the_o whole_a triangle_n io_o π_n be_v because_o their_o top_n be_v part_n of_o the_o line_n o_o π_n which_o be_v the_o only_a side_n of_o the_o say_a triangle_n that_o show_v the_o hour_n as_o we_o mention_v before_o now_o for_o the_o demonstration_n of_o all_o it_o follow_v in_o the_o next_o operation_n operation_n ii_o how_o to_o describe_v a_o horizontal_n dial_n by_o the_o globe_n for_o the_o elevation_n of_o london_n the_o second_o way_n describe_v a_o circle_n of_o what_o bigness_n you_o please_v and_o draw_v a_o construction_n meridian_n or_o 12_o a_o clock_n line_n throu_fw-fr '_o it_o as_o before_z then_o count_v in_o the_o horizon_n of_o your_o globe_n how_o many_o degree_n there_o be_v between_o the_o hour-circle_n of_o 12_o and_o 1_o or_o which_o be_v the_o same_o thing_n between_o 12_o and_o 11_o and_o you_o will_v find_v their_o number_n to_o be_v about_o 11._o 40′_n these_o place_n on_o both_o side_n of_o your_o say_a meridian_n line_n by_o the_o help_n of_o a_o 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meridian_n dial_n be_v the_o height_n of_o the_o style_n now_o to_o describe_v this_o dial_n geometrical_o it_o be_v yet_o more_o easy_o perform_v for_o if_o you_o draw_v as_o in_o scheme_n 24._o the_o line_n ab_fw-la parallel_n to_o the_o horizon_n and_o then_o take_v a_o point_n in_o the_o middle_n of_o it_o suppose_v k_o do_v but_o prick_v on_o both_o side_n of_o it_o the_o tangent_fw-la of_o 15_o 30_o 45_o 60_o and_o 75_o and_o the_o several_a perpendicular_o draw_v throu_fw-fr these_o prick_n will_v be_v true_a hour-line_n which_o you_o may_v figure_v as_o you_o see_v in_o the_o before_o mention_v 24_o scheme_n and_o as_o for_o the_o style_n the_o tangent_fw-la of_o 45_o or_o distance_n between_o the_o 12_o a_o clock_n line_n and_o that_o of_o 9_o or_o 3_o give_v you_o its_o height_n which_o be_v to_o be_v a_o pin_n or_o gallow_n style_v as_o before_o and_o the_o 12_o a_o clock_n line_v the_o substilar_a operation_n xx._n how_o to_o describe_v a_o direct_a recline_a north_n or_o 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degree_n from_o the_o zenith_n of_o the_o globe_n then_o see_v your_o plane_n have_v a_o southern_a aspect_n and_o so_o lie_v beyond_o your_o say_a zenith_n northward_o move_v your_o string_n till_o it_o cut_v in_o the_o horizon_n 40_o degree_n westward_o from_o the_o northern_a meridian_n or_o back_o part_n of_o the_o 12_o a_o clock_n hour_n circle_n in_o the_o next_o place_n take_v a_o thread_n and_o tie_v it_o about_o your_o globe_n so_o that_o it_o lie_v not_o only_o on_o your_o bead_n but_o cross_n also_o the_o horizon_n at_o 40_o degree_n from_o the_o east_n point_n northward_o and_o 40_o degree_n from_o the_o west_n point_v southward_o the_o say_a thread_n will_v represent_v your_o plane_n recline_v and_o decline_a as_o aforesaid_a or_o in_o short_a fix_v a_o small_a needle_n in_o the_o point_n where_o the_o bead_n lie_v which_o we_o suppose_v at_o a_o in_o sch._n 26._o and_o fasten_v to_o it_o a_o thread_n or_o part_n of_o the_o string_n draw_v it_o over_o the_o horizon_n at_o 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the_o point_n k_o to_o which_o if_o you_o draw_v a_o fair_a line_n from_o the_o centre_n it_o will_v be_v the_o 12_o a_o clock_n line_n of_o your_o dial_n and_o the_o distance_n from_o the_o say_a station_n of_o your_o bead_n or_o needle_n to_o the_o intersection_n of_o the_o thread_n with_o the_o next_o hour-circle_n will_v give_v you_o l_o the_o mark_n of_o the_o 11_o a_o clock_n line_n and_o in_o this_o manner_n you_o must_v run_v over_o all_o other_o intersection_n of_o your_o thread_n and_o hour-circle_n to_o the_o very_a horizon_n on_o both_o side_n of_o the_o globe_n i_o mean_v on_o the_o morning_n and_o evening_n side_n of_o it_o represent_v by_o scheme_n 26_o and_o 27_o and_o place_v their_o distance_n on_o your_o blind_a circle_n on_o both_o side_n of_o the_o aforesaid_a oi_o do_v but_o draw_v line_n to_o they_o from_o the_o centre_n and_o your_o dial_n be_v describe_v and_o here_o you_o must_v observe_v that_o i_o have_v in_o scheme_n 26._o or_o memorandum_n eastern_a face_n 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distance_n between_o each_o point_n and_o a_o in_o any_o great_a circle_n 82._o it_o will_v give_v you_o the_o degree_n or_o distance_n between_o a_o and_o your_o style_n substilar_n and_o each_o hour-line_n and_o consequent_o perform_v the_o second_o way_n as_o we_o have_v all_o along_o mention_v of_o describe_v dial_n by_o the_o globe_n as_o for_o the_o demonstration_n of_o this_o dial_n what_o we_o have_v former_o demonstration_n say_v about_o the_o rest_n prove_v it_o also_o for_o suppose_v that_o the_o thread_n represent_v true_o your_o plane_n and_o that_o the_o hour_n line_n of_o a_o dial_n be_v as_o i_o have_v show_v you_o all_o along_o the_o several_a intersection_n of_o the_o hour-circle_n with_o the_o plane_n this_o dial_n must_v be_v true_a
the_o horizontal_n draught_n with_o the_o figure_n 12_o as_o the_o meridian_n line_n and_o 2_o and_o 10_o min._n with_o figureâ—_n and_o so_o on_o all_o along_o whereas_o if_o the_o declination_n be_v westward_o then_o 11_o and_o 10_o minute_n will_v be_v the_o say_a meridian_n line_n 10_o and_o 10_o minute_n your_o 1_o a_o clock_n line_n for_o thus_o you_o must_v operate_v in_o all_o other_o case_n that_o be_v to_o say_v you_o must_v still_o allow_v by_o the_o new_a figure_n the_o difference_n of_o longitude_n that_o chance_v to_o be_v between_o you_o and_o they_o to_o who_o the_o decline_a plane_n be_v horizontal_n but_o because_o this_o manner_n of_o dial_v may_v seem_v to_o some_o troublesome_a and_o confuse_a especial_o when_o the_o say_a difference_n of_o longitude_n happen_v to_o be_v a_o fraction_n and_o not_o even_a hour_n i_o shall_v here_o adjoin_v a_o second_o geometrical_a way_n operation_n xvi_o how_o to_o describe_v geometrical_o a_o dial_n decline_v 40_o degree_n 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and_o be_o equal_a to_o xm_o the_o height_n of_o the_o style_n above_o it_o thus_o than_o we_o see_v that_o the_o fabric_n of_o a_o decline_a dial_n which_o be_v wont_a to_o terrify_v young_a student_n be_v in_o a_o manner_n as_o quick_a and_o easy_a as_o that_o of_o the_o horizontal_n since_o two_o ordinary_a line_n more_o viz._n gd_v and_o bp_o give_v we_o all_o the_o point_n necessary_a for_o its_o description_n the_o demonstration_n and_o reason_n of_o this_o dial_n be_v evident_a for_o demonstration_n the_o horizontal_n be_v by_o construction_n true_a any_o erect_a plane_n face_v the_o south_n that_o cross_v its_o meridian_n or_o 12_o a_o clock_n line_n ac_fw-la at_o right_a angleâ—_n will_v represent_v a_o primary_n vertical_a or_o direct_a south_n plane_n and_o then_o the_o centre_n of_o the_o dial_n describe_v on_o it_o will_v be_v distant_a from_o p_o the_o intersection_n of_o the_o two_o plane_n on_o the_o say_v ac_fw-la the_o tangent_fw-la of_o the_o elevation_n as_o i_o 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great_a extuberancy_n and_o this_o circle_n be_v 90_o degree_n from_o the_o point_n of_o the_o globe_n which_o lie_v direct_o under_o our_o zenith_n it_o must_v differ_v from_o the_o horizon_n of_o the_o globe_n as_o many_o degree_n as_o its_o zenith_n differ_v from_o that_o in_o the_o heaven_n therefore_o the_o way_n prescribe_v be_v at_o least_o speculative_o true_a operation_n ii_o to_o find_v the_o sun_n almucantar_n or_o height_n there_o be_v three_o distinct_a way_n of_o perform_v this_o independent_a of_o the_o follow_a operation_n and_o each_o of_o great_a use_n for_o the_o first_o give_v you_o the_o sun_n height_n in_o a_o instant_n if_o he_o shine_v the_o second_o if_o you_o have_v the_o least_o glimpse_n of_o he_o or_o can_v guess_v at_o his_o place_n in_o a_o cloud_n the_o three_o if_o you_o know_v the_o hour_n by_o any_o good_a watch_n pendulum_n or_o the_o like_a whether_o we_o see_v the_o heaven_n or_o no._n i._o as_o for_o the_o first_o way_n it_o be_v this_o your_o 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way_n for_o both_o the_o former_a we_o reckon_v but_o way_n one_o turn_v the_o meridian_n of_o your_o globe_n to_o the_o sun_n as_o before_o or_o because_o we_o suppose_v he_o not_o to_o shine_v outright_o direct_v by_o your_o eye_n the_o say_a meridian_n so_o that_o it_o lie_v in_o the_o same_o plain_a with_o he_o and_o this_o you_o may_v do_v in_o a_o manner_n as_o well_o if_o you_o have_v the_o least_o glimpse_n of_o he_o or_o can_v by_o any_o accident_n guess_v whereabout_o he_o be_v as_o if_o you_o have_v the_o forementioned_a help_v of_o the_o pin_n shade_n in_o the_o zenith_n have_v thus_o do_v take_v your_o string_n in_o both_o hand_n and_o cross_v with_o it_o as_o exact_o as_o you_o can_v at_o right_a angle_n that_o part_n of_o the_o meridian_n next_o your_o body_n whether_o it_o happen_v to_o be_v the_o quad._n of_o alt._n or_o that_o of_o proportion_n then_o put_v your_o face_n close_o to_o it_o and_o move_v your_o ey_fw-mi lower_v and_o low_o till_o by_o reason_n of_o the_o extuberancy_n you_o can_v but_o just_a see_v the_o sun_n or_o his_o suppose_a place_n in_o heaven_n do_v but_o bring_v your_o string_n hold_v as_o before_o to_o this_o point_n viz._n bring_v your_o string_n towards_o you_o till_o it_o just_o take_v away_o the_o sun_n or_o his_o suppose_a place_n from_o your_o ey_fw-mi and_o the_o degree_n in_o the_o meridian_n on_o which_o it_o then_o lie_v will_v be_v count_v from_o the_o zenith_n the_o height_n require_v for_o so_o far_o his_o ray_n will_v reach_v do_v he_o shine_v outright_o the_o three_o way_n be_v when_o we_o know_v the_o hour_n by_o any_o watch_n pendulum_n way_n etc._n etc._n thus_o find_v among_o the_o aequin_n or_o diurnal_a parallel_n that_o belong_v to_o the_o present_a day_n which_o we_o will_v suppose_v apr._n 10._o and_o draw_v your_o string_n from_o the_o zenith_n over_o that_o point_n in_o the_o say_a parallel_n where_o it_o be_v cut_v by_o the_o hour_n give_v i._n e._n by_o the_o morning_n 9_o a_o clock_n circle_n 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