Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	let_v	line_n	perpendicular_a	1,964	5	14.8700	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