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sine_fw-la of_o 13_o and_o enter_v one_o foot_n of_o it_o on_o the_o sine_fw-la of_o 38_o 28′_n and_o to_o the_o other_o foot_n lay_v the_o thread_n and_o in_o the_o limb_n it_o show_v the_o amplitude_n seek_v to_o be_v 21_o 12′_n by_o change_v the_o place_n of_o the_o two_o middle_a term_n this_o example_n will_v be_v turn_v into_o a_o parralel_n entrance_n lay_v the_o thread_n to_o the_o compliment_n of_o the_o latitude_n in_o the_o limb_n and_o enter_v the_o sine_fw-la of_o the_o declination_n between_o it_o and_o the_o scale_n and_o you_o will_v find_v the_o same_o ark_n in_o the_o sin_n for_o the_o amplitude_n seek_v as_o be_v before_o find_v in_o the_o limb._n such_o proportion_n of_o the_o great_a to_o the_o less_o wherein_o the_o radius_fw-la be_v not_o ingredient_n that_o have_v two_o fix_a or_o constant_a term_n may_v be_v most_o ready_o perform_v by_o the_o single_a line_n of_o sines_n without_o the_o help_n of_o the_o limb._n a_o example_n for_o find_v the_o sun_n 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of_o a_o lesser_a circle_n if_o a_o quadrant_n want_v tangent_n or_o secant_v in_o the_o limb_n but_o may_v admit_v of_o a_o sine_fw-la from_o the_o centre_n the_o tangent_fw-la and_o secant_fw-la of_o the_o latitude_n &c_n &c_n may_v be_v take_v out_o by_o what_o have_v be_v assert_v to_o half_a the_o common_a radius_fw-la and_o mark_v on_o the_o limb_n and_o the_o quadrant_n thereby_o fit_v to_o perform_v most_o of_o the_o proposition_n of_o the_o sphere_n in_o one_o latitude_n and_o how_o to_o supply_v the_o defect_n of_o a_o line_n of_o verse_v sin_n in_o the_o limb_n shall_v afterward_o be_v show_v what_o have_v be_v speak_v concern_v a_o line_n of_o sines_n graduate_v on_o a_o quadrant_n from_o the_o centre_n may_v by_o help_n of_o the_o equal_a limb_n be_v perform_v without_o it_o 1._o a_o proportional_a sine_fw-la may_v be_v take_v off_o to_o any_o diminutive_a radius_fw-la by_o the_o definition_n of_o sines_n the_o right_a sine_fw-la of_o a_o arch_n be_v a_o line_n fall_v from_o the_o end_n of_o that_o arch_n perpendicular_o to_o the_o radius_fw-la draw_v to_o the_o other_o end_n of_o the_o say_a arch_n so_o the_o line_n h_o k_n fall_v perpendicular_o on_o the_o radius_fw-la f_o g_o shall_v be_v the_o sine_fw-la of_o the_o arch_n h_o g_o and_o by_o the_o same_o definition_n the_o line_n g_o i_o fall_v perpendicular_o on_o the_o radius_fw-la f_o h_n shall_v also_o be_v the_o sine_fw-la of_o the_o say_a arch_n and_o whether_o the_o radius_fw-la be_v big_a or_o lesser_a this_o definition_n be_v common_a but_o the_o line_n g_o i_o on_o a_o quadrant_n represent_v the_o near_a distance_n from_o the_o radius_fw-la to_o the_o thread_n therefore_o a_o sine_fw-la may_v be_v take_v off_o from_o the_o limb_n to_o any_o diminutive_a radius_fw-la to_o perform_v which_o enter_v the_o length_n or_o radius_fw-la propose_v down_o the_o straight_a line_n that_o come_v from_o the_o centre_n of_o the_o quadrant_n and_o limit_n the_o limb_n observe_v where_o the_o compass_n 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equidistant_a one_o from_o another_o but_o have_v determine_v the_o distance_n between_o the_o two_o extreme_a latitude_n to_o which_o they_o be_v fit_v for_o the_o the_o large_a sine_fw-la it_o will_v hold_v as_o the_o difference_n of_o the_o secant_v of_o the_o two_o extreme_a latitude_n it_o to_o the_o distance_n between_o the_o line_n fit_v thereto_o so_o be_v the_o difference_n of_o the_o secant_v of_o the_o lesser_a extreme_a latitude_n and_o any_o other_o intermediate_v latitude_n to_o the_o distance_n thereof_o from_o the_o lesser_a extreme_a and_o so_o for_o the_o lesser_a sine_fw-la continue_v the_o other_o way_n have_v place_v the_o two_o extreme_n under_o the_o two_o former_a extreme_n to_o place_v the_o imtermediate_v line_n the_o canon_n will_v be_v as_o the_o difference_n of_o the_o sin_n of_o the_o two_o extreme_a latitude_n be_v to_o the_o distance_n between_o the_o line_n fit_v thereto_o so_o be_v the_o difference_n of_o the_o sin_n of_o the_o lesser_a extreme_a 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zenith_n distance_n at_o the_o hour_n of_o six_o and_o of_o half_a his_o zenith_n distance_n to_o any_o other_o propose_v altitude_n or_o depression_n then_o as_o the_o sine_fw-la of_o the_o four_o arch_n be_v to_o the_o sine_fw-la of_o the_o sum_n so_o be_v the_o sine_fw-la of_o the_o difference_n to_o the_o sine_fw-la of_o the_o hour_n from_o six_o towards_o noon_n or_o midnight_n according_a as_o the_o altitude_n or_o depression_n be_v great_a or_o lesser_a than_o the_o altitude_n or_o depression_n at_o six_o observe_v that_o the_o sine_fw-la of_o a_o arch_n great_a than_o a_o quadrant_n be_v the_o sine_fw-la of_o that_o ark_n compliment_n to_o a_o semicircle_n of_o the_o star_n place_v upon_o the_o quadrant_n below_o the_o projection_n all_o the_o star_n place_v upon_o the_o projection_n be_v such_o as_o fall_v between_o the_o tropic_n and_o the_o hour_n may_v be_v find_v by_o they_o with_o the_o projection_n as_o in_o the_o use_n of_o the_o small_a quadrant_n which_o may_v also_o 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the_o star_n hour_n must_v be_v always_o reckon_v from_o the_o meridian_n it_o be_v last_o upon_o in_o this_o example_n it_o will_v be_v 5_o minute_n past_o 9_o feré_fw-la of_o the_o quadrant_n of_o ascension_n on_o the_o backside_n this_o quadrant_n be_v divide_v into_o 24_o hour_n with_o their_o quarter_n and_o subdivision_n and_o serve_v to_o give_v the_o right_a ascension_n of_o a_o star_n as_o in_o the_o small_a quadrant_n to_o be_v cast_v up_o by_o the_o pen._n it_o also_o serve_v to_o find_v the_o true_a hour_n of_o the_o night_n with_o compass_n first_o have_v find_v the_o star_n hour_n take_v the_o distance_n on_o the_o quadrant_n of_o ascension_n in_o the_o same_o 12_o hour_n between_o the_o star_n and_o the_o sun_n ascension_n give_v by_o the_o foreside_n of_o the_o quadrant_n the_o say_a extent_n shall_v reach_v from_o the_o star_n hour_n to_o the_o true_a hour_n of_o the_o night_n and_o the_o foot_n of_o the_o compass_n always_o fall_v upon_o the_o quadrant_n which_o 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do_v also_o represent_v the_o tangent_fw-la of_o the_o angle_n at_o a_o therefore_o seek_v the_o natural_a sine_fw-la of_o the_o ark_n c_o d_o in_o the_o table_n of_o natural_a tangent_n and_o the_o ark_n correspond_v thereto_o will_v give_v the_o quantity_n of_o the_o angle_n d_o a_o c_o then_z because_o the_o point_n a_o fall_n in_o the_o circumference_n of_o the_o circle_n where_o a_o angle_n be_v but_o half_a so_o much_o as_o it_o be_v at_o the_o centre_n by_o 31_o prop._n 3._o euc._n double_a the_o angle_n find_v and_o from_o a_o quadrant_n divide_v into_o 90_o equal_a part_n and_o their_o subdivision_n by_o help_n of_o a_o table_n so_o make_v may_v the_o quadrant_n of_o latitude_n be_v accurate_o
it_o will_v be_v for_o there_o be_v give_v the_o radius_fw-la c_o d_o and_o the_o tangent_fw-la b_o e_o the_o two_o first_o term_n of_o the_o proportion_n with_o the_o line_n c_o b_o the_o sum_n of_o the_o three_o and_o four_o term_n to_o find_v out_o the_o say_a term_n respective_o and_o it_o will_v hold_v by_o compound_v the_o proportion_n as_o the_o sum_n of_o the_o first_o and_o second_o term_n be_v to_o the_o second_o term_n so_o be_v the_o sum_n of_o the_o three_o and_o four_o term_n to_o the_o four_o term_n that_o be_v as_o c_z d_o +_o b_o e_o be_v to_o b_o e_o so_o be_v c_o f_o +_o f_o b_o =_o c_o b_o to_o f_o b_o see_v 18_o prop._n of_o 5_o of_o euclid_n or_o page_n 18_o of_o the_o english_a clavis_fw-la mathematicae_fw-la of_o the_o famous_a and_o learned_a mr_n oughtre_v after_o the_o same_o manner_n be_v the_o line_n sol_fw-mi or_o proportional_a sin_n make_v that_o be_v also_o such_o a_o line_n that_o any_o ark_n be_v assume_v in_o it_o to_o be_v a_o sine_fw-la the_o distance_n from_o that_o ark_n to_o the_o other_o end_n of_o the_o diameter_n shall_v be_v the_o radius_fw-la thereto_o a_o demonstration_n to_o prove_v that_o the_o line_n of_o hour_n and_o latitude_n will_v joint_o prick_v off_o the_o hour_n distance_n in_o the_o same_o angle_n as_o if_o they_o be_v calculate_v and_o prick_v off_o by_o chord_n draw_v the_o two_o line_n a_o b_o and_o c_o b_o cross_v one_o another_o at_o right_a angle_n at_o b_o and_o prick_v off_o b_o c_z the_o quantity_n of_o any_o ark_n out_o of_o the_o line_n of_o latitude_n and_o then_o fit_a in_o the_o scale_n of_o hour_n so_o that_o one_o end_n of_o it_o meet_v with_o the_o point_n c_o the_o other_o may_v meet_v with_o the_o other_o leg_n of_o the_o right_a angle_n at_o a_o from_o whence_o draw_v a_o e_o parralel_n to_o b_o c_o so_o a_o b_o be_v become_v radius_fw-la b_o c_o be_v the_o sine_fw-la of_o the_o arch_n first_o prick_v down_o from_o the_o line_n of_o latitude_n from_o the_o point_n b_o through_o any_o 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the_o second_o so_o the_o radius_fw-la to_o a_o four_o again_o as_o the_o radius_fw-la be_v to_o that_o four_o so_o be_v the_o three_o term_n give_v to_o the_o four_o proportional_a seek_v in_o illustrate_v the_o matter_n i_o shall_v make_v use_n of_o that_o theorem_n for_o vary_v of_o proportion_n that_o the_o tangent_n of_o arch_n and_o the_o tangent_n of_o their_o compliment_n be_v in_o reciprocal_a proportion_n as_o tangent_fw-la 23_o to_z tangent_fw-la 35_o so_o tangent_fw-la 55_o to_o the_o tangent_fw-la of_o 67d._o in_o work_v of_o this_o proportion_n the_o last_o term_n may_v be_v find_v to_o the_o equal_a semicircle_n or_o on_o the_o diameter_n 1._o in_o the_o semicircle_n extend_v the_o thread_n through_o 23_o on_o the_o diameter_n and_o through_o 3â—_n in_o the_o semicircle_n and_o where_o it_o intersect_v the_o circle_n on_o the_o opposite_a side_n there_o hold_v one_o end_n of_o it_o then_o extend_v the_o other_o part_n of_o it_o over_o 55_o in_o the_o diameter_n and_o 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proportion_n derive_v from_o the_o 16_o case_n of_o right_a angle_a spherical_a triangle_n have_v the_o radius_fw-la ingredient_n will_v be_v wrought_v without_o any_o motion_n of_o the_o thread_n a_o example_n for_o find_v the_o sun_n azimuth_n at_o the_o hour_n of_o 6._o as_o the_o radius_fw-la to_o the_o cousin_n of_o the_o latitude_n so_o the_o tangent_fw-la of_o the_o declination_n to_o the_o tangent_fw-la of_o the_o azimuth_n from_o the_o vertical_a towards_o midnight_n meridian_n extend_v the_o thread_n over_o the_o compliment_n of_o the_o latitude_n in_o the_o upper_a quadrant_n and_o over_o the_o declination_n in_o the_o semicircle_n and_o on_o the_o diameter_n it_o show_v the_o azimuth_n seek_v so_o when_o the_o sun_n have_v 15_o of_o declination_n his_o
quadrant_n of_o latitude_n whereto_o belong_v the_o two_o parallel_n line_n of_o sines_n in_o the_o opposite_a quadrant_n the_o upermost_a be_v extend_v across_o the_o quadrant_n of_o latitude_n the_o proportion_n not_o have_v the_o radius_fw-la ingredient_n and_o be_v of_o the_o great_a to_o the_o less_o account_v the_o first_o term_n in_o the_o line_n sol_fw-mi and_o the_o second_o in_o the_o upper_a sine_fw-la extend_v the_o thread_n through_o they_o and_o where_o it_o intersect_v the_o opposite_a parallel_n hold_v it_o then_o lay_v the_o thread_n to_o the_o three_o term_n in_o the_o line_n sol_fw-mi and_o it_o will_v intersect_v the_o four_o proportional_a on_o the_o upper_a parallel_n as_o the_o sine_fw-la of_o 30_o to_z the_o sine_z of_o any_o arch_n so_o be_v the_o cousin_n of_o that_o arch_n to_o the_o sine_fw-la of_o the_o double_a arch_n and_o the_o converse_n by_o try_v this_o canon_n the_o use_n of_o these_o line_n will_v be_v sudden_o attain_v example_n as_o the_o sine_fw-la of_o 30_o to_z the_o sine_z of_o 20_o so_o be_v the_o sine_fw-la of_o 70_o to_z the_o sine_z of_o 40d._o but_o if_o it_o be_v of_o the_o less_o to_o the_o great_a the_o answer_n must_v be_v find_v on_o the_o line_n sol._n account_v the_o first_o term_n on_o the_o upper_a sine_fw-la and_o the_o second_o in_o the_o line_n sol_fw-mi and_o hold_v the_o thread_n at_o the_o intersection_n of_o the_o opposite_a parallel_n then_o lay_v the_o thread_n to_o the_o three_o term_n on_o the_o uper_n parallel_n and_o on_o the_o line_n sol_fw-mi it_o will_v intersect_v the_o four_o proportional_a if_o it_o be_v less_o than_o the_o radius_fw-la but_o proportion_n have_v the_o radius_fw-la ingredient_n will_v be_v wrought_v without_o any_o motion_n of_o the_o thread_n as_o the_o cousin_n of_o the_o latitude_n to_o radius_fw-la so_o be_v the_o sine_fw-la of_o the_o declination_n to_o the_o sine_fw-la of_o the_o amplitude_n so_o in_o our_o latitude_n of_o london_n when_o the_o declination_n 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7._o also_o proportion_n out_o the_o tangent_fw-la of_o 30_o and_o prick_v it_o down_o from_o a_o to_o 4_o and_o from_o b_o to_z 8_o and_o draw_v line_n into_o the_o centre_n and_o so_o the_o hour-line_n be_v finish_v and_o for_o those_o that_o fall_v above_o the_o 6_o of_o clock_n line_n they_o be_v only_o the_o opposite_a hour_n continue_v after_o the_o like_a manner_n be_v the_o half_n and_o quarter_n to_o be_v prick_v down_o last_o by_o chord_n prick_v off_o the_o style_v height_n equal_a to_o the_o latitude_n of_o the_o place_n and_o let_v it_o be_v place_v to_o its_o due_a elevation_n over_o the_o meridian_n line_n of_o upright_o decliner_n divers_a ark_n for_o such_o plain_n be_v to_o be_v calculate_v and_o may_v be_v find_v on_o the_o circle_n before_o describe_v 1._o the_o substiles_a distance_n from_o the_o meridian_n by_o the_o substilar_a line_n be_v mean_v a_o line_n over_o which_o the_o style_n or_o cock_n of_o the_o dyal_n direct_o hang_v in_o its_o near_a distance_n from_o the_o plain_a by_o some_o term_v the_o line_n of_o deflexion_n and_o be_v the_o ark_n of_o the_o plain_a between_o the_o meridian_n of_o the_o plain_a and_o the_o meridian_n of_o the_o place_n the_o distance_n thereof_o from_o the_o hour-line_n of_o 12_o be_v to_o be_v find_v by_o this_o proportion_n as_o the_o radius_fw-la to_o the_o sine_fw-la of_o the_o plain_n declination_n so_o the_o cotangent_fw-la of_o the_o latitude_n to_o the_o tangent_fw-la of_o the_o substile_a from_o the_o meridian_n 2._o for_o the_o angle_n of_o 12_o and_o 6._o a_o ark_n use_v when_o the_o hour-line_n be_v prick_v down_o from_o the_o meridian_n line_n in_o a_o triangle_n or_o parallellogram_n and_o not_o from_o
the_o substile_a without_o collect_v angle_n at_o the_o pole_n as_o the_o radius_fw-la be_v to_o the_o sine_fw-la of_o the_o plain_n declination_n so_o be_v the_o tangent_fw-la of_o the_o latitude_n to_o the_o tangent_fw-la of_o a_o ark_n the_o compliment_n whereof_o be_v the_o angle_n of_o 12_o and_o 6._o 3._o inclination_n of_o meridian_n be_v a_o ark_n of_o the_o equinoctial_a between_o the_o meridian_n of_o the_o plain_a and_o the_o meridian_n of_o the_o place_n or_o it_o be_v a_o angle_n or_o space_n of_o time_n elapse_v between_o the_o passage_n of_o the_o shadow_n of_o the_o style_n from_o the_o substilar_a line_n into_o the_o meridian_n line_n by_o some_o term_v the_o plain_n difference_n of_o longitude_n and_o not_o improper_o for_o it_o show_v in_o what_o longitude_n from_o the_o meridian_n where_o the_o plain_n be_v the_o say_a plain_n will_v become_v a_o horizontal_n dyal_n and_o the_o style_n height_n show_v the_o latitude_n this_o ark_n be_v use_v in_o calculate_v hour_n distance_n by_o the_o table_n and_o in_o prick_v down_o dial_n by_o the_o line_n of_o latitude_n and_o hour_n from_o the_o substile_a as_o the_o radius_fw-la be_v to_o the_o sine_fw-la of_o the_o latitude_n so_o the_o cotangent_fw-la of_o the_o plain_n declination_n to_o the_o cotangent_fw-la of_o the_o inclination_n of_o meridian_n or_o as_o the_o sine_fw-la of_o the_o latitude_n to_o radius_fw-la so_o be_v the_o tangent_fw-la of_o the_o plain_n declination_n to_o the_o tangent_fw-la of_o inclination_n of_o meridian_n 4._o the_o style_n height_n above_o the_o substile_a as_o the_o radius_fw-la be_v to_o the_o cousin_n of_o the_o latitude_n so_o be_v the_o cousin_n of_o the_o plain_n declination_n to_o the_o sine_fw-la of_o the_o style_n height_n or_o the_o substiles_a distance_n be_v know_v as_o the_o radius_fw-la to_o the_o sine_fw-la of_o the_o substiles_a distance_n from_o the_o meridian_n so_o be_v the_o cotangent_fw-la of_o the_o declination_n to_o the_o tangent_fw-la of_o the_o 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proportion_n be_v sufficient_a for_o all_o plain_n to_o find_v the_o like_a ark_n without_o have_v any_o more_o if_o the_o manner_n of_o refer_v decline_a recline_a incline_v plain_n to_o a_o new_a latitude_n and_o a_o new_a declination_n in_o which_o they_o shall_v stand_v as_o upright_a plain_n be_v but_o well_o explain_v for_o east_n or_o west_n recline_v incline_v plain_n their_o new_a latitude_n be_v the_o compliment_n of_o their_o old_a latitude_n and_o their_o new_a declination_n be_v the_o compliment_n of_o their_o reclination_n inclination_n which_o i_o count_v always_o from_o the_o zenith_n and_o upon_o such_o a_o supposition_n take_v their_o new_a latitude_n and_o declination_n those_o that_o will_v try_v shall_v find_v that_o these_o proportion_n will_v calculate_v all_o the_o ark_n necessary_a to_o such_o dial_n so_o if_o a_o upright_a plain_n decline_v 25_o in_o our_o latitude_n of_o london_n from_o the_o meridian_n the_o substiles_a distance_n from_o the_o meridian_n be_v 18_o 34′_n the_o angle_n of_o 12_o and_o 6_o be_v 62_o 00_o the_o inclination_n of_o meridian_n be_v 30_o 47_o the_o style_n height_n be_v 34_o 19_o to_o delineate_v the_o same_o dial_n from_o the_o substile_a by_o the_o line_n of_o latitude_n and_o scale_n of_o hour_n in_o a_o equicrutal_a triangle_n to_o draw_v a_o upright_o decliner_n an_o upright_o south_n plain_a for_o the_o latitude_n of_o london_n decline_a 25_o eastward_n to_o prick_v down_o this_o dial_n by_o the_o line_n of_o latitude_n and_o scale_n of_o hour_n in_o a_o isoceles_a triangle_n draw_z c_z 12_o the_o meridian_n line_n perpendicular_a to_o the_o horizontal_n line_n of_o the_o plain_a and_o with_o a_o line_n of_o chord_n make_v the_o angle_n f_o c_o 12_o equal_a to_o the_o substiles_a distance_n from_o the_o meridian_n and_o draw_v the_o line_n f_o c_o for_o the_o substile_a draw_v the_o line_n b_o a_o perpendicular_a thereto_o and_o pass_v through_o the_o centre_n at_o c_o and_o out_o of_o the_o line_n of_o 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true_a hour-line_n require_v on_o this_o side_n the_o substile_a again_o fit_v in_o the_o scale_n of_o hour_n from_o b_o to_o f_o count_v from_o that_o end_n at_o b_o the_o former_a ark_n of_o time_n ho_o min_n  _fw-fr 00_o 03_o from_o b_o to_z 4_o 1_o 3_o 5_o 2_o 3_o 6_o 3_o 3_o 7_o 4_o 3_o 8_o 5_o 3_o 9_o and_o make_v point_n at_o the_o termination_n through_o which_o draw_v line_n into_o the_o centre_n and_o they_o shall_v be_v the_o hour_n line_n require_v on_o the_o other_o side_n the_o substile_a the_o like_a must_v be_v do_v for_o the_o half_n and_o quarter_n get_v the_o difference_n between_o the_o half_a hour_n next_z lesser_a in_o this_o example_n 22_o 30′_n under_o the_o ark_n call_v the_o inclination_n of_o meridian_n the_o difference_n be_v 1_o 17′_n in_o time_n 33′_n near_o to_o be_v continual_o augment_v a_o hour_n at_o a_o time_n and_o so_o prick_v off_o as_o before_o be_v do_v for_o the_o whole_a hour_n by_o three_o facile_a proportion_n may_v be_v find_v the_o style_n height_n the_o inclination_n of_o meridian_n and_o the_o substiles_a distance_n from_o the_o plain_n perpendicular_a for_o all_o plain_n decline_a recline_a or_o incline_v which_o be_v sufficient_a to_o prick_v off_o the_o dyal_n after_o the_o manner_n here_o describe_v which_o must_v be_v refer_v to_o another_o place_n if_o the_o scale_n of_o hour_n reach_v above_o the_o plain_a as_o at_o b_o so_o that_o b_o c_o can_v be_v prick_v down_o then_o may_v a_o angle_n be_v prick_v off_o with_o chord_n on_o the_o upper_a side_n the_o substile_a equal_a to_o the_o angle_n f_o c_o a_o on_o the_o under_o side_n and_o thereby_o the_o scale_n of_o hour_n lay_v in_o its_o true_a situation_n have_v first_o find_v the_o point_n f_o on_o the_o under_o side_n to_o prick_v down_o the_o former_a dyal_n in_o a_o rectangular_a ☉_o blong_v or_o long_o square_a figure_n from_o the_o substile_a have_v set_v off_o the_o substilar_a f_o c_o assume_v any_o distance_n in_o it_o as_o at_o f_o to_o be_v the_o radius_fw-la and_o through_o the_o fame_n at_o right_a angle_n draw_v the_o line_n e_o f_o d_o then_o have_v make_v f_o c_o any_o distance_n radius_fw-la take_v out_o the_o sine_fw-la of_o the_o style_n height_n to_o the_o same_o radius_fw-la and_o enter_v it_o at_o the_o end_n of_o the_o scale_n of_o three_o hour_n make_v it_o the_o radius_fw-la of_o a_o tangent_fw-la and_o proportion_n out_o tangent_n to_o 3′_n and_o set_v they_o off_o from_o f_o to_o 10_o 1_o hour_n 3_o and_o set_v they_o off_o from_o f_o to_o g_z 2_o 3_o and_o set_v they_o off_o from_o f_o to_o h_n again_o take_v out_o the_o tangent_n of_o the_o compliment_n of_o the_o first_o ark_n increase_v it_o each_o time_n by_o the_o augmentation_n of_o a_o hour_n namely_o 57′_n and_o prick_v
they_o from_o f_o to_o i_o and_o from_o the_o point_v 1_o ho._n 57_o and_o prick_v they_o from_o f_o to_o k_o and_o from_o the_o point_v 2_o 57_o and_o prick_v they_o from_o f_o to_o e_z and_o from_o the_o point_n thus_o find_v draw_v line_n into_o the_o centre_n then_o for_o the_o other_o side_n of_o the_o square_n make_v c_o f_o the_o radius_fw-la of_o the_o dyall_a tangent_fw-la of_o 3_o hour_n and_o proportion_n out_o tangent_n to_o the_o former_a ark_n namely_o 3′_n and_o prick_v they_o from_o b_o to_o p_o also_o to_o the_o latter_a ark_n 57′_n and_o prick_v they_o from_o a_o to_o n_o 1_o ho._n 3_o and_o prick_v they_o from_o b_o to_z o_o also_o to_o the_o latter_a arks._n 1_o h._n 57_o and_o prick_v they_o from_o a_o to_o m_n 2_o 3_o and_o prick_v they_o from_o b_o to_z l_o also_o to_o the_o latter_a arks._n 2_o 57_o and_o prick_v they_o from_o a_o to_o d_o and_o draw_v line_n from_o these_o termination_n into_o the_o centre_n and_o the_o hour-line_n be_v finish_v after_o the_o same_o manner_n must_v the_o half_n and_o quarter_n be_v finish_v and_o how_o this_o trouble_n in_o proportion_v out_o the_o tangent_n may_v be_v shun_v without_o draw_v any_o line_n on_o the_o plain_a but_o the_o hour-line_n may_v be_v speak_v to_o hereafter_o whereby_o this_o way_n of_o dyall_v and_o those_o that_o follow_v will_v be_v render_v more_o commodious_a last_o the_o style_n may_v be_v prick_v off_o with_o chord_n or_o take_v b_o c_o and_o set_v one_o foot_n in_o f_o with_o that_o extent_n sweep_v the_o touch_n of_o a_o occult_a arch_n and_o from_o c_o draw_v a_o line_n just_o touch_v the_o outward_a extremity_n of_o the_o say_a arch_n and_o it_o shall_v prick_v off_o the_o angle_n of_o the_o style_n height_n above_o the_o substile_a to_o prick_v off_o the_o former_a dyal_n in_o a_o oblique_a parallellogram_n or_o scalenon_fw-mi alias_o unequal_a side_v triangle_n from_o the_o meridian_n first_o in_o a_o oblique_a parallellogram_n draw_v ce_fw-fr the_o meridian_n line_n 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distance_n sweep_v occult_a arch_n therewith_o intersect_n will_v find_v the_o points_z h_z and_o g_z limit_v the_o angle_n of_o the_o parallellogram_n then_z making_z e_z h_z or_o c_z d_o radius_fw-la proportion_n out_o the_o tangent_n of_o 15_o and_o prick_v they_o down_o from_o e_z to_z 1_o and_o 11_o and_o 30_o and_o prick_v they_o down_o from_o e_z to_z 2_o and_o 10_o and_o draw_v line_n into_o the_o centre_n through_o those_o point_n and_o the_o angular_a point_n of_o the_o parallellogram_n at_o h_n and_o g_o and_o there_o will_v be_v 6_o hour_n draw_v beside_o the_o meridian_n line_n or_o hour_n line_n of_o 12._o then_z making_z d_o g_z radius_fw-la proportion_n out_o the_o tangent_fw-la of_o 15_o and_o prick_v it_o down_o from_o d_o upward_o to_o 5_o and_o downward_z to_z 7_o also_o proportion_n out_o the_o tangent_fw-la of_o 30_o and_o prick_v it_o from_o d_o to_z 8_o and_o from_o f_o to_o 4_o and_o draw_v line_n into_o the_o centre_n and_o so_o the_o hour_n line_n be_v finish_v after_o the_o same_o manner_n be_v the_o half_n and_o quarter_n to_o be_v proportion_v out_o and_o prick_v down_o and_o if_o this_o work_n be_v to_o be_v do_v upon_o the_o plain_n itself_o the_o parallel_n f_o h_n will_v excur_v above_o the_o plain_a in_o that_o case_n because_o the_o parallel_n distance_n of_o f_o h_n from_o the_o meridian_n be_v equal_a to_o the_o parallel_a distance_n of_o d_o g_o the_o space_n g._n 8._o may_v be_v set_v from_o h_n to_o 4_o and_o so_o all_o the_o hour_n line_n prick_v down_o to_o prick_v down_o this_o dyal_n in_o a_o scalenon_fw-mi or_o unequal_a side_v triangle_n from_o the_o meridian_n from_o e_z to_z d_o draw_v the_o straight_a line_n d_o e_o and_o from_o the_o same_o point_n draw_v another_o to_o f_o and_o each_o of_o they_o the_o former_a hour_n line_n be_v first_o draw_v shall_v thereby_o be_v divide_v into_o a_o line_n of_o double_a tangent_n or_o scale_v of_o 6_o hour_n such_o a_o one_o as_o be_v in_o the_o diameter_n of_o the_o circle_n on_o this_o quadrant_a or_o on_o the_o right_a edge_n of_o the_o foreside_n and_o therefore_o by_o help_n of_o either_o of_o they_o line_n if_o it_o be_v require_v to_o prick_v down_o the_o dyal_n it_o may_v be_v do_v by_o proportion_v they_o out_o take_v the_o extent_n d_o e_o and_o prick_v it_o from_o one_o extremity_n of_o the_o diameter_n in_o the_o semicircle_n on_o the_o quadrant_a and_o from_o the_o point_n of_o termination_n draw_v a_o line_n with_o black_a lead_n to_o the_o other_o extremity_n which_o will_v easy_o rub_v out_o again_o either_o with_o bread_n or_o leather_n pare_n and_o take_v the_o near_a distance_n from_o 15_o of_o the_o diameter_n to_o the_o say_a line_n and_o the_o say_a extent_n 30_o of_o the_o diameter_n to_o the_o say_a line_n and_o the_o say_a extent_n 45_o of_o the_o diameter_n to_o the_o say_a line_n and_o the_o say_a extent_n shall_v reach_v from_o e_z to_z 11_o and_o from_o d_o to_z 7_o shall_v reach_v from_o e_z to_z 10_o and_o from_o d_o to_z 8_o shall_v reach_v from_o e_z to_z 9_o and_o from_o d_o to_z 9_o and_o the_o like_a must_v be_v do_v for_o the_o line_n e_o f_o enter_v that_o in_o the_o semicirle_n as_o before_o or_o without_o draw_v line_n on_o the_o quadrant_a if_o a_o hole_n be_v drill_v at_o one_o end_n of_o the_o diameter_n and_o a_o thread_n fit_v into_o it_o lay_v the_o thread_n over_o the_o point_n in_o the_o diameter_n and_o take_v the_o near_a distance_n thereto_o last_o from_o a_o line_n of_o chord_n prick_v off_o the_o substilar_a line_n and_o the_o style_n height_n as_o we_o before_o find_v it_o this_o way_n of_o dyall_v in_o a_o parallellogram_n be_v first_o invent_v by_o john_n ferrereus_n a_o spaniard_n long_v since_o and_o afterward_o large_o handle_v by_o clavius_n who_o demonstrate_v it_o and_o show_v how_o to_o fit_v it_o into_o all_o plain_n whatsoever_o albeit_o they_o decline_v recline_v or_o incline_v without_o refer_v they_o to_o a_o new_a latitude_n the_o triangular_a way_n be_v also_o build_v upon_o the_o same_o demonstration_n and_o be_v already_o publish_v by_o mr_n foster_n in_o his_o posthuma_n for_o it_o be_v no_o other_o than_o dyall_v in_o a_o parallellogram_n if_o the_o meridian_n line_n c_o e_o be_v continue_v upward_o and_o c_o e_o set_n off_o upward_o and_o line_n draw_v from_o the_o point_n so_o find_v to_o d_o and_o e_z shall_v constitute_v a_o parallellogram_n a_o advertisement_n about_o observe_v of_o altitude_n imagine_v a_o line_n draw_v from_o the_o begin_n of_o the_o line_n sol_fw-mi to_o the_o end_n of_o the_o diameter_n and_o therein_o suppose_v a_o pair_n of_o sight_n place_v with_o a_o thread_n and_o bullet_n hang_v from_o the_o begin_n of_o the_o say_a line_n as_o from_o a_o centre_n i_o say_v the_o line_n wherein_o the_o sight_n be_v place_v make_v a_o right_a angle_n with_o the_o line_n of_o sin_n on_o the_o other_o side_n of_o sol_n and_o so_o may_v represent_v a_o quadrant_a the_o equal_a limb_n whereof_o be_v either_o represent_v by_o the_o 90_o of_o the_o equal_a semicirle_n or_o by_o the_o 90_o of_o the_o diameter_n and_o thereby_o a_o altitude_n may_v be_v take_v now_o to_o make_v a_o isoceles_a equicrural_a or_o equal_a legged_a triangle_n make_v of_o three_o straight_a ruler_n the_o long_a whereof_o will_n be_v the_o base_a or_o hipotenusal_a line_n thus_o to_o serve_v for_o a_o quadrant_a to_o take_v altitude_n withal_o will_v be_v much_o cheap_a and_o more_o certain_a in_o wood_n than_o the_o great_a arch_a wooden_a frame_v quadrant_n moreover_o the_o say_a diameter_n line_n supply_v all_o the_o use_n of_o the_o
either_o under_o the_o window_n or_o any_o other_o convenient_a place_n in_o the_o room_n place_v the_o centre_n of_o the_o say_v horizontal_n dial_n in_o the_o centre_n of_o the_o hole_n or_o nodus_fw-la also_o situate_a the_o say_a dial_n exact_o parallel_v to_o the_o horizon_n and_o the_o meridian_n of_o the_o say_a dial_n in_o the_o meridian_n of_o the_o world_n which_o as_o before_o may_v easy_o be_v do_v if_o at_o that_o instant_n you_o know_v the_o true_a hour_n of_o the_o day_n then_o take_v the_o thread_n who_o end_n be_v fix_v in_o a_o point_n in_o the_o direct_a axis_n and_o move_v it_o to_o and_o fro_o until_o the_o say_a thread_n do_v interpose_v between_o your_o eye_n and_o the_o hour-line_n on_o the_o say_v horizontal_n dial_n which_o you_o intend_v to_o draw_v and_o then_o keep_v your_o eye_n at_o that_o situation_n make_v a_o point_n or_o mark_v in_o any_o place_n where_o you_o please_v or_o under_o the_o window_n so_o that_o the_o say_a thread_n or_o string_n may_v 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knot_n augment_v that_o thread_n until_o the_o end_n thereof_o touch_v the_o wall_n or_o ceiling_n and_o there_o make_v a_o mark_n or_o point_n so_o be_v there_o one_o point_n find_v on_o the_o wall_n or_o ceiling_n in_o the_o reflect_v horizon_n of_o the_o world_n then_o i_o begin_v again_o and_o remove_v the_o position_n of_o that_o thread_n which_o go_v overthwart_o the_o room_n either_o high_a or_o low_a at_o pleasure_n still_o have_v regard_n that_o i_o may_v from_o the_o most_o part_n of_o the_o say_a thread_n see_v the_o reflect_v glass_n and_o therein_o the_o same_o horizontal_a thread_n without_o the_o room_n then_o as_o before_z i_o move_v the_o say_a knot_n on_o the_o say_a thread_n to_o &_o fro_o until_o as_o before_o by_o look_v in_o the_o say_a glass_n i_o find_v from_o my_o eye_n the_o say_a knot_n and_o part_n of_o the_o horizontal_n thread_n both_o in_o one_o right_a line_n the_o one_o interpose_v the_o sight_n of_o the_o other_o and_o by_o the_o say_a knot_n i_o 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according_a to_o the_o situation_n of_o the_o glass_n 2_o to_o draw_v the_o reflect_v meridian_n according_a to_o the_o situation_n of_o any_o recline_a glass_n whatsoever_o first_o take_v a_o lath_n or_o thin_a piece_n of_o wood_n of_o any_o convenient_a length_n at_o pleasure_n as_o some_o one_o and_o a_o half_a or_o two_o foot_n long_o and_o at_o each_o end_n thereof_o make_v a_o hole_n the_o one_o to_o hang_v a_o thread_n and_o plummet_n and_o the_o other_o be_v to_o put_v a_o small_a nail_n therein_o to_o fasten_v it_o in_o some_o part_n of_o the_o window_n over_o the_o centre_n of_o the_o glass_n so_o that_o the_o thread_n and_o plummet_n may_v hang_v without_o the_o room_n then_o by_o help_n of_o the_o sun_n azimuth_n you_o may_v draw_v the_o meridian_n line_n as_o before_o as_o if_o the_o glass_n be_v horizontal_a and_o move_v the_o lath_n with_o the_o thread_n and_o plummet_n at_o the_o end_n of_o it_o to_o and_o fro_o until_o the_o thread_n and_o plummet_n be_v in_o the_o 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bring_v it_o just_a to_o touch_v the_o say_a knot_n i_o augment_v that_o thread_n until_o the_o end_n thereof_o touch_v the_o say_a wall_n or_o ceiling_n and_o the_o say_a thread_n also_o touch_v the_o knot_n as_o before_o then_o in_o that_o place_n where_o the_o end_n of_o the_o say_a thread_n touch_v the_o wall_n or_o ceiling_n i_o make_v a_o mark_n which_o mark_n or_o point_n will_v be_v direct_o in_o the_o reflect_a meridian_n of_o the_o world_n according_a to_o the_o situation_n of_o that_o glass_n then_o again_o i_o remove_v that_o thread_n overthwart_o the_o room_n on_o which_o the_o say_a knot_n be_v either_o high_o or_o low_a than_o it_o former_o be_v at_o pleasure_n still_o have_v regard_n that_o from_o some_o part_n of_o the_o say_a thread_n within_o you_o may_v see_v both_o the_o recline_a glass_n and_o the_o perpendicular_a thread_n without_o at_o one_o time_n and_o as_o before_o move_v the_o say_v slip_v knot_n on_o the_o say_a thread_n until_o by_o look_v in_o the_o say_v recline_v glass_n you_o see_v the_o say_a knot_n and_o some_o part_n of_o the_o perpendicular_a thread_n without_o in_o one_o right_a line_n so_o as_o the_o one_o shadow_n or_o hinder_v the_o sight_n of_o the_o other_o as_o before_o which_o knot_n then_o must_v not_o be_v remove_v from_o its_o situation_n then_o take_v that_o thread_n who_o end_n be_v fasten_v in_o the_o glass_n and_o bring_v it_o to_o touch_v that_o knot_n the_o end_n of_o the_o say_a thread_n be_v continue_v to_o touch_v the_o wall_n or_o ceiling_n so_o be_v that_o point_n of_o touch_n on_o the_o ceiling_n another_o point_n find_v in_o the_o reflect_v meridian_n of_o the_o world_n so_o be_v there_o two_o point_n find_v in_o the_o say_v reflect_v meridian_n on_o the_o wall_n or_o ceiling_n by_o which_o if_o a_o thread_n as_o before_o be_v so_o situate_v that_o it_o may_v interpose_v between_o the_o eye_n and_o the_o say_v two_o point_n many_o point_n thereby_o in_o the_o say_v reflect_v meridian_n may_v be_v make_v at_o every_o bend_n or_o angle_n of_o the_o wall_n or_o ceiling_n whereby_o the_o reflect_v meridian_n desire_v may_v be_v draw_v by_o draw_v a_o line_n from_o point_n to_o point_v oblique_o in_o the_o room_n which_o will_v be_v the_o true_a reflect_v meridian_n of_o the_o world_n according_a to_o the_o situation_n of_o that_o glass_n now_o this_o reflect_v horizon_n and_o meridian_n be_v first_o draw_v they_o will_v be_v of_o great_a use_n in_o draw_v the_o hour-line_n together_o with_o all_o the_o furniture_n that_o possible_o can_v be_v draw_v on_o any_o dial_n to_o draw_v the_o reflect_v hour-line_n to_o any_o recline_a glass_n on_o any_o plane_n whatsoever_o that_o the_o sun_n
59_o 17_o 04_o 31_o 15_o 03_o 17_o 21_o day_n november_n ☉_o r._n a._n ☉_o decl._n h._n m._n d._n m._n 1_o 15_o 07_o 17_o 38_o 2_o 15_o 11_o 17_o 54_o 3_o 15_o 15_o 18_o 10_o 4_o 15_o 19_o 18_o 26_o 5_o 15_o 23_o 18_o 41_o 6_o 15_o 27_o 18_o 56_o 7_o 15_o 31_o 19_o 11_o 8_o 15_o 36_o 19_o 26_o 9_o 15_o 40_o 19_o 40_o 10_o 15_o 45_o 19_o 53_o 11_o 15_o 49_o 20_o 07_o 12_o 15_o 53_o 20_o 19_o 13_o 15_o 58_o 20_o 32_o 14_o 16_o 02_o 20_o 44_o 15_o 16_o 07_o 20_o 56_o 16_o 16_o 11_o 21_o 08_o 17_o 16_o 15_o 21_o 19_o 18_o 16_o 19_o 21_o 29_o 19_o 16_o 23_o 21_o 39_o 20_o 16_o 28_o 21_o 49_o 21_o 16_o 32_o 21_o 58_o 22_o 16_o 36_o 22_o 08_o 23_o 16_o 40_o 22_o 16_o 24_o 16_o 44_o 22_o 24_o 25_o 16_o 49_o 22_o 32_o 26_o 16_o 53_o 22_o 39_o 27_o 16_o 57_o 22_o 46_o 28_o 17_o 02_o 22_o 52_o 29_o 17_o 06_o 22_o 58_o 30_o 17_o 11_o 23_o 03_o 31_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr day_n december_n ☉_o r._n a._n ☉_o decl._n h._n m._n d._n m._n 1_o 17_o 15_o 23_o 08_o 2_o 17_o 20_o 23_o 13_o 3_o 17_o 25_o 23_o 17_o 4_o 17_o 29_o 23_o 20_o 5_o 17_o 34_o 23_o 23_o 6_o 17_o 38_o 23_o 26_o 7_o 17_o 42_o 23_o 28_o 8_o 17_o 47_o 23_o 29_o 9_o 17_o 51_o 23_o 30_o 10_o 17_o 56_o 23_o 31_o 11_o 18_o 00_o 23_o 31½_n 12_o 18_o 05_o 23_o 31_o 13_o 18_o 09_o 23_o 30_o 14_o 18_o 14_o 23_o 29_o 15_o 18_o 19_o 23_o 27_o 16_o 18_o 24_o 23_o 25_o 17_o 18_o 28_o 23_o 22_o 18_o 18_o 33_o 23_o 19_o 19_o 18_o 37_o 23_o 15_o 20_o 18_o 41_o 23_o 11_o 21_o 18_o 45_o 23_o 07_o 22_o 18_o 49_o 23_o 02_o 23_o 18_o 54_o 22_o 56_o 24_o 18_o 58_o 22_o 50_o 25_o 19_o 03_o 22_o 43_o 26_o 19_o 07_o 22_o 36_o 27_o 19_o 11_o 22_o 29_o 28_o 19_o 16_o 22_o 21_o 29_o 19_o 20_o 22_o 13_o 30_o 19_o 25_o 22_o 04_o 31_o 19_o 30_o 21_o 55_o a_o rectify_v table_n for_o the_o sun_n declination_n  _fw-fr year_n year_n year_n  _fw-fr 1657_o 1661._o 1665_o 1669_o 1673_o 1659._o 1663._o 1667_o 1671_o 1675_o 1660_o 1664_o 1668_o 1672_o 1676_o month_n min._n min._n min._n january_n 3_o s_o 2_o a_o 5_o a_o 4_o s_z 3_o a_o 7_o a_o 5_o s_z 4_o a_o 9_o a_o february_n 5_o s_z 5_o a_o 10_o a_o 5_o s_z 5_o a_o 11_o a_o 6_o s_z 5_o a_o 11_o a_o march_z 6_o s_z 5_o a_o 13_o s_z 5_o a_o 5_o s_z 12_o a_o 5_o a_o 5_o s_z 12_o a_o april_n 5_o a_o 5_o s_z 11_o a_o 5_o a_o 5_o s_z 10_o a_o 4_o a_o 4_o s_z 9_o a_o may_v 4_o a_o 4_o s_z 8_o a_o 3_o a_o 3_o s_z 6_o a_o 2_o a_o 2_o s_z 4_o a_o june_n 1_o a_o 1_o s_o 2_o a_o 0_o s_o 0_o a_o 0_o s_o 1_o s_z 1_o a_o 3_o s_o july_n 2_o s_z 2_o a_o 5_o s_z 3_o s_z 3_o a_o 7_o s_z 4_o s_z 4_o a_o 9_o s_o august_n 5_o s_z 5_o a_o 10_o s_z 5_o s_z 5_o a_o 11_o s_z 6_o s_z 5_o a_o 12_o s_o september_n 6_o s_z 5_o a_o 13_o s_z 6_o a_o 5_o s_z 13_o a_o 6_o a_o 5_o s_z 12_o a_o october_n 6_o a_o 5_o s_z 12_o a_o 5_o a_o 5_o s_z 11_o a_o 4_o a_o 5_o s_z 9_o a_o novem._n 3_o a_o 4_o s_z 7_o a_o 2_o a_o 3_o s_z 5_o a_o 1_o a_o 2_o s_z 3_o a_o decemb._n 0_o a_o 1_o s_z 1_o a_o 1_o s_o 0_o a_o 1_o s_z 2_o s_z 1_o a_o 3_o s_z the_o use_n of_o the_o rectify_v table_n note_v that_o the_o minute_n under_o the_o respective_a year_n be_v to_o be_v add_v or_o substract_v to_o or_o from_o the_o sun_n declination_n in_o the_o former_a table_n as_o be_v note_v with_o the_o letter_n a_o or_o s_o and_o also_o note_v that_o the_o first_o figure_n in_o each_o month_n stand_v for_o the_o first_o 10_o day_n of_o the_o month_n and_o the_o second_o for_o the_o second_o 10_o day_n &_o the_o three_o for_o the_o last_o 10_o day_n except_o in_o march_n or_o september_n which_o in_o march_n will_v be_v the_o first_o 9_o day_n only_o and_o in_o september_n the_o first_o 12_o day_n example_n i_o will_v know_v the_o sun_n declination_n the_o 15_o day_n of_o may_n 1668._o now_o because_o this_o day_n of_o the_o month_n fall_v in_o the_o second_o 10_o day_n i_o look_v in_o the_o table_n under_o the_o year_n 1663._o and_o right_a against_o may_v you_o shall_v find_v that_o in_o the_o second_o place_n of_o the_o month_n stand_v 6_o a_o which_o show_v i_o that_o i_o must_v add_v 6_o minute_n to_o the_o sun_n declination_n in_o the_o former_a table_n 21_o degree_n 5_o min._n that_o stand_v against_o the_o 15_o day_n of_o may_n and_o then_o i_o find_v that_o the_o sun_n will_v have_v 21_o deg_n 11_o min._n of_o north_n declination_n and_o so_o for_o the_o rest_n which_o will_v never_o differ_v above_o two_o minute_n from_o the_o truth_n but_o seldom_o so_o much_o and_o for_o the_o most_o part_n true_a note_v that_o the_o former_a table_n of_o the_o sun_n declination_n be_v fit_v exact_o for_o the_o year_n 1666._o by_o the_o rule_n mr._n wright_n give_v in_o his_o correction_n of_o error_n and_o from_o his_o table_n and_o may_v indifferent_o serve_v for_o the_o year_n 1658_o 1662._o 1670_o 1674_o without_o any_o sensible_a error_n and_o the_o table_n of_o right_a ascension_n will_v not_o vary_v a_o minute_n of_o time_n in_o many_o year_n finis_fw-la error_n in_o the_o horizontal_n quadrant_n page_n 5_o line_n 6_o in_o a_o italian_a letter_n shall_v not_o have_v be_v distinct_a nor_o in_o another_o letter_n from_o the_o former_a line_n page_n 5._o line_n 9_o for_o quarter_n read_v half_a p._n 5._o l._n 13._o r._n of_o a_o quadrant_a p._n 11._o l._n 7._o r._n 63_o d._n 26′_n p._n 19_o l._n 7._o r._n the_o same_o day_n to_o p._n 23._o l._n 17._o r._n and_o end_n at_o 32′_n past_o 9_o p._n 27._o l._n 7._o for_o n_o r_o r._n n_o z._n p._n 28._o l._n 4._o r._n in_o the_o parallel_n p._n 30._o l._n 9_o &_o l._n 10._o r._n 23_o d._n 31′_n p._n 38._o l._n 4._o r._n be_v to_o the_o sine_fw-la p._n 50._o l._n 5._o r._n whereof_o the_o diameter_n a_o appendix_n touch_v reflective_a dial_v by_o john_n lyon_n professor_n of_o this_o or_o any_o other_o part_n of_o the_o mathematics_n near_o somerset_n house_n in_o the_o strand_n london_n print_v anno_fw-la domini_fw-la 1658._o direct_v dial_v by_o a_o hole_n or_o nodus_fw-la to_o draw_v a_o dial_n under_o any_o window_n that_o the_o sun_n shine_v upon_o by_o help_n of_o a_o thread_n fasten_v in_o any_o point_n of_o the_o direct_a axis_n find_v in_o the_o ceiling_n and_o a_o hole_n in_o any_o pane_n of_o glass_n or_o a_o knob_v or_o nodus_fw-la upon_o any_o side_n of_o the_o window_n or_o window-post_n constructio_fw-la first_o draw_v on_o pasteboard_n or_o other_o material_a a_o horizontal_n dial_n for_o the_o latitude_n propose_v then_o by_o help_n of_o the_o sun_n azimuth_n which_o may_v be_v find_v by_o help_n of_o a_o general_a quadrant_n at_o any_o time_n or_o by_o know_v the_o true_a hour_n of_o the_o day_n with_o the_o help_n of_o the_o say_v horizontal_n dial_n and_o draw_v that_o true_a meridian_n from_o the_o hole_n or_o nodus_fw-la propose_v both_o above_o on_o the_o ceiling_n and_o below_o on_o the_o wall_n and_o floor_n of_o the_o room_n so_o that_o if_o a_o right_a line_n be_v extend_v from_o the_o say_a hole_n or_o nodus_fw-la by_o any_o point_n in_o any_o of_o those_o line_n it_o will_v be_v in_o the_o meridian_n circle_n of_o the_o world_n to_o find_v a_o point_n in_o the_o direct_a axis_n of_o the_o world_n which_o will_v ever_o fall_v to_o be_v in_o the_o say_a meridian_n in_o which_o point_n the_o end_n of_o a_o thread_n be_v to_o be_v fasten_v first_o fix_v the_o end_n of_o a_o thread_n or_o small_a silk_n in_o the_o centre_n of_o the_o hole_n or_o nodus_fw-la and_o move_v the_o other_o end_n thereof_o up_o or_o down_o in_o the_o say_a meridian_n former_o draw_v on_o the_o ceiling_n or_o wall_n until_o by_o apply_v the_o side_n of_o a_o quadrant_n to_o that_o thread_n it_o be_v find_v to_o be_v elevate_v equal_a to_o the_o latitude_n of_o the_o place_n so_o be_v that_o thread_n direct_o situate_v parallel_n to_o the_o axis_n of_o the_o world_n and_o the_o point_n where_o the_o end_n of_o that_o thread_n touch_v the_o meridian_n either_o on_o the_o ceiling_n or_o wall_n be_v that_o point_n in_o the_o direct_a axis_n seek_v for_o wherein_o fix_v one_o end_n of_o a_o thread_n which_o thread_n will_v be_v of_o present_a use_n in_o project_v of_o hour-point_n in_o any_o place_n propose_v then_o to_o find_v the_o hour-point_n