line_n c_o e_o which_o be_v the_o perpendicular_a which_o be_v desire_v to_o be_v let_v fall_n from_o the_o give_v point_n c_o unto_o the_o middle_n of_o the_o give_v line_n d_o e_o f._n chap._n vi_o to_o raise_v a_o perpendicular_a upon_o the_o end_n of_o a_o line_n give_v suppose_v the_o line_n whereupon_o you_o will_v have_v a_o perpendicular_a to_o be_v raise_v be_v the_o line_n b_o c_o &_o from_o the_o point_n b_o a_o perpendicular_a be_v to_o be_v raise_v first_o open_v your_o compass_n unto_o any_o convenient_a distance_n which_o here_o we_o suppose_v to_o be_v the_o distance_n b_o e_o and_o set_v one_o foot_n of_o your_o compass_n in_o b_o with_o the_o other_o draw_v the_o arch_n ed_z than_o this_o distance_n be_v keep_v set_v one_o foot_n of_o your_o compass_n in_o the_o point_n e_o and_o with_o the_o other_o make_v a_o mark_n in_o the_o former_a arch_n e_o d_o as_o at_z d_o still_o keep_v the_o same_o distance_n set_v one_o foot_n in_o the_o point_n d_o and_o with_o the_o other_o draw_v the_o arch_a line_n f_o over_o the_o give_v point_n b_o now_o lay_v a_o ruler_n upon_o the_o two_o point_n e_z and_z d_o see_v where_o it_o cross_v the_o arch_a line_n f_o which_o will_v be_v at_o f_o from_o which_o point_n f_o draw_v the_o line_n f_o b_o which_o shall_v be_v a_o perpendicular_a line_n unto_o the_o give_v line_n b_o c_o raise_v from_o the_o end_n b_o as_o be_v require_v chap._n vii_o to_o let_v a_o perpendicular_a fall_n from_o a_o point_n assign_v unto_o the_o end_n of_o a_o line_n give_v let_v the_o line_n d_o e_o be_v give_v unto_o which_o it_o be_v require_v to_o let_v a_o perpendicular_a fall_n from_o the_o assign_a point_n a_o unto_o the_o end_n d._n first_o from_o the_o assign_a point_n a_o draw_v a_o line_n unto_o any_o part_n of_o the_o give_v line_n d_o e_o which_o may_v be_v the_o line_n a_o b_o c_o then_o find_v the_o middle_n of_o the_o line_n a_o c_o which_o will_v be_v at_o b_o place_z therefore_o one_o foot_n of_o your_o compass_n in_o the_o point_n b_o and_o extend_v the_o other_o unto_o a_o or_o c_o with_o which_o distance_n draw_v the_o semicircle_n a_o d_o c_o so_fw-mi shall_v it_o cut_v the_o give_v line_n d_o e_o in_o the_o point_n d_o from_o which_o point_n d_o draw_v the_o line_n a_o d_o which_o shall_v be_v the_o perpendicular_a let_v fall_v from_o the_o assign_a point_n a_o unto_o the_o end_n d_o of_o the_o give_a line_n d_o e_o as_o be_v require_v chap._n viii_o certain_a definition_n astronomical_a meet_a to_o be_v understand_v of_o the_o unlearned_a before_o the_o proceed_n in_o this_o art_n of_o dial_v in_o the_o former_a chapter_n i_o have_v show_v the_o meaning_n of_o some_o term_n of_o geometry_n which_o be_v most_o helpful_a unto_o this_o art_n of_o dial_v with_o the_o draw_n of_o a_o parallel_a line_n at_o any_o distance_n or_o by_o a_o point_n assign_v so_o likewise_o have_v i_o show_v the_o manner_n either_o how_o to_o raise_v or_o let_v fall_v a_o perpendicular_a either_o from_o or_o unto_o any_o part_n of_o a_o line_n give_v so_o likewise_o now_o i_o think_v it_o will_v not_o be_v unnecessary_a for_o to_o show_v unto_o the_o unlearned_a the_o meaning_n of_o some_o of_o the_o most_o useful_a term_n in_o astronomy_n and_o most_o fit_v this_o art_n of_o dial_v definition_n 1._o a_o sphere_n be_v a_o certain_a solid_a superficies_n in_o who_o middle_a be_v a_o point_n from_o which_o all_o line_n draw_v unto_o the_o circumference_n be_v equal_a which_o point_n be_v the_o centre_n of_o the_o sphere_n definition_n 2._o the_o pole_n be_v a_o prick_n or_o point_n imagine_v in_o the_o heaven_n whereof_o be_v two_o the_o north_n pole_n be_v the_o centre_n to_o a_o circle_n describe_v by_o the_o motion_n of_o the_o north_n star_n or_o the_o tale_n of_o the_o little_a bear_n from_o which_o point_n aforesaid_a be_v a_o line_n imagine_v to_o pass_v through_o the_o centre_n of_o the_o sphere_n and_o pass_v direct_o to_o the_o opposite_a part_n of_o the_o heaven_n show_v there_o to_o be_v the_o south_n pole_n and_o this_o line_n so_o imagine_v to_o pass_v from_o one_o pole_n to_o the_o other_o through_o the_o centre_n of_o the_o sphere_n be_v call_v the_o axletree_n of_o the_o world_n because_o it_o have_v be_v former_o suppose_v that_o the_o sun_n moon_n and_o star_n together_o with_o the_o whole_a heaven_n have_v be_v turn_v about_o from_o east_n to_o west_n once_o round_o in_o 24_o hour_n by_o a_o true_a equal_a course_n like_a much_o in_o like_a time_n which_o diurnal_a revolution_n be_v perform_v about_o this_o axletree_n of_o the_o world_n and_o this_o axletree_n be_v set_v out_o unto_o you_o in_o the_o follow_a figure_n by_o the_o line_n p_o a_o d_o the_o pole_n whereof_o be_v p_o and_o d._n definition_n 3._o a_o sphere_n accidental_o be_v divide_v into_o two_o part_n that_o be_v to_o say_v into_o a_o right_a sphere_n and_o a_o oblique_a sphere_n a_o right_a sphere_n be_v only_o unto_o those_o that_o dwell_v under_o the_o equinoctial_a to_o who_o neither_o of_o the_o pole_n of_o the_o world_n be_v see_v but_o lie_v hide_v in_o the_o horizon_n a_o oblique_a sphere_n be_v unto_o those_o that_o inhabit_v on_o either_o side_n of_o the_o equinoctial_a unto_o who_o one_o of_o the_o pole_n be_v ever_o see_v and_o the_o orhe_a hide_v under_o the_o horizon_n definition_n 4._o the_o circle_n whereof_o the_o sphere_n be_v compose_v be_v divide_v into_o two_o sort_n that_o be_v to_o say_v into_o great_a circle_n and_o lesser_a the_o great_a circle_n be_v those_o that_o divide_v the_o sphere_n into_o two_o equal_a part_n and_o they_o be_v in_o number_n six_o viz._n the_o equinoctial_a the_o ecliptic_a line_n the_o two_o colour_n the_o meridian_n and_o the_o horizon_n the_o lesser_a circle_n be_v such_o as_o divide_v the_o sphere_n into_o two_o part_n unequal_o and_o they_o be_v four_o in_o number_n as_o the_o tropic_a of_o cancer_n the_o tropic_a of_o capricorn_n the_o circle_n arctic_a and_o the_o circle_n antartique_n chap._n ix_o of_o the_o six_o great_a circle_n definition_n 5._o the_o equinoctial_a be_v a_o circle_n that_o cross_v the_o pole_n of_o the_o world_n at_o right_a angle_n and_o divide_v the_o sphere_n into_o two_o equal_a part_n and_o be_v call_v the_o equinoctial_a because_o when_o the_o sun_n come_v unto_o it_o which_o be_v twice_o in_o the_o year_n viz._n at_o the_o sun_n entrance_n into_o aries_n and_o libra_n it_o make_v the_o day_n &_o night_n of_o equal_a length_n throughout_o the_o whole_a world_n and_o in_o the_o figure_n follow_v be_v describe_v by_o the_o line_n s_o a_o n._n definition_n 6._o the_o meridian_n be_v a_o great_a circle_n pass_v through_o the_o pole_n of_o the_o world_n and_o the_o pole_n of_o the_o horizon_n or_o zenith_n point_v right_a over_o our_o head_n and_o be_v so_o call_v because_o that_o in_o any_o time_n of_o the_o year_n or_o in_o any_o place_n of_o the_o world_n when_o the_o sun_n by_o the_o motion_n of_o the_o heaven_n come_v unto_o that_o circle_n it_o be_v then_o noon_n or_o 12_o of_o the_o clock_n and_o it_o be_v to_o be_v understand_v that_o all_o town_n and_o place_n that_o lie_v east_n and_o west_n one_o of_o another_o have_v every_o one_o a_o several_a meridian_n but_o all_o place_n that_o lie_v north_n and_o south_n one_o of_o another_o have_v one_o and_o the_o same_o meridian_n this_o circle_n be_v declare_v in_o the_o figure_n follow_v by_o the_o circle_n e_o b_o w_n c._n definition_n 7._o the_o horizon_n be_v a_o circle_n divide_v the_o superior_a hemisphere_n from_o the_o inferior_a whereupon_o it_o be_v call_v horizon_n that_o be_v to_o say_v the_o bound_n of_o sight_n or_o the_o far_a distance_n that_o the_o eye_n can_v see_v and_o be_v set_v forth_o unto_o you_o by_o the_o line_n c_o a_o b_o in_o the_o follow_a figure_n definition_n 8._o colour_n be_v two_o great_a circle_n pass_v through_o both_o the_o pole_n of_o the_o world_n cross_v one_o the_o other_o in_o the_o say_a pole_n at_o right_a angle_n and_o divide_v the_o equinoctial_a and_o the_o zodiaque_fw-la into_o four_o equal_a part_n make_v thereby_o the_o four_o season_n of_o the_o year_n the_o one_o colour_n pass_v through_o the_o two_o tropical_a point_n of_o cancer_n and_o capricorn_n show_v the_o beginning_n of_o summer_n &_o also_o of_o winter_n at_o which_o time_n the_o day_n and_o night_n be_v long_a and_o short_a the_o other_o colour_n pass_v through_o the_o equinoctial_a point_n aries_n and_o libra_n show_v the_o beginning_n of_o the_o spring_n time_n and_o autumn_n at_o which_o two_o time_n the_o day_n and_o night_n be_v of_o equal_a length_n throughout_o the_o whole_a world_n definition_n 9_o the_o ecliptic_a
surface_n of_o the_o diameter_n as_o the_o semicircle_n c_o b_o d_o which_o be_v half_a of_o the_o circle_n c_o b_o d_o e_o and_o be_v contain_v above_o the_o diameter_n c_o a_o d._n definition_n 11._o a_o quadrant_n be_v the_o four_o part_n of_o a_o circle_n and_o be_v contain_v betwixt_o the_o semidiameter_n of_o the_o circle_n &_o a_o line_n draw_v perpendicular_a unto_o the_o diameter_n of_o the_o same_o circle_n from_o the_o centre_n thereof_o divide_v the_o semicircle_n into_o two_o equal_a part_n of_o the_o which_o part_n the_o one_o be_v the_o quadrant_n or_o four_o part_n of_o the_o same_o circle_n as_o for_o example_n the_o diameter_n of_o the_o circle_n b_o d_o e_o c_o be_v the_o line_n c_o a_o d_o divide_v the_o circle_n into_o two_o equal_a part_n then_o from_o the_o centre_n a_o raise_v the_o perpendicular_a a_o b_o divide_v the_o semicircle_n likewise_o into_o two_o equal_a part_n so_o be_v a_o b_o d_o or_o a_o b_o c_o the_o quadrant_n of_o the_o circle_n c_o b_o d_o e._n definition_n 12._o a_o segment_n or_o portion_n of_o a_o circle_n be_v a_o figure_n contain_v under_o a_o right_a line_n and_o a_o part_n of_o a_o circumference_n either_o great_a or_o lesser_a than_o the_o semicircle_n as_o in_o the_o figure_n you_o may_v see_v that_o f_o b_o g_o h_o be_v a_o segment_n or_o part_n of_o the_o circle_n c_o b_o d_o e_o and_o be_v contain_v under_o the_o right_a line_n fhg_v which_o be_v less_o than_o the_o diameter_n c_o a_o d_o and_o a_o part_n of_o the_o whole_a circumference_n as_o f_o b_o g._n and_o here_o note_v that_o these_o part_n and_o such_o like_a of_o the_o circumference_n so_o divide_v be_v common_o call_v arch_n or_o arch_a line_n and_o all_o line_n less_o than_o the_o diameter_n draw_v through_o and_o apply_v to_o any_o part_n of_o the_o circumference_n be_v call_v chord_n or_o chord_n line_n of_o those_o arch_n which_o they_o subtend_v definition_n 13._o a_o parallel_n line_n be_v a_o line_n draw_v by_o the_o side_n of_o another_o line_n in_o such_o sort_n that_o they_o may_v be_v equidistant_a in_o all_o place_n and_o of_o such_o parallel_n two_o only_o belong_v unto_o this_o work_n of_o dial_v that_o be_v to_o say_v the_o right_n line_v parallel_n and_o the_o circular_a parallel_n right_o line_v parallel_n be_v two_o right_a line_n equidistant_a in_o all_o place_v one_o from_o the_o other_o which_o be_v draw_v forth_o infinite_o will_v never_o meet_v or_o concur_v as_o may_v be_v see_v by_o these_o two_o line_n a_o and_o b._n definition_n 14._o a_o circular_a parallel_n be_v a_o circle_n draw_v either_o within_o or_o without_o another_o circle_n upon_o the_o same_o centre_n as_o you_o may_v plain_o see_v by_o the_o two_o circle_n b_o c_o d_o e_o and_o f_o g_o h_o i_o these_o circle_n be_v both_o draw_v upon_o the_o same_o centre_n a_o and_o therefore_o be_v parallel_v the_o one_o to_o the_o other_o definition_n 16._o a_o degree_n be_v the_o 360_o part_n of_o the_o circumference_n of_o any_o circle_n so_o that_o divide_v the_o circumference_n of_o any_o circle_n into_o 360_o part_n and_o each_o of_o those_o part_n be_v call_v a_o degree_n so_o shall_v the_o semicircumference_n contain_v 180_o of_o those_o degree_n and_o 90_o of_o those_o degree_n make_v a_o quadrant_n or_o a_o quarter_n of_o the_o circumference_n of_o any_o circle_n definition_n 16._o a_o minute_n be_v the_o 60_o part_n of_o a_o degree_n be_v understand_v of_o measure_n but_o in_o time_n a_o minute_n be_v the_o 60_o part_n of_o a_o hour_n or_o the_o four_o part_n of_o a_o degree_n 15_o degree_n answer_v to_o a_o hour_n and_o 4_o minute_n to_o a_o degree_n definition_n 17._o the_o quantity_n or_o measure_n of_o a_o angle_n be_v the_o number_n of_o degree_n contain_v in_o the_o arch_n of_o a_o circle_n describe_v from_o the_o point_n of_o the_o same_o angle_n and_o intercept_v between_o the_o two_o side_n of_o that_o angle_n as_o for_o example_n the_o measure_n of_o the_o angle_n a_o b_o c_o be_v the_o number_n of_o degree_n contain_v in_o the_o arch_n a_o c_o which_o subtend_v the_o angle_n b_o be_v find_v to_o be_v 60._o definition_n 18._o the_o compliment_n of_o a_o arch_n less_o than_o a_o quadrant_n be_v so_o much_o as_o that_o arch_n want_v of_o 90_o degree_n as_o for_o example_n the_o arch_a a_o b_o be_v 60_o degree_n which_o be_v take_v from_o 90_o degree_n leave_v b_o c_o for_o the_o compliment_n thereof_o which_o be_v 30_o degree_n definition_n 19_o the_o compliment_n of_o a_o arch_n less_o than_o a_o semicircle_n be_v so_o much_o as_o that_o arch_n want_v of_o a_o semicircle_n or_o of_o 180_o degree_n as_o for_o example_n the_o arch_n d_o c_o b_o being_n 120_o degree_n this_o be_v take_v from_o 180_o degree_n the_o whole_a semicircle_n leave_v a_o b_o for_o the_o compliment_n thereof_o which_o will_v be_v find_v to_o be_v 60_o degree_n and_o here_o note_v that_o what_o be_v say_v of_o the_o compliment_n of_o arch_n the_o same_o be_v mean_v by_o the_o compliment_n of_o angle_n chap._n 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at_o right_a angle_n with_o any_o perpendicular_a wall_n in_o such_o manner_n that_o it_o may_v lie_v parallel_n unto_o the_o horizon_n first_o draw_v your_o quadrant_n a_o b_o c_o d_o as_o be_v teach_v in_o the_o last_o chapter_n &_o place_v the_o length_n of_o your_o gnomon_n from_o a_o to_o e_o which_o here_o we_o will_v suppose_v to_o be_v 12_o foot_n as_o before_o in_o the_o last_o chapter_n then_o draw_v the_o line_n e_o f_o parallel_n to_o a_o b_o then_o suppose_v the_o length_n of_o the_o shadow_n to_o be_v 9_o foot_n as_o before_o this_o i_o place_n from_o e_z to_z g_z
the_o distance_n c_o e_o and_o set_v in_o your_o trigon_n from_o o_o unto_o e_fw-la and_o draw_v the_o line_n o_o e_o 4_o represent_v the_o hour_n of_o 4_o and_o 8._o and_o thus_o must_v you_o do_v with_o the_o rest_n of_o the_o hour_n in_o your_o plane_n if_o occasion_n require_v these_o line_n o_o a_o o_fw-fr b_o o_o c_o o_o d_o and_z o_o e_o in_o your_o trigon_n be_v extend_v do_v cut_v the_o tropic_a of_o cancer_n p_o a_o in_o the_o point_v 12_o 1_o 2_o and_z 3_o therefore_o out_o of_o your_o trigon_n take_v the_o distance_n o_o 12_o o_o 1_o o_o 2_o o_o 3_o o_o 4_o and_o set_v they_o upon_o their_o correspondent_a hour_n line_n of_o your_o plane_n from_o the_o centre_n c_o unto_o g_o h_o i_o k_o and_o l_o so_fw-mi shall_v the_o point_n g_o h_o i_o k_o and_o l_o be_v the_o point_n upon_o the_o houre-line_n through_o which_o the_o tropic_a of_o cancer_n must_v pass_v and_o be_v therefore_o note_v with_o the_o character_n of_o cancer_n ♋_o at_o both_o end_n ¶_o now_o before_o you_o 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and_o recline_v and_o for_o the_o horizontal_a line_n in_o all_o recline_a or_o incline_v plane_n it_o must_v pass_v through_o the_o foot_n of_o the_o perpendicular_a stile_n and_o the_o intersection_n of_o the_o equinoctial_a with_o the_o hour_n of_o fix_v chap._n ii_o show_v how_o to_o inscribe_v the_o parallel_n of_o the_o length_n of_o the_o day_n on_o any_o plane_n the_o parallel_n of_o the_o length_n of_o the_o day_n and_o those_o of_o the_o sign_n be_v inscribe_v upon_o all_o kind_n of_o plane_n by_o one_o and_o the_o same_o rule_n they_o be_v in_o the_o sphere_n the_o same_o circle_n so_o that_o as_o when_o you_o put_v on_o the_o parallel_n of_o the_o sun_n entrance_n into_o the_o 12_o sign_n you_o seek_v what_o declination_n he_o have_v and_o according_o proceed_v as_o before_o so_o now_o for_o the_o parallel_n of_o the_o length_n of_o the_o day_n you_o must_v seek_v what_o declination_n the_o sun_n have_v at_o such_o a_o length_n of_o the_o day_n as_o you_o will_v put_v into_o your_o plane_n which_o that_o you_o may_v do_v i_o have_v here_o add_v the_o rule_n follow_v ¶_o consider_v how_o much_o long_o or_o short_a your_o day_n propose_v be_v then_o 12_o hour_n and_o take_v the_o difference_n than_o the_o proportion_n will_v be_v as_o the_o sine_fw-la of_o 90_o degree_n be_v to_o the_o sine_fw-la of_o half_a the_o difference_n so_o be_v the_o tangent_fw-la compliment_n of_o the_o latitude_n of_o the_o place_n to_o the_o tangent_fw-la of_o the_o declination_n that_o the_o sun_n shall_v have_v when_o the_o day_n be_v at_o such_o a_o length_n as_o you_o require_v as_o for_o example_n let_v it_o be_v require_v to_o know_v what_o declination_n the_o sun_n shall_v have_v when_o the_o day_n be_v 16_o hour_n long_o in_o the_o latitude_n of_o 52_o deg_fw-la 30_o min._n the_o difference_n betwixt_o 16_o hour_n and_o 12_o hour_n be_v 4_o hour_n or_o 60_o deg_fw-la the_o half_a of_o which_o be_v 30_o deg_fw-la therefore_o say_v as_o the_o sine_fw-la of_o 90_o 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such_o time_n that_o the_o day_n be_v either_o 8_o 9_o 10_o 11_o 12_o 13_o 14_o 15_o or_o 16_o hour_n long_o in_o the_o latitude_n of_o 52_o deg_fw-la 30_o min._n which_o table_n be_v make_v by_o the_o precede_a rule_n by_o which_o table_n you_o may_v see_v length_n of_o the_o day_n the_o sun_n declination_n d_o m_o 8_o 20_o 59_o 9_o 16_o 22_o 10_o 11_o 14_o 11_o 5_o 43_o 12_o 0_o 0_o 13_o 5_o 43_o 14_o 11_o 14_o 15_o 16_o 22_o 16_o 20_o 59_o that_o when_o the_o day_n be_v 12_o hour_n long_o the_o sun_n have_v then_o no_o declination_n but_o be_v in_o the_o equinoctial_a but_o when_o the_o day_n be_v either_o 11_o or_o 13_o hour_n long_o the_o declination_n be_v then_o 5_o deg_fw-la 43_o min._n and_o when_o the_o day_n be_v either_o 9_o or_o 15_o hour_n long_o the_o sun_n have_v 16_o deg_fw-la 22_o min._n of_o declination_n and_o so_o for_o the_o rest_n as_o in_o the_o table_n for_o the_o place_n of_o these_o parallel_n of_o the_o length_n of_o the_o day_n upon_o any_o of_o the_o 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of_o the_o almicanter_n or_o circle_n of_o altitude_n the_o circle_n of_o altitude_n have_v the_o same_o relation_n to_o the_o azimuth_n as_o the_o tropic_n and_o parallel_n of_o declination_n have_v to_o the_o houre-line_n and_o therefore_o as_o the_o parallel_n of_o declination_n in_o the_o equinoctial_a plane_n be_v perfect_a circle_n so_o be_v the_o circle_n of_o altitude_n in_o a_o horizontall_a plane_n the_o inscription_n of_o these_o into_o all_o kind_n of_o plane_n be_v in_o a_o manner_n the_o same_o with_o the_o parallel_n of_o declination_n but_o whereas_o in_o the_o draw_v the_o parallel_n of_o declination_n you_o take_v the_o houre-line_n out_o of_o your_o plane_n and_o put_v they_o in_o a_o trigon_n so_o in_o this_o you_o must_v take_v the_o azimuth_n out_o of_o your_o plane_n and_o put_v they_o into_o a_o trigon_n for_o that_o purpose_n and_o so_o transfer_v they_o to_o the_o plane_n again_o as_o you_o do_v the_o other_o and_o because_o these_o be_v small_a circle_n therefore_o they_o become_v conic_a section_n except_o on_o such_o plane_n as_o lie_v parallel_n to_o the_o zenith_n which_o be_v only_o the_o horizontall_a chap._n vii_o how_o to_o draw_v a_o dial_n on_o the_o ceiling_n of_o a_o room_n because_o the_o direct_a beam_n of_o the_o sun_n can_v never_o shine_v upon_o the_o ceiling_n of_o a_o room_n they_o must_v therefore_o be_v reflect_v thither_o by_o help_n of_o a_o small_a piece_n of_o look_a glass_n convenient_o fix_v in_o some_o transam_fw-la of_o the_o window_n so_o that_o it_o may_v lie_v exact_o parallel_v to_o the_o horizon_n the_o place_n be_v choose_v and_o the_o glass_n therein_o fix_v you_o must_v draw_v upon_o the_o ceiling_n of_o the_o room_n a_o meridian_n line_n as_o you_o be_v teach_v in_o the_o former_a book_n which_o meridian_n line_n must_v be_v so_o draw_v that_o it_o may_v pass_v direct_o over_o the_o glass_n before_o place_v which_o you_o may_v perceive_v how_o to_o do_v by_o hold_v a_o thread_n and_o plummet_n from_o the_o top_n of_o the_o ceiling_n till_o it_o fall_v direct_o upon_o the_o superficies_n of_o the_o glass_n the_o hour_n the_o angle_n that_o each_o houre-line_n make_v with_o the_o merid._n the_o compliment_n of_o each_o houre-line_n angle_v with_o the_o meridian_n  _fw-fr 12_o  _fw-fr 00d_o 00m_fw-la 90d_o 00m_fw-la 1_o  _fw-fr 11_o 12_o 00_o 78_o 00_o 2_o  _fw-fr 10_o 24_o 37_o 65_o 23_o 3_o  _fw-fr 9_o 38_o 25_o 51_o 35_o 4_o  _fw-fr 8_o 53_o 58_o 36_o 2_o 5_o  _fw-fr 7_o 71_o 20_o 18_o 40_o  _fw-fr 6_o  _fw-fr 90_o 00_o 00_o 00_o have_v these_o thing_n prepare_v let_v the_o line_n l_o r_n in_o the_o follow_a figure_n represent_v a_o meridian_n line_v draw_v upon_o the_o ceiling_n of_o a_o room_n and_o let_v k_o be_v the_o glass_n fix_v direct_o under_o the_o say_a meridian_n upon_o some_o transam_fw-la of_o the_o window_n then_o lay_v one_o end_n of_o a_o string_n upon_o the_o glass_n at_o k_o extend_v the_o other_o up_o to_o the_o meridian_n at_o l_o which_o point_n l_o you_o may_v find_v by_o move_v the_o string_n to_o and_o fro_o upon_o the_o meridian_n line_n till_o another_o hold_v the_o side_n of_o a_o quadrant_n to_o the_o movable_a string_n he_o shall_v find_v the_o thread_n and_o plummet_n to_o fall_v direct_o upon_o the_o compliment_n of_o the_o latitude_n which_o in_o this_o example_n be_v 37_o deg_fw-la 30_o min._n the_o point_n l_o being_n thus_o find_v upon_o the_o meridian_n draw_v the_o line_n l_o ae_n perpendicular_a to_o the_o meridian_n l_o r_o which_o line_n shall_v be_v the_o equinoctial_a have_v thus_o do_v upon_o a_o table_n or_o such_o like_a draw_v a_o line_n which_o shall_v be_v of_o equal_a length_n with_o lk_n the_o distance_n from_o the_o glass_n to_o the_o point_n l_o on_o the_o ceiling_n which_o line_n divide_v into_o 10_o equal_a part_n and_o each_o of_o those_o or_o at_o least_o one_o of_o they_o into_o 10_o other_o part_n so_o shall_v you_o have_v in_o all_o 100_o part_n each_o of_o which_o you_o must_v suppose_v to_o 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till_o a_o more_o convenient_a opportunity_n and_o therefore_o in_o the_o mean_a time_n farewell_n finis_fw-la
by_o which_o point_n g_z draw_v the_o line_n a_o g_o c_o as_o be_v former_o do_v in_o the_o last_o chapter_n by_o which_o we_o have_v proceed_v thus_o far_o but_o as_o in_o the_o last_o chapter_n the_o arch_n b_o c_o be_v the_o height_n of_o the_o sun_n desire_v so_o by_o this_o chapter_n the_o arch_n c_o d_o shall_v be_v the_o height_n of_o the_o sun_n which_o be_v apply_v unto_o your_o scale_n will_v give_v you_o 36_o deg_fw-la 52_o min._n for_o the_o height_n of_o the_o sun_n desire_v chap._n v._o the_o almicanter_n or_o height_n of_o the_o sun_n be_v give_v to_o find_v the_o length_n of_o the_o right_a shadow_n by_o right_a shadow_n be_v mean_v the_o shadow_n of_o any_o staff_n post_n steeple_n or_o any_o gnomon_n whatsoever_o that_o stand_v at_o right_a angle_n with_o the_o horizon_n the_o one_o end_n thereof_o respect_v the_o zenith_n of_o the_o place_n and_o the_o other_o the_o nadir_n first_o therefore_o according_a unto_o the_o three_o chapter_n describe_v the_o quadrant_n a_o b_o d_o then_o suppose_v the_o height_n of_o your_o gnomon_n or_o substance_n yield_v shadow_n to_o be_v 12_o foot_n as_o in_o the_o former_a chapter_n this_o do_v i_o set_v down_o from_o a_o to_o e_o and_o from_o the_o point_n e_o draw_v the_o line_n e_o f_o parallel_n to_o a_o b_o then_o set_v the_o almicanter_n which_o here_o we_o will_v suppose_v to_o be_v 53_o de_fw-la and_o 8_o min._n as_o it_o be_v find_v by_o the_o three_o chapter_n from_o b_o unto_o c_o from_o which_o point_n c_z draw_v the_o line_n c_o a_o cut_v the_o line_n e_o f_o in_o the_o point_n g_o so_o shall_v e_z g_z be_v the_o length_n of_o the_o right_a shadow_n desire_v which_o be_v take_v betwixt_o your_o compass_n and_o apply_v unto_o your_o scale_n will_v give_v you_o 9_o of_o those_o division_n whereof_o a_o e_z be_v 12_o which_o here_o do_v signify_v 9_o foot_n chap._n vi_o the_o almicanter_n or_o height_n of_o the_o sun_n be_v give_v to_o find_v the_o length_n of_o the_o contrary_a shadow_n by_o the_o contrary_a shadow_n be_v understand_v the_o length_n of_o any_o shadow_n that_o be_v make_v by_o a_o staff_n or_o gnomon_n stand_v at_o right_a angle_n against_o any_o perpendicular_a wall_n in_o such_o a_o manner_n that_o it_o may_v lie_v parallel_n unto_o the_o horizon_n the_o length_n of_o the_o contrary_a shadow_n do_v increase_v as_o the_o sun_n rise_v in_o height_n whereas_o contrariwise_o the_o right_a shadow_n do_v decrease_v in_o length_n as_o the_o sun_n do_v increase_v in_o height_n therefore_o the_o way_n to_o find_v out_o the_o length_n of_o the_o verse_v shadow_n be_v as_o follow_v first_o draw_v your_o quadrant_n as_o be_v teach_v in_o the_o three_o chapter_n now_o suppose_v the_o length_n of_o your_o gnomon_n to_o be_v 12_o foot_n place_v it_o from_o a_o to_o e_o likewise_z from_z e_z draw_v the_o line_n e_o f_o parallel_n to_o a_o b_o as_o before_z now_o suppose_v the_o height_n of_o the_o sun_n to_o be_v 36_o deg_fw-la 52_o min._n take_v it_o from_o your_o scale_n and_o place_n it_o from_o d_o to_z c_z from_o which_o point_n c_z draw_v the_o line_n c_o a_o cut_v the_o line_n e_o f_o in_o the_o point_n g_o so_o shall_v g_z e_z be_v the_o length_n of_o the_o contrary_a shadow_n which_o here_o will_v be_v find_v to_o be_v 9_o foot_n the_o thing_n desire_v chap._n vii_o have_v the_o distance_n of_o the_o sun_n from_o the_o next_o equinoctial_a point_n to_o find_v his_o declination_n first_o draw_v the_o line_n a_o b_o then_o upon_o the_o end_n a_o raise_v the_o perpendicular_a a_o d_o then_o open_v your_o compass_n to_o the_o radius_fw-la of_o the_o scale_n place_n one_o foot_n in_o the_o centre_n a_o and_o with_o the_o other_o draw_v the_o quadrant_n b_o c_o d_o then_o suppose_v the_o sun_n to_o be_v either_o in_o the_o 29_o degree_n of_o taurus_n or_o in_o the_o first_o degree_n of_o leo_n both_o which_o point_n be_v 59_o degree_n distant_a from_o the_o next_o equinoctial_a point_n aries_n or_o if_o the_o sun_n shall_v be_v in_o the_o 29_o degree_n of_o scorpio_n or_o in_o the_o first_o degree_n of_o aquarius_n both_o which_o be_v also_o 59_o degree_n distant_a from_o the_o equinoctial_a point_n libra_n therefore_o take_v 59_o degree_n from_o your_o scale_n and_o place_n it_o from_o b_o to_z c_z and_o draw_v the_o line_n c_o a_o then_o place_v the_o great_a declination_n of_o the_o sun_n from_o b_o unto_o f_o which_o be_v 23_o degree_n 30_o minute_n then_o fix_v one_o foot_n of_o your_o compass_n in_o the_o point_n f_o with_o the_o other_o take_v the_o near_a distance_n unto_o the_o line_n a_o b_o which_o you_o may_v do_v by_o open_v or_o shuting_z of_o your_o compass_n still_o turn_v they_o to_o and_o fro_o till_o the_o move_a point_n thereof_o do_v only_o touch_v the_o line_n a_o b_o this_o distance_n be_v keep_v set_v one_o foot_n of_o your_o compass_n in_o the_o point_n a_o and_o with_o the_o other_o make_v a_o mark_n in_o the_o line_n a_o c_o as_o at_z e_z from_o which_o point_n e_z take_v the_o near_a extent_n 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declination_n of_o the_o sun_n upon_o the_o chord_n from_o d_o unto_z b_o which_o be_v 23_o degree_n and_o 30_o minute_n then_o from_o the_o point_n b_o take_v the_o short_a extent_n unto_o the_o line_n a_o d_o this_o distance_n be_v keep_v set_v one_o foot_n in_o the_o point_n a_o and_o with_o the_o other_o describe_v the_o small_a quadrant_n g_o h_n i_o then_o set_v the_o declination_n of_o the_o sun_n which_o in_o this_o example_n be_v 20_o degree_n from_o d_o unto_o c_o from_o which_o point_n c_z take_v the_o short_a extent_n unto_o the_o line_n a_o d_o this_o distance_n be_v keep_v place_n one_o foot_n in_o the_o arch_a line_n g_o h_n i_o after_o such_o a_o manner_n that_o the_o other_o foot_n be_v turn_v about_o may_v but_o only_o touch_v the_o line_n a_o d_o so_o shall_v the_o fix_a foot_n stay_v upon_o the_o point_n h_n through_o which_o point_n h_n draw_v the_o line_n a_o h_n e_o cut_v the_o arch_n d_o f_o in_o the_o point_n e_o so_o shall_v the_o arch_n d_o e_o be_v the_o 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ay_o from_o which_o point_n i_o take_v the_o near_a extent_n unto_o the_o line_n a_o b_o which_o distance_n be_v keep_v place_n one_o foot_n of_o your_o compass_n in_o the_o arch_a line_n f_o g_o h_n so_o that_o the_o move_a foot_n may_v but_o only_o touch_v the_o line_n a_o b_o at_o the_o short_a extent_n so_o shall_v the_o fix_a foot_n rest_n in_o the_o arch_a line_n f_o g_o h_n at_o g_z through_o which_o point_n g_z draw_v the_o line_n a_o g_o c_o then_o suppose_v the_o sun_n to_o be_v in_o the_o 29_o degree_n of_o