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 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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 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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
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 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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 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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 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through_o 40_o 50_o yea_o 60._o degree_n of_o the_o horizon_n in_o one_o hour_n time_n viz_o while_o 15._o degree_n of_o the_o equator_fw-la pass_v through_o the_o meridian_n but_o in_o a_o other_o hour_n time_n you_o will_v scarce_o have_v 4_o or_o 5_o degree_n pass_v through_o the_o horizon_n while_o 15_o degree_n of_o the_o equator_fw-la pass_v through_o the_o meridian_n but_o that_o you_o may_v know_v the_o motion_n of_o the_o sun_n represent_v by_o this_o meridian_n line_n through_o the_o horizon_n in_o all_o latitude_n elevate_v the_o pole_n to_o the_o elevation_n of_o your_o place_n and_o choose_v instead_o of_o a_o meridian_n line_v draw_v through_o the_o place_n of_o the_o sun_n the_o vernal_a colour_n to_o be_v your_o meridian_n line_n both_o because_o it_o be_v most_o visible_a and_o because_o from_o thence_o the_o degree_n of_o the_o equator_fw-la be_v begin_v to_o
respect_n of_o warp_a and_o shrink_v i_o have_v have_v few_o globe_n come_v to_o mend_v that_o have_v not_o have_v either_o break_a orison_n or_o some_o other_o notorious_a fault_n occasion_v through_o the_o sleightness_n of_o the_o orison_n in_o the_o use_v the_o globe_n keep_v the_o east_n side_n of_o the_o horizon_n always_o towards_o you_o unless_o your_o proposition_n require_v the_o turn_n of_o it_o which_o east_n side_n you_o may_v know_v by_o the_o word_n east_n place_v on_o the_o outmost_a verge_n thereof_o for_o then_o have_v you_o the_o graduated_a side_n of_o the_o meridian_n always_o towards_o you_o the_o quadrant_n of_o altitude_n before_o you_o and_o the_o globe_n divide_v exact_o into_o two_o equal_a part_n so_o oft_o as_o i_o name_n to_o at_z of_o or_o under_o the_o meridian_n or_o horizon_n i_o mean_v the_o east_n side_n of_o the_o meridian_n and_o superficies_n of_o the_o horizon_n because_o the_o east_n side_n of_o the_o meridian_n pass_v through_o the_o north_n and_o south_n point_n both_o of_o the_o globe_n and_o horizon_n and_o agree_v just_a with_o the_o middle_n of_o the_o axis_n and_o the_o superficies_n of_o the_o horizon_n divide_v the_o globe_n exact_o into_o two_o equal_a part_n it_o you_o happen_v to_o use_v the_o globe_n on_o the_o south_n side_n the_o equator_fw-la you_o must_v draw_v the_o wire_n out_o of_o either_o pole_n and_o change_v they_o to_o the_o contrary_a pole_n put_v the_o long_a wire_n into_o the_o south_n pole_n and_o because_o on_o the_o other_o side_n the_o equator_fw-la the_o south_n pole_n be_v elevate_v therefore_o you_o must_v elevate_v the_o south_n pole_n of_o the_o globe_n above_o the_o horizon_n according_a to_o the_o south_n latitude_n of_o your_o place_n as_o shall_v be_v show_v hereafter_o in_o the_o work_a some_o problem_n it_o will_v be_v require_v that_o you_o turn_v the_o globe_n to_o look_v on_o the_o west_n side_n thereof_o which_o turn_v will_v be_v apt_a to_o jog_v the_o ball_n so_o as_o the_o degree_n that_o be_v at_o the_o horizon_n or_o meridian_n will_v be_v move_v away_o and_o thereby_o the_o position_n of_o the_o globe_n alter_v to_o avoid_v which_o inconvenince_n you_o may_v make_v use_n of_o a_o quill_n thrust_v the_o feather_n end_n between_o the_o ball_n and_o the_o brazen_a meridian_n and_o so_o wedge_n it_o up_o without_o wrong_v the_o globe_n at_o all_o till_o your_o proposition_n be_v answer_v problem_n i._n to_o find_v the_o longitude_n and_o latitude_n of_o place_n on_o the_o terrestrial_a globe_n seek_v the_o place_n on_o the_o terrestrial_a globe_n who_o longitude_n and_o latitude_n you_o will_v know_v and_o bring_v that_o place_n to_o the_o brazen_a meridian_n and_o see_v how_o many_o degree_n of_o the_o equator_fw-la be_v cut_v by_o the_o meridian_n from_o the_o first_o general_a meridian_n which_o on_o my_o globe_n pass_v through_o gratiosa_fw-la one_o of_o the_o isle_n of_o the_o azore_n for_o that_o number_n of_o degree_n be_v the_o longitude_n of_o the_o place_n example_n i_o desire_v to_o know_v the_o longitude_n of_o london_n and_o close_o to_o the_o name_n london_n i_o find_v a_o small_a mark_n 0_o thus_o which_o small_a mark_n be_v in_o some_o globe_n and_o map_n adorn_v with_o the_o picture_n of_o a_o steeple_n etc._n etc._n therefore_o i_o do_v not_o bring_v the_o word_n london_n to_o the_o meridian_n but_o that_o small_a mark_n for_o that_o always_o represent_v the_o the_o town_n or_o city_n seek_v for_o and_o keep_v the_o globe_n steady_a in_o this_o position_n i_o examine_v how_o many_o degree_n of_o the_o equator_fw-la be_v contain_v between_o the_o brazen_a meridian_n and_o the_o first_o general_a meridian_n which_o i_o find_v to_o be_v 24._o deg_n 00._o min._n therefore_o i_o say_v the_o longitude_n of_o london_n be_v 24._o degree_n 00._o min._n for_o the_o latitude_n see_v on_o the_o brazen_a meridian_n how_o many_o degree_n be_v contain_v between_o the_o equator_fw-la and_o the_o mark_n for_o london_n which_o in_o this_o example_n be_v 51½_n therefore_o i_o say_v london_n have_v 51½_n degree_n north_n latitude_n problem_n ii_o the_o longitude_n and_o latitude_n be_v know_v to_o rectify_v the_o globe_n fit_a for_o use_v 1._o when_o you_o rectify_v the_o globe_n to_o any_o particular_a latitude_n you_o must_v move_v the_o brazen_a meridian_n through_o the_o notch_n of_o the_o horizon_n till_o the_o same_o number_n of_o degree_n account_v on_o the_o meridian_n from_o the_o pole_n about_o which_o the_o hour-circle_n be_v towards_o the_o north_n point_n in_o the_o horizon_n if_o in_o north_n latitude_n and_o towards_o the_o south_n if_o in_o south_n latitude_n come_v just_a to_o the_o edge_n of_o the_o horizon_n example_n by_o the_o former_a proposition_n i_o find_v the_o latitude_n of_o london_n to_o be_v 51½_n degree_n north_n latitude_n therefore_o i_o count_v 51½_n degree_n from_o the_o pole_n downward_o towards_o my_o right_a hand_n and_o turn_v the_o meridian_n through_o the_o notch_n of_o the_o horizon_n till_o those_o 51½_n degree_n come_v exact_o to_o the_o uppermost_a edge_n of_o the_o north_n point_n in_o the_o horizon_n and_o then_o be_v the_o meridian_n rectify_v to_o the_o latitude_n of_o london_n 2._o next_o rectify_v the_o quadrant_n of_o altitude_n after_o this_o manner_n screw_v the_o edge_n of_o the_o nut_n that_o be_v even_o with_o the_o graduated_a edge_n of_o the_o thin_a plate_n to_o 51½_n degree_n of_o the_o brazen_a meridian_n account_v from_o the_o equinoctial_a on_o the_o southern_a side_n the_o horizon_n which_o be_v just_a the_o zenith_n of_o london_n and_o then_o be_v your_o quadrant_n rectify_v 3._o bring_v the_o degree_n of_o the_o ecliptic_a the_o sun_n be_v in_o that_o day_n to_o the_o meridian_n which_o you_o shall_v learn_v to_o know_v by_o the_o next_o problem_n and_o then_o turn_v the_o index_n of_o the_o hour_n circle_n to_o the_o hour_n 12._o on_o the_o south_n side_n the_o hour_n circle_n and_o then_o be_v your_o hour_n circle_n also_o rectify_v fit_a to_o use_v for_o that_o day_n 4._o last_o if_o you_o will_v rectify_v the_o globe_n to_o correspond_v in_o all_o respect_n with_o the_o position_n and_o situation_n of_o the_o sphere_n you_o must_v set_v the_o four_o quarter_n of_o the_o horizon_n viz._n east_n west_n north_n and_o south_n agreeable_a with_o the_o four_o quarter_n of_o the_o world_n which_o you_o may_v do_v by_o the_o needle_n in_o the_o bottom_n of_o the_o horizon_n for_o you_o must_v turn_v the_o globe_n so_o long_o till_o the_o needle_n point_fw-fr just_a to_o the_o flower_n de_fw-fr luce_fw-fr next_o you_o must_v set_v the_o plain_a of_o the_o wooden_a horizon_n parallel_v to_o the_o horizon_n of_o the_o world_n which_o you_o may_v try_v by_o set_v a_o common_a level_n on_o the_o four_o quatre_n of_o the_o horizon_n and_o then_o posit_v the_o degree_n of_o the_o ecliptic_a the_o sun_n be_v in_o to_o the_o height_n above_o or_o depth_n below_o the_o horizon_n the_o sun_n have_v in_o heaven_n as_o by_o the_o 11_o problem_n your_o globe_n be_v make_v correspondent_a in_o all_o point_n with_o the_o frame_n of_o the_o sphere_n for_o that_o particular_a time_n and_o latitude_n problem_n iii_o to_o find_v the_o place_n of_o the_o sun_n in_o the_o ecliptic_a the_o day_n of_o the_o month_n be_v first_o know_v seek_v the_o day_n of_o the_o month_n in_o the_o circle_n of_o month_n upon_o the_o horizon_n and_o right_a against_o it_o in_o the_o circle_n of_o sign_n be_v the_o degree_n of_o the_o ecliptic_a the_o sun_n be_v in_o example_n imagine_v the_o day_n to_o be_v give_v be_v may_v 10._o therefore_o i_o seek_v on_o the_o horizon_n in_o the_o circle_n of_o month_n for_o may_v and_o find_v the_o month_n divide_v into_o so_o many_o part_n as_o there_o be_v day_n in_o the_o month_n which_o part_n be_v mark_v with_o arithmetical_a figure_n from_o the_o begin_n of_o the_o month_n to_o the_o end_n and_o denote_v the_o number_n of_o the_o day_n of_o the_o month_n that_o each_o division_n represent_v therefore_o among_o the_o division_n i_o seek_v for_o 10_o and_o direct_o against_o it_o in_o the_o circle_n of_o sign_n i_o find_v ♉_o 29._o degree_n therefore_o i_o say_v may_v 10._o the_o sun_n place_n be_v in_o 29._o degree_n of_o ♉_o but_o note_n that_o if_o it_o be_v leap_v year_n instead_o of_o the_o 10._o of_o may_v you_o must_v take_v the_o 11._o of_o may_n because_o february_n have_v in_o a_o leap_v year_n 29._o day_n the_o 29._o of_o february_n must_v be_v reckon_v for_o the_o first_o of_o march_n and_o the_o first_o of_o march_n for_o the_o second_o of_o march_n the_o second_o of_o march_n for_o the_o three_o of_o march_n and_o so_o throughout_o the_o year_n the_o leap_v year_n be_v cause_v by_o the_o six_o odd_a hour_n more_o than_o 365._o day_n that_o be_v assign_v to_o
quadrant_n of_o altitude_n the_o same_o degree_n on_o it_o will_v lie_v on_o both_o the_o star_n so_o shall_v the_o index_n of_o the_o hour-circle_n point_n at_o the_o hour_n of_o the_o night_n prob._n xli_o the_o hour_n give_v that_o any_o star_n in_o heaven_n come_v to_o the_o meridian_n to_o know_v thereby_o the_o place_n of_o the_o sun_n and_o by_o consequence_n the_o day_n of_o the_o month_n though_o it_o be_v lose_v bring_v the_o star_n propose_v to_o the_o meridian_n and_o turn_v the_o index_n of_o the_o hour-circle_n to_o the_o hour_n give_v then_o turn_v about_o the_o globe_n till_o the_o index_n point_n at_o the_o hour_n of_o 12_o for_o noon_n and_o the_o place_n of_o the_o sun_n in_o the_o ecliptic_a shall_v be_v cut_v by_o the_o meridian_n example_n march_n 7._o at_o 11_o aclock_o at_o night_n the_o pointer_n come_v to_o the_o meridian_n of_o london_n therefore_o i_o place_v the_o pointer_n on_o the_o celestial_a globe_n under_o the_o meridian_n and_o turn_v the_o index_n of_o the_o hour-circle_n to_o 11._o past_a noon_n afterward_o i_o turn_v back_o the_o globe_n till_o the_o index_n point_n to_o 12._o at_o noon_n then_o look_v in_o the_o ecliptic_a i_o find_v the_o meridian_n cut_v it_o in_o ♓_o 26._o 45._o minute_n therefore_o i_o say_v when_o the_o pointer_n come_v to_o the_o meridian_n at_o 11._o a_o clock_n at_o night_n the_o place_n of_o the_o sun_n be_v ♓_o 26._o 45._o have_v thus_o the_o place_n of_o the_o sun_n i_o may_v find_v the_o day_n of_o the_o month_n by_o the_o four_o problem_n and_o so_o either_o know_v the_o day_n that_o the_o pointer_n come_v to_o the_o meridian_n at_o 11._o a_o clock_n at_o night_n or_o at_o any_o other_o hour_n give_v the_o day_n of_o the_o month_n may_v also_o be_v find_v by_o the_o declination_n and_o the_o quarter_n of_o the_o ecliptic_a the_o sun_n be_v in_o give_v for_o the_o meridian_n will_v cut_v the_o degree_n of_o the_o sun_n place_n in_o the_o ecliptic_a in_o the_o parallel_n of_o declination_n so_o that_o have_v respect_n to_o the_o quarter_n of_o the_o ecliptic_a you_o will_v find_v the_o sun_n place_n and_o have_v the_o sun_n place_n you_o may_v as_o aforesaid_a find_v the_o day_n of_o the_o month_n prob._n xlii_o the_o day_n of_o the_o month_n give_v to_o find_v in_o the_o circle_n of_o letter_n on_o the_o plain_a of_o the_o horizon_n the_o day_n of_o the_o week_n the_o seven_o day_n of_o the_o week_n be_v by_o the_o idolatry_n of_o the_o ancient_a roman_a heathenish_a time_n dedicate_v to_o the_o honour_n of_o seven_o of_o their_o god_n which_o we_o call_v planet_n the_o first_o be_v the_o most_o eminent_a and_o therefore_o doubtless_o by_o they_o set_v in_o the_o first_o place_n call_v dia_n solis_n or_o the_o sun_n day_n the_o second_o dia_n luna_n the_o moon_n day_n the_o three_o dia_n martis_n the_o day_n of_o mars_n by_o we_o call_v tuesday_n the_o four_o dia_n mercurius_n mercury_n day_n by_o we_o call_v wednesday_n from_o woden_n a_o idol_n the_o saxon_n worship_v to_o who_o honour_n they_o dedicate_v that_o day_n and_o be_v by_o all_o those_o german_a nation_n still_o call_v wodensdagh_n the_o five_o dia_n jovis_n jupiter_n or_o jove_n day_n which_o doubtless_o the_o saxon_n from_o who_o probable_o we_o receive_v it_o call_v donderdagh_a because_o jupiter_n be_v the_o god_n of_o thunder_n and_o we_o either_o by_o corruption_n or_o for_o shortness_n or_o both_o call_v it_o thursday_n the_o six_o dia_n veneris_n the_o day_n of_o venus_n but_o the_o saxon_n transfer_v her_o honour_n to_o another_o of_o their_o goddess_n name_v fria_fw-la call_v it_o fridagh_o and_o we_o from_o they_o call_v it_o friday_n the_o seven_o be_v dia_n saturnis_n satyrus_n day_n the_o same_o day_n of_o the_o month_n in_o other_o year_n happen_v not_o on_o the_o same_o day_n of_o the_o week_n therefore_o the_o dominical_a letter_n for_o one_o year_n be_v not_o the_o same_o it_o be_v the_o next_o now_o because_o you_o can_v come_v to_o the_o knowledge_n of_o the_o day_n of_o the_o week_n unless_o you_o first_o know_v the_o sunday_n letter_n therefore_o have_v i_o in_o prob._n 5â—_n insert_v a_o table_n of_o m_o r_o palmer_n by_o which_o you_o may_v find_v the_o dominical_a or_o sunday_n letter_n for_o ever_o and_o have_v the_o dominical_a letter_n you_o may_v in_o the_o circle_n of_o letter_n on_o the_o horizon_n find_v it_o near_o the_o day_n of_o that_o month_n and_o count_v that_o for_o sunday_n the_o next_o under_o it_o for_o monday_n the_o next_o under_o that_o for_o tuesday_n and_o so_o in_o order_n till_o you_o come_v to_o the_o day_n of_o the_o month_n example_n i_o will_v know_v what_o day_n of_o the_o week_n june_n 1._o anno_fw-la 1658._o old_a style_n fall_v on_o i_o find_v by_o the_o table_n aforesaid_a the_o dominical_a letter_n be_v c_o then_z i_o look_v in_o the_o calendar_n of_o old_a style_n for_o june_n 1._o and_o against_o it_o i_o find_v letter_n e_o which_o because_o it_o be_v the_o second_o letter_n in_o order_n from_o c_o therefore_o it_o be_v the_o second_o day_n in_o order_n from_o sunday_n which_o be_v tuesday_n prob._n xliii_o the_o azimuth_n of_o any_o star_n give_v to_o find_v its_o hour_n in_o any_o give_a latitude_n the_o hour_n of_o a_o star_n be_v the_o number_n of_o hour_n that_o a_o star_n be_v distant_a from_o the_o meridian_n to_o find_v which_o rectify_v the_o globe_n and_o quadrant_n of_o altitude_n and_o bring_v the_o star_n propose_v 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 place_v the_o low_a end_n of_o the_o quadrant_n of_o altitude_n to_o the_o give_v azimuth_n in_o the_o horizon_n and_o turn_v the_o globe_n till_o the_o star_n come_v to_o the_o graduated_a edge_n of_o the_o quadrant_n of_o altitude_n so_o shall_v the_o index_n of_o the_o hour-circle_n point_n at_o the_o hour_n of_o the_o star_n only_o this_o caution_n you_o must_v take_v if_o the_o star_n be_v turn_v from_o the_o meridian_n towards_o the_o eastern_a side_n of_o the_o horizon_n you_o must_v subtract_v the_o number_n of_o hour_n the_o index_n point_v at_o from_o 12._o and_o the_o remainder_n shall_v be_v the_o hour_n of_o the_o star_n but_o if_o the_o star_n be_v turn_v from_o the_o meridian_n towards_o the_o west_n side_n the_o horizon_n the_o hour_n the_o index_n point_v at_o be_v without_o more_o ado_n the_o hour_n of_o the_o star_n prob._n xliv_o how_o you_o may_v learn_v to_o know_v all_o the_o star_n in_o heaven_n by_o the_o celestial_a globe_n rectify_v the_o globe_n quadrant_n hour-index_n and_o horizon_n as_o by_o prob._n 2._o then_o turn_v about_o the_o globe_n till_o the_o index_n of_o the_o hour-circle_n point_n at_o the_o hour_n of_o the_o night_n on_o the_o hour-circle_n then_o if_o every_o star_n on_o the_o globe_n have_v a_o hole_n in_o the_o midst_n and_o your_o ey_fw-mi be_v place_v in_o the_o centre_n of_o the_o globe_n you_o may_v by_o keep_v your_o ey_fw-mi in_o the_o centre_n and_o look_v through_o any_o star_n on_o the_o globe_n see_v its_o maâ—ch_n in_o heaven_n that_o be_v the_o same_o star_n in_o heaven_n which_o that_o star_n on_o the_o globe_n represent_v for_o from_o the_o centre_n of_o the_o globe_n there_o proceed_v a_o straight_a line_n through_o the_o star_n on_o the_o globe_n even_o to_o the_o same_o star_n in_o heaven_n therefore_o those_o star_n that_o be_v in_o the_o zenith_n in_o heaven_n will_v then_o be_v in_o the_o zenith_n on_o the_o globe_n those_o that_o be_v in_o the_o east_n in_o heaven_n will_v be_v in_o the_o east_n on_o the_o globe_n those_o in_o the_o west_n in_o heaven_n in_o the_o west_n on_o the_o globe_n and_o those_o star_n that_o be_v in_o any_o altitude_n in_o heaven_n will_v at_o the_o same_o time_n have_v the_o same_o altitude_n on_o the_o globe_n so_o that_o if_o you_o see_v any_o star_n in_o heaven_n who_o name_n you_o desire_v to_o know_v you_o need_v but_o observe_v its_o azimuth_n and_o altitude_n and_o in_o the_o same_o azimuth_n and_o altitude_n on_o the_o globe_n you_o may_v find_v the_o same_o star_n and_o if_o it_o be_v a_o eminent_a star_n you_o will_v find_v its_o name_n adjoin_v to_o it_o example_n december_n 10._o at_o half_a a_o hour_n past_o 9_o a_o clock_n at_o night_n here_o at_o london_n i_o see_v two_o bright_a star_n at_o a_o pretty_a distance_n one_o from_o another_o in_o the_o south_n i_o desire_v to_o know_v the_o name_n of_o they_o therefore_o have_v the_o globe_n rectify_v to_o the_o latitude_n of_o london_n and_o the_o quadrant_n of_o altitude_n screw_v to_o the_o zenith_n the_o hour-index_n also_o rectify_v and_o the_o horizon_n posit_v horizontal_o as_o by_o prob._n 2._o i_o observe_v the_o altitude_n of_o those_o star_n in_o
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
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 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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
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 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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 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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 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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
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