degree_n and_o minute_n of_o the_o ecliptic_a upon_o the_o cusp_n of_o six_o of_o the_o house_n the_o opposite_a degree_n and_o minute_n of_o the_o ecliptic_a shall_v immediate_o possess_v the_o cusp_n of_o every_o opposite_a house_n then_o move_v the_o circle_n of_o position_n over_o 30._o degree_n more_o of_o the_o equinoctial_a so_o shall_v the_o degree_n of_o the_o ecliptic_a cut_n by_o the_o circle_n of_o position_n be_v the_o degree_n of_o the_o ecliptic_a upon_o the_o cusp_n of_o the_o eleven_o house_n and_o its_o opposite_a degree_n in_o the_o ecliptic_a shall_v be_v upon_o the_o cusp_n of_o the_o five_o house_n the_o degree_n of_o the_o ecliptic_a upon_o the_o cusp_n of_o the_o ten_o and_o four_o house_n be_v find_v as_o before_o then_o remove_v the_o circle_n of_o position_n to_o the_o western_a side_n of_o the_o meridian_n and_o let_v it_o fall_v towards_o the_o horizon_n till_o 30._o degree_n of_o the_o equator_fw-la be_v contain_v between_o the_o meridian_n and_o it_o so_o shall_v the_o degree_n of_o the_o ecliptic_a cut_n by_o the_o semicircle_n of_o position_n be_v the_o degree_n of_o the_o ecliptic_a on_o the_o cuâ—p_n of_o the_o nine_o house_n and_o the_o opposite_a degree_n of_o the_o ecliptic_a shall_v be_v upon_o the_o cusp_n of_o the_o three_o house_n let_v the_o semicircle_n of_o position_n fall_v yet_o low_o till_o it_o pass_v over_o 30._o degree_n more_o of_o the_o equator_fw-la so_o shall_v the_o degree_n of_o the_o ecliptic_a cut_n by_o the_o semicircle_n of_o position_n be_v the_o degree_n of_o the_o ecliptic_a on_o the_o cusp_n of_o the_o eight_o house_n and_o the_o opposite_a degree_n of_o the_o ecliptic_a shall_v be_v upon_o the_o cusp_n of_o the_o second_o house_n the_o degree_n of_o the_o ecliptic_a on_o the_o cusp_n of_o the_o seven_o house_n and_o ascendent_n be_v find_v as_o before_o example_n i_o will_v erect_v a_o figure_n of_o heaven_n for_o july_n 27._o 5._o hour_n oâ—_n minute_n afternoon_n 1658._o in_o the_o latitude_n of_o london_n viz._n 51½_n degree_n north_n latitude_n i_o first_o place_n the_o planet_n ☊_o and_o ☋_o on_o the_o globe_n as_o by_o prob._n 55._o of_o the_o second_o book_n be_v direct_v yet_o not_o exact_o as_o i_o find_v they_o in_o the_o ephemeris_fw-la for_o that_o show_v only_o their_o place_n in_o the_o ecliptic_a at_o noon_n therefore_o i_o consider_v how_o many_o degree_n or_o minute_n each_o planet_n motion_n be_v in_o a_o whole_a day_n or_o 24._o hour_n by_o substract_v the_o elliptical_a degree_n and_o minute_n of_o the_o planet_n place_v that_o day_n at_o noon_n from_o the_o elliptical_a degree_n and_o minute_n of_o the_o planet_n place_v the_o next_o day_n at_o noon_n or_o contrary_o if_o the_o planet_n be_v retrograde_a for_o the_o remain_v of_o those_o degree_n and_o minute_n be_v the_o motion_n of_o the_o planet_n that_o day_n therefore_o proportionable_o to_o that_o motion_n i_o place_v the_o planet_n forward_o in_o the_o ecliptic_a or_o backward_o if_o it_o be_v retrograde_a as_o if_o the_o sun_n shall_v move_v forward_o 1_o degree_n that_o be_v 60_o minute_n in_o a_o whole_a day_n or_o 24_o hour_n then_o in_o 12_o hour_n he_o shall_v move_v 30_o minute_n in_o 6_o hour_n 15_o minute_n in_o 4_o hour_n 10_o minute_n in_o 1_o hour_n 2½_n minute_n and_o so_o proportionable_o for_o any_o other_o space_n of_o time_n which_o i_o consider_v before_o i_o place_v the_o planet_n on_o the_o globe_n prob._n ii_o to_o erect_v a_o figure_n of_o heaven_n according_a to_o campanus_n regiomontanus_n as_o aforesaid_a make_v the_o beginning_n of_o every_o house_n to_o be_v the_o semi_a circle_n draw_v by_o the_o side_n of_o the_o semi_a circle_n of_o position_n according_a to_o the_o succession_n of_o every_o 30_o the_o degree_n of_o the_o equator_fw-la from_o the_o horizon_n but_o camp_n 〈◊〉_d make_v it_o to_o be_v the_o semicircle_n draw_v by_o the_o side_n of_o the_o semicircle_n 〈◊〉_d position_n according_a to_o the_o succession_n of_o every_o 30_o the_o degree_n of_o 〈◊〉_d prime_a verticle_n or_o east_n azimuth_n which_o be_v represent_v by_o the_o quadrant_n of_o altitude_n place_v at_o the_o east_n point_fw-fr the_o four_o cardinal_n be_v the_o same_o both_o according_a to_o regiomontanus_n and_o campanus_n but_o the_o other_o eight_o house_n differ_v therefore_o when_o you_o will_v find_v they_o according_a to_o campanus_n rectify_v the_o globe_n and_o quadrant_n of_o altitude_n and_o bring_v the_o low_a end_n 〈◊〉_d the_o quadrant_n of_o altitude_n to_o the_o east_n point_n in_o the_o horizon_n then_o count_v from_o the_o horizon_n upward_o 30_o degree_n oâ—_n the_o quadrant_n 〈◊〉_d altitude_n and_o bring_v the_o circle_n of_o position_n to_o those_o 30_o degreeâ—_n examine_v where_o the_o circle_n of_o position_n cut_v the_o ecliptic_a which_o 〈◊〉_d the_o aforesaid_a time_n be_v in_o 〈◊〉_d 29._o 40_o for_o that_o degree_n and_o minute_n upon_o the_o cusp_n of_o the_o twelve_o house_n and_o its_o opposite_a degree_n 〈◊〉_d minute_n in_o the_o ecliptic_a viz._n ♉_o 29._o 40._o be_v upon_o the_o cusp_n of_o 〈◊〉_d six_o house_n lift_v up_o the_o circle_n of_o position_n 30_o degree_n highâ—_n upon_o the_o quadrant_n of_o altitude_n viz._n to_o 60_o degree_n and_o 〈◊〉_d circle_n of_o position_n will_v cut_v the_o ecliptic_a in_o 〈◊〉_d 15._o degree_n for_o the_o cusp_n of_o the_o eleven_o house_n and_o its_o opposite_a degree_n and_o minute_n in_o the_o ecliptic_a viz._n ♉_o 15._o be_v upon_o the_o cusp_n of_o the_o first_o house_n the_o degree_n and_o minute_n of_o the_o ecliptic_a on_o the_o cusp_n 〈◊〉_d the_o ten_o and_o four_o house_n be_v at_o the_o meridian_n then_o transfer_v the_o circle_n of_o position_n to_o the_o west_n side_n of_o the_o meridian_n and_o the_o quadrant_n of_o altitude_n to_o the_o west_n point_n in_o the_o horizon_n let_v the_o semicircle_n of_o position_n fall_v 30_o degree_n from_o the_o meridian_n on_o the_o quadrant_n of_o altitude_n and_o it_o will_v cut_v in_o the_o ecliptic_a ♎_o 16_o degree_n for_o the_o cusp_n of_o the_o nine_o house_n and_o its_o opposite_a degree_n and_o minute_n in_o the_o ecliptic_a viz._n ♈_o 16._o be_v upon_o the_o cusp_n of_o the_o three_o house_n let_v fall_v the_o circle_n of_o position_n 30_o degree_n low_a on_o the_o quadrant_n of_o altitude_n and_o it_o will_v cut_v the_o ecliptic_a in_o 〈◊〉_d 2_o degree_n for_o the_o cusp_n of_o the_o eight_o house_n and_o its_o opposite_a degree_n viz._n ♓_o 2._o degree_n be_v on_o the_o cusp_n of_o the_o second_o house_n the_o cusp_n of_o the_o seven_o and_o ascendent_n be_v the_o same_o with_o regiomontanus_n viz._n 〈◊〉_d 27._o 47_o and_o â™_o 27._o 47._o the_o figure_n follow_v prob._n iii_o to_o find_v the_o length_n of_o a_o planetary_a hour_n astrologer_n divide_v the_o artificial_a day_n be_v it_o long_o or_o short_a into_o 12_o equal_a part_n and_o the_o night_n into_o 12_o equal_a part_n these_o part_n they_o call_v planetary_a hour_n the_o first_o of_o these_o planetary_a hour_n take_v its_o
order_n or_o late_a author_n give_v the_o plain_n their_o name_n upon_o the_o same_o ground_n you_o may_v also_o learn_v to_o know_v they_o i_o confess_v both_o way_n admit_v of_o some_o just_a exception_n against_o for_o in_o the_o old_a rule_n a_o plain_a about_o the_o pole_n be_v call_v a_o equinoctial_a plain_n when_o as_o to_o a_o sudden_a apprehension_n it_o will_v sound_v more_o significant_a to_o call_v it_o a_o polar_a plain_n as_o late_a author_n do_v again_o late_a author_n call_v a_o horizontall_a plain_n a_o vertical_a plain_n when_o as_o it_o sound_v more_o significant_a to_o call_v it_o a_o horizontal_n plain_n as_o old_a author_n do_v because_o it_o lie_v flat_a upon_o the_o horizon_n but_o i_o shall_v give_v you_o the_o name_n according_a to_o both_o rule_n and_o leave_v you_o to_o your_o liberty_n to_o accept_v of_o which_o you_o please_v first_o therefore_o you_o have_v a_o equinoctial_a plain_n otherwise_o call_v a_o polar_a plain_n this_o plain_n have_v two_o face_n upper_a and_o under_z these_o two_o face_n lie_v in_o the_o plain_a of_o the_o equinoctial_a the_o upper_a face_n behold_v the_o elevate_v pole_n the_o under_z face_n the_o depress_v pole_n 2._o a_o horizontal_n plain_n otherwise_o call_v a_o vertical_a plain_n it_o lie_v in_o the_o plain_a of_o the_o horizon_n direct_o behold_v the_o zenith_n erect_a plain_n otherwise_o call_v horizontal_n plain_n be_v the_o side_n of_o wall_n and_o these_o be_v of_o seven_o sort_n viz_o 1._o erect_v direct_v vertical_a north_n or_o south_n 2._o erect_v direct_n east_n or_o west_n 3._o erect_v vertical_a decline_a 4._o erect_v incline_v direct_a 5._o erect_v incline_v decline_a 6._o erect_a recline_a direct_a 7._o erect_a recline_a decline_a 3._o erect_v vertical_a north_n or_o south_n direct_v otherwise_o call_v direct_a north_n or_o south_n horizontal_n behold_v the_o north_n or_o south_n direct_o and_o lie_v in_o the_o east_n or_o west_n azimuth_n 4._o erect_v direct_a east_n or_o west_n otherwise_o call_v direct_a east_n or_o west_n equinoctial_o behold_v the_o east_n or_o west_n direct_o and_o lie_v in_o the_o plain_a of_o the_o meridian_n have_v its_o pole_n in_o the_o equinoctial_a 5._o erect_v vertical_a decline_a plain_n otherwise_o call_v decline_a horizontal_n do_v not_o behold_v the_o north_n or_o south_n direct_o but_o swerve_v from_o they_o so_o much_o as_o the_o azimuth_n parallel_n to_o their_o plain_n swerve_v or_o decline_v from_o they_o 6._o erect_v incline_v direct_a plain_n have_v the_o upper_a side_n of_o their_o plain_n incline_v or_o come_v towards_o you_o and_o their_o plain_n do_v exact_o behold_v either_o the_o east_n west_n north_n or_o south_n 7._o erect_a recline_a direct_a plain_n have_v the_o upper_a side_n of_o their_o plain_n recline_v or_o fall_v from_o you_o and_o their_o plain_n exact_o behold_v either_o the_o east_n west_n north_n or_o south_n 8._o eâ—â—ct_n recline_a decline_a or_o erect_v incline_v decline_a plain_n be_v those_o plain_n which_o be_v either_o incline_v or_o recline_v but_o 〈◊〉_d behold_v the_o east_n west_n north_n or_o south_n direct_o but_o 〈◊〉_d or_o decline_v more_o or_o less_o from_o they_o 9_o polar_a plain_n be_v parallel_v to_o the_o axis_n of_o the_o world_n and_o to_o the_o mâ—ridians_n that_n cut_v the_o east_n and_o west_n or_o north_n and_o south_n point_n of_o the_o horizon_n all_o these_o kind_n of_o plain_n have_v two_o face_n the_o one_o behold_v the_o north_n pole_n with_o the_o same_o respect_n that_o the_o other_o behold_v the_o south_n pole_n except_o the_o equinoctial_a plain_n which_o because_o neither_o pole_n be_v elevate_v have_v but_o one_o face_n yet_o that_o one_o contain_v as_o many_o hour_n line_n as_o two_o other_o face_n these_o two_o face_n or_o plain_n will_v receive_v just_a 24._o hour_n line_n foâ—_n the_o 24_o hour-line_n of_o day_n and_o night_n for_o so_o much_o as_o the_o one_o side_n or_o face_n want_v or_o exceed_v 12._o the_o other_o side_n shall_v either_o exceed_v or_o want_v of_o 12._o every_o dyal_n plain_n be_v parallel_n to_o the_o horizon_n of_o some_o country_n or_o other_o in_o the_o world_n therefore_o a_o dyal_n make_v for_o any_o horizon_n in_o the_o world_n may_v be_v set_v to_o such_o a_o position_n that_o it_o will_v show_v you_o the_o hour_n of_o the_o day_n in_o your_o own_o habitation_n at_o least_o for_o so_o long_o as_o the_o sun_n continue_v upon_o that_o planâ—_n all_o plain_n may_v be_v apt_o demonstrate_v by_o the_o globe_n by_o set_v it_o correspondent_a to_o all_o the_o circle_n in_o heaven_n as_o by_o prob._n 2._o of_o the_o second_n b_o ok_n for_o if_o you_o imagine_v the_o globe_n in_o that_o position_n be_v press_v flat_a into_o the_o plain_a of_o any_o circle_n that_o flat_a shall_v represent_v a_o dyal_n plain_a which_o shall_v be_v call_v after_o the_o name_n of_o that_o circle_n it_o be_v press_v into_o thus_o if_o the_o quadrant_n of_o altitude_n be_v apply_v to_o any_o degree_n of_o azimuth_n and_o you_o imagine_v the_o globe_n be_v press_v flat_a to_o the_o edge_n of_o the_o quadrant_n of_o altitude_n so_o much_o as_o that_o azimuth_n decline_v from_o the_o east_n west_n north_n or_o south_n in_o the_o horizon_n so_o much_o shall_v that_o flat_a on_o the_o globe_n be_v say_v to_o decline_v either_o from_o the_o east_n west_n north_n or_o south_n or_o if_o you_o imagine_v the_o globe_n be_v press_v flat_o down_o even_o with_o the_o plain_a of_o the_o horizon_n that_o flat_o shall_v represent_v a_o horizontal_n plain_a because_o as_o be_v say_v before_o the_o plain_n lie_v in_o that_o circle_n call_v the_o horizon_n the_o style_n or_o gnomon_n be_v that_o straight_a wire_n that_o cast_v the_o shadow_n upon_o the_o hour_n of_o the_o day_n it_o be_v always_o place_v parallel_n to_o the_o axis_n of_o the_o world_n there_o be_v several_a way_n to_o find_v the_o situation_n of_o all_o plain_n but_o the_o ready_a and_o speedy_a be_v by_o a_o clinatory_n the_o clinatory_n be_v make_v of_o a_o square_a board_n as_o a_o b_o c_o d_o of_o a_o good_a thickness_n and_o the_o large_a the_o better_o between_o two_o of_o the_o side_n be_v describe_v on_o the_o centre_n a_o a_o quadrant_n as_o e_o f_o divide_v into_o 90_o equal_a part_n or_o degree_n which_o be_v figure_v with_o 10_o 20_o 30_o to_o 90_o and_o then_o back_o again_o with_o the_o compliment_n of_o the_o same_o number_n to_o 90_o between_o the_o limb_n and_o the_o two_o semidiameter_n be_v make_v a_o round_a box_n into_o which_o a_o magnetical_a needle_n be_v fit_v and_o a_o card_n of_o the_o sea_n compass_n divide_v into_o 4_o ninety_n begin_v their_o number_n at_o the_o east_n west_n north_n and_o south_n point_v of_o the_o compass_n from_o which_o point_v the_o opposite_a side_n of_o the_o clinatory_n receive_v their_o name_n of_o east_n west_n north_n or_o south_n upon_o the_o centre_n a_o whereon_o the_o quadrant_n be_v describe_v be_v fasten_v a_o plumb-line_n have_v a_o plumbet_n of_o lead_n or_o brass_n fasten_v to_o the_o end_n of_o it_o which_o plumb-line_n be_v of_o such_o length_n that_o the_o plumbet_n may_v fall_v just_a into_o the_o grove_n g_o h_n below_o the_o quadrant_n which_o be_v for_o that_o purpose_n make_v of_o such_o a_o depth_n that_o the_o plumbet_n may_v ride_v free_o within_o it_o without_o stop_v at_o the_o side_n of_o it_o see_v the_o figure_n annex_v but_o admit_v there_o be_v variation_n have_v by_o prob._n 19_o of_o the_o three_o book_n find_v the_o number_n of_o degree_n of_o this_o variation_n towards_o the_o east_n or_o west_n count_v the_o same_o number_n of_o degree_n from_o the_o north_n point_n in_o the_o card_n either_o to_o the_o eastward_n or_o westward_n and_o note_v the_o degree_n in_o the_o card_n terminate_a at_o that_o number_n for_o that_o degree_n shall_v be_v the_o north_n point_n and_o its_o opposite_a degree_n the_o south_n point_n 90._o degree_n from_o it_o either_o way_n shall_v be_v the_o east_n and_o west_n point_v therefore_o whereas_o before_o you_o be_v direct_v to_o turn_v the_o clinatory_n till_o the_o north_n point_n of_o the_o needle_n point_n to_o the_o flower-de-luce_n on_o the_o â—aid_v you_o mâ—st_v now_o turn_v or_o move_z the_o clinatory_n till_o the_o north_n point_n of_o the_o needle_n â—arg_fw-mi just_a over_o the_o degree_n of_o variation_n thus_o sound_a and_o then_o a_o line_n draw_v as_o aforesaid_a by_o the_o side_n of_o the_o clinatory_a parallel_n to_o the_o needle_n shall_v be_v a_o north_n and_o south_n line_n or_o to_o speak_v more_o proper_o a_o meridional_a line_n you_o may_v fiâ—d_v a_o meridian_n liâ—e_z several_a other_o way_n as_o first_o if_o the_o sun_n shine_v just_a at_o noon_n hold_v up_o a_o plumb-line_n so_o as_o the_o shadow_n of_o it_o may_v fall_v upon_o your_o plain_n and_o
minute_n then_o to_o find_v all_o the_o before_o noon_n hour_n line_n i_o turn_v the_o globe_n east-ward_n till_o the_o index_n point_v to_o 11_o a_o clock_n or_o till_o 15_o degr_n of_o the_o equator_fw-la pass_v through_o the_o meridian_n and_o find_v the_o colour_n cut_v the_o gnomonical_a semicircle_n in_o 15._o 8_o count_v from_o the_o middle_n of_o the_o gnomonical_a semi_a circle_n 10_o 18._o 56_o 9_o 22._o 37_o 8_o 26._o 52_o 7_o 32._o 37_o 6_o 42._o 5_o 5_o 62._o 43_o and_o these_o be_v the_o distance_n of_o the_o before_o noon_n hour_n line_n to_o which_o distance_n you_o may_v set_v prick_n on_o the_o west_n side_n the_o semi_a circle_n of_o the_o plane_n viz._n from_o b_o to_o c._n the_o after_o noon_n hour_n line_n be_v find_v by_o bring_v the_o colour_n again_o to_o the_o meridian_n and_o the_o index_n of_o the_o hour_n circle_n to_o 12._o for_o then_o turn_v the_o globe_n westwaâ—s_v till_o the_o index_n point_v to_o 1_o a_o clock_n or_o till_o 15_o degr_n of_o the_o equator_fw-la pass_v throug_n the_o meridian_n i_o find_v the_o colour_n cut_v the_o gnomon_n semicircle_n in_o 5._o 45_o count_v from_o the_o middle_n of_o the_o gnomon_n semicircle_n 2_o 2._o 54_o 3_o 20._o 52_o 4_o 64._o 36_o have_v draw_v the_o hour-line_n i_o remove_v the_o quadrant_n of_o altitude_n to_o the_o degree_n of_o the_o horizon_n opposite_a to_o the_o degree_n it_o be_v at_o before_o viz._n to_o 30._o degree_n from_o the_o south_n westward_n which_o be_v so_o much_o as_o the_o plane_n decline_v eastward_n but_o i_o let_v the_o gnomonical_a semi_a circle_n stand_v as_o it_o do_v and_o turn_v about_o the_o globe_n till_o the_o colour_n cut_v the_o quadrant_n of_o altitude_n in_o 20._o degree_n count_v from_o the_o horizon_n upward_o viz._n the_o degree_n of_o reclination_n i_o find_v 18._o degree_n 40._o minute_n contain_v between_o the_o middle_n of_o the_o gnomonical_a semi_a circle_n and_o the_o brazen_a meridian_n which_o be_v the_o distance_n of_o the_o substyle_n from_o the_o perpendicular_a and_o i_o find_v the_o gnomonical_a semi_a circle_n cut_v the_o colour_n in_o 13._o degree_n 49._o minute_n from_o the_o pole_n which_o be_v the_o height_n that_o the_o style_n must_v be_v raise_v over_o the_o substyle_n therefore_o i_o prick_v off_o in_o the_o semi_a circle_n on_o the_o plane_n the_o distance_n of_o the_o substyle_n 18._o degree_n 40._o minute_n from_o the_o perpendicular_a westward_n because_o this_o plane_n decline_v eastward_n and_o from_o the_o centre_n a_o i_o draw_v through_o that_o prick_n the_o line_n a_o e_o which_o shall_v be_v the_o substyle_n and_o from_o this_o substyle_n either_o way_n i_o count_v in_o the_o semi_a circle_n on_o the_o plane_n 13_o degree_n 49._o minute_n and_o there_o make_v a_o prick_n then_o from_o the_o centre_n a_o i_o draw_v through_o that_o prick_v the_o line_n a_o f_o to_o represent_v the_o style_n or_o gnomon_n then_o i_o let_v fall_v the_o perpendicule_a f_o g_z upon_o the_o substyle_n a_o g_o so_o be_v a_o triangle_n make_v which_o if_o it_o be_v erect_v perpendicular_o upon_o the_o substyle_n a_o g_o the_o style_n a_o f_o shall_v be_v parallel_n to_o the_o axis_n of_o the_o world_n and_o cast_v a_o shadow_n upon_o the_o hour_n of_o the_o day_n have_v make_v this_o dyal_n you_o have_v make_v four_o several_a dial_n whereof_o this_o be_v one_o and_o his_o opposite_a viz._n north_n decline_a westward_n 30._o degree_n incline_v to_o the_o horizon_n 70._o degree_n be_v another_o the_o south_n decline_a westward_n 30._o degree_n recline_v from_o the_o zenith_n 20._o degree_n be_v another_o and_o his_o opposite_a viz._n north_n decline_a eastward_n 30._o degree_n incline_v to_o the_o horizon_n 70._o degree_n be_v the_o other_o prob._n xiii_o to_o make_v a_o dyal_n upon_o a_o decline_a incline_v plane_n the_o precept_n for_o make_v these_o dial_n be_v deliver_v in_o the_o forego_n problem_n therefore_o we_o shall_v at_o first_o come_v to_o a_o example_n i_o will_v make_v a_o dyal_n upon_o a_o plane_n in_o london_n latitude_n decline_a from_o the_o south_n westward_n 25._o degree_n and_o incline_v towards_o the_o horizon_n by_o the_o space_n of_o a_o arch_n contain_v 14._o degree_n have_v first_o describe_v on_o the_o plane_n a_o semi_a circle_n as_o be_v direct_v prob._n 4._o i_o rectify_v the_o globe_n quadrant_n of_o altitude_n colour_n and_o hour_n index_n as_o by_o the_o same_o problem_n and_o bring_v the_o low_a end_n of_o the_o quadrant_n of_o altitude_n to_o the_o degree_n of_o the_o plane_n declination_n viz._n to_o 25._o degree_n count_v from_o the_o south_n westward_n and_o the_o end_n of_o the_o gnomonical_a semi_a circle_n to_o the_o degree_n of_o azimuth_n the_o plane_n lie_v in_o viz._n to_o 25._o degree_n from_o the_o west_n northwards_o and_o the_o middle_n of_o the_o gnomonical_a semi_a circle_n to_o the_o degree_n of_o the_o plane_n inclination_n viz._n 14._o degree_n count_v from_o the_o zenith_n downward_o on_o the_o quadrant_n of_o altitude_n then_o count_v the_o degree_n of_o the_o gnomonical_a semi_a circle_n contain_v between_o the_o middle_n of_o the_o same_o and_o the_o brazen_a meridian_n i_o find_v 5._o degree_n 30._o minute_n these_o 5._o degree_n 30._o minute_n show_v the_o distance_n of_o the_o 12_o a_o clock_n line_n from_o the_o perpendicular_a therefore_o i_o number_n in_o the_o semi_a circle_n describe_v on_o the_o plane_n from_o the_o perpendicular_a westward_n because_o the_o middle_n of_o the_o gnomonical_a semi_a circle_n lie_v westward_n on_o the_o globe_n from_o the_o meridian_n and_o for_o find_v all_o the_o forenoon_n hour-distance_n i_o turn_v the_o globe_n east-ward_n till_o the_o index_n point_v to_o 11_o a_o clock_n or_o till_o 15_o degr_n of_o the_o equa_fw-la pass_v throug_n the_o meridian_n and_o find_v the_o colour_n cut_v the_o gnomon_n semicircle_n in_o 20._o 5_o count_v from_o the_o middle_n of_o the_o gnomon_n semicircle_n 10_o 36._o 57_o 9_o 56._o 24_o 8_o 76._o 31_o and_o these_o be_v the_o distance_n of_o all_o the_o before_o noon_n hour_n line_n to_o which_o several_a distance_n i_o make_v prick_n on_o the_o west_n side_n the_o semi_a circle_n on_o the_o plane_n viz._n from_o b_o to_o c._n the_o after_o noon_n hour_n line_n be_v find_v by_o bring_v the_o colour_n again_o to_o the_o meridian_n and_o the_o index_n of_o the_o hour_n circle_n to_o 12._o for_o then_o turn_v the_o globe_n westward_n till_o the_o index_n point_v to_o 1_o a_o clock_n or_o till_o 15._o degree_n of_o the_o equator_fw-la pass_v through_o the_o meridian_n i_o find_v the_o colour_n cut_v the_o gnomonical_a semicircle_n in_o 6._o 20_o count_v from_o the_o middle_n of_o the_o gnomonical_a semi_a circle_n 2_o 18._o 2_o 3_o 28._o 45_o 4_o 39_o 56_o 5_o 52._o 30_o 6_o 67._o 19_o 7_o 84._o 13_o and_o these_o be_v the_o distance_n of_o the_o after_o noon_n hour_n line_n which_o i_o also_o prick_v down_o at_o their_o respective_a distance_n from_o the_o perpendicular_a eastward_n viz._n from_o b_o towards_z d_o on_o the_o plane_n and_o by_o draw_v line_n from_o the_o centre_n a_o through_o all_o the_o prick_n i_o have_v all_o the_o hour_n line_n that_o this_o plane_n will_v admit_v of_o have_v make_v this_o dyal_n you_o have_v also_o four_o dial_n made_n as_o well_o as_o in_o the_o former_a problem_n for_o this_o be_v one_o and_o its_o opposite_a viz._n north_n decline_v eastward_n 25._o degree_n recline_v 76._o degree_n be_v another_o the_o south_n decline_v eastward_n 25._o degree_n incline_v 14_o degree_n be_v another_o and_o its_o opposite_a viz._n north_n decline_v westward_n 25._o degree_n recline_v 76._o degree_n be_v another_o prob._n fourteen_o to_o find_v in_o what_o place_n of_o the_o earth_n any_o manner_n of_o plane_n that_o in_o your_o habitation_n be_v not_o horizontal_n shall_v be_v horizontal_n it_o be_v say_v in_o the_o preface_n that_o all_o manner_n of_o planes_n however_o situate_a be_v parallel_v to_o some_o country_n or_o other_o on_o the_o earth_n therefore_o all_o manner_n of_o planes_n be_v indeed_o horizontal_n planes_n and_o the_o distance_n of_o the_o hour_n line_n to_o be_v â—â—scribed_v on_o they_o may_v be_v find_v as_o the_o distance_n of_o the_o hour_n line_n of_o the_o horizontal_n dyal_n in_o prob._n 3._o it_o rest_v now_o to_o learn_v in_o what_o place_n of_o the_o earth_n any_o plane_n that_o be_v not_o horizontal_n in_o your_o habitation_n shall_v become_v horizontal_n and_o for_o help_v of_o your_o understanding_n herein_o take_v these_o follow_a rule_n 1._o if_o your_o plane_n be_v erect_a direct_a north_n or_o south_n it_o shall_v be_v a_o horizontal_n in_o the_o same_o longitude_n at_o 90._o degree_n distance_n on_o the_o meridian_n count_v from_o the_o zenith_n of_o your_o place_n through_o the_o equinoctial_a see_v a_o example_n of_o this_o