plain_n the_o top_n of_o this_o radius_fw-la in_o the_o gnomon_n be_v call_v nodus_fw-la because_o you_o must_v there_o set_v a_o knot_n bede_n or_o button_n to_o give_v shade_n or_o else_o cut_v there_o a_o notch_n in_o the_o gnomon_n or_o cut_v off_o the_o gnomon_n in_o the_o place_n of_o nodus_fw-la that_o the_o end_n may_v give_v the_o shadow_n for_o those_o lineament_n let_v not_o your_o nodus_fw-la stand_v too_o high_a above_o the_o plain_a for_o then_o the_o shadow_n will_v fall_v beside_o your_o plain_n for_o too_o great_a a_o part_n of_o the_o plain_n day_n nor_o let_v it_o stand_v too_o low_a for_o then_o the_o lineament_n will_v run_v too_o close_o together_o a_o mean_a must_v be_v choose_v at_o the_o foot_n of_o this_o radius_fw-la take_v your_o centre_n and_o describe_v a_o circle_n on_o the_o plain_a and_o divide_v it_o into_o equal_a degree_n and_o from_o the_o centre_n draw_v line_n through_o those_o degree_n infinite_o that_o be_v so_o far_o as_o your_o dyal-plain_a will_v bear_v these_o line_n shall_v be_v the_o azimuth_n of_o the_o horizon_n of_o the_o plain_a and_o shall_v be_v number_v from_o his_o meridian_n or_o sub_n style_n and_o to_o divide_v the_o say_a azimuth_n line_n you_o use_v the_o table_n of_o tangent_n with_o a_o scale_n of_o equal_a part_n or_o else_o plot_v the_o tangent_n thus_o on_o paper_n set_z a_o b_o equal_a to_o the_o radius_fw-la of_o your_o horizon_n and_o with_o that_o radius_fw-la draw_v the_o quadrant_n a_o b_o c_o or_o a_o b_o c_o and_o divide_v the_o quadrant_n number_v the_o degree_n from_o c_o to_o b_o and_o have_v draw_v the_o tangent_fw-la b_o d_o or_o b_o d_o parallel_n to_o a_o c_o draw_z line_n from_o the_o centre_n through_o the_o several_a degree_n to_o the_o say_a tangent-line_n so_o shall_v this_o tangent-line_n be_v divide_v for_o your_o purpose_n and_o from_o it_o you_o may_v transfer_v the_o division_n to_o your_o plain_n now_o if_o your_o plain_a lie_n in_o the_o horizon_n of_o your_o place_n as_o the_o vertical_a plain_n do_v these_o azimuth_n and_o almicantars_n may_v be_v of_o some_o use_n to_o show_v you_o the_o altitude_n and_o azimuth_n of_o the_o sun_n for_o any_o time_n see_v they_o in_o the_o scheam_n chapter_n 30._o but_o if_o your_o plain_n lie_v not_o in_o the_o horizon_n of_o your_o place_n than_o you_o shall_v draw_v the_o say_v almicantars_n or_o azimuth_n or_o so_o many_o of_o they_o as_o you_o shall_v need_v in_o deleble_a line_n because_o here_o they_o serve_v only_o the_o horizon_n of_o the_o plain_a yet_o shall_v they_o help_v you_o to_o describe_v the_o equator_fw-la and_o his_o parallel_n with_o the_o horizon_n of_o your_o place_n in_o any_o dyal_n and_o when_o they_o have_v do_v this_o unless_o your_o dyal_n be_v vertical_a they_o may_v be_v go_v chap._n xxviii_o how_o by_o help_n of_o the_o proper_a azimuth_n and_o almicantars_n of_o the_o plain_a to_o describe_v the_o equator_fw-la and_o his_o parallel_n on_o the_o polar_a or_o orthognomonical_a dyal_n it_o shall_v suffice_v here_o to_o show_v how_o the_o parallel_n of_o the_o sign_n may_v be_v describe_v because_o the_o parallel_n of_o declination_n and_o of_o the_o length_n of_o the_o day_n be_v describe_v by_o like_a reason_n and_o know_v that_o in_o the_o polar_a plain_n because_o the_o gnomon_n be_v perpendicular_a to_o the_o plain_a the_o same_o gnomon_n shall_v serve_v both_o hour_n and_o azimuth_n for_o the_o hour-line_n be_v azimuth_n in_o this_o plain_a note_v also_o that_o the_o sun_n be_v never_o elevate_v above_o this_o plain_a more_o than_o he_o decline_v from_o the_o equator_fw-la which_o at_o the_o most_o be_v 23_o ½_n degree_n and_o that_o if_o the_o height_n of_o nodus_fw-la be_v above_o a_o six_o part_n of_o the_o semidiameter_n of_o the_o plain_a the_o ten_o first_o almicantars_n will_n fall_v beside_o the_o plain_a a_o six_o part_n therefore_o must_v serve_v and_o that_o will_v give_v you_o all_o the_o altitude_n above_o to_o degree_n and_o the_o parallel_n of_o the_o sign_n who_o declination_n be_v more_o than_o 10._o describe_v therefore_o the_o almicantars_n here_o as_o you_o be_v teach_v chapter_n 27._o for_o in_o the_o hour_n line_n you_o have_v already_o every_o 15_o azimuth_n and_o may_v draw_v more_o if_o you_o please_v chap._n xxix_o how_o to_o inscribe_v the_o equator_fw-la and_o his_o parallel_n in_o the_o equinoctial_a or_o parallelognomonical_a dyal_n if_o this_o plain_a decline_v not_o the_o hour_n line_n of_o your_o country_n will_v serve_v you_o for_o they_o be_v also_o the_o hour_n line_n of_o the_o plain_a and_o the_o noon-line_n be_v sub_n style_n if_o it_o do_v decline_v you_o shall_v draw_v in_o deleble_a line_n the_o proper_a dyal_n of_o the_o plain_a by_o chapter_n 23._o which_o decline_v not_o and_o have_v here_o the_o azimuth_n or_o almicantars_n of_o the_o plain_a draw_v by_o chapter_n 27._o you_o shall_v observe_v upon_o your_o planisphear_n at_o what_o altitude_n or_o at_o what_o azimuth_n the_o parallel_n cut_v the_o several_a hour_n line_n and_o where_o the_o like_a altitude_n or_o azimuth_n cut_v the_o same_o hour_n line_n upon_o the_o plain_a you_o shall_v make_v mark_n and_o through_o those_o mark_n draw_v the_o parallel_n which_o shall_v be_v all_o conical_a section_n except_o the_o equator_fw-la which_o because_o he_o be_v a_o great_a circle_n shall_v be_v a_o straight_a line_n on_o those_o plain_n and_o in_o all_o other_o plain_n except_o the_o polar_a where_o he_o be_v a_o circle_n in_o the_o equator_fw-la the_o azimuth_n be_v always_o the_o same_o full_a east_n or_o west_n and_o so_o upon_o your_o plain_n he_o must_v needs_o be_v a_o straight_a line_n the_o altitude_n in_o the_o equator_fw-la be_v 15_o 30_o 45_o 60_o 75_o 90._o the_o hour_n alike_o distant_a from_o the_o meridian_n on_o both_o side_n be_v alike_o and_o so_o be_v the_o parallel_n alike_o distant_a from_o the_o equator_fw-la alike_o also_o when_o you_o have_v therefore_o gather_v a_o table_n out_o of_o your_o planisphear_n for_o the_o morning_n hour_n of_o the_o north_n parallel_n and_o of_o the_o equator_fw-la as_o i_o have_v do_v here_o in_o haste_n for_o the_o equator_fw-la and_o tropic_n of_o cancer_n you_o may_v by_o that_o table_n prick_v down_o the_o parallel_n upon_o one_o quarter_n of_o your_o dyal_n and_o by_o that_o also_o draw_v the_o rest_n for_o as_o you_o may_v see_v upon_o your_o planisphear_n all_o the_o 4._o quarter_n be_v alike_o note_v that_o the_o azimuth_n cut_v the_o hour_n line_n too_o oblique_o it_o be_v best_a therefore_o to_o trust_v to_o the_o almicantars_n and_o so_o shall_v you_o have_v easy_a and_o sure_a work_n though_o you_o meddle_v not_o with_o the_o azimuth_n at_o all_o chap._n xxx_o how_o to_o inscribe_v the_o equator_fw-la and_o his_o parallel_n in_o a_o oblique_a or_o scalenognomonical_a dyal_n if_o the_o plain_a neither_o decline_v nor_o recline_v and_o so_o be_v a_o vertical_a plain_n the_o hour_n line_n of_o your_o place_n will_v serve_v you_o for_o they_o be_v also_o the_o hour_n line_n of_o the_o plain_a and_o the_o noon_n line_n be_v the_o sub-style_n if_o it_o either_o decline_v or_o recline_v or_o both_o decline_v and_o recline_v you_o shall_v draw_v in_o deleble_a line_n the_o proper_a dyal_n of_o the_o plain_a by_o chapter_n 23._o and_o so_o this_o dyal_n shall_v be_v reduce_v to_o a_o vertical_a dyal_n and_o be_v as_o easy_o furnish_v with_o the_o parallel_n as_o the_o vertical_a and_o when_o you_o have_v by_o the_o deleble_a hour_n line_n of_o the_o plain_a inscribe_v the_o parallel_n you_o may_v wipe_v out_o those_o hour_n line_n of_o the_o plain_a and_o let_v the_o hour_n line_n of_o the_o place_n and_o the_o parallel_n stand_v have_v therefore_o draw_v the_o azimuth_n or_o almicantars_n of_o your_o plain_n by_o chapter_n 27_o take_v your_o planisphear_n in_o the_o meridional_a projection_n set_v the_o finitor_n to_o the_o latitude_n of_o your_o plain_n then_o find_v your_o equator_fw-la and_o parallel_n on_o the_o mater_n and_o where_o the_o several_a hour_n line_n intersect_v they_o above_o the_o finitor_n mark_v what_o azimuth_n or_o rather_o what_o almicantar_n pass_v through_o these_o intersection_n for_o in_o the_o same_o azimuth_n and_o almicantar_n shall_v the_o parallel_n cut_v the_o hour_n line_n of_o the_o plain_a upon_o the_o plain_a example_n in_o the_o vertical_a dyal_n for_o our_o latitude_n 52.15_o minute_n i_o set_v the_o finitor_n to_o this_o latitude_n and_o go_v first_o to_o the_o tropic_n of_o cancer_n i_o begin_v at_o the_o limb_n that_o be_v at_o noon_n there_o i_o see_v the_o azimuth_n full_a south_n the_o altitude_n 61.15_o minute_n at_o 1._o a_o clock_n azimuth_n 27._o altitude_n 59_o at_o 2._o azimuth_n 49_o ½_n altitude_n 53_o ⅓_n at_o 3._o azimuth_n 67._o altitude_n 45_o ½_n etc._n etc._n therefore_o where_o i_o find_v
to_o take_v your_o point_n in_o the_o tropique_n at_o the_o large_a distance_n as_o i_o have_v here_o do_v if_o there_o be_v room_n enough_o on_o the_o ceiling_n but_o because_o it_o often_o happen_v that_o part_n of_o your_o dyal_n fall_v beside_o the_o ceiling_n and_o the_o plain_a of_o the_o ceiling_n and_o of_o the_o wall_n be_v often_o interrupt_v and_o make_v irregular_a by_o beam_n wal-plate_n corrish_n wainscot_n chimney-peece_n and_o such_o like_a body_n i_o will_v â—hew_v you_o one_o absolute_a device_n to_o carry_v on_o your_o hour_n line_n over_o all_o extend_v the_o thread_n for_o any_o hour_n line_n to_o the_o tropic_n of_o cancerâ—n_n â—n_z the_o ceiling_n as_o you_o where_o teach_v before_o and_o fix_v it_o there_o and_o extend_v another_o thread_n in_o like_a manner_n to_o the_o tropic_n of_o copricorn_n where_o ever_o it_o shall_v happen_v as_o perhaps_o beyond_o the_o middle_a beam_n or_o quite_o beyond_o the_o ceiling_n upon_o the_o wall_n and_o fix_v that_o thread_n also_o then_o place_v your_o ey_fw-mi so_o behind_o these_o thread_n that_o one_o of_o they_o may_v cover_v the_o other_o and_o at_o the_o same_o instant_n where_o the_o upper_a line_n to_o your_o sight_n or_o imagination_n cut_v the_o ceiling_n beam_n wall_n or_o any_o regular_a or_o irregular_a body_n above_o the_o end_n of_o the_o low_a line_n there_o shall_v the_o hour_n line_n pass_v from_o tropic_n to_o tropic_n direct_v any_o by-stander_n to_o make_v mark_n as_o many_o as_o you_o shall_v need_v and_o by_o these_o mark_n draw_v the_o hour_n line_n according_a to_o your_o desire_n if_o the_o arch_n of_o the_o horizon_n between_o the_o tropique_n be_v within_o view_n of_o your_o window_n you_o shall_v draw_v the_o same_o on_o the_o wall_n to_o bound_v the_o parallel_n the_o orison_n altitude_n you_o know_v be_v nothing_o and_o therefore_o he_o will_v be_v a_o level_a line_n and_o the_o sun_n azimuth_n when_o he_o rise_v common_o call_v amplitude_n and_o ortive_a latitude_n be_v in_o cancer_n 40.40_o minute_n east_n northward_o and_o in_o capricorn_n as_o much_o southward_n and_o these_o will_v be_v reflect_v to_o the_o contrary_a coast_n on_o the_o dyal_n the_o end_n of_o the_o five_o book_n a_o brief_a description_n of_o a_o crossstaff_n the_o crossstaff_n consist_v of_o two_o rule_n join_v by_o a_o socket_n or_o else_o pin_v in_o the_o form_n of_o a_o roman_a t_n and_o three_o sight_n or_o more_o the_o long_a ruler_n be_v call_v radius_fw-la index_n and_o the_o yard_n as_o a_o b_o of_o which_o i_o call_v a_o the_o near_a end_n b_o the_o further_a end_n the_o breadth_n will_v be_v ¾_n of_o a_o inch_n the_o depth_n a_o inch_n and_o half_a the_o length_n 70_o or_o 80._o inch_n and_o every_o of_o those_o inch_n will_v be_v divide_v by_o parallel_n and_o diagonal_a line_n into_o 100_o equal_a part_n the_o short_a ruler_n e_o f_o be_v call_v the_o transom_n it_o will_v be_v half_a a_o inch_n or_o three_o quarter_n both_o in_o breadth_n and_o depth_n and_o in_o length_n about_o 2._o foot_n for_o the_o sight_n there_o if_o i_o may_v advise_v you_o will_v never_o be_v set_v above_o 20_o inch_n asunder_o this_o transom_n will_v be_v divide_v into_o whole_a inch_n only_o begin_v in_o the_o midst_n at_o b_o in_o the_o visual_a line_n ☉_o b._n and_o number_v to_o 10_o both_o way_n the_o sight_n c_o and_o d_o must_v have_v socket_n at_o the_o bottom_n through_o which_o the_o transom_n must_v pass_v so_o that_o the_o sight_n may_v be_v set_v to_o any_o division_n of_o the_o transom_n the_o vane_n or_o top_n of_o those_o sight_n must_v have_v only_o two_o edge_n on_o their_o side_n visible_a to_o your_o eye_n namely_o those_o edge_n which_o touch_v the_o transom_n and_o the_o two_o other_o edge_n must_v be_v pare_v away_o the_o middle_a sight_n at_o b_o will_v have_v half_a his_o head_n cut_v away_o and_o a_o shoulder_n leave_v as_o in_o the_o figure_n and_o a_o tenon_n at_o the_o bottom_n fit_v to_o a_o mortess_n make_v in_o the_o middle_n of_o the_o transom_n that_o you_o may_v stick_v he_o in_o and_o take_v he_o out_o when_o you_o please_v for_o to_o this_o mortess_n you_o shall_v do_v well_o to_o fit_v two_o other_o movable_a sight_n very_o narrow_a for_o observe_v the_o diameter_n of_o the_o moon_n or_o the_o distance_n of_o star_n which_o be_v very_o near_o one_o may_v be_v about_o half_a a_o inch_n broad_a and_o the_o other_o about_o a_o quarter_n this_o crossstaff_n be_v exact_o make_v by_o mr._n anthony_n thomson_n in_o hosier_n lane_n london_n when_o you_o will_v use_v this_o staff_n you_o shall_v first_o set_v the_o sight_n of_o the_o transom_n to_o like_a inch_n as_o at_o 10_o and_o 10._o if_o the_o angle_n be_v great_a or_o at_o 5_o and_o 5._o as_o in_o the_o figure_n they_o be_v place_v always_o set_v they_o at_o whole_a inch_n and_o at_o like_a number_n on_o both_o side_n from_o the_o middle_n of_o the_o transom_n and_o choose_v to_o place_v those_o sight_n so_o that_o your_o eyesight_n may_v be_v far_o distant_a from_o they_o in_o observe_v for_o so_o you_o may_v the_o more_o distinct_o observe_v the_o minute_n and_o second_n of_o the_o angle_n inquire_v then_o rest_v the_o further_a end_n of_o the_o index_n upon_o a_o wall_n or_o some_o device_n fit_v for_o that_o purpose_n put_v the_o near_a end_n over_o your_o right_a shoulder_n and_o set_v your_o ey_fw-mi to_o the_o ey-hole_n slip_v the_o index_n backward_o or_o forward_o till_o you_o see_v the_o object_n by_o the_o side_n of_o the_o sight_n of_o the_o transom_n and_o mark_v what_o number_n the_o backside_n of_o the_o eyesight_n cut_v upon_o the_o index_n for_o that_o shall_v give_v you_o the_o angle_n seek_v in_o this_o manner_n example_n the_o sight_n of_o the_o transom_n be_v set_v at_o 5_o and_z 5_o that_o be_v 10._o inch_n asunder_o i_o observe_v two_o steeple_n by_o their_o edge_n and_o the_o eyesight_n then_o cut_v upon_o the_o index_n 6625._o that_o be_v inch_n 66_o ¼_n from_o the_o transom_n i_o say_v therefore_o as_o c_o b_o 500_o to_o b_o g_z 6625._o so_z c_o b_o radius_fw-la or_o 100000._o to_o b_o g_o the_o co-tangent_a of_o half_a the_o angle_n here_o i_o have_v no_o more_o to_o do_v then_o to_o divide_v 662500000._o by_o 500_o or_o 6625000._o by_o 5._o which_o be_v a_o easy_a work_n and_o the_o quotient_a 1325000._o be_v the_o co-tangent_a of_o 4._o degree_n 18._o minute_n 57_o second_o 43._o three_o for_o half_a the_o angle_n note_v here_o that_o if_o the_o sight_n have_v stand_v at_o 10_o and_o 10._o then_o have_v the_o number_n 6625._o be_v the_o very_a co-tangent_a of_o half_a the_o angle_n and_o remember_v that_o your_o radius_fw-la on_o the_o transom_n have_v but_o 1000_o actual_a part_n go_v to_o the_o canon_n and_o cut_v off_o so_o many_o place_n as_o may_v leave_v the_o radius_fw-la there_o but_o 1000_o you_o shall_v find_v your_o number_n 6625_o to_o be_v the_o co-tangent_a of_o 8._o 35_o minute_n note_v also_o that_o you_o may_v observe_v the_o angle_n between_o the_o middle_a sight_n and_o one_o of_o the_o other_o and_o then_o you_o find_v the_o co-tangent_a of_o the_o whole_a angle_n to_o that_o radius_fw-la to_o which_o your_o sight_n be_v set_v on_o the_o transom_n as_o to_o the_o radius_fw-la 200._o 300._o or_o any_o other_o even_o hundred_o to_o 1000_o note_v further_o that_o you_o must_v evermore_o observe_v near_o the_o top_n of_o your_o sight_n that_o the_o visual_a line_n may_v run_v above_o the_o transom_n as_o much_o as_o the_o ey_fw-mi be_v place_v above_o the_o plain_a of_o it_o he_o that_o will_v may_v have_v room_n to_o set_v several_a scale_n of_o degree_n and_o minute_n to_o several_a radiuss_n as_o one_o to_o the_o radius_fw-la 300._o another_o to_o 500_o another_o to_o 700._o by_o which_o the_o very_a degree_n and_o minute_n may_v be_v present_o have_v without_o recourse_n to_o the_o table_n to_o i_o the_o scale_n of_o equal_a part_n be_v in_o stead_n of_o all_o the_o commodity_n of_o this_o disposition_n of_o the_o staff_n be_v these_o 1._o it_o be_v better_a manage_v when_o it_o rest_v upon_o the_o shoulder_n and_o the_o eyesight_n be_v make_v to_o move_v while_o the_o transom_n and_o his_o sight_n stand_v fix_v shall_v save_v you_o much_o labour_n of_o course_v up_o and_o down_o from_o one_o end_n of_o the_o staff_n to_o the_o â—â—â—er_n in_o observe_v 2._o the_o eyesight_n be_v make_v to_o show_v the_o angle_n by_o the_o length_n of_o the_o co-tangents_a shall_v always_o give_v you_o large_a difference_n insomuch_o that_o if_o your_o staff_n be_v but_o 6._o foot_n long_o you_o may_v observe_v to_o second_o and_o three_o in_o less_o angle_n and_o till_o you_o come_v beyond_o 20._o degree_n your_o sight_n shall_v seldom_o move_v
010352_o 16_o 02867_o 010402_o 17_o 03057_o 010456_o 18_o 03249_o 010514_o 19_o 03443_o 010576_o 20_o 03639_o 010641_o 21_o 03838_o 010711_o 22_o 04040_o 010785_o 23_o 04244_o 010863_o 23.30_o 04348_o 010904_o 24_o 04452_o 010946_o 25_o 04663_o 011033_o 26_o 04877_o 011126_o 27_o 05095_o 011223_o 28_o 05317_o 011325_o 29_o 05543_o 011433_o 30_o 05773_o 011547_o 31_o 06008_o 011666_o 32_o 06248_o 011791_o 33_o 06494_o 011923_o 34_o 06745_o 012062_o 35_o 07002_o 012207_o 36_o 07265_o 012360_o 37_o 07535_o 012521_o 38_o 07812_o 012690_o 39_o 08097_o 012867_o 40_o 08390_o 013054_o 41_o 08692_o 013250_o 42_o 09004_o 013456_o 43_o 09325_o 013673_o 44_o 09656_o 013901_o 45_o 10000_o 014142_o 46_o 10355_o 014395_o 47_o 10723_o 014662_o 48_o 11106_o 014944_o 49_o 11503_o 015242_o 50_o 11917_o 015557_o 51_o 12348_o 015890_o 52_o 12799_o 016242_o 53_o 13270_o 016616_o 54_o 13763_o 017013_o 55_o 14281_o 017434_o 56_o 14825_o 017882_o 57_o 15398_o 018360_o 58_o 16003_o 018870_o 59_o 16642_o 019416_o 60_o 17320_o 02000_o 61_o 18040_o 020626_o 62_o 18807_o 021300_o 63_o 19626_o 022026_o 64_o 20503_o 022811_o 65_o 21445_o 023662_o 66_o 22460_o 024585_o 66.30_o 22998_o 025078_o 67_o 23558_o 025693_o 68_o 24750_o 026694_o 69_o 26050_o 027904_o 70_o 27474_o 029238_o 71_o 29042_o 030715_o 72_o 30776_o 032360_o 73_o 32708_o 034203_o 74_o 34874_o 036279_o 75_o 37320_o 038637_o 76_o 40107_o 041335_o 77_o 43314_o 044454_o 78_o 47046_o 048097_o 79_o 51445_o 052408_o 80_o 56712_o 057587_o 81_o 63137_o 063924_o 82_o 71153_o 071852_o 83_o 8144â—_n 082055_o 84_o 9514â—_n 095667_o 85_o 11430_o 114737_o 86_o 14300_o 143355_o 87_o 19081_o 191073_o 88_o 28636_o 286537_o 89_o 57289_o 572986_o 90_o  _fw-fr  _fw-fr chap._n four_o to_o find_v the_o centre_n of_o the_o parallel_n six_o several_a way_n the_o first_o way_n but_o the_o worst_a for_o our_o purpose_n as_o be_v say_v before_o for_o the_o meridian_n be_v by_o the_o five_o proposition_n of_o the_o four_o book_n of_o euclid_n to_o find_v the_o centre_n of_o the_o circle_n circumscribe_v the_o triangle_n make_v by_o the_o three_o point_n give_v 2_o a_o better_a way_n be_v by_o proffer_n take_v this_o upon_o trust_n that_o as_o you_o find_v the_o centre_n of_o all_o the_o meridian_n in_o the_o equator_fw-la so_o shall_v you_o find_v the_o centre_n of_o all_o the_o parallel_n in_o the_o axtree_n line_n prolong_v and_o by_o make_v like_o proffer_n as_o you_o be_v teach_v for_o the_o centre_n of_o the_o meridian_n chap._n 3_o you_o may_v quick_o find_v the_o centre_n of_o the_o parallel_n 3_o a_o three_o way_n you_o must_v consider_v that_o the_o axtree_n line_n represent_v the_o east_n meridian_n as_o well_o as_o the_o axis_n of_o the_o world_n which_o be_v a_o common_a diameter_n to_o all_o the_o meridian_n also_o that_o every_o parallel_n cut_v the_o east_n meridian_n as_o it_o do_v the_o rest_n in_o two_o point_n equidistant_a from_o the_o equinoctial_a and_o two_o equidistant_n also_o from_o the_o pole_n therefore_o 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cut_v the_o great_a meridian_n you_o raise_v a_o tangent_fw-la line_n this_o tangent_fw-la shall_v cut_v the_o axtree_n line_n in_o the_o centre_n of_o the_o parallel_n example_n the_o say_v 50th_o parallel_n cut_v the_o great_a meridian_n at_o h_n there_o i_o raise_v the_o targent_n h_n g_o perpendicular_a to_o the_o radius_fw-la e_o h._n and_o this_o tangent_fw-la as_o you_o see_v cut_v the_o axtree_n line_n in_o g_o the_o centre_n of_o the_o parallel_n 5_o hence_o arise_v a_o five_o way_n for_o it_o appear_v by_o this_o figure_n that_o the_o tangent_fw-la of_o the_o parallel_n distance_n from_o the_o pole_n be_v equal_a to_o his_o semidiameter_n and_o that_o the_o secant_fw-la of_o his_o distance_n from_o the_o pole_n be_v equal_a to_o the_o distance_n of_o his_o centre_n from_o the_o centre_n of_o the_o great_a meridian_n for_o here_o e_o h_n be_v radius_fw-la h_o b_o a_o arch_n of_o 40_o degr_n h_o g_z the_o tangent_fw-la thereof_o and_o semidiameter_n of_o the_o parallel_n e_z g_z the_o secant_fw-la thereof_o and_o the_o distance_n of_o the_o centre_n of_o the_o parallel_n from_o the_o centre_n of_o the_o meridian_n and_o all_o this_o be_v evident_a by_o the_o structure_n in_o the_o scheam_n wherefore_o make_v e_z h_z radius_fw-la take_v from_o your_o scale_n or_o sector_n with_o your_o compass_n the_o secant_fw-la of_o the_o parallel_n distance_n from_o the_o pole_n and_o set_v it_o from_o e_o in_o the_o axtree_n line_n and_o it_o shall_v end_v in_o the_o centre_n of_o the_o parallel_n or_o take_v the_o tangent_fw-la of_o the_o parallel_n distance_n from_o the_o pole_n and_o set_v it_o from_o the_o point_n of_o his_o section_n with_o the_o meridian_n towards_o the_o extension_n of_o the_o axtree_n line_n and_o where_o the_o end_n of_o it_o just_o touch_v the_o axtree_n line_n there_o be_v the_o centre_n 6_o for_o want_v of_o a_o sector_n or_o other_o fit_a scale_n of_o tangent_n and_o secant_v you_o may_v do_v thus_o set_v one_o foot_n of_o your_o compass_n in_o the_o centre_n e_o and_o extend_v the_o other_o upon_o the_o diameter_n of_o the_o equator_fw-la or_o axtree_n line_n to_o twice_o so_o many_o degr_n as_o your_o parallel_n be_v distant_a from_o the_o pole_n that_o distance_n be_v the_o very_a tangent_fw-la you_o seek_v for_o example_n for_o the_o 40th_o parallel_n from_o the_o pole_n i_o number_n from_o e_z toward_z d_o 80_o degr_n to_o 8._o now_o e_z 8_o be_v the_o tangent_fw-la of_o 40_o degr_n though_o it_o contain_v just_a twice_o so_o many_o degr_n of_o the_o circle_n foreshortn_v in_o this_o projection_n as_o have_v be_v show_v chap._n 3._o sect._n 3_o and_o so_o if_o you_o will_v have_v the_o secant_fw-la of_o 40_o degr_n take_v with_o your_o compass_n the_o length_n from_o 8_o where_o the_o tangent_fw-la end_n to_o a._n and_o that_o be_v the_o secant_fw-la to_o be_v use_v as_o be_v teach_v in_o the_o last_o section_n thus_o have_v you_o way_n enough_o for_o find_v the_o centre_n of_o the_o meridian_n and_o parallel_n and_o you_o may_v have_v occasion_n in_o the_o make_n of_o the_o instrument_n to_o use_v most_o of_o they_o one_o time_n or_o other_o however_o the_o knowledge_n of_o they_o be_v both_o pleasant_a and_o useful_a for_o the_o right_a understanding_n of_o this_o and_o other_o projection_n of_o the_o sphere_n as_o also_o for_o the_o examination_n of_o your_o work_n when_o you_o shall_v chance_v to_o doubt_v of_o it_o chap._n v._o how_o to_o draw_v the_o straight_a meridian_n and_o parallel_n who_o semidiameter_n be_v very_o long_o it_o may_v trouble_v you_o very_o much_o to_o draw_v those_o meridian_n and_o parallel_n which_o lie_v near_o to_o the_o diameter_n because_o they_o be_v arch_n of_o great_a circle_n and_o require_v compass_n large_a than_o you_o can_v well_o get_v or_o manage_v when_o you_o have_v get_v they_o till_o you_o come_v to_o the_o 80th_o meridian_n from_o the_o limb_n a_o beam-compass_n of_o a_o yard_n long_o will_v reach_v if_o your_o mater_n be_v not_o above_o a_o foot_n diameter_n and_o a_o long_a beam_n you_o can_v well_o manage_v for_o it_o will_v be_v apt_a to_o tremble_v with_o its_o own_o weight_n and_o draw_v double_a line_n though_o it_o be_v make_v very_o thick_a and_o massy_a but_o the_o 89th_o meridian_n will_v require_v a_o beam-compass_n of_o almost_o ten_o yard_n long_o for_o his_o semidiameter_n will_v contain_v the_o semidiameter_n of_o the_o great_a meridian_n 57_o time_n therefore_o to_o draw_v the_o 10_o last_v meridian_n and_o the_o 10_o last_o parallel_n you_o may_v help_v yourself_o one_o of_o these_o way_n 1._o guido_n vbaldus_n have_v devise_v a_o instrument_n for_o this_o purpose_n consist_v of_o three_o ruler_n in_o form_n of_o a_o obtuse_a triangle_n the_o description_n and_o use_n thereof_o you_o may_v see_v in_o blagr_n l._n 4._o c_o 2_o 3._o and_o in_o vbaldus_n his_o book_n
the_o noon_n line_n of_o my_o plain_a cut_n by_o the_o almicantar_n 61_o ¼_n i_o make_v a_o prick_n and_o in_o the_o hour_n line_n of_o 11_o and_o of_o 1._o where_o the_o azimuth_n 27_o and_o the_o almicantar_n 59_o meet_a i_o make_v prick_n and_o where_o the_o azimuth_n 49_o ½_n and_o the_o almicantar_n 53_o ⅓_n do_v meet_v upon_o the_o hour_n line_n of_o 10.2_o i_o make_v prick_n and_o so_o for_o the_o rest_n last_o i_o draw_v with_o a_o even_a hand_n a_o crooked_a line_n without_o angle_n through_o those_o prick_n and_o that_o shall_v be_v the_o parallel_n or_o tropic_n of_o cancer_n and_o in_o like_a manner_n i_o put_v in_o all_o the_o other_o parallel_n and_o the_o equator_fw-la in_o the_o midst_n of_o they_o though_o for_o the_o equator_fw-la you_o may_v draw_v he_o more_o speedy_o by_o strike_v a_o line_n through_o the_o centre_n of_o the_o almicantars_n make_v right_a angle_n with_o the_o substyle_n and_o that_o may_v be_v a_o general_a rule_n for_o the_o equator_fw-la in_o all_o dial_n which_o have_v a_o substyle_n and_o in_o the_o polar_a dyal_n where_o there_o be_v no_o substyle_n the_o equator_fw-la shall_v be_v a_o circle_n as_o before_o be_v show_v note_v here_o that_o if_o your_o dyal_n be_v great_a and_o you_o have_v not_o point_n enough_o to_o govern_v you_o in_o the_o draught_n of_o the_o conical_a section_n you_o may_v draw_v half-hour-line_n and_o find_v point_n in_o they_o also_o after_o the_o same_o manner_n chap._n xxxi_o to_o do_v the_o same_o by_o the_o hour-line_n of_o the_o place_n although_o the_o plain_n decline_v or_o recline_v if_o you_o like_v not_o to_o draw_v the_o proper_a dyal_n of_o the_o plain_a where_o it_o decline_v or_o recline_v because_o be_v useless_a in_o your_o country_n it_o must_v be_v wipe_v out_o again_o it_o shall_v suffice_v you_o to_o find_v the_o hour_n line_n of_o your_o country_n upon_o the_o plain_a by_o chapter_n 21_o and_o 22_o and_o in_o the_o posture_n your_o planisphear_n have_v in_o those_o chapter_n to_o observe_v what_o almicantars_n or_o azimuth_n do_v cross_v those_o hour_n line_n at_o the_o several_a hour_n in_o any_o parallel_n and_o thereby_o make_v prick_n upon_o the_o hour_n line_n of_o your_o place_n as_o in_o the_o former_a chapter_n you_o do_v upon_o the_o hour_n line_n of_o your_o plain_n and_o by_o these_o prick_v you_o may_v draw_v your_o parallel_n as_o before_o note_v that_o if_o you_o work_v this_o way_n you_o shall_v find_v the_o sun_n great_a altitude_n to_o be_v in_o the_o meridian_n of_o the_o plain_a or_o substyle_n and_o not_o in_o the_o noon-line_n of_o your_o place_n whereat_o you_o must_v not_o wonder_v so_o if_o the_o substyle_n be_v about_o 9_o in_o the_o morning_n there_o you_o shall_v find_v the_o sun_n at_o high_a and_o that_o his_o altitude_n decrease_v from_o thence_o till_o he_o leave_v the_o plain_a chap._n xxxii_o how_o to_o inscribe_v the_o horizon_n of_o the_o place_n with_o his_o azimuth_n and_o almicantars_n in_o the_o horizontal_n dyal_n the_o nodus_fw-la may_v be_v choose_v in_o any_o part_n of_o the_o gnomon_n but_o with_o the_o eaution_n give_v chapter_n 27._o and_o a_o perpendicular_a fall_n from_o the_o nodus_fw-la on_o the_o sub-style_n shall_v touch_v the_o centre_n of_o the_o azimuth_n and_o almicantars_n of_o the_o plain_a as_o have_v be_v show_v chapter_n 27._o here_o you_o have_v no_o use_n of_o those_o azimuth_n and_o almicantars_n but_o through_o the_o centre_n of_o they_o you_o shall_v draw_v a_o horizontal_n line_n by_o chapter_n 3._o and_o that_o shall_v be_v horizon_n now_o if_o your_o plain_n decline_v not_o from_o the_o meridian_n and_o so_o this_o centre_n fall_v upon_o the_o noon_n line_n you_o shall_v divide_v your_o horizon_n both_o way_n from_o the_o centre_n as_o you_o be_v teach_v to_o divide_v the_o azimuthal_o line_n by_o tangent_n chapter_n 27._o and_o shall_v number_v those_o division_n from_o the_o centre_n on_o both_o side_n 5_o 10_o 15_o 20._o etc._n etc._n and_o from_o the_o several_a point_n so_o make_v for_o 5_o 10_o 15_o etc._n etc._n in_o the_o horizontal_n line_n let_v fall_v perpendicular_o or_o vertical_a line_n on_o the_o plain_a and_o they_o shall_v be_v azimuth_n of_o your_o place_n but_o if_o your_o plain_n decline_v you_o shall_v divide_v the_o horizontal_n line_n thus_o draw_v a_o short_a vertical_a line_n through_o the_o say_a centre_n downward_o by_o chapter_n 3._o which_o shall_v be_v the_o verticle_n of_o your_o plain_n for_o the_o almicantars_n they_o will_v not_o be_v so_o handsome_a line_n but_o if_o you_o will_v have_v they_o do_v thus_o if_o the_o plain_n decline_v not_o set_v the_o finitor_n to_o the_o latitude_n of_o your_o place_n as_o chapter_n 10._o and_o if_o it_o decline_v set_v the_o finitor_n to_o the_o latitude_n of_o your_o plain_n as_o chapter_n 21._o then_o keep_v your_o eye_n above_o the_o horizon_n and_o within_o the_o tropique_n mark_v what_o hour_n line_n the_o 10_o almicantar_n for_o example_n cut_v and_o what_o azimuth_n there_o with_o he_o cut_v the_o same_o hour_n line_n also_o and_o in_o the_o interfection_n of_o the_o same_o azimuth_n and_o hour_n line_n upon_o your_o plain_n you_o shall_v make_v mark_n through_o which_o the_o ten_o almicantar_n shall_v be_v draw_v and_o so_o of_o the_o rest_n note_v here_o that_o your_o azimuth_n and_o almicantars_n must_n not_o be_v draw_v beyond_o the_o tropique_n nor_o beyond_o the_o horizon_n neither_o must_v the_o hour_n line_n if_o the_o nodus_fw-la be_v the_o end_n of_o the_o gnomon_n the_o scheam_n show_v you_o how_o the_o azimuth_n may_v be_v draw_v on_o the_o dyal_n of_o chapter_n 12._o and_o 21._o decline_a east_n 30_o degree_n chap._n xxxiii_o how_o by_o the_o help_n of_o this_o furniture_n to_o place_v any_o movable_a dyal-plain_a in_o his_o true_a situation_n and_o consequent_o to_o find_v the_o meridian-line_n of_o the_o place_n without_o any_o other_o instrument_n than_o the_o dyal_n itself_o set_v the_o dyal_n upon_o a_o level_a table_n or_o 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projection_n the_o concurrent_a circle_n meet_v in_o the_o pole_n a_o and_o b_o be_v meridian_n those_o meridian_n be_v 180_o in_o number_n and_o divide_v the_o equator_fw-la c_o d_o into_o 360._o degree_n because_o every_o one_o of_o they_o cut_v it_o twice_o that_o be_v once_o in_o each_o hemisphere_n by_o these_o be_v number_v the_o right_a ascension_n of_o the_o star_n and_o planet_n and_o the_o hour_n and_o minute_n of_o day_n and_o night_n for_o every_o 15_o of_o these_o meridian_n number_v from_o the_o limb_n be_v a_o hour_n circle_n as_o have_v be_v show_v book_n 1.6_o they_o be_v number_v from_o d_o to_z c_z that_o be_v from_o septentrio_fw-la to_o meridies_n 1.2.3_o etc._n etc._n for_o the_o morning_n hour_n and_o back_o again_o from_o c_z to_z d_o in_o like_a manner_n for_o the_o afternoon_n the_o axletree_n line_n a_o b_o fall_v out_o to_o be_v the_o six_o a_o clock_n line_v both_o way_n by_o those_o meridian_n also_o be_v number_v the_o longitude_n of_o town_n and_o country_n in_o geography_n the_o circle_n or_o semicircle_n cross_v these_o meridian_n be_v the_o parallel_n of_o declination_n they_o be_v lesser_a circle_n who_o property_n it_o be_v to_o divide_v the_o sphere_n into_o unequal_a part_n in_o the_o midst_n of_o they_o lie_v the_o equator_fw-la c_o d_o be_v here_o a_o straight_a line_n and_o cut_v the_o axtree-line_n a_o b_o at_o right_a angle_n in_o the_o centre_n e_o the_o parallel_n be_v great_a near_o the_o equator_fw-la and_o from_o thence_o they_o lessen_v towards_o the_o pole_n they_o be_v 180_o in_o number_n i._n e._n 90_o on_o each_o side_n the_o equator_fw-la save_v that_o the_o two_o extreme_a parallel_n be_v reduce_v to_o two_o point_n in_o the_o pole_n by_o these_o parallel_n be_v number_v the_o declination_n of_o the_o star_n in_o astronomy_n and_o the_o latitude_n of_o town_n and_o country_n in_o geography_n and_o this_o name_n and_o use_n have_v the_o circle_n of_o the_o mater_n always_o in_o the_o meridional_a 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azimuth_n shall_v be_v almicanter_n or_o circle_n of_o altitude_n the_o diameter_n cross_v the_o axletree_n of_o the_o reet_n at_o right_a angle_n shall_v be_v the_o horizon_n or_o finiter_n who_o graduation_n be_v set_v to_o he_o in_o a_o border_n below_o the_o centre_n and_o from_o he_o be_v the_o almicanter_n reckon_v upward_o to_o the_o zenith_n the_o azimuth_n may_v be_v reckon_v from_o the_o north_n or_o south_n semicircle_n of_o the_o meridian_n or_o from_o the_o axtree_n line_n of_o the_o reet_n which_o be_v the_o east_n or_o west_n azimuth_n common_o call_v the_o prime_n vertical_a when_o i_o bid_v you_o set_v the_o vertex_fw-la of_o the_o reet_n to_o the_o latitude_n of_o your_o place_n you_o must_v first_o know_v what_o your_o latitude_n be_v it_o be_v the_o near_a distance_n of_o your_o place_n from_o the_o terrestrial_a equinoctial_a number_v in_o degree_n and_o minute_n of_o a_o great_a circle_n the_o latitude_n of_o london_n be_v 31_o degr_n 32_o min._n north._n the_o 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the_o mater_n or_o the_o innermost_a circle_n of_o the_o ring_n now_o be_v the_o upper_a semicircle_n of_o your_o meridian_n divide_v into_o four_o notable_a part_n from_o the_o zenith_n southward_o to_o the_o equator_fw-la be_v the_o latitude_n 51._o degree_n 32_o minute_n from_o thence_o to_o the_o horizon_n be_v the_o compliment_n of_o the_o latitude_n 38._o degree_n 28._o minute_n make_v up_o a_o quadrant_n again_o from_o the_o zenith_n northerly_a to_o the_o pole_n be_v the_o compliment_n of_o latitude_n 38._o degr_n 28._o minute_n as_o before_o and_o from_o thence_o to_o the_o north_n of_o the_o horizon_n be_v the_o elevation_n of_o the_o pole_n above_o your_o horizon_n which_o be_v always_o equal_a to_o the_o latitude_n of_o your_o place_n for_o where_o in_o a_o right_a sphere_n the_o poles_o in_o the_o horizon_n and_o have_v on_o elevation_n there_o the_o equator_fw-la pass_v through_o the_o zenith_n and_o if_o you_o go_v from_o such_o a_o country_n northward_o till_o the_o 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the_o arch_n of_o the_o ecliptic_a from_o the_o ascendant_n to_o the_o midheaven_n and_o his_o match_n take_v so_o many_o degree_n on_o the_o other_o side_n the_o centre_n give_v the_o other_o arch_n of_o the_o ecliptic_a from_o the_o midheaven_n to_o the_o descendant_n the_o rest_n of_o the_o meridian_n and_o the_o parallel_n be_v in_o this_o mode_n of_o no_o use_n the_o almicanter_n and_o azimuth_n of_o the_o reet_n here_o show_v you_o the_o altitude_n and_o azimuth_n of_o every_o degree_n of_o the_o ecliptic_a at_o one_o view_n chap._n two_o of_o the_o equinoctial_a projection_n show_v the_o northern_a or_o southern_a hemisphear_n the_o equinoctial_a projection_n represent_v the_o northern_a or_o southern_a hemisphere_n project_v upon_o the_o plain_a of_o the_o equator_fw-la here_o the_o limb_n or_o outmost_a circle_n of_o the_o mater_n and_o reet_n be_v equator_fw-la the_o eye-point_n be_v the_o north_n or_o south_n pole_n which_o you_o will_v by_o turn_n which_o pole_n be_v here_o 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about_o the_o label_n with_o the_o point_n it_o shall_v describe_v a_o circle_n which_o will_v serve_v for_o both_o the_o tropic_n and_o so_o may_v you_o make_v any_o other_o of_o the_o parallel_n i_o do_v not_o advise_v you_o to_o draw_v the_o meridian_n and_o parallel_n in_o this_o form_n lest_o you_o cumber_v your_o instrument_n but_o i_o show_v you_o how_o you_o may_v represent_v any_o of_o they_o in_o a_o moment_n when_o occasion_n require_v the_o meridian_n of_o the_o mater_n that_o be_v so_o call_v in_o the_o meridional_a projection_n be_v here_o turn_v into_o the_o several_a orison_n of_o the_o world_n and_o the_o parallel_n here_o serve_v only_o to_o graduate_v those_o orison_n out_o of_o these_o orison_n choose_v your_o own_o horizon_n and_o distinguish_v he_o if_o you_o will_v that_o you_o may_v ready_o find_v he_o when_o you_o shall_v look_v for_o he_o your_o horizon_n be_v thus_o inquire_v because_o the_o elevation_n of_o the_o pole_n at_o northampton_n be_v 52._o degree_n 15._o minute_n therefore_o from_o the_o centre_n now_o north_n pole_n number_n in_o the_o meridian_n line_n northward_o 52._o degree_n 15._o minute_n and_o there_o cut_v the_o the_o north_n semicircle_n of_o our_o horizon_n or_o there_o you_o may_v imagine_v he_o between_o the_o 52_o and_o 53_o orison_n and_o the_o southern_a semicircle_n thereof_o lie_v 52_o degree_n 15_o minute_n on_o the_o other_o side_n the_o centre_n towards_o meridies_n this_o may_v seem_v strange_a that_o the_o north_n and_o south_n point_v of_o the_o horizon_n which_o in_o the_o sphere_n be_v unequal_o distant_a from_o the_o north_n pole_n viz._n the_o one_o but_o 51._o degree_n 15._o minute_n and_o the_o other_o 127._o degree_n 45._o minute_n the_o supplement_n thereof_o shall_v be_v equal_o distant_a in_o this_o projection_n but_o the_o reason_n be_v because_o the_o centre_n be_v both_o north_n and_o south_n pole_n here_o at_o pleasure_n and_o the_o northern_a and_o southern_a hemisphear_n be_v both_o here_o represent_v by_o turn_n carry_v this_o in_o your_o head_n and_o then_o lie_v the_o eabel_n upon_o the_o south_n part_n of_o the_o meridian_n and_o number_n thereon_o from_o the_o centre_n now_o north_n pole_n outward_a to_o the_o equator_fw-la at_o the_o limb_n 90._o degree_n thence_o number_n backward_o towards_o the_o centre_n now_o the_o south_n pole_n the_o elevation_n of_o the_o equator_fw-la which_o be_v always_o compliment_n of_o the_o elevation_n of_o the_o pole_n and_o be_v here_o 37._o degree_n 45_o minute_n there_o be_v the_o southern_a point_n of_o the_o horizon_n and_o be_v distant_a from_o the_o centre_n now_o south_n pole_n only_a 52_o degree_n 15_o minute_n but_o from_o the_o centre_n be_v north_n pole_n 127._o degree_n 45._o minute_n and_o from_o the_o northern_a point_n of_o the_o horizon_n before_o find_v just_a 180._o degree_n as_o it_o be_v in_o the_o sphere_n have_v find_v the_o north_n arch_n of_o your_o horizon_n 52._o degr_n 15._o min._n behind_o the_o centre_n count_v as_o many_o degree_n and_o minute_n forward_o in_o the_o meridian_n before_o the_o centre_n towards_o meridies_n and_o the_o arch_n cross_v there_o shall_v be_v his_o match_n to_o make_v up_o the_o whole_a circle_n and_o so_o may_v you_o find_v your_o whole_a horizon_n upon_o the_o mater_n whatsoever_o your_o latitude_n be_v here_o you_o must_v remember_v that_o star_n which_o have_v northern_a declination_n rise_v and_o set_v upon_o the_o northern_a arch_n of_o the_o horizon_n and_o those_o which_o have_v southern_a declination_n upon_o the_o southern_a arch_n remember_v also_o that_o many_o star_n between_o the_o tropic_n which_o have_v northern_a latitude_n have_v nevertheless_o southern_a declination_n and_o contrary_a many_o which_o have_v southern_a latitude_n have_v northern_a declination_n the_o lineament_n of_o the_o reet_n serve_v you_o in_o this_o projection_n be_v only_o the_o ecliptic_a and_o the_o fix_a star_n the_o almicanter_n and_o azimuth_n here_o be_v of_o no_o use_n the_o meridian_n and_o parallel_n be_v supply_v by_o the_o label_n for_o the_o reet_n as_o well_o as_o for_o the_o mater_n and_o whereas_o the_o ecliptic_a here_o seem_v to_o be_v irregular_a see_v the_o solstitial_a point_n of_o cancer_n and_o caprcorn_n be_v not_o distant_a 180_o degree_n as_o they_o shall_v be_v you_o must_v imagine_v that_o the_o southern_a arch_n of_o the_o ecliptic_a be_v project_v by_o the_o eye_n place_v in_o the_o north_n pole_n and_o for_o the_o northern_a arch_n the_o eye_n place_n in_o the_o south_n pole_n and_o the_o centre_n serve_v for_o both_o the_o pole_n alike_o as_o have_v be_v show_v number_n therefore_o as_o you_o be_v teach_v for_o the_o horizon_n in_o this_o projection_n for_o the_o reason_n of_o the_o draught_n of_o the_o horizon_n and_o of_o the_o ecliptic_a in_o this_o projection_n be_v the_o same_o chap._n iii_o of_o the_o nonagesimal_n projection_n show_v the_o eastern_a and_o western_a part_n of_o the_o sphere_n be_v divide_v by_o the_o azimuth_n of_o the_o nonagesimus_fw-la gradus_fw-la number_n in_o the_o limb_n from_o the_o equinoctial_a line_n towards_o the_o pole_n the_o altitude_n of_o the_o nonagesimus_fw-la gradus_fw-la which_o be_v the_o high_a degree_n of_o the_o ecliptic_a and_o thereto_o set_v the_o finitor_n turn_v the_o almicanter_n either_o to_o the_o north_n or_o to_o the_o south_n as_o your_o work_n propose_v shall_v require_v now_o be_v the_o finiter_n ecliptic_a his_o point_n at_o the_o limbis_a nonagesimus_fw-la gradus_fw-la the_o centre_n of_o the_o planisphear_n be_v ascendant_n and_o descendant_n the_o east_n and_o west_n point_v of_o the_o horizon_n be_v here_o distant_a from_o the_o centre_n as_o much_o as_o the_o amplitude_n of_o the_o ascendant_n come_v to_o to_o be_v count_v from_o the_o centre_n upon_o the_o eqinoctial_a line_n of_o the_o mater_n which_o here_o stand_v for_o horizon_n the_o meridian_n and_o parallel_n of_o the_o mater_n be_v here_o
and_o the_o great_a angle_v 77.43_o i_o number_n in_o the_o limb_n from_o meridies_n towards_o oriens_fw-la 77._o degree_n 43._o minute_n and_o there_o i_o set_v the_o label_n than_o i_o look_v the_o 60._o degree_n of_o the_o label_n number_v from_o the_o centre_n at_o that_o 60_o degree_n be_v c_z where_o the_o hypotenusa_fw-la and_o cathetus_n meet_v here_o therefore_o the_o meridian_n that_o cut_v the_o label_n in_o 60_o degree_n make_v the_o cathetus_n i_o follow_v he_o down_o to_o the_o equator_fw-la and_o find_v his_o length_n 57_o degree_n 48_o minute_n and_o from_o the_o point_n where_o he_o cut_v the_o equator_fw-la i_o go_v straight_o to_o the_o centre_n and_o find_v 20_o degree_n 12_o minute_n the_o length_n of_o b_o a._n last_o for_o the_o angle_n c_o turn_v the_o triangle_n set_v c_o at_o the_o centre_n and_o call_v it_o b_o and_o you_o shall_v find_v c_o as_o chap._n 3._o for_o whereas_o your_o hypotenusa_fw-la be_v 60_o and_o your_o cathetus_n 20_o degree_n 12_o minute_n lay_v the_o 60_o degree_n of_o the_o label_n upon_o the_o 20_o parallel_n and_o the_o label_n shall_v cut_v in_o the_o limb_n 23_o degree_n 30_o minute_n the_o measure_n of_o the_o angle_n c._n chap._n vi_o probl._n four_o a_o leg_n and_o a_o angle_n give_v to_o find_v the_o rest_n if_o the_o leg_n be_v conterminate_a or_o adjoin_v to_o the_o angle_n give_v then_o make_v the_o give_v leg_n base_a set_v it_o upon_o the_o equator_fw-la and_o move_v the_o label_n from_o the_o equator_fw-la towards_o the_o pole_n so_o many_o degr_n as_o the_o give_v angle_n b_o comes_z to_z then_o mark_v what_o meridian_n cut_v the_o end_n of_o the_o base_a that_o meridian_n make_v the_o cathetus_n follow_v he_o till_o he_o cross_v the_o label_n in_o that_o cross_n be_v the_o angle_n c_o of_o your_o triangle_n from_o whence_o you_o reckon_v the_o length_n of_o the_o cathetus_n to_o the_o equinoctial_a and_o the_o length_n of_o the_o hypotenusa_fw-la next_o way_n from_o c_o to_o the_o centre_n and_o now_o have_v all_o the_o side_n to_o get_v the_o angle_n c_o you_o shall_v turn_v the_o triangle_n and_o get_v he_o as_o in_o the_o 3_o chapter_n but_o if_o the_o leg_n be_v opposite_a to_o the_o angle_n give_v make_v the_o give_v leg_n cathetus_n that_o the_o angle_n give_v may_v be_v at_o the_o centre_n example_n in_o the_o former_a triangle_n i_o have_v give_v the_o less_o angle_n 23_o degree_n ½_n and_o the_o leg_n opposite_a thereto_o 20._o degr_n 12._o min._n i_o open_v therefore_o the_o label_n from_o the_o equator_fw-la to_o 23_o deg_fw-la 30._o min._n on_o the_o lamb_n and_o mark_v where_o he_o cut_v the_o 20_o ⅕_n parallel_n for_o there_o be_v the_o angle_n c_o of_o the_o triangle_n thence_o you_o shall_v have_v a_o meridian_n for_o the_o cathetus_n go_v to_o the_o equator_fw-la who_o length_n be_v 20_o degree_n 12_o minute_n thence_o in_o the_o equator_fw-la to_o the_o centre_n be_v the_o base_a 57_o degree_n 47_o minute_n and_o thence_o in_o the_o label_n to_o c_z again_o be_v the_o hypotenusa_fw-la 60_o degree_n and_o now_o have_v all_o the_o side_n to_o get_v the_o angle_n c_o you_o shall_v turn_v the_o triangle_n and_o get_v he_o as_o in_o the_o 3_o chapter_n chap._n vii_o probl._n v._o the_o angles_n give_v to_o find_v the_o side_n this_o shall_v have_v be_v the_o three_o problem_n consider_v what_o be_v give_v but_o because_o the_o way_n of_o resolve_v this_o case_n differ_v from_o all_o the_o former_a therefore_o i_o have_v reserve_v it_o to_o the_o last_o place_n in_o plain_a triangle_n this_o case_n be_v insoluble_a but_o in_o spherical_a triangle_n it_o may_v be_v resolve_v on_o the_o planisphear_n two_o way_n 1._o the_o first_o way_n have_v m._n elagrave_n 5_o 24._o he_o sets_z b_o c_z on_o the_o limb_n between_o the_o pole_n of_o the_o mater_n and_o the_o vertex_fw-la of_o the_o reet_n b_o a_o and_o c_o a_o one_o on_o a_o meridian_n and_o the_o other_o on_o a_o azimuth_n cross_v one_o another_o at_o a_o right_a angle_n within_o the_o limb._n which_o to_o do_v you_o must_v work_v thus_o example_n in_o the_o former_a triangle_n the_o angle_n be_v give_v a_o 90_o b_o 23_o degr_n 30._o min._n c_o 77_o degr_n 43._o min._n now_o first_o i_o will_v guess_v that_o the_o hypotenusa_fw-la be_v 40_o degree_n and_o set_v the_o zenith_n 40_o degree_n from_o the_o pole_n that_o arch_n of_o the_o limb_n between_o pole_n and_o zenith_n i_o take_v for_o my_o hypotenusa_fw-la yet_o unknown_a at_o the_o pole_n shall_v be_v b_o and_o at_o the_o zenith_n c._n then_o because_o b_o be_v 23_o ½_n i_o take_v the_o twentie-third_a meridian_n from_o my_o hypotenusa_fw-la which_o be_v on_o the_o limb_n and_o between_o that_o and_o the_o 24_o i_o imagine_v a_o meridian_n which_o shall_v make_v b_o a_o of_o my_o triangle_n also_o because_o the_o angle_n at_o c_z be_v 77_o deg_fw-la 43._o min._n i_o take_v a_o imaginary_a azimuth_n near_o the_o 78th_o number_v from_o my_o hypotenusa_fw-la which_o be_v on_o the_o limb_n and_o that_o azimuth_n shall_v make_v c_o a_o of_o my_o triangle_n now_o have_v i_o the_o angle_n b_o and_o c_o and_o three_o arch_n of_o which_o all_o the_o side_n of_o my_o triangle_n shall_v be_v make_v but_o whether_o b_o a_o and_z c_o a_o cross_n at_o right_a angle_n i_o know_v not_o and_o therefore_o i_o know_v not_o yet_o certain_o the_o length_n of_o any_o side_n now_o to_o make_v the_o angle_n at_o a_o a_o right_a angle_n mark_v where_o your_o azimuth_n which_o you_o have_v take_v for_o c_o a_o cut_v the_o finiter_n and_o from_o that_o point_n number_n in_o the_o finiter_fw-la towards_o the_o centre_n to_o 90_o degree_n and_o there_o be_v the_o pole_n of_o your_o azimuth_n viz._n 12_o degree_n 17_o minute_n from_o the_o limb_n make_v a_o prick_n with_o ink_n at_o that_o pole_n and_o then_o look_v whether_o your_o meridian_n 23_o ½_n which_o you_o take_v for_o b_o a_o cut_v this_o pole_n which_o yet_o he_o do_v not_o as_o you_o will_v find_v therefore_o turn_v the_o reet_n till_o the_o say_a meridian_n do_v cut_v this_o pole_n of_o the_o say_a azimuth_n and_o then_o you_o may_v be_v sure_a that_o meridian_n and_o azimuth_n wherever_o they_o cross_v do_v make_v right_a angle_n by_o pitisc_n trigonom_fw-la 1_o 57_o therefore_o now_o have_v you_o all_o the_o angle_n set_v on_o the_o planisphear_n and_o thereby_o all_o the_o side_n find_v viz._n b_o c_o in_o the_o limb_n 60_o degr_n b_o a_o in_o the_o meridian_n 57_o degree_n 48_o minute_n c_o at_fw-fr in_o the_o azimuth_n 20_o degree_n 12_o minute_n as_o they_o ought_v to_o be_v 2._o the_o second_o way_n m._n oughtred_a use_v it_o be_v this_o for_o the_o rectangled_a triangle_n who_o three_o angle_n be_v give_v you_o shall_v frame_v another_o oblique_a triangle_n who_o side_n shall_v be_v equal_a to_o the_o angle_n of_o the_o first_o triangle_n and_o so_o the_o angle_n of_o the_o second_o triangle_n to_o be_v find_v on_o the_o planisphear_n shall_v be_v equal_a to_o the_o side_n of_o the_o first_o triangle_n which_o be_v inquire_v the_o triangle_n which_o serve_v for_o a_o example_n throughout_o this_o book_n have_v his_o angle_n a_o 90_o degree_n c_o 77_o degree_n 43_o minute_n b_o 23_o degree_n 30_o minute_n here_o to_o find_v the_o side_n for_o the_o angle_n a_o i_o take_v half_a the_o axis_n of_o the_o mater_n from_o the_o centre_n to_o the_o pole_n and_o that_o shall_v be_v a_o side_n of_o 90_o degree_n for_o the_o lesser_a angle_n b_o i_o reckon_v upon_o the_o label_n from_o the_o centre_n a_o side_n of_o 23_o degree_n 30_o minute_n and_o at_o the_o end_n thereof_o make_v a_o prick_n on_o the_o label_n i_o turn_v this_o prick_n upon_o the_o parallel_n from_o the_o pole_n 77_o degree_n 43_o minute_n and_o the_o meridian_n there_o cross_v shall_v be_v the_o three_o side_n of_o this_o triangle_n follow_v this_o meridian_n to_o the_o equator_fw-la and_o from_o his_o cut_n there_o to_o the_o centre_n be_v the_o measure_n of_o the_o lesser_a angle_n of_o this_o second_o triangle_n which_o be_v equal_a to_o the_o lesser_a leg_n of_o the_o first_o triangle_n 20_o degr_n 12_o minute_n likewise_o the_o arch_n of_o the_o limb_n from_o the_o pole_n to_o the_o label_n be_v the_o measure_n of_o the_o middle_a angle_n of_o the_o second_o triangle_n which_o be_v equal_a to_o the_o middle_a side_n that_o be_v to_o the_o great_a leg_n of_o the_o first_o triangle_n 57_o degree_n 48_o minute_n and_o now_o have_v find_v the_o leg_n of_o the_o first_o rectangle_v triangle_n you_o may_v by_o the_o first_o problem_n find_v the_o hypotenusa_fw-la to_o be_v 60_o degree_n the_o rectangled_a triangle_n use_v in_o the_o first_o way_n and_o the_o oblique_a quadrantal_a triangle_n use_v in_o this_o second_o
reet_n till_o the_o sun_n place_n in_o the_o ecliptic_a or_o the_o point_n of_o the_o star_n touch_v your_o proper_a horizon_n and_o that_o on_o the_o north_n side_n if_o the_o declination_n be_v north_n or_o on_o the_o south_n side_n if_o it_o be_v south_n lay_v the_o label_n to_o the_o sun_n or_o star_n in_o the_o horizon_n and_o between_o the_o label_n and_o meridies_n upon_o the_o limb_n you_o shall_v have_v the_o semi-diurnal_a arch_n both_o in_o degree_n and_o in_o hour_n and_o minute_n and_o you_o shall_v observe_v that_o those_o star_n who_o declination_n be_v great_a than_o the_o compliment_n of_o your_o latitude_n as_o lyra_n be_v in_o the_o last_o chap._n will_v never_o touch_v the_o horizon_n at_o all_o for_o star_n of_o such_o declination_n if_o they_o be_v north_n never_o set_v and_o if_o they_o be_v south_n never_o rise_v at_o our_o town_n but_o what_o shall_v i_o do_v if_o the_o star_n be_v not_o in_o my_o reet_n then_o will_v i_o number_v his_o right_a ascension_n on_o the_o limb_n of_o the_o reet_n and_o have_v thereto_o lay_v the_o label_n i_o will_v number_v his_o declination_n upon_o the_o label_n from_o the_o limb_n inward_o and_o where_o it_o end_v make_v a_o prick_n by_o the_o edge_n of_o the_o label_n in_o the_o reet_n for_o he_o for_o there_o be_v the_o place_n of_o the_o sta_n but_o if_o the_o star_n place_v happen_v to_o be_v in_o a_o window_n of_o the_o reet_n where_o the_o reet_n be_v perforate_v than_o i_o will_v make_v the_o prick_n upon_o the_o label_n edge_n at_o the_o star_n declination_n and_o turn_v that_o prick_n to_o the_o horizon_n i_o may_v pintch_v the_o label_n close_o with_o the_o reet_n and_o turn_n both_o together_o which_o will_v be_v the_o handsome_a way_n but_o if_o i_o move_v the_o label_n prick_v alone_o to_o the_o horizon_n it_o be_v sufficient_a for_o this_o problem_n which_o need_v no_o more_o word_n chap._n xix_o to_o find_v the_o beginning_n and_o end_n of_o twilight_n by_o the_o sun_n declination_n and_o the_o latitude_n of_o the_o place_n set_v the_o planisphear_n in_o the_o first_o mode_n of_o the_o meridional_a projection_n then_o turn_v the_o planisphear_n that_o the_o zenich_n may_v be_v downward_o and_o the_o almicanter_n most_o below_o the_o horizon_n then_o go_v to_o the_o 18_o almicanter_n below_o the_o horizon_n and_o wheresoever_o the_o parallel_n of_o the_o sun_n declination_n do_v cut_v that_o almicanter_n there_o be_v the_o beginning_n and_o end_n of_o twilight_n and_o because_o every_o parallel_n be_v divide_v by_o the_o meridian_n into_o 12_o hour_n or_o 180_o degr_n every_o 15_o degr_n be_v one_o hour_n therefore_o you_o may_v easy_o count_v how_o far_o the_o point_n where_o twilight_n begin_v be_v distant_a from_o midnight_n or_o from_o noon_n or_o from_o sun-rise_n or_o sunset_n in_o the_o horizon_n example_n in_o our_o latitude_n 52_o degr_n 15_o min._n my_o planisphear_n set_v as_o aforesaid_a i_o find_v that_o where_o the_o 18_o almicanter_n cut_v the_o equator_fw-la under_o the_o horizon_n there_o cut_v also_o in_o the_o same_o intersection_n the_o 30_o meridian_n or_o second_o hour_n circle_n from_o the_o axis_n and_o centre_n by_o which_o i_o gather_v that_o when_o the_o sun_n be_v in_o the_o equator_fw-la the_o twilight_n begin_v two_o hour_n before_o 6_o or_o sunrising_n and_o end_n likewise_o at_o 8_o of_o the_o clock_n at_o night_n the_o sun_n then_o set_v as_o you_o may_v see_v at_o 6._o likewise_o where_o the_o winter_n tropic_n cut_v the_o 18_o almicanter_n there_o cut_v also_o the_o first_o meridian_n from_o the_o axis_n southward_o show_v that_o in_o the_o depth_n of_o winter_n twilight_n begin_v 4_o minute_n after_o 6_o in_o the_o morning_n and_o last_v till_o 5_o hour_n 56_o minute_n afternoon_n likewise_o i_o see_v that_o about_o the_o begin_n of_o ♊_o where_o the_o sun_n decline_v north-ward_n about_o 20_o degree_n the_o twilight_n last_v till_o midnight_n and_o that_o from_o that_o time_n till_o the_o sun_n come_v to_o ♌_o that_o be_v from_o may_n 11_o to_o july_n 11_o or_o thereabouts_o we_o have_v no_o dark_a night_n at_o all_o unless_o the_o sky_n be_v cloudy_a for_o in_o all_o that_o time_n the_o sun_n be_v never_o find_v above_o 18_o degree_n under_o the_o horizon_n chap._n xx._n to_o find_v the_o time_n of_o the_o cosmical_a rise_n and_o set_v of_o the_o star_n by_o their_o declination_n and_o right_a ascension_n and_o the_o latitude_n of_o the_o place_n astar_n be_v say_v to_o rise_v cosmical_o when_o he_o rise_v at_o the_o same_o instant_n with_o the_o sun_n to_o find_v it_o use_v the_o equinoctial_a projection_n turn_v the_o star_n be_v find_v in_o your_o reet_n to_o the_o east_n part_n of_o your_o horizon_n and_o look_v what_o degree_n of_o the_o ecliptic_a cut_v the_o same_o east_n part_n of_o your_o horizon_n for_o when_o the_o sun_n come_v to_o that_o degree_n the_o star_n and_o sun_n shall_v rise_v both_o together_o if_o the_o star_n be_v not_o in_o your_o reet_n put_v he_o in_o with_o ink_n as_o you_o put_v in_o the_o rest_n book_n 1.7_o if_o his_o place_n light_n upon_o a_o window_n or_o hole_n of_o the_o reet_n prick_v he_o on_o the_o edge_n of_o the_o label_n and_o hold_v reet_a and_o label_n close_o together_o while_o you_o turn_v he_o to_o the_o horizon_n example_n sirius_n i_o have_v among_o 40_o other_o principal_a star_n in_o my_o reet_n and_o will_v advise_v you_o not_o to_o be_v without_o he_o for_o he_o be_v a_o little_a sun_n in_o a_o winter_n night_n to_o tell_v you_o how_o the_o time_n pass_v he_o be_v call_v by_o the_o latin_v both_o canis_n and_o canicula_fw-la for_o they_o have_v no_o name_n for_o the_o little_a dog_n but_o call_v he_o by_o the_o greek_a name_n procyon_n as_o pliny_n witness_v lib._n 18_o chap._n 28_o yet_o i_o have_v see_v a_o late_a writer_n who_o take_v upon_o he_o to_o teach_v the_o college_n of_o physician_n both_o physic_n and_o astrology_n before_o he_o have_v well_o learned_a either_o of_o they_o who_o in_o his_o obtrectation_n upon_o the_o pharmacopaea_n lond._n in_o the_o chapter_n of_o vinum_fw-la scilliticum_fw-la galeni_fw-la betray_v his_o ignorance_n herein_o as_o elsewhere_o in_o 100_o other_o thing_n which_o i_o can_v show_v for_o in_o that_o very_a chapter_n pag._n 147_o of_o his_o four_o impression_n in_o 24_o short_a line_n he_o commit_v 5_o absurd_a error_n 1._o he_o make_v it_o doubtful_a whether_o canis_n be_v to_o be_v take_v for_o sirius_n or_o procyon_n 2._o he_o go_v about_o to_o teach_v galen_n where_o squill_n grow_v and_o that_o there_o be_v no_o hilly_a ground_n near_o the_o sea_n 3._o he_o suppose_v that_o the_o acronycal_a rise_n of_o the_o dog_n which_o happen_v in_o the_o depth_n of_o winter_n be_v a_o fit_a time_n to_o gather_v squil_n than_o the_o heliacal_a rise_n which_o happen_v near_o unto_o the_o cosmical_a in_o the_o heat_n of_o summer_n 4._o he_o either_o suppose_v that_o squil_n grow_v in_o the_o parallel_n of_o london_n or_o that_o by_o the_o rise_n of_o the_o dog_n at_o london_n man_n shall_v gather_v squil_n in_o greece_n or_o spain_n 5._o he_o tell_v the_o college_n that_o both_o the_o dog_n be_v between_o the_o equator_fw-la and_o the_o south_n pole_n which_o indeed_o be_v news_n if_o it_o be_v true_a let_v the_o ingenuous_a reader_n pardon_v this_o digression_n and_o i_o proceed_v this_o sirius_n i_o bring_v to_o our_o horizon_n the_o 52_o ¼_n and_o find_v that_o there_o rise_v with_o he_o in_o the_o ecliptic_a ♌_o 18_o ½_n in_o like_a manner_n with_o procyon_n rise_v ♌_o 6_o â…“_n therefore_o sirius_n rise_v cosmical_o with_o we_o august_n 1_o and_o procyon_n 12_o day_n soon_o but_o in_o greece_n and_o spain_n in_o the_o latitude_n 38_o degr_n sirius_n rise_v with_o ♌_o 4_o ½_n that_o be_v a_o fortnight_n soon_o a_o star_n be_v say_v to_o set_a cosmical_o when_o the_o sun_n rise_v at_o his_o set_n place_v the_o star_n therefore_o on_o the_o west_n part_n of_o your_o horizon_n then_o look_v what_o degree_n of_o the_o ecliptic_a rise_v in_o the_o east_n part_n for_o when_o the_o sun_n come_v to_o that_o degree_n the_o star_n shall_v set_v cosmical_o example_n i_o bring_v sirius_n to_o the_o south-west_n part_n of_o our_o horizon_n where_o he_o use_v to_o set_v and_o in_o the_o southeast_n part_n i_o see_v â™_o 23_o degree_n in_o the_o ecliptic_a rise_n therefore_o when_o the_o sun_n be_v in_o â™_o 23._o which_o be_v about_o november_n 5._o than_o shall_v sirius_n set_v cosmical_o but_o at_o athens_n in_o lat._n 37_o ¼_n his_o cosmical_a rise_n be_v ☉_o in_o ♌_o 4._o july_n 17_o his_o cosmical_a set_v be_v ☉_o in_o â™_o 9_o nou._n 20_o the_o pleyade_n in_o our_o lat_fw-mi cosmical_o rise_v ☉_o in_o ♉_o 12_o ½_n apr._n 22._o the_o
30_o degree_n i_o say_v here_z begins_z â™’_o and_o go_v on_o 26._o 22._o minute_n further_o i_o say_v thus_o far_o be_v the_o star_n go_v in_o longitude_n now_o here_o cut_v the_o finiter_n by_o this_o account_n the_o azimuth_n 35_o â…“_n from_o the_o limb_n in_o this_o azimuth_n i_o number_v the_o star_n latitude_n by_o the_o almicantars_n 22.07_o ½_n and_o at_o the_o end_n of_o that_o number_n in_o the_o say_a azimuth_n i_o prick_v the_o star_n place_n and_o here_o i_o see_v the_o 8_o parallel_v of_o north_n declination_n upon_o the_o mater_n cut_v he_o and_o the_o meridian_n 51_o â…“_n from_o the_o limb_n show_v the_o excess_n of_o his_o right_a ascension_n above_o 270._o which_o i_o keep_v before_o therefore_o i_o conclude_v the_o right_a ascension_n of_o eniph_n alpharat_n anno_fw-la dom._n 1600_o be_v 321._o 20_o minute_n and_o his_o declination_n 8._o deg_fw-la north._n past_o this_o on_o fol._n 102_o so_o as_o it_o may_v lie_v open_a while_o that_o chapter_n be_v read_v another_o way_n to_o place_v the_o star_n in_o the_o mater_fw-la by_o their_o declination_n and_o horary-distance_n from_o the_o meridian_n see_v hereafter_o chapter_n 52._o chap._n xxxvi_o the_o latitude_n and_o declination_n of_o a_o star_n give_v to_o find_v his_o longitude_n and_o right_a ascension_n set_v your_o planisphear_n in_o the_o second_o mode_n of_o the_o meridional_a projection_n turn_v the_o zenith_n northward_o or_o southward_o as_o the_o star_n latitude_n happen_v to_o be_v north_n or_o south_n then_o look_v where_o the_o parallel_n of_o the_o star_n latitude_n in_o the_o reet_n cut_v the_o parallel_n of_o the_o star_n declination_n on_o the_o mater_n the_o azimuth_n cut_v that_o intersection_n show_v the_o longitude_n of_o the_o star_n and_o the_o meridian_n there_o cut_v show_v his_o right_a ascension_n example_n the_o declination_n of_o spica_fw-la â™_o anno_fw-la dom._n 1670._o will_v be_v 9_o ½_n south_n the_o latitude_n be_v always_o 1._o 59_o minute_n south_n now_o where_o the_o second_o almicantar_n cut_v the_o 9_o ½_n parallel_v of_o south_n declination_n there_o pass_v the_o 19_o ¼_n azimuth_n from_o the_o axis_n towards_o my_o left_a hand_n show_v spica_n longitude_n ♎_o 19_o ¼_n and_o the_o 17_o meridian_n from_o the_o axis_n to_o which_o i_o add_v a_o semicircle_n because_o ♎_o 0._o be_v at_o the_o centre_n and_o i_o make_v 197_o degree_n the_o right_a ascension_n of_o spica_fw-la for_o 1670._o chap._n xxxvii_o the_o longitude_n and_o latitude_n of_o two_o star_n give_v to_o find_v their_o distance_n make_v one_o of_o the_o pole_n of_o the_o mater_n to_o be_v pole_n of_o the_o ecliptic_a for_o this_o turn_n and_o set_v the_o star_n which_o have_v most_o latitude_n at_o his_o distance_n in_o the_o limb_n and_o turn_v the_o zenith_n to_o he_o count_v thence_o by_o the_o meridian_n the_o difference_n of_o longitude_n till_o you_o come_v to_o the_o other_o side_n of_o your_o triangle_n and_o in_o that_o side_n number_n either_o the_o latitude_n from_o the_o equator_fw-la or_o his_o compliment_n from_o the_o pole_n at_o the_o end_n of_o this_o number_n be_v the_o other_o star_n and_o the_o azimuth_n pass_v from_o he_o to_o the_o zenith_n show_v the_o distance_n this_o be_v do_v by_o the_o second_o problem_n of_o obliquangled_a triangle_n book_n 3.15_o example_n in_o tycho'es_n table_n for_o 1600._o aldebarans_n longitude_n be_v ♊_o 4.12_o ½_n latitude_n 5._o 31._o min._n a._n sirius_n longitude_n ♋_o 8._o 35_o ½_n latitude_n 39_o 30_o ½_n a._n difference_n of_o longitude_n 34._o 23._o i_o number_v therefore_o 39_o 30_o minute_n ½_n the_o latitude_n of_o sirius_n from_o the_o equator_fw-la in_o the_o limb_n or_o the_o compliment_n thereof_o from_o the_o pole_n all_o be_v one_o there_o i_o set_v the_o zenith_n to_o stand_v for_o sirius_n then_o because_o aldebaran_n be_v distant_a from_o sirius_n in_o longitude_n 34._o 23._o minute_n i_o take_v the_o 34_o ½_n meridian_n from_o the_o zenith_n and_o where_o the_o 5_o ½_n parallel_n cut_v he_o there_o say_v i_o be_v aldebaran_n and_o c_o of_o my_o triangle_n and_o the_o azimuth_n pass_v thence_o to_o the_o zenith_n measure_v the_o distance_n of_o the_o star_n 46_o degree_n almost_o chap._n xxxviii_o the_o declination_n and_o right_a ascension_n of_o any_o two_o star_n give_v to_o find_v their_o distance_n do_v here_o with_o the_o right_a ascension_n and_o declination_n as_o you_o shall_v do_v with_o the_o longitude_n and_o latitude_n by_o the_o former_a chapter_n for_o the_o case_n be_v like_a and_o require_v the_o same_o manner_n of_o work_v chap._n thirty-nine_o the_o declination_n of_o a_o star_n or_o planet_n and_o his_o distance_n from_o a_o know_a star_n give_v to_o find_v his_o right_a ascension_n because_o this_o case_n be_v the_o converse_n of_o the_o precedent_n and_o soluble_a by_o the_o first_o problem_n of_o obliquangled_a triangle_n book_n 3._o 14._o a_o example_n or_o two_o shall_v suffice_v past_o this_o on_o fol._n 105_o so_o as_o it_o may_v lie_v open_a while_o that_o chapter_n be_v read_v a_o b_o the_o distance_n of_o mandibulae_fw-la from_o the_o pole_n 87._o 20_o minute_n i_o set_v between_o the_o pole_n and_o nadir_n in_o the_o limb_n because_o b_o c_o will_n reach_n beyond_o the_o finitor_n for_o a_o c_o the_o distance_n of_o the_o star_n i_o seek_v the_o 13_o parallel_v from_o the_o pole_n and_o for_o b_o c_o i_o seek_v the_o 94._o 50_o minute_n almicantar_n count_v from_o the_o nadir_n that_o be_v the_o 5_o almost_o above_o the_o finitor_n and_o where_o the_o say_a parallel_n and_o almicantar_n cross_v there_o be_v cor_fw-la caeti_fw-la and_o c_o of_o my_o triangle_n through_o it_o there_o cut_v the_o azimuth_n 10_o â…”_n show_v the_o difference_n of_o the_o right_a ascension_n of_o the_o star_n which_o difference_n i_o subtract_v out_o of_o the_o right_a ascension_n of_o mandibula_fw-la because_o he_o be_v further_a east_n and_o there_o remain_v the_o right_a ascension_n of_o cor_fw-la caeti_fw-la 30._o 16_o minute_n or_o rather_o 13_o minute_n and_o i_o have_v here_o also_o number_v by_o the_o meridian_n the_o angle_n a_o at_o mandibula_fw-la 120_o degr_fw-la though_o un-required_n another_o example_n january_n 7._o 1656_o 7_o i_o observe_v by_o my_o brass_n quadrant_n of_o 12_o inch_n in_o radius_fw-la the_o meridian_n altitude_n of_o jupiter_n 56._o 20_o minute_n out_o of_o which_o subtract_v the_o height_n of_o the_o equator_fw-la here_o at_o ecton_n 37._o 45_o minute_n i_o find_v his_o declination_n 18._o 35_o minute_n north_n his_o distance_n then_o from_o lucida_n pleiadum_fw-la i_o observe_v by_o my_o crossstaff_n 5._o 12_o minute_n and_o from_o aldebaran_n 10.07_o minute_n the_o compliment_n of_o decli_n of_o lucida_n pleiadum_fw-la be_v 67.00_o mi._n the_o compliment_n of_o ♃_o his_o declination_n be_v observe_v 71._o 25._o and_o these_o two_o compliment_n with_o the_o distance_n of_o ♃_o and_o lucida_n pleiadum_fw-la 5._o 12_o minute_n make_v a_o triangle_n soluble_a by_o the_o first_o problem_n of_o obliquangled_a triangle_n whereby_o you_o may_v find_v the_o angle_n of_o the_o difference_n of_o right_a ascension_n of_o lucida_n pleiadum_fw-la and_o ♃_o be_v 2._o 56_o minute_n which_o add_v to_o the_o right_a ascension_n of_o lucida_n pleiadum_fw-la because_o ♃_o be_v eastward_o make_v 54._o 44_o minute_n the_o right_a ascension_n of_o jupiter_n chap._n xl._n the_o latitude_n of_o a_o star_n or_o planet_n and_o his_o distance_n from_o a_o know_a star_n give_v to_o find_v his_o longitude_n do_v here_o with_o the_o longitude_n and_o latitude_n as_o you_o be_v teach_v to_o do_v with_o the_o right_a ascension_n and_o declination_n in_o the_o former_a chapter_n chap._n xli_o to_o find_v the_o distance_n of_o two_o star_n by_o their_o altitude_n and_o their_o difference_n of_o azimuth_n observe_v at_o the_o same_o time_n the_o compliment_n of_o the_o altitude_n be_v the_o distance_n of_o the_o star_n from_o the_o zenith_n set_v one_o of_o the_o star_n at_o the_o pole_n and_o set_v the_o zenith_n as_o much_o from_o he_o in_o the_o limb_n as_o the_o compliment_n of_o his_o altitude_n come_v to_o then_o consider_v what_o difference_n of_o azimuth_n the_o star_n have_v take_v the_o azimuth_n of_o like_a distance_n from_o the_o limb_n begin_v from_o that_o side_n of_o the_o limb_n where_o the_o pole_n aforesaid_a be_v and_o in_o that_o azimuth_n reckon_v from_o the_o finitor_n the_o altitude_n of_o the_o other_o star_n or_o the_o compliment_n of_o his_o altitude_n from_o the_o zenith_n all_o be_v one_o at_o the_o end_n thereof_o be_v c_o and_o the_o other_o star_n and_o the_o meridian_n that_o pass_v from_o he_o to_o the_o pole_n show_v the_o distance_n of_o the_o star_n this_o case_n be_v so_o like_a that_o of_o chapter_n 37._o that_o he_o who_o know_v one_o may_v know_v the_o other_o also_o chap._n xlii_o to_o find_v the_o angle_n of_o
follow_v this_o azimuth_n to_o the_o finitor_n there_o be_v nonagesimus_fw-la gradus_fw-la and_o the_o altitude_n thereof_o 42_o degree_n count_v from_o the_o limb_n here_o horizon_n the_o azimuth_n thereof_o lie_v in_o the_o limb_n between_o the_o finitor_n and_o the_o meridian_n 36_o ⅓_n as_o before_o equal_a to_o the_o amplitude_n of_o the_o ascendent_n i_o number_v also_o from_o ♓_o 25_o ½_n in_o the_o meridian_n 23._o 41_o minute_n to_o the_o left_a hand_n still_o and_o there_o i_o have_v ♈_o 19_o 11_o minute_n the_o sun_n place_n which_o cut_v on_o the_o label_n 41_o ⅔_n for_o the_o altitude_n of_o the_o sun_n there_o and_o the_o label_n at_o the_o same_o time_n cut_v in_o the_o limb_n about_o 29._o from_o south_n eastward_o for_o the_o azimuth_n of_o the_o sun_n and_o after_o the_o same_o manner_n you_o have_v before_o you_o the_o altitude_n and_o azimuth_n of_o every_o other_o degree_n of_o the_o ecliptic_a for_o the_o time_n propose_v chap._n lviii_o to_o do_v the_o same_o by_o the_o nonagesimal_n projection_n if_o the_o altitude_n of_o nonagesimus_fw-la gradus_fw-la be_v first_o give_v instead_o of_o the_o altitude_n of_o culmen_fw-la caeli_fw-la set_v your_o planisphear_n in_o the_o nonagesimal_n projection_n by_o book_n 2.3_o that_o be_v make_v the_o limb_n now_o to_o represent_v the_o circle_n of_o longitude_n or_o azimuth_n for_o it_o be_v both_o which_o cut_v the_o nonagesimus_fw-la gradus_fw-la and_o make_v the_o equinoctial_a line_n here_o to_o be_v horizon_n and_o from_o the_o equinectial_a line_n number_n in_o the_o limb_n the_o altitude_n of_o nonagesimus_fw-la gradus_fw-la and_o thereto_o set_v the_o finitor_n so_o shall_v the_o finitor_n be_v ecliptic_a the_o nonagesimus_fw-la gradus_fw-la at_o the_o limb_n the_o ascendent_n and_o descendent_a at_o the_o centre_n and_o because_o the_o equinoctial_a line_n be_v horizon_n in_o this_o projection_n therefore_o the_o meridian_n become_v azimuth_n and_o the_o parallel_n almicantars_n show_v the_o altitude_n and_o azimuth_n of_o every_o degree_n of_o the_o ecliptic_a if_o you_o reckon_v as_o you_o ought_v in_o this_o manner_n reckon_v in_o the_o equinoctial_a line_n here_o horizon_n from_o the_o centre_n the_o amplitude_n of_o the_o ascendent_n to_o the_o right_a hand_n if_o it_o be_v a_o north_n sign_n and_o contrary_o if_o it_o be_v a_o south_n sign_n where_o this_o amplitude_n end_n be_v the_o east_n point_n from_o whence_o you_o shall_v reckon_v all_o your_o azimuth_n count_n thence_o to_o the_o limb_n and_o back_n again_o if_o need_v be_v in_o the_o say_v equinoctial_a line_n till_o you_o have_v make_v 90_o degree_n there_o be_v your_o meridian_n as_o far_o distant_a from_o the_o limb_n as_o the_o east_n point_n be_v from_o the_o ascendent_n follow_v this_o meridian_n to_o the_o finitor_n and_o there_o he_o show_v you_o culmen_fw-la caeli_fw-la and_o the_o parallel_n there_o cut_v show_v the_o altitude_n thereof_o now_o may_v you_o find_v every_o degree_n of_o the_o ecliptic_a above_o the_o horizon_n if_o you_o know_v but_o what_o ascend_v or_o descend_v or_o culminate_v and_o of_o every_o such_o degree_n the_o parallel_n show_v you_o the_o altitude_n and_o the_o meridian_n show_n his_o azimuth_n if_o you_o begin_v your_o number_n from_o the_o east_n or_o south_n azimuth_n example_n when_o ♋_o 24_o degree_n be_v ascend_v as_o in_o the_o example_n before_o use_v as_o by_o consequence_n ♈_o 24._o in_o nonagisimo_fw-la gradu_fw-la ♂_o be_v in_o ♉_o 4._o 45_o minute_n and_o have_v but_o 3._o or_o 4._o minute_n south_n latitude_n i_o will_v know_v ♂_o his_o altitude_n and_o azimuth_n set_v go_v the_o finitor_n above_o the_o equinoctial_a line_n 42_o degree_n which_o be_v the_o altitude_n of_o nonagesimus_fw-la gradus_fw-la i_o say_v because_o the_o nonagesimus_fw-la gradus_fw-la at_o the_o end_n of_o the_o finitor_n in_o the_o limb_n be_v ♈_o 24._o therefore_o i_o must_v count_v back_o 10._o 45_o minute_n towards_o the_o ascendent_n for_o mars_n and_o there_o the_o parallel_n 41_o degree_n with_o 10_o minute_n cut_v the_o finitor_n for_o the_o altitude_n of_o ♂_o and_o the_o 14_o meridian_n eastward_o from_o the_o limb_n give_v i_o his_o azimuth_n which_o if_o i_o begin_v to_o reckon_v from_o the_o east_n point_n fall_v out_o to_o be_v almost_o the_o 40th_o azimuth_n from_o the_o east_n mars_n his_o latitude_n here_o be_v not_o regard_v chap._n lix_n the_o nonagesimus_fw-la gradus_fw-la and_o his_o altitude_n and_o azimuth_n give_v as_o in_o the_o former_a chapter_n how_o in_o the_o same_o projection_n to_o get_v the_o altitude_n and_o azimuth_n of_o any_o planet_n or_o star_n by_o his_o longitude_n and_o latitude_n your_o palnisphear_n set_v as_o in_o the_o former_a chapter_n you_o shall_v number_v the_o longitude_n of_o the_o star_n upon_o the_o finitor_n here_o ecliptic_a beginning_n at_o the_o descendent_a or_o nonagesimus_fw-la gardus_fw-la and_o in_o the_o azimuth_n serve_v his_o longitude_n count_v his_o latitude_n by_o the_o almicantars_n at_o the_o end_n of_o which_o account_n be_v the_o star_n place_n for_o this_o time_n the_o parallel_n cut_v there_o show_v his_o altitude_n and_o the_o meridian_n cut_v there_o show_v his_o azimuth_n if_o you_o count_v from_o the_o east_n point_n as_o you_o be_v teach_v in_o the_o former_a chapter_n example_n lucida_n pleiadum_fw-la be_v in_o longitude_n ♉_o 25._o 10_o minute_n latitude_n 4_o degree_n 00_o minute_n north._n therefore_o from_o the_o nonagesimus_fw-la gradus_fw-la ♈_o 24._o i_o number_n in_o the_o finitor_n towards_o the_o ascendent_n 31._o 10_o minute_n and_o there_o be_v the_o longitude_n of_o lucida_n pleiaedum_n in_o the_o azimuth_n that_o cut_v here_o i_o go_v up_o northward_o 4_o degree_n and_o there_o i_o make_v a_o prick_n for_o lucida_n pleiadum_fw-la now_o the_o parallel_n 38_o ½_n show_v i_o his_o altitude_n and_o the_o 48th_o ½_n meridian_n from_o the_o centre_n show_v i_o that_o lucida_n pleiadum_fw-la be_v go_v 48_o ½_n in_o azimuth_n from_o the_o ascendent_n but_o from_o the_o east_n point_n only_o 12_o degree_n 10_o minute_n chap._n lx._n the_o altitude_n and_o azimuth_n of_o any_o star_n take_v and_o either_o the_o ascendent_n nonagesimus_fw-la gradus_fw-la or_o culmen_fw-la caeli_fw-la know_v how_o by_o the_o same_o nonagesimal_a projection_n to_o find_v the_o star_n longitude_n and_o latitude_n if_o you_o know_v either_o the_o ascendent_n nonagesimus_fw-la gradus_fw-la or_o culmen_fw-la caeli_fw-la you_o have_v enough_o to_o put_v your_o planisphear_n in_o the_o nonagesimal_n projection_n by_o the_o former_a chapter_n and_o your_o planisphear_n so_o set_v you_o shall_v seek_v out_o the_o meridian_n which_o stand_v for_o the_o azimuth_n in_o which_o you_o observe_v the_o star_n and_o therein_o number_n from_o the_o equinoctial_a line_n the_o altitude_n observe_v the_o azimuth_n and_o almicantar_n cut_v there_o show_v the_o longitude_n and_o latitude_n of_o the_o star_n inquire_v if_o the_o azimuth_n reach_v not_o the_o place_n of_o the_o star_n turn_v the_o reet_a half_a round_n and_o let_v the_o zenith_n and_o nadir_n point_v change_v place_n and_o your_o turn_n be_v serve_v example_n febr._n 13_o 1657_o 8._o i_o observe_v somewhat_o near_o that_o ♃_o be_v go_v westward_o from_o the_o meridian_n in_o azimuth_n 14_o degree_n and_o that_o his_o altitude_n be_v 61_o degree_n sirius_n be_v then_o in_o the_o meridian_n by_o which_o i_o have_v the_o ascendent_n culmen_fw-la and_o nonagesimus_fw-la gradus_fw-la any_o or_o all_o of_o they_o give_v for_o when_o in_o the_o equinoctial_a projection_n i_o bring_v sirius_n to_o the_o meridian_n line_n it_o be_v all_o one_o as_o if_o i_o have_v set_v the_o sun_n place_n to_o the_o hour_n of_o the_o night_n by_o chapter_n 46._o and_o i_o see_v there_o culminate_v with_o sirius_n ♋_o 7._o 10_o minute_n who_o meridian_n altitude_n by_o the_o 46._o be_v 61._o 5_o minute_n and_o i_o see_v ♎_o 5_o ½_n ascend_v in_o my_o horizon_n and_o ♈_o 5_o ½_n descend_v therefore_o ♋_o 5_o ½_n be_v nonagesimus_fw-la gradus_fw-la which_o be_v 90_o degree_n distant_a both_o from_o the_o ascendent_n and_o descendent_a his_o altitude_n by_o chapter_n 55._o 61._o 10_o minute_n almost_o therefore_o i_o set_v the_o finitor_n 61._o 10_o minute_n above_o meridies_n as_o chapter_n 58._o and_o in_o the_o finitor_n at_o the_o limb_n i_o count_v ♋_o 5_o ½_n nonagesimus_fw-la gradus_fw-la thence_o i_o go_v inward_o in_o the_o finitor_n 1._o 40_o minute_n where_o i_o come_v to_o ♋_o 7._o 10._o the_o degree_n of_o culmination_n this_o degree_n be_v cut_v by_o the_o four_o meridian_n from_o the_o limb_n whereby_o i_o learn_v that_o this_o four_o meridian_n will_v be_v the_o meridian_n of_o my_o place_n and_o that_o the_o amplitude_n of_o the_o nonagesimus_fw-la gradus_fw-la and_o likewise_o of_o the_o ascendent_n be_v 4_o degree_n now_o to_o place_v ♃_o in_o the_o mater_fw-la i_o count_v his_o azimuth_n first_o beginning_n from_o the_o meridian_n of_o my_o
london_n from_o jerusalem_n chap._n lxx_o the_o latitude_n and_o distance_n of_o two_o place_n give_v to_o find_v the_o difference_n of_o longitude_n the_o triangle_n will_v stand_v as_o in_o the_o former_a chapter_n there_o by_o two_o side_n and_o the_o angle_n comprehend_v you_o seek_v the_o three_o side_n by_o problem_n 2._o obliquangled_a triangle_n here_o by_o three_o side_n give_v you_o seek_v a_o angle_n by_o problem_n 1_o obliquangled_a triangle_n make_v the_o pole_n pole_n and_o set_v the_o zenith_n to_o the_o latitude_n of_o one_o of_o the_o place_n as_o you_o do_v london_n chapter_n 69._o 38._o 28_o minute_n from_o the_o pole_n than_o number_n the_o compliment_n of_o the_o latitude_n of_o the_o other_o place_n from_o the_o pole_n by_o the_o parallel_n and_o the_o distance_n of_o the_o two_o place_n from_o the_o zenith_n by_o the_o almicantars_n and_o where_o the_o last_o parallel_n and_o last_o almicantar_n meet_v be_v c_o of_o your_o triangle_n see_v book_n 3._o 14._o now_o count_v how_o many_o meridian_n there_o be_v between_o c_o and_z the_o limb_n so_o many_o degree_n be_v the_o angle_n at_o the_o pole_n seek_v for_o the_o difference_n of_o longitude_n example_n have_v the_o distance_n of_o london_n from_o the_o pole_n 38._o 28_o minute_n and_o of_o jerusalem_n from_o the_o pole_n 58._o 5_o minute_n and_o the_o distance_n of_o london_n from_o jerusalem_n 2300._o common_a english_a mile_n of_o which_o 60._o make_v a_o degree_n i_o set_v the_o zenith_n for_o london_n 38._o 28_o minute_n from_o the_o pole_n in_o the_o limb_n then_o because_o jerusalem_n be_v distant_a from_o the_o pole_n 58._o 5_o minute_n i_o go_v to_o the_o 58th_o parallel_n from_o the_o pole_n and_o lay_v one_o finger_n or_o the_o point_n of_o a_o bodkin_n on_o he_o and_o because_o london_n be_v distant_a from_o jerusalem_n 38_o degree_n 20_o minute_n i_o count_v from_o the_o zenith_n to_o the_o almicantar_n 38._o 20_o minute_n now_o where_o this_o almicantar_n cross_v the_o parallel_n last_o find_v there_o be_v c_o of_o the_o triangle_n and_o the_o place_n of_o jerusalem_n and_o you_o may_v see_v that_o you_o must_v cross_v 46._o meridian_n before_n you_o can_v go_v thence_o to_o the_o zenith_n in_o the_o limb_n which_o show_v that_o the_o angle_n at_o the_o pole_n for_o the_o difference_n of_o longitude_n be_v 46._o chap._n lxxi_o to_o find_v what_o degree_n of_o the_o ecliptic_a culminate_v in_o another_o country_n at_o any_o time_n propose_v if_o the_o difference_n of_o longitude_n be_v know_v in_o the_o equinoctial_a projection_n bring_v the_o sun_n place_n to_o the_o hour_n propose_v by_o help_n of_o the_o label_n and_o in_o the_o noon-line_n you_o see_v present_o what_o degree_n culminate_v in_o your_o country_n as_o chapter_n 46_o be_v show_v now_o to_o know_v this_o for_o another_o town_n set_v the_o label_n so_o many_o degree_n from_o the_o noon-line_n as_o the_o difference_n of_o longitude_n require_v and_o that_o eastward_o if_o the_o place_n propose_v be_v east_n or_o westward_o if_o it_o bear_v west_n and_o so_o the_o label_n shall_v cut_v the_o degree_n of_o culmination_n for_o the_o place_n propose_v example_n if_o it_o be_v demand_v what_o degree_n be_v culminate_v at_o jerusalem_n march_v 10._o at_o 10._o a_o clock_n before_o noon_n i_o will_v set_v the_o sun_n place_n ♈_o 0._o to_o the_o hour_n and_o i_o see_v upon_o the_o noon_n line_n which_o be_v our_o meridian_n there_o culminate_v ♒_o 28_o almost_o now_o for_o the_o meridian_n of_o jerusalem_n i_o must_v lay_v the_o label_n 46_o degree_n eastward_o that_o be_v from_o meridies_n towards_o oriens_fw-la and_o look_v what_o star_n or_o degree_n of_o the_o ecliptic_a be_v then_o cut_v by_o the_o label_n that_o be_v then_o culminate_v in_o the_o meridian_n at_o jerusalem_n as_o here_o i_o find_v ♈_o 17_o ½_n for_o in_o this_o projection_n the_o label_n lay_v he_o where_o you_o will_v be_v a_o meridian_n chap._n lxxii_o to_o find_v what_o a_o clock_n it_o be_v in_o another_o country_n by_o know_v the_o hour_n at_o home_n and_o the_o difference_n of_o longitude_n this_o be_v do_v easy_o enough_o without_o a_o instrument_n for_o if_o you_o turn_v the_o difference_n of_o longitude_n into_o hour_n and_o minute_n and_o add_v the_o same_o to_o your_o hour_n for_o any_o place_n which_o lie_v eastward_o or_o subtract_v the_o same_o for_o any_o place_n which_o lie_v westward_o you_o shall_v make_v the_o hour_n of_o the_o place_n example_n the_o difference_n of_o longitude_n between_o london_n and_o jerusalem_n be_v 46._o or_o be_v convert_v into_o time_n 3_o hour_n 4_o minute_n therefore_o add_v this_o to_o the_o time_n at_o london_n i_o say_v when_o it_o be_v noon_n at_o london_n it_o be_v 4_o minute_n past_o 3_o a_o clock_n after_o noon_n at_o jerusalem_n and_o when_o it_o be_v 2_o a_o clock_n at_o london_n it_o be_v 5._o and_o 4_o minute_n at_o jerusalem_n if_o you_o will_v do_v it_o by_o the_o planisphear_n you_o shall_v do_v it_o in_o the_o equinoctial_a projection_n thus_o whereas_o the_o limb_n of_o your_o rect_a be_v graduate_v into_o 360_o degree_n if_o you_o distinguish_v the_o hour_n also_o at_o every_o 15_o degree_n begin_v at_o the_o zenith_n which_o shall_v be_v 12_o and_o number_v thence_o in_o the_o limb_n of_o your_o reet_n to_o your_o right_a hand_n or_o westward_o 1_o 2_o 3_o etc._n etc._n then_o shall_v you_o need_v to_o do_v no_o more_o but_o set_v the_o zenith_n to_o the_o difference_n of_o longitude_n east_n or_o west_n from_o your_o meridian_n as_o the_o strange_a place_n happen_v to_o be_v situate_a for_o then_o the_o label_n lay_v to_o the_o hour_n of_o your_o country_n in_o the_o limb_n of_o the_o mater_n shall_v show_v the_o hour_n of_o the_o other_o country_n in_o the_o limb_n of_o the_o reet_n and_o so_o the_o zenith_n be_v lay_v to_o 60_o degree_n westward_o which_o be_v the_o meridian_n of_o the_o isle_n of_o barbados_n the_o label_n lay_v to_o meridies_n shall_v cut_v in_o the_o limb_n of_o the_o reet_n 8_o of_o the_o clock_n before_o noon_n which_o show_v i_o that_o when_o it_o be_v noon_n with_o we_o it_o be_v at_o barbados_n but_o eight_o in_o the_o morning_n the_o end_n of_o the_o four_o book_n chap._n lxxiii_o the_o longitude_n and_o latitude_n of_o one_o place_v know_v and_o the_o rumb_n and_o distance_n of_o a_o second_o place_n to_o find_v both_o the_o longitude_n and_o latitude_n of_o the_o second_o place_n set_v the_o zenith_n to_o the_o latitude_n of_o the_o first_o place_n then_o seek_v the_o azimuth_n which_o serve_v for_o the_o rumb_n of_o the_o second_o place_n and_o in_o that_o azimuth_n count_v his_o distance_n from_o the_o zenith_n where_o this_o distance_n end_v there_o be_v the_o second_o place_n whole_a latitude_n be_v show_v you_o by_o the_o parallel_n which_o cut_v he_o and_o the_o meridian_n cut_v there_o also_o show_v his_o longitude_n example_n let_v z_o be_n london_n and_o because_o jerusalem_n bear_v from_o london_n almost_o s_n b_o e_o or_o 77_o ½_n from_o south_n eastward_o therefore_o i_o choose_v the_o azimuth_n 77_o ½_n z_o k._n therein_o i_o number_v jerusalem_n distance_n from_o london_n z_o i_o 2300._o mile_n or_o minute_n that_o be_v 38._o 20._o minute_n now_o in_o the_o triangle_n z_o p_o i_o i_o may_v find_v p_o i_o the_o compliment_n of_o jerusalem_n latitude_n 58._o 05._o minute_n and_o z_o p_o i_o the_o difference_n of_o longitude_n 46_o which_o must_v be_v add_v to_o the_o longitude_n of_o london_n to_o make_v the_o longitude_n of_o jerusalem_n chap._n lxxiv_o the_o latitude_n and_o distance_n of_o two_o place_n give_v to_o find_v the_o rumb_n and_o the_o difference_n of_o longitude_n count_n in_o the_o meridian_n from_o p_o the_o pole_n the_o compliment_n of_o the_o latitude_n of_o the_o first_o place_n and_o thereto_o set_v z_o the_o zenith_n count_n also_o from_o p_o the_o compliment_n of_o the_o latitude_n of_o the_o second_o place_n and_o lay_v your_o finger_n on_o the_o parallel_n at_o which_o your_o number_n end_v count_n also_o from_o z_o the_o distance_n of_o the_o place_n in_o degree_n and_o minute_n and_o note_v the_o almicantar_n at_o which_o this_o number_n end_v where_o this_o almicantar_n cross_v the_o aforesaid_a parallel_n there_o be_v c_o of_o your_o triangle_n but_o here_o mark_v i_o look_v what_o azimuth_n cut_v here_o it_o show_v the_o rumb_n and_o the_o meridian_n that_o cut_v here_o if_o you_o count_v his_o distance_n from_o the_o limb_n show_v the_o difference_n of_o the_o longitude_n of_o the_o place_n this_o be_v so_o plain_a from_o chapter_n 69_o 70_o and_o 73_o that_o it_o need_v no_o example_n the_o same_o scheam_n serve_v these_o 4_o chapter_n the_o end_n of_o the_o four_o book_n the_o five_o book_n show_v the_o way_n to_o resolve_v all_o gnomonical_a
be_v place_v upon_o the_o sole_a of_o the_o window_n shall_v supply_v the_o use_n of_o the_o nodus_fw-la in_o the_o gnomon_n and_o the_o beam_n of_o the_o sun_n be_v reflect_v by_o this_o glass_n or_o water_n shall_v show_v the_o hour_n upon_o the_o ceiling_n the_o planisphear_n shall_v help_v you_o to_o make_v this_o dyal_n two_o way_n if_o the_o window_n decline_v not_o much_o from_o the_o south_n you_o may_v make_v it_o most_o easy_o the_o first_o way_n but_o if_o it_o decline_v much_o and_o so_o the_o line_n fall_v much_o upon_o the_o partition_n wall_n or_o if_o you_o will_v adorn_v this_o dyal_n with_o the_o parallel_n or_o other_o circle_n you_o shall_v use_v the_o second_o way_n the_o first_o way_n be_v this_o draw_v a_o meridian_n line_n upon_o the_o floor_n by_o book_n 4.3_o so_o that_o it_o may_v point_v upon_o the_o perpendicular_a which_o you_o shall_v imagine_v to_o fall_v from_o the_o nodus_fw-la upon_o the_o plain_a of_o the_o floor_n prolong_v and_o this_o may_v be_v most_o easy_o do_v if_o you_o hang_v a_o plumb-line_n in_o the_o window_n dnecuy_v over_o the_o nodus_fw-la of_o place_n of_o the_o glais_n for_o the_o shadow_n which_o that_o plumb-line_n give_v upon_o the_o floor_n at_o noon_n be_v the_o meridian_n line_n seek_v and_o by_o a_o ruler_n or_o a_o line_n stretch_v upon_o it_o you_o may_v prolong_v it_o as_o far_o as_o you_o shall_v need_v then_o let_v a_o plumb_n line_n fall_n from_o the_o ceiling_n upon_o this_o meridian_n line_n of_o the_o floor_n and_o behind_o it_o northward_o or_o southward_o place_v your_o ey_fw-mi so_o that_o the_o plumb-line_n may_v hide_v the_o meridian_n line_n of_o the_o floor_n from_o your_o ey_fw-mi then_o keep_v your_o head_n steady_a cast_v you_o ay_o up_o to_o the_o ceiling_n and_o direct_v one_o to_o make_v two_o point_n at_o a_o good_a distance_n in_o the_o line_n upon_o the_o ceiling_n which_o the_o plumb-line_n now_o cover_v from_o your_o ey_fw-mi and_o by_o these_o point_v you_o shall_v draw_v a_o straight_a meridian_n on_o the_o ceiling_n then_o have_v fasten_v one_o end_n of_o a_o line_n at_o nodus_fw-la let_v another_o stretch_v this_o line_n up_o to_o the_o meridian_n on_o the_o ceiling_n and_o let_v he_o move_v his_o hand_n near_o or_o further_o in_o the_o meridian_n till_o you_o find_v by_o a_o quadrant_n that_o this_o line_n point_v up_o northward_o as_o many_o degree_n as_o the_o elevation_n of_o the_o equator_fw-la be_v in_o your_o country_n and_o then_o you_o shall_v cause_v he_o to_o make_v a_o point_n where_o the_o line_n touch_v the_o meridian_n of_o the_o ceiling_n and_o through_o that_o point_n you_o shall_v draw_v the_o equinoctial_a line_n of_o your_o dyal_n cut_v the_o say_a meridian_n at_o right_a angle_n the_o length_n of_o the_o thread_n from_o the_o nodus_fw-la to_o the_o point_n in_o the_o meridian_n where_o the_o equinoctial_a cut_v he_o be_v radius_fw-la of_o the_o equinoctial_a to_o that_o radius_fw-la you_o shall_v find_v the_o tangent_n of_o 15_o 30_o 45_o 60_o 75._o as_o you_o find_v the_o co-tangents_a chapter_n 27._o know_v that_o the_o co-tangents_a of_o 80_o and_o 70._o be_v the_o tangent_n of_o 10_o and_o 20_o and_o so_o of_o the_o rest_n and_o begin_v in_o the_o meridian_n make_v prick_n in_o the_o equinoctial_a line_n at_o the_o end_n of_o the_o tangent_fw-la of_o 15._o eastward_o for_o 1._o and_o westward_n for_o 11._o and_o at_o the_o end_n of_o the_o tangent_fw-la of_o 30._o prick_v eastward_o 2._o and_o westward_o 10._o etc._n etc._n then_o by_o chapter_n 9_o seek_v what_o angle_v the_o hour_n line_n of_o a_o vertical_a dyal_n make_v at_o the_o centre_n which_o in_o our_o latitude_n be_v 1.11.58_o minute_n 2.24.32_o minute_n 3.38.20_o minute_n 4.53.52_o minute_n 5.71.17_o minute_n and_o with_o the_o compliment_n of_o these_o angle_n shall_v these_o hour_n line_n across_o the_o equinoctial_a so_o the_o hour_n line_n of_o 1._o shall_v incline_v to_o the_o meridian_n on_o the_o south_n side_n the_o equinoctial_a line_n and_o shall_v make_v his_o lesser_a angle_n with_o the_o equinoctial_a 78.02_o minute_n and_o the_o rest_n as_o in_o the_o figure_n the_o second_o way_n be_v this_o fit_a a_o plain_a smooth_a board_n about_o a_o foot_n square_a to_o lie_v level_a from_o the_o foal_n of_o the_o window_n inward_o and_o near_o the_o outer_a edge_n thereof_o make_v a_o centre_n in_o the_o board_n in_o the_o very_a place_n of_o nodus_fw-la or_o a_o little_a under_o it_o remember_v that_o the_o nodus_fw-la or_o centre_n of_o the_o glass_n must_v be_v set_v so_o much_o high_a than_o this_o board_n as_o the_o centre_n of_o your_o quadrant_n be_v place_v high_a in_o the_o project_v of_o the_o dyal_n upon_o that_o centre_n take_v in_o the_o board_n describe_v as_o much_o of_o a_o circle_n as_o you_o may_v with_o the_o semidiameter_n of_o your_o quadrant_n which_o circle_n shall_v be_v horizon_n draw_v here_o from_o the_o centre_n to_o the_o horizon_n inward_o a_o meridian_n line_n by_o book_n 4.3_o and_o where_o it_o cut_v the_o horizon_n begin_v to_o graduate_v the_o horizon_n into_o degree_n of_o azimuth_n both_o way_n which_o you_o may_v speedy_o do_v by_o transfer_v the_o graduation_n of_o your_o quadrant_n or_o so_o much_o as_o you_o shall_v need_v to_o this_o horizon_n next_o you_o must_v devise_v to_o make_v your_o quadrant_n stand_v firm_a and_o upright_o upon_o one_o of_o his_o straight_a side_n which_o i_o will_v call_v his_o foot_n for_o this_o time_n and_o that_o you_o may_v thus_o do_v take_v a_o short_a piece_n of_o a_o ruler_n or_o sinal_n transom_n and_o see_v in_o one_o side_n of_o it_o a_o notch_n perperdicular_o in_o which_o notch_n you_o may_v stick_v fast_o or_o wedge_n the_o heel_n or_o the_o toe_n of_o your_o quadrant_n in_o such_o sort_n that_o his_o foot_n may_v come_v close_o to_o the_o board_n and_o the_o other_o straight_o side_n or_o leg_n may_v stand_v perpendicular_a upon_o it_o those_o thing_n prepare_v put_v your_o planisphear_n in_o the_o meridional_a projection_n with_o the_o finitor_n at_o your_o latitude_n and_o first_o observe_v there_o the_o altitude_n of_o the_o sun_n in_o the_o meridian_n which_o in_o latitude_n 52.15_o minute_n you_o shall_v find_v in_o the_o tropic_n of_o ♋_o 61.15_o minute_n in_o the_o equator_fw-la 37.45_o minute_n and_o in_o the_o tropic_n of_o ♑_o 14.15_o minute_n now_o have_v stick_v a_o short_a needle_n in_o the_o centre_n of_o the_o horizon_n close_o to_o which_o you_o must_v always_o keep_v the_o centre_n of_o your_o quadrant_n set_v the_o foot_n of_o your_o quadrant_n in_o the_o meridian_n line_n of_o the_o board_n and_o from_o the_o centre_n of_o your_o quadrant_n extend_v a_o thread_n by_o 14.15_o minute_n of_o altitude_n straight_o on_o to_o the_o ceiling_n the_o thread_n only_o touch_v the_o plain_a of_o the_o quadrant_n and_o make_v no_o angle_n with_o it_o but_o hold_v parallel_n and_o where_o the_o thread_n thus_o extend_v touch_v the_o ceiling_n make_v a_o point_n than_o the_o quadrant_n unmoved_a extend_v the_o thread_n by_o 61.15_o minute_n of_o altitude_n and_o make_v another_o point_n as_o before_o and_o between_o these_o two_o point_n draw_v a_o straight_a line_n and_o that_o shall_v be_v your_o meridian_n and_o shall_v be_v long_o enough_o for_o your_o use_n then_o extend_v the_o thread_n by_o 37.45_o minute_n of_o altitude_n and_o where_o it_o touch_v this_o meridian_n across_o the_o meridian_n at_o right_a angle_n with_o a_o infinite_a line_n which_o shall_v be_v the_o equator_fw-la then_o seek_v upon_o your_o planisphear_n for_o one_o a_o clock_n and_o you_o shall_v find_v in_o the_o tropic_n of_o ♑_o the_o sun_n azimuth_n 14._o and_o his_o altitude_n 13.06_o in_o the_o tropic_n of_o ♋_o his_o azimuth_n 27½_n and_o his_o altitude_n 59.04_o minute_n therefore_o set_v the_o foot_n of_o the_o quadrant_n in_o the_o azimuth_n 14._o from_o the_o meridian_n eastward_o i_o extend_v the_o thread_n by_o 13.06_o of_o altitude_n and_o make_v a_o prick_n in_o the_o ceiling_n and_o again_o set_v the_o foot_n of_o the_o quadrant_n in_o azimuth_n 27_o ½_n and_o extend_v the_o thread_n by_o 59.04_o minute_n of_o altitude_n i_o make_v another_o prick_n in_o the_o ceiling_n and_o the_o straight_a line_n which_o i_o shall_v draw_v between_o these_o two_o prick_n shall_v be_v all_o the_o hourline_v of_o one_o and_o so_o of_o the_o rest_n and_o if_o you_o be_v mind_v to_o have_v the_o other_o parallel_n draw_v you_o may_v find_v point_n for_o they_o as_o you_o have_v do_v for_o the_o tropique_n and_o by_o those_o point_n draw_v they_o and_o note_v that_o two_o point_n make_v in_o the_o ceiling_n for_o the_o same_o hour_n line_n in_o any_o two_o parailel_n or_o in_o the_o equator_fw-la and_o any_o parallel_n shall_v suffice_v to_o direct_v the_o line_n though_o it_o be_v best_o
and_o mars_n in_o twain_o set_v forward_o and_o come_v round_o again_o then_o in_o one_o year_n the_o sun_n display_v three_o hundred_o sixty_o and_o five_o day_n and_o near_o a_o quarter_n which_o in_o four_o encompassing_n make_v one_o day_n more_o between_o the_o sun_n and_o we_o there_o fly_v fair_a venus_n and_o swift_a mercury_n these_o always_o near_o the_o sun_n we_o find_v not_o far_o before_o nor_o far_o behind_o the_o moon_n be_v the_o low_a who_o in_o seven_o and_o twenty_o day_n go_v round_o the_o heaven_n and_o above_o two_o day_n more_o do_v run_v before_o she_o overtake_v the_o sun_n so_o twenty_o nine_o and_o a_o half_a in_o all_o do_v make_v a_o month_n synodical_a these_o planet_n make_v their_o course_n to_o the_o east_n though_o they_o be_v fast_o hurl_v west_n and_o six_o degree_n the_o rest_n may_v stray_v beside_o the_o sun_n ecliptic_a way_n the_o circle_n of_o the_o sphere_n fix_v great_a circle_n mark_v you_o shall_v which_o equal_o divide_v this_o ball._n just_o in_o the_o midst_n between_o the_o pole_n from_o east_n to_o west_n the_o equator_fw-la roll_n the_o ecliptic_a cut_v he_o and_o do_v slide_v scarce_o twenty_o four_o degree_n aside_o horizon_n even_o with_o the_o ground_n from_o star_n below_o our_o sight_n do_v bind_v meridian_n upright_o do_v rise_v part_v the_o east_n and_o western_a sky_n two_o colour_n through_o the_o pole_n do_v run_v quarr_v the_o circle_n of_o the_o sun_n one_o where_o the_o spring_n and_o fall_v begin_v the_o other_o where_o long_a day_n come_v in_o four_z lesser_a circle_n mark_v they_o well_o be_v to_o the_o equator_fw-la parallel_n two_o tropique_n bind_v the_o sun_n high_a way_n show_v the_o long_a and_o short_a day_n the_o arctique_a circle_n cur_n the_o bear_n the_o antarctique_a opposite_a appear_v meridian_n half_n twenty_o four_o for_o hour_n and_o for_o degree_n ninescore_o through_o both_o the_o pole_n of_o the_o world_n do_v pass_v and_o the_o equinoctial_a down_o right_a cross_n and_o ninescore_o parallel_n have_v that_o line_n by_o which_o star_n north_n and_o south_n decline_v the_o ecliptic_a have_v his_o longitude_n and_o parallel_n of_o latitude_n for_o star_n but_o in_o geography_n the_o town_n beside_o the_o equator_fw-la lie_n over_o our_o head_n and_o under_o foot_n the_o ninescore_o azimuth_n do_v meet_v and_o here_o as_o many_o parallel_n of_o altitude_n horizon_n tell_v longitude_n and_o meridian_n all_o and_o azimuth_n great_a circle_n call_v but_o all_o their_o parallel_n in_o heaven_n be_v lesser_a cut_v the_o globe_n uneven_a degree_n three_o hundred_o and_o threescore_o have_v every_o circle_n and_o no_o more_o when_o i_o consider_v thy_o heaven_n the_o work_n of_o thy_o finger_n the_o moon_n and_o the_o star_n which_o thou_o have_v ordain_v what_o be_v man_n that_o thou_o be_v mindful_a of_o he_o or_o the_o son_n of_o man_n that_o thou_o visite_a he_o ps_n 8._o errata_fw-la some_o fault_n have_v be_v commit_v between_o the_o writer_n and_o the_o printer_n the_o chief_n whereof_o the_o reader_n be_v desire_v to_o amend_v as_o follow_v pag._n and_o line_n fault_n amendment_n 2_o 3_o 4._o etc._n etc._n to_o pag._n 30._o in_o the_o title_n the_o first_o book_n of_o the_o fabric_n of_o the_o planisphere_n the_o first_o book_n of_o the_o fabric_n of_o the_o planisphear_n 31_o and_o 32._o in_o the_o title_n the_o second_o book_n of_o the_o projection_n of_o the_o sphere_n the_o second_o book_n of_o the_o projection_n of_o the_o sphere_n 1._o 13._o mossy_a massy_a 2._o 7._o declination_n delineation_n 3._o ant_n declination_n delineation_n 4._o 16._o look_v up_o look_v upon_o 4._o 36._o eye_n beam_n eye-beame_n 5._o 13._o euclid_n 4_o 5._o euclid_n 4.5_o 22._o require_v of_o your_o compass_n over_o reach_n require_v if_o your_o compass_n reach_v short_a 5._o 23._o if_o it_o reach_v short_a if_o it_o overreach_v 6._o 39_o structure_n structure_n 8._o secant_fw-la 67._o 25693._o 25593._o  _fw-fr the_n 5._o last_o tangent_n want_v a_o 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deg_fw-la 125_o degr_n 110._o pen._n by_o oblique_a problem_n by_o probl_n 2_o obliqu_n 111._o 25._o in_o 39_o ½_n in_o all_o 39_o ½_n 114._o 17._o agree_v set_v agree_v set_v 11._o house_n also_o house_n also_o 31._o 49_o 30_o 50_o 51._o 118._o 6_o 7._o 49_o 50_o 50_o 51._o 24._o and_o so_o and_o to_o 119._o 1_o astrologer_n astrology_n 17._o futurus_fw-la futurus_fw-la 122._o 29._o no_o man_n no_o man_n 123._o 3._o princeps_fw-la nero_n princeps_fw-la nero_n 4._o citherae_fw-la citharae_fw-la 10._o dereliquit_fw-la nero_n dereliquit_fw-la nero_n 12._o persuesum_fw-la persuasum_fw-la 27._o se_z nore_z temerè_fw-la 128._o 26._o as_o by_o and_o by_o 29._o set_v go_v set_v therefore_o 130._o 34._o jupiter_n in_o that_o meridian_n jupiter_n in_o that_o meridian_n 139._o 6._o christ_n time_n christ_n time_n 17._o ticius_n tacitus_n 141._o 6._o 4_o 5._o 11._o 4._o 5_o 11._o 145._o 13._o sun_n dial_n sun_n dial_n 147._o 5._o or_o equinoctial_a deleatur_fw-la 19_o so_o the_o hour_n line_n 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