Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	draw_v	line_n	perpendicular_a	3,095	5	14.0786	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A93914	Horometria: or The compleat diallist. Wherein the whole mystery of the art of dialling is plainly taught three several wayes; two of which are performed geometrically by rule and compass onely: and the third instrumentally, by a quadrant fitted for that purpose. With the working of such propositions of the sphere, as are most usefull in astronomy and navigation ... By Thomas Stirrup, philomath. Whereunto is added an appendix, shewing how the parallels of declination; the Jewish, Babylonish, & Italian houres; the azimuths, almicanters, &c. may be easily inscribed on any dial whatsoever, by rule and compasse onely. And to draw a diall on the seeling of a room, by W. Leybourn. Also, Dialling Vniversal, performed by an easie and most speedy way, ... by certain scales set on a small portable ruler, by G.S. practitioner in the mathematicks.	Stirrup, Thomas.; Leybourn, William, 1626-1716. Appendix, shewing how the parallels of declination; the Jewish, Babylonish, & Italian hours; the asimuths, almicanters &c. may be easily inscribed on any dial whatsoever.; Serle, George. Dialling universal.	1658 (1658)	Wing S5689; Thomason E956_2; ESTC R207639	89,665	174

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_a 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 &_o be_v contain_v under_o the_o right_a line_n f_o h_o g_o 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 &_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 &_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 &_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 15._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_a 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_a 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 deg_fw-la 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 deg_fw-la 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 ii_o to_o a_o line_n give_v to_o draw_v a_o parallel_n line_n at_o any_o distance_n require_v suppose_v the_o line_n give_v to_o be_v a_o b_o unto_o which_o line_n it_o be_v require_v to_o draw_v a_o parallel_n line_n first_o open_v your_o compass_n to_o the_o distance_n require_v then_o set_v one_o foot_n in_o the_o end_n a_o and_o with_o the_o other_o strike_v a_o arch_a line_n on_o that_o side_n the_o give_v line_n whereunto_o the_o parallel_a line_n be_v to_o be_v draw_v as_o the_o arch_a line_n c_o this_o be_v do_v draw_v the_o like_a arch_a line_n upon_o the_o end_n b_o as_o the_o arch_a line_n d_o and_o by_o the_o convexity_n of_o those_o two_o arch_a line_n c_o and_o d_o draw_v the_o line_n c_o d_o which_o shall_v be_v parallel_n to_o the_o give_v line_n as_o be_v require_v chap._n iii_o to_o perform_v the_o former_a proposition_n at_o a_o distance_n require_v and_o by_o a_o point_n limit_v suppose_v the_o line_n give_v to_o be_v d_o e_o unto_o which_o line_n it_o be_v require_v to_o draw_v a_o parallel_n line_n at_o the_o distance_n and_o by_o the_o point_n f._n first_o therefore_o place_n one_o foot_n of_o the_o compass_n in_o the_o point_n f_o from_o whence_o take_v the_o short_a extension_n to_o the_o line_n de_fw-fr as_o f_o e_o at_o which_o distance_n place_z one_o foot_n of_o the_o compass_n in_o the_o end_n d_o and_o with_o the_o other_o strike_v the_o arch_a line_n g_o by_o the_o convexity_n of_o which_o arch_a line_n and_o the_o limit_a point_n f_o draw_v the_o line_n f_o g_o which_o be_v parallel_n to_o the_o give_v line_n d_o e_o as_o be_v require_v chap._n iu._n the_o manner_n how_o to_o raise_v a_o perpendicular_a line_n from_o the_o middle_n of_o alone_a give_v let_v the_o line_n give_v be_v a_o b_o and_o let_v c_o be_v a_o point_n therein_o whereon_o it_o be_v require_v to_o raise_v a_o perpendicular_a first_o therefore_o open_v the_o compass_n to_o any_o convenient_a distance_n and_o set_v one_o foot_n in_o the_o point_n c_o with_o the_o other_o foot_n mark_v on_o either_o side_n thereof_o the_o equal_a distance_n c_o a_n and_o c_o b_o then_o open_v your_o compass_n to_o any_o convenient_a wide_a distance_n with_o one_o foot_n in_o the_o point_n a_o with_o the_o other_o strike_v the_o arch_a line_n e_o over_o the_o point_n c_o then_o with_o the_o same_o distance_n of_o your_o compass_n set_v one_o foot_n in_o b_o and_o with_o the_o other_o draw_v the_o arch_a line_n f_o cross_v the_o arch_n e_o in_o the_o point_n d_o from_o which_o point_n d_o draw_v the_o line_n dc_o which_o line_n be_v perpendicular_a unto_o the_o give_v line_n a_o b_o from_o the_o point_n c_o as_o be_v require_v chap._n v._o to_o let_v a_o perpendicular_a fall_n from_o a_o point_n assign_v unto_o the_o middle_n of_o a_o line_n give_v let_v the_o line_n give_v whereupon_o you_o will_v have_v a_o perpendicular_a let_v fall_v be_v the_o line_n d_o e_o f_o and_o the_o point_n assign_v to_o be_v the_o point_n c_o from_o whence_o you_o will_v have_v a_o perpendicular_a let_v fall_v upon_o the_o give_v line_n d_o e_o f._n first_n set_v one_o foot_n of_o your_o compass_n in_o the_o point_n c_o and_o open_v your_o compass_n to_o any_o convenient_a distance_n so_o that_o it_o be_v more_o than_o the_o distance_n c_o e_o make_v a_o arch_n of_o a_o circle_n with_o the_o other_o foot_n so_o that_o it_o may_v cut_v the_o line_n d_o e_o f_o twice_o that_o be_v at_z i_o and_o g_o then_o find_v the_o middle_n between_o those_o two_o intersection_n which_o will_v be_v in_o the_o point_n e_o from_o which_o point_n e_z draw_v the_o 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 and_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 e_o d_o 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 &_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 abc_n 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_n 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 un-necessary_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 circ_n l_o describe_v by_o the_o motion_n of_o the_o north_n star_n or_o the_o tail_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_o 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 hat_n in_o habit_n 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 other_o 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 vix_fw-la 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 and_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 and_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 be_v a_o great_a circle_n also_o divide_v the_o equinoctial_a into_o two_o equal_a part_n by_o the_o head_n of_o aries_n and_o libra_n the_o one_o half_a thereof_o do_v decline_v unto_o the_o northward_o and_o the_o other_o towards_o the_o south_n the_o great_a declination_n thereof_o according_a to_o the_o observation_n of_o that_o late_a famous_a mathematician_n master_n edward_n wright_n be_v 23_o degree_n 31_o minute_n 30_o second_n note_v also_o that_o the_o circle_n be_v divide_v into_o 12_o equal_a part_n which_o part_n be_v attribute_v unto_o the_o 12_o sign_n aries_n taurus_n gemini_fw-la cancer_n leo_n virgo_fw-la libra_n scorpio_n sagittarius_fw-la capricornus_fw-la aquarius_n and_o pisces_fw-la out_o of_o this_o line_n

radius_fw-la of_o your_o scale_n set_v one_o soot_n in_o the_o end_n a_o and_o with_o the_o other_o describe_v the_o arch_n bcd_n then_o open_v your_o compass_n unto_o the_o whole_a 90_o deg_fw-la with_o one_o foot_n in_o b_o with_o the_o other_o mark_v the_o arch_n b_o c_o d_o in_o the_o point_n d_o from_o which_o point_n d_o draw_v the_o line_n dam_fw-ge which_o shall_v be_v perpendicular_a unto_o the_o line_n ab_fw-la and_o make_v the_o quadrant_a abcd_n 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 the_o line_n a_o e_o which_o here_o we_o will_v suppose_v to_o be_v 12_o foot_n therefore_o take_v 12_o of_o your_o equal_a division_n from_o your_o scale_n as_o here_o i_o have_v take_v 12_o quarter_n for_o this_o our_o purpose_n and_o set_v they_o down_o from_o a_o to_o e_o and_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 for_o this_o 9_o foot_n must_v i_o take_v 9_o of_o the_o same_o division_n as_o i_o do_v before_o and_o place_v they_o from_o e_z to_z g_z by_o which_o point_n g_z draw_v the_o line_n a_o g_o c_o from_o the_o centre_n a_o through_o the_o point_n g_o until_o it_o cut_v the_o arch_n b_o f_o c_o d_o in_o the_o point_n g_o so_o shall_v the_o arch_n b_o c_o be_v the_o height_n of_o the_o sun_n desire_v which_o in_o this_o example_n will_v be_v find_v to_o be_v 53_o deg_fw-la 8_o min._n the_o thing_n desire_v chap._n iv_o to_o find_v the_o altitude_n of_o the_o sun_n by_o the_o shadow_n of_o a_o gnomon_n stand_v 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_a a_o b_o c_o d_o as_o be_v teach_v in_o the_o last_o chapter_n and_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_z in_o the_o last_o chapter_n then_o draw_v the_o line_n of_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 by_o which_o point_n g_z draw_z the_o sine_z 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 m._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_a 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 of_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 deg_fw-la &_o 8_o m._n as_o it_o be_v find_v by_o the_o three_o chap._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_a 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 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_a bcd_n 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 deg_fw-la 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 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 deg_fw-la 30_o min._n then_o fix_v one_o foot_n or_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 &_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 unto_o the_o line_n a_o b_o this_o distance_n betwixt_o your_o compass_n be_v keep_v fix_v one_o foot_n in_o the_o arch_n b_o c_o d_o move_v it_o either_o upward_o or_o downward_o still_o keep_v it_o direct_o in_o the_o arch_a line_n until_o by_o move_v the_o other_o foot_n to_o and_o fro_o you_o find_v it_o to_o touch_v the_o line_n a_o b_o and_o no_o more_o so_o shall_v the_o fix_a foot_n rest_n in_o the_o point_n g_o which_o shall_v be_v the_o declination_n of_o the_o sun_n account_v from_o b_o which_o in_o this_o example_n will_v be_v find_v to_o be_v about_o 20_o degree_n the_o thing_n desire_v chap._n viii_o the_o declination_n of_o the_o sun_n and_o the_o quarter_n of_o the_o ecliptic_a which_o he_o possess_v be_v give_v to_o find_v his_o true_a place_n let_v the_o declination_n give_v be_v ●0_n degree_n and_o the_o quarter_n that_o he_o possess_v be_v betwixt_o the_o head_n of_o aries_n and_o cancer_n first_o draw_v the_o quadrant_a a_o d_o e_o f_o then_o set_v the_o great_a 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_a g_o h_n i_o then_o set_v the_o declination_n of_o

the_o elevation_n of_o the_o pole_n above_o the_o plane_n 6_o deg_fw-la 4_o min._n and_o the_o inclination_n of_o both_o meridian_n 82_o deg_fw-la 5_o min._n but_o if_o they_o lean_a to_o the_o horizon_n they_o be_v then_o call_v incliner_n these_o may_v incline_v either_o to_o the_o east_n part_n of_o the_o horizon_n or_o to_o the_o west_n and_o each_o of_o they_o have_v two_o face_n the_o upper_a towards_o the_o zenith_n the_o low_a towards_o the_o nadir_n wherein_o know_v the_o latitude_n of_o the_o place_n and_o the_o inclination_n of_o the_o plane_n to_o the_o horizon_n we_o be_v to_o consider_v three_o thing_n more_o before_o we_o can_v come_v to_o the_o draw_v of_o the_o dial._n i._o the_o elevation_n of_o the_o pole_n above_o the_o plane_n ii_o the_o distance_n of_o the_o substile_a from_o the_o meridian_n iii_o the_o angle_n of_o inclination_n betwixt_o both_o meridian_n these_o three_o may_v be_v find_v after_o this_o manner_n little_o differ_v from_o the_o 14._o chap._n then_o take_v the_o distance_n s_o h_n and_o set_v it_o in_o the_o line_n e_o r_n from_o r_n to_o k_o through_o which_o point_n k_o draw_v the_o line_n a_o k_o l_o cut_v the_o arch_n of_o the_o quadrant_a in_o the_o point_n l_o so_fw-mi shall_v the_o arch_n cl_n be_v the_o distance_n of_o the_o substile_a from_o the_o meridian_n and_o be_v in_o this_o example_n 33_o deg_fw-la 5_o min._n this_o be_v do_v from_o the_o point_n s_o draw_v the_o line_n l_o t_o parallel_n to_o the_o line_n a_o c_o cut_v the_o arch_n g_o d_o in_o the_o point_n o_o through_o which_o point_n o_o draw_v the_o line_n a_o o_o i_o cut_v the_o arch_n of_o the_o quadrant_a b_o c_o in_o the_o point_n i_o so_o shall_v the_o arch_n ci_o be_v the_o inclination_n of_o the_o meridian_n of_o the_o plane_n to_o the_o meridian_n of_o the_o place_n and_o in_o this_o example_n be_v find_v to_o be_v 43_o deg_fw-la 28_o min._n which_o be_v resolve_v into_o time_n do_v give_v about_o two_o hour_n and_o 54_o min_fw-mi from_o the_o meridian_n for_o the_o place_n of_o the_o substile_a among_o the_o hour-line_n chap._n xvii_o to_o draw_v a_o dial_n upon_o the_o meridian_n incline_v plane_n have_v by_o the_o second_o chapter_n find_v the_o inclination_n of_o this_o plane_n to_o be_v 30_o degree_n and_o so_o by_o the_o last_o chapter_n find_v the_o elevation_n of_o the_o pole_n above_o the_o plane_n to_o be_v 43_o degr_n 23_o min._n and_o the_o distance_n of_o the_o substile_a from_o the_o meridian_n to_o be_v 33_o deg_fw-la 5_o min._n and_o likewise_o the_o angle_n of_o inclination_n to_o be_v 43_o deg_fw-la 38_o min._n we_o may_v proceed_v to_o make_v the_o dial_n after_o this_o manner_n first_o draw_v the_o horizontal_a line_n a_o b_o serve_v for_o the_o meridian_n and_o hour_n of_o 12_o about_o the_o middle_n of_o this_o line_n make_v choice_n of_o a_o centre_n at_o c_o upon_o which_o describe_v a_o circle_n for_o your_o dial_n as_o a_o d_o b_o e._n then_o see_v this_o be_v the_o upper_a face_n of_o the_o plane_n set_v 33_o degree_n 5_o minute_n the_o distance_n of_o the_o substile_a from_o the_o meridian_n in_o the_o dial_n circle_n from_o the_o north_n end_n of_o the_o horizontal_n line_n upward_o as_o from_o b_o to_o h_n and_o draw_v the_o line_n c_o h_n for_o the_o substile_a but_o if_o this_o have_v be_v the_o under_o face_n the_o substile_a must_v have_v fall_v below_o the_o horizontal_a line_n now_o through_o the_o centre_n c_o draw_v the_o diameter_n e_o f_o make_v right_a angle_n with_o the_o substile_a c_o h._n then_o set_v 43_o degree_n 23_o minute_n from_o h_n unto_o d_o for_o the_o stile_n and_o draw_v the_o line_n c_o d_o unto_o s_n and_o from_o the_o end_n of_o the_o substile_a draw_v the_o crooked_a line_n h_o s_o cut_v the_o line_n of_o the_o stile_n in_o the_o point_n s_o so_o shall_v the_o triangle_n s_o c_o h_n be_v the_o true_a pattern_n of_o your_o cock_n for_o this_o dial._n now_o take_v each_o perpendicular_a betwixt_o your_o compass_n and_o with_o one_o foot_n in_o the_o centre_n c_o with_o the_o other_o make_v mark_n in_o the_o line_n of_o the_o stile_n from_o which_o take_v the_o near_a extent_n unto_o the_o substile_a and_o lay_v they_o down_o upon_o their_o own_o proper_a perpendicular_o from_o the_o substile_a so_o may_v you_o make_v mark_n through_o which_o and_o from_o the_o centre_n you_o may_v draw_v the_o hour-line_n this_o dial_n be_v thus_o draw_v for_o the_o upper_a face_n of_o a_o meridian_n plane_n incline_v towards_o the_o west_n you_o must_v fix_v the_o cock_n in_o the_o centre_n c_o hang_v over_o the_o substile_a c_o h_n with_o a_o angle_n equal_a to_o the_o angle_n s_o c_o h_n so_o that_o it_o may_v point_v to_o the_o north_n pole_n because_o upon_o the_o upper_a face_n of_o all_o meridian_n incliner_n the_o north_n pole_n be_v elevate_v and_o therefore_o contrary_o the_o south_n pole_n must_v needs_o be_v elevate_v above_o their_o under_a face_n this_o dial_n be_v draw_v in_o paper_n for_o the_o the_o upper_a face_n of_o this_o plane_n will_v also_o serve_v for_o the_o under_o face_n thereof_o if_o you_o turn_v the_o pattern_n about_o so_o that_o the_o horizontal_n line_n a_o b_o may_v lie_v still_o parallel_n to_o the_o horizon_n and_o the_o stile_n with_o the_o substile_a lie_v under_o the_o horizontal_n line_n may_v point_v downward_o to_o the_o south_n pole_n the_o paper_z be_v oil_v or_o prick_v through_o so_o that_o you_o may_v take_v the_o back_n side_n thereof_o for_o the_o fore-side_n without_o alter_v the_o number_n set_v to_o the_o hour_n chap._n xviii_o the_o inclination_n and_o declination_n of_o any_o plane_n be_v give_v in_o a_o know_a latitude_n to_o find_v the_o angle_n of_o intersection_n botween_n the_o plane_n and_o the_o meridian_n the_o aseension_n and_o elevation_n of_o the_o meridian_n with_o the_o arch_n thereof_o between_o the_o pole_n and_o the_o plane_n and_o also_o the_o elevation_n of_o the_o pole_n above_o the_o plane_n the_o distance_n of_o the_o substile_a from_o the_o meridian_n with_o the_o inclination_n between_o both_o meridian_n if_o a_o plane_n shall_v decline_v from_o the_o south_n and_o also_o incline_v to_o to_o the_o horizon_n it_o be_v then_o call_v by_o the_o name_n of_o a_o decline_a incline_a plane_n of_o these_o there_o be_v several_a sort_n for_o the_o inclination_n be_v northward_o the_o plane_n may_v fall_v betwixt_o the_o horizon_n and_o the_o pole_n or_o betwixt_o the_o zenith_n and_o the_o pole_n or_o else_o they_o may_v lie_v in_o the_o pole_n of_o the_o world_n or_o the_o inclination_n may_v be_v southward_a and_o so_o fall_v below_o the_o intersection_n of_o the_o meridian_n and_o the_o equator_fw-la or_o above_o it_o or_o the_o plane_n may_v fall_v direct_o in_o the_o intersection_n of_o the_o meridian_n with_o the_o equator_fw-la each_o of_o these_o plane_n have_v two_o face_n the_o upper_a towards_o the_o zenith_n and_o the_o low_a towards_o the_o nadir_n now_o have_v the_o latitude_n of_o the_o place_n with_o the_o declination_n and_o inclination_n of_o the_o plane_n we_o have_v seven_o thing_n more_o to_o consider_v before_o we_o can_v come_v to_o the_o draw_v of_o the_o dial._n i._o the_o angle_n of_o intersection_n betwixt_o the_o plane_n and_o the_o meridian_n ii_o the_o arch_n of_o the_o plane_n betwixt_o the_o horizon_n and_o the_o meridian_n iii_o the_o arch_n of_o the_o meridian_n betwixt_o the_o horizon_n and_o the_o plane_n iv_o the_o arch_n of_o the_o meridian_n between_o the_o pole_n and_o the_o plane_n v._o the_o elevation_n of_o the_o pole_n above_o the_o plane_n vi_o the_o distance_n of_o the_o substile_a from_o the_o meridian_n vii_o the_o angle_n of_o inclination_n betwixt_o the_o meridian_n of_o the_o plane_n and_o the_o meridian_n of_o the_o place_n all_o these_o seven_o may_v be_v find_v out_o after_o this_o manner_n first_o describe_v the_o quadrant_n a_o b_o c_o then_o suppose_v the_o plane_n to_o decline_v from_o the_o south_n towards_o the_o east_n 35_o deg_fw-la and_o to_o incline_v towards_o the_o horizon_n 25_o deg_fw-la set_v 35_o deg_fw-la the_o declination_n of_o the_o plane_n from_o c_o to_o e_z in_o the_o quadrant_n arch_n c_o b_o and_o draw_v the_o line_n a_o e_o then_o set_v 25_o deg_fw-la the_o inclination_n of_o the_o plane_n in_o the_o same_o arch_n from_o b_o to_o f_o and_o draw_v the_o line_n e_o z_o parallel_n to_o a_o c_o cut_v the_o line_n a_o b_o in_o the_o point_n z_o and_o with_o the_o distance_n f_o z_o and_o one_o foot_n place_v in_o the_o centre_n a_o with_o the_o other_o describe_v the_o arch_n g_o h_n 1_n cut_v the_o line_n a_o e_o in_o the_o point_n h_n through_o which_o point_n h_n draw_v the_o line_n k_o l_o parallel_n to_o a_o c_z

latitude_n which_o be_v equal_a to_o the_o height_n of_o the_o stile_n above_o such_o recline_a plain_n they_o be_v horizontal_n plane_n one_o example_n therefore_o in_o one_o plane_n will_v be_v sufficient_a for_o the_o rest_n therefore_o in_o latitude_n of_o 52_o deg_fw-la 30_o min._n let_v it_o be_v require_v to_o describe_v the_o equinoctial_a and_o the_o two_o tropic_n in_o a_o full_a south_n erect_v plane_n have_v draw_v your_o dial_n with_o the_o hour_n half_n and_o quarter_n as_o also_o the_o line_n c_o qui_fw-fr for_o the_o stile_n you_o must_v make_v choice_n of_o some_o convenient_a point_n in_o the_o stile_n as_o at_o s_n for_o the_o nodus_fw-la or_o knot_n which_o must_v give_v the_o shadow_n to_o the_o tropic_n and_o other_o parallel_n of_o declination_n for_o all_o these_o astronomical_a conclusion_n be_v not_o show_v by_o the_o shadow_n of_o the_o whole_a length_n of_o the_o stile_n or_o axis_n as_o the_o hour_n be_v but_o by_o some_o point_n therein_o which_o represent_v the_o centre_n of_o the_o earth_n which_o in_o the_o dial_n follow_v be_v the_o point_n and_o the_o triangular_a stile_n in_o that_o dial_n be_v represent_v by_o the_o triangle_n c_o s_o l_o whereof_z c_o l_o be_v call_v the_o substilar_a c_o s_o the_o axis_n of_o the_o stile_n and_o s_o l_o the_o perpendicular_a stile_n the_o top_n of_o which_o viz._n s_n be_v the_o point_n we_o be_v in_o this_o place_n to_o respect_n the_o dial_n be_v draw_v and_o the_o triangle_n c_o s_o l_o mad_a equal_a to_o the_o cock_n of_o the_o dial_n you_o must_v upon_o a_o piece_n of_o pasteboard_n draw_v the_o triangle_n o_o p_o r_o equal_a to_o the_o stile_n in_o your_o dial_n c_o s_o l_o making_z r_z o_o equal_a to_o c_o l_o the_o substilar_a p_o o_o equal_a to_o c_o s_o the_o axis_n of_o the_o stile_n and_o p_o r_o equal_a to_o s_o l_o the_o length_n of_o the_o perpendicular_a stile_n then_o from_o the_o point_n p_o raise_v a_o perpendicular_a as_o p_o b_o represent_v the_o equinoctial_a and_o on_o pas_n a_o centre_n describe_v the_o arch_n a_o b_o c_o now_o because_o the_o tropic_n of_o cancer_n and_o capricorn_n do_v decline_v 23_o deg_fw-la 31_o min._n from_o the_o equinoctial_a therefore_o take_v 23_o deg_fw-la 31_o min._n from_o your_o scale_n of_o chord_n and_o set_v it_o off_o upon_o the_o arch_n a_o b_o c_o from_o b_o t_z a_o and_z from_z b_o to_z c_z and_o draw_v the_o line_n p_o a_n and_o p_o c_o represent_v the_o two_o tropic_n of_o cancer_n and_o capricorn_n this_o do_v extend_v the_o line_n of_o the_o substilar_a r_n o_o which_o 〈◊〉_d north_n or_o south_n erect_v direct_a plane_n i_o tell_v you_o be_v always_o the_o same_o with_o the_o twelve_o a_o clock_n line_n from_o o_o to_o 12_o cut_v the_o equinoctial_a line_n p_o b_o in_o the_o point_n a_o then_o with_o your_o compass_n take_v the_o distance_n o_o a_o out_o of_o your_o trigon_n and_o place_n it_o in_o your_o plane_n from_o the_o centre_n c_o unto_o a_o and_o draw_v the_o line_n ♈_o a_fw-fr ♎_o perpendicular_a to_o the_o substile_a or_o line_n of_o 12._o the_o equinoctial_a be_v draw_v first_o take_v out_o of_o your_o plane_n the_o distance_n c_o b_o and_z place_z that_o distance_n in_o your_o trigon_n from_o o_o unto_o b_o and_o draw_v the_o line_n o_o b_o 1_o represent_v the_o hour_n of_o 1_o or_o 11_o in_o your_o dial._n second_o take_v out_o of_o your_o plane_n the_o distance_n c_o c_o and_o place_n that_o in_o your_o trigon_n from_o o_o unto_fw-la c_o and_z draw_z the_o line_n o_o c_o 2_o represent_v the_o hour-line_n of_o 2_o or_o 10._o three_o take_v out_o of_o your_o plane_n the_o distance_n c_o d_o and_o place_n it_o in_o your_o trigon_n from_o o_o unto_o d_o and_o draw_v the_o line_n o_o d_o 3_o for_o the_o hour_n of_o 9_o and_o 3._o four_o from_o our_o plane_n take_v 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_o 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-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 hour-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 draw_v the_o tropic_a of_o capricorn_n it_o be_v necessary_a to_o draw_v the_o horizontal_n line_n of_o your_o plane_n a_o b_o which_o line_n in_o all_o upright_a plane_n must_v be_v draw_v through_o the_o point_n l_o the_o foot_n of_o the_o perpendicular_a stile_n and_o perpendicular_a to_o the_o meridian_n or_o line_n of_o 12_o and_o in_o all_o plane_n whatsoever_o this_o line_n must_v be_v draw_v through_o the_o intersection_n of_o the_o equinoctial_a with_o the_o hour_n of_o six_o this_o line_n ought_v first_o to_o be_v draw_v because_o it_o be_v very_o improper_a to_o extend_v the_o tropic_n or_o other_o parallel_n of_o declination_n above_o the_o horizontal_n line_n because_o at_o what_o hour_n any_o parallel_n of_o declination_n cut_v this_o line_n on_o either_o side_n of_o the_o meridian_n at_o that_o time_n do_v the_o sun_n rise_v or_o set_v as_o be_v instance_a in_o the_o last_o now_o the_o tropic_a of_o capricorn_n must_v be_v put_v upon_o your_o plane_n in_o the_o same_o manner_n as_o that_o of_o cancer_n by_o take_v out_o of_o your_o trigon_n the_o distance_n from_o o_o where_o the_o several_a hour-line_n a_o b_o c_o d_o e_o do_v cut_v the_o tropic_a of_o capricorn_n p_o c_o and_o place_v they_o on_o your_o plane_n from_o the_o centre_n c_o upon_o the_o respective_a hour-line_n and_o through_o those_o point_n so_o find_v draw_v the_o line_n ♑_o ♑_o represent_v the_o tropic_a of_o capricern_v ¶_o and_o in_o the_o same_o manner_n may_v the_o parallel_n of_o the_o other_o sign_n be_v draw_v upon_o your_o plane_n by_o place_v they_o into_o your_o trigon_n according_a to_o their_o declination_n and_o afterward_o transfer_v they_o into_o your_o plane_n as_o you_o see_v in_o the_o former_a figure_n the_o rule_n that_o have_v be_v here_o give_v for_o the_o describe_v of_o the_o parallel_n of_o the_o sign_n in_o this_o erect_v direct_a plane_n be_v universal_a in_o all_o plane_n observe_v this_o one_o exception_n that_o whereas_o in_o all_o erect_v direct_a plane_n the_o eqninoctial_a be_v draw_v perpendicular_a to_o the_o meridian_n or_o line_n of_o 12_o so_o in_o all_o other_o plane_n whatsoever_o the_o equinoctial_a must_v be_v draw_v perpendicular_a to_o the_o substile_a and_o then_o the_o work_n will_v be_v the_o same_o in_o all_o respect_n as_o may_v appear_v more_o large_o in_o the_o next_o section_n §_o 3._o in_o decline_a or_o decline_a recline_a dial_n the_o last_o caution_n precede_v be_v sufficient_a for_o the_o perform_n of_o this_o work_n and_o therefore_o need_v no_o example_n however_o suppose_v a_o upright_a plane_n to_o decline_v 32_o deg_fw-la from_o the_o south_n eastward_n in_o the_o latitude_n of_o 52_o deg_fw-la 30_o min._n and_o let_v it_o be_v require_v to_o describe_v the_o two_o tropic_n and_o the_o equinoctial_a upon_o such_o a_o plane_n and_o here_o note_v that_o whatsoever_o be_v say_v of_o upright_a decliner_n the_o same_o be_v also_o to_o be_v understand_v of_o those_o plane_n which_o both_o decline_n 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 six_o chap._n ii_o show_v how_o to_o inscribe_v though_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

29_o 08_o 19_o 3_o 02_o 14_o 10_o 21_o 30_o 23_o 23_o 18_o 18_o 13_o 07_o 56_o 3_o 25_o 14_o 29_o 21_o 40_o 23_o 20_o 19_o 17_o 57_o 07_o 33_o 3_o 48_o 14_o 48_o 21_o 49_o 23_o 16_o 20_o 17_o 40_o 07_o 10_o 4_o 11_o 15_o 06_o 21_o 58_o 23_o 13_o 21_o 17_o 24_o 06_o 47_o 4_o 34_o 15_o 24_o 22_o 06_o 23_o 09_o 22_o 17_o 07_o 06_o 24_o 4_o 57_o 15_o 42_o 22_o 14_o 23_o 04_o 23_o 16_o 49_o 06_o 01_o 5_o 20_o 15_o 59_o 22_o 22_o 23_o 59_o 24_o 16_o 32_o 05_o 38_o 5_o 43_o 16_o 17_o 22_o 29_o 22_o 54_o 25_o 16_o 14_o 05_o 15_o 6_o 06_o 16_o 34_o 22_o 36_o 22_o 48_o 26_o 15_o 55_o 05_o 52_o 6_o 29_o 16_o 50_o 22_o 34_o 22_o 42_o 27_o 15_o 37_o 04_o 29_o 6_o 51_o 17_o 07_o 22_o 49_o 22_o 36_o 28_o 15_o 18_o 04_o 04_o 7_o 14_o 17_o 23_o 22_o 54_o 22_o 29_o 29_o 14_o 59_o 03_o 41_o 7_o 36_o 17_o 39_o 22_o 59_o 22_o 21_o 30_o 14_o 40_o  _fw-fr 7_o 58_o 17_o 54_o 23_o 04_o 22_o 13_o 31_o 14_o 21_o  _fw-fr 8_o 20_o  _fw-fr 23_o 09_o  _fw-fr for_o the_o year_n 1660_o 1664_o 1668_o 1672._o day_n july_n aug._n septen_n octob._n noven_fw-la decem._n north_n north_n north_n south_n south_n south_n 1_o 22_o 05_o 15_o 07_o 4_o 18_o 07_o 21_o 17_o 44_o 23_o 10_o 2_o 21_o 57_o 14_o 49_o 4_o 55_o 07_o 44_o 18_o 00_o 23_o 14_o 3_o 21_o 48_o 14_o 31_o 3_o 32_o 08_o 06_o 18_o 16_o 23_o 18_o 4_o 21_o 39_o 14_o 12_o 3_o 09_o 08_o 29_o 18_o 32_o 23_o 21_o 5_o 21_o 30_o 13_o 53_o 2_o 45_o 08_o 51_o 18_o 47_o 23_o 24_o 6_o 21_o 20_o 13_o 34_o 2_o 22_o 09_o 13_o 19_o 02_o 23_o 27_o 7_o 21_o 10_o 13_o 15_o 1_o 59_o 09_o 35_o 19_o 17_o 23_o 29_o 8_o 20_o 59_o 12_o 55_o 1_o 35_o 09_o 57_o 19_o 31_o 23_o 30_o 9_o 20_o 48_o 12_o 36_o 1_o 12_o 10_o 19_o 19_o 45_o 23_o 31_o 10_o 20_o 37_o 12_o 16_o 0_o 49_o 10_o 41_o 19_o 59_o 23_o 31_o 11_o 20_o 25_o 11_o 56_o 0_o 25_o 11_o 02_o 20_o 12_o 23_o 32_o 12_o 20_o 13_o 11_o 36_o 0_o 02_o 11_o 23_o 20_o 25_o 23_o 31_o 13_o 20_o 00_o 11_o 15_o 0s22_n 11_o 44_o 20_o 37_o 23_o 30_o 14_o 19_o 48_o 10_o 54_o 0_o 45_o 12_o 05_o 20_o 49_o 23_o 29_o 15_o 19_o 35_o 10_o 34_o 1_o 09_o 12_o 26_o 21_o 01_o 23_o 27_o 16_o 19_o 21_o 10_o 13_o 1_o 33_o 12_o 47_o 21_o 12_o 23_o 24_o 17_o 19_o 08_o 09_o 51_o 1_o 56_o 13_o 07_o 21_o 23_o 23_o 21_o 18_o 18_o 54_o 09_o 30_o 2_o 19_o 13_o 27_o 21_o 33_o 23_o 18_o 19_o 18_o 39_o 09_o 09_o 2_o 43_o 13_o 47_o 21_o 43_o 23_o 15_o 20_o 18_o 25_o 08_o 47_o 3_o 06_o 14_o 07_o 21_o 53_o 23_o 11_o 21_o 18_o 10_o 08_o 25_o 3_o 30_o 14_o 26_o 22_o 02_o 23_o 06_o 22_o 17_o 55_o 08_o 03_o 3_o 53_o 14_o 46_o 22_o 11_o 23_o 01_o 23_o 17_o 40_o 07_o 41_o 4_o 17_o 15_o 05_o 22_o 19_o 22_o 55_o 24_o 17_o 24_o 07_o 19_o 4_o 40_o 15_o 24_o 22_o 27_o 22_o 49_o 25_o 17_o 07_o 06_o 57_o 5_o 03_o 15_o 42_o 22_o 35_o 22_o 42_o 26_o 16_o 51_o 06_o 34_o 5_o 26_o 16_o 00_o 22_o 42_o 22_o 35_o 27_o 16_o 34_o 06_o 12_o 5_o 49_o 16_o 18_o 22_o 48_o 22_o 28_o 28_o 16_o 17_o 05_o 50_o 6_o 12_o 16_o 36_o 22_o 54_o 22_o 20_o 29_o 16_o 00_o 05_o 27_o 6_o 35_o 16_o 54_o 23_o 00_o 22_o 12_o 30_o 15_o 44_o 05_o 04_o 6_o 58_o 17_o 11_o 23_o 05_o 22_o 03_o 31_o 15_o 25_o 04_o 41_o  _fw-fr 17_o 28_o  _fw-fr 21_o 51_o the_o end_n of_o the_o first_o book_n the_o second_o book_n show_v geometrical_o how_o to_o resolve_v all_o such_o astronomical_a proposition_n as_o be_v of_o ordinary_a use_n as_o well_o in_o the_o art_n of_o navigation_n as_o in_o this_o art_n of_o dial_v chap._n i._n the_o description_n of_o the_o scale_n whereby_o this_o work_n may_v be_v perform_v this_o scale_n for_o this_o work_n needs_o to_o be_v divide_v but_o into_o two_o part_n the_o first_o whereof_o may_v be_v a_o scale_n of_o equal_a division_n of_o 16_o in_o a_o inch_n and_o may_v serve_v for_o ordinary_a measure_n the_o second_o part_n of_o the_o scale_n may_v be_v a_o single_a chord_n of_o a_o circle_n or_o a_o chord_n of_o 90_o and_o be_v divide_v into_o 90_o unequal_a division_n represent_v the_o 90_o deg_fw-la of_o the_o quadrant_a and_o be_v number_v with_o 10_o 20_o 30_o 40_o etc._n etc._n unto_o 90._o this_o chord_n be_v in_o use_n to_o measure_v any_o part_n or_o arch_n of_o a_o circle_n not_o surmount_v 90_o degree_n the_o number_n of_o these_o degree_n from_o 1_o unto_o 60_o be_v call_v the_o radius_fw-la of_o the_o scale_n upon_o which_o distance_n all_o circle_n be_v to_o be_v draw_v whereupon_o 60_o of_o these_o degree_n be_v the_o semidiameter_n of_o any_o circle_n that_o be_v draw_v upon_o that_o radius_fw-la the_o manner_n how_o to_o divide_v the_o line_n of_o chord_n although_o the_o make_n or_o divide_v of_o this_o line_n of_o chord_n be_v well_o know_v unto_o all_o those_o that_o do_v make_v mathematical_a instrument_n yet_o i_o will_v not_o have_v they_o that_o shall_v make_v use_n of_o this_o book_n be_v ignorant_a of_o the_o divide_n of_o this_o line_n therefore_o first_o draw_v the_o diameter_n a_o d_o c_o which_o be_v do_v upon_o the_o centre_n d_o describe_v the_o semicircle_n a_o b_o c_o which_o semicircle_n divide_v into_o two_o equal_a part_n or_o quadrant_n by_o the_o point_n b_o then_o divide_v one_o of_o these_o quadrant_n into_o 90_o equal_a part_n or_o degree_n you_o be_v prepare_v as_o here_o you_o see_v in_o the_o quadrant_a a_o b._n now_o this_o be_v do_v set_v one_o foot_n of_o your_o compass_n in_o the_o point_n a_o and_o let_v the_o other_o be_v extend_v unto_o each_o degree_n of_o the_o quadrant_a a_o b_o and_o these_o extent_n transfer_v into_o the_o line_n adc_n as_o here_o you_o see_v be_v do_v this_o line_n so_o divide_v into_o 90_o unequal_a division_n from_o the_o point_n a_o and_o number_v by_o 10_o 20_o 30_o 40_o etc._n etc._n unto_o 90_o be_v call_v a_o line_n of_o chord_n and_o may_v be_v set_v on_o your_o rule_n as_o here_o you_o see_v be_v do_v and_o this_o may_v be_v as_o well_o perform_v within_o the_o quadrant_a d_o at_fw-fr b_o by_o transfer_v the_o degree_n of_o the_o quadrant_a a_o b_o into_o the_o line_n a_o e_o b_o or_o into_o any_o other_o line_n and_o here_o you_o may_v see_v that_o when_o you_o open_v your_o compass_n unto_o 60_o degree_n in_o the_o quadrant_a and_o transfer_v it_o into_o the_o line_n a_o d_o that_o it_o will_v light_v upon_o the_o centre_n d_o whereby_o it_o do_v plain_o appear_v that_o 60_o of_o those_o degree_n be_v equal_a to_o the_o semidiameter_n of_o the_o same_o circle_n and_o therefore_o be_v the_o radius_fw-la upon_o which_o all_o circle_n be_v draw_v as_o be_v show_v before_o in_o this_o chapter_n chap._n ii_o how_o speedy_o with_o rule_n and_o compass_n to_o make_v a_o angle_n contain_v any_o degree_n assign_v or_o to_o get_v the_o degree_n of_o any_o angle_n make_v first_o therefore_o to_o make_v a_o angle_n of_o any_o quantity_n open_v your_o compass_n to_o the_o radius_fw-la of_o your_o scale_n and_o set_v one_o foot_n thereof_o in_o the_o point_n a_o with_o the_o other_o foot_n describe_v the_o arch_a bc_n then_o draw_v the_o line_n a_o b_o then_z opening_z your_o compass_n to_o so_o many_o degree_n upon_o your_o line_n of_o chord_n as_o you_o will_v lay_v down_o which_o here_o we_o will_v suppose_v to_o be_v 40_o degree_n and_o set_v one_o foot_n in_o b_o with_o the_o other_o make_v a_o mark_n in_o the_o arch_a bc_n as_o at_o c_o from_o which_o point_n c_z draw_v the_o line_n ca_n which_o shall_v make_v the_o angle_n b_o a_o c_o contain_v 40_o deg_fw-la as_o be_v require_v and_o if_o you_o desire_v to_o find_v the_o quantity_n of_o a_o angle_n open_v the_o compass_n to_o the_o radius_fw-la of_o your_o scale_n and_o set_v one_o foot_n thereof_o in_o the_o point_n a_o and_o with_o the_o other_o describe_v the_o arch_n b_o c_o then_z taking_z the_o distance_n betwixt_o b_o and_o c_o that_o be_v where_o the_o two_o leg_n and_o the_o arch_a line_n cross_v and_o apply_v it_o unto_o the_o line_n of_o chord_n and_o there_o it_o will_v show_v you_o the_o number_n of_o degree_n contain_v in_o that_o angle_n which_o here_o will_v be_v find_v to_o be_v 40_o degree_n chap._n iii_o to_o find_v the_o altitude_n of_o the_o sun_n by_o the_o shadow_n of_o a_o gnomon_n set_v perpendicular_a to_o the_o horizon_n first_o draw_v the_o line_n a_o b_o then_z opening_z your_o compass_n to_o the_o

other_o great_a circle_n or_o plane_n whatsoever_o chap._n vi_o the_o draw_v of_o a_o dial_n upon_o the_o direct_a polar_a plane_n a_o direct_v polar_a plane_n be_v that_o which_o be_v parallel_n to_o the_o circle_n of_o the_o hour_n of_o six_o therefore_o have_v draw_v the_o horizontal_n line_n a_o b_o and_o cross_v it_o at_o right_a angle_n about_o the_o middle_n of_o the_o line_n at_o c_o with_o the_o perpendicular_a c_o e_z if_o you_o shall_v find_v the_o plane_n inclination_n towards_o the_o north_n to_o be_v equal_a to_o the_o latitude_n of_o the_o place_n and_o the_o horizontal_a line_n direct_o in_o the_o line_n of_o east_n and_o west_n and_o so_o to_o have_v no_o declination_n you_o may_v be_v sure_a this_o plane_n lie_v parallel_n to_o the_o hour_n of_o six_o and_o be_v therefore_o call_v a_o polar_a plane_n the_o horizontal_a line_n be_v draw_v at_o the_o length_n of_o the_o plane_n divide_v it_o into_o seven_o equal_a part_n and_o set_v down_o one_o of_o they_o in_o the_o line_n of_o inclination_n from_o c_o unto_o d_o &_o upon_o the_o centre_n d_o describe_v the_o equinoctial_a circle_n which_o you_o may_v divide_v into_o 24_o equal_a part_n if_o you_o will_v but_o one_o quarter_n thereof_o into_o 6_o will_v serve_v as_o well_o then_o at_o the_o distance_n c_o e_o draw_v the_o line_n f_o g_o parallel_n to_o ab_fw-la then_o have_v divide_v the_o aequator_fw-la either_o into_o 24_o equal_a part_n or_o one_o quarter_n thereof_o into_o 6_o you_o may_v be_v a_o rule_n lay_v the_o centre_n d_o and_o each_o of_o those_o six_o part_n make_v mark_n in_o the_o horizontal_a line_n a_o b_o which_o here_o be_v instead_o of_o the_o contingent-line_n as_o you_o may_v see_v by_o the_o prick_a line_n these_o distance_n from_o the_o meridian_n be_v apply_v upon_o the_o same_o line_n on_o the_o other_o side_n of_o the_o meridian_n and_o also_o on_o both_o side_n the_o meridian_n in_o the_o upper_a line_n the_o line_n draw_v from_o point_n to_o point_n parallel_n to_o the_o meridian_n c_o e_o shall_v be_v the_o hour-line_n the_o line_n c_o e_o shall_v be_v the_o meridian-line_n the_o hour_n of_o 12_o and_o must_v also_o be_v the_o substilar-line_n whereon_o the_o stile_n must_v stand_v which_o may_v be_v a_o plate_n of_o iron_n or_o some_o other_o metal_n be_v so_o broad_a as_o the_o semidiameter_n of_o the_o circle_n be_v as_o be_v show_v in_o the_o figure_n this_o stile_n must_v be_v place_v along_o upon_o the_o line_n of_o 12_o make_v right_a angle_n therewith_o the_o upper_a edge_n whereof_o must_v be_v parallel_n to_o the_o plane_n so_o shall_v it_o cast_v a_o true_a shadow_n upon_o the_o hour-line_n the_o under_o face_n of_o this_o polar_a plane_n and_o also_o of_o the_o former_a equinoctial_a plane_n be_v make_v altogether_o like_a unto_o the_o upper_a face_n here_o describe_v without_o any_o difference_n at_o all_o chap._n vii_o the_o make_n of_o a_o erect_a meridian_n dial_n a_o meridian_n plane_n be_v that_o which_o be_v parallel_n to_o the_o meridian_n circle_n of_o the_o sphere_n therefore_o have_v draw_v the_o horizontal_a line_n a_o b_o and_o find_v it_o to_o decline_v 90_o deg_fw-la from_o the_o south_n the_o plane_n be_v erect_a i_o conclude_v it_o to_o lie_v parallel_n to_o the_o meridian_n circle_n of_o the_o sphere_n and_o be_v therefore_o call_v a_o meridian_n plane_n for_o the_o style_n of_o this_o dial_n it_o may_v be_v either_o a_o plate_n of_o some_o metal_n be_v so_o broad_a as_o the_o semidiameter_n of_o the_o circle_n be_v and_o so_o place_v perpendicular_o along_o over_o the_o line_n of_o the_o hour_n of_o six_o the_o upper_a edge_n thereof_o be_v parallel_n to_o the_o plane_n or_o it_o may_v be_v a_o straight_a pin_n fix_v in_o the_o centre_n of_o the_o circle_n make_v right_a angle_n with_o the_o plane_n be_v just_a so_o long_o as_o the_o semidiameter_n of_o the_o circle_n be_v only_o show_v the_o hour_n with_o the_o very_a top_n or_o end_v thereof_o this_o plane_n have_v two_o face_n one_o to_o the_o east_n the_o other_o to_o the_o west_n the_o make_v whereof_o be_v both_o alike_o only_o in_o name_v the_o hour_n for_o the_o one_o contain_v the_o hour_n for_o the_o forenoon_n the_o other_o for_o the_o afternoon_n as_o you_o may_v perceive_v by_o the_o figure_n chap._n viii_o to_o draw_v a_o dial_n upon_o a_o horizontal_a plane_n a_fw-la horizontal_n plane_n be_v that_o which_o be_v parallel_n to_o the_o horizontal_n circle_n of_o the_o sphere_n which_o be_v find_v by_o the_o first_o chapter_n to_o be_v level_a with_o the_o horizon_n you_o may_v by_o the_o four_o chapter_n draw_v the_o meridian_n line_n a_o b_o serve_v for_o the_o meridian_n the_o hour_n of_o 12_o and_o the_o substilar_a in_o this_o meridian_n make_v choice_n of_o a_o centre_n as_o at_o c_o through_o which_o point_n c_z draw_v the_o line_n d_o e_o cross_v the_o meridian_n at_o right_a angle_n this_o line_n shall_v be_v the_o line_n of_o east_n and_o west_n and_o be_v the_o six_o a_o clock_n line_n both_o for_o morning_n and_o evening_n then_o by_o the_o second_o chapter_n of_o the_o second_o book_n draw_v the_o line_n s_o c_o make_v the_o angle_n s_o c_o a_o equal_a to_o the_o latitude_n of_o the_o place_n which_o here_o we_o will_v suppose_v to_o be_v 52_o deg_fw-la 30_o min._n this_o line_n shall_v represent_v the_o cock_n of_o the_o dial_n and_o the_o axletree_n of_o the_o world_n then_o at_o the_o north_n end_n of_o the_o meridian_n line_n draw_v another_o line_n as_o f_o g_o cross_v the_o meridian_n in_o the_o point_n a_o at_o right_a angle_n this_o line_n be_v call_v the_o touch-line_n or_o line_n of_o contingence_n then_o 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 take_v the_o necrest_n extent_n unto_o the_o line_n s_o c_o or_o the_o stile_n with_o this_o distance_n turn_v your_o compass_n about_o with_o one_o foot_n still_o in_o the_o point_n a_o with_o the_o other_o make_v a_o mark_n in_o the_o meridian_n as_o at_o i_o which_o shall_v be_v the_o centre_n of_o the_o equinoctial_a upon_o which_o describe_v the_o equinoctial_a circle_n a_o d_o b_o e_o with_o this_o same_o distance_n set_v one_o foot_n in_o the_o point_n a_o make_v a_o mark_n at_o f_o on_o the_o one_o side_n of_o the_o meridian_n and_o another_o at_o g_z on_o the_o other_o side_n thereof_o both_o which_o must_v be_v in_o the_o line_n of_o contingence_n by_o which_o two_o point_n and_o the_o centre_n c_o you_o may_v draw_v the_o hour-line_n of_o 3_o and_o 9_o thus_o by_o divide_v but_o half_o a_o quarter_n of_o the_o equinoctial_a circle_n into_o three_o equal_a part_n you_o may_v describe_v your_o whole_a dial._n and_o whereas_o in_o summer_n the_o 4_o and_o 5_o in_o the_o morning_n and_o also_o 7_o and_o 8_o at_o evening_n shall_v be_v necessary_a in_o this_o kind_n of_o dial_n prolong_v or_o draw_v the_o line_n of_o 4_o and_o 5_o at_o evening_n beyond_o the_o centre_n c_o and_o they_o shall_v show_v the_o hour_n of_o 4_o and_o 5_o in_o the_o morning_n and_o likewise_o the_o 7_o and_o 8_o in_o the_o morning_n for_o 7_o and_o 8_o at_o evening_n what_o be_v here_o speak_v concern_v the_o hour_n the_o like_a be_v to_o be_v do_v in_o draw_v the_o half_a hour_n as_o well_o in_o this_o kind_n as_o in_o all_o they_o which_o follow_v the_o stile_n must_v be_v fix_v in_o the_o centre_n c_o hang_v direct_o over_o the_o meridian_n line_n a_o c_o with_o so_o great_a a_o angle_n as_o the_o line_n s_o c_o at_fw-fr make_v which_o be_v the_o true_a pattern_n of_o the_o cock_n this_o and_o all_o other_o kind_n of_o dial_n may_v be_v draw_v upon_o a_o clean_a paper_n and_o then_o with_o the_o help_n of_o your_o compass_n place_v on_o your_o plane_n chap._n ix_o to_o draw_v a_o dial_n upon_o a_o erect_v direct_a vertical_a plane_n common_o call_v a_o south_n or_o north_n dial._n a_o vertical_a plane_n be_v that_o which_o be_v parallel_n to_o the_o prime_n vertical_a circle_n it_o have_v two_o face_n one_o to_o the_o south_n the_o other_o to_o the_o north_n therefore_o have_v draw_v the_o horizontal_a line_n a_o b_o and_o from_o the_o middle_n thereof_o let_v fall_v the_o perpendicular_a c_o d_o which_o if_o you_o find_v by_o the_o second_o chapter_n to_o be_v erect_v and_o the_o horizontal_n line_n a_o b_o to_o lie_n in_o the_o line_n of_o east_n &_o west_n and_o so_o to_o have_v no_o declination_n you_o may_v be_v sure_a this_o plane_n be_v parallel_n to_o the_o prime_n vertical_a circle_n of_o the_o sphere_n and_o therefore_o be_v call_v a_o vertical_a plane_n this_o perpendicular_a c_o d_o shall_v serve_v for_o the_o meridian_n the_o hour_n of_o 12_o and_o the_o substilar_a line_n which_o

horizontal_a plane_n otherwise_o then_o in_o the_o eight_o chapter_n be_v show_v although_o i_o have_v plain_o and_o perfect_o show_v the_o make_n of_o the_o horizontal_a the_o direct_a south_n or_o north_n as_o well_o erect_v as_o incline_v and_o the_o south_n or_o north_n crect_v decline_v dial_n in_o the_o four_o former_a chapter_n yet_o to_o satisfy_v they_o that_o delight_n in_o variety_n i_o have_v here_o declare_v another_o way_n whereby_o you_o may_v make_v they_o most_o artificial_o and_o geometrical_o not_o be_v tie_v to_o the_o use_n of_o the_o canon_n which_o indeed_o of_o all_o other_o be_v most_o exact_a but_o not_o so_o easy_a to_o be_v understand_v nor_o to_o any_o one_o instrument_n which_o may_v be_v absent_a from_o i_o when_o i_o shall_v need_v it_o although_o in_o this_o treatise_n i_o do_v perform_v the_o whole_a by_o a_o plain_a quadrant_n therefore_o by_o the_o first_o chapter_n have_v find_v the_o plane_n to_o be_v horizontal_a by_o the_o four_o chapter_n draw_v the_o meridian_n line_n a_o b_o and_o cross_v it_o at_o right_a angle_n in_o the_o middle_n with_o the_o line_n d_o e_o which_o be_v the_o line_n of_o east_n and_o west_n and_o serve_v for_o the_o hour_n of_o six_o at_o morning_n and_o six_o at_o evening_n then_o upon_o the_o centre_n c_o which_o be_v the_o point_n of_o intersection_n describe_v a_o circle_n for_o your_o dial_n as_o large_a as_o your_o plane_n will_v give_v leave_n which_o let_v be_v the_o circle_n a_o d_o b_o e_o then_o take_v the_o latiude_n of_o the_o place_n which_o be_v here_o 52_o deg_fw-la 30_o min._n and_o set_v it_o from_o a_o to_o n_n in_o the_o quadrant_a a_o d_o and_o draw_v the_o line_n c_o n_o s_o then_o from_o a_o raise_v the_o perpendicular_a a_o s_n to_o cut_v the_o line_n c_o s_n at_o s_n so_o shall_v the_o triangle_n a_o c_o s_o be_v the_o true_a pattern_n for_o your_o cock_n this_o be_v do_v divide_v the_o two_o quarter_n of_o your_o circle_n a_o e_o and_o a_o d_o each_z into_o six_o equal_a part_n so_o shall_v you_o have_v in_o each_o quadrant_n five_o ponit_n by_o which_o you_o may_v draw_v the_o five_o chord_n line_n i_o f_o g_o h_n and_o a_o as_o here_o you_o see_v then_o take_v one_o half_a of_o the_o chord-line_n a_o and_o set_v it_o in_o the_o line_n of_o the_o stile_n from_o c_o to_o o_o from_o which_o point_n o_o take_v the_o near_a extent_n unto_o the_o meridian_n with_o this_o distance_n set_v one_o foot_n in_o the_o point_n a_o with_o the_o other_o make_v a_o mark_n on_o each_o side_n of_o the_o meridian_n in_o the_o same_o chord-line_n a_o through_o which_o point_v you_o shall_v draw_v the_o hour-line_n of_o 1_o and_o 11._o so_o likewise_o you_o may_v take_v one_o half_a of_o the_o chord_n h_n and_o place_n it_o in_o the_o line_n of_o the_o stile_n from_o c_o to_o k_o from_o which_o point_n k_o take_v the_o short_a extent_n unto_o the_o meridian_n with_o this_o distance_n set_v one_o foot_n in_o h_n and_o with_o the_o other_o make_v on_o each_o side_n the_o meridian_n a_o mark_n in_o the_o same_o chord-line_n through_o which_o you_o shall_v draw_v the_o hour-line_n of_o 2_o and_o 10._o and_o thus_o you_o may_v proceed_v with_o the_o rest_n of_o the_o line_n as_o the_o figure_n will_v show_v better_a than_o many_o word_n for_o this_o be_v soon_o wrought_v then_o speak_v and_o if_o you_o will_v have_v the_o hour_n before_o and_o after_o six_o you_o may_v extend_v they_o through_o the_o centre_n as_o be_v show_v in_o the_o eight_o chapter_n chap._n xiii_o to_o draw_v a_o dial_n upon_o a_o direct_a vertical_a plane_n as_o well_o erect_v as_o incline_v otherwise_o then_o in_o the_o nine_o chapter_n be_v show_v the_o work_n of_o this_o be_v almost_o like_a unto_o the_o other_o before_o the_o difference_n be_v only_o in_o the_o elevation_n of_o the_o pole_n above_o the_o plane_n for_o in_o the_o horizontal_a plane_n the_o elevation_n be_v equal_a to_o the_o latitude_n of_o the_o place_n and_o in_o all_o direct_a vertical_n be_v erect_v the_o elevation_n of_o the_o pole_n above_o the_o plane_n be_v equal_a to_o the_o compliment_n of_o the_o latitude_n but_o if_o they_o shall_v incline_v towards_o the_o horizon_n then_o shall_v you_o find_v the_o elevation_n of_o the_o pole_n above_o the_o plane_n by_o the_o 10_o chapter_n the_o elevation_n of_o the_o pole_n above_o the_o plane_n be_v know_v the_o make_n of_o these_o dial_n be_v all_o alike_o therefore_o by_o the_o second_o chapter_n draw_v the_o line_n e_o w_n parallel_n to_o the_o horizon_n and_o from_o the_o middle_n thereof_o let_v fall_v the_o perpendicular_a z_o n_n which_o shall_v be_v the_o meridian_n of_o the_o plane_n and_o also_o the_o meridian_n of_o the_o place_n serve_v for_o the_o line_n of_o 12_o and_o also_o for_o the_o substile_a over_o which_o the_o stile_n must_v hang_v both_o in_o erect_v and_o incline_a plane_n be_v direct_a then_o upon_o the_o centre_n z_o describe_v your_o dial_n circle_n or_o rather_o the_o semicircle_n e_o n_n w_n and_o see_v this_o plane_n be_v erect_v and_o also_o direct_a therefore_o the_o elevation_n of_o the_o pole_n above_o the_o plane_n be_v 37_o d._n 30_o m._n equal_a to_o the_o compliment_n of_o our_o latitude_n which_o take_v from_o your_o scale_n &_o place_v it_o from_o n_n to_o h_n in_o your_o dial_n semicicircle_n and_o draw_v the_o line_n z_o h_o s_o for_o the_o line_n of_o the_o stile_n then_o from_o the_o end_n of_o the_o meridian_n as_o at_o n_n draw_v the_o crooked_a line_n n_o s_o cut_v the_o line_n of_o the_o stile_n in_o the_o point_n s_o so_o shall_v the_o triangle_n s_o z_o n_n be_v the_o true_a pattern_n for_o your_o cock_n this_o be_v do_v divide_v each_o quadrant_a of_o your_o semicircle_n into_o six_o equal_a part_n so_o shall_v you_o have_v five_o point_n by_o which_o you_o may_v draw_v five_o chord-line_n cut_v the_o meridian_n at_o right_a angle_n in_o the_o point_v i_o k_o l_o m_o n._n this_o be_v do_v take_v the_o half_a of_o each_o chord_n and_o place_n it_o from_o the_o centre_n z_o along_o upon_o the_o line_n of_o the_o stile_n as_o here_o you_o see_v the_o half_a of_o the_o chord_n n_n from_o z_o to_o a_o and_o one_o half_a the_o chord_n m_o from_o z_o to_o b_o and_o half_a the_o chord_n l_o from_o z_o to_o c_o and_o one_o half_a the_o chord-line_n i_o and_o k_o set_v from_o z_o unto_o d_o and_z g_z now_o from_o each_o of_o these_o point_n take_v the_o near_a extent_n unto_o the_o meridian_n z_o n_n &_o place_v they_o upon_o their_o proper_a chord-line_n from_o the_o meridian_n on_o both_o side_n thereof_o so_o shall_v you_o have_v two_o point_n on_o each_o chord_n through_o which_o you_o shall_v draw_v the_o hour-line_n from_o the_o centre_n of_o your_o dial_n as_o the_o short_a extent_n from_o the_o point_n a_o unto_o the_o meridian_n set_v in_o the_o chord_n n_n from_o the_o meridian_n both_o way_n shall_v give_v you_o the_o point_n for_o 1_o and_o 11_o so_o shall_v the_o short_a extent_n from_o the_o point_n b_o be_v place_v from_o the_o meridian_n both_o way_n in_o the_o chord_n m_o give_v you_o the_o two_o point_n for_o 10_o and_o 2_o and_o so_o you_o may_v proceed_v with_o the_o rest_n thus_o do_v you_o shall_v have_v in_o each_o chord_n two_o point_n on_o each_o side_n the_o meridian_n one_o through_o which_o and_o from_o the_o centre_n z_o you_o may_v draw_v your_o hour-line_n at_o pleasure_n without_o exceed_v the_o limit_n of_o your_o plane_n and_o see_v this_o be_v the_o south_n face_n of_o this_o plane_n therefore_o the_o stile_n must_v point_v downward_o be_v fix_v in_o the_o centre_n z_o in_o the_o upper_a part_n of_o the_o meridian_n line_n z_o n_n over_o which_o the_o stile_n must_v direct_o hang_v make_v therewith_o a_o angle_n equal_a to_o the_o angle_n n_o z_o s_o but_o if_o it_o have_v be_v the_o north_n face_n then_o must_v the_o centre_n be_v place_v in_o the_o low_a part_n of_o the_o meridian_n and_o the_o stile_n with_o the_o substile_a and_o also_o the_o hour-line_n must_v point_v upward_o chap._n fourteen_o the_o declination_n of_o a_o upright_a plane_n be_v give_v how_o thereby_o to_o find_v the_o elevation_n of_o the_o pole_n above_o the_o same_o with_o the_o angle_n of_o deflexion_n or_o the_o distance_n of_o the_o substile_a from_o the_o meridian_n and_o also_o the_o angle_n of_o inclination_n betwixt_o both_o meridian_n in_o all_o erect_a decline_a plane_n when_o the_o declination_n be_v find_v there_o be_v three_o thing_n more_o to_o be_v consider_v before_o we_o can_v come_v to_o the_o draw_v of_o the_o dial._n i._o the_o elevation_n of_o the_o pole_n above_o the_o plane_n ii_o the_o distance_n of_o the_o substile_a

from_o the_o meridian_n iii_o the_o angle_n contain_v betwixt_o the_o meridian_n of_o the_o plane_n and_o the_o meridian_n of_o the_o place_n which_o here_o we_o call_v the_o inclination_n of_o meridian_n this_o angle_n be_v make_v at_o the_o pole_n and_o serve_v to_o show_v we_o where_o we_o shall_v begin_v to_o divide_v our_o dial-circle_n into_o 24_o equal_a part_n these_o three_o may_v be_v both_o artificial_o easy_o and_o speedy_o perform_v after_o this_o manner_n follow_v first_o describe_v a_o quadrant_n as_o a_o b_o c_o then_o suppose_v your_o latitude_n to_o be_v 52_o deg_fw-la 30_o min._n take_v it_o from_o your_o scale_n and_o set_v it_o from_o b_o to_z e_z in_o the_o arch_n of_o the_o quadrant_n and_o draw_v the_o line_n e_o d_o parallel_n to_o a_o b_o cut_v the_o line_n a_o c_o in_o the_o point_n d_o then_o take_v the_o distance_n d_o e_o and_o set_v one_o foot_n in_o the_o centre_n a_o with_o the_o other_o describe_v the_o arch_n g_o h_o o_o r._n then_o suppose_v your_o declination_n to_o be_v 32_o deg_fw-la this_o set_n from_o b_o to_o f_o in_o the_o arch_n b_o e_o c_o and_o draw_v the_o line_n f_o a_n cut_v the_o arch_n g_o r_o in_o the_o point_n h._n through_o which_o point_n draw_v the_o line_n s_o h_n n_n cut_v the_o arch_n b_o e_o c_o in_o n_n so_o shall_v the_o arch_n c_o n_n be_v the_o elevation_n of_o the_o pole_n above_o the_o plane_n which_o in_o this_o example_n be_v find_v to_o be_v 31_o deg_fw-la 5_o min._n now_o from_o the_o point_n l_o draw_v the_o line_n l_o t_o parallel_n to_o the_o line_n a_o c_o cut_v the_o arch_n g_o r_o in_o the_o point_n o_o through_o which_o point_n o_o draw_v the_o line_n a_o o_o i_o cut_v the_o arch_n b_o c_o in_o the_o point_n i_o so_o shall_v the_o arch_n c_o i_o be_v the_o inclination_n of_o both_o meridian_n and_o be_v find_v by_o this_o example_n to_o be_v 38_o deg_fw-la 13_o min._n so_o that_o by_o this_o example_n the_o meridian_n of_o the_o plane_n will_v fall_v betwixt_o the_o hour_n of_o 2_o and_o 3_o if_o the_o plane_n shall_v decline_v westward_o but_o if_o it_o shall_v decline_v eastward_o then_o shall_v it_o fall_v betwixt_o the_o hour_n of_o 9_o and_o 10_o before_o noon_n chap._n xv._o to_o draw_v a_o dial_n upon_o a_o erect_a or_o vertical_a plane_n decline_v otherwise_o then_o in_o the_o 11_o chapter_n be_v show_v have_v by_o the_o three_o chapter_n find_v the_o declination_n of_o this_o plane_n to_o be_v 32_o degree_n and_o so_o by_o the_o last_o chapter_n find_v the_o elevation_n of_o the_o pole_n above_o the_o plane_n to_o be_v 31_o deg_fw-la 5_o min._n and_o the_o distance_n of_o the_o substile_a from_o the_o meridian_n to_o be_v 22_o degr_n 8_o minute_n and_o likewise_o the_o angle_n of_o inclination_n between_o both_o meridians_fw-la to_o be_v 38_o degreee_n 13_o minute_n we_o may_v proceed_v to_o make_v the_o dial_n after_o this_o manner_n first_o draw_v the_o horizontal_a w_n e_o and_o the_o perpendicular_a line_n z_o n_n cross_v the_o horizontal_a line_n at_o right_a angle_n which_o be_v the_o meridian_n of_o the_o place_n and_o the_o line_n of_o 12._o then_o in_o the_o meridian_n make_v choice_n of_o some_o point_n with_o most_o convenience_n as_o the_o centre_n c_o whereupon_o describe_v your_o dial-circle_n e_o n_o w._n then_o take_v a_o chord_n of_o 22_o degree_n 8_o minute_n from_o your_o scale_n for_o the_o distance_n of_o the_o substile_a from_o the_o meridian_n and_o inscribe_v it_o into_o this_o circle_n from_o the_o meridian_n upon_o these_o condition_n that_o if_o the_o plane_n decline_v west_n then_o must_v the_o substile_a be_v place_v east_n of_o the_o plumb_n line_n but_o if_o the_o declination_n shall_v be_v east_n then_o must_v the_o substile_a be_v place_v west_n from_o the_o meridian_n as_o here_o it_o be_v this_o 22_o degree_n 8_o minute_n be_v set_v in_o the_o dial-circle_n from_o the_o meridian_n at_o n_n unto_o m_n i_o draw_v the_o line_n c_o m_o for_o the_o substile_a then_o through_o the_o centre_n c_o draw_v the_o diameter_n a_o b_o make_v right_a angle_n with_o the_o substile_a c_o m_o above_o this_o diameter_n there_o need_v no_o hour_n line_n to_o be_v draw_v if_o the_o plane_n be_v erect_v then_o take_v 31_o deg_fw-la 5_o min._n and_o set_v they_o from_o m_n to_o d_o and_o draw_v the_o line_n c_o d_o s_o for_o the_o stile_n then_o from_o m_n the_o end_n of_o the_o stile_n draw_v the_o crooked_a line_n m_o s_o cut_v the_o line_n of_o the_o stile_n in_o the_o point_n s_o so_o shall_v the_o triangle_n s_o c_o m_o be_v the_o true_a pattern_n for_o the_o cock_n of_o the_o dial._n this_o be_v do_v take_v 38_o deg_fw-la 13_o min._n and_o set_v they_o always_o on_o that_o side_n the_o substile_a whereon_o the_o line_n of_o 12_o lie_v '_o as_o here_o from_o m_n to_o a_o so_o shall_v the_o point_n h_n be_v the_o point_n where_o you_o shall_v begin_v to_o divide_v your_o dial-circle_n into_o 24_o equal_a part_n but_o those_o point_n shall_v be_v only_o in_o use_n which_o do_v fall_v below_o the_o diameter_n a_o c_o b._n and_o if_o the_o line_n of_o the_o substile_a fall_v not_o direct_o upon_o one_o of_o the_o hour-line_n then_o shall_v you_o have_v six_o point_n on_o each_o side_n thereof_o from_o which_o you_o may_v let_v perpendicular_o fall_v unto_o the_o line_n of_o the_o substile_a as_o here_o you_o see_v do_v now_o take_v each_o perpendicular_a betwixt_o your_o compass_n and_o with_o one_o foot_n in_o the_o centre_n c_o with_o the_o other_o make_v mark_n in_o the_o line_n of_o the_o stile_n from_o which_o take_v the_o near_a extent_n unto_o the_o line_n of_o the_o substile_a and_o lay_v they_o upon_o their_o own_o proper_a perpendicular_o from_o the_o substile_a so_o may_v you_o make_v point_n through_o which_o you_o may_v draw_v hour-line_n and_o by_o thus_o do_v with_o each_o perpendicular_a on_o both_o side_n the_o substile_a you_o may_v describe_v your_o whole_a dial_n as_o here_o you_o see_v which_o may_v serve_v for_o four_o face_n by_o observe_v what_o be_v speak_v in_o the_o 11_o chapter_n when_o you_o have_v draw_v and_o describe_v your_o dial_n upon_o paper_n for_o any_o plane_n whasoever_o you_o may_v cut_v off_o the_o hour-line_n cock_n and_o all_o with_o a_o lesser_a circle_n than_o the_o dial_n circle_n either_o with_o a_o concentrique_fw-la or_o a_o excentrique_fw-la circle_n and_o so_o make_v a_o dial_n less_o than_o the_o circle_n by_o which_o you_o frame_v it_o of_o a_o plane_n fall_v near_o the_o meridian_n when_o as_o the_o declination_n of_o a_o plane_n shall_v cause_v it_o to_o lie_v near_o the_o meridian_n as_o that_o the_o declination_n and_o inclination_n shall_v cause_v it_o to_o lie_v near_o the_o pole_n then_o do_v the_o elevation_n of_o the_o pole_n above_o the_o plane_n grow_v so_o small_a and_o the_o hour-line_n so_o exceed_v near_o together_o that_o except_o the_o plane_n be_v very_o large_a they_o will_v hardly_o serve_v to_o good_a purpose_n as_o here_o in_o this_o figure_n be_v a_o plane_n which_o be_v erect_v and_o decline_v from_o the_o south_n 80_o deg_fw-la towards_o the_o east_n therefore_o first_o draw_v your_o dial_n very_o true_a as_o before_o have_v be_v teach_v upon_o a_o large_a paper_n make_v your_o circle_n as_o big_a as_o you_o can_v then_o extend_v the_o hour-line_n with_o the_o substile_a and_o the_o line_n of_o the_o stile_n a_o great_a way_n beyond_o the_o dial_n circle_n until_o they_o do_v spread_v so_o that_o they_o will_v fill_v the_o plane_n indifferent_a well_o and_o then_o cut_v they_o off_o with_o a_o long_a square_n as_o o_o n_n in_o the_o follow_a figure_n so_o will_v it_o show_v almost_o like_o the_o meridian_n dial_n of_o the_o 7_o chapter_n for_o the_o hour_n will_v be_v almost_o parallel_v the_o one_o to_o the_o other_o and_o the_o stile_n almost_o parallel_n to_o the_o substile_a as_o you_o may_v see_v by_o the_o figure_n chap._n xvi_o the_o inclination_n of_o a_o meridian_n plane_n be_v give_v how_o thereby_o to_o find_v the_o elevation_n of_o the_o pole_n above_o the_o plane_n the_o distance_n of_o the_o substile_a from_o the_o meridian_n and_o the_o angle_n of_o the_o inclination_n of_o the_o meridian_n of_o the_o plane_n to_o the_o meridian_n of_o the_o place_n all_o those_o plane_n wherein_o the_o horizontal_a line_n be_v the_o same_o with_o the_o meridian_n line_n be_v therefore_o call_v meridian_n plane_n if_o they_o may_v make_v right_a angle_n with_o the_o horizon_n they_o be_v call_v erect_v meridian_n plane_n and_o be_v describe_v before_o a_o erect_a dial_n decline_v from_o the_o south_n 80_o deg_fw-la towards_o the_o east_n the_o distance_n of_o the_o substile_a from_o the_o meridian_n 37_o d._n 4_o min._n

cut_v the_o arch_n c_o b_o in_o the_o point_n k_o then_o take_v the_o distance_n h_o l_o and_o set_v it_o in_o the_o line_n f_o z_o from_o zunto_o o_o through_o which_o point_n o_o draw_v the_o line_n aom_n cut_v the_o arch_n b_o c_o in_o the_o point_n m_o from_o which_o point_n m_n draw_v the_o line_n m_o p_o n_o parallel_n to_o a_o b_o cut_v the_o arch_n g_o i_o in_o the_o point_n p_o through_o which_o point_n p_o draw_v the_o line_n a_o p_o qui_fw-fr cut_v the_o arch_n b_o c_o in_o the_o point_n g_o so_o shall_v the_o arch_n b_o k_n be_v 75_o deg_fw-la 58_o min._n the_o inclination_n of_o the_o plane_n to_o the_o meridian_n and_o the_o arch_n b_o q_o will_v be_v 57_o deg_fw-la 36_o min._n for_o the_o meridian_n ascension_n or_o the_o arch_n of_o the_o plane_n betwixt_o the_o horizon_n and_o the_o meridian_n and_o the_o arch_n b_o m_o shall_v be_v 20_o deg_fw-la 54_o min._n for_o the_o elevation_n of_o the_o meridian_n or_o the_o arch_n of_o the_o meridian_n betwixt_o the_o horizon_n and_o the_o plane_n now_o if_o the_o plane_n shall_v incline_v towards_o the_o south_n add_v this_o elevation_n of_o the_o meridian_n to_o your_o latitude_n and_o the_o sum_n of_o both_o shall_v be_v the_o position_n latitude_n or_o the_o arch_n of_o the_o meridian_n betwixt_o the_o pole_n and_o the_o plane_n and_o if_o the_o sum_n shall_v exceed_v 90_o deg_fw-la take_v it_o out_o of_o 180_o deg_fw-la and_o that_o which_o remain_v shall_v be_v the_o position_n latitude_n or_o the_o arch_n of_o the_o meridian_n between_o the_o pole_n and_o the_o plane_n but_o if_o the_o inclination_n shall_v be_v northward_o then_o compare_v the_o elevation_n of_o the_o meridian_n with_o your_o latitude_n and_o take_v the_o lesser_a out_o of_o the_o great_a and_o so_o shall_v the_o difference_n be_v the_o position_n latitude_n as_o here_o in_o this_o example_n suppose_v the_o inclination_n to_o be_v northward_o we_o take_v 20_o deg_fw-la 54_o min._n the_o elevation_n of_o the_o meridian_n out_o of_o 52_o deg_fw-la 30_o min._n the_o latitude_n propose_v and_o there_o will_v remain_v 31_o deg_fw-la 36_o min_fw-mi for_o the_o position_n latitude_n or_o the_o arch_n of_o the_o meridian_n between_o the_o pole_n and_o the_o plane_n this_o be_v do_v set_v 31_o deg_fw-la 36_o min._n the_o position_n latitude_n from_o b_o to_o t_n in_o the_o arch_n b_o c_o and_o draw_v the_o line_n a_o t_o then_o with_o the_o distance_n k_o l_o upon_o the_o centre_n a_o describe_v the_o arch_n y_fw-fr m_o w_n cut_v the_o line_n a_o t_o in_o the_o point_n m_o through_o which_o point_n m_n draw_v the_o line_n r_o s_o parallel_n to_o a_o b_o cut_v the_o arch_n b_o c_o in_o the_o point_n s_o so_o shall_v the_o arch_n b_o s_n be_v 30_o degree_n 33_o minute_n the_o height_n of_o the_o pole_n above_o the_o plane_n then_o lay_v your_o rule_n upon_o the_o point_n s_o and_o the_o centre_n a_o and_o where_o it_o shall_v cut_v the_o line_n k_o l_o the_fw-mi make_v a_o mark_n as_o at_o v._o through_o which_o point_n v_n draw_v the_o line_n d_o v_o n_o w_n parallel_n to_o a_o b_o cut_v the_o arch_n y_o w_n in_o the_o point_n n_n and_o the_o arch_n b_o c_o in_o w_n so_o shall_v the_o arch_n b_o w_n be_v 8_o deg_fw-la 35_o min_fw-mi the_o distance_n of_o the_o substile_a from_o the_o meridian_n last_o through_o the_o point_n n_n draw_v the_o line_n y_o x_o parallel_n to_o ac_fw-la cut_v the_o arch_a bc_n in_o the_o point_n x_o so_o shall_v the_o arch_a bx_n be_v 16_o deg_fw-la 20_o min._n the_o inclination_n of_o the_o meridian_n of_o the_o plane_n to_o the_o meridian_n of_o the_o place_n chap._n xix_o to_o draw_v a_o dial_n upon_o a_o decline_a incline_a plane_n have_v by_o the_o second_o chapter_n find_v the_o inclination_n to_o be_v 25_o deg_fw-la towards_o the_o north_n and_o by_o the_o three_o chapter_n the_o declination_n from_o the_o south_n towards_o the_o east_n to_o be_v 35_o deg_fw-la and_o so_o by_o the_o last_o chapter_n the_o meridians_fw-la ascension_n to_o be_v 57_o deg_fw-la 36_o min._n the_o elevation_n of_o the_o pole_n above_o the_o plane_n 30_o deg_fw-la 33_o min._n the_o distance_n of_o the_o substile_a from_o the_o meridian_n 8_o degree_n 35_o min._n and_o the_o inclination_n of_o both_o meridians_fw-la 17_o deg_fw-la 30_o min._n we_o may_v proceed_v to_o make_v the_o dial_n after_o this_o manner_n first_o draw_v the_o line_n a_o b_o parallel_n to_o the_o horizon_n in_o which_o line_n make_v choice_n of_o a_o centre_n as_o at_o c_o whereon_o describe_v your_o dial_n circle_n a_o d_o b_o e_o a_o then_o take_v 57_o deg_fw-la 36_o min._n the_o meridians_fw-la ascension_n and_o set_v it_o from_o b_o that_o end_n of_o the_o horizontal_n line_n with_o the_o declination_n of_o the_o plane_n as_o from_o b_o to_o n_n and_o draw_v the_o line_n c_o n_n for_o the_o hour_n of_o 12._o then_o set_v 8_o deg_fw-la 35_o min._n the_o distance_n of_o the_o substile_a from_o the_o meridian_n from_o n_n to_o m_n on_o that_o side_n the_o meridian_n which_o be_v contrary_a to_o the_o declination_n of_o the_o plane_n and_o draw_v the_o line_n c_o m_o for_o the_o substile_a and_o set_v 30_o deg_fw-la 33_o min._n from_o m_n to_o d_o and_o draw_v the_o line_n c_o d_o unto_o s_n and_o from_o the_o end_n of_o the_o substile_a draw_v the_o crooked_a line_n m_o s_o cut_v the_o line_n of_o the_o style_n in_o s_n so_o shall_v the_o triangle_n m_o c_o s_o be_v the_o true_a pattern_n of_o this_o dial_n cock._n then_o set_v 17_o deg_fw-la 30_o min._n the_o inclination_n of_o meridians_fw-la from_o m_n unto_o o_o which_o be_v the_o point_n where_o you_o must_v begin_v to_o divide_v your_o dial_n circle_n into_o 24_o equal_a part_n from_o which_o point_n let_v down_o so_o many_o perpendicular_o to_o the_o substile_a as_o there_o shall_v be_v point_n on_o that_o side_n the_o diameter_n f_o e_o next_z the_o substile_a and_o so_o by_o work_v as_o before_o have_v be_v show_v you_o may_v draw_v the_o hour-line_n and_o set_v up_o the_o stile_n as_o in_o the_o former_a plane_n now_o here_o i_o will_v have_v you_o well_o to_o consider_v what_o have_v be_v here_o speak_v concern_v these_o kind_n of_o dial_n and_o also_o what_o follow_v the_o same_o for_o if_o you_o mark_v the_o diversity_n which_o do_v arise_v by_o reason_n of_o the_o elevation_n of_o the_o meridian_n you_o may_v perceive_v thereby_o three_o sundry_a kind_n of_o dial_n to_o arise_v out_o of_o a_o north_n incline_v plane_n decline_v and_o also_o in_o a_o south_n incline_v decline_a plane_n yet_o in_o effect_n they_o be_v but_o one_o if_o you_o consider_v what_o follow_v here_o concern_v they_o in_o all_o which_o the_o stile_n with_o the_o substile_a and_o such_o like_a material_n be_v find_v out_o according_a to_o the_o last_o chapter_n therefore_o have_v draw_v your_o horizontal_a line_n you_o must_v consider_v which_o pole_n be_v elevate_v above_o your_o plane_n and_o how_o to_o place_v the_o meridian_n from_o the_o horizontal_n line_n for_o upon_o the_o upper_a face_n of_o all_o north_n incliner_n who_o meridians_fw-la elevation_n be_v less_o than_o the_o latitude_n of_o the_o place_n on_o the_o under_o face_n of_o all_o north_n incliner_n who_o meridians_fw-la elevation_n be_v great_a than_o the_o latitude_n of_o the_o place_n and_o on_o the_o upper_a face_n of_o all_o south_n incliner_n the_o north_n pole_n be_v elevate_v now_o for_o place_v the_o meridian_n from_o the_o horizontal_a line_n upon_o the_o upper_a face_n of_o all_o south_n incliner_n who_o meridians_fw-la elevation_n be_v great_a than_o the_o latitude_n compliment_n on_o the_o under_o face_n of_o all_o south_n incliner_n who_o meridians_fw-la elevation_n be_v less_o than_o the_o latitude_n compliment_n on_o the_o under_o face_n of_o all_o north_n incliner_n who_o meridians_fw-la elevation_n be_v great_a than_o the_o latitude_n of_o the_o place_n and_o on_o the_o upper_a face_n of_o all_o north_n incliner_n who_o meridian_n elevation_n be_v less_o than_o the_o latitude_n of_o the_o place_n the_o meridian_n must_v be_v place_v above_o the_o horizontal_n line_n as_o here_o in_o this_o example_n and_o therefore_o by_o the_o contrary_a upon_o the_o upper_a face_n of_o all_o south_n incliner_n who_o meridians_fw-la elevation_n be_v less_o than_o the_o latitude_n compliment_n on_o the_o under_o face_n of_o all_o south_n incliner_n who_o meridians_fw-la elevation_n be_v great_a than_o the_o latitude_n compliment_n on_o the_o under_o face_n of_o all_o north_n incliner_n who_o meridians_fw-la elevation_n be_v less_o than_o the_o latitude_n of_o the_o place_n and_o on_o the_o upper_a face_n of_o all_o north_n incliner_n who_o meridians_fw-la elevation_n be_v great_a than_o the_o latitude_n of_o the_o place_n the_o

meridian_n must_v be_v place_v below_o the_o horizontal_n line_n but_o here_o you_o must_v observe_v that_o if_o it_o be_v either_o the_o upper_a or_o under_o face_n of_o a_o south_n incline_v plane_n who_o meridians_fw-la elevation_n be_v great_a than_o the_o latitude_n compliment_n or_o either_o the_o upper_a or_o under_o face_n of_o a_o north_n incline_v plane_n who_o meridians_fw-la elevation_n be_v less_o than_o the_o latitude_n of_o the_o place_n that_o then_o the_o meridian_n must_v be_v place_v from_o that_o end_n of_o the_o horizontal_a line_n with_o the_o declination_n of_o the_o plane_n but_o on_o all_o the_o other_o face_n of_o these_o kind_n of_o plane_n the_o meridian_n must_v be_v place_v from_o that_o end_n of_o the_o horizontal_a line_n which_o be_v contrary_a to_o the_o declination_n of_o the_o plane_n and_o here_o note_v that_o if_o the_o inclination_n shall_v be_v southward_o and_o the_o elevation_n of_o the_o meridian_n equal_a to_o the_o compliment_n of_o your_o latitude_n then_o shall_v the_o substile_a lie_n square_a to_o the_o meridian_n and_o if_o the_o inclination_n shall_v be_v northward_o and_o the_o elevation_n of_o the_o meridian_n equal_a to_o the_o latitude_n of_o the_o place_n then_o shall_v neither_o pole_n be_v elevate_v above_o this_o plane_n and_o therefore_o shall_v be_v a_o polar_a decline_a plane_n wherein_o the_o meridian_n be_v place_v according_a to_o his_o ascension_n from_o the_o horizontal_a line_n shall_v be_v in_o place_n of_o the_o substile_a unto_o which_o if_o you_o draw_v a_o line_n square_n it_o shall_v serve_v for_o the_o equator_fw-la then_o set_v one_o foot_n of_o your_o compass_n in_o the_o intersection_n of_o the_o substile_a with_o the_o equator_fw-la and_o open_v the_o other_o to_o any_o convenient_a distance_n upon_o the_o substile_a and_o describe_v the_o equinoctial_a circle_n as_o in_o the_o six_o chapter_n of_o this_o book_n be_v show_v upon_o the_o centre_n whereof_o make_v a_o angle_n with_o the_o line_n of_o the_o substile_a equal_a to_o the_o inclination_n of_o both_o meridians_fw-la namely_o the_o meridian_n of_o the_o plane_n and_o the_o meridian_n of_o the_o place_n which_o shall_v show_v you_o where_o to_o begin_v to_o divide_v your_o equinoctial_a circle_n into_o 24_o equal_a part_n these_o thing_n be_v know_v you_o may_v proceed_v to_o make_v your_o dial_n and_o set_v up_o the_o cock_n according_a to_o the_o 6_o chapter_n as_o for_o example_n in_o our_o latitude_n of_o 52_o deg_fw-la 30_o min._n a_o plane_n be_v propose_v to_o decline_v from_o the_o south_n towards_o the_o east_n 35_o deg_fw-la as_o before_o but_o incline_v northward_o 57_o deg_fw-la 50_o min._n the_o meridian_n ascension_n by_o the_o 18_o chapter_n will_v be_v find_v to_o be_v 69_o deg_fw-la 33_o min._n and_o his_o elevation_n 52_o deg_fw-la 30_o min._n equal_a to_o the_o latitude_n of_o the_o place_n and_o therefore_o neither_o pole_n be_v elevate_v above_o this_o plane_n and_o so_o no_o distance_n between_o the_o substile_a and_o the_o meridian_n for_o the_o meridian_n and_o the_o stile_n with_o the_o substile_n will_v be_v as_o it_o be_v all_o one_o line_n which_o be_v the_o axletree_n of_o the_o world_n so_o that_o here_o the_o stile_n must_v be_v parallel_n to_o the_o plane_n and_o the_o hour-line_n parallel_v one_o to_o the_o other_o as_o in_o the_o meridian_n and_o direct_v polar_a plane_n therefore_o first_o draw_v the_o horizontal_n line_n a_o b_o wherein_z make_v choice_n of_o a_o centre_n as_o at_o c_o whereon_o describe_v a_o occult_a arch_n of_o a_o circle_n as_o b_o e_z then_o into_o this_o arch_n inscribe_v the_o meridians_fw-la ascension_n 69_o deg_fw-la 33_o min._n from_o b_o to_z e_z and_o draw_v the_o line_n c_o e_z for_o the_o meridian_n of_o the_o plane_n and_o for_o the_o substilar_a and_o if_o you_o draw_v a_o line_n square_n to_o this_o substilar_a it_o shall_v be_v the_o equator_fw-la then_o set_v one_o foot_n of_o your_o compass_n in_o the_o point_n of_o intersection_n d_o and_o with_o the_o other_o open_v to_o a_o convenient_a wideness_n draw_v a_o circle_n for_o the_o equator_fw-la unto_o which_o you_o may_v draw_v two_o touch-line_n square_a to_o the_o substile_a as_o in_o the_o direct_a polar_a plane_n the_o end_n of_o the_o three_o book_n the_o four_o book_n show_v how_o to_o resolve_v all_o such_o astronomical_a proposition_n as_o be_v of_o ordinary_a use_n in_o this_o art_n of_o dial_v by_o help_n of_o a_o quadrant_n fit_v for_o the_o same_o purpose_n chap._n i._n the_o description_n of_o the_o quadrant_n have_v in_o the_o second_o and_o three_o book_n show_v geometrical_o the_o work_n of_o most_o of_o the_o ordinary_a proposition_n astronomical_a with_o the_o delineation_n of_o all_o kind_n of_o plain_a wall_n dial_n howsoever_o or_o in_o what_o latitude_n soever_o situate_v 〈◊〉_d i_o keep_v within_o the_o limit_n of_o our_o plane_n and_o yet_o not_o tie_v to_o the_o use_n of_o any_o instrument_n i_o will_v now_o show_v how_o you_o may_v perform_v the_o former_a work_n exact_o easy_o and_o speedy_o by_o a_o plain_a quadrant_n fit_v for_o that_o purpose_n the_o description_n whereof_o be_v after_o this_o manner_n have_v prepare_v a_o piece_n of_o box_n or_o brass_n in_o manner_n of_o a_o quadrant_n draw_v thereon_o the_o two_o semidiameter_n a_o b_o and_o a_o c_o equal_o distant_a or_o parallel_a to_o the_o edge_n cut_v one_o the_o other_o at_o right_a angle_n in_o the_o centre_n a_o upon_o which_o centre_n a_o with_o the_o semidiameter_n a_o b_o or_o a_o c_o describe_v the_o arch_n b_o c_o this_o arch_n be_v call_v the_o limb_n and_o be_v divide_v into_o 90_o equal_a part_n or_o degree_n and_o subdivide_v into_o as_o many_o part_n as_o quantity_n will_v give_v leave_n be_v number_v from_o the_o left_a hand_n towards_o the_o right_n after_o the_o usual_a manner_n then_o let_v the_o semidiameter_n a_o b_o be_v divide_v into_o 90_o unequal_a part_n call_v right_a sines_n either_o from_o the_o table_n of_o natural_a sin_n by_o help_n of_o a_o decimal_n scale_n equal_a to_o the_o semidiameter_n a_o b_o or_o else_o by_o take_v the_o near_a extent_n from_o each_o degree_n of_o your_o quadrant_n unto_o the_o side_n a_o b_o and_o place_v they_o upon_o the_o side_n a_o b_o each_o after_o other_o from_o the_o centre_n a_o towards_o b_o you_o shall_v exact_o divide_v the_o semidiameter_n a_o b_o into_o 90_o unequal_a division_n call_v right_a sin_n this_o be_v do_v draw_v the_o line_n d_o e_z from_o the_o sine_fw-la of_o 45_o degree_n count_v in_o the_o line_n of_o sin_n unto_o 45_o degree_n count_v in_o the_o quadrant_n then_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 make_v the_o square_a a_o d_o e_o f_o the_o side_n d_o e_z whereof_z for_o distinction_n may_v be_v call_v a_o tangent_fw-la line_n and_o the_o side_n f_o f_o a_o co-tangent_a line_n then_o draw_v the_o diagonal_a line_n a_o e_o which_o you_o may_v call_v the_o line_n of_o latitude_n then_o upon_o the_o centre_n a_o with_o the_o distance_n a_o d_o or_o a_o f_o describe_v the_o arch_n d_o f_o which_o you_o may_v divide_v into_o six_o equal_a part_n by_o lay_v your_o rule_n upon_o each_o 15_o degree_n in_o the_o quadrant_n and_o the_o centre_n a_o as_o at_o g_o h_o i_o k_o l_o f_o from_o which_o point_n draw_v slope_v line_n to_o each_o 15_o degree_n in_o the_o quadrant_n number_v backward_o as_o f_o p_o l_o o_o k_o e_o i_o n_z h_z m_z g_o b_o these_o line_n so_o draw_v be_v to_o be_v account_v as_o hour_n then_o divide_v each_o space_n into_o two_o equal_a part_n draw_v other_o slope_n line_n stand_v for_o half_a hour_n which_o may_v be_v distinguish_v from_o the_o other_o as_o they_o be_v in_o the_o figure_n now_o because_o in_o the_o latter_a part_n of_o this_o book_n there_o be_v often_o require_v to_o use_v a_o line_n of_o chord_n to_o several_a radiuss_n therefore_o upon_o the_o edge_n of_o the_o quadrant_n a_o c_o you_o may_v have_v a_o line_n of_o chord_n divide_v as_o in_o the_o figure_n and_o so_o the_o quadrant_n be_v at_o hand_n will_v supply_v the_o use_n of_o the_o scale_n mention_v in_o the_o precede_a book_n and_o also_o a_o chord_n of_o any_o circle_n who_o radius_fw-la be_v less_o than_o the_o line_n a_o c_o may_v be_v take_v off_o and_o in_o that_o case_n supply_v the_o use_n of_o a_o sector_n to_o this_o quadrant_n as_o to_o all_o other_o of_o this_o kind_n in_o their_o use_n be_v add_v sight_n with_o a_o thread_n bead_n and_o plummet_n according_a to_o the_o usual_a manner_n chap._n ii_o of_o the_o use_n of_o the_o line_n of_o sines_n any_o radius_fw-la not_o exceed_v the_o line_n of_o sines_n be_v know_v to_o find_v the_o right_n sine_fw-la of_o any_o arch_n or_o angle_v thereunto_o belong_v

quadrant_a upon_o the_o upper_a side_n of_o your_o ruler_n so_o that_o the_o centre_n may_v hang_v a_o little_a over_o the_o end_n of_o your_o ruler_n and_o hold_v up_o a_o thread_n and_o plummet_n so_o that_o it_o may_v play_v upon_o the_o centre_n if_o it_o shall_v fall_v direct_o upon_o his_o level_a line_n a_o c_o make_v no_o angle_n therewith_o it_o be_v a_o horizontal_n plane_n as_o here_o you_o may_v see_v by_o this_o figure_n chap._n ii_o of_o the_o try_v of_o plane_n whether_o they_o be_v erect_v or_o incline_v and_o to_o find_v the_o quantity_n of_o their_o inclination_n if_o the_o plane_n seem_v to_o be_v erect_v you_o may_v try_v it_o by_o hold_v the_o quadrant_a so_o that_o the_o thread_n may_v fall_v on_o the_o plumb_n line_n a_o c_o for_o than_o if_o that_o side_n of_o the_o quadrant_a shall_v lie_v close_o to_o the_o plane_n it_o be_v erect_v and_o a_o line_n draw_v by_o that_o side_n of_o the_o quadrant_a shall_v be_v a_o vertical_a line_n and_o the_o line_n which_o cross_v this_o vertical_a line_n at_o right_a angle_n will_v be_v the_o horizontal_n line_n as_o here_o you_o may_v see_v in_o this_o figure_n the_o plane_n d_o e_o f_o g_o being_n erect_v and_o the_o line_n d_o e_o being_n vertical_a the_o line_n f_o g_o must_v be_v horizontal_a but_o if_o the_o plane_n shall_v incline_v the_o quantity_n of_o inclination_n may_v be_v find_v out_o after_o this_o manner_n first_o you_o must_v draw_v thereon_o the_o horizontal_n line_n which_o you_o may_v do_v upon_o the_o under_o face_n by_o apply_v the_o side_n a_o b_o of_o your_o quadrant_a thereunto_o so_o as_o the_o thread_n and_o plummet_n may_v fall_v upon_o the_o plumb_n line_n a_o c_o the_o side_n a_o b_o lying_z close_n with_o the_o plane_n by_o which_o if_o you_o draw_v a_o line_n it_o shall_v be_v parallel_n to_o the_o horizon_n or_o you_o may_v draw_v a_o horizontal_a line_n upon_o the_o uppe_n face_n by_o lay_v a_o ruler_n thereupon_o and_o apply_v the_o side_n a_o b_o of_o your_o quadrant_a to_o the_o under_o side_n thereof_o still_o move_v your_o rule_n until_o the_o thread_n and_o plummet_n do_v fall_v direct_o upon_o the_o plumb_n line_n a_o c_o the_o rule_n lie_v thus_o close_o to_o the_o plane_n you_o may_v thereby_o draw_v a_o line_n parallel_n to_o the_o horizon_n have_v draw_v this_o horizontal_n line_n m_o n_n cross_v it_o at_o right_a angle_n with_o the_o perpendicular_a k_o d_o unto_o which_o if_o it_o be_v the_o under_o face_n apply_v the_o side_n a_o b_o of_o your_o quadrant_a so_o shall_v the_o thread_n upon_o the_o limb_n give_v you_o the_o angle_n of_o inclination_n require_v but_o if_o it_o be_v the_o upper_a face_n of_o the_o plane_n then_o lay_v a_o ruler_n to_o the_o perpendicular_a k_o d_o unto_o the_o under_o side_n whereof_o apply_v the_o side_n a_o b_o of_o your_o quadrant_a as_o be_v here_o show_v in_o this_o figure_n so_o shall_v the_o degree_n of_o the_o quadrant_a give_v you_o c_o a_o h_o the_o angle_n of_o inclination_n require_v but_o if_o it_o be_v so_o that_o you_o can_v apply_v the_o side_n of_o your_o quadrant_a to_o the_o under_o side_n of_o your_o ruler_n than_o set_v it_o upon_o the_o upper_a side_n thereof_o so_o that_o the_o centre_n thereof_o may_v hang_v a_o little_a over_o the_o end_n of_o the_o ruler_n and_o hold_v up_o a_o thread_n and_o plummet_n so_o that_o it_o may_v fall_v upon_o the_o centre_n a_o and_o it_o shall_v show_v upon_o the_o limb_n the_o inclination_n of_o the_o plane_n which_o be_v the_o angle_n c_o a_o h_o equal_a to_o the_o former_a angle_n here_o you_o must_v be_v heedful_a that_o both_o edge_n of_o your_o ruler_n be_v straight_o and_o one_o parallel_n to_o the_o other_o chap._n iii_o to_o find_v the_o declination_n of_o a_o plane_n to_o find_v out_o this_o declination_n you_o must_v make_v two_o observation_n by_o the_o sun_n the_o first_o be_v of_o the_o angle_n make_v between_o the_o horizontal_n line_n of_o the_o plane_n and_o the_o azimuth_n wherein_o the_o sun_n be_v at_o the_o time_n of_o observation_n the_o second_o be_v of_o the_o sun_n altitude_n both_o these_o observation_n shall_v be_v make_v at_o one_o instant_a first_o for_o the_o horizontal_n distance_n have_v draw_v upon_o your_o plane_n a_o line_n parallel_n to_o the_o horizon_n apply_v the_o side_n of_o your_o quadrant_a thereunto_o hold_v it_o parallel_n to_o the_o horizon_n then_o hold_v up_o a_o thread_n and_o plummet_n at_o full_a liberty_n so_o as_o the_o shadow_n thereof_o may_v pass_v through_o the_o centre_n of_o the_o quadrant_a observe_v the_o angle_n make_v upon_o the_o quadrant_a by_o the_o shadow_n of_o the_o thread_n and_o that_o side_n with_o the_o horizontal_n line_n for_o that_o be_v the_o distance_n here_o require_v then_o at_o the_o same_o instant_n as_o near_o as_o may_v be_v take_v the_o sun_n altitude_n that_o so_o you_o may_v find_v the_o sun_n azimuth_n from_o the_o east_n or_o west_n point_n by_o the_o 21_o chap._n of_o the_o four_o book_n have_v thus_o get_v the_o horizontal_a distance_n with_o the_o azimuth_n of_o the_o sun_n for_o the_o same_o time_n describe_v a_o circle_n as_o a_o b_o c_o d_o represent_v the_o horizontal_a circle_n and_o draw_v the_o diameter_n a_o c_o which_o shall_v represent_v the_o horizontal_a line_n f_o g_o of_o of_o the_o last_o chapter_n now_o suppose_v the_o horizontal_a distance_n to_o be_v 38_o deg_fw-la 30_o min._n the_o angle_n o_o a_o b_o of_o the_o last_o chapter_n place_v it_o from_o c_o south_n ward_n to_o e_z that_o be_v from_o the_o same_o end_n of_o the_o horizontal_a line_n with_o which_o the_o angle_n be_v make_v upon_o the_o plane_n and_o draw_v the_o line_n e_o z_o then_o suppose_v the_o altitude_n of_o the_o sun_n at_o the_o same_o time_n to_o be_v 30_o deg_fw-la 45_o min._n with_o 11_o deg_fw-la 30_o min._n north_n declination_n and_o so_o by_o the_o 21_o chapter_n of_o the_o four_o book_n the_o azimuth_n will_v be_v find_v to_o be_v 23_o deg_fw-la 17_o min._n from_o the_o east_n southward_o be_v the_o observation_n be_v make_v in_o the_o before_o noon_n this_o 23_o deg_fw-la 17_o min._n i_o place_v from_o e_z the_o place_z of_o the_o sun_n at_o the_o time_n of_o observation_n unto_o r_n which_o be_v the_o true_a point_n of_o the_o east_n and_o draw_v the_o line_n h_o r_n represent_v the_o vertical_a circle_n so_o shall_v the_o angle_v make_v between_o the_o horizontal_a line_n of_o the_o plane_n and_o the_o line_n of_o east_n and_o west_n be_v the_o declination_n of_o the_o plane_n which_o in_o this_o example_n be_v find_v to_o be_v 15_o deg_fw-la 13_o m._n the_o angle_n c_o z_o r._n or_o you_o may_v observe_v the_o angle_n make_v between_o the_o shadow_n of_o the_o thread_n and_o that_o side_n of_o the_o quadrant_a which_o lie_v perpendicular_a unto_o the_o horizontal_a line_n of_o the_o plane_n which_o in_o this_o example_n be_v 51_o deg_fw-la 30_o min._n the_o compliment_n of_o the_o former_a angle_n and_o it_o be_v the_o angle_n o_o a_o c_o in_o the_o former_a chap_n upon_o the_o quadrant_a now_o have_v draw_v your_o horizontal_n circle_n as_o before_o and_o the_o diameter_n a_o c_o for_o the_o horizontal_a line_n of_o the_o plane_n you_o may_v cross_v it_o at_o right_a angle_n with_o the_o diameter_n b_o d_o for_o the_o axis_fw-la of_o the_o plane_n horizontal_a line_n from_o which_o as_o from_o d_o you_o may_v set_v your_o horizontal_a distance_n on_o the_o same_o side_n thereof_o as_o before_o you_o find_v it_o by_o your_o observation_n as_o here_o from_o d_o to_z e_z and_o draw_v the_o line_n e_o z_o for_o the_o line_n of_o the_o shadow_n and_o have_v find_v the_o azimuth_n of_o the_o sun_n 23_o deg_fw-la 17_o min._n from_o the_o east_n southward_o you_o may_v set_v it_o from_o e_z the_o place_z of_o the_o sun_n northward_o to_o r_n and_o draw_v the_o line_n rzh_n for_o the_o line_n of_o east_n and_o west_n as_o before_o or_o if_o you_o take_v the_o sun_n azimuth_n from_o the_o south_n which_o in_o this_o example_n will_v be_v 66_o deg_fw-la 43_o min._n the_o compliment_n of_o the_o former_a 23_o deg_fw-la 17_o min._n you_o may_v set_v it_o from_o e_z the_o place_z of_o the_o sun_n unto_o s_n southward_o and_o draw_v the_o line_n s_o z_o n_n for_o the_o meridian_n so_o shall_v the_o arch_n s_o d_o or_o r_o c_o be_v 15_o deg_fw-la 13_o min._n for_o the_o declination_n as_o before_o chap._n iv_o to_o draw_v the_o hour-line_n upon_o the_o horizontal_n the_o full_a north_n or_o south_n plane_n whether_o erect_v or_o incline_v see_v the_o make_n of_o these_o dial_n be_v all_o after_o one_o manner_n we_o will_v here_o proceed_v to_o make_v a_o horizontal_n dial_n by_o help_n of_o the_o line_n

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 deg_fw-la 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 deg_fw-la 10,000000_o be_v to_o the_o sine_fw-la of_o 30_o d._n which_o be_v half_a the_o difference_n 9,698970_o so_o the_o tangent_fw-la compliment_n of_o the_o latitude_n 37_o d._n 30._o m._n 9,884980_o to_o the_o tangent_fw-la of_o the_o declination_n of_o the_o sun_n 20_o d._n 59_o m._n 9,583950_o and_o such_o declination_n shall_v the_o sun_n have_v when_o the_o day_n be_v either_o 16_o hour_n or_o 8_o hour_n long_o in_o the_o latitude_n of_o 52_o deg_fw-la 30_o min._n now_o if_o the_o day_n be_v above_o 12_o hour_n long_o the_o sun_n have_v north_n declination_n but_o if_o less_o than_o 12_o hour_n long_o he_o have_v south_n declination_n for_o those_o who_o be_v ignorant_a of_o these_o kind_n of_o proportion_n they_o have_v best_a to_o read_v mr._n norwoods_n dctorine_n of_o triangle_n but_o that_o nothing_o may_v be_v want_v and_o not_o much_o to_o trouble_v the_o learuer_n i_o have_v here_o add_v a_o table_n show_v what_o declination_n the_o sun_n have_v at_o 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 d._n 30_o m._n which_o table_n be_v make_v by_o the_o precede_a rule_n length_n of_o the_o day_n the_o sun_n declination_n  _fw-fr 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 by_o which_o table_n you_o may_v see_v 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 one_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 forementioned_a plane_n you_o must_v insert_v these_o angle_n and_o declination_n unto_o your_o trigon_n between_o the_o tropic_n and_o proceed_v in_o all_o respect_n as_o before_o i_o will_v therefore_o give_v you_o but_o one_o example_n which_o shall_v be_v in_o a_o full_a south_n plane_n upon_o which_o and_o the_o horizontal_n these_o arch_n do_v appear_v most_o uniform_a now_o let_v it_o be_v require_v to_o draw_v the_o parallel_n of_o the_o sun_n course_n when_o the_o day_n be_v 8_o 9_o 10_o 11_o 12_o 13_o 14_o 15_o and_o 16_o hour_n long_o upon_o a_o full_a south_n plane_n in_o the_o latitude_n of_o 52_o deg_fw-la 30_o min._n have_v draw_v your_o dial_n with_o hour_n half_n and_o quarter_n and_o also_o make_v choice_n of_o some_o convenient_a point_n in_o the_o stile_n to_o give_v the_o shadow_n and_o draw_v the_o horizontal_a line_n c_o d_o then_o make_v the_o triangle_n s_o a_o r_o in_o this_o trigon_n equal_a to_o the_o triangle_n s_o a_o r_o in_o the_o follow_a south_n dial_n as_o s_n a_o equal_a to_o the_o axis_n of_o the_o stile_n a_o r_n equal_a to_o the_o substilar_a and_o r_o s_o equal_a to_o the_o perpendicular_a stile_n then_o draw_v the_o perpendicular_a s_o g_z for_o the_o equinoctial_a and_o describe_v the_o arch_n o_o g_o p_o making_z g_z o_o and_o g_o p_o each_o of_o they_o 23_o deg_fw-la 31_o min._n for_o the_o two_o tropic_n which_o you_o must_v transfer_v into_o your_o plane_n as_o before_o now_o for_o the_o draw_v of_o the_o parallel_n of_o the_o length_n of_o the_o day_n you_o must_v have_v recourse_n to_o the_o little_a table_n before_o go_v and_o therein_o see_v what_o declination_n the_o sun_n have_v at_o such_o a_o day_n as_o you_o will_v put_v into_o your_o plane_n as_o when_o the_o day_n be_v either_o 8_o or_o 16_o hour_n long_o the_o declination_n be_v 20_o deg_fw-la 59_o min._n therefore_o place_n in_o your_o trigon_n 20_o deg_fw-la 59_o m._n from_o g_z unto_o a_o both_o way_n and_o draw_v the_o line_n s_o a_fw-fr and_n s_o a_o mark_v they_o at_o the_o end_n with_o 8_o and_o 16_o the_o length_n of_o the_o day_n for_o which_o they_o serve_v likewise_o when_o the_o day_n be_v either_o 9_o or_o 15_o hour_n long_o than_o the_o sun_n declination_n be_v 16_o deg_fw-la 22_o min._n therefore_o set_v 16_o deg_fw-la 22_o min._n from_o g_z unto_z b_o both_o way_n and_o draw_v s_o b_o and_z 8_o b._n also_o when_o the_o day_n be_v either_o 10_o or_o 14_o hour_n long_o than_o the_o declination_n be_v 11_o deg_fw-la 14_o min_fw-mi which_z set_v from_o g_z to_z c_o both_o way_n and_o draw_v s_o c_o and_o s_o c._n last_o when_o the_o day_n be_v 11_o or_o 13_o hour_n long_o the_o declination_n be_v 5_o deg_fw-la 43_o min._n which_o set_v from_o g_z unto_z d_o both_o way_n and_o draw_v s_o d_o and_o s_o d_o note_v they_o with_o number_n answer_v to_o the_o length_n of_o the_o day_n as_o you_o see_v in_o the_o trigon_n when_o the_o day_n be_v just_a 12_o hour_n long_v it_o be_v equinoctial_a and_o have_v no_o declination_n and_o be_v signify_v in_o the_o trigon_n by_o the_o line_n s_o g._n for_o the_o manner_n how_o to_o transfer_v these_o parallel_n of_o the_o length_n of_o the_o day_n into_o the_o plane_n it_o be_v to_o be_v perform_v in_o all_o respect_v as_o in_o the_o former_a chapter_n for_o the_o insert_v of_o the_o sign_n not_o at_o all_o differ_v therefrom_o and_o therefore_o i_o shall_v forbear_v to_o give_v you_o any_o far_a instruction_n for_o the_o performance_n thereof_o but_o give_v you_o the_o figure_n of_o a_o south_n plane_n with_o these_o parallel_n draw_v thereon_o which_o will_v instruct_v more_o than_o a_o whole_a chapter_n of_o information_n and_o thus_o much_o for_o the_o draw_v of_o the_o parallel_n of_o the_o sign_n and_o diurnal_a arch_n in_o all_o kind_n of_o plane_n i_o will_v now_o proceed_v to_o show_v you_o how_o some_o other_o astronomical_a conclusion_n which_o be_v very_o please_v and_o delightful_a may_v be_v inscribe_v upon_o all_o sort_n of_o dial_n chap._n iii_o show_v how_o the_o italian_a and_o babylonish_n hour_n may_v be_v draw_v upon_o all_o kind_n of_o plane_n the_o italian_n account_v their_o hour_n from_o the_o sun_n set_v and_o the_o babylonian_n from_o his_o rise_n so_o that_o these_o kind_n of_o hour-line_n be_v draw_v upon_o any_o plane_n you_o know_v by_o inspection_n only_o how_o many_o hour_n be_v pass_v since_o the_o last_o set_n or_o rise_v of_o the_o sun_n the_o inscription_n of_o these_o hour-line_n into_o any_o of_o the_o former_a plane_n be_v very_o easy_a the_o work_n of_o the_o last_o chapter_n be_v well_o understand_v because_o that_o upon_o a_o full_a south_n or_o a_o horizontal_n plane_n these_o hour-line_n show_v themselves_o most_o uniform_a i_o have_v therefore_o for_o example_n sake_n make_v choice_n of_o a_o full_a south_n dial_n upon_o which_o it_o shall_v be_v show_v how_o to_o draw_v both_o the_o italian_a and_o babylonish_n hour_n your_o dial_n be_v draw_v and_o the_o two_o tropic_n and_o the_o equinoctial_a thereon_o inscribe_v and_o also_o the_o horizontal_n line_n you_o must_v draw_v in_o your_o dial_n two_o obscure_a parallel_n of_o the_o length_n of_o the_o day_n one_o when_o the_o day_n be_v 8_o hour_n and_o the_o other_o when_o the_o day_n be_v 16_o hour_n long_o express_v in_o the_o follow_a dial_n by_o the_o two_o prick_v arch_n near_o the_o two_o tropic_n the_o uppermost_a of_o which_o be_v the_o parallel_n of_o the_o sun_n course_n when_o the_o day_n be_v 8_o hour_n long_o and_o the_o

two_o parallel_n just_o upon_o the_o hour_n half_n and_o quarter_n of_o the_o common_a hour-line_n and_o so_o be_v the_o easy_a draw_v now_o the_o point_n through_o which_o every_o one_o of_o the_o jewish_a hour_n must_v pass_v be_v exact_o show_v by_o this_o little_a table_n wherein_o you_o may_v see_v that_o the_o first_o jewish_n hour_n must_v be_v draw_v through_o 5_o hour_n 45_o mi._n or_o 5_o hour_n three_o quarter_n in_o the_o parallel_n of_o 15_o through_z 7_o hour_n in_o the_o equinoctial_a and_o through_o 8_o hour_n and_o a_o quarter_n in_o the_o parallel_n of_o 9_o hour_n in_o like_a manner_n the_o second_o jewish_a hour_n must_v be_v draw_v in_o your_o plane_n through_o 7_o of_o the_o clock_n in_o the_o parallel_n of_o 15_o through_o 8_o a_o clock_n in_o the_o equinoctial_a and_o through_o 9_o of_o the_o clock_n in_o the_o parallel_n of_o 9_o hour_n and_o so_o of_o all_o the_o rest_n according_a as_o you_o see_v in_o thsi_fw-fr table_n and_o as_o you_o may_v perceive_v they_o draw_v in_o the_o south_n plane_n the_o number_n belong_v to_o these_o hour_n be_v set_v at_o both_o end_n of_o each_o hour-line_n chap._n v._o show_v how_o to_o draw_v the_o azimuth_n or_o vertical_a circle_n in_o all_o kind_n of_o plane_n the_o azimuth_n be_v great_a circle_n of_o the_o sphere_n meet_v together_o in_o the_o zenith_n of_o the_o place_n and_o be_v various_o inscribe_v on_o all_o plane_n according_a to_o their_o situation_n in_o the_o horizontal_n plane_n they_o meet_v in_o a_o centre_n with_o equal_a angle_n in_o all_o upright_a plane_n whether_o direct_a or_o decline_a they_o be_v parallel_v to_o the_o meridian_n or_o line_n of_o 12._o and_o in_o all_o recline_a plane_n they_o meet_v together_o in_o a_o point_n which_o be_v the_o zenith_n of_o the_o place_n these_o azimuth_n be_v great_a circle_n in_o the_o sphere_n be_v therefore_o straight_a line_n in_o all_o plane_n and_o may_v be_v draw_v as_o follow_v §._o 1_o in_o the_o horizontal_n plane_n in_o the_o horizontal_n plane_n these_o azimuth_n be_v most_o easy_o insert_v for_o your_o dial_n be_v draw_v with_o the_o tropic_n thereon_o you_o have_v no_o more_o to_o do_v but_o upon_o the_o foot_n of_o the_o perpendicular_a stile_n to_o describe_v a_o circle_n which_o you_o may_v divide_v into_o 2_o equal_a part_n begin_v at_o the_o meridian_n answer_v to_o the_o 3_o point_n of_o the_o mariner_n compass_n or_o else_o you_o may_v divide_v the_o same_o circle_n into_o 90_o equal_a part_n according_a to_o the_o astronomical_a division_n and_o through_o each_o of_o those_o point_n draw_v straight_a line_n from_o the_o foot_n of_o the_o stile_n and_o set_v number_n or_o letter_n to_o they_o either_o by_o 10_o 20_o 30_o 40_o &c_n &c_n if_o you_o divide_v it_o into_o 90_o or_o else_o by_o south_n s_n by_o w_n s_o s_o w_n s_o w_n by_o s_n &c_n &c_n if_o you_o divide_v the_o circle_n according_a the_o mariner_n compass_n this_o be_v so_o plain_a that_o it_o need_v no_o example_n §_o 2._o in_o the_o east_n or_o west_n erect_v plane_n your_o dial_n be_v finish_v you_o may_v draw_v upon_o a_o piece_n of_o pasteboard_n the_o line_n m_o e_o n_o represent_v the_o horizontal_n line_n men_n in_o your_o dial_n then_o on_o the_o point_n e_o raise_v the_o perpendicular_a e_o qui_fw-fr equal_a to_o the_o line_n e_o g_z in_o your_o dial_n and_o on_o q_o as_o a_o centre_n describe_v the_o semicircle_n k_o e_o l_o and_o divide_v one_o half_a thereof_o namely_o the_o quadrant_a into_o eight_o equal_a part_n represent_v one_o quarter_n of_o the_o mariner_n compass_n and_o from_o the_o centre_n q_o draw_v line_n through_o each_o of_o those_o division_n extend_v they_o till_o they_o cut_v the_o line_n m_o e_o n_o in_o the_o point_n ☉_o ☉_o ☉_o ☉_o ☉_o ☉_o then_o with_o your_o compass_n take_v the_o distance_n from_o e_o to_o every_o one_o of_o these_o point_n ☉_o ☉_o etc._n etc._n and_o prick_v they_o down_o in_o the_o horizontal_n line_n of_o your_o plane_n from_o e_o to_o ☉_o ☉_o ☉_o ☉_o ☉_o ☉_o from_o which_o point_n draw_v line_n perpendicular_a to_o the_o horizontal_a line_n m_o e_o n_n which_o shall_v be_v the_o azimuth_n or_o point_n of_o the_o compass_n between_o the_o east_n and_o the_o south_n divide_v likewise_o the_o other_o quadrant_a of_o the_o circle_n eke_o into_o eight_o equal_a part_n and_o draw_v line_n from_o the_o centre_n q_o through_o three_o of_o they_o till_o they_o cut_v the_o horizontal_a line_n as_o you_o see_v in_o the_o figure_n and_o there_o also_o draw_v line_n perpendicular_a to_o the_o horizon_n and_o these_o line_n shall_v be_v the_o azimuth_n between_o the_o east_n and_o the_o north_n viz._n so_o many_o of_o they_o as_o your_o plane_n be_v capable_a to_o receive_v which_o the_o follow_a figure_n do_v most_o plain_o show_v ¶_o here_o note_n that_o as_o the_o east_n dial_n show_v all_o the_o morning_n hour_n from_o sun_n rise_v to_o the_o meridian_n and_o the_o west_n dial_n show_v all_o the_o afternoon_n hour_n from_o the_o meridian_n to_o his_o set_n so_o do_v the_o east_n dial_n show_v all_o the_o azimuth_n from_o the_o sun_n rise_v till_o noon_n and_o the_o west_n dial_n all_o the_o azimuth_n from_o noon_n till_o his_o set_n §_o 3._o in_o the_o full_a north_n and_o south_n erect_v plane_n the_o draw_v of_o the_o azimuth_n upon_o the_o full_a north_n or_o south_n erect_v plane_n be_v very_o little_a different_a from_o the_o draw_n of_o the_o same_o circle_n upon_o the_o east_n or_o west_n plane_n but_o for_o example_n let_v it_o be_v require_v to_o draw_v the_o azimuth_n upon_o the_o full_a south_n dial_n the_o tropic_n and_o the_o equinoctial_a be_v draw_v together_o with_o the_o horizontal_n line_n you_o must_v upon_o a_o piece_n of_o pasteboard_n draw_v the_o line_n a_o l_o b_o represent_v the_o horizontal_n line_n a_o l_o b_o in_o the_o south_n dial_n next_o follow_v then_o on_o the_o point_n l_o raise_v the_o perpendicular_a l_o s_n make_v l_o s_o equal_a to_o l_o s_o the_o perpendicular_a stile_n of_o the_o dial_n and_o on_o s_n as_o a_o centre_n describe_v the_o semicircle_n e_o l_o f_o and_o divide_v each_o quadrant_a thereof_o namely_o e_z l_o and_o l_o f_o into_o 8_o equal_a part_n each_o quadrant_a represent_v one_o quarter_n of_o the_o mariner_n compass_n and_o through_o each_o of_o those_o division_n draw_v line_n from_o the_o centre_n s_o till_o they_o cut_v the_o line_n a_o l_o b_o in_o the_o point_n m_o n_o o_o p_o and_o q_o then_o with_o your_o compass_n take_v the_o distance_n l_o q_o and_o set_v that_o distance_n upon_o the_o horizontal_n line_n of_o your_o plane_n from_o l_o unto_o q_o both_o way_n likewise_o take_v the_o distance_n l_o p_o and_o set_v that_o distance_n in_o your_o plane_n upon_o the_o horizontal_a line_n thereof_o from_o l_o unto_o p_o both_o way_n also_o take_v the_o distance_n l_o o_fw-fr l_o n_z and_o l_o m_o and_o set_v they_o upon_o the_o horizontal_a line_n in_o your_o dial_n from_o l_o to_o o_o and_z n_z and_z m_z on_o each_o side_n of_o the_o meridian_n last_o if_o from_o the_o point_n m_o n_z o_o p_o and_o q_o you_o draw_v line_n parallel_v to_o the_o meridian_n or_o line_n of_o 12_o they_o shall_v be_v the_o true_a azimuth_n upon_o your_o plane_n and_o these_o azimuth_n may_v be_v put_v on_o either_o according_a to_o the_o astronomical_a account_n by_o 10_o 20_o 30_o 40_o etc._n etc._n or_o else_o by_o the_o point_n of_o the_o compass_n as_o in_o this_o figure_n according_a as_o you_o shall_v divide_v the_o semicircle_n e_o l_o f_o and_o thus_o much_o concern_v erect_v direct_v plane_n §_o 4._o in_o erect_v decline_a plane_n in_o upright_a decline_a plane_n the_o azimuth_n be_v easy_o in_o scribe_v little_o differ_v from_o the_o former_a draw_v therefore_o your_o dial_n which_o we_o will_v suppose_v to_o be_v the_o south_n decline_v plane_n before_o use_v in_o the_o three_o section_n of_o the_o first_o chapter_n of_o this_o appendix_n which_o decline_v from_o the_o south_n eastward_o 32_o deg_fw-la last_o with_o your_o compass_n take_v the_o distance_n o_o a_o o_o b_o o_o c_o o_o d_o etc._n etc._n out_o of_o your_o pasteboard_n and_o prick_v the_o same_o distance_n down_o in_o your_o plane_n from_o o_o to_o a_o b_o c_o d_o e_o f_o g_o h_o i_o k_o l_o and_o m_o and_o from_o those_o point_n draw_v line_n parallel_v to_o the_o meridian_n which_o line_n shall_v be_v the_o azimuth_n require_v which_o you_o must_v number_v according_a to_o the_o situation_n of_o the_o plane_n viz._n the_o western_a azimuth_n on_o the_o east_n side_n of_o the_o meridian_n and_o the_o eastern_a azimuth_n on_o the_o west_n side_n of_o your_o dial_n as_o you_o see_v they_o here_o number_v