5_o n_o 30_o dolphin_n head_n 3_o 307_o 53_o 20_o 32_o 15_o 0_o n._n 31_o pegassus_n mouth_n 1_o 321_o 50_o 21_o 27_o 8_o 19_o n_o 32_o pomahant_n 3_o 339_o 30_o 22_o 38_o 31_o 17_o s._n 33_o pegassus_n lower_v wing_n 2_o 358_o 50_o 23_o 55_o 13_o 22_o n._n as_o for_o example_n to_o find_v the_o sun_n declination_n for_o the_o year_n 1670_o on_o the_o 12_o day_n of_o may_n first_o if_o you_o divide_v 70_o be_v the_o ten_o only_o of_o the_o year_n of_o our_o lord_n by_o 4_o reject_v the_o 100_o s_o you_o shall_v find_v 2_o as_o a_o remainder_n which_o note_v it_o to_o be_v the_o second_o after_o leap-year_n and_o if_o 0_o remain_n than_o it_o be_v leap-year_n then_o look_v in_o the_o table_n of_o declination_n for_o 1666_o the_o second_o after_o leap-year_n as_o the_o year_n 1670_o be_v and_o find_v the_o month_n in_o the_o head_n of_o the_o table_n and_o the_o day_n on_o one_o side_n and_o in_o the_o meeting-point_n you_o shall_v find_v 20_o deg_n 31_o min._n for_o the_o declination_n on_o that_o day_n at_o noon_n require_v or_o if_o you_o use_v the_o triangule_a quadrant_n extend_v the_o thread_n from_o the_o centre_n over_o the_o 12_o of_o may_n and_o you_o shall_v find_v it_o to_o cut_v in_o the_o degree_n just_a 20_o deg_n 31_o min._n the_o true_a declination_n for_o that_o year_n and_o day_n note_v that_o if_o you_o have_v occasion_n to_o use_v the_o declination_n before_o noon_n then_o observe_v that_o the_o difference_n between_o stroke_n and_o stroke_n be_v the_o difference_n of_o declination_n for_o one_o day_n and_o by_o consequence_n one_o half_a of_o that_o space_n for_o half_a a_o day_n and_o a_o quarter_n for_o a_o quarter_n of_o a_o day_n etc._n etc._n as_o thus_o for_o example_n suppose_v i_o will_v have_v the_o sun_n declination_n the_o 18_o of_o august_n 1666_o at_o 6_o in_o the_o morning_n here_o you_o must_v note_v that_o the_o 18_o stroke_n from_o the_o begin_n of_o august_n represent_v the_o 18_o day_n at_o noon_n just_a now_o the_o time_n require_v be_v 6_o hour_n before_o noon_n lay_v the_o thread_n one_o four_o part_n of_o the_o distance_n for_o one_o day_n towards_o the_o 17_o day_n and_o then_o in_o the_o degree_n the_o thread_n shall_v cut_v on_o 9-43′_a whereas_o at_o noon_n just_a it_o will_v be_v but_o 9-38_a and_o the_o next_o or_o 19_o day_n at_o noon_n it_o be_v 9_o degree_n 16_o min._n and_o 3_o quarter_n of_o a_o min._n as_o the_o three_o prick_n thus_o ..._o in_o the_o table_n do_v plain_o show_v but_o by_o the_o rule_n a_o minute_n be_v as_o much_o as_o can_v be_v see_v and_o so_o near_o with_o care_n may_v you_o come_v note_v also_o far_o that_o if_o you_o shall_v use_v it_o in_o place_n that_o be_v 4_o hour_n 6_o or_o 8_o 10_o or_o 12_o hour_n more_o eastward_o or_o westward_o in_o longitude_n the_o same_o rule_n will_v tell_v you_o the_o minute_n to_o be_v add_v in_o western-longitude_n or_o to_o be_v substract_v in_o eastern-longitude_n as_o reason_n and_o experience_n will_v dictate_v unto_o you_o with_o due_a consideration_n for_o if_o be_v eastward_n the_o sun_n come_v to_o the_o meridian_n of_o that_o place_n before_o it_o come_v to_o the_o meridian_n of_o london_n then_o lay_v the_o thread_n as_o in_o morning_n hour_n but_o if_o the_o place_n be_v to_o the_o westward_n where_o it_o come_v late_a then_o lay_v the_o thread_n so_o many_o hour_n beyond_o the_o noon-stroke_n for_o london_n as_o the_o place_n have_v hour_n of_o western-longitude_n more_o than_o london_n count_v 15_o degree_n for_o a_o hour_n and_o 4_o minute_n for_o every_o degree_n and_o then_o shall_v you_o have_v the_o declination_n to_o one_o minute_n of_o the_o very_a truth_n but_o if_o it_o happen_v to_o be_v the_o leap-year_n or_o the_o first_o or_o three_o year_n after_o the_o leap-year_n than_o thus_o suppose_v for_o the_o 5_o of_o october_n 1671_o be_v the_o three_o after_o leap-year_n i_o will_v have_v the_o declination_n first_o if_o you_o lay_v the_o thread_n over_o the_o 5_o of_o october_n in_o the_o degree_n it_o give_v 08_o deg_n 42_o minute_n for_o the_o declination_n in_o the_o second_o year_n after_o leap-year_n then_o because_o this_o be_v the_o three_o year_n look_v in_o the_o rectifying-table_n for_o the_o 5_o of_o october_n and_o there_o you_o find_v s._n 4_o for_o subtract_v 4_o minute_n and_o a_o half_a from_o 8-42_a rest_v 8-38_a the_o true_a declination_n require_v for_o the_o 5_o of_o october_n 1671._o the_o like_a work_n serve_v for_o any_o other_o day_n or_o year_n but_o for_o every_o 5_o and_o 10_o day_n you_o have_v the_o declination_n set_v down_o in_o a_o table_n for_o all_o 4_o year_n to_o prove_v and_o try_v the_o truth_n of_o your_o operation_n and_o by_o that_o and_o the_o line_n of_o number_n or_o the_o rule_n of_o three_o you_o may_v continue_v it_o to_o every_o day_n by_o this_o proportion_n as_o 5_o day_n or_o 120_o hour_n to_o the_o difference_n of_o declination_n in_o the_o table_n between_o one_o 5_o day_n and_o another_o so_o be_v any_o part_n of_o 5_o day_n or_o 120_o hour_n to_o the_o difference_n in_o declination_n to_o be_v add_v or_o substract_v to_o the_o 5_o day_n declination_n immediate_o foregoing_a the_o day_n require_v example_n suppose_v for_o the_o 18_o of_o february_n 1669_o the_o first_o after_o leap-year_n i_o will_v know_v the_o declination_n by_o the_o table_n make_v to_o every_o 5_o day_n only_o on_o the_o 20_o of_o february_n i_o find_v 6-53_a ½_o on_o the_o 15_o day_n 8-47_a the_o difference_n between_o they_o be_v 1-53_a ½_o then_o the_o extent_n of_o the_o compass_n from_o 5_o the_o number_n of_o day_n to_o 1-53_a the_o minute_n difference_n count_v proper_o every_o 10_o for_o 6_o minute_n shall_v reach_v from_o 3_o the_o day_n from_o 15_o towards_o 18_o to_o 1_o degree_n 7_o minute_n and_o a_o half_a which_o take_v from_o 8-47′_a the_o declination_n for_o the_o 15_o day_n leave_v 7_o degree_n 38_o minute_n and_o a_o half_a the_o true_a declination_n for_o the_o 18_o day_n of_o february_n in_o the_o first_o after_o leap-year_n or_o by_o the_o line_n of_o number_n thus_o the_o extent_n from_o 5_o the_o difference_n in_o day_n to_o 113_o ½_o the_o difference_n in_o min._n for_o 5_o day_n shall_v reach_v from_o 3_o the_o difference_n in_o day_n to_o 68_o the_o difference_n in_o minute_n for_o 3_o day_n to_o be_v add_v or_o substract_v according_a to_o the_o increase_n or_o decrease_v of_o the_o declination_n at_o that_o time_n of_o the_o year_n prove_v thus_o if_o you_o subtract_v 5′_n ½_o from_o 7_o deg_n 44_o ..._o the_o declination_n in_o the_o second_o year_n there_o remain_v 7_o deg_n 38′_n ½_o the_o declination_n for_o the_o 18_o of_o february_n 1669._o these_o table_n may_v serve_v very_o well_o for_o 30_o year_n and_o not_o differ_v 6_o minute_n in_o declination_n about_o the_o equinoctial_a where_o the_o difference_n be_v most_o and_o in_o june_n and_o december_n not_o at_o all_o to_o be_v perceive_v thus_o you_o may_v by_o the_o rule_n and_o rectify_v table_n find_v the_o sun_n declination_n to_o a_o minute_n at_o any_o time_n without_o the_o trouble_n of_o calculation_n chap._n iu._n the_o use_n of_o the_o trianguler-quadrant_n in_o the_o operative_a part_n of_o navigation_n use_v i._o to_o find_v how_o many_o league_n or_o miles_n answer_v to_o one_o degree_n of_o longitude_n in_o any_o latitude_n between_o the_o equinoctial_a and_o pole_n first_o it_o be_v convenient_a to_o be_v resolve_v how_o many_o league_n or_o mile_n be_v in_o one_o degree_n in_o the_o meridian_n or_o equinoctial_a which_o mr._n norwood_n and_o mr._n collins_n have_v state_v about_o 24_o league_n or_o 72_o mile_n or._n if_o you_o keep_v the_o old_a number_n make_v the_o mile_n great_a viz._n 60_o mile_n or_o 20_o league_n then_o the_o proportion_n by_o the_o number_n sin_n and_o tangent_n run_v thus_o as_o sine_fw-la 90_o to_o 20_o on_o the_o number_n for_o league_n so_o be_v cousin_a of_o the_o latitude_n to_o the_o league_n on_o the_o number_n contain_v in_o one_o degree_n of_o longitude_n in_o that_o latitude_n but_o in_o miles_n to_o have_v the_o answer_n work_v thus_o as_o sine_fw-la 90_o to_o 60_o on_o number_n so_o cousin_a latitude_n to_o the_o number_n of_o mile_n example_n latitude_n 51°_n 32′_n as_o sine_fw-la 90_o to_o 60_o so_o sine_fw-la 38-28_a to_o 37_o mile_n 30_o 100_o but_o by_o the_o trianguler-quadrant_n or_o sector_n work_v thus_o take_v the_o latteral_a 20_o for_o league_n or_o 60_o for_o mile_n from_o the_o line_n of_o line_n from_o the_o centre_n downward_o and_o make_v it_o a_o parallel_n in_o the_o sine_fw-la of_o 90_o lay_v the_o thread_n to_o the_o near_a distance_n then_o the_o near_a distance_n
sector_n be_v set_v to_o the_o small_a tangent_fw-la and_o by_o turn_v 4_o time_n you_o have_v the_o remainder_n of_o the_o great_a tangent_fw-la above_o 45_o when_o the_o sector_n be_v set_v to_o the_o great_a line_n of_o 45_o as_o in_o the_o polar_a dial._n or_o else_o alter_v the_o sector_n to_o the_o radius_fw-la of_o 45_o in_o the_o great_a tangent_fw-la that_o go_v but_o to_o 45_o and_o take_v out_o the_o =_o tangent_n of_o 30_o and_o lay_v it_o from_o 6_o both_o way_n for_o 4_o &_o 8_o and_o the_o =_o tangent_fw-la of_o 15_o and_o lay_v it_o from_o 6_o both_o way_n for_o 7_o &_o 5._o and_o last_o by_o all_o those_o point_n draw_v line_n =_o to_o 6_o for_o the_o hour-line_n require_v and_o number_v the_o east-dial_n with_o the_o morning-hour_n and_o the_o west_n with_o the_o afternoon-hour_n the_o style_n be_v to_o be_v a_o plate_n or_o a_o upright_a point_n the_o top_n of_o who_o edge_n or_o point_n be_v to_o be_v equal_a to_o the_o tangent_fw-la of_o 45_o as_o the_o sector_n stand_v to_o prick_v down_o the_o hour-line_n 4._o to_o draw_v the_o horizontal-plain_a the_o four_o plain_n next_o in_o a_o natural_a order_n of_o easiness_n to_o apprehend_v as_o i_o judge_v be_v the_o horizontal_a dial_n that_o lie_v with_o its_o plain_a =_o to_o the_o horizon_n and_o the_o zenith_n be_v the_o pole_n thereof_o represent_v by_o the_o primitive_a circle_n s.n.e.w._n in_o the_o general_a scheam_n wherein_o only_o the_o hour_n ark_n and_o style_n be_v require_v the_o style_n elevation_n be_v always_o equal_a to_o the_o latitude_n and_o therefore_o give_v the_o substile_a be_v always_o in_o the_o hour_n 12_o be_v the_o meridian-line_n the_o hour-line_n be_v find_v by_o this_o general_a canon_n as_o the_o sine_fw-la of_o 90_o the_o right_a angle_n pn_n 1_o general-scheam_a to_o the_o sine_fw-la of_o pn_n a_o side_n always_o equal_a to_o the_o latitude_n or_o style_n elevation_n 51-30_a so_o be_v the_o tangent_fw-la of_o the_o angle_n np_n 1_o 15_o or_o np_v 2_o 30_o etc._n etc._n the_o angle_n at_o the_o pole_n to_o the_o tangent_fw-la of_o n_o 1_o a_o side_n or_o n_o 2_o a_o second_o side_n the_o several_a hour-arks_a on_o the_o plain_a require_v find_v by_o the_o artificial_a sin_n and_o tangent_n as_o fast_o as_o one_o can_v write_v they_o down_o thus_o the_o extent_n of_o the_o compass_n from_o the_o sine_fw-la of_o 90_o the_o sine_fw-la of_o the_o latitude_n 51-30_a be_v lay_v the_o same_o way_n from_o the_o tangent_fw-la of_o 15_o shall_v reach_v to_o the_o tangent_fw-la of_o 11-50_a and_o if_o you_o turn_v the_o compass_n the_o other_o way_n from_o the_o tangent_fw-la of_o 15_o it_o shall_v give_v the_o tangent_fw-la of_o 71-6_a for_o the_o hour_n of_o 5_o as_o well_o as_o 11_o which_o number_n be_v gather_v into_o a_o table_n and_o lay_v off_o by_o chord_n or_o sin_n in_o a_o semicircle_n shall_v be_v the_o true_a hour-point_n to_o draw_v the_o line_n by_o but_o i_o shall_v not_o insist_v further_o thereon_o but_o show_v how_o to_o draw_v it_o more_o ready_o and_o as_o true_o by_o the_o sector_n thus_o first_o draw_v a_o straight_a line_n in_o the_o meridian_n if_o the_o plain_n be_v fix_v for_o 12_o as_o the_o line_n ab_fw-la then_o design_v a_o point_n in_o that_o line_n to_o serve_v for_o a_o centre_n as_o at_o c_o then_o on_o the_o centre_n c_o erect_v a_o perpendiculer-line_n to_o ab_fw-la and_o draw_v it_o through_o the_o centre_n c_o for_o the_o two_o 6_o a_o clock_n hour-line_n as_o the_o line_n de_fw-fr then_o draw_v two_o line_n equal_o distant_a from_o and_o =_o to_o the_o first_o line_n ab_fw-la on_o either_o side_n as_o large_a as_o the_o plain_n will_v give_v leave_n as_o df_n and_o eglantine_n which_o may_v common_o serve_v for_o margin_n to_o put_v the_o figure_n in_o then_o take_v the_o distance_n cd_o and_o make_v it_o a_o =_o secant_fw-la of_o 00_o and_o take_v out_o the_o =_o secant_fw-la of_o the_o compliment_n of_o the_o latitude_n and_o lay_v it_o from_o d_o to_o f_o and_o from_o e_z to_z g_z on_o the_o two_o parallel-line_n and_o draw_v the_o line_n fg._n then_o last_o for_o prick_v down_o the_o style_n note_v that_o the_o =_o tangent_fw-la of_o 38-30_a the_o compliment_n of_o the_o latitude_n as_o the_o sector_n stand_v for_o the_o noon_n hour_n lay_v from_o d_o to_o h_n gives_z a_o point_n to_o draw_v it_o true_o by_o or_o the_o sine_fw-la of_o 51-30_a the_o latitude_n lay_v from_o b_o at_o near_a distance_n about_o h_n as_o the_o sector_n stand_v for_o the_o morning-hour_n will_v do_v as_o well_o the_o style_n be_v to_o be_v a_o plate_n or_o a_o bend_a wire_n cut_v or_o bend_a according_a to_o the_o angle_n hcb_n and_o erect_v perpendicular_o on_o the_o line_n 12_o so_o long_o as_o the_o sun_n be_v 62_o degree_n high_a may_v cause_v the_o shadow_n thereof_o to_o reach_v the_o hour_n of_o 12_o and_o then_o set_v due_o north_n &_o south_n and_o horizontal_a the_o shadow_n will_v show_v the_o true_a hour_n of_o the_o day_n note_v the_o figure_n note_v also_o that_o a_o horizontal_a dial_n draw_v for_o any_o one_o latitude_n may_v serve_v for_o any_o other_o latitude_n north_n or_o south_n elevate_a or_o depress_v the_o style_n till_o it_o look_v to_o the_o pole-point_n that_o be_v by_o make_v it_o to_o recline_v northward_o or_o southward_o as_o much_o as_o the_o difference_n of_o the_o latitude_n viz._n that_o the_o dial_n be_v make_v for_o and_o that_o wherein_o it_o be_v to_o be_v use_v shall_v be_v 5._o to_o draw_v a_o north_n or_o south_n plain_a the_o next_o plain_n to_o this_o and_o most_o like_o it_o be_v the_o direct_a north_n and_o south_n dial_n who_o plain_a lie_n =_o to_o the_o prime_n virtical_a or_o circle_n of_o east_n and_o west_n and_o its_o pole_n in_o the_o south_n and_o north_n part_n of_o the_o horizon_n and_o represent_v by_o the_o line_n ezw_n in_o the_o general_a scheam_n who_o style_n be_v always_o equal_a to_o the_o compliment_n of_o the_o latitude_n as_o the_o horizontal_n be_v equal_a to_o the_o latitude_n and_o consequent_o give_v the_o hour_n ark_v on_o the_o plain_a be_v find_v by_o the_o former_a canon_n viz._n as_o the_o sine_fw-la of_o 90_o viz._n the_o angle_n pze_v be_v to_o the_o sine_fw-la of_o the_o side_n pz_n the_o co-latitude_n or_o style_n elevation_n the_o ark_n on_o the_o plain_a find_v as_o before_o by_o artificial_a sin_n and_o tangent_n and_o be_v draw_v into_o a_o table_n to_o be_v lay_v off_o by_o chord_n or_o sines_n or_o by_o the_o sector_n thus_o draw_v a_o perpendiculer-line_n for_o the_o substile_a or_o 12_o a_o clock_n line_n and_o in_o that_o line_n design_v a_o point_n for_o a_o centre_n as_o the_o point_n a_o in_o the_o line_n ab_fw-la through_o which_o point_n a_o draw_v another_o line_n cross_v the_o former_a at_o right_a angle_n for_o a_o horizontal-line_n and_o the_o two_o six_o as_o you_o do_v in_o the_o horizontal_a then_o on_o each_o side_n and_o equi-distant_a from_o 12_o make_v two_o line_n =_o to_o ab_fw-la as_o marginal-line_n as_o cf_n and_o de_fw-fr the_o distance_n ad_fw-la of_o the_o parallel_n make_v a_o =_o secant_fw-la of_o 00_o and_o take_v out_o the_o =_o secant_fw-la of_o 51-30_a the_o latitude_n of_o the_o place_n and_o lay_v it_o from_o c_o to_o f_o and_o from_o d_o to_z e_z and_o draw_v the_o line_n fe_o then_o make_v df_n a_o tangent_fw-la of_o 45_o and_o lay_v off_o the_o hour_n and_o quarter_n as_o you_o do_v in_o the_o horizontal_a in_o all_o respect_n also_o make_v bf_o a_o =_o tangent_fw-la of_o 45_o and_o lay_v off_o the_o =_o tangent_n of_o every_o hour_n and_o quarter_n if_o you_o please_v from_o b_o both_o way_n toward_z e_z and_o f_o and_o by_o those_o point_n draw_v line_n for_o the_o hour_n require_v the_o angle_n of_o the_o style_n may_v be_v lay_v off_o by_o sines_n tangent_n or_o chord_n as_o before_o be_v show_v to_o the_o quantity_n of_o the_o compliment_n of_o the_o latitude_n and_o may_v be_v a_o plate_n or_o wyre_n as_o you_o please_v as_o the_o angle_n gab._n the_o north_n dial_n be_v the_o same_o with_o the_o south_n for_o manner_n of_o make_v only_o the_o noon-hour_n be_v neglect_v and_o the_o morning_n and_o evening-hour_n both_o before_o and_o after_o 6_o on_o each_o side_n only_o insert_v and_o the_o centre_n of_o the_o dial_n for_o that_o cause_n appoint_v in_o the_o middle_n of_o the_o plain_a and_o not_o on_o the_o upper-part_n as_o in_o the_o south_n and_o the_o stile-point_n upward_o as_o in_o the_o south_n it_o point_v downward_o note_v the_o figure_n 6._o to_o draw_v the_o hour_n on_o a_o direct_a recliner_n the_o next_o plain_n to_o be_v consider_v be_v also_o direct_v but_o not_o erect_a or_o upright_o but_o lean_v from_o
but_o when_o the_o sun_n be_v in_o the_o equinoctial_a it_o behold_v the_o south-plain_a at_o the_o rise_n be_v at_o 6_o a_o clock_n in_o the_o morning_n and_o shine_v on_o it_o all_o day_n till_o sun_n set_v be_v at_o 6_o at_o night_n and_o then_o the_o north_n dial_n be_v useless_a 2._o for_o a_o declining-plain_a suppose_v 30_o degree_n southeast_n first_o set_v the_o scheam_n in_o his_o right_a situation_n for_o a_o southeast_n plain_a then_o if_o you_o count_v 30_o degree_n from_o saint_n towards_o e_o for_o the_o pole_n of_o the_o plain_a and_o 30_o degree_n from_o w_n towards_o saint_n or_o from_o e_z toward_z n_o and_o draw_v that_o line_n that_o shall_v represent_v the_o plain_a than_o you_o shall_v find_v that_o the_o sun_n be_v in_o cancer_n will_v begin_v to_o shine_v on_o this_o plain_a just_a a_o quarter_n before_o 5_o in_o the_o morning_n and_o continue_v till_o near_o half_a a_o hour_n after_o 2._o but_o about_o the_o middle_n of_o january_n it_o will_v shine_v on_o it_o till_o a_o quarter_n after_o 4_o viz._n till_o sun_n set_v and_o all_o the_o hour_n after_o 2_o belong_v to_o the_o northwest_n plain_a that_o decline_v 30_o degree_n and_o one_o hour_n in_o the_o morning_n also_o viz._n from_o a_o quarter_n before_o till_o three_o quarter_n after_o 4._o the_o like_a work_n serve_v for_o any_o decliner_n whatsoever_o in_o any_o latitude_n 3._o but_o for_o decliner_n and_o recliner_n draw_v a_o long_a line_n as_o ab_fw-la and_o cross_v it_o with_o a_o perpendicule_a in_o the_o centre_n c_o and_o lay_v off_o from_o c_o towards_o a_o and_o b_o the_o tangent_fw-la of_o 45_o or_o the_o semi-tangent_a of_o 90_o equal_a to_o the_o largeness_n of_o your_o scheam_n then_o lay_v off_o the_o semi-tangent_a of_o the_o reclination_n from_o c_o to_o d_o up_z and_o down_o both_o way_n then_o take_v out_o the_o secant_fw-la of_o the_o compliment_n of_o the_o reclination_n which_o will_v be_v a_o radius_fw-la to_o draw_v the_o ark_n adb_n which_o paper_n you_o must_v cut_v out_o and_o apply_v the_o two_o point_n of_o the_o paper_n adbd_v to_o the_o two_o point_n of_o declination_n of_o the_o plain_a note_v in_o the_o scheam_n with_o a_o and_o b_o that_o be_v put_v a_o to_o a_o and_o b_o to_z b_o then_o the_o round_a or_o convex-edge_n of_o the_o paper_n represent_v the_o recline_a plain_n and_o the_o same_o edge_n on_o the_o other_o part_n next_o the_o horizon_n southwards_o represent_v the_o south-west_n incliner_n example_n suppose_v i_o make_v the_o paper_n adb_n to_o recline_v 35-50_a the_o reclination_n of_o the_o equinoctial-plain_a then_o first_o set_v the_o scheam_n right_a before_o you_o in_o its_o right_a situation_n and_o put_v the_o point_v a_o in_o the_o paper_n on_o a_o on_o the_o scheam_n and_o b_o in_o the_o paper_n to_o b_o on_o the_o scheam_n i_o shall_v find_v it_o to_o be_v even_o with_o the_o recline_a circle_n aeb_n then_o follow_v the_o tropic_a of_o cancer_n i_o find_v that_o it_o shine_v on_o the_o north_n recliner_n from_o the_o rise_n till_o near_o 2_o at_o which_o time_n it_o leave_v the_o north-recline_a decline_v eastward_o and_o begin_v to_o shine_v upon_o the_o opposite_a plain_n viz._n the_o south-west_n incliner_n decline_v 55-0_a and_o recline_v 35-50_a and_o so_o continue_v till_o sunset_n but_o note_n that_o if_o the_o line_n that_o represent_v the_o plain_a cut_v the_o tropic_a twice_o as_o the_o line_n ewe_n for_o a_o north-plain_a then_o though_o the_o sun_n leave_v the_o plain_a in_o the_o morning_n it_o will_v shine_v on_o it_o again_o in_o the_o afternoon_n note_v also_o that_o a_o north-east_n recliner_n be_v represent_v by_o the_o other_o convex-edge_n of_o the_o paper_n as_o here_o a_o north-east_n decliner_n 55_o and_o incline_v 35-50_a the_o sun_n will_v shine_v but_o till_o 3_o quarter_n after_o 8_o in_o cancer_n but_o in_o capricorn_n it_o shine_v till_o half_a a_o hour_n after_o 9_o and_o come_v no_o more_o on_o it_o that_o day_n and_o note_v always_o that_o when_o it_o leave_v any_o plain_a that_o then_o it_o begin_v to_o shine_v on_o his_o opposite_a as_o here_o the_o opposite_a to_o this_o north-east_n incliner_n be_v the_o south-west_n recliner_n be_v represent_v by_o the_o same_o line_n or_o circle_n adb_n that_o the_o north_n recliner_n be_v only_o you_o must_v count_v that_o side_n of_o the_o line_n next_o to_o the_o horizon_n the_o inclining-plain_a and_o that_o side_n next_o the_o zenith_n the_o reclining-plain_a for_o the_o line_n that_o represent_v it_o have_v no_o breadth_n can_v be_v no_o otherwise_o distinguish_v unless_o you_o will_v make_v a_o material_a armilary_n sphere_n of_o pasteboard_n or_o brass_n as_o the_o follow_a discourse_n do_v plain_o demonstrate_v in_o these_o several_a operation_n for_o the_o better_a conceive_n of_o these_o mathematical_a excercitation_n thus_o you_o have_v the_o way_n of_o make_v all_o manner_n of_o sun_n dial_n upon_o any_o plain_a superficies_n the_o axis_n of_o the_o world_n be_v the_o suppose_a style_n to_o all_o these_o plain_n as_o for_o those_o curiosity_n of_o upright_a style_n and_o eliptical_a dial_n and_o draw_v of_o dial_n by_o the_o horizontal_a or_o equinoctial_a dial_n you_o have_v they_o in_o the_o work_v of_o mr._n samuel_n foster_n and_o other_o and_o in_o kerkers_n ars_fw-la magna_fw-la etc._n etc._n but_o i_o intend_v not_o a_o volumn_n of_o shadow_n but_o only_o a_o further_a improvement_n of_o the_o trianguler-quadrant_n as_o you_o will_v see_v in_o the_o next_o chapter_n of_o draw_v the_o furniture_n or_o ornament_n of_o dial_n which_o be_v but_o seldom_o use_v i_o shall_v here_o crave_v a_o apology_n for_o the_o brevity_n therein_o fear_v lest_o that_o to_o the_o young_a practitioner_n it_o may_v seem_v somewhat_o hard_a to_o conceive_v though_o to_o the_o exercise_v in_o these_o matter_n it_o may_v be_v plain_a enough_o then_o for_o a_o conclusion_n you_o shall_v have_v a_o easy_a mechanic_n way_n to_o draw_v a_o dial_n on_o the_o ceiling_n of_o a_o room_n that_o lie_v flat_a or_o horizontal_a which_o will_v be_v very_o good_a for_o painter_n or_o plasterer_n to_o ornament_n a_o room_n withal_o and_o be_v not_o yet_o treat_v on_o that_o way_n as_o ever_o i_o read_v of_o chap._n viii_o to_o furnish_v any_o dial_n with_o the_o usual_a mathematical_a ornament_n by_o the_o trianguler-quadrant_n as_o parallel_n of_o the_o sun_n declination_n or_o the_o sun_n place_n or_o length_n of_o the_o day_n to_o find_v the_o horizontal_a and_o virtical_a line_n and_o point_n to_o draw_v the_o azimuth_n and_o almicanter_n the_o jewish_a italian_a &_o babylonish_n hour_n and_o 12_o house_n on_o any_o plain_a before_o mention_v 1._o to_o draw_v the_o tropic_n or_o parallel_n of_o the_o sun_n declination_n or_o the_o length_n of_o the_o day_n artificial_a on_o any_o dial._n but_o note_n that_o if_o it_o be_v a_o perpendicule_a style_n who_o upper_a point_n or_o apex_n be_v to_o be_v the_o nodus_fw-la to_o give_v the_o shadow_n than_o you_o must_v strain_v a_o thread_n very_o hard_o or_o apply_v a_o rule_n for_o the_o present_a whereon_o to_o rest_v the_o moving-leg_n on_o instead_o of_o the_o axis_n or_o else_o you_o may_v do_v it_o thus_o as_o mr._n gunter_n show_v first_o to_o make_v the_o trygon_n if_o the_o rule_n or_o quadrant_n prove_v too_o large_a for_o your_o small_a dial._n on_o a_o sheet_n of_o pasteboard_n or_o slate_n draw_v a_o long_a straight_a line_n as_o ab_fw-la to_o which_o line_n erect_v two_o perpendiculer_o one_o at_o the_o upper_a and_o the_o other_o at_o the_o low_a end_n as_o cd_o and_o of_o then_o make_v ab_fw-la a_o tangent_fw-la of_o 45_o degree_n then_o have_v first_o make_v these_o little_a table_n that_o follow_v by_o the_o trianguler-quadrant_n which_o be_v only_o the_o sun_n declination_n at_o his_o entrance_n into_o the_o whole_a sign_n or_o at_o a_o even_a half-hour_n of_o rise_v lay_v of_o both_o way_n from_o b_o the_o tangent_n of_o the_o sun_n declination_n at_o ♈_o ♉_o ♊_o ♋_o as_o in_o the_o table_n follow_v and_o draw_v line_n to_o these_o point_n from_o the_o centre_n a_o as_o in_o the_o figure_n annex_v and_o then_o set_v the_o mark_n to_o they_o and_o this_o be_v the_o trigon_n figure_n i._n sun_n declination_n for_o the_o parallel_n of_o the_o length_n of_o the_o day_n hour_n declin_n 16-26_a 23-31_a 16-0_a 21-41_a 15-0_a 16-55_a 14_o 11-37_a 13_o 5-53_a 12_o 0-00_a 11_o 5-53_a 10_o 11-37_a 9_o 16-55_a 8_o 21-41_a 7-34_a 23-31_a for_o the_o sign_n of_o the_o zodiac_n sign_n declin_n ♋_o 23-31_a ♌_o ♊_o 20-14_a ♉_o â™_o 11-31_a ♈_o ♎_o 0-00_a ♓_o â™_o 11-31_a â™’_o â™_o 20-14_a ♑_o 23-31_a declination_n 5-0_a 100l_a 15-0_a 20-0_a 23-31_a both_o way_n then_o from_o the_o centre_n a_o any_o way_n on_o the_o line_n cd_o at_o such_o a_o convenient_a distance_n as_o you_o
00_o 00_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 15_o 56_o 13_o 25_o 06_o 41_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 13_o 44_o 11_o 11_o 04_o 23_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 11_o 35_o 8_o 59_o 02_o 08_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 5_o 9_o 32_o 6_o 50_o 00_o 06_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 7_o 23_o 4_o 44_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 5_o 26_o 2_o 41_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 3_o 36_o 0_o 41_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 4_o 1_o 32_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr the_o description_n and_o some_o use_v of_o the_o sphere_n for_o dial_v and_o for_o the_o better_a understanding_n of_o the_o general_a and_o particular_a scheme_n next_o the_o foot_n and_o semicircle_n frame_v for_o support_v of_o it_o you_o may_v consider_v 1._o the_o fix_a horizon_n to_o which_o the_o foot_n be_v fasten_v with_o 4_o screw_n number_v and_o divide_v into_o 360_o degree_n or_o four_o 90_o deg_n who_o count_n begin_v at_o the_o dividee_n side_n of_o the_o meridian-circle_n 2._o the_o meridian_n circle_n who_o fore-side_n at_o the_o nadir-point_n stand_v in_o the_o centre_n of_o the_o foot_n this_o be_v also_o divide_v into_o 4_o 90_o s_o and_o begin_v to_o be_v number_v at_o the_o south_n and_o north_n part_n of_o the_o horizon_n upward_o towards_o the_o zenith_n and_o downward_o towards_o the_o nadir_n which_o circle_n be_v always_o fix_v as_o the_o horizon_n be_v 3._o the_o equinoctial_a circle_n make_v fast_o at_o the_o east_n and_o west_n point_v of_o the_o horizon_n move_v up_o and_o down_o upon_o the_o meridian-circle_n according_a to_o the_o elevation_n of_o the_o equinoctial_a in_o any_o latitude_n this_o be_v divide_v â—â—kewise_o into_o four_o 90_o s_o &_o number_v from_o the_o meridian_n each_o way_n to_o the_o east_n and_o west_n point_v of_o the_o horizon_n 4._o on_o the_o meridian_n circle_n be_v set_v 2_o movable_a pole_n to_o be_v elevate_v or_o depress_v fit_a to_o the_o latitude_n of_o any_o place_n on_o the_o fiducial-edge_n of_o which_o be_v fasten_v the_o thread_n represent_v the_o axis_n of_o the_o world_n at_o any_o elevation_n of_o the_o pole_n 5._o on_o the_o 2_o pole_n point_n be_v fasten_v the_o hour_n circle_n which_o delineate_v or_o represent_v the_o motion_n of_o the_o sun_n or_o any_o fix_a star_n move_v in_o its_o suppose_a diurnal_a motion_n about_o the_o pole_n of_o the_o world_n and_o may_v not_o improper_o be_v call_v the_o movable_a meridian_n circle_n or_o hour_n circle_n divide_v as_o before_o 6._o the_o movable_a horizon_n that_o move_v about_o to_o any_o azimuth_n and_o slide_v or_o move_v in_o the_o fix_a horizon_n 7._o the_o plain_a fix_v in_o 2_o opposite_a point_n to_o the_o move_a horizon_n be_v set_v either_o horizontal_a when_o it_o lie_v parallel_v to_o the_o fix_a horizon_n or_o erect_v when_o perpendicule_a thereunto_o or_o set_v to_o any_o reclination_n or_o inclination_n by_o help_n of_o the_o semicircle_n of_o reclination_n fasten_v to_o the_o backside_n of_o the_o plain_a in_o the_o 2_o pole_n thereof_o 8._o you_o have_v the_o upper_a move_a semicircle_n in_o turn_v about_o of_o which_o whatever_o degree_n the_o fore-side_n of_o the_o semicircle_n cut_v the_o perpendiculer-point_n cut_v the_o compleâ—ment_n thereof_o and_o to_o be_v call_v the_o upper_a semicircle_n or_o circle_n always_o perpendicuâ—ler_n to_o the_o plain_a 9_o there_o aught_o to_o be_v a_o thread_n fasten_v in_o the_o centre_n of_o the_o plain_a to_o be_v extend_v to_o any_o altitude_n or_o azimuth_n require_v thus_o much_o for_o description_n repeat_v again_o in_o short_a thus_o the_o horizon_n the_o meridian_n the_o equinoctial_a circle_n the_o 2_o pole_n point_n and_o axis_n the_o hour_n circle_n or_o movable_a meridian_n the_o movable_a horizon_n the_o plain_a the_o semicircle_n of_o reclination_n the_o upper_a semicircle_n and_o the_o thread_n note_v also_o every_o circle_n be_v divide_v into_o 4_o time_n 90_o and_o number_v the_o most_o useful_a way_n also_o on_o the_o plain_n be_v set_v the_o 12_o month_n and_o every_o single_a day_n on_o which_o every_o respective_a day_n if_o you_o extend_v the_o thread_n then_o in_o the_o degree_n be_v the_o sun_n right_a ascension_n in_o degree_n on_o the_o innermost_a circle_n the_o same_o in_o hour_n and_o quarter_n from_o the_o next_o equinoctial-point_n on_o the_o line_n of_o declination_n his_o mean_a declination_n on_o the_o line_n of_o â—he_n sun_n place_n his_o mean_a true_a place_n sufficient_o true_a for_o any_o illustration_n in_o mathematical_a practice_n the_o use_v whereof_o in_o some_o part_n follow_v 1._o to_o rectify_v the_o sphere_n to_o any_o latitude_n count_v the_o elevation_n of_o the_o pole_n on_o the_o meridian_n circle_n from_o the_o horizon_n upward_o and_o downward_o from_o the_o north_n and_o south_n part_n of_o the_o horizon_n and_o there_o make_v fast_o with_o the_o help_n of_o the_o small_a screw_n the_o fiducial-edge_n of_o the_o pole_n point_n carry_v the_o hour_n circle_v fix_v upon_o they_o than_o the_o pole_n be_v right_o elevate_v 2._o count_n the_o compliment_n of_o the_o pole_n elevation_n on_o the_o meridian_n from_o the_o south_n part_n of_o the_o horizon_n and_o to_o it_o set_v the_o divide_a side_n of_o the_o equinoctial_a circle_n then_o be_v that_o rectify_v also_o in_o the_o northern_a hemisphere_n or_o in_o the_o southern_a if_o you_o call_v the_o north_n pole_n the_o south_n pole_n 3._o extend_v the_o thread_n or_o axis_n pass_v through_o the_o centre_n to_o the_o south_n pole_n and_o there_o make_v it_o fast_o and_o then_o the_o sphere_n be_v rectify_v for_o many_o use_v in_o that_o latitude_n use_v i._o the_o day_n of_o the_o month_n be_v give_v to_o find_v the_o sun_n true_a place_n lay_v the_o thread_n in_o the_o centre_n of_o the_o plain_a on_o the_o day_n of_o the_o month_n and_o in_o the_o line_n of_o the_o sun_n place_n you_o have_v his_o place_n example_n on_o the_o 5_o of_o november_n it_o be_v 23_o degree_n in_o â™_o or_o if_o the_o sun_n place_n be_v give_v look_v for_o that_o and_o just_a against_o it_o in_o the_o month_n be_v the_o day_n require_v example_n the_o sun_n place_n be_v 15_o degree_n ♌_o i_o look_v for_o it_o in_o the_o line_n of_o his_o place_n and_o just_a against_o it_o i_o find_v july_n 28_o day_n use_v ii_o to_o find_v his_o declination_n any_o day_n look_v for_o the_o day_n give_v and_o right_a against_o it_o in_o the_o line_n of_o declination_n be_v his_o due_a declination_n require_v example_n august_n the_o 5_o the_o declination_n be_v 14_o degree_n 5_o minute_n from_o the_o next_o equinoctial-point_n viz._n ♎_o note_v in_o the_o northern_a sin_n or_o summertime_n the_o sun_n have_v north_n declination_n or_o in_o southern_a sin_n or_o winter-month_n the_o sun_n have_v south_n declination_n or_o if_o you_o have_v the_o sun_n declination_n find_v that_o in_o the_o line_n declination_n and_o right_a against_o it_o in_o the_o month_n be_v the_o day_n require_v example_n 21_o degree_n south_n declination_n begin_v from_o the_o equinoctial_a towards_o the_o winter_n solstice_n i_o find_v novemb_n 15._o the_o like_a work_n have_v be_v if_o the_o sun_n place_n have_v be_v give_v to_o find_v his_o declination_n use_v iii_o the_o day_n give_v to_o find_v the_o sun_n rightascention_n this_o be_v usual_o reckon_v from_o ♈_o to_o ♈_o round_a in_o 24_o hour_n but_o twice_o 12_o be_v as_o useful_a and_o then_o it_o be_v thus_o find_v the_o day_n among_o the_o month_n and_o day_n and_o just_a against_o it_o in_o the_o time_n of_o hour_n be_v the_o sun_n right_a ascension_n but_o note_n it_o be_v not_o right_o figure_v for_o this_o use_n count_v onward_o from_o ♈_o or_o the_o 10_o of_o march_n to_o the_o 13_o of_o septemb_n and_o from_o thence_o to_o aries_n again_o likewise_o the_o degree_n be_v to_o be_v reckon_v from_o ♈_o onward_o as_o the_o month_n proceed_v example_n on_o the_o 12_o of_o may_n what_o be_v the_o sun_n right_a ascension_n lay_v the_o thread_n on_o the_o 12_o of_o may_n and_o in_o the_o line_n of_o hour_n it_o cut_v 9-57′_a count_v from_o aries_n onward_o or_o in_o degree_n 59-15_a count_v as_o before_o thus_o if_o any_o one_o of_o these_o 4_o general_a thing_n be_v give_v the_o other_o may_v be_v find_v use_v iu._n the_o sun_n declination_n and_o latitude_n be_v give_v to_o find_v the_o sun_n meridian_n altitude_n the_o sphere_n be_v rectify_v count_v the_o declination_n on_o the_o meridian_n from_o the_o equinoctial_a that_o way_n the_o declination_n be_v either_o north_n or_o south_n and_o where_o the_o count_v end_n there_o be_v the_o meridian_n altitude_n require_v for_o that_o day_n or_o declination_n example_n june_n 11._o declination_n 23-30′_a count_v 23-30_a from_o 38-30_a the_o place_n where_o
show_v also_o 60_o degree_n on_o the_o innermost-edge_n of_o the_o loose-piece_n the_o calendar_n of_o month_n and_o day_n and_o degree_n of_o the_o sun_n place_n and_o right_a ascension_n on_o the_o moveable-leg_n for_o the_o speedy_a and_o ready_a find_v the_o sun_n place_n and_o declination_n which_o you_o may_v do_v to_o a_o minute_n at_o all_o time_n by_o help_n of_o the_o rectify_v table_n and_o astronomical_a caution_n of_o time_n and_o longitude_n also_o on_o the_o head-leg_n be_v the_o general_a scale_n of_o sines_n and_o line_n to_o the_o great_a and_o lesser_a radius_fw-la as_o in_o the_o figure_n and_o thus_o much_o will_v serve_v both_o for_o observation_n and_o operation_n as_o in_o the_o follow_a discourse_n will_v full_o appear_v 4._o to_o this_o instrument_n do_v chief_o belong_v the_o sight_n for_o the_o observation_n at_o sea_n where_o the_o horizon_n be_v make_v use_n of_o in_o the_o take_n the_o sun_n or_o star_n altitude_n and_o to_o this_o instrument_n belong_v the_o index_n and_o square_n that_o make_v it_o a_o most_o complete_a sinical-quadrant_n for_o the_o plain_a and_o easy_a resolve_v of_o all_o plain_a triangle_n also_o a_o weighty_a plummet_n and_o thread_n and_o a_o pair_n of_o large_a wood_n or_o brass_n compass_n for_o operation_n thus_o much_o for_o description_n be_v all_o put_v on_o one_o side_n only_o unless_o you_o shall_v be_v please_v to_o add_v the_o artificial_a number_n sin_n and_o tangent_n on_o the_o outer-edge_n and_o a_o meridian-line_n and_o his_o scale_n on_o the_o inner-edge_n and_o natural_a sin_n and_o natural_a versed-sines_n on_o the_o sector-side_n but_o these_o as_o you_o please_v chap._n ii_o the_o use_n of_o the_o trianguler-quadrant_n in_o observation_n that_o the_o discourse_n may_v be_v plain_a and_o brief_a and_o general_a there_o be_v 10_o term_n to_o be_v name_v and_o describe_v before_o i_o come_v to_o the_o use_v and_o example_n which_o be_v as_o follow_v 1._o first_o the_o head-leg_n of_o the_o instrument_n in_o which_o the_o brass-rivit_a be_v fix_v and_o about_o which_o the_o other_o leg_n turn_v as_o ab_fw-la in_o the_o figure_n on_o which_o leg_n the_o general_a scale_n of_o sines_n and_o line_n be_v usual_o set_v 2._o the_o moveable-leg_n on_o which_o the_o month_n and_o day_n be_v as_o in_o the_o figure_n note_v by_o bd_o which_o leg_n turn_v about_o the_o head-leg_n 3._o the_o loose-piece_n that_o be_v join_v to_o the_o head_n and_o moving-leg_n by_o two_o tennon_n at_o each_o end_n thereof_o note_v by_o da_fw-la in_o the_o figure_n 4._o the_o head-center_n or_o center-pin_n on_o the_o round-part_n of_o the_o head-leg_n be_v centre_n to_o the_o 60_o degree_n on_o the_o inside_n of_o the_o loose-piece_n which_o point_n be_v know_v by_o b_o in_o the_o figure_n 5._o the_o leg-center_n be_v near_o the_o end_n of_o the_o head-leg_n which_o be_v the_o centre_n to_o the_o degree_n on_o the_o moving-leg_n and_o outside_n of_o the_o loose-piece_n be_v in_o all_o 180_o degree_n and_o note_v in_o the_o figure_n by_o the_o letter_n c._n 6._o the_o great_a radius_fw-la or_o great_a line_n of_o sines_n issue_v from_o the_o leg-center_n towards_o the_o head_n have_v the_o tangent_n on_o the_o moveable-leg_n to_o the_o same_o radius_fw-la and_o the_o measure_n from_o the_o leg-center_n to_o the_o tangent_fw-la on_o the_o moving-leg_n a_o secant_fw-la to_o the_o same_o radius_fw-la as_o ce_fw-fr in_o the_o figure_n 7._o the_o little_a radius_fw-la that_o issue_n from_o the_o leg-center_n towards_o the_o end_n have_v the_o tangent_n on_o the_o outside_n of_o the_o loose-piece_n to_o the_o same_o radius_fw-la and_o the_o measure_n from_o the_o centre_n to_o those_o tangent_n for_o secant_v to_o the_o same_o radius_fw-la as_o cf._n 8._o the_o turn_a sight_n always_o to_o be_v skrew_v to_o the_o head_n or_o leg-center_n know_v by_o his_o shape_n and_o skrew-hole_n as_o 9_o the_o slide_a horizon-sight_n to_o slide_v on_o the_o moving-leg_n and_o loose-piece_n note_v with_o its_o bigness_n and_o hole_n to_o look_v through_o as_o 10._o the_o shadow_n sight_n and_o 2_o other_o to_o pin_v the_o instrument_n together_o which_o you_o may_v call_v the_o object-sight_n always_o fix_v in_o the_o two_o hole_n at_o the_o end_n of_o the_o moving-leg_n and_o the_o head-leg_n and_o the_o shadow-sight_n be_v to_o set_v to_o and_o fro_o to_o any_o place_n require_v note_v in_o the_o figure_n with_o 〈◊〉_d and_o the_o other_o two_o with_o 〈◊〉_d and_o thus_o you_o have_v their_o name_n and_o description_n at_o large_a which_o in_o brief_a take_v thus_o for_o easy_a remember_v 1._o the_o head-leg_n 2._o the_o moveable-leg_n 3._o the_o loose-piece_n 4._o the_o head-center_n 5._o the_o leg-center_n 6._o the_o great_a radius_fw-la 7._o the_o less_o radius_fw-la 8._o the_o turning-sight_n 9_o the_o horizon_n sliding-sight_n 10._o the_o shadow-sight_n and_o the_o two_o objest-sight_n the_o open-part_n in_o one_o be_v next_o to_o and_o the_o other_o remote_a from_o the_o rule_n to_o answer_v to_o the_o upper_a or_o lower-hole_n in_o the_o turning-sight_n according_a as_o you_o please_v to_o use_v they_o in_o observation_n thus_o much_o for_o the_o term_n the_o use_v follow_v use_v i._o to_o find_v the_o sun_n or_o a_o star_n altitude_n by_o a_o forward_a observation_n as_o by_o a_o fore-staff_n screw_v the_o turning-sight_n to_o the_o head-center_n and_o put_v the_o object-sight_n into_o the_o hole_n at_o the_o end_n of_o the_o head-leg_n and_o put_v the_o slide_a horizon-sight_n on_o the_o inside_n of_o the_o loose-piece_n then_o set_v the_o turning-sight_n to_o your_o eye_n and_o hold_v the_o loose-piece_n in_o your_o right-hand_a and_o the_o moveable-leg_n towards_o your_o body_n then_o with_o your_o thumb_n on_o the_o right-hand_a thrust_v upward_o or_o pull_v downward_o the_o horizon-sight_n till_o you_o see_v the_o sun_n through_o the_o object-sight_n and_o the_o horizon_n through_o the_o horizon-sight_n then_o the_o degree_n cut_v by_o the_o line_n on_o the_o middle_n of_o the_o horizon-sight_n shall_v show_v the_o true_a altitude_n require_v also_o observe_v that_o if_o you_o like_v to_o use_v the_o upper_a or_o lower-edge_n of_o the_o horizon-sight_n instead_o of_o the_o small_a bar_n across_o the_o open-hole_n after_o the_o manner_n of_o the_o end_n of_o a_o fore-staff_n that_o then_o the_o degree_n and_o minute_n cut_v by_o the_o edge_n of_o the_o brass_n be_v the_o altitude_n require_v to_o be_v count_v as_o it_o be_v figure_v from_o the_o object-sight_n towards_o the_o horizon-sight_n the_o degree_n between_o they_o be_v the_o angle_n require_v note_v also_o that_o if_o the_o altitude_n of_o the_o sun_n or_o star_n be_v above_o 30_o degree_n you_o will_v find_v it_o a_o hard_a matter_n to_o behold_v the_o horizon_n and_o sun_n with_o a_o bare_a roll_v the_o ball_n of_o the_o eye_n only_o and_o a_o stir_v of_o the_o head_n will_v easy_o cause_v a_o stir_v of_o the_o hand_n which_o will_v spoil_v the_o exactness_n of_o observation_n unless_o the_o instrument_n shall_v be_v fix_v to_o a_o ball-socket_n and_o three-legged-staff_n which_o be_v not_o usual_a at_o sea_n therefore_o to_o remedy_v this_o you_o may_v observe_v with_o the_o open_a oval-hole_n in_o the_o turning-sight_n set_v to_o the_o eye_n or_o take_v the_o turning-sight_n quite_o away_o observe_v just_a as_o you_o do_v with_o a_o fore-staffe_n set_v the_o round_a part_n of_o the_o head_n to_o the_o hollow-part_n beside_o your_o eye_n so_o as_o the_o head-center-pin_n may_v be_v as_o near_o the_o very_a sight_n of_o your_o eye_n as_o possible_o as_o you_o can_v which_o centre_n be_v the_o centre_n to_o the_o degree_n now_o use_v in_o a_o forward_a way_n of_o observation_n or_o rather_o use_v this_o way_n when_o the_o wether_n will_v suffer_v by_o a_o thread_n and_o plummet_n which_o i_o shall_v add_v as_o a_o second_o use._n use_v ii_o to_o observe_v the_o sun_n or_o a_o star_n altitude_n by_o a_o forward_a observation_n use_v the_o thread_n and_o plummet_n screw_v the_o turning-sight_n to_o the_o head-center_n as_o before_o and_o put_v the_o two_o object-sight_n into_o the_o two_o hole_n at_o the_o two_o end_n of_o the_o rule_n and_o on_o the_o leg-center-pin_n hang_v the_o thread_n with_o a_o weighty_a plummet_n of_o two_o pound_n or_o above_o a_o pound_n at_o least_o then_o hold_v up_o the_o trianguler-quadrant_n set_v the_o small-hole_n on_o the_o turning-sight_n close_o to_o your_o eye_n and_o if_o the_o sun_n or_o star_n be_v under_o 25_o degree_n high_a then_o look_v to_o the_o sun_n or_o star_n through_o the_o turning-sight_n and_o that_o object-sight_n which_o stand_v in_o the_o end_n of_o the_o moveable-leg_n let_v the_o thread_n and_o plummet_n play_v between_o your_o thumb_n and_o forefinger_n as_o a_o brick-layer_n plummet_n in_o his_o plum-rule_n do_v in_o a_o bendid_a hole_n that_o you_o may_v keep_v it_o in_o order_n whilst_o you_o look_v
prick_n after_o note_v a_o quarter_n of_o a_o minute_n and_o two_o prick_n half_o a_o minute_n and_o three_o prick_n three_o quarter_n of_o a_o minute_n more_o now_o by_o the_o rule_n you_o may_v count_v to_o a_o minute_n and_o the_o rectify_v table_n tell_v you_o how_o many_o minute_n more_o you_o must_v add_v to_o or_o subtract_v from_o the_o degree_n and_o minute_n the_o table_n or_o rule_n shall_v show_v it_o be_v in_o the_o second_o year_n a_o table_n of_o the_o sun_n declination_n every_o day_n at_o noon_n for_o london_n in_o the_o year_n 1666_o the_o second_o year_n after_o the_o leap-year_n according_a to_o mr._n street_n table_n of_o longitude_n calculate_v by_o john_n brown_n 1668._o month_n day_n janu._n febr._n march_v april_n may._n june_n d.m._n d.m._n d.m._n d.m._n d.m._n d.m._n 1_o 21_o 45_o ..._o 13_o 50._o 03_o 29._o 08_o 31._o 18_o 02_o 23_o 11._o 2_o 21_o 36_o 13_o 30._o 03_o 05._o 08_o 53._o 18_o 17._o 23_o 14._o 3_o 21_o 25._o 13_o 10._o 02_o 42_o 09_o 15._o 18_o 32_o 23_o 18._o 4_o 21_o 14_o ..._o 12_o 49_o ..._o 02_o 18._o 09_o 36_o ..._o 19_o 46_o ..._o 23_o 21_o 5_o 21_o 03._o 12_o 29_o 01_o 54_o ..._o 09_o 58_o 19_o 01_o 23_o 23_o ..._o 6_o 20_o 51_o 12_o 08._o 01_o 31_o 10_o 19_o 19_o 14_o ..._o 23_o 26_o 7_o 20_o 40_o 11_o 47._o 01_o 07_o 10_o 40_o ..._o 19_o 28._o 23_o 27_o ..._o 8_o 20_o 27._o 11_o 25_o ..._o 00_o 43._o 11_o 01_o 19_o 41._o 23_o 29._o 9_o 20_o 15_o 11_o 04._o s._n 19_o ..._o 11_o 22_o 19_o 54._o 23_o 30._o 10_o 20_o 01_o ..._o 10_o 43_o n._n 04._o 11_o 42_o ..._o 20_o 07_o 23_o 30_o ..._o 11_o 19_o 48._o 10_o 21_o 00_o 27_o ..._o 12_o 03_o 20_o 19_o 23_o 31_o 12_o 19_o 34._o 09_o 59_o 00_o 51._o 12_o 23_o 20_o 31_o 23_o 30._o 13_o 19_o 20._o 09_o 37_o 01_o 15_o 12_o 43._o 20_o 42._o 23_o 30_o 14_o 19_o 06_o 01_o 15_o 01_o 38._o 13_o 03_o 20_o 54_o 23_o 29_o 15_o 18_o 51_o 08_o 52_o 02_o 02._o 13_o 22._o 21_o 04._o 23_o 37._o 16_o 18_o 35_o ..._o 08_o 29_o ..._o 02_o 26_o 13_o 42_o 21_o 15._o 23_o 15._o 17_o 18_o 20._o 08_o 07._o 04_o 49._o 14_o 01_o 21_o 25._o 23_o 23_o 18_o 18_o 04_o 07_o 44_o ..._o 03_o 13_o 14_o 20_o 21_o 35_o 23_o 20._o 19_o 17_o 48_o 07_o 22_o 03_o 36_o 14_o 38._o 21_o 44._o 23_o 17._o 20_o 17_o 31._o 06_o 59_o 03_o 59_o 14_o 57_o 21_o 53._o 23_o 14_o 21_o 17_o 14._o 06_o 36_o 04_o 22._o 15_o 15_o 22_o 01_o ..._o 23_o 10_o 22_o 16_o 57_o 06_o 13_o 04_o 45_o ..._o 15_o 33_o 22_o 10._o 23_o 05._o 23_o 16_o 40_o 05_o 50_o 05_o 0â—_n ..._o 15_o 50_o ..._o 22_o 17_o ..._o 23_o 01_o 24_o 16_o 22._o 05_o 26._o 05_o 32_o 16_o 08_o 22_o 25._o 22_o 55_o ..._o 25_o 16_o 03_o ..._o 05_o 03._o 05_o 34._o 16_o 25._o 22_o 32._o 22_o 50._o 26_o 15_o 45_o 04_o 39_o ..._o 06_o 17._o 16_o 42_o 22_o 39_o 22_o 44._o 27_o 15_o 27_o 04_o 16._o 06_o 40_o 16_o 58._o 22_o 45._o 22_o 37_o ..._o 28_o 15_o 08_o 03_o 52_o ..._o 07_o 02._o 17_o 14_o ..._o 22_o 51._o 22_o 31_o 29_o 14_o 49_o  _fw-fr 07_o 25_o 17_o 30_o ..._o 22_o 57_o 22_o 23_o ..._o 30_o 14_o 29._o  _fw-fr 07_o 47_o 17_o 47_o 23_o 02_o 22_o 16._o 31_o 14_o 10._o  _fw-fr 08_o â—9_n  _fw-fr 23_o 06._o  _fw-fr a_o table_n of_o the_o sun_n declination_n every_o day_n at_o noon_n etc._n etc._n month_n day_n july_n augu._n septem_fw-la octob._n novem_n decem_fw-la d.m._n d.m._n d.m._n d.m._n d.m._n d.m._n 1_o 22_o 09_o 15_o 14._o 04_o 26._o 07_o 12._o 17_o 37_o ..._o 23_o 07._o 2_o 22_o 00._o 14_o 56_o 04_o 03_o ..._o 07_o 35._o 17_o 35_o ..._o 23_o 12_o 3_o 21_o 51._o 14_o 37._o 03_o 40_o ..._o 07_o 58_o ..._o 18_o 10._o 23_o 16_o 4_o 21_o 42._o 14_o 19_o 03_o 17._o 08_o 20._o 18_o 25._o 23_o 19_o 5_o 21_o 33_o 14_o 00_o ..._o 02_o 54._o 08_o 42._o 18_o 41._o 23_o 22._o 6_o 21_o 23._o 13_o 41._o 02_o 31_o 09_o 04_o ..._o 18_o 56._o 23_o 25_o 7_o 21_o 13._o 13_o 22._o 02_o 08._o 09_o 27_o 19_o 10_o ..._o 23_o 27._o 8_o 21_o 02._o 13_o 03_o 01_o 44._o 09_o 49_o 19_o 25._o 23_o 28_o ..._o 9_o 20_o 52_o 12_o 43._o 01_o 20_o ..._o 10_o 11_o 19_o 39_o 23_o 30_o 10_o 20_o 41_o 12_o 23_o 00_o 57_o 10_o 32._o 19_o 53_o 23_o 30_o ..._o 11_o 20_o 29_o 12_o 02_o ..._o n_o 34_o 10_o 53_o ..._o 20_o 06._o 23_o 31_o 12_o 20_o 17._o 11_o 43_o n_o 10._o 11_o 15._o 20_o 19_o 23_o 30._o 13_o 20_o 05_o 11_o 21._o s_o 13._o 11_o 36._o 20_o 31_o ..._o 23_o 30_o 14_o 19_o 52_o ..._o 11_o 02_o 00_o 36_o ..._o 11_o 57_o 20_o 44_o 23_o 29_o 15_o 19_o 39_o 10_o 41._o 01_o 00_o ..._o 12_o 18._o 20_o 55_o ..._o 23_o 27_o 16_o 19_o 26_o ..._o 10_o 20._o 01_o 24_o 12_o 38_o ..._o 21_o 07_o 23_o 25._o 17_o 19_o 13._o 09_o 59_o 01_o 47._o 12_o 59_o 21_o 18._o 23_o 22._o 18_o 18_o 59_o 09_o 38_o 02_o 10_o ..._o 13_o 20_o 21_o 28_o ..._o 23_o 19_o 19_o 18_o 44_o ..._o 09_o 16_o ..._o 02_o 34._o 13_o 39_o ..._o 21_o 38_o ..._o 23_o 16_o 20_o 18_o 30._o 08_o 55._o 02_o 58_o 13_o 59_o 21_o 48._o 23_o 11_o ..._o 21_o 18_o 15_o ..._o 08_o 33._o 03_o 21._o 14_o 19_o 21_o 58_o 23_o 07._o 22_o 18_o 00._o 08_o 11._o 03_o 44._o 14_o 38_o 22_o 07_o 23_o 02._o 23_o 17_o 45._o 07_o 49_o ..._o 04_o 08_o 14_o 57_o 22_o 15._o 22_o 57_o 24_o 17_o 29._o 07_o 27._o 04_o 31._o 15_o 16_o 22_o 23._o 22_o 51._o 25_o 17_o 31._o 07_o 05._o 04_o 54._o 15_o 35_o 22_o 31_o 22_o 44_o ..._o 26_o 16_o 57_o 06_o 43_o 05_o 18._o 15_o 53._o 22_o 38._o 22_o 38_o 27_o 16_o 40._o 06_o 20._o 05_o 41_o 16_o 11._o 22_o 45_o 22_o 30._o 28_o 16_o 24_o 05_o 57_o 06_o 04_o 16_o 29._o 22_o 51._o 22_o 23_o 29_o 16_o 06._o 05_o 35._o 06_o 27_o 16_o 46_o ..._o 22_o 57_o 22_o 15_o 30_o 15_o 49._o 05_o 12._o 06_o 49._o 17_o 03_o ..._o 23_o 02_o ..._o 22_o 06._o 31_o 15_o 32_o  _fw-fr  _fw-fr 17_o 20._o  _fw-fr 21_o 57_o a_o table_n of_o the_o sun_n declination_n for_o every_o 5_o and_o 10_o day_n of_o every_o month_n of_o the_o four_o year_n calculate_v from_o mr._n street_n table_n of_o the_o sun_n place_n make_v for_o the_o year_n 1665_o 1666_o 1667_o and_o 1668_o the_o near_a extant_a m._n d_o 1._o 1665_o 2._o 1666_o 3._o 1667_o l.y._n 68_o january_n 05_o 21_o 01_o 21_o 03._o 21_o 06._o 21_o 09._o 10_o 19_o 58._o 20_o 01_o ..._o 20_o 05_o 20_o 08._o 15_o 18_o 47._o 18_o 51_o 18_o 54._o 18_o 58._o 20_o 17_o 27._o 17_o 31._o 17_o 35_o 17_o 39_o 25_o 15_o 59_o ..._o 16_o 03_o ..._o 16_o 08_o 16_o 12_o ..._o 30_o 14_o 25_o 14_o 29_o ..._o 14_o 34._o 14_o 39_o february_n 05_o 12_o 24_o 12_o 29_o 12_o 34_o 12_o 39_o 10_o 10_o 39_o 10_o 43_o 10_o 48_o 10_o 53._o 15_o 08_o 47_o 08_o 52._o 08_o 57_o ..._o 09_o 03._o 20_o 06_o 53._o 06_o 59_o 07_o 04_o ..._o 07_o 10._o 25_o 04_o 57_o 05_o 03._o 05_o 08_o ..._o 05_o 14._o 28_o 03_o 47._o saint_n 03_o 52_o ..._o 03_o 58._o 04_o 04._o march_n 05_o 01_o 48_o ..._o 01_o 54_o ..._o 02_o 00._o 01_o 42._o saint_n 10_o 00_o 10_o n_o 00_o 04._o n_o 00_o 01_o ..._o s_o 00_o 16._o n_o 15_o 02_o 08_o 02_o 02._o 01_o 56._o n_o 02_o 14._o 20_o 04_o 05_o 03_o 59_o 03_o 54_o 04_o 11._o 25_o 06_o 00._o 05_o 54._o 05_o 49._o 06_o 06._o 30_o 07_o 52_o ..._o 07_o 47_o 07_o 42._o 07_o 58._o april_n 05_o 10_o 03._o 09_o 58_o 09_o 53_o 10_o 09_o 10_o 11_o 47_o ..._o 11_o 42_o ..._o 11_o 37_o ..._o 11_o 35._o 15_o 13_o 27._o 13_o 22._o 13_o 17._o 13_o 32._o 20_o 15_o 01._o 14_o 57_o 15_o 52._o 15_o 06._o 25_o 16_o 29._o 16_o 29._o 16_o 21._o 16_o 34_o 30_o 17_o 50._o 17_o 47_o 17_o 42_o ..._o 17_o 54._o may._n 05_o 19_o 04._o 19_o 01_o 18_o 57_o 19_o 08_o 10_o 20_o 10_o 20_o 07_o 20_o 04_o 20_o 13._o 15_o 21_o 07_o 21_o 04._o 21_o 02_o 21_o 10_o 20_o 21_o 55._o 21_o 53._o 21_o 51_o ..._o 21_o 57_o ..._o 25_o 22_o 34_o 22_o 32._o 22_o 30_o ..._o 22_o 36_o 30_o 23_o 03_o 23_o 02_o 23_o 01_o 23_o 04._o june_n 05_o 23_o 24_o 23_o 23_o ..._o 23_o 23_o 23_o 25._o 10_o 23_o 30_o ..._o 23_o 30_o ..._o 23_o 30._o 23_o 31_o 15_o 23_o 27_o 23_o 27._o 23_o 28_o 23_o 26_o ..._o 20_o 23_o 13_o 23_o 14_o 23_o 15_o ..._o 23_o 12_o 25_o 22_o 48_o ..._o 22_o 50._o 22_o 51_o ..._o 22_o
count_v the_o fiducial_a line_n in_o which_o the_o leg-center-pin_n stand_v always_o for_o the_o meridian_n of_o one_o place_n and_o some_o where_o in_o that_o line_n according_a to_o the_o latitude_n thereof_o count_v the_o leg-center_n the_o pole_n of_o the_o world_n and_o the_o index_n be_v hang_v thereon_o by_o the_o tangent_n prick_v down_o the_o latitude_n there_o i_o say_v knock_v in_o a_o pin_n to_o stay_v a_o thread_n for_o one_o place_n then_o on_o the_o degree_n count_v the_o difference_n of_o longitude_n from_o the_o head-leg_n and_o lay_v the_o index_n to_o it_o and_o bring_v the_o thread_n fasten_v as_o before_z till_o on_o the_o index_n it_o cut_v the_o degree_n and_o part_n of_o the_o other_o latitude_n and_o there_o make_v the_o thread_n fast_o with_o another_o pin_n in_o the_o loose-piece_n then_o if_o you_o move_v the_o index_n to_o any_o degree_n of_o longitude_n between_o those_o place_n the_o thread_n shall_v cut_v on_o the_o index_n the_o degree_n of_o latitude_n that_o answer_v unto_o it_o or_o if_o you_o make_v the_o thread_n cut_v any_o degree_n of_o latitude_n the_o index_n give_v the_o longitude_n require_v for_o that_o latitude_n note_v if_o the_o latitude_n be_v small_a as_o between_z 10_o and_o 30_o the_o small_a tangent_n be_v most_o convenient_a but_o if_o it_o be_v between_o 40_o and_o 80_o the_o great_a tangent_fw-la line_n be_v best_a note_v that_o two_o thread_n and_o a_o pair_n of_o compass_n may_v serve_v but_o the_o index_n be_v much_o better_a and_o quick_a in_o operation_n example_n let_v the_o two_o place_n be_v the_o summer-island_n and_o the_o lizard-point_n the_o same_o example_n that_o you_o find_v in_o mr._n norwood_n pag._n 126_o and_o in_o mr._n phillip_n geometrical-seaman_n pag._n 55._o that_o you_o may_v the_o more_o ready_o compare_v the_o truth_n thereof_o by_o their_o operation_n the_o latitude_n of_o the_o lizard_n point_n be_v 50_o degree_n the_o longitude_n be_v 10._o the_o latitude_n of_o the_o summer_n island_n be_v 32-25_a the_o longitude_n be_v 300._o the_o difference_n of_o longitude_n be_v 70_o as_o be_v compute_v by_o their_o observation_n then_o hang_v or_o put_v the_o center-hole_n of_o the_o index_n over_o the_o leg-center-pin_n and_o count_v the_o fiducial-line_n on_o the_o head-leg_n for_o the_o meridian_n of_o one_o place_n count_v on_o the_o tangent_fw-la line_n on_o the_o index_n the_o co-tangent_a of_o one_o latitude_n as_o suppose_v the_o latitude_n of_o the_o lizard-point_n the_o centre_n always_o count_v as_o 90_o and_o there_o knock_v in_o a_o pin_n in_o a_o small_a hole_n to_o hang_v a_o thread_n on_o then_o count_v 70_o degree_n the_o difference_n in_o longitude_n on_o the_o degree_n from_o the_o head-leg_n and_o there_o stay_v it_o then_o draw_v the_o thread_n put_v over_o the_o first_o pin_n till_o it_o cut_v the_o compliment_n of_o the_o other_o latitude_n and_o by_o help_n of_o another_o pin_n stay_v it_o there_o which_o you_o may_v convenient_o do_v by_o one_o of_o the_o sliding-sight_n then_o the_o thread_n be_v so_o lay_v slide_v the_o index_n to_o every_o single_a degree_n or_o five_o degree_n of_o longitude_n and_o then_o the_o thread_n shall_v show_v on_o the_o index_n the_o co-tangent_a of_o the_o latitude_n answerable_a to_o that_o degree_n of_o longitude_n as_o in_o the_o table_n annex_v also_o if_o you_o will_v have_v equal_a degree_n of_o latitude_n and_o will_v find_v the_o longitude_n according_a to_o it_o then_o slide_v the_o index_n to_o and_o fro_o till_o the_o thread_n cut_v on_o the_o index_n a_o even_a degree_n of_o latitude_n then_o on_o the_o degree_n you_o have_v the_o difference_n of_o longitude_n from_o either_o place_n also_o note_n that_o the_o draw_v of_o one_o line_n only_o on_o the_o triangule_a instrument_n in_o the_o beginning_n according_a to_o the_o direction_n of_o lay_v of_o the_o thread_n with_o the_o thread_n and_o compass_n will_v perform_v this_o work_n also_o the_o table_n long_o d.l._n latitude_n 300_o 09_o 32_o 25_o 305_o 05_o 35_o 52_o 310_o 10_o 38_o 51_o 315_o 15_o 41_o 24_o 320_o 20_o 43_o 34_o 325_o 25_o 45_o 24_o 330_o 30_o 46_o 54_o 335_o 35_o 48_o 07_o 340_o 40_o 49_o 04_o 345_o 45_o 49_o 47_o 350_o 50_o 50_o 15_o 355_o 55_o 50_o 31_o 360_o 60_o 50_o 33_o 05_o 65_o 50_o 23_o 10_o 70_o 50_o 00_o if_o this_o work_n fit_v not_o any_o case_n that_o may_v happen_v there_o be_v another_o way_n mention_v in_o page_n 75_o of_o the_o geometrical_a seaman_n by_o the_o steriographick_a projection_n and_o that_o scheam_n be_v draw_v the_o same_o way_n as_o the_o horizontal-projection_n for_o dyall_v be_v and_o somewhat_o easy_o and_o any_o two_o point_n give_v in_o a_o circle_n you_o may_v draw_v a_o great_a circle_n to_o cut_v they_o and_o the_o first_o circle_n into_o two_o equal-part_n by_o the_o direction_n in_o page_z 15_o and_o the_o application_n thereof_o you_o have_v very_o plain_o in_o mr._n phillip_n his_o book_n to_o which_o i_o refer_v you_o have_v say_v more_o than_o at_o first_o i_o intend_v which_o be_v chief_o the_o use_n thereof_o in_o observation_n only_o so_o for_o the_o present_a i_o conclude_v this_o discourse_n and_o shall_v endeavour_v a_o further_a advantage_n in_o the_o next_o impression_n according_a as_o time_n and_o opportunity_n shall_v offer_v farewell_o the_o end_n of_o the_o second_o part._n the_o table_n of_o the_o thing_n contain_v in_o this_o second_o part._n the_o definition_n and_o kind_n of_o dial_n page_n 7_o direction_n to_o draw_v the_o scheam_n 9_o to_o draw_v line_n to_o represent_v the_o several_a sort_n of_o plain_n in_o the_o scheam_n 13_o to_o draw_v a_o scheam_n particular_o for_o one_o dial_n 14_o to_o draw_v the_o equinoctial_a dial_n 19_o to_o try_v when_o a_o plain_a lie_v equinoctial_a 20_o to_o draw_v a_o polar-dial_n 21_o to_o draw_v a_o erect_a east_n or_o west-dial_n 24_o to_o draw_v a_o horizontal-dial_n 27_o the_o demonstration_n of_o the_o canon_n for_o hour_n ib._n to_o draw_v a_o direct_a erect_a south_n or_o north-dial_n 30_o to_o draw_v a_o direct_a recliner_n 33_o the_o use_n of_o the_o figure_n 35_o to_o draw_v a_o direct_a east_n or_o west_n recliner_n 37_o to_o make_v the_o table_n of_o ark_n at_o the_o pole_n 42_o to_o refer_v those_o dial_n to_o a_o new_a latitude_n and_o a_o new_a declination_n wherein_o they_o may_v become_v erect_a decliner_n 46_o to_o find_v the_o requisite_n by_o the_o scheam_n ibid._n to_o find_v the_o declination_n of_o a_o plain_a by_o the_o needle_n or_o by_o the_o sun_n 49_o to_o take_v off_o a_o angle_n or_o set_v the_o sector_n to_o any_o angle_n require_v 53_o precept_n to_o find_v the_o declination_n by_o the_o sun_n and_o example_n also_o of_o the_o same_o 58_o to_o draw_v a_o erect_a declining-dial_n 62_o the_o proportion_n for_o the_o requisite_n of_o erect_a decliner_n 64_o to_o find_v the_o requisite_n three_o way_n 66_o to_o draw_v the_o erect_a south_n decliner_n 67_o to_o draw_v the_o line_n on_o a_o north_n decliner_n 70_o to_o draw_v the_o hour-line_n on_o a_o plain_a that_o decline_v above_o 60_o degree_n 73_o of_o decline_a recline_a plain_n 77_o the_o first_o sort_n of_o south_n recliner_n 79_o the_o second_o sort_n of_o south_n recliner_n be_v polar_n 90_o the_o three_o sort_n of_o south-recliners_a 98_o the_o first_o sort_n of_o north_n recliner_n 106_o the_o second_o sort_n of_o north_n recliner_n be_v equinoctial_a 114_o the_o three_o sort_n of_o north_n recliner_n 119_o of_o incline_v diâ—ls_n 126_o to_o find_v the_o useful_a hour_n in_o all_o plain_n 130_o to_o draw_v the_o mathematical_a ornament_n on_o all_o sort_n of_o dial_n 134_o to_o draw_v the_o tropic_n or_o length_n of_o the_o day_n 136_o to_o make_v the_o trygon_n 138_o to_o draw_v the_o planetary_a or_o jewish_a hour_n 142_o to_o draw_v the_o italian_a hour_n 144_o to_o draw_v the_o babylonish_n hour_n 145_o to_o draw_v the_o azimuth_n line_n 146_o to_o draw_v the_o almicanter_n 154_o to_o draw_v the_o circle_n of_o position_n or_o house_n 160_o to_o draw_v the_o hour_n and_o all_o the_o rest_n on_o the_o ceiling_n of_o a_o room_n 165_o the_o figure_n of_o the_o instrument_n explain_v 166_o a_o table_n of_o the_o sun_n azimuth_n at_o every_o hour_n and_o quarter_n in_o the_o whole_a sign_n 168_o a_o table_n of_o the_o sun_n altitude_n the_o same_o time_n 169_o the_o description_n and_o use_v of_o the_o armilary-sphear_n for_o dyall_v several_a way_n 172_o the_o description_n and_o use_v of_o the_o poor-man_n dial-sphear_n for_o dyall_v and_o several_a uses_n thereof_o 203_o how_o to_o remedy_n several_a inconvenience_n in_o the_o use_n of_o the_o gunter_n rule_n 220_o the_o use_n and_o a_o further_a description_n of_o the_o trianguler-quadrant_n for_o navigation_n or_o observation_n at_o sea_n 227_o for_o a_o fore-observation_n with_o
that_o it_o carry_v the_o needle_n a_o competent_a distance_n from_o the_o wall_n to_o prevent_v that_o attraction_n but_o if_o it_o happen_v to_o be_v so_o near_o a_o meridian_n or_o east_n and_o west-plain_a that_o the_o angle_n by_o the_o sector_n can_v well_o be_v take_v then_o you_o may_v only_o apply_v the_o side_n of_o the_o box_n and_o needle_n to_o the_o wall_n and_o the_o needle_n itself_o will_v show_v the_o declination_n on_o the_o degree_n on_o the_o bottom_n of_o the_o box._n yet_o for_o exactness_n the_o way_n by_o the_o sun_n be_v always_o the_o best_a where_o you_o may_v come_v to_o make_v a_o good_a observation_n and_o then_o the_o needle_n only_o be_v not_o to_o be_v trust_v to_o a_o better_a way_n with_o opportunity_n offer_v itself_o to_o fâ—nd_v a_o declination_n of_o a_o wall_n by_o the_o sun_n for_o this_o purpose_n you_o must_n or_o ought_v to_o have_v another_o thread_n and_o plummet_n which_o thread_n may_v be_v a_o fine_a even_o small_a packthread_n and_o it_o be_v convenient_a to_o have_v it_o ready_a hang_v up_o near_o the_o wall_n so_o far_o off_o as_o the_o trianguler-quadrant_n may_v pass_v along_o between_o it_o and_o the_o wall_n that_o you_o may_v not_o be_v trouble_v to_o hold_v it_o up_o and_o lay_v it_o down_o and_o be_v annoy_v with_o the_o inconvenience_n of_o your_o hand_n shake_v and_o time_n waste_v to_o more_o uncertainty_n than_o need_v be_v also_o you_o must_v needs_o take_v notice_n of_o the_o two_o meridian_n viz._n one_o of_o the_o place_n which_o be_v the_o meridian_n or_o 12_o a_o clock_n to_o which_o place_n when_o the_o sun_n or_o a_o star_n come_v it_o be_v say_v to_o be_v in_o the_o meridian_n and_o the_o other_o be_v the_o meridian_n of_o the_o plain_a in_o which_o line_n the_o pole-point_n of_o every_o plain_n be_v be_v 90_o degree_n distant_a from_o the_o plain_a every_o way_n and_o in_o all_o upright-dials_n their_o pole_n be_v in_o the_o horizon_n and_o that_o degree_n of_o azimuth_n in_o which_o the_o pole-point_n lie_v count_v from_o south_n or_o north_n towards_o east_n or_o west_n be_v always_o the_o declination_n thereof_o so_o that_o by_o find_v the_o sun_n azimuth_n at_o any_o time_n and_o the_o distance_n of_o the_o sun_n at_o the_o same_o time_n from_o the_o meridian_n of_o the_o plain_a be_v get_v the_o declination_n the_o azimuth_n of_o the_o sun_n from_o the_o meridian_n of_o the_o place_n be_v find_v by_o the_o 26_o 27_o 28_o 30_o 32_o 34_o 39_o uses_n of_o the_o 15_o chapter_n but_o the_o azimuth_n of_o the_o sun_n from_o the_o meridian_n of_o the_o plain_a be_v find_v by_o apply_v the_o head-leg_n against_o the_o plain_a horizontal_o slip_v it_o to_o and_o fro_o till_o the_o shadow_n of_o the_o thread_n hang_v or_o hold_v up_o play_v right_a over_o the_o centre_n of_o the_o trianguler-quadrant_n on_o the_o head-leg_n then_o what_o deg_n soever_o the_o thread_n cut_v count_v from_o 60â—0_n on_o the_o loose-piece_n be_v the_o perpendicule_a or_o pole-point_n of_o the_o plain_a shall_v be_v the_o azimuth_n of_o the_o sun_n from_o the_o meridian_n of_o the_o plain_a this_o be_v the_o operation_n the_o application_n or_o use_n be_v word_v several_a way_n by_o several_a man_n i_o hope_v i_o shall_v do_v it_o as_o full_o and_o as_o brief_o as_o some_o other_o the_o sun_n to_o our_o appearance_n pass_v from_o east_n by_o the_o meridian_n to_o the_o west_n every_o day_n therefore_o in_o the_o morning_n it_o want_v of_o come_v to_o the_o meridian_n at_o noon_n it_o be_v for_o a_o moment_n just_a in_o the_o meridian_n and_o in_o the_o afternoon_n it_o be_v pass_v the_o meridian_n of_o the_o place_n even_o so_o it_o begin_v to_o shine_v on_o and_o be_v direct_o against_o and_o leave_v to_o shine_v upon_o most_o plain_n when_o it_o begin_v to_o shine_v upon_o or_o be_v not_o direct_o against_o i_o say_v it_o want_v of_o come_v to_o the_o pole_n or_o meridian_n of_o the_o plain_a when_o it_o be_v direct_o against_o the_o plain_a than_o it_o be_v in_o the_o meridian_n or_o pole_n of_o the_o plain_a when_o it_o â—s_v pass_v it_o be_v past_a or_o begin_v to_o leave_v the_o plain_a which_o thâ—ee_o variety_n i_o intend_v thus_o brief_o to_o eâ—press_v azimuth_n want_n or_o w_n in_o the_o morning_n only_o azimuth_n direct_v at_o noon_n azimuth_n past_a or_o p_o be_v in_o the_o afternoon_n the_o other_o three_o variety_n let_v be_v shadow_n want_v shadow_n direct_v shadow_n past_a all_o which_o may_v be_v in_o several_a plain_n at_o several_a time_n that_o be_v to_o say_v at_o morning_n noon_n and_o night_n these_o observation_n and_o caution_n premise_v the_o rule_n be_v thus_o 1._o if_o the_o azimuth_n and_o shadow_n be_v both_o want_v or_o both_o past_a subtract_v the_o loss_a out_o of_o the_o great_a and_o the_o residue_n be_v the_o declination_n but_o if_o one_o want_v and_o the_o other_o be_v past_a than_o the_o sum_n of_o they_o be_v the_o declination_n 2._o if_o the_o sun_n come_v to_o the_o meridian_n of_o the_o plain_a before_o it_o come_v to_o the_o meridian_n of_o the_o place_n it_o be_v a_o east_n plain_a but_o if_o it_o come_v to_o the_o meridian_n of_o the_o place_n before_o it_o come_v to_o the_o meridian_n of_o the_o plain_a it_o be_v a_o west_n plain_a 3._o if_o the_o sum_n or_o remainder_n after_o addition_n or_o substraction_n be_v under_o 90_o it_o be_v a_o southeast_n or_o south-west_n plain_a decline_v so_o many_o degree_n as_o the_o sum_n or_o residue_n be_v but_o if_o the_o sum_n or_o remainder_n be_v above_o 90_o it_o be_v a_o north-east_n or_o a_o northwest_n plain_a and_o the_o compliment_n of_o the_o sum_n or_o remainder_n to_o 180_o be_v the_o quantity_n of_o declination_n north-east_n or_o northwest_n 4._o if_o the_o sum_n or_o remainder_n be_v 00_o it_o be_v just_a south_n if_o 90_o just_a east_n or_o west_n but_o if_o it_o be_v 180_o it_o be_v a_o direct_a north_n plain_a it_o shall_v be_v further_o explain_v by_o two_o or_o three_o example_n suppose_v that_o on_o the_o first_o of_o may_n in_o the_o forenoon_n i_o come_v and_o apply_v the_o head-leg_n of_o the_o trianguler-quadrant_n to_o the_o wall_n and_o hold_v of_o it_o level_v the_o shadow_n of_o the_o thread_n hold_v up_o steady_a cut_v the_o centre_n and_o 60_o degree_n on_o the_o moving-leg_n that_o be_v 60_o deg_n want_v which_o i_o present_o set_v down_o in_o a_o paper_n ready_a prepare_v thus_o may_v 1_o 1669._o forenoon_n shadow_n 60_o 00_o want_n altitude_n 20_o 00_o  _fw-fr azimuth_n 94_o 00_o want_n subtract_v 34_o 00_o southeast_n then_o as_o soon_o as_o possible_a or_o rather_o by_o some_o body_n else_o at_o the_o same_o moment_n find_v the_o sun_n altitude_n which_o suppose_v to_o be_v 20_o degree_n but_o if_o you_o be_v alone_o and_o have_v a_o thread_n ready_a hang_v up_o then_o take_v the_o altitude_n first_o and_o the_o shadow_n will_v be_v have_v present_o after_o the_o thread_n hang_v steady_o and_o set_v that_o down_o also_o as_o here_o you_o see_v then_o by_o the_o 26_o use_n of_o the_o 15_o chapter_n you_o shall_v find_v the_o sun_n azimuth_n at_o that_o time_n and_o altitude_n to_o be_v 94_o degree_n and_o after_o substraction_n remain_v 34-0_a for_o the_o wall_n declination_n eastward_o because_o the_o remainder_n be_v under_o 90_o and_o the_o sun_n come_v to_o the_o meridian_n of_o the_o plain_a before_o it_o come_v to_o the_o meridian_n of_o the_o place_n or_o south_n again_o in_o a_o morning_n june_n 13_o i_o observe_v the_o altitude_n and_o find_v it_o 15_o degree_n and_o instant_o the_o shadow_n and_o find_v it_o to_o be_v 10_o degree_n past_o the_o plain_n viz._n on_o the_o loose-piece_n towards_o the_o head-leg_n i_o set_v both_o altitude_n and_o shadow_n with_o the_o day_n and_o time_n down_o thus_o june_n 13_o forenoon_n altitude_n 15_o 0_o  _fw-fr shadow_n 10_o 0_o past._n azimuth_n 109_o 0_o want_n sum_n be_v 119_o 0_o  _fw-fr  _fw-fr 180_o 0_o  _fw-fr  _fw-fr 061_o 0_o north-east_n and_o then_o find_v the_o azimuth_n at_o that_o time_n and_o altitude_n to_o be_v 109_o degree_n here_o the_o term_n be_v unlike_a i_o add_v they_o together_o and_o the_o sum_n be_v above_o 90_o i_o know_v it_o must_v be_v a_o north_n plain_a and_o because_o the_o sun_n come_v to_o the_o plain_a before_o it_o come_v to_o the_o meridian_n of_o the_o place_n it_o be_v north-east_n and_o the_o compliment_n of_o 119_o to_o 180_o be_v 61-0_a north-east_n again_o june_n 13_o afternoon_n altitude_n 15_o 0_o  _fw-fr shadow_n 20_o 0_o want_n azimuth_n 109_o 0_o past._n sum_n be_v 129_o 0_o  _fw-fr  _fw-fr 180_o 0_o  _fw-fr  _fw-fr 051_o 0_o northwest_n but_o if_o you_o happen_v to_o come_v when_o the_o sun_n be_v in_o the_o meridian_n of_o the_o plain_a than_o
according_a to_o what_o time_n of_o year_n you_o will_v know_v when_o the_o sun_n begin_v and_o cease_v to_o shine_v on_o any_o plain_a and_o turn_v the_o hour-circle_n with_o the_o thread_n so_o lay_v till_o the_o thread_n do_v but_o just_a touch_n the_o plain_a and_o the_o hour-circle_n do_v on_o the_o equinoctial_a cut_v the_o hour_n and_o minuit_n require_v when_o the_o sun_n come_v on_o the_o east-side_n and_o when_o it_o go_v off_o from_o the_o westside_n of_o the_o plain_a example_n suppose_v you_o have_v a_o direct_v north-plain_a that_o recline_v from_o the_o zenith_n towards_o the_o equinoctial_a 25_o degree_n you_o shall_v find_v the_o style_n elevation_n to_o be_v 63-30_a the_o substile_a from_o 12._o the_o north-pole_n to_o be_v elevate_v on_o the_o recliner_n and_o the_o south-pole_n on_o the_o incliner_n and_o that_o the_o sun_n shine_v on_o the_o north-recline_a in_o the_o long_a day_n viz._n 23-31_a declination_n from_o the_o rise_a 13′_n before_o 4_o till_z 10_o and_o than_o it_o begin_v to_o shine_v on_o the_o south-incline_a and_o shine_v till_o 2_o afternoon_n than_o it_o come_v on_o the_o north-recline_a again_o and_o continues_z till_o it_o set_v but_o in_o the_o short_a day_n when_o the_o declination_n be_v 23-30_a towards_o south_n then_o on_o the_o north-recline_a it_o shine_v not_o at_o all_o but_o only_o on_o the_o south-incline_a from_o rise_v to_o set_v and_o so_o do_v it_o all_o the_o time_n the_o sun_n have_v south-declination_n this_o rule_n serve_v for_o all_o sort_n of_o dial_n whatsoever_o note_v that_o the_o circle_n of_o the_o sphere_n show_v the_o canon_n to_o work_v this_o question_n exact_o whereof_o you_o have_v a_o large_a discourse_n in_o wells_n his_o art_n of_o shadow_n from_o pag._n 391_o to_o 408_o in_o 35_o chap._n 4._o for_o a_o direct_a east_n or_o west_n erect-dial_n the_o sphere_n be_v rectify_v to_o the_o latitude_n bring_v the_o notch_n in_o the_o move_a horizon_n to_o the_o east_n or_o west-point_n on_o the_o fix_a horizon_n viz._n to_o 90_o degree_n then_o set_v the_o plain_a erect_a and_o make_v it_o fast_o there_o than_o you_o shall_v perceive_v the_o axis_n lie_v close_o to_o the_o plain_a it_o show_v the_o style_n to_o have_v no_o elevation_n but_o must_v be_v set_v parallel_n to_o the_o plain_a at_o any_o quantity_n you_o please_v which_o be_v to_o be_v the_o radius_fw-la of_o a_o tangent-line_n whereby_o to_o prâ—â—k_v down_o the_o hour_n and_o that_o the_o substile_a or_o place_n where_o the_o cock_n or_o style_n must_v stand_v be_v in_o 6_o be_v the_o hour-circle_n till_o it_o be_v â—ust_z against_o the_o upper_a semicircle_n touch_v the_o thread_n and_o in_o the_o equinoctial_a it_o cut_v 6_o the_o true_a place_n where_o the_o style_n must_v stand_v also_o by_o the_o foregoing_a rule_n you_o shall_v find_v the_o sun_n shine_v all_o the_o year_n from_o the_o rise_n till_o 12_o on_o the_o east-side_n and_o on_o the_o westside_n from_o 12_o till_o his_o set_v 5._o for_o a_o east_n or_o west-recline_a turn_v the_o move_a horizon_n to_o 90_o degree_n in_o the_o fix_a as_o before_z then_o set_v the_o plain_a to_o his_o due_a reclination_n and_o make_v it_o fast_o there_o and_o pull_v the_o axis_n straight_o and_o bring_v the_o upper_a semicircle_n just_a to_o touch_v it_o and_o straightway_o you_o have_v the_o style_n and_o substile_a and_o 12_o the_o inclination_n meridian_n and_o hour-arks_a on_o the_o plain_a as_o for_o example_n a_o east-plain_a recline_a from_o the_o zenith_n towards_o the_o horizon_n 45_o degree_n have_v his_o meridian_n or_o 12_o a_o clock_n line_n in_o the_o horizon_n for_o if_o you_o extend_v the_o thread_n from_o the_o centre_n to_o the_o fore-side_n of_o the_o meridian_n just_o there_o the_o 12_o a_o clock_n line_n must_v always_o be_v which_o in_o this_o plain_n lie_v in_o the_o horizon_n the_o substile_n do_v lie_v 41-40_a from_o thence_o upward_o as_o the_o upper_a semicircle_n do_v show_v the_o inclination_n meridian_n be_v thus_o find_v bring_v the_o hour-circle_n till_o it_o stand_v even_o and_o parallel_v to_o the_o upper_a semicircle_n then_o on_o the_o equinoctial_a it_o cut_v 58-7′_a the_o inclination_n of_o the_o meridian_n with_o which_o you_o must_v make_v a_o table_n of_o hour_n or_o ark_n at_o the_o pole_n to_o calculate_v the_o ark_n on_o the_o plain_a if_o you_o work_v arithmetical_o but_o by_o the_o sphere_n set_v the_o hour-circle_n to_o the_o hour_n on_o the_o equinoctial_a and_o the_o thread_n be_v bring_v along_o the_o plain_a till_o it_o touch_v the_o hour-circle_n shall_v show_v on_o the_o plain_a the_o angle_n from_o the_o horizon_n or_o perpendicule_a or_o with_o some_o more_o trouble_n from_o substile_n or_o 12._o also_o it_o show_v that_o the_o north-pole_n be_v elevate_v on_o the_o west-reclining_a and_o the_o south_n on_o the_o east-inclining_a opposite_a thereunto_o and_o that_o the_o recliner_n in_o ♋_o show_v from_o 9_o in_o the_o forenoon_n till_o 8_o at_o night_n and_o the_o east_n incliner_n from_o the_o rise_n till_o 9_o forenoon_n in_o summer_n and_o in_o winter_n till_o a_o 11_o in_o the_o forenoon_n now_o to_o make_v these_o plain_n as_o erect_a decliner_n let_v the_o compliment_n latitude_n become_v a_o new_a latitude_n and_o the_o compliment_n declination_n a_o new_a declination_n then_o they_o may_v become_v erect_a decliner_n as_o in_o the_o next_o sort_n follow_v 6._o of_o erect_a decliner_n east_n or_o west_n by_o declination_n i_o mean_v the_o quantity_n of_o the_o angle_n that_o the_o meridian_n or_o pole_n of_o place_n make_v between_o the_o meridian_n or_o pole_n of_o the_o plain_a therefore_o to_o set_v the_o sphere_n to_o any_o declination_n do_v thus_o the_o sphere_n be_v set_v to_o the_o latitude_n turn_v the_o sphere_n as_o well_o as_o you_o can_v guess_v to_o the_o situation_n of_o the_o place_n that_o be_v put_v the_o north_n part_n of_o the_o meridian_n towards_o the_o north_n and_o the_o south_n part_n towards_o the_o south_n then_o turn_v the_o notch_n of_o the_o movable_a horizon_n always_o to_o the_o degree_n of_o the_o plain_n declination_n from_o north_n or_o south_n towards_o either_o east_n or_o west_n and_o upright_o also_o as_o in_o erect_a dial_n then_o be_v the_o plain_a set_v to_o his_o declination_n viz._n the_o distance_n of_o the_o horizon_n between_o the_o meridian_n or_o pole-place_n which_o be_v always_o 12_o a_o clock_n and_o the_o meridian_n and_o pole_n of_o the_o plain_a be_v always_o just_a where_o the_o notch_n be_v in_o the_o move_a horizon_n now_o according_a to_o these_o rule_n a_o plain_a that_o decline_v 30_o degree_n from_o south_n to_o west_n the_o style_n elevation_n be_v 32-35_a the_o substile_a from_o 12_o 21-40_a the_o inclination_n of_o the_o meridian_n 36-24_a the_o south_n pole_n be_v elevate_v on_o the_o southside_n and_o the_o north_n pole_n on_o the_o north-side_n and_o the_o sun_n shine_v on_o the_o north-side_n from_o rise_v to_o 8_o and_o on_o the_o southside_n from_o 8_o to_o 7_o at_o night_n and_o on_o the_o north_n again_o till_o sunsetting_a by_o work_v as_o in_o the_o former_a direction_n be_v express_v note_v in_o those_o erect_a decliner_n who_o declination_n be_v above_o 60_o degree_n you_o shall_v find_v the_o style_n elevation_n to_o be_v very_o small_a therefore_o to_o make_v it_o exact_v you_o must_v use_v arithmetical_a calculation_n for_o the_o do_v of_o which_o the_o sphere_n with_o due_a consideration_n give_v the_o best_a direction_n with_o these_o proportion_n or_o canon_n as_o sine_fw-la 90_o zn_n 90-00_a to_o sine_fw-la declination_n nc_n 30-00_a so_o co-tangent_a latitude_n pz_n 38-30_a to_o tang._n sub_v from_o 12._o zh_n 21-40_a as_o sine_fw-la 90_o zn_n 90-00_a to_o cousin_a declination_n na_n 60-00_a so_o cousin_a latitude_n zp_v 38-30_a to_o sine_fw-la stiles_n elevation_n ph_n 32-25_a as_o sine_fw-la latitude_n pn_n 51-30_a to_o sine_fw-la 90_o pae_n 90-00_a so_o tangent_fw-la declination_n nc_n 30-00_a to_o tangent_fw-la elevation_n merid._n aei_n 36-24_a as_o co-tangent_a latitude_n zp_v 38-30_a to_o sine_fw-la of_o 90_o zpq_n 90-00_a so_o sine_fw-la declination_n zia_n 30-00_a to_o co-tang_n 6_o from_o 12_o aq_n 57-50_a note_n if_o you_o set_v p_o at_o the_o pole_n z_o at_o the_o zenith_n n_o at_o the_o north-end_n of_o the_o horizon_n at_o the_o declination_n or_o pole-plain_a h_o on_o the_o plain_a just_a against_o the_o move_a semicircle_n or_o substile_n a_o at_o the_o plain_a on_o the_o horizon_n ae_n on_o the_o equinoctial_a ay_o at_o the_o hour-circle_n cut_v the_o equinoctial_a set_v just_a against_o the_o upper_a semicircle_n note_v q_n be_v to_o be_v set_v on_o the_o plain_a right_o against_o the_o hour-circle_n be_v set_v to_o the_o hour_n have_v i_o say_v by_o these_o rule_n and_o the_o like_a make_v and_o find_v the_o requisite_n then_o proceed_v to_o draw_v the_o dial_n thus_o by_o
at_o the_o sun_n or_o star_n and_o the_o weighty_a plummet_n will_v pull_v the_o thread_n straight_o and_o let_v you_o know_v by_o feel_v which_o way_n it_o be_v play_v till_o it_o play_v even_o and_o true_o whilst_o you_o have_v the_o object_n precise_o in_o the_o midst_n thereof_o whether_o it_o be_v sun_n moon_n or_o any_o star_n or_o other_o object_n who_o altitude_n you_o will_v observe_v then_o i_o say_v when_o the_o plummet_n play_v well_o and_o you_o behold_v the_o object_n right_a bend_v back_o the_o quadrant_n and_o see_v what_o the_o thread_n cut_v on_o the_o degree_n on_o the_o moveable-leg_n which_o shall_v be_v the_o true_a altitude_n require_v and_o in_o my_o opinion_n must_v needs_o be_v more_o exact_a than_o any_o other_o way_n of_o a_o forward_a observation_n because_o you_o be_v not_o trouble_v to_o mind_v the_o horizon_n and_o sun_n both_o at_o at_o once_o a_o objection_n may_v be_v the_o boisterous_a wind_n and_o the_o roll_a of_o the_o ship_n will_v hinder_v such_o a_o observation_n answ._n so_o it_o will_v any_o other_o way_n though_o happy_o not_o so_o much_o again_o i_o answer_v one_o object_n be_v better_a and_o more_o certain_o see_v than_o two_o at_o any_o time_n together_o and_o though_o the_o wind_n blow_v hard_a if_o you_o can_v stand_v to_o observe_v at_o all_o the_o heavy_a plummet_n will_v be_v sure_a to_o draw_v the_o thread_n perpendicule_a and_o for_o aught_o i_o know_v you_o may_v come_v as_o near_o this_o way_n as_o any_o other_o however_o this_o at_o most_o time_n may_v confirm_v and_o prove_v the_o other_o and_o may_v be_v useful_a in_o river_n and_o harbour_n and_o misty-daye_n when_o you_o may_v see_v the_o sun_n well_o enough_o but_o not_o the_o horizon_n at_o all_o use_v iii_o to_o find_v the_o sun_n altitude_n by_o a_o backward_a observation_n as_o with_o a_o back-staff_n or_o davis-quadrant_n screw_v the_o turning-sight_n to_o the_o leg-center_n or_o centre_n to_o the_o degree_n on_o the_o moveable-leg_n and_o set_v the_o object-sight_n to_o the_o long_a stroke_n by_o 00-60_a on_o the_o outside_n of_o the_o loose-piece_n and_o put_v the_o slide_a horizon-sight_n on_o the_o outside_n of_o the_o moveable-leg_n then_o hold_v the_o object-sight_n upward_o and_o the_o small-hole_n in_o the_o piece_n turn_v on_o the_o â—dge_n or_o to_o the_o small-hole_n in_o the_o middle_a of_o the_o horizon-sight_n which_o you_o please_v close_o to_o your_o eye_n and_o look_v through_o that_o hole_n and_o the_o middle-hole_n of_o the_o turning-sight_n to_o the_o true_a horizon_n turn_v yourself_o about_o and_o lift_v up_o or_o press_v down_o the_o horizon-sight_n close_o to_o the_o moveable-leg_n till_o the_o shadow_n of_o the_o upper-edge_n of_o the_o shadow-sight_n be_v next_o to_o the_o sun_n fall_v at_o the_o same_o time_n just_a on_o the_o middle_n of_o the_o turning-sight_n then_o i_o say_v the_o edge_n or_o middle_n of_o the_o horizon-sight_n that_o you_o look_v through_o shall_v cut_v the_o true_a altitude_n of_o the_o sun_n require_v be_v the_o same_o way_n as_o you_o do_v observe_v with_o a_o davis-quadrant_n or_o back-staff_n use_v iv._o to_o find_v the_o sun_n distance_n from_o the_o zenith_n by_o the_o trianguler-quadrant_n screw_v the_o turning-sight_n to_o the_o leg-center_n and_o put_v the_o object-sight_n who_o oval-hole_n be_v remote_a from_o the_o quadrant_n in_o the_o hole_n in_o the_o end_n of_o the_o head-leg_n or_o rather_o in_o a_o hole_n on_o the_o general_a scale_n between_o the_o turning-sight_n and_o the_o sun_n and_o put_v the_o horizon-sight_n on_o the_o outside_n of_o the_o moveable-leg_n then_o hold_v the_o turning-sight_n towards_o the_o sun_n and_o the_o small-hole_n in_o the_o edge_n of_o the_o horizon-sight_n to_o your_o eye_n then_o look_v through_o that_o hole_n and_o the_o turning-sight_n till_o you_o see_v the_o shadow_n the_o object-sight_n to_o fall_v just_a on_o the_o turning-sight_n or_o the_o shadow_n of_o the_o turning-sight_n to_o fall_v just_a on_o the_o object-sight_n which_o be_v all_o one_o though_o the_o first_o be_v more_o easy_a because_o you_o shall_v see_v the_o horizon_n through_o the_o turning-sight_n and_o that_o both_o at_o once_o then_o i_o say_v the_o degree_n cut_v by_o the_o horizon-sight_n shall_v be_v the_o sun_n distance_n from_o the_o zenith_n require_v be_v the_o very_a same_o work_n and_o do_v in_o the_o same_o manner_n and_o produce_v the_o same_o answer_n viz._n the_o sun_n distance_n from_o the_o zenith_n that_o the_o davis-quadrant_n do_v note_v that_o this_o way_n you_o may_v observe_v very_o convenient_o till_o the_o sun_n be_v 20_o degree_n distance_n from_o the_o zenith_n and_o by_o the_o add_v of_o a_o 60_o arch_n as_o in_o davis_n quadrant_n or_o to_o 45_o will_v be_v enough_o it_o will_v do_v as_o well_o as_o any_o davis_n quadrant_n be_v then_o the_o same_o thing_n but_o i_o conceive_v the_o compliment_n of_o the_o altitude_n be_v the_o same_o will_v do_v as_o well_o which_o altitude_n be_v better_a find_v by_o this_o instrument_n than_o the_o distance_n from_o the_o zenith_n by_o a_o davis_n quadrant_n be_v as_o in_o the_o next_o use_n will_v be_v see_v use_v v._o to_o find_v the_o sun_n altitude_n when_o near_o the_o zenith_n or_o above_o 90_o degree_n above_o some_o part_n of_o the_o horizon_n in_o small_a latitude_n or_o in_o place_n near_o the_o equinoctial_a or_o under_o it_o the_o sun_n will_v be_v find_v to_o be_v in_o or_o near_o the_o zenith_n and_o if_o you_o count_v from_o some_o part_n of_o the_o horizon_n above_o 90_o degree_n distant_a from_o it_o then_o instead_o of_o set_v the_o slide_a object-sight_n to_o the_o long_a stroke_n at_o 00_o on_o the_o loose-piece_n you_o must_v set_v it_o 30_o degree_n more_o towards_o the_o head-leg_n then_o observe_v as_o you_o do_v before_o and_o whatsoever_o the_o horizon-sight_n cut_v you_o must_v add_v 30_o degree_n more_o to_o it_o and_o the_o sum_n shall_v be_v the_o true_a altitude_n require_v example_n suppose_v that_o in_o the_o latitude_n of_o 10_o deg_n north_n on_o the_o 10_o of_o june_n when_o the_o sun_n declination_n be_v 23_o degree_n and_o 31_o min._n northward_o suppose_v that_o at_o noon_n i_o observe_v the_o sun_n meridian_n altitude_n screw_v the_o turning-sight_n to_o the_o leg-center_n and_o set_v the_o object-sight_n to_o the_o 30_o degree_n on_o the_o loose-piece_n near_o the_o end_n of_o the_o head-leg_n and_o the_o horizon-sight_n on_o the_o movable-leg_n then_o hold_v up_o the_o quadrant_n with_o the_o shadow-sight_n towards_o the_o sun_n and_o the_o small-hole_n in_o the_o horizon-sight_n towards_o your_o eye_n and_o look_v to_o the_o horizon_n through_o that_o and_o the_o turning-sight_n the_o shadow_n of_o the_o right-edge_n of_o the_o shadow-sight_n that_o cut_v the_o degree_n of_o 30_o at_o the_o same_o time_n fall_v on_o the_o middle_n of_o the_o turning-sight_n you_o shall_v find_v the_o horizon-sight_n to_o cut_v on_o 46-29_a minute_n to_o which_o if_o you_o add_v 30_o the_o degree_n the_o shadow-sight_n be_v set_v forward_o it_o make_v up_o 76-29_a the_o sun_n true_a altitude_n on_o that_o day_n in_o that_o latitude_n 76-29_a the_o meridian_n altitude_n and_o 23-31_a the_o declination_n add_v together_o make_v 100_o deg_n 00_o from_o which_o taking_n 90_o there_o remain_v 10_o the_o latitude_n of_o the_o place_n 1._o in_o this_o observation_n first_o you_o may_v note_v this_o that_o if_o you_o have_v stand_v with_o your_o back_n towards_o the_o south_n you_o will_v have_v have_v 103_o degree_n and_o 31_o minute_n for_o the_o slide_a horizon-sight_n will_v have_v stay_v at_o 73_o degree_n 30_o to_o which_o if_o you_o add_v 30_o it_o make_v 103-31_a which_o a_o davis_n quadrant_n will_v not_o do_v 2._o in_o the_o hold_v it_o you_o may_v lean_v the_o head_n of_o the_o rule_n to_o your_o breast_n and_o command_v it_o the_o better_a as_o to_o steady_a hold_v 3._o you_o may_v turn_v the_o turning-sight_n about_o to_o any_o convenient_a angle_n to_o make_v it_o fit_a to_o look_v through_o to_o the_o horizon_n and_o also_o to_o receive_v the_o shadow_n of_o the_o shadow-sight_n if_o the_o brightness_n of_o the_o sun_n offend_v the_o eye_n you_o may_v easy_o apply_v a_o red_a or_o a_o blue_a glass_n to_o darken_v the_o sun_n beam_n and_o the_o sight_n may_v be_v paint_v white_a to_o make_v a_o shadow_n be_v see_v better_a use_v vi_o to_o find_v the_o latitude_n at_o sea_n by_o a_o forward_a meridian_n observation_n of_o the_o altitude_n according_a to_o mr_n gunter_n bow_n screw_v the_o turning-sight_n to_o the_o leg-center_n and_o set_v the_o shadow-sight_n to_o the_o suns-declination_n and_o the_o horizon-sight_n to_o the_o move_a leg_n or_o loose-piece_n and_o the_o turning-sight_n to_o your_o eye_n then_o let_v the_o shadow-sight_n cut_v the_o horizon_n and_o the_o horizon-sight_n the_o sun_n move_v it_o high_o or_o low_a
from_o a_o great_a or_o a_o less_o radius_fw-la as_o your_o occasion_n serve_v and_o note_v the_o place_n as_o thus_o for_o example_n in_o this_o operation_n the_o extent_n from_o the_o point_n at_o 5-45_a on_o the_o sin_n to_o the_o sine_fw-la of_o 10_o degree_n i_o set_v the_o same_o way_n from_o the_o point_n at_o 0-34_a ½_o and_o note_n the_o place_n which_o will_v be_v at_o near_o 1_o degree_n then_o the_o work_n be_v thus_o as_o the_o place_n against_o the_o middle_n 1_o instead_o of_o 90_o be_v to_o the_o place_n last_o find_v for_o 10_o so_o be_v the_o sine_fw-la of_o 20_o to_o sine_fw-la of_o 3_o deg_n 24′_n ⅓_n the_o four_o term_v require_v but_o in_o those_o line_n of_o number_n sin_n and_o tangent_n where_o the_o number_n be_v double_a this_o be_v perform_v by_o work_v across_o only_o 4._o when_o the_o last_o term_n in_o tangent_n happen_v to_o be_v above_o 45_o than_o the_o remedy_n be_v two_o way_n as_o thus_o as_o sine_fw-la of_o 30_o to_o sine_fw-la of_o 90_o so_o be_v the_o tang._n of_o 30_o to_o tang._n 49-07_a which_o here_o happen_v beyond_o 45._o apply_v the_o end_n of_o the_o rule_n next_o 90_o close_a and_o even_o with_o any_o thing_n on_o which_o the_o point_n of_o the_o compass_n may_v stay_v till_o you_o take_v from_o thence_o to_o 45_o for_o that_o distance_n lay_v from_o 45_o shall_v reach_v to_o 49-07_a read_v the_o tangent_n as_o number_v beyond_o 45._o or_o more_o neat_o thus_o the_o compass_n be_v set_v from_o the_o sine_fw-la of_o 30_o to_o the_o sine_fw-la of_o 90_o set_v one_o point_n in_o the_o tangent_fw-la of_o 45_o and_o turn_v the_o other_o on_o the_o tangent_n and_o keep_v it_o there_o fix_a then_o remove_v the_o other_o from_o 45_o and_o close_o it_o to_o the_o three_o term_n be_v here_o the_o tangent_fw-la of_o 30_o then_o this_o last_o extent_n lay_v from_o 45_o shall_v reach_v to_o 49-07_a the_o tangent_fw-la require_v 5._o when_o the_o first_o term_n be_v a_o tangent_fw-la above_o 45_o and_o the_o second_o under_o 45._o take_v the_o excess_n of_o the_o first_o number_n above_o 45_o and_o set_v it_o the_o same_o way_n from_o the_o second_o number_n then_o the_o extent_n from_o the_o second_o number_n to_o 45_o shall_v be_v the_o true_a distance_n between_o the_o first_o and_o second_o term_n example_n as_o the_o tangent_fw-la of_o 51-30_a to_o the_o tangent_fw-la of_o 30_o so_o be_v the_o tangent_fw-la of_o 40_o to_o tangent_fw-la 21-04′_a for_o the_o extent_n from_o 45_o to_o 51-30_a on_o the_o tangent_n set_v the_o same_o way_n from_o 30_o do_v reach_v to_o about_o 24-30_a then_o the_o extent_n from_o thence_o to_o 45_o shall_v reach_v from_o 40_o to_o 21-04_a on_o the_o tangent_n the_o four_o number_n require_v or_o if_o it_o have_v be_v from_o a_o tangent_fw-la above_o 45_o to_o a_o sine_fw-la the_o same_o way_n will_v have_v remedy_v the_o defect_n 6._o when_o the_o three_o term_n exceed_v 45_o of_o tangent_n than_o thus_o example_n as_o sine_fw-la 90_o to_o sine_fw-la 30_o so_o be_v the_o tang._n of_o 50_o to_o tang._n of_o 30-48_a the_o compass_n set_v from_o the_o first_o term_n sine_fw-la 90_o to_o sine_fw-la of_o 30_o the_o second_o a_o less_o then_o set_v one_o point_n in_o the_o tangent_fw-la of_o 45_o and_o extend_v the_o other_o backward_o in_o the_o tangent_n and_o note_v the_o place_n keep_v one_o point_n there_o close_o the_o other_o to_o 50_o the_o three_o term_n be_v above_o 45_o by_o count_v backward_o then_o i_o say_v that_o extent_n lay_v from_o tangent_fw-la 45_o shall_v reach_v to_o tangent_fw-la 30-48_a the_o four_o proportional_a tangent_fw-la require_v if_o the_o proportion_n have_v be_v increase_v then_o there_o have_v be_v no_o trouble_n at_o all_o also_o note_n that_o work_v across_o or_o change_v the_o term_n be_v a_o good_a remedy_n also_o as_o thus_o as_o sine_fw-la 90_o to_o tang._n 50_o which_o be_v proper_o increase_v for_o the_o tang._n of_o 50_o being_n more_o than_o the_o sine_fw-la of_o 90_o yet_o take_v on_o the_o rule_n from_o 90_o to_o 40_o the_o compliment_n thereof_o as_o if_o it_o be_v decrease_v so_o be_v sine_fw-la 30_o to_o tang._n 30-48_a the_o contrary_a way_n therefore_o as_o from_o the_o first_o term_n proper_o count_v to_o the_o second_o 7._o last_o when_o one_o or_o two_o radiuss_n or_o alteration_n of_o the_o characteristic_a fall_v between_o the_o first_o and_o second_o term_n as_o thus_o for_o example_n first_o by_o the_o line_n of_o number_n only_o as_o 8000_o be_v to_o 10_o so_o be_v 5000_o to_o 6_o ¼_n or_o 25._o to_o work_v this_o proper_o and_o natural_o the_o unite_v on_o the_o number_n shall_v be_v four_o time_n repeat_v which_o be_v seldom_o more_o do_v than_o twice_o as_o here_o but_o this_o and_o any_o other_o by_o the_o line_n of_o number_n be_v not_o interrupt_v have_v a_o due_a respect_n to_o the_o number_n of_o place_n for_o to_o work_v this_o the_o best_a way_n be_v change_v of_o term_n thus_o as_o 8000_o to_o 5000_o in_o the_o same_o radius_fw-la so_o be_v 10_o to_o 6-25_a in_o the_o same_o radius_fw-la also_o or_o without_o change_v as_o 8000_o to_o the_o next_o 1_o so_o be_v 5000_o turn_v the_o compass_n the_o same_o way_n to_o 6-25_a but_o to_o call_v it_o so_o and_o not_o 625_o your_o reason_n must_v guide_v you_o more_o than_o precept_n but_o in_o use_v sin_n and_o tangent_n the_o way_n in_o the_o three_o remedy_n will_v fit_v you_o example_n as_o sine_fw-la 90_o to_o 1_o degree_n or_o under_o so_o be_v sine_fw-la 30_o degree_n to_o sine_fw-la 30_o minute_n this_o be_v too_o wide_a a_o extent_n for_o the_o compass_n the_o three_o rule_n be_v a_o remedy_n for_o it_o which_o on_o a_o large_a radius_fw-la several_a time_n repeat_v as_o in_o mr._n oughtred_n circle_n of_o proportion_n be_v as_o easy_a as_o may_v be_v be_v sure_a to_o remember_v the_o number_n of_o radiuss_n between_o the_o first_o and_o second_o term_n that_o you_o may_v have_v so_o many_o between_o the_o three_o and_o four_o term_n also_o much_o more_o may_v have_v be_v say_v as_o to_o this_o but_o this_o observation_n be_v always_o keep_v that_o as_o the_o extent_n from_o the_o first_o term_n to_o the_o second_o be_v either_o increase_n or_o decrease_v so_o always_o must_v the_o extent_n be_v from_o the_o three_o to_o the_o four_o increase_v or_o decrease_v in_o like_a manner_n when_o you_o use_v sines_n and_o tangent_n and_o number_n also_o except_o as_o before_z in_o a_o few_o particular_a rule_n than_o you_o will_v be_v true_o resolve_v the_o end_n of_o the_o book_n of_o dyall_v a_o appendix_n to_o the_o use_v of_o the_o trianguler-quadrant_n in_o navigation_n where_o it_o perform_v the_o uses_n of_o the_o davis-quadrant_n the_o cross-staff_n bow_n sinical-quadrant_n and_o sector_n with_o as_o much_o ease_n and_o exactness_n as_o any_o or_o all_o of_o they_o will_v do_v in_o observation_n or_o operation_n naturally_n or_o artificial_o be_v first_o thus_o contrive_v and_o make_v by_o john_n brown_n dwell_v at_o the_o sign_n of_o the_o sphere_n and_o sundial_n in_o the_o 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