Selected quad for the lemma: end_n

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

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A08582	The circles of proportion and the horizontal instrument The former shewing the maner how to work proportions both simple and compound: and the ready and easy resolving of quæstions both in arithmetic, geometrie, & astronomie: and is newly increased with an additament for navigation. All which rules may also be wrought with the penne by arithmetic, and the canon of triangles. The later teaching how to work most quæstions, which may be performed by the globe: and to delineat dialls upon any kind of plaine. Invented, and written in latine by W.O. Translated into English, and set out for the public benefit, by William Forster.	Oughtred, William, 1575-1660.; Forster, William, mathematician.; Oughtred, William, 1575-1660. Addition unto the use of the circles of proportion. aut	1633 (1633)	STC 18899B; ESTC S120820	74,822	159

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shall_v be_v the_o semidiameter_n of_o hour_n circle_n and_o that_o you_o may_v know_v for_o what_o circle_n every_o centre_n and_o semidiameter_n serve_v you_o shall_v note_v every_o five_o line_n from_o the_o beginning_n with_o the_o figure_n 5_o 10_o 15_o 20_o etc._n etc._n set_a under_o the_o second_o parallel_n unto_o 90_o which_o will_v fall_v upon_o the_o long_a perpendicular_a that_o so_o you_o may_v ready_o find_v the_o centre_n and_o semidiameter_n of_o any_o circle_n require_v again_o divide_v the_o first_o 45_o degree_n of_o the_o quadrant_n in_o the_o midst_n and_o apply_v your_o ruler_n to_o the_o centre_n and_o to_o every_o one_o of_o those_o half_a division_n where_o in_o each_o place_n the_o ruler_n cut_v the_o first_o parallel_n or_o tangent_fw-la line_n make_v a_o prick_n so_o shall_v you_o have_v upon_o the_o tangent_fw-la line_n between_o the_o short_a perpendicular_a and_o the_o middlemost_a line_n 45_o a_o three_o scale_n which_o be_v the_o scale_n of_o 90_o 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and_o upon_o it_o to_o trace_v such_o line_n and_o arch_n as_o you_o have_v occasion_n to_o use_v that_o so_o your_o instrument_n may_v be_v keep_v clean_o and_o last_v long_o for_o as_o much_o as_o in_o delineat_v the_o horary_a circle_n which_o be_v within_o 30_o degree_n of_o the_o meridian_n the_o semidiameter_n will_v be_v too_o long_o for_o your_o compass_n you_o may_v in_o that_o straight_a thus_o help_v yourself_o first_o say_v as_o the_o radius_fw-la be_v to_o the_o sine_fw-la of_o the_o elevation_n of_o the_o pole_n so_o be_v the_o tang_n of_o the_o distance_n of_o any_o horary_a circle_n from_o the_o meridian_n suppose_v 25_o or_o 20_o or_o 15_o or_o 10_o or_o 5_o degree_n to_o the_o arch_n of_o the_o horizon_n between_o the_o meridian_n and_o that_o horary_a circle_n reckon_v this_o distance_n on_o the_o limb_n of_o your_o instrument_n from_o both_o end_n of_o the_o meridian_n and_o mark_v it_o thus_o do_v for_o the_o 25_o 20_o 15_o 10_o and_o 5_o horary_a circle_n on_o both_o side_n of_o each_o end_n of_o the_o meridian_n then_o in_o any_o piece_n of_o clean_a paper_n through_o the_o midst_n of_o the_o long_a way_n draw_v alone_a and_o towards_o one_o end_n which_o i_o call_v the_o upper_a end_n across_o the_o same_o with_o a_o perpendicular_a line_n exact_o equal_a to_o the_o diameter_n of_o your_o instrument_n the_o point_n of_o intersection_n be_v the_o centre_n take_v with_o your_o compass_n out_o of_o the_o paper_n of_o scale_n the_o semidiameter_n of_o 60._o degr_n which_o you_o may_v well_o do_v for_o a_o ordinary_a instrument_n and_o set_v one_o foot_n on_o either_o end_n of_o the_o diameter_n that_o point_n wherein_o the_o other_o foot_n shall_v cut_v the_o first_o long_a line_n make_v your_o centre_n and_o thereon_o draw_v a_o arch_n through_o both_o end_n of_o the_o diameter_n and_o cut_v the_o upper_a part_n of_o the_o first_o long_a line_n this_o arch_n be_v equal_a to_o that_o horary_a circle_n which_o be_v distant_a from_o the_o meridian_n 30_o degree_n the_o compliment_n of_o 60._o divide_v each_o half_n of_o the_o diameter_n into_o 3_o equal_a part_n with_o 4_o point_n and_o from_o every_o of_o those_o point_n unto_o the_o arch_n draw_v line_n parallel_v to_o the_o first_o long_a line_n and_o have_v divide_v every_o one_o of_o those_o five_o parallel_a line_n intercept_v between_o the_o diameter_n and_o the_o arch_n into_o 6_o equal_a part_n for_o the_o 6_o time_n 5_o degree_n which_o remain_v to_o the_o meridian_n draw_v through_o those_o division_n from_o the_o end_n of_o the_o diameter_n with_o a_o smooth_a and_o even_a hand_n the_o arch_n 25_o 20_o 15_o 10_o and_o 5._o those_o arch_n you_o may_v transfer_v from_o the_o paper_n to_o your_o instrument_n in_o this_o manner_n rub_v the_o back_n side_n of_o the_o paper_n against_o the_o arch_n with_o fine_a powder_n of_o black_a lead_n then_o apply_v the_o paper_n with_o arch_n to_o your_o instrument_n that_o the_o end_n of_o the_o diameter_n may_v exact_o fall_v upon_o the_o two_o opposite_a mark_n in_o the_o limb_n of_o your_o instrument_n which_o serve_v for_o the_o horary_a circle_n that_o you_o will_v draw_v either_o 25_o 20_o 15_o 10_o or_o 5_o trace_v over_o that_o arch_n with_o the_o point_n of_o any_o hard_a piece_n of_o wood_n sharpen_v and_o the_o black_a lead_n on_o the_o back_n side_n will_v upon_o the_o instrument_n leave_v the_o print_n of_o that_o arch._n xxv_o use_v to_o set_v a_o upright_a wall_n or_o plain_a upon_o the_o instrument_n and_o to_o find_v how_o many_o hour_n the_o sun_n shall_v shine_v thereon_o at_o some_o time_n of_o the_o year_n the_o situation_n of_o wall_n or_o plain_n be_v consider_v either_o in_o respect_n of_o the_o meridian_n or_o of_o the_o horizon_n and_o unto_o both_o it_o be_v either_o perpendicular_a or_o oblique_a or_o parallel_v the_o

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pole_n be_v elevate_v or_o downward_o from_o the_o centre_n if_o the_o south_n pole_n be_v elevate_v xxix_o use_v the_o make_n of_o all_o manner_n of_o plain_a dial_n not_o have_v centre_n if_o the_o plain_a represent_v on_o the_o instrument_n as_o be_v teach_v before_o in_o the_o xxv_o and_o xxvi_o use_v cut_v the_o pole_n of_o the_o aequinoctial_a it_o be_v a_o horary_a circle_n either_o one_o of_o they_o which_o be_v draw_v in_o the_o instrument_n or_o fall_v between_o some_o two_o of_o they_o and_o the_o dial_n plain_a itself_o shall_v not_o cross_v the_o axis_fw-la of_o the_o world_n but_o lie_v parallel_n to_o it_o without_o any_o angle_n of_o elevation_n and_o therefore_o such_o a_o dyal_n can_v have_v no_o centre_n but_o the_o stile_n the_o substile_a and_o all_o the_o hour_n line_n shall_v be_v parallel_n one_o to_o another_o every_o such_o plain_a represent_v on_o the_o instrument_n either_o first_o it_o be_v the_o meridian_n of_o the_o place_n the_o horizontall_a intersection_n whereof_o be_v the_o 12_o a_o clock_n line_n draw_v from_o north_n to_o south_n and_o the_o dial_n make_v thereon_o be_v a_o direct_a east_n or_o west_n upright_o dyal_n in_o which_o the_o substile_a be_v distant_a from_o the_o line_n in_o the_o circle_n of_o the_o dial_n plain_a parallel_n to_o the_o horizon_n with_o a_o arch_n equal_a to_o the_o elevation_n of_o the_o pole_n and_o upward_o towards_o the_o pole_n and_o be_v also_o the_o 6_o a_o clock_n line_n in_o your_o dyal_n the_o rest_n of_o the_o hour_n line_n be_v thus_o describe_v draw_v through_o the_o substile_a in_o any_o point_n a_o long_a line_n at_o right_a angle_n that_o line_n shall_v be_v the_o aequinoctial_a intersection_n usual_o call_v the_o contingent_a line_n and_o take_v a_o convenient_a distance_n for_o the_o stile_n to_o hang_v parallel_n over_o the_o substile_a according_a to_o the_o greatness_n of_o your_o dial_n plain_a measure_v it_o upon_o the_o substile_a from_o the_o aequinoctial_a intersection_n and_o upon_o the_o end_n of_o that_o measure_n describe_v half_o a_o circle_n for_o the_o aequinoctial_a itself_o divide_v each_o quadrant_n thereof_o from_o the_o substile_a into_o 6_o equal_a part_n or_o hour_n then_o apply_v a_o ruler_n to_o the_o centre_n and_o to_o every_o one_o of_o those_o division_n several_o where_o in_o every_o place_n the_o ruler_n shall_v cut_v the_o long_a line_n of_o aequinoctial_a intersection_n make_v prick_n and_o through_o those_o prick_v draw_v the_o hour_n line_n parallel_n to_o the_o substile_a or_o 6_o a_o clock_n line_n distinguish_v so_o many_o of_o they_o as_o be_v needful_a with_o their_o figure_n that_o be_v all_o the_o forenoon_n hour_n on_o the_o east_n plain_a and_o all_o the_o afternoon_n hour_n on_o the_o west_n plain_a but_o in_o these_o dial_n there_o be_v no_o 12_o a_o clock_n line_n it_o be_v infinite_o distant_a from_o the_o substile_a last_o hang_v the_o stile_n direct_o over_o the_o substile_a and_o parallel_v to_o it_o at_o the_o distance_n former_o take_v and_o thus_o be_v your_o east_n and_o west_n dial_n finish_a or_o second_o it_o be_v the_o sixth_o hour_n circle_n the_o horizontal_n intersection_n whereof_o be_v the_o line_n of_o east_n and_o west_n and_o the_o dyal_n make_v thereon_o be_v direct_a north_n incline_v or_o south_n recline_v with_o a_o arch_n equal_a to_o the_o compliment_n of_o the_o height_n of_o the_o pole_n and_o the_o parallel_n to_o the_o horizon_n be_v the_o aequinoctial_a intersection_n and_o the_o line_n perpendicular_a to_o it_o be_v the_o 12_o a_o clock_n line_n and_o also_o the_o substile_a the_o rest_n of_o the_o hour_n line_n from_o 7_o a_o clock_n in_o the_o morning_n to_o 5_o in_o the_o evening_n be_v thus_o describe_v take_v a_o convenient_a distance_n for_o the_o style_n from_o the_o substile_a measure_v it_o upon_o the_o substile_a from_o the_o aequinoctial_a intersection_n and_o on_o the_o end_n of_o that_o space_n describe_v the_o semicircle_n of_o the_o aequinoctial_a to_o be_v divide_v on_o both_o side_n of_o the_o substile_a into_o 6_o hour_n through_o every_o one_o of_o which_o out_o of_o the_o centre_n a_o ruler_n be_v apply_v at_o the_o point_n of_o the_o several_a intersection_n of_o the_o ruler_n with_o the_o aequinoctial_a intersection_n draw_v the_o hour_n line_n parallel_v to_o the_o substile_a or_o 12_o a_o clock_n line_n distinguish_v they_o with_o their_o figure_n namely_o 11_o 10_o 9_o 8_o 7_o on_o the_o west_n side_n and_o 1_o 2_o 3_o 4_o 5_o on_o the_o east_n side_n but_o in_o these_o dial_n there_o be_v no_o six_o a_o clock_n line_n it_o be_v infinite_o distant_a from_o the_o substile_a last_o hang_v the_o style_n direct_o over_o the_o substile_a and_o parallel_v to_o it_o at_o the_o distance_n former_o take_v or_o three_o it_o be_v north_n incline_v or_o south_n

recline_v and_o also_o decline_a in_o which_o as_o the_o tangent_fw-la of_o the_o elevation_n of_o the_o pole_n be_v to_o the_o radius_fw-la so_o be_v the_o sine_fw-la of_o the_o compl_a of_o declination_n to_o the_o tang_n of_o the_o compl_a of_o inclination_n or_o reclination_n the_o plain_a be_v set_v upon_o the_o instrument_n by_o the_o arch_n of_o declination_n and_o stoop_v thereof_o as_o have_v be_v teach_v in_o xxv_o ●_o use_v shall_v cut_v the_o pole_n of_o the_o aequinoctial_a apply_v therefore_o a_o ruler_n to_o the_o pole_n of_o the_o plain_a and_o to_o the_o pole_n of_o the_o aequinoctial_a and_o the_o point_n in_o which_o it_o cut_v the_o limb_n mark_v for_o the_o substile_a which_o be_v to_o be_v transfer_v unto_o the_o circle_n of_o the_o dyal_n plain_a by_o take_v the_o distance_n between_o that_o point_n and_o the_o next_o horizontal_n intersection_n and_o set_v it_o on_o that_o circle_n from_o the_o line_n parallel_n to_o the_o horizon_n upward_o if_o the_o plain_a be_v north_n or_o downward_o if_o the_o plain_a be_v south_n and_o on_o that_o side_n which_o be_v contrary_a to_o the_o declination_n the_o substile_a be_v thus_o sound_a draw_v a_o long_a line_n perpendicular_a to_o it_o for_o the_o aequinoctial_a intersection_n and_o take_v a_o convenient_a distance_n for_o the_o stile_n from_o the_o substile_a measure_v it_o upon_o the_o substile_a from_o the_o aequinoctial_a intersection_n and_o on_o the_o end_n of_o that_o space_n describe_v the_o semicircle_n of_o the_o aequinoctial_a then_o look_v in_o your_o instrument_n how_o many_o degree_n of_o the_o aequinoctial_a be_v intercept_v between_o the_o meridian_n and_o the_o arch_n represent_v your_o plain_n and_o reckon_v the_o same_o number_n of_o degree_n upon_o the_o aequinoctial_a of_o the_o dyal_n plain_a from_o the_o substile_a towards_o the_o side_n of_o declination_n there_o make_v a_o mark_n for_o the_o meridian_n point_v thereof_o in_o which_o you_o must_v begin_v to_o divide_v the_o aequinoctial_a semicircle_n into_o hour_n both_o way_n and_o that_o be_v divide_v apply_v a_o ruler_n to_o the_o centre_n and_o to_o every_o one_o of_o the_o division_n and_o at_o the_o point_n of_o the_o several_a intersection_n of_o the_o ruler_n with_o the_o aequinoctial_a intersection_n draw_v the_o hour_n line_n parallel_v to_o the_o substile_a set_a 12_o at_o that_o hour_n line_n which_o be_v draw_v at_o the_o intersection_n through_o the_o meridian_n point_n of_o the_o equinoctial_a and_o 11_o 10_o 9_o 8_o etc._n etc._n on_o the_o west_n side_n and_o 1_o 2_o 3_o 4_o &c_n &c_n on_o the_o east_n side_n last_o hang_v the_o stile_n direct_o over_o the_o substile_a and_o parallel_v to_o it_o at_o the_o distance_n former_o take_v xxx_o use_v how_o by_o sines_n and_o tangent_n to_o calculate_v the_o place_n of_o the_o meridian_n and_o substile_a and_o the_o height_n of_o the_o style_n above_o it_o and_o the_o distance_n of_o the_o meridian_n of_o the_o aequinoctial_a from_o the_o substile_a together_o with_o the_o place_n of_o hour_n line_n both_o by_o calculation_n and_o also_o geometrical_o i_o have_v already_o teach_v the_o make_n of_o all_o manner_n of_o plain_a dial_n most_o easy_o by_o the_o instrument_n for_o the_o same_o height_n of_o the_o pole_n but_o if_o any_o man_n either_o want_v a_o instrument_n or_o else_o desire_v great_a exactness_n i_o will_v also_o here_o show_v how_o to_o perform_v the_o same_o by_o calculation_n on_o the_o other_o side_n of_o the_o instrument_n in_o a_o plain_a erect_a dial_n decline_v as_o the_o radius_fw-la be_v to_o the_o sine_fw-la of_o doclination_n so_o be_v the_o tang_n of_o the_o compl_a of_o the_o pole_n height_n to_o the_o tang_n of_o the_o distance_n of_o the_o substile_a from_o the_o meridian_n in_o plain_a dial_n both_o decline_v and_o also_o incline_v and_o recline_v as_o the_o radius_fw-la be_v to_o the_o sine_fw-la of_o inclination_n reclination_n so_o be_v the_o tang_n of_o declination_n to_o the_o tang_n of_o the_o compl_a of_o the_o distance_n of_o the_o meridian_n from_o the_o line_n parallel_n to_o the_o horizon_n again_o as_o the_o radius_fw-la be_v to_o the_o sine_fw-la of_o the_o compl_a of_o declination_n so_o be_v the_o tang_n of_o the_o compl_a of_o the_o pole_n height_n to_o the_o tang_n of_o base_a i._n if_o the_o dial_n be_v south_n recline_v or_o north_n incline_v the_o sum_n of_o base_a i_o and_o of_o the_o compliment_n of_o inclination_n or_o reclination_n shall_v be_v base_a ii_o but_o if_o the_o plain_n be_v south_n incline_v or_o north_n recline_v the_o difference_n of_o base_a i_o and_o of_o the_o compliment_n of_o inclination_n or_o reclination_n shall_v be_v base_a ii_o then_o say_v three_o as_o the_o sine_fw-la of_o the_o compl_a of_o base_a i_o be_v to_o the_o sine_fw-la of_o the_o compl_a or_o excess_n of_o base_a two_o so_o be_v the_o sine_fw-la of_o the_o height_n of_o the_o pole_n to_o the_o sine_fw-la of_o the_o height_n of_o the_o stile_n above_o the_o substile_a four_o as_o the_o sine_fw-la of_o the_o compl_a of_o the_o height_n of_o the_o stile_n above_o the_o substile_a be_v to_o the_o sine_fw-la of_o declination_n so_o be_v the_o sine_fw-la of_o the_o compl_a of_o the_o height_n of_o the_o pole_n to_o the_o sine_fw-la of_o the_o compl_a of_o the_o distance_n of_o the_o substile_a from_o the_o line_n parallel_n to_o the_o horizon_n again_o as_o the_o radius_fw-la be_v to_o the_o sine_fw-la of_o the_o compl_a of_o declination_n so_o be_v the_o sine_fw-la of_o the_o compl_a of_o the_o pole_n height_n to_o the_o sine_fw-la of_o the_o height_n of_o the_o stile_n above_o the_o substile_a three_o as_o the_o sine_fw-la of_o the_o pole_n height_n be_v to_o the_o radius_fw-la so_o be_v the_o tang_n of_o declination_n to_o the_o tang_n of_o the_o distance_n of_o the_o meridian_n of_o the_o aequinoctial_a from_o the_o substile_a and_o this_o distance_n be_v ever_o less_o than_o 90_o degree_n in_o a_o plain_a east_n and_o west_n incline_v and_o recline_a dial_n as_o the_o radius_fw-la be_v to_o the_o sine_fw-la of_o the_o compl_a of_o inclination_n reclination_n so_o be_v the_o tang_n of_o the_o height_n of_o the_o pole_n to_o the_o tang_n of_o the_o distance_n of_o the_o substile_a from_o the_o meridian_n again_o as_o the_o radius_fw-la be_v to_o the_o sine_fw-la of_o inclination_n reclination_n so_o be_v the_o sine_fw-la of_o the_o height_n of_o the_o pole_n to_o the_o sine_fw-la of_o the_o height_n of_o the_o stile_n above_o the_o substile_a three_o as_o the_o sine_fw-la of_o the_o compl_a of_o the_o pole_n height_n be_v to_o the_o radius_fw-la so_o be_v the_o tang_n of_o the_o compl_a of_o inclination_n reclination_n to_o the_o tang_n of_o the_o distance_n of_o the_o meridian_n of_o the_o aequinoctial_a from_o the_o substile_a and_o this_o distance_n be_v ever_o great_a than_o 90_o degree_n five_o as_o the_o sine_fw-la of_o the_o compl_a of_o the_o height_n of_o the_o stile_n above_o the_o substile_a be_v to_o the_o sine_fw-la of_o declination_n so_o be_v the_o sine_fw-la of_o the_o compl_a of_o inclination_n reclination_n to_o the_o sine_fw-la of_o the_o distance_n of_o the_o meridian_n of_o the_o aequinoctial_a from_o the_o substile_a and_o note_v that_o in_o south_n recline_v and_o north_n incline_v plain_n if_o base_a two_o be_v less_o than_o a_o quadrant_a the_o contrary_a pole_n be_v elevate_v above_o the_o plain_a and_o if_o base_a two_o be_v equal_a to_o a_o quadrant_a the_o plain_n do_v cut_v the_o pole_n of_o the_o aequinoctial_a now_o concern_v the_o place_n of_o the_o substile_a upon_o the_o dial_n plain_a as_o i_o have_v already_o in_o the_o xxviii_o use_v show_v for_o the_o meridian_n we_o be_v to_o know_v first_o that_o the_o substile_a be_v to_o be_v draw_v upward_o from_o the_o line_n parallel_n to_o the_o horizon_n if_o the_o plain_n be_v northern_a or_o downward_o from_o it_o if_o it_o be_v southern_a except_o in_o north_n recline_v and_o south_n incline_v dial_n in_o which_o the_o base_a i_o exceed_v the_o compliment_n of_o inclination_n and_o reclination_n for_o in_o they_o it_o be_v quite_o contrary_a and_o second_o that_o the_o substile_a be_v to_o be_v draw_v in_o the_o contrary_a side_n from_o the_o declination_n but_o in_o north_n incline_v and_o south_n recline_v dial_n in_o which_o the_o contrary_a pole_n be_v elevate_v the_o substile_a must_v be_v draw_v through_o the_o centre_n into_o the_o opposite_a quadrant_a of_o your_o dial_n circle_n last_o the_o hour_n line_n in_o all_o manner_n of_o plain_a dial_n be_v thus_o to_o be_v find_v if_o the_o substile_a and_o hour_n be_v both_o on_o the_o same_o side_n of_o the_o meridian_n the_o arch_n of_o the_o aequinoctial_a between_o the_o substile_a and_o the_o hour_n line_n shall_v be_v equal_a to_o the_o difference_n of_o the_o two_o distance_n namely_o of_o the_o

with_o unnecessary_a hour_n line_n for_o example_n suppose_v that_o the_o former_a plain_n which_o with_o the_o south_n decline_v eastward_o 35_o deg_fw-la do_v also_o incline_v 41_o deg_fw-la 30_o min._n wherefore_o also_o with_o the_o north_n side_n it_o shall_v decline_v westward_o 35_o deg_fw-la and_o recline_v 41_o deg_fw-la 30_o min._n describe_v this_o plain_a upon_o your_o instrument_n with_o a_o arch_n of_o a_o circle_n find_v out_o as_o be_v teach_v last_o before_o and_o it_o will_v appear_v that_o upon_o the_o incline_v side_n shall_v be_v draw_v all_o the_o hour_n line_n from_o almost_o 4_o in_o the_o morning_n to_o 4_o in_o the_o afternoon_n and_o upon_o the_o recline_a side_n shall_v be_v draw_v first_o 4_o and_o 5_o in_o the_o morning_n and_o then_o begin_v at_o 0_o a_o clock_n all_o hour_n to_o sun_n set_v and_o note_v that_o in_o all_o northern_a plain_n the_o north_n pole_n be_v elevate_v and_o in_o all_o southern_a plain_n the_o south_n pole_n be_v elevate_v except_o such_o north_n incline_v and_o south_n recline_v plain_n that_o in_o the_o instrument_n fall_v below_o the_o north_n pole_n between_o it_o and_o the_o horizon_n for_o in_o they_o the_o contrary_a pole_n be_v elevate_v and_o also_o that_o a_o direct_a east_n and_o west_n plain_a if_o it_o recline_v have_v the_o north_n pole_n elevate_v and_o if_o it_o incline_v the_o south_n pole_n xxvii_o use_v the_o plain_a be_v set_v upon_o the_o instrument_n to_o find_v the_o distance_n of_o the_o hour_n line_n and_o substile_a from_o the_o horizontall_a intersection_n and_o also_o the_o height_n of_o the_o style_n above_o the_o substile_a every_o dial_n either_o have_v a_o centre_n in_o which_o all_o the_o hour_n line_n together_o with_o the_o substile_a and_o style_n do_v meet_v or_o else_o it_o have_v no_o centre_n &_o so_o they_o be_v all_o parallel_a one_o to_o another_o if_o the_o plain_a be_v set_v upon_o the_o instrument_n cut_v the_o pole_n of_o the_o aequinoctial_a that_o be_v the_o point_n in_o which_o all_o the_o horary_a circle_n across_o the_o meridian_n the_o dyal_n to_o be_v draw_v upon_o that_o plain_n shall_v have_v no_o centre_n but_o if_o it_o cut_v not_o the_o pole_n the_o dyal_n shall_v have_v a_o centre_n and_o of_o these_o dial_n with_o centre_n we_o will_v first_o entreat_v as_o be_v most_o proper_a for_o the_o use_n of_o the_o instrument_n behold_v therefore_o the_o pole_n of_o your_o plain_n heedy_o what_o horary_a circle_n it_o fall_v upon_o or_o if_o it_o fall_v between_o any_o two_o the_o distance_n of_o each_o be_v reasonable_o apportion_v imagine_v a_o horary_a circle_n pass_v through_o it_o mark_v in_o what_o point_n that_o horary_a circle_n either_o real_a or_o imagine_v do_v cut_v the_o plain_a that_o same_o point_n shall_v be_v the_o place_n of_o the_o substile_a in_o your_o plain_n and_o the_o height_n of_o the_o style_n above_o it_o be_v the_o arch_n of_o that_o horary_a circle_n intercept_v betwixt_o the_o pole_n of_o the_o aequinoctial_a and_o the_o point_n of_o the_o substile_a note_v in_o the_o plain_a therefore_o apply_v a_o ruler_n to_o the_o pole_n of_o your_o plain_n carry_v it_o about_o unto_o all_o the_o intersection_n of_o the_o plain_a with_o the_o hour_n circle_n and_o the_o substile_a several_o and_o where_o in_o every_o place_n the_o ruler_n shall_v cut_v the_o innermost_a circle_n of_o the_o limb_n there_o make_v a_o visible_a mark_n for_o the_o arch_n of_o the_o limb_n intercept_v between_o the_o horizontall_a point_n of_o your_o plain_n and_o every_o one_o of_o those_o mark_n shall_v be_v the_o distance_n intend_v to_o be_v seek_v but_o for_o the_o horizontall_a plain_a the_o end_n of_o the_o hour_n circle_n in_o the_o limb_n of_o your_o instrument_n do_v give_v the_o distance_n without_o any_o more_o ado_n concern_v the_o height_n of_o the_o style_n above_o the_o substile_a it_o be_v apparent_a by_o the_o instrument_n that_o in_o a_o horizontal_n dyal_a the_o 6_o a_o clock_n line_n lie_v direct_o east_n and_o west_n and_o the_o meridian_n perpendicular_a to_o it_o direct_o north_n and_o south_n and_o that_o the_o meridian_n be_v the_o substile_a and_o that_o the_o height_n of_o the_o style_n above_o the_o substile_a be_v equal_a to_o the_o height_n of_o the_o pole_n in_o that_o place_n it_o be_v also_o apparent_a that_o in_o all_o direct_a north_n and_o south_n dial_n the_o 6_o a_o clock_n line_n be_v draw_v parallel_n to_o the_o horizon_n and_o the_o meridian_n perpendicular_a to_o it_o and_o that_o the_o meridian_n be_v the_o substile_a and_o that_o the_o height_n of_o the_o style_n above_o the_o substile_a if_o the_o plain_a be_v upright_o be_v equal_a to_o the_o compliment_n of_o the_o height_n of_o the_o pole_n but_o if_o it_o be_v north_n incline_v or_o south_n recline_v it_o be_v equal_a to_o the_o difference_n of_o the_o height_n of_o the_o pole_n and_o the_o arch_n of_o inclination_n or_o reclination_n and_o if_o the_o plain_a be_v north_n recline_v or_o south_n incline_v it_o be_v equal_a to_o the_o sum_n of_o the_o compliment_n of_o the_o height_n of_o the_o pole_n and_o of_o the_o arch_n of_o inclination_n or_o reclination_n and_o if_o the_o plain_a fall_n upon_o the_o aequinoctial_a the_o stile_n shall_v stand_v up_o perpendicular_a upon_o it_o in_o the_o centre_n and_o the_o hour_n line_n shall_v be_v draw_v all_o at_o equal_a angle_n viz._n 15_o degree_n one_o from_o another_o in_o such_o dial_n as_o have_v not_o the_o meridian_n for_o the_o substile_a the_o height_n of_o the_o style_n above_o the_o substile_a be_v thus_o sound_a by_o the_o instrument_n it_o be_v show_v before_o that_o the_o height_n of_o the_o stile_n above_o the_o substile_a be_v the_o arch_n of_o the_o horary_a circle_n through_o the_o pole_n of_o the_o plain_a intercept_v between_o the_o pole_n of_o the_o aequinoctial_a and_o the_o point_n note_v in_o the_o plain_a for_o the_o substile_a therefore_o from_o the_o horizontall_a point_n or_o intersection_n of_o that_o horary_a circle_n reckon_v 90_o degree_n both_o way_n and_o thereto_o through_o the_o centre_n draw_v a_o obscure_a line_n in_o which_o line_n shall_v be_v both_o the_o inclination_n of_o that_o horary_a circle_n which_o be_v the_o distance_n of_o the_o intersection_n or_o uppermost_a point_n thereof_o from_o the_o centre_n and_o also_o the_o pole_n then_o with_o your_o compass_n take_v that_o distance_n or_o inclination_n and_o set_v it_o upon_o the_o scale_n of_o degree_n in_o your_o paper_n see_v how_o many_o degree_n it_o contain_v upon_o that_o scal●_n again_o upon_o the_o same_o scale_n take_v with_o your_o compass_n the_o compliment_n of_o that_o inclination_n or_o distance_n which_o be_v set_v upon_o the_o obscure_a line_n on_o the_o other_o side_n of_o the_o centre_n shall_v show_v the_o pole_n of_o that_o horary_a circle_n last_o apply_v a_o ruler_n to_o the_o pole_n of_o that_o horary_a circle_n and_o both_o to_o the_o pole_n of_o the_o aequinoctial_a and_o to_o the_o point_n of_o the_o substile_a in_o the_o plain_a several_o mark_v where_o in_o both_o place_n the_o ruler_n cut_v the_o innermost_a limb_n of_o your_o instrument_n for_o the_o degree_n of_o the_o limb_n intercept_v betwixt_o those_o mark_n shall_v be_v the_o height_n of_o the_o stile_n above_o the_o substile_a which_o be_v seek_v for_o and_o by_o this_o which_o have_v be_v teach_v you_o shall_v find_v that_o in_o a_o upright_a dial_n decline_v as_o before_o 35_o deg_fw-la from_o the_o south_n into_o the_o east_n or_o from_o the_o north_n into_o the_o west_n the_o substile_a shall_v fall_v upon_o that_o horary_a circle_n which_o be_v about_o 3_o deg_fw-la after_o 9_o a_o clock_n in_o the_o morning_n and_o the_o stile_n elevate_v above_o the_o substile_a about_o 31_o deg_fw-la and_o also_o that_o in_o a_o south_n dial_n decline_v eastward_o 35_o deg_fw-la and_o incline_v 41_o deg_fw-la 30_o min_fw-mi or_o in_o a_o north_n decline_v westward_o 35_o deg_fw-la and_o recline_v 41_o deg_fw-la 30_o min_fw-mi the_o substile_a shall_v fall_v upon_o that_o horary_a circle_n which_o be_v about_o 8_o degree_n after_o 6_o a_o clock_n and_o the_o stile_n elevate_v above_o the_o substile_a about_o 63_o deg_fw-la 30_o minute_n xxviii_o use_v the_o make_n of_o all_o manner_n of_o plain_a dial_n with_o centre_n i_o have_v already_o show_v how_o to_o find_v out_o in_o our_o instrument_n the_o distance_n of_o all_o the_o hour_n line_n and_o the_o substile_a from_o the_o horizontal_n intersection_n now_o the_o delineat_n of_o a_o dyal_n be_v nothing_o else_o but_o to_o transfer_v those_o distance_n out_o of_o your_o instrument_n into_o the_o dyal_n plain_a every_o one_o in_o his_o due_a situation_n and_o then_o through_o they_o out_o of_o the_o centre_n to_o draw_v such_o hour_n line_n as_o shall_v be_v of_o use_n together_o with_o the_o

hour_n line_n from_o noon_n and_o of_o the_o meridian_n of_o the_o aequinoctial_a from_o the_o substile_a but_o if_o the_o substile_a be_v upon_o one_o side_n of_o the_o meridian_n and_o the_o hour_n on_o the_o other_o side_n it_o shall_v be_v equal_a to_o the_o sum_n thereof_o then_o say_v as_o the_o radius_fw-la be_v to_o the_o sine_fw-la of_o the_o height_n of_o the_o stile_n above_o the_o substile_a so_o be_v the_o tang_n of_o the_o arch_n of_o the_o equinoctial_a between_o the_o substile_a and_o the_o hour_n line_n to_o the_o tang_n of_o the_o arch_n of_o the_o circle_n of_o your_o dial_n plain_a between_o the_o substile_a and_o that_o low_a line_n or_o else_o you_o may_v without_o calculation_n geometrical_o inscribe_v the_o hour_n line_n in_o dial_n have_v centre_n for_o how_o to_o do_v it_o in_o dial_n not_o have_v centre_n i_o have_v already_o show_v in_o the_o xix_o use_v thus_o describe_v in_o your_o dial_n plain_a a_o line_n for_o the_o stile_n at_o the_o same_o height_n or_o distance_n from_o the_o substile_a that_o the_o true_a stile_n ought_v to_o have_v take_v also_o in_o the_o substile_a as_o in_o reason_n you_o shall_v see_v fit_a a_o point_n and_o through_o it_o draw_v at_o right_a angle_n a_o long_a line_n for_o the_o contingent_a or_o aequinoctial_a intersection_n again_o from_o the_o same_o point_n let_v fall_v a_o perpendicular_a unto_o the_o stile_n the_o length_n of_o this_o perpendicular_a be_v the_o near_a distance_n between_o that_o point_n and_o the_o stile_n and_o it_o be_v also_o the_o distance_n of_o the_o centre_n of_o the_o aequinoctial_a from_o that_o point_n measure_v it_o therefore_o upon_o the_o substile_a the_o contrary_a way_n from_o the_o centre_n of_o the_o dial_n and_o have_v thus_o the_o centre_n of_o the_o aequinoctial_a describe_v thereupon_o towards_o the_o contingent_a line_n one_o half_a of_o the_o aequinoctial_a circle_n which_o if_o the_o substile_a be_v the_o meridian_n or_o 12_o a_o clock_n line_n of_o your_o dial_n you_o must_v begin_v to_o divide_v into_o hour_n at_o the_o substile_a but_o if_o the_o substile_a and_o meridian_n of_o your_o dial_n be_v several_a line_n apply_v a_o ruler_n to_o the_o centre_n of_o the_o aequinoctial_a and_o to_o the_o intersection_n of_o the_o 12_o a_o clock_n line_n with_o the_o contingent_a and_o there_o draw_v a_o line_n this_o line_n shall_v be_v the_o meridian_n of_o the_o aequinoctial_a at_o which_o you_o must_v begin_v to_o divide_v the_o aequinoctial_a circle_n into_o hour_n both_o way_n then_o apply_v a_o ruler_n unto_o the_o centre_n of_o the_o aequinoctial_a &_o every_o one_o of_o those_o division_n where_o the_o ruler_n in_o every_o place_n shall_v cut_v the_o contingent_a line_n there_o make_v a_o mark_n and_o last_o through_o every_o one_o of_o those_o mark_n from_o the_o centre_n of_o the_o dial_n draw_v the_o hour_n line_n themselves_o and_o if_o in_o any_o hour_n line_n it_o shall_v happen_v that_o the_o ruler_n so_o apply_v will_v not_o reach_v to_o intersecat_n the_o contingent_a line_n you_o may_v thus_o help_v yourself_o which_o rule_n also_o may_v serve_v you_o to_o find_v the_o meridian_n of_o the_o aequinoctial_a as_o often_o as_o the_o intersection_n of_o the_o meridian_n of_o the_o dial_n with_o the_o contingent_a fall_v without_o your_o paper_n or_o plain_a draw_v the_o hour_n line_n as_o far_o as_o it_o will_v go_v and_o take_v with_o your_o compass_n the_o distance_n of_o the_o intersection_n point_n of_o the_o contingent_a with_o the_o substile_a both_o from_o the_o centre_n of_o the_o dyal_n &_o from_o the_o centre_n of_o the_o aequinoctial_a and_o take_v at_o all_o adventure_n a_o point_n in_o the_o contingent_a line_n on_o that_o side_n in_o which_o the_o hour_n line_n be_v measure_n from_o that_o point_n on_o the_o contingent_a both_o those_o distance_n and_o at_o the_o end_n of_o they_o both_o draw_v two_o line_n parallel_v to_o the_o substile_a cross_v the_o contingent_a then_o apply_v a_o ruler_n to_o the_o point_n which_o you_o take_v at_o all_o adventure_n and_o to_o the_o intersection_n of_o the_o parallel_n which_o have_v the_o distance_n of_o that_o centre_n whence_o the_o hour_n line_n give_v proceed_v with_o that_o hour_n line_n where_o the_o ruler_n shall_v cut_v the_o other_o parallel_n make_v a_o prick_n and_o measure_v the_o distance_n between_o that_o prick_n and_o the_o contingent_a upon_o the_o former_a parallel_n on_o the_o other_o side_n of_o the_o contingent_a last_o out_o of_o the_o proper_a centre_n through_o the_o end_n of_o that_o measure_n draw_v a_o line_n which_o shall_v be_v that_o you_o desire_v a_o example_n of_o this_o geometrical_a way_n of_o delineat_a th●_n hour_n line_n you_o shall_v find_v in_o the_o description_n of_o a_o south_n upright_o dial_n decline_v 35_o degr_n and_o recline_a degr_n 41_o min._n 30._o by_o consider_v whereof_o these_o rule_n will_v be_v find_v exceed_v plain_o set_v down_o as_o also_o all_o the_o other_o rule_v and_o observation_n here_o deliver_v to_o one_o that_o be_v any_o whit_n pregnant_a and_o ingenious_a will_v need_v no_o other_o exemplification_n than_o the_o inspection_n of_o the_o instrument_n itself_o and_o of_o these_o several_a dial_n follow_v finis_fw-la a_o north_n dial_n decline_v eastward_n 35_o deg_fw-la recline_v 41_o deg_fw-la 30_o min._n latitude_n 51_o deg_fw-la 30_o min._n a_o horizontall_a dial_n south_n direct_v upright_o south_n direct_v incline_v 24_o deg_fw-la north_n direct_v recline_v 24_o deg_fw-la south_n direct_v recline_v equal_a to_o the_o compliment_n of_o the_o pole_n height_n west_n direct_v upright_o east_n direct_v recline_v 32_o deg_fw-la south_n upright_o decline_v eastward_o 35_o deg_fw-la south_n decline_v westward_o 76_o degr_n recline_v 48_o deg_fw-la south_n decline_v westward_o 61_o degr_n recline_v 21_o deg_fw-la ●½_n min._n the_o translator_n to_o the_o reader_n gentle_a reader_n by_o reason_n of_o my_o absence_n while_o this_o book_n be_v in_o 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