Linguistic DNA - Concept Modelling Demonstrator

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

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A93913	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 compasse 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 astronomie and navigation, both geometrically and instrumentally. / By Thomas Stirrup, philomath. Whereunto is added an appendix, shewing now the parallels of declination; the Jewish, Babylonish, and Italian houres; the azimuths, almicanters, &c. may be easily inscribed on any diall whatsoever, by rule and compasse onely. Also how to draw a diall on the seeling of a room, by W.L.	Stirrup, Thomas.; W. L.	1652 (1652)	Wing S5688; Thomason E667_1; ESTC R203655	83,318	192

surface_n of_o the_o diameter_n as_o the_o semicircle_n c_o b_o d_o which_o be_v half_a of_o the_o circle_n c_o b_o d_o e_o and_o be_v contain_v above_o the_o diameter_n c_o a_o d._n definition_n 11._o a_o quadrant_n be_v the_o four_o part_n of_o a_o circle_n and_o be_v contain_v betwixt_o the_o semidiameter_n of_o the_o circle_n &_o a_o line_n draw_v perpendicular_a unto_o the_o diameter_n of_o the_o same_o circle_n from_o the_o centre_n thereof_o divide_v the_o semicircle_n into_o two_o equal_a part_n of_o the_o which_o part_n the_o one_o be_v the_o quadrant_n or_o four_o part_n of_o the_o same_o circle_n as_o for_o example_n the_o diameter_n of_o the_o circle_n b_o d_o e_o c_o be_v the_o line_n c_o a_o d_o divide_v the_o circle_n into_o two_o equal_a part_n then_o from_o the_o centre_n a_o raise_v the_o perpendicular_a a_o b_o divide_v the_o semicircle_n likewise_o into_o two_o equal_a part_n so_o be_v a_o b_o d_o or_o a_o b_o c_o the_o quadrant_n of_o the_o circle_n c_o b_o d_o 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line_n c_o e_o which_o be_v the_o perpendicular_a which_o be_v desire_v to_o be_v let_v fall_n from_o the_o give_v point_n c_o unto_o the_o middle_n of_o the_o give_v line_n d_o e_o f._n chap._n vi_o to_o raise_v a_o perpendicular_a upon_o the_o end_n of_o a_o line_n give_v suppose_v the_o line_n whereupon_o you_o will_v have_v a_o perpendicular_a to_o be_v raise_v be_v the_o line_n b_o c_o &_o from_o the_o point_n b_o a_o perpendicular_a be_v to_o be_v raise_v first_o open_v your_o compass_n unto_o any_o convenient_a distance_n which_o here_o we_o suppose_v to_o be_v the_o distance_n b_o e_o and_o set_v one_o foot_n of_o your_o compass_n in_o b_o with_o the_o other_o draw_v the_o arch_n ed_z than_o this_o distance_n be_v keep_v set_v one_o foot_n of_o your_o compass_n in_o the_o point_n e_o and_o with_o the_o other_o make_v a_o mark_n in_o the_o former_a arch_n e_o d_o as_o at_z d_o still_o keep_v the_o same_o distance_n set_v one_o foot_n in_o the_o point_n d_o and_o with_o the_o 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the_o zodiaque_fw-la into_o four_o equal_a part_n make_v thereby_o the_o four_o season_n of_o the_o year_n the_o one_o colour_n pass_v through_o the_o two_o tropical_a point_n of_o cancer_n and_o capricorn_n show_v the_o beginning_n of_o summer_n &_o also_o of_o winter_n at_o which_o time_n the_o day_n and_o night_n be_v long_a and_o short_a the_o other_o colour_n pass_v through_o the_o equinoctial_a point_n aries_n and_o libra_n show_v the_o beginning_n of_o the_o spring_n time_n and_o autumn_n at_o which_o two_o time_n the_o day_n and_o night_n be_v of_o equal_a length_n throughout_o the_o whole_a world_n definition_n 9_o the_o ecliptic_a

come_v unto_o the_o zenith_n these_o be_v circle_n that_o do_v measure_v the_o elevation_n of_o the_o pole_n or_o height_n of_o the_o sun_n moon_n or_o star_n above_o the_o horizon_n which_o be_v call_v the_o almicanter_n of_o the_o sun_n moon_n or_o star_n the_o arch_n of_o the_o sun_n or_o star_n almicanter_n be_v a_o portion_n of_o a_o azimuth_n contain_v betwixt_o that_o almicanter_n which_o pass_v through_o the_o centre_n of_o the_o star_n and_o the_o horizon_n thus_o have_v set_v forth_o unto_o the_o view_n of_o the_o unlearned_a for_o who_o sake_n this_o treatise_n be_v intend_v the_o meaning_n of_o some_o of_o the_o useful_a term_n of_o geometry_n which_o be_v most_o attendant_a unto_o this_o art_n of_o dial_v and_o also_o a_o description_n of_o some_o peculiar_a thing_n concern_v the_o point_n line_n and_o circle_n imagine_v in_o the_o sphere_n be_v very_o fit_a to_o be_v understand_v of_o all_o such_o as_o intend_v to_o practice_v either_o in_o the_o art_n of_o navigation_n 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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_n 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 or_o the_o quadrant_n a_o b_o and_o these_o extent_n transfer_v into_o the_o line_n a_o d_o c_o 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 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thereof_o in_o the_o point_n a_o with_o the_o other_o foot_n describe_v the_o arch_n b_o c_o 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_n b_o c_o as_o at_z c_z from_o which_o point_n c_z draw_v the_o line_n c_o a_o which_o shall_v make_v the_o angle_n b_o a_o c_o contain_v 40_o degree_n 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 &_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 gnomen_fw-la set_v perpendicular_a to_o the_o horizon_n ffirst_o draw_v the_o line_n a_o b_o then_z opening_z your_o compass_n to_o the_o radius_fw-la of_o your_o scale_n set_v one_o foot_n in_o the_o end_n a_o and_o with_o the_o other_o describe_v the_o arch_n b_o c_o d_o then_z opening_z your_o compass_n unto_o the_o whole_a 90_o degree_n 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 d_o a_o which_o shall_v be_v perpendicular_a unto_o the_o line_n a_o b_o and_o make_v the_o quadrant_n a_o b_o c_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 the_o line_n a_o e_o which_o 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at_o right_a angle_n with_o any_o perpendicular_a wall_n in_o such_o manner_n that_o it_o may_v lie_v parallel_n unto_o the_o horizon_n first_o draw_v your_o quadrant_n a_o b_o c_o d_o as_o be_v teach_v in_o the_o last_o chapter_n &_o place_v the_o length_n of_o your_o gnomon_n from_o a_o to_o e_o which_o here_o we_o will_v suppose_v to_o be_v 12_o foot_n as_o before_o in_o the_o last_o chapter_n then_o draw_v the_o line_n e_o f_o parallel_n to_o a_o b_o then_o suppose_v the_o length_n of_o the_o shadow_n to_o be_v 9_o foot_n as_o before_o this_o i_o place_n from_o e_z to_z g_z

by_o which_o point_n g_z draw_v the_o line_n a_o g_o c_o as_o be_v former_o do_v in_o the_o last_o chapter_n by_o which_o we_o have_v proceed_v thus_o far_o but_o as_o in_o the_o last_o chapter_n the_o arch_n b_o c_o be_v the_o height_n of_o the_o sun_n desire_v so_o by_o this_o chapter_n the_o arch_n c_o d_o shall_v be_v the_o height_n of_o the_o sun_n which_o be_v apply_v unto_o your_o scale_n will_v give_v you_o 36_o deg_fw-la 52_o min._n for_o the_o height_n of_o the_o sun_n desire_v chap._n v._o the_o almicanter_n or_o height_n of_o the_o sun_n be_v give_v to_o find_v the_o length_n of_o the_o right_a shadow_n by_o right_a shadow_n be_v mean_v the_o shadow_n of_o any_o staff_n post_n steeple_n or_o any_o gnomon_n whatsoever_o that_o stand_v at_o right_a angle_n with_o the_o horizon_n the_o one_o end_n thereof_o respect_v the_o zenith_n of_o the_o place_n and_o the_o other_o the_o nadir_n first_o therefore_o according_a unto_o the_o three_o chapter_n describe_v the_o quadrant_n a_o b_o d_o then_o suppose_v the_o height_n of_o your_o gnomon_n or_o substance_n yield_v shadow_n to_o be_v 12_o foot_n as_o in_o the_o former_a chapter_n this_o do_v i_o set_v down_o from_o a_o to_o e_o and_o from_o the_o point_n e_o draw_v the_o line_n e_o f_o parallel_n to_o a_o b_o then_o set_v the_o almicanter_n which_o here_o we_o will_v suppose_v to_o be_v 53_o de_fw-la and_o 8_o min._n as_o it_o be_v find_v by_o the_o three_o chapter_n from_o b_o unto_o c_o from_o which_o point_n c_z draw_v the_o line_n c_o a_o cut_v the_o line_n e_o f_o in_o the_o point_n g_o so_o shall_v e_z g_z be_v the_o length_n of_o the_o right_a shadow_n desire_v which_o be_v take_v betwixt_o your_o compass_n and_o apply_v unto_o your_o scale_n will_v give_v you_o 9_o of_o those_o division_n whereof_o a_o e_z be_v 12_o which_o here_o do_v signify_v 9_o foot_n chap._n vi_o the_o almicanter_n or_o height_n of_o the_o sun_n be_v give_v to_o find_v the_o length_n of_o the_o contrary_a shadow_n by_o the_o 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and_o place_n it_o from_o d_o to_z c_z from_o which_o point_n c_z draw_v the_o line_n c_o a_o cut_v the_o line_n e_o f_o in_o the_o point_n g_o so_o shall_v g_z e_z be_v the_o length_n of_o the_o contrary_a shadow_n which_o here_o will_v be_v find_v to_o be_v 9_o foot_n the_o thing_n desire_v chap._n vii_o have_v the_o distance_n of_o the_o sun_n from_o the_o next_o equinoctial_a point_n to_o find_v his_o declination_n first_o draw_v the_o line_n a_o b_o then_o upon_o the_o end_n a_o raise_v the_o perpendicular_a a_o d_o then_o open_v your_o compass_n to_o the_o radius_fw-la of_o the_o scale_n place_n one_o foot_n in_o the_o centre_n a_o and_o with_o the_o other_o draw_v the_o quadrant_n b_o c_o d_o then_o suppose_v the_o sun_n to_o be_v either_o in_o the_o 29_o degree_n of_o taurus_n or_o in_o the_o first_o degree_n of_o leo_n both_o which_o point_n be_v 59_o degree_n distant_a from_o the_o next_o equinoctial_a point_n aries_n or_o if_o the_o sun_n shall_v be_v in_o the_o 29_o 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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 20_o 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_n 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_n g_o h_n i_o then_o set_v the_o declination_n of_o the_o sun_n which_o in_o this_o example_n be_v 20_o degree_n from_o d_o unto_o c_o from_o which_o point_n c_z take_v the_o short_a extent_n unto_o the_o line_n a_o d_o this_o distance_n be_v keep_v place_n one_o foot_n in_o the_o arch_a line_n g_o h_n i_o after_o such_o a_o manner_n that_o the_o other_o foot_n be_v turn_v about_o may_v but_o only_o touch_v the_o line_n a_o d_o so_o shall_v the_o fix_a foot_n stay_v upon_o the_o point_n h_n through_o which_o point_n h_n draw_v the_o line_n a_o h_n e_o cut_v the_o arch_n d_o f_o in_o the_o point_n e_o so_o shall_v the_o arch_n d_o e_o be_v the_o distance_n of_o the_o sun_n from_o the_o head_n of_o aries_n which_o here_o will_v be_v find_v to_o be_v 59_o degree_n so_o that_o the_o sun_n do_v hereby_o appear_v to_o be_v in_o 29_o degree_n of_o taurus_n at_o such_o time_n as_o he_o do_v possess_v that_o quarter_n of_o the_o ecliptic_a betwixt_o the_o head_n of_o aries_n and_o cancer_n chap._n ix_o have_v the_o latitude_n of_o the_o place_n and_o the_o distance_n of_o the_o sun_n from_o the_o next_o equinoctial_a point_n to_o find_v his_o amplitude_n first_o make_v the_o quadrant_n a_o b_o c_o d_o then_o take_v from_o your_o scale_n 37_o deg_fw-la 30_o min._n which_o here_o we_o will_v suppose_v to_o be_v the_o compliment_n of_o the_o latitude_n and_o place_n it_o from_o b_o unto_o e_z then_o take_v the_o near_a distance_n betwixt_o the_o point_n e_o and_o the_o line_n a_o b_o with_o one_o foot_n set_v in_o a_o with_o the_o other_o draw_v the_o arch_n f_o g_o h_n then_o place_v the_o sun_n great_a declination_n from_o b_o unto_o ay_o from_o which_o point_n i_o take_v the_o near_a extent_n unto_o the_o line_n a_o b_o which_o distance_n be_v keep_v place_n one_o foot_n of_o your_o compass_n in_o the_o arch_a line_n f_o g_o h_n so_o that_o the_o move_a foot_n may_v but_o only_o touch_v the_o line_n a_o b_o at_o the_o short_a extent_n so_o shall_v the_o fix_a foot_n rest_n in_o the_o arch_a line_n f_o g_o h_n at_o g_z through_o which_o point_n g_z draw_v the_o line_n a_o g_o c_o then_o suppose_v the_o sun_n to_o be_v in_o the_o 29_o degree_n of_o

the_o distance_n c_o e_o and_o set_v in_o your_o trigon_n from_o o_o unto_o e_fw-la and_o draw_v the_o line_n o_o e_o 4_o represent_v the_o hour_n of_o 4_o and_o 8._o and_o thus_o must_v you_o do_v with_o the_o rest_n of_o the_o hour_n in_o your_o plane_n if_o occasion_n require_v these_o line_n o_o a_o o_fw-fr b_o o_o c_o o_o d_o and_z o_o e_o in_o your_o trigon_n be_v extend_v do_v cut_v the_o tropic_a of_o cancer_n p_o a_o in_o the_o point_v 12_o 1_o 2_o and_z 3_o therefore_o out_o of_o your_o trigon_n take_v the_o distance_n o_o 12_o o_o 1_o o_o 2_o o_o 3_o o_o 4_o and_o set_v they_o upon_o their_o correspondent_a hour_n line_n of_o your_o plane_n from_o the_o centre_n c_o unto_o g_o h_o i_o k_o and_o l_o so_fw-mi shall_v the_o point_n g_o h_o i_o k_o and_o l_o be_v the_o point_n upon_o the_o houre-line_n through_o which_o the_o tropic_a of_o cancer_n must_v pass_v and_o be_v therefore_o note_v with_o the_o character_n of_o cancer_n â™‹_o at_o both_o end_n Â¶_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 horizontall_a 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 horizontall_a 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 houre-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 houre-line_n and_o through_o those_o point_n so_o find_v draw_v the_o line_n â™‘_o â™‘_o represent_v the_o tropic_a of_o capricorn_n Â¶_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 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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 fix_v chap._n ii_o show_v how_o to_o inscribe_v the_o parallel_n of_o the_o length_n of_o the_o day_n on_o any_o plane_n the_o parallel_n of_o the_o length_n of_o the_o day_n and_o those_o of_o the_o sign_n be_v inscribe_v upon_o all_o kind_n of_o plane_n by_o one_o and_o the_o same_o rule_n they_o be_v in_o the_o sphere_n the_o same_o circle_n so_o that_o as_o when_o you_o put_v on_o the_o parallel_n of_o the_o sun_n entrance_n into_o the_o 12_o sign_n you_o seek_v what_o declination_n he_o have_v and_o according_o proceed_v as_o before_o so_o now_o for_o the_o parallel_n of_o the_o length_n of_o the_o day_n you_o must_v seek_v what_o declination_n the_o sun_n have_v at_o such_o a_o length_n of_o the_o day_n as_o you_o will_v put_v into_o your_o plane_n which_o that_o you_o may_v do_v i_o have_v here_o add_v the_o rule_n follow_v Â¶_o consider_v how_o much_o long_o or_o short_a your_o day_n propose_v be_v then_o 12_o hour_n and_o take_v the_o difference_n than_o the_o proportion_n will_v be_v as_o the_o sine_fw-la of_o 90_o degree_n be_v to_o the_o sine_fw-la of_o half_a the_o difference_n so_o be_v the_o tangent_fw-la compliment_n of_o the_o latitude_n of_o the_o place_n to_o the_o tangent_fw-la of_o the_o declination_n that_o the_o sun_n shall_v have_v when_o the_o day_n be_v at_o such_o a_o length_n as_o you_o require_v as_o for_o example_n let_v it_o be_v require_v to_o know_v what_o declination_n the_o sun_n shall_v have_v when_o the_o day_n be_v 16_o hour_n long_o in_o the_o latitude_n of_o 52_o deg_fw-la 30_o min._n the_o difference_n betwixt_o 16_o hour_n and_o 12_o hour_n be_v 4_o hour_n or_o 60_o deg_fw-la the_o half_a of_o which_o be_v 30_o deg_fw-la therefore_o say_v as_o the_o sine_fw-la of_o 90_o deg_fw-la 10,000000_o be_v to_o the_o sine_fw-la of_o 30_o deg_fw-la 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 deg_fw-la 30_o min._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 deg_fw-la 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 prportion_n they_o have_v best_a to_o read_v mr._n norwoods_n doctrine_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 learner_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 deg_fw-la 30_o min._n which_o table_n be_v make_v by_o the_o precede_a rule_n by_o which_o table_n you_o may_v see_v length_n of_o the_o day_n the_o sun_n declination_n d_o m_o 8_o 20_o 59_o 9_o 16_o 22_o 10_o 11_o 14_o 11_o 5_o 43_o 12_o 0_o 0_o 13_o 5_o 43_o 14_o 11_o 14_o 15_o 16_o 22_o 16_o 20_o 59_o that_o when_o the_o day_n be_v 12_o hour_n long_o the_o sun_n have_v then_o no_o declination_n but_o be_v in_o the_o equinoctial_a but_o when_o the_o day_n be_v either_o 11_o or_o 13_o hour_n long_o the_o declination_n be_v then_o 5_o deg_fw-la 43_o min._n and_o when_o the_o day_n be_v either_o 9_o or_o 15_o hour_n long_o the_o sun_n have_v 16_o deg_fw-la 22_o min._n of_o declination_n and_o so_o for_o the_o rest_n as_o in_o the_o table_n for_o the_o place_n of_o these_o parallel_n of_o the_o length_n of_o the_o day_n upon_o any_o of_o the_o forementioned_a plane_n you_o must_v insert_v these_o angle_n of_o declination_n into_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 horizontall_a 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

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_n line_n the_o line_n c_o e_o shall_v be_v the_o meridian_n line_n the_o hour_n of_o 12_o and_o must_v also_o be_v the_o substilar_a 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 style_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_n 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 horizontall_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 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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 near_a extent_n unto_o the_o line_n s_o c_o or_o the_o style_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 markâ—â—_n 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_n line_n of_o 3_o and_o 9_o this_o same_o distance_n of_o your_o compass_n be_v keep_v with_o one_o foot_n still_o in_o the_o centre_n a_o with_o the_o other_o make_v the_o mark_n t_o and_o v_n in_o the_o equinoctial_a circle_n each_o of_o which_o distance_n be_v a_o arch_n of_o 60_o degree_n or_o four_o hour_n of_o time_n the_o half_a of_o which_o arch_n be_v 30_o degree_n or_o two_o hour_n from_o the_o meridian_n this_o divide_a in_o the_o half_n will_v be_v 15_o deg_fw-la or_o one_o hour_n from_o the_o meridian_n then_o lay_v your_o rule_n upon_o the_o centre_n i_o of_o the_o equinoctial_a and_o upon_o these_o two_o last_o division_n in_o the_o circle_n thereof_o where_o the_o rule_n shall_v touch_v the_o line_n of_o contingence_n there_o mark_v it_o as_o at_o h_n and_o o_o by_o which_o point_n and_o the_o centre_n c_o you_o may_v draw_v the_o hour-line_n of_o 10_o and_o 11_o the_o like_a may_v you_o do_v on_o the_o other_o side_n of_o the_o meridian_n so_o have_v you_o six_o of_o your_o hour-line_n draw_v and_o now_o because_o the_o contingent_a will_v outrun_v our_o plane_n we_o may_v from_o the_o intersection_n of_o the_o hour_n of_o 9_o and_o 3_o with_o the_o touch_n line_n draw_v the_o line_n f_o d_o and_o g_o e_o parallel_n to_o the_o meridian_n a_o b_o until_o they_o cut_v the_o line_n of_o east_n and_o west_n in_o the_o point_n d_o and_o e_o then_o draw_v the_o line_n a_o d_o and_o a_o e_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 h_n and_o with_o the_o other_o take_v the_o near_a extent_n unto_o the_o line_n a_o e_o this_o distance_n be_v keep_v fix_v one_o foot_n in_o the_o line_n g_o e_o so_o as_o the_o other_o may_v but_o touch_v the_o line_n a_o e_o so_o shall_v the_o fix_a foot_n rest_n in_o the_o point_n n_n by_o which_o and_o the_o centre_n c_o you_o may_v draw_v the_o 7_o a_o clock_n hour-line_n in_o like_a manner_n may_v you_o place_v one_o foot_n in_o the_o point_n o_o and_o with_o the_o other_o take_v the_o short_a extent_n unto_o the_o line_n a_o e_o with_o this_o distance_n fix_v one_o foot_n in_o the_o line_n g_o e_o so_o as_o the_o other_o may_v but_o only_o touch_v the_o line_n a_o e_o so_o shall_v the_o fix_a foot_n rest_n in_o the_o point_n r_o by_o which_o and_o the_o centre_n c_o you_o may_v draw_v the_o 8_o a_o clock_n hour-line_n the_o like_a may_v be_v do_v on_o the_o other_o side_n of_o the_o meridian_n or_o you_o may_v by_o these_o distance_n thus_o find_v prick_n out_o the_o like_a on_o the_o other_o side_n of_o the_o meridian_n 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 style_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 caap._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

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 deg_fw-la 8_o min._n and_o likewise_o the_o angle_n of_o inclination_n between_o both_o meridian_n to_o be_v 38_o deg_fw-la 13_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 horizontall_a w_n e_o and_o the_o perpendicular_a line_n z_o n_n cross_v the_o horizontall_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_n circle_n e_o n_o w._n then_o take_v a_o chord_n of_o 22_o deg_fw-la 8_o min._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 deg_fw-la 8_o min._n be_v set_v in_o the_o dial_n 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 houre-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 style_n then_o from_o m_n the_o end_n of_o the_o style_n 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 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 as_o here_o from_o m_n to_o h_n 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_n 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_n 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 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 whatsoever_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 or_o if_o you_o extend_v the_o hour-line_n beyond_o the_o dial_n circle_n you_o may_v cut_v they_o off_o either_o with_o a_o great_a concentrique_fw-la circle_n and_o so_o make_v a_o big_a dial_n or_o else_o you_o may_v cut_v they_o off_o with_o a_o square_n as_o here_o you_o see_v in_o the_o follow_a figure_n or_o any_o other_o form_n what_o you_o shall_v think_v most_o convenient_a 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 &_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 houre-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_a as_o o_o n_n in_o the_o follow_a figure_n so_o will_v it_o show_v almost_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 deg_fw-la 4_o min._n 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 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 horizontall_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 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 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 first_o describe_v a_o quadrant_n as_o a_o b_o c_o then_o set_v 52_o deg_fw-la 30_o min._n your_o latitude_n from_o c_o to_o e_z in_o the_o arch_n of_o your_o quadrant_n c_o b_o and_o draw_v the_o line_n e_o r_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 r_o and_o with_o the_o distance_n e_o r_o with_o one_o foot_n in_o the_o centre_n a_o with_o the_o other_o draw_v the_o arch_n g_o h_o o_o d_o then_o let_v your_o inclination_n be_v 30_o deg_fw-la which_o set_v in_o the_o arch_n of_o the_o quadrant_n from_o b_o to_o f_o and_o draw_v the_o line_n a_o f_o cut_v the_o arch_n g_o o_fw-fr d_o in_o the_o point_n h_n through_o which_o point_n h_n draw_v the_o line_n s_o h_n n_n cut_v the_o arch_n of_o the_o quadrant_n in_o the_o point_n 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 43_o deg_fw-la 23_o min._n this_o be_v do_v 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 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_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 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._n from_o the_o meridian_n for_o the_o place_n of_o the_o substile_a among_o the_o houre-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 deg_fw-la 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 deg_fw-la 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 horizontall_a line_n a_o b_o serve_v for_o the_o meridian_n and_o the_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 deg_fw-la 5_o min._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 horizontall_a 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 horizontall_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 deg_fw-la 23_o min._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 then_o set_v 43_o deg_fw-la 28_o min._n from_o h_n unto_o m_n for_o the_o difference_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 now_o here_o at_o m_o must_v you_o begin_v to_o divide_v your_o 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 e_o f_o next_o the_o substile_a 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 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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 f_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 i_o 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 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 z_o unto_o o_o through_o which_o point_n o_o draw_v the_o line_n a_o o_fw-fr m_o 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 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._n 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 a_o c_o cut_v the_o arch_n b_o c_o in_o the_o point_n x_o so_o shall_v the_o arch_n b_o x_o 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 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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 meridian_n from_z m_o 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 houre-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 and_o upon_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 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 and_o on_o the_o under_o face_n of_o all_o south_n incliner_n the_o south_n pole_n be_v elevate_v now_o for_o place_v the_o meridian_n from_o the_o horizontall_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 horizontall_a 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 horizontall_a 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 horizontall_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 horizontall_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 meridirn_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 horizontall_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 sixth_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 twenty_o four_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 six_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 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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 caap._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 if_o the_o radius_fw-la of_o the_o circle_n give_v be_v equal_a to_o the_o line_n of_o sines_n there_o need_v no_o far_a work_n but_o to_o take_v the_o other_o sin_n also_o out_o of_o the_o line_n of_o sines_n but_o if_o it_o be_v lesser_a then_o take_v it_o betwixt_o your_o compass_n and_o set_v one_o foot_n in_o the_o sine_fw-la of_o 90_o degree_n and_o with_o the_o other_o lie_v the_o thread_n to_o the_o near_a distance_n which_o you_o may_v do_v by_o turn_v the_o compass_n about_o till_o the_o move_a point_n thereof_o do_v only_o touch_v the_o thread_n and_o no_o more_o the_o threrd_v lie_v still_o in_o this_o position_n take_v the_o near_a extent_n thereunto_o from_o any_o sine_fw-la you_o think_v good_a and_o it_o shall_v be_v the_o like_a sine_fw-la agreeable_a to_o the_o radius_fw-la give_v as_o for_o example_n let_v the_o circle_n b_o c_o d_o e_o in_o the_o follow_a chapter_n represent_v the_o meridian_n circle_n let_v b_o d_o be_v the_o horizon_n and_o c_o e_o the_o vertical_a circle_n and_o let_v f_o g_z be_v the_o diameter_n of_o a_o almicanter_n and_o so_o f_o h_n the_o semidiameter_n thereof_o which_o be_v give_v it_o be_v require_v to_o find_v the_o sin_n both_o of_o 30_o and_o 50_o

a_o horizontall_a line_n upon_o the_o upper_a 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_n 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 horizontall_a 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_n 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_n as_o be_v here_o show_v in_o 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a_o b_o of_o the_o last_o chapter_n place_v it_o from_o c_o southward_n to_o e_z that_o be_v from_o the_o same_o end_n of_o the_o horizontall_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 forenoon_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 horizontall_a line_n of_o the_o plane_n and_o 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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 r_o z_o h_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 houre-line_n upon_o the_o horizontall_a 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 horizontall_a dial_n by_o help_n of_o the_o line_n upon_o the_o quadrant_n fit_v for_o that_o purpose_n therefore_o have_v by_o the_o 10_o chapter_n of_o the_o three_o book_n find_v the_o elevation_n of_o the_o pole_n above_o the_o plane_n we_o may_v proceed_v after_o this_o manner_n first_o draw_v the_o line_n d_o a_o f_o of_o sufficient_a length_n out_o of_o the_o middle_n whereof_o let_v fall_v the_o perpendicular_a a_o b_o for_o the_o meridian_n and_o substile_n then_o take_v the_o line_n d_o e_o or_o e_o f_o out_o of_o your_o quadrant_n and_o set_v it_o from_o a_o to_o b_o in_o the_o meridian_n through_o which_o point_n b_o draw_v the_o line_n e_o b_o c_o parallel_n to_o d_o a_o f_o now_o suppose_v the_o elevation_n of_o the_o pole_n above_o the_o plane_n to_o be_v 52_o deg_fw-la 30_o min._n the_o latitude_n of_o the_o place_n from_o the_o sine_fw-la thereof_o take_v the_o near_a extent_n unto_o a_o e_o the_o line_n of_o latitude_n and_o set_v it_o from_o a_o to_o d_o and_o from_o a_o to_o f_o both_o way_n and_o from_o b_o to_z c_z and_z from_z b_o to_z e_z and_o draw_v the_o line_n d_o c_o and_o e_o f_o make_v the_o long_a square_a c_o d_o f_o e_o the_o two_o angle_n whereof_o c_z and_z e_z shall_v be_v the_o point_n for_o the_o hour_n of_o 3_o and_o 9_o in_o all_o these_o kind_n of_o plane_n that_o decline_v not_o from_o the_o north_n or_o south_n for_o the_o hour-line_n before_o six_o and_o after_o you_o may_v extend_v their_o opposite_a hour_n line_n beyond_o the_o centre_n as_o be_v show_v in_o the_o 8_o chapter_n of_o the_o three_o book_n what_o be_v here_o show_v concern_v the_o hour_n the_o like_a may_v be_v understand_v for_o the_o half_a hour_n by_o apply_v the_o thread_n thereunto_o in_o the_o limb_n chap._n v._o to_o draw_v a_o dial_n upon_o a_o south_n or_o north_n erect_v decline_a plane_n in_o the_o draw_n of_o all_o these_o kind_n of_o dial_n by_o help_n of_o this_o quadrant_n when_o the_o latitude_n of_o the_o place_n and_o the_o declination_n of_o the_o plane_n be_v know_v two_o thing_n more_o be_v to_o be_v consider_v first_o the_o elevation_n of_o the_o pole_n above_o the_o plane_n second_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 both_o which_o will_v speedy_o be_v find_v when_o you_o be_v ready_a for_o they_o first_o therefore_o draw_v the_o line_n d_o a_o f_o as_o before_o from_o the_o middle_n whereof_o let_v fall_v

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when_o the_o day_n be_v 12_o hour_n long_o your_o dial_n be_v thus_o prepare_v and_o these_o parallel_n thus_o insert_v the_o inscription_n of_o these_o houre-line_n be_v very_o easy_a and_o plain_a to_o be_v understand_v to_o begin_v then_o with_o the_o inscription_n of_o the_o babylonish_n hour_n which_o be_v the_o hour_n from_o the_o sun_n rise_v first_o it_o be_v apparent_a that_o when_o the_o day_n be_v 8_o hour_n long_o that_o the_o sun_n rise_v at_o 8_o in_o the_o morning_n so_o that_o at_o that_o time_n the_o first_o hour_n after_o the_o sun_n rise_v be_v 9_o in_o the_o morning_n second_o when_o the_o day_n be_v 12_o hour_n long_o the_o sun_n rise_v at_o 6_o in_o the_o morning_n so_o that_o at_o that_o time_n the_o first_o hour_n after_o the_o sun_n rise_v be_v 7_o in_o the_o morning_n three_o when_o the_o day_n be_v 16_o hour_n long_o the_o sun_n rise_v at_o 4_o in_o the_o morning_n so_o that_o the_o first_o hour_n after_o his_o rise_n be_v 5_o in_o the_o morning_n as_o plain_o appear_v by_o this_o table_n Â _fw-fr length_n of_o the_o day_n 8_o 12_o 16_o hour_n from_o sun_n rise_v 1_o 9_o 7_o 5_o 2_o 10_o 8_o 6_o 3_o 11_o 9_o 7_o 4_o 12_o 10_o 8_o 5_o 1_o 11_o 9_o 6_o 2_o 12_o 10_o 7_o 3_o 1_o 11_o 8_o 4_o 2_o 12_o 9_o 5_o 3_o 1_o 10_o 6_o 4_o 2_o 11_o 7_o 5_o 3_o by_o which_o you_o may_v perceive_v that_o when_o the_o day_n be_v 8_o hour_n long_o the_o seven_o hour_n from_o sun_n rise_v be_v 3_o in_o the_o afternoon_n when_o the_o day_n be_v 12_o hour_n long_o the_o seven_o hour_n from_o sun_n rise_v be_v 1_o in_o the_o afternoon_n and_o when_o the_o day_n be_v 16_o hour_n long_o the_o seven_o hour_n from_o the_o sun_n rise_v be_v 11_o before_o noon_n as_o by_o this_o table_n do_v evident_o appear_v and_o therefore_o a_o straight_a line_n draw_v in_o your_o dial_n through_o those_o point_n where_o the_o common_a houre-line_n of_o your_o dial_n cross_v the_o respective_a parallel_n of_o the_o day_n length_n shall_v show_v the_o true_a quantity_n of_o hour_n since_o the_o sun_n rise_v at_o all_o time_n of_o the_o year_n which_o be_v the_o babylonish_n hour_n for_o example_n let_v it_o be_v require_v to_o draw_v the_o seven_o hour_n from_o the_o sun_n rise_v in_o your_o dial_n first_o by_o the_o table_n you_o see_v that_o in_o the_o parallel_n of_o 8_o hour_n for_o the_o length_n of_o the_o day_n the_o seven_o hour_n from_o the_o sun_n rise_v be_v 3_o in_o the_o afternoon_n therefore_o observe_v where_o the_o houre-line_n of_o three_o cross_v the_o parallel_n of_o 8_o hour_n which_o be_v at_o a._n second_o by_o the_o table_n you_o see_v that_o in_o the_o parallel_n of_o 12_o hour_n for_o the_o length_n of_o the_o day_n the_o seven_o hour_n from_o sun_n rise_v be_v then_o 1_o in_o the_o afternoon_n wherefore_o observe_v where_o the_o houre-line_n of_o 1_o cross_v the_o equinoctial_a which_o be_v at_o b._n three_o by_o the_o table_n you_o see_v that_o in_o the_o parallel_n of_o 16_o hour_n for_o the_o length_n of_o the_o day_n the_o seve_v hour_n from_o the_o sun_n rise_v be_v 11_o before_o noon_n therefore_o observe_v where_o the_o houre-line_n of_o 11_o cross_v the_o parallel_n of_o 16_o hour_n which_o be_v at_o c_o then_o draw_v the_o straight_a line_n a_o b_o c_o which_o shall_v be_v the_o seven_o babylonish_n hour_n or_o the_o seven_o hour_n from_o the_o sun_n rise_v all_o the_o year_n long_o and_o by_o this_o rule_n and_o the_o help_n of_o the_o table_n you_o may_v draw_v all_o the_o other_o hour_n from_o sun_n rise_v as_o you_o see_v they_o draw_v in_o the_o figure_n

of_o the_o almicanter_n or_o circle_n of_o altitude_n the_o circle_n of_o altitude_n have_v the_o same_o relation_n to_o the_o azimuth_n as_o the_o tropic_n and_o parallel_n of_o declination_n have_v to_o the_o houre-line_n and_o therefore_o as_o the_o parallel_n of_o declination_n in_o the_o equinoctial_a plane_n be_v perfect_a circle_n so_o be_v the_o circle_n of_o altitude_n in_o a_o horizontall_a plane_n the_o inscription_n of_o these_o into_o all_o kind_n of_o plane_n be_v in_o a_o manner_n the_o same_o with_o the_o parallel_n of_o declination_n but_o whereas_o in_o the_o draw_v the_o parallel_n of_o declination_n you_o take_v the_o houre-line_n out_o of_o your_o plane_n and_o put_v they_o in_o a_o trigon_n so_o in_o this_o you_o must_v take_v the_o azimuth_n out_o of_o your_o plane_n and_o put_v they_o into_o a_o trigon_n for_o that_o purpose_n and_o so_o transfer_v they_o to_o the_o plane_n again_o as_o you_o do_v the_o other_o and_o because_o these_o be_v small_a circle_n therefore_o they_o become_v conic_a section_n except_o on_o such_o plane_n as_o lie_v parallel_n to_o the_o zenith_n which_o be_v only_o the_o horizontall_a chap._n vii_o how_o to_o draw_v a_o dial_n on_o the_o ceiling_n of_o a_o room_n because_o the_o direct_a beam_n of_o the_o sun_n can_v never_o shine_v upon_o the_o ceiling_n of_o a_o room_n they_o must_v therefore_o be_v reflect_v thither_o by_o help_n of_o a_o small_a piece_n of_o look_a glass_n convenient_o fix_v in_o some_o transam_fw-la of_o the_o window_n so_o that_o it_o may_v lie_v exact_o parallel_v to_o the_o horizon_n the_o place_n be_v choose_v and_o the_o glass_n therein_o fix_v you_o must_v draw_v upon_o the_o ceiling_n of_o the_o room_n a_o meridian_n line_n as_o you_o be_v teach_v in_o the_o former_a book_n which_o meridian_n line_n must_v be_v so_o draw_v that_o it_o may_v pass_v direct_o over_o the_o glass_n before_o place_v which_o you_o may_v perceive_v how_o to_o do_v by_o hold_v a_o thread_n and_o plummet_n from_o the_o top_n of_o the_o ceiling_n till_o it_o fall_v direct_o upon_o the_o superficies_n of_o the_o glass_n the_o hour_n the_o angle_n that_o each_o houre-line_n make_v with_o the_o merid._n the_o compliment_n of_o each_o houre-line_n angle_v with_o the_o meridian_n Â _fw-fr 12_o Â _fw-fr 00d_o 00m_fw-la 90d_o 00m_fw-la 1_o Â _fw-fr 11_o 12_o 00_o 78_o 00_o 2_o Â _fw-fr 10_o 24_o 37_o 65_o 23_o 3_o Â _fw-fr 9_o 38_o 25_o 51_o 35_o 4_o Â _fw-fr 8_o 53_o 58_o 36_o 2_o 5_o Â _fw-fr 7_o 71_o 20_o 18_o 40_o Â _fw-fr 6_o Â _fw-fr 90_o 00_o 00_o 00_o have_v these_o thing_n prepare_v let_v the_o line_n l_o r_n in_o the_o follow_a figure_n represent_v a_o meridian_n line_v draw_v upon_o the_o ceiling_n of_o a_o room_n and_o let_v k_o be_v the_o glass_n fix_v direct_o under_o the_o say_a meridian_n upon_o some_o transam_fw-la of_o the_o window_n then_o lay_v one_o end_n of_o a_o string_n upon_o the_o glass_n at_o k_o extend_v the_o other_o up_o to_o the_o meridian_n at_o l_o which_o point_n l_o you_o may_v find_v by_o move_v the_o string_n to_o and_o fro_o upon_o the_o meridian_n line_n till_o another_o hold_v the_o side_n of_o a_o quadrant_n to_o the_o movable_a string_n he_o shall_v find_v the_o thread_n and_o plummet_n to_o fall_v direct_o upon_o the_o compliment_n of_o the_o latitude_n which_o in_o this_o example_n be_v 37_o deg_fw-la 30_o min._n the_o point_n l_o being_n thus_o find_v upon_o the_o meridian_n draw_v the_o line_n l_o ae_n perpendicular_a to_o the_o meridian_n l_o r_o which_o line_n shall_v be_v the_o equinoctial_a have_v thus_o do_v upon_o a_o table_n or_o such_o like_a draw_v a_o line_n which_o shall_v be_v of_o equal_a length_n with_o lk_n the_o distance_n from_o the_o glass_n to_o the_o point_n l_o on_o the_o ceiling_n which_o line_n divide_v into_o 10_o equal_a part_n and_o each_o of_o those_o or_o at_o least_o one_o of_o they_o into_o 10_o other_o part_n so_o shall_v you_o have_v in_o all_o 100_o part_n each_o of_o which_o you_o must_v suppose_v to_o be_v divide_v into_o 10_o other_o small_a part_n so_o shall_v the_o whole_a line_n contain_v 1000_o part_n as_o in_o the_o figure_n be_v express_v by_o the_o line_n s._n now_o because_o the_o centre_n of_o the_o dial_n be_v without_o the_o room_n so_o that_o you_o can_v make_v use_n of_o that_o to_o draw_v the_o hour_n by_o you_o must_v therefore_o place_v one_o foot_n of_o your_o compass_n in_o the_o point_n l_o m_o n_o p_o and_o q_o with_o the_o other_o draw_v obscure_a arch_n of_o circle_n as_o *****_o and_o out_o of_o the_o last_o column_n of_o the_o former_a table_n take_v the_o compliment_n of_o every_o hour_n arch_a from_o the_o meridian_n and_o place_v they_o upon_o the_o respective_a hour_n arch_n from_o the_o equinoctial_a to_o the_o point_n *****_o as_o you_o see_v in_o the_o figure_n last_o if_o you_o draw_v the_o line_n *_o m_o *_o n_o *_o p_o *_o q_o they_o shall_v be_v the_o true_a hour_n upon_o the_o ceiling_n in_o the_o inscription_n of_o the_o azimuth_n in_o decline_a recline_a plane_n and_o in_o draw_v the_o circle_n of_o altitude_n in_o all_o kind_n of_o plane_n i_o confess_v i_o shall_v have_v be_v somewhat_o large_a in_o give_v you_o a_o example_n in_o each_o plane_n as_o i_o do_v with_o the_o other_o variety_n before_o but_o pre-supposing_a the_o ingenious_a practitioner_n sufficient_o to_o understand_v that_o which_o go_v before_o he_o can_v but_o with_o small_a pain_n overcome_v the_o rest_n but_o i_o shall_v not_o have_v be_v so_o brief_a can_v i_o possible_o have_v procure_v more_o time_n which_o by_o no_o mean_n will_v be_v grant_v also_o my_o intent_n in_o this_o place_n be_v to_o have_v show_v you_o the_o inscription_n of_o the_o circle_n of_o position_n and_o other_o variety_n also_o the_o frame_n of_o divers_a geometrical_a body_n and_o to_o furnish_v they_o with_o variety_n of_o dial_n and_o the_o make_n of_o divers_a instrumental_a dial_n but_o these_o with_o many_o other_o horological_a conceit_n and_o invention_n i_o reserve_v till_o a_o more_o convenient_a opportunity_n and_o therefore_o in_o the_o mean_a time_n farewell_n finis_fw-la

and_o put_v number_n to_o they_o as_o you_o see_v there_o do_v Â¶_o 1_o note_v that_o if_o any_o of_o the_o point_v you_o be_v to_o make_v use_n of_o for_o the_o draw_v of_o any_o of_o these_o hour_n fall_v without_o your_o plane_n you_o must_v in_o this_o case_n extend_v your_o houre-line_n parallel_n and_o equinoctial_a beyond_o the_o limit_n of_o your_o diall-plane_n and_o there_o make_v use_n of_o the_o point_n but_o you_o need_v extend_v the_o line_n you_o draw_v no_o far_o than_o the_o bound_n of_o the_o plane_n as_o here_o in_o the_o figure_n you_o see_v the_o first_o hour_n from_o sun_n rise_v cross_v not_o the_o equinoctial_a and_o the_o houre-line_n of_o 7_o within_o the_o plane_n but_o if_o the_o equinoctial_a and_o the_o houre-line_n of_o 7_o be_v extend_v it_o will_v cross_v Â¶_o 2_o note_v that_o if_o any_o of_o the_o three_o point_n you_o be_v to_o make_v use_n of_o do_v so_o far_o exceed_v the_o limit_n of_o your_o plane_n that_o it_o will_v be_v either_o impossible_a 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little_a table_n and_o the_o rule_n and_o caution_n deliver_v in_o this_o chapter_n and_o therefore_o more_o example_n be_v superfluous_a chap._n iu._n show_v how_o the_o jewish_a hour_n may_v be_v draw_v upon_o any_o plane_n it_o be_v the_o custom_n of_o the_o ancient_n to_o divide_v their_o day_n and_o also_o their_o night_n whether_o long_o or_o short_a into_o 12_o equal_a part_n begin_v their_o day_n at_o the_o sun_n rise_v and_o their_o night_n at_o the_o sun_n set_v so_o that_o 12_o of_o the_o clock_n at_o noon_n be_v always_o the_o six_o hour_n of_o their_o day_n and_o 12_o at_o night_n be_v always_o the_o six_o hour_n of_o their_o night_n and_o according_a to_o this_o division_n be_v their_o dial_n drawn_z so_o that_o all_o the_o summer_n the_o hour_n of_o their_o day_n be_v long_o than_o the_o hour_n of_o their_o night_n and_o all_o the_o winter_n the_o hour_n of_o their_o night_n be_v long_o than_o those_o of_o their_o day_n and_o when_o the_o sun_n be_v in_o the_o 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parallel_n of_o 9_o hour_n and_o 15_o hour_n both_o which_o be_v three_o hour_n different_a from_o the_o equinoctial_a on_o either_o side_n thereof_o and_o these_o two_o parallel_n be_v the_o most_o convenient_a for_o this_o our_o purpose_n because_o the_o jewish_a hour_n will_v fall_v in_o these_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 houre-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 min._n or_o 5_o hour_n three_o quarter_n in_o the_o parallel_n of_o 15_o through_o 7_o hour_n in_o the_o equinoctial_a jewish_n hour_n the_o parallel_n of_o 15_o hour_n equinoctial_a the_o parallel_n of_o 9_o hour_n h._n m._n h._n h._n m._n 1_o 5_o 45_o 7_o 8_o 15_o 2_o 7_o 0_o 8_o 9_o 0_o 3_o 8_o 15_o 9_o 9_o 45_o 4_o 9_o 30_o 10_o 10_o 30_o 5_o 10_o 45_o 11_o 11_o 15_o 6_o 12_o 0_o 12_o 12_o 0_o 7_o 1_o 15_o 1_o 0_o 45_o 8_o 2_o 30_o 2_o 1_o 30_o 9_o 3_o 45_o 3_o 2_o 15_o 10_o 5_o 0_o 4_o 3_o 0_o 11_o 6_o 15_o 5_o 3_o 45_o 12_o 7_o 30_o 6_o 4_o 30_o &_o through_o 8_o hour_n &_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 this_o 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 houre-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 horizontall_a 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 Â§._o 1._o in_o the_o horizontall_a plane_n in_o the_o horizontall_a 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 32_o equal_a part_n begin_v at_o the_o meridian_n answer_v to_o the_o 32_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 etc._n etc._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 etc._n etc._n if_o you_o divide_v the_o circle_n according_a to_o the_o mariner_n compass_n this_o be_v so_o plain_a that_o it_o need_v no_o example_n Â§._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 horizontall_a line_n m_o e_o n_o 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 eglantine_n 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_n e_o l_o into_o eight_z 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 â˜‰_o â˜‰_o â˜‰_o â˜‰_o â˜‰_o â˜‰_o then_o with_o your_o compass_n

Selected quad for the lemma: end_n

Text snippets containing the quad