deg_n −_o 0′_n from_o the_o south_n towards_o the_o west_n take_v out_o the_o chord_n of_o 35_o deg_n and_o lay_v if_o from_o saint_n to_o c_o and_o from_o w_o to_o a_o and_o from_o n_o to_z d_o and_o from_o e_z to_z b_o for_o the_o more_o exact_a draw_v of_o the_o line_n ab_fw-la cd_o the_o line_n cd_o represent_v the_o pole_n of_o the_o plain_a and_o the_o line_n ab_fw-la the_o decline_a plain_n itself_o then_o from_o z_o towards_o d_o lay_v off_o the_o tangent_fw-la of_o 10_o deg_n be_v the_o half_a tangent_fw-la of_o 20_o degree_n the_o give_v declination_n to_o e._n also_o take_v out_o the_o secant_fw-la of_o 70_o degree_n the_o compliment_n of_o 20_o to_o the_o same_o radius_fw-la and_o that_o lay_v from_o the_o point_n e_o on_o the_o line_n dc_o produce_v shall_v be_v the_o centre_n to_o draw_v the_o circle_n afeb_fw-mi that_o represent_v the_o decline_a recline_a plain_a that_o decline_v 35_o degree_n and_o recline_v 20_o degree_n also_o lay_v off_o half_a the_o tangent_fw-la of_o the_o compliment_n of_o the_o reclination_n viz._n 35_o degree_n for_o the_o reclination_n be_v 20_o the_o compliment_n whereof_o be_v 70_o and_o the_o half_a of_o 70_o be_v 35_o from_o z_o to_z q._n then_o to_o draw_v the_o line_n qp_n do_v thus_o observe_v how_o many_o degree_n you_o count_v from_o z_o to_o the_o point_n e_o count_v from_o the_o centre_n count_v so_o many_o in_o the_o manner_n of_o half_a tangent_n from_o 45_o and_o the_o latteral_a distance_n from_o thence_o to_o the_o centre_n lay_v from_o the_o centre_n z_o on_o the_o line_n cd_o give_v a_o three_o point_n viz._n the_o point_n i_o which_o three_o point_n qpi_n bring_v into_o a_o circle_n will_v cut_v the_o circle_n n.e.s.w._n into_o two_o equal_a part_n or_o thus_o the_o semi-tangent_a of_o the_o compliment_n of_o the_o reclination_n to_o 180_o degree_n lay_v from_o z_o on_o the_o line_n cd_o will_v find_v the_o point_n 1._o as_o thus_o the_o reclination_n be_v 20_o the_o compliment_n 70_o be_v take_v from_o 180_o rest_n 110_o who_o half_a be_v 55_o the_o tangent_fw-la of_o zi_n or_o more_o brief_o thus_o set_v one_o point_n of_o the_o compass_n in_o the_o small_a tangent_fw-la of_o 45_o and_o count_v the_o reclination_n from_o thence_o in_o the_o way_n of_o semi-tangents_a both_o way_n both_o above_o and_o under_o 45_o and_o lay_v one_o viz._n that_o under_o 45_o from_o c_o to_o q_o and_o the_o other_o viz._n that_o above_o 45_o from_o d_o to_o i_o then_o on_o the_o middle_a point_n between_o q_o and_o i_o last_o find_v raise_v a_o perpendicule_a to_o cd_o and_o in_o that_o line_n will_v be_v the_o centre_n to_o draw_v ipq._n also_o chap._n ii_o to_o draw_v the_o hour-line_n on_o all_o ordinary_a dial_n the_o easy_a in_o the_o first_o place_n 1._o and_o first_o for_o the_o first_o equinoctial_a dial_n a_o equinoctial_a plain_n as_o before_o be_v show_v be_v that_o who_o plain_a or_o flat_a superficies_n lie_v parallel_n to_o the_o equinoctial_a and_o be_v represent_v by_o the_o line_n waee_n in_o the_o general_a scheam_n and_o therefore_o need_v no_o other_o scheam_n to_o represent_v it_o in_o which_o dial_n all_o the_o hour-line_n be_v equal_a one_o to_o the_o other_o be_v just_a 15_o degree_n asunder_o so_o that_o to_o draw_v the_o hour-line_n here_o describe_v a_o circle_n as_o the_o circle_n 12.6.12.6_o and_o fit_a the_o radius_fw-la in_o the_o sine_fw-la of_o 30_o degree_n or_o the_o chord_n of_o 60_o and_o take_v out_o the_o parallel_n sine_fw-la of_o 7_o degree_n 30_o minute_n the_o half_a of_o 15_o degree_n and_o number_v it_o from_o 12_o round_o about_o and_o that_o shall_v divide_v the_o whole_a circle_n into_o 24_o equal_a part_n for_o the_o 24_o hour_n for_o the_o true_a hour-line_n on_o the_o equinoctial-plain_a and_o be_v the_o same_o in_o all_o latitude_n only_o in_o the_o set_n of_o it_o the_o pole_n of_o it_o be_v to_o be_v set_v due_a north_n and_o south_n the_o horizontal-line_n on_o the_o plain_a lie_v parallel_n to_o the_o east_n and_o west-point_n of_o the_o horizon_n and_o the_o style_n thereof_o only_o a_o wire_n or_o sharp_a edge_n stand_v perpendiculer_o on_o the_o centre_n which_o be_v so_o set_v must_v point_v direct_o to_o the_o north_n and_o south_n pole_n of_o the_o world_n the_o recline_a dials-stile_n point_v to_o the_o north-pole_n and_o the_o incline_a dials-stile_n point_v to_o the_o south_n pole_n then_o be_v the_o dial_n true_o place_v to_o set_v a_o plain_a or_o to_o try_v whether_o a_o plain_a be_v set_v polar_a or_o parallel_v to_o the_o equinoctial_a do_v thus_o but_o to_o try_v the_o incline_v plain_a apply_v the_o loose-piece_n to_o the_o plain_a with_o the_o head-end_n downward_o or_o else_o apply_v the_o head-leg_n to_o the_o plain_a with_o the_o head-end_n downward_o and_o the_o thread_n shall_v cut_v on_o 38-30_a in_o london_n latitude_n if_o the_o plain_n be_v set_v parallel_n to_o the_o equinoctial_a 2._o to_o draw_v a_o direct_a polar_a dial._n the_o next_o dial_n shall_v be_v a_o direct_a polar-dial_n which_o be_v represent_v in_o the_o general_a scheam_n by_o the_o hour-line_n of_o 6_o viz._n the_o line_n epw_o and_o here_o also_o the_o horizontal-line_n on_o the_o plain_a be_v parallel_n to_o the_o east_n &_o west-point_n of_o the_o horizon_n and_o the_o pole_n or_o point_v opposite_a to_o the_o plain_a be_v in_o the_o equinoctial-point_n the_o hour-line_n in_o this_o plain_a be_v all_o parallel_n because_o the_o axis_n or_o stile-line_n in_o all_o plain_n be_v parallel_n to_o the_o pole_n of_o the_o world_n and_o this_o plain_n itself_o be_v so_o parallel_n the_o style_n or_o axis_n therein_o make_v no_o angle_n therefore_o the_o hour-line_n must_v needs_o be_v parallel_n also_o and_o the_o way_n of_o draw_v those_o hour-line_n be_v thus_o first_o draw_v the_o perpendiculer-line_n on_o the_o plain_a which_o be_v do_v thus_o by_o the_o trianguler-quadrant_n hang_v a_o plummet_n and_o thread_n on_o the_o centre_n and_o apply_v the_o moveable-leg_n to_o the_o plain_a to_o and_o fro_o till_o the_o thread_n fall_v neat_o on_o 600_o and_o draw_v that_o line_n along_o by_o the_o moveable-leg_n which_o shall_v be_v a_o true_a horizontal-line_n on_o any_o recline_a plain_n and_o a_o perpendiculer-line_n thereunto_o be_v the_o perpendicule_a line_n on_o the_o plain_a or_o else_o when_o the_o sun_n shine_v the_o sun_n begin_v in_o the_o pole_n of_o the_o plain_a hold_v up_o a_o thread_n and_o plummet_n till_o the_o shadow_n of_o the_o thread_n fall_v on_o the_o plain_a make_v two_o point_n in_o that_o shadow_n at_o the_o remote_a distance_n asunder_o then_o a_o line_n draw_v through_o those_o two_o point_n shall_v be_v a_o true_a perpendiculer-line_n this_o shall_v need_v no_o more_o repetition_n then_o the_o several_a =_o tangent_n of_o 60-45_a 30_o &_o 15_o lay_v both_o way_n from_o 12_o on_o both_o the_o horizontal-line_n shall_v give_v you_o poâ—nâ—s_v whereby_o to_o draw_v all_o the_o hour-line_n in_o their_o true_a place_n also_o the_o =_o tangent_fw-la of_o 45_o shall_v be_v the_o true_a breadth_n of_o the_o plate_n that_o must_v be_v a_o sâ—â—â—e_n to_o this_o dial_n or_o the_o length_n of_o a_o upright_a wyre_n set_v any_o where_o in_o the_o line_n 12._o note_v that_o for_o the_o hour_n under_o 45_o you_o may_v take_v =_o 45_o from_o the_o small_a tangent_n and_o make_v it_o a_o =_o tangent_fw-la of_o 45_o in_o the_o great_a tangent_n and_o then_o take_v oâ—_n =_o tangent_fw-la of_o 30_o &_o 30_o for_o 2_o &_o 10_o anâ—_n the_o =_o tangent_fw-la of_o 15_o for_o 11_o &_o 1_o and_o if_o you_o want_v they_o above_o 45_o then_o take_v the_o =_o tangent_fw-la of_o 60_o &_o 60_o from_o the_o small_a tangent_n and_o turn_v that_o extent_n 4_o time_n from_o 12_o both_o way_n on_o both_o the_o horizontal-line_n and_o those_o shall_v be_v the_o point_n for_o 8_o in_o the_o forenoon_n and_o 4_o afternoon_n and_o last_o the_o =_o tangent_fw-la of_o 75_o take_v and_o turn_v 4_o time_n from_o 12_o to_o 7_o in_o the_o morning_n and_o to_o 5_o in_o the_o afternoon_n will_v fit_v and_o fill_v a_o plain_a of_o 4_o foot_n in_o breadth_n with_o a_o sector_n of_o one_o foot_n shut_z 3._o to_o draw_v a_o direct_a east_n or_o west-dial_n the_o next_o dial_n in_o the_o three_o place_n be_v the_o direct_a east_n or_o west-dial_n which_o be_v represent_v in_o the_o general_a scheam_n by_o the_o line_n nzs_n who_o pole_n be_v in_o the_o line_n ezw_n who_o plain_n also_o be_v =_o to_o the_o pole_n &_o draw_v in_o the_o same_o manner_n as_o the_o polar_a dial_n be_v yet_o with_o this_o difference_n the_o equinoctial-line_n whereon_o to_o prick_v the_o hour_n be_v not_o the_o horizontal-line_n but_o be_v thus_o find_v thus_o you_o may_v take_v the_o tangent_n under_o 45_o when_o the_o
hour-angle_n at_o the_o pole_n by_o the_o direction_n chap._n 2._o which_o be_v make_v as_o in_o the_o table_n draw_v the_o dial_n in_o this_o manner_n 12_o 33-28_a  _fw-fr 1_n 18-28_a  _fw-fr 2_o 3-28_a  _fw-fr  _fw-fr  _fw-fr sub._n 3_o 11-32_a  _fw-fr 4_o 26-32_a  _fw-fr 5_o 41-32_a  _fw-fr 6_o 56-32_a  _fw-fr 7_o 71-32_a  _fw-fr 8_o 86-32_a  _fw-fr 9_o 78-28_a  _fw-fr 10_o 63-28_a  _fw-fr 11_o 48-28_a  _fw-fr 12_o 33-28_a  _fw-fr upon_o ab_fw-la the_o horizontal-line_n of_o your_o plain_n describe_v the_o semicircle_n aeb_fw-mi and_o from_o the_o perpendiculer-line_n ce_fw-fr of_o the_o plain_a lay_v off_o 13-28_a eastward_o for_o the_o 12_o a_o clock_n line_n on_o the_o plain_a or_o the_o compliment_n thereof_o 76-32_a from_o the_o east-end_n at_o b_o to_o +_o &_o draw_v the_o line_n c_o +_o again_o set_v further_o eastward_o from_o 12_o 7-58_a the_o distance_n of_o the_o substile_a from_o 12_o to_o f_o and_o draw_v the_o line_n cf_n for_o the_o substile_a and_o beyond_o that_o set_v off_o from_o f_o 12-13_a the_o style_n height_n above_o the_o substile_a to_o g_z and_o draw_v cg_n also_o then_o draw_v a_o contingent_a line_n perpendicule_a to_o the_o substile_a cf_n as_o far_o from_o the_o centre_n as_o you_o can_v as_o the_o line_n he_o then_o take_v the_o near_a distance_n from_o the_o point_n f_o to_o the_o line_n cg_n and_o make_v it_o a_o =_o tangent_fw-la of_o 45_o then_o the_o sector_n be_v so_o set_v take_v out_o the_o =_o tangent_n of_o all_o the_o hour-arks_a in_o the_o table_n and_o lay_v they_o both_o way_n from_o f_o towards_o h_n and_o i_o as_o they_o proceed_v then_o line_n draw_v from_o the_o centre_n c_o and_o those_o point_n shall_v be_v the_o hour_n require_v or_o have_v in_o that_o manner_n prick_v down_o 12_o 6_o &_o 3_o or_o any_o other_o hour_n 3_o hour_n distant_a draw_v two_o line_n on_o each_o side_n 12_o =_o to_o 12_o and_o measure_v the_o distance_n from_o 6_o to_o 3_o in_o the_o =_o and_o lay_v it_o from_o c_o the_o centre_n on_o the_o line_n 12_o and_o by_o those_o two_o point_n draw_v a_o three_o line_n =_o to_o the_o 6_o a_o clock-line_n then_o 6-3_a and_o 12-3_a make_v a_o =_o tangent_fw-la of_o 45_o shall_v be_v the_o two_o radiuss_n to_o lay_v off_o the_o hour-line_n from_o 6_o &_o 12_o as_o before_o in_o the_o former_a dial_n and_o the_o =_o tangent_fw-la of_o inclination_n of_o meridian_n do_v prove_v the_o truth_n of_o your_o work_n here_o also_o as_o well_o as_o in_o the_o decliner_n erect_v but_o note_n that_o this_o dial_n be_v better_a to_o be_v augment_v by_o the_o lose_v the_o hour_n of_o 8_o and_o 9_o in_o the_o morning_n which_o make_v the_o hour_n more_o apparent_a as_o you_o see_v also_o the_o requisite_n former_o sound_v may_v geometrical_o be_v find_v by_o the_o scheam_n be_v large_a and_o true_o draw_v as_o before_o be_v show_v in_o the_o other_o dial_n thus_o 1._o a_o rule_n lay_v from_o q_n the_o pole-point_n of_o the_o plain_a to_o g_z the_o point_n of_o 12_o on_o the_o plain_a give_v in_o the_o limb_n the_o point_n 12_o d_o 12_o 13-28_a be_v the_o distance_n of_o 12_o a_o clock-line_n on_o the_o plain_a from_o the_o plain_n perpendiculer-line_n zd_v and_o to_o be_v lay_v from_o the_o perpendiculer-line_n on_o the_o plain_a eastward_n in_o the_o dial_n and_o the_o distance_n on_o the_o limb_n from_o a_o to_o 12_o be_v the_o meridian_n distance_n from_o the_o east-end_n of_o the_o horizontal-line_n on_o the_o plain_a namely_o 76-32_a 2._o a_o rule_n lay_v from_o q_o to_o f_o on_o the_o limb_n give_v the_o point_n sub_n for_o the_o substile_a and_o the_o ark_n sub._n 12_o 7-58_a be_v the_o distance_n from_o 12_o or_o the_o ark_n sub._n d_o 21-26_a the_o distance_n from_o the_o perpendicule_a 3._o a_o rule_n lay_v from_o q_o to_o 6_o the_o place_n where_o the_o 6_o a_o clock_n hour-line_n on_o the_o scheam_n cut_v the_o plain_a give_v on_o the_o limb_n the_o point_n 6_o the_o ark_n 6_o 12_o 25-38_a or_o 6_o d_o 38-56_a be_v the_o distance_n of_o the_o hour-line_n of_o 6_o on_o the_o plain_a from_o the_o hour-line_n 12_o or_o the_o perpendicule_a 4._o a_o rule_n lay_v from_o y_o the_o pole-point_n of_o the_o circle_n qfp_n to_o p_o &_o f_o on_o the_o limb_n give_v two_o point_n ik_fw-mi and_o the_o ark_n ik_fw-mi be_v the_o style_n elevation_n 12-13_a 5._o a_o rule_n lay_v from_o p_o to_o y_o on_o the_o limb_n give_v the_o point_n m_o em_n be_v the_o inclination_n of_o meridian_n or_o a_o rule_n lay_v from_o p_o to_o the_o intersection_n of_o the_o circle_n pfq_n and_o the_o equinoctial-line_n give_v a_o point_n in_o the_o limb_n near_o c_o which_o ark_n cs_n be_v more_o natural_o the_o angle_n between_o the_o two_o meridian_n 33-28_a or_o if_o you_o like_v the_o way_n of_o refer_v this_o plain_a to_o a_o new_a latitude_n and_o to_o a_o new_a declination_n in_o that_o new_a latitude_n then_o thus_o by_o the_o scheam_n 6._o a_o rule_n lay_v from_o e_o to_o p_o and_o g_o in_o the_o limb_n give_v l_o and_o o_o the_o ark_n lo_o be_v the_o compliment_n of_o the_o new_a latitude_n be_v the_o ark_n pg_n the_o second_o requisite_a in_o the_o former_a calculation_n be_v 14-33_a the_o distance_n on_o the_o meridian_n from_o the_o pole_n to_o the_o plain_a but_o note_n that_o this_o dial_n be_v better_a to_o be_v augment_v by_o the_o lose_v the_o hour_n of_o 8_o and_o 9_o in_o the_o morning_n which_o make_v the_o hour_n more_o apparent_a as_o you_o see_v also_o the_o requisite_n former_o find_v may_v geometrical_o be_v find_v by_o the_o scheam_n be_v large_a and_o true_o draw_v as_o before_o be_v show_v in_o the_o other_o dial_n thus_o 1._o a_o rule_n lay_v from_o q_n the_o pole-point_n of_o the_o plain_a to_o g_z the_o point_n of_o 12_o on_o the_o plain_a give_v in_o the_o limb_n the_o point_n 12_o d_o 12_o 13-28_a be_v the_o distance_n of_o 12_o a_o clock-line_n on_o the_o plain_a from_o the_o plain_n perpendiculer-line_n zd_v and_o to_o be_v lay_v from_o the_o perpendiculer-line_n on_o the_o plain_a eastward_n in_o the_o dial_n and_o the_o distance_n on_o the_o limb_n from_o a_o to_o 12_o be_v the_o meridian_n distance_n from_o the_o east-end_n of_o the_o horizontal-line_n on_o the_o plain_a namely_o 76-32_a 2._o a_o rule_n lay_v from_o q_o to_o f_o on_o the_o limb_n give_v the_o point_n sub_n for_o the_o substile_a and_o the_o ark_n sub._n 12_o 7-58_a be_v the_o distance_n from_o 12_o or_o the_o ark_n sub._n d_o 21-26_a the_o distance_n from_o the_o perpendicule_a 3._o a_o rule_n lay_v from_o q_o to_o 6_o the_o place_n where_o the_o 6_o a_o clock_n hour-line_n on_o the_o scheam_n cut_v the_o plain_a give_v on_o the_o limb_n the_o point_n 6_o the_o ark_n 6_o 12_o 25-38_a or_o 6_o d_o 38-56_a be_v the_o distance_n of_o the_o hour-line_n of_o 6_o on_o the_o plain_a from_o the_o hour-line_n 12_o or_o the_o perpendicule_a 4._o a_o rule_n lay_v from_o y_o the_o pole-point_n of_o the_o circle_n qfp_n to_o p_o &_o f_o on_o the_o limb_n give_v two_o point_n ik_fw-mi and_o the_o ark_n ik_fw-mi be_v the_o style_n elevation_n 12-13_a 5._o a_o rule_n lay_v from_o p_o to_o y_o on_o the_o limb_n give_v the_o point_n m_o em_n be_v the_o inclination_n of_o meridian_n or_o a_o rule_n lay_v from_o p_o to_o the_o intersection_n of_o the_o circle_n pfq_n and_o the_o equinoctial-line_n give_v a_o point_n in_o the_o limb_n near_o c_o which_o ark_n cs_n be_v more_o natural_o the_o angle_n between_o the_o two_o meridian_n 33-28_a or_o if_o you_o like_v the_o way_n of_o refer_v this_o plain_a to_o a_o new_a latitude_n and_o to_o a_o new_a declination_n in_o that_o new_a latitude_n then_o thus_o by_o the_o scheam_n 6._o a_o rule_n lay_v from_o e_o to_o p_o and_o g_o in_o the_o limb_n give_v l_o and_o o_o the_o ark_n lo_o be_v the_o compliment_n of_o the_o new_a latitude_n be_v the_o ark_n pg_n the_o second_o requisite_a in_o the_o former_a calculation_n be_v 14-33_a the_o distance_n on_o the_o meridian_n from_o the_o pole_n to_o the_o plain_a 7._o a_o rule_n lay_v from_o g_o to_o q_o on_o the_o limb_n give_v r_o the_o ark_n sir_n be_v the_o new_a declination_n in_o that_o new_a latitude_n 32-37_a or_o else_o find_v it_o by_o this_o rule_n as_o sine_fw-la of_o 90_o to_o the_o cousin_a of_o the_o reclination_n or_o inclination_n so_o be_v the_o sine_fw-la of_o the_o old_a declination_n to_o the_o sine_fw-la of_o the_o new_a in_o this_o example_n be_v 32-37_a and_o general_o the_o same_o way_n as_o the_o old_a declination_n be_v only_o observe_v that_o when_o the_o north-pole_n be_v elevate_v on_o south_n recliner_n you_o must_v draw_v they_o as_o north-decliners_a and_o northwest_n
and_o north-east_n incliner_n that_o have_v the_o south-pole_n elevate_v you_o must_v draw_v they_o as_o southeast_n and_o west-decliners_a which_o will_v direct_v as_o to_o the_o right_a way_n of_o place_v the_o substile_a and_o hour_n of_o 6_o from_o 12._o in_o this_o place_n i_o shall_v also_o insert_v the_o general_a way_n by_o calculation_n to_o find_v the_o new_a latitude_n as_o well_o as_o new_a declination_n which_o be_v thus_o as_o radius_fw-la or_o sine_fw-la of_o 90_o to_o the_o cousin_a of_o the_o plain_n old_a declination_n so_o be_v the_o co-tangent_a of_o the_o reclination_n or_o inclin_n to_o the_o tang._n of_o a_o four_o ark._n then_o in_o south_n recliner_n and_o in_o north_n incliner_n get_v the_o difference_n between_o this_o four_o ark_n and_o the_o latitude_n of_o your_o place_n and_o the_o compliment_n of_o that_o difference_n be_v the_o new_a latitude_n if_o the_o four_o ark_n be_v less_o than_o the_o old_a latitude_n than_o the_o contrary_a pole_n be_v elevate_v but_o if_o it_o be_v equal_a to_o the_o old_a latitude_n it_o be_v a_o polar-plain_a but_o in_o south_n incliner_n and_o in_o north_n recliner_n the_o difference_n between_o the_o four_o ark_n and_o the_o compliment_n of_o the_o latitude_n of_o the_o place_n or_o old_a latitude_n shall_v be_v the_o new_a latitude_n when_o the_o four_o ark_n and_o old_a latitude_n be_v equal_a it_o be_v a_o equinoctial-plain_a thus_o in_o this_o example_n as_o sine_fw-la 90_o to_o cousin_a of_o 35_o the_o old_a declination_n so_o be_v co-tangent_a of_o 20_o the_o reclination_n to_o 66-03_a for_o a_o four_o ark_n from_o which_o take_v 51-32_a the_o old_a latitude_n rest_v 14-31_a the_o compliment_n of_o the_o new_a latitude_n which_o will_v be_v find_v to_o be_v 75-29_a the_o new_a latitude_n by_o which_o new_a latitude_n and_o new_a declination_n if_o you_o work_v as_o for_o a_o erect_a dial_n you_o shall_v find_v the_o same_o requisite_n as_o by_o the_o former_a operation_n you_o have_v do_v and_o the_o distance_n of_o the_o perpendicule_a and_o meridian_n will_v set_v all_o right_a the_o second_o variety_n of_o south_n recliner_n recline_v just_a to_o the_o pole_n 1._o the_o scheam_n be_v draw_v as_o before_o to_o the_o same_o declination_n and_o the_o same_o way_n viz._n 35_o degree_n westward_o and_o recline_v 33-3′_a now_o to_o try_v whether_o such_o a_o plain_n be_v just_o a_o polar-plain_a or_o no_o use_v this_o proportion_n by_o the_o sector_n as_o the_o sine_fw-la of_o 90_o da_fw-la 90-0_a to_o cousin_a of_o declin_n no_z 55-0_a so_o co-tang_n of_o reclin_n de_fw-fr 56-57_a to_o tang._n of_o latitude_n np_v 51-32_a as_o cousin_a declination_n na_n 55-00_a to_o =_o sine_fw-la of_o ad_fw-la 90-00_a so_n be_v =_o co-tang_n of_o reclin_n de_fw-fr 56-57_a being_n take_v from_o the_o small_a tangent_n to_o tangent_fw-la of_o np_v 51-32_a be_v measure_v from_o the_o centre_n on_o the_o same_o small_a tangent_n which_o four_o ark_n if_o it_o hit_v to_o be_v right_o the_o latitude_n than_o it_o be_v a_o decline_a polar-plain_a or_o else_o not_o 2._o if_o you_o have_v a_o declination_n give_v to_o which_o you_o will_v find_v a_o reclination_n to_o make_v it_o polar_a than_o reason_n thus_o by_o the_o sector_n as_o the_o cousin_a of_o the_o declin_n a_o 55-0_a to_o the_o radius_fw-la or_o sine_fw-la of_o ad_fw-la 90-0_a so_n be_v the_o tang._n of_o the_o lat._n pn_n 51-32_a to_o the_o co-tang_n of_o the_o reclin_n de_fw-fr 56-57_a as_o tangent_fw-la of_o np_v 51-30_a to_o =_o sine_fw-la of_o a_o 55-00_a so_o =_o sine_fw-la of_o ad_fw-la 90-00_a to_o tangent_fw-la of_o de_fw-fr 56-57_a 3._o if_o the_o reclination_n be_v give_v and_o the_o declination_n require_v to_o make_v it_o a_o polar_a than_o the_o canon_n may_v be_v thus_o by_o the_o sector_n as_o the_o co-tang_n of_o the_o reclin_n de_fw-fr 56-57_a to_o the_o radius_fw-la or_o sine_fw-la of_o ad_fw-la 90-00_a so_n be_v the_o tang._n of_o the_o lat._n np_v 51-32_a to_o the_o cousin_a of_o the_o declin_n no_z 55-00_a as_o co-tang_n reclination_n de_fw-fr 56-57_a to_z =_o sine_fw-la of_o ad_fw-la 90-00_a so_n tang._n of_o latitude_n nd_o 51-32_a to_o =_o cousin_a of_o declination_n na_fw-mi 55-00_a but_o by_o the_o scheam_n these_o three_o operation_n be_v find_v by_o draw_v the_o scheam_n 1._o for_o if_o the_o line_n or_o circle_n represent_v the_o plain_a cut_v the_o pole_n p_o it_o be_v a_o polar-dial_n 2._o if_o ab_fw-la the_o codeclination_n be_v give_v then_o draw_v the_o circle_n apb_n and_o it_o give_v e_z then_z see_fw-mi be_v the_o reclination_n measure_v by_o half_a tangent_n or_o a_o rule_n lay_v from_o a_o to_o e_o on_o the_o limb_n give_v a_o ark_n from_o b_o which_o measure_v on_o fit_a chord_n be_v the_o reclination_n 3._o if_o p_o the_o pole-point_n and_o see_fw-mi the_o reclinatin_n be_v give_v then_o with_o the_o distance_n see_fw-mi on_o z_o as_o a_o centre_n draw_v a_o ark_n of_o a_o circle_n in_o that_o quadrant_n which_o be_v contrary_a to_o the_o coast_n of_o declination_n observe_v the_o letter_n in_o the_o scheam_n then_o by_o the_o convexity_n of_o that_o ark_n and_o the_o pole-point_n p_o draw_v the_o circle_n pe_n cut_v the_o limb_n into_o two_o equal_a part_n which_o be_v the_o point_v a_o &_o b_o the_o declination_n require_v this_o be_v premise_v there_o be_v two_o thing_n requisite_a to_o be_v find_v before_o you_o can_v draw_v the_o dial._n viz._n the_o substile_a from_o the_o perpendicule_a or_o horizon_n and_o the_o inclination_n of_o meridian_n 1._o and_o first_o for_o the_o substile_a by_o the_o sector_n as_o the_o sine_fw-la of_o pez_n 90-0_a to_o the_o cousin_a of_o the_o lat._n pz_fw-fr 38-28_a so_o the_o sine_fw-la of_o the_o declination_n pze_v 35-00_a to_o the_o sine_fw-la of_o substile_n from_o perp._n pe_n 20-54_a as_o sine_z of_o declination_n pze_v 35-0_a to_o =_o sine_fw-la of_o pez_n 90-0_a so_o =_o sine_fw-la of_o co-latitude_n pz_n 38-28_a to_o sine_z of_o substile_n from_o perp._n fe_o 20-54_a the_o distance_n of_o the_o substile_a from_o the_o perpendicule_a who_o compliment_n 69-06_a be_v the_o elevation_n above_o the_o horizon_n or_o a_o rule_n lay_v from_o q_o to_o p_o give_v i_o diego_n be_v 20-54_a 2._o for_o the_o inclination_n of_o meridian_n say_v by_o the_o sector_n as_o the_o cousin_a of_o the_o latitude_n pz_fw-fr 38-28_a to_o the_o sine_fw-la of_o pez_n 90-00_a so_o the_o sine_fw-la of_o the_o reclin_n see_fw-mi 33-03_a to_o the_o cousin_a of_o incl._n mer._n zpe_v 61-15_a who_o compliment_n zpq_n 28-45_a be_v the_o inclination_n of_o meridian_n require_v as_o sine_z of_o reclination_n see_fw-mi 33-3_a to_z =_o cousin_a of_o latitude_n pz_n 38-28_a so_o =_o sine_fw-la of_o 90_o pez_n 90-00_a to_o cousin_a of_o incl._n mer._n zpe_v 61-15_a who_o compliment_n qpz_n 28-45_a be_v the_o inclin_n of_o meridian_n require_v or_o a_o rule_n lay_v from_o p_o to_o y_o gives_z m_n em_n be_v 28-45_a the_o inclination_n of_o meridian_n again_o 8_o 88_o 45_o  _fw-fr 81_o 15_o 9_o 73_o 45_o  _fw-fr 56_o 15_o 10_o 58_o 45_o  _fw-fr 51_o 15_o 11_o 43_o 45_o  _fw-fr 36_o 15_o 12_o 28_o 45_o  _fw-fr 21_o 15_o 1_o 13_o 45_o  _fw-fr 6_o 15_o 2_o 1_o 15_o  _fw-fr 8_o 45_o 3_o 16_o 15_o  _fw-fr 23_o 45_o 4_o 31_o 15_o  _fw-fr 38_o 45_o 5_o 46_o 15_o  _fw-fr 53_o 45_o 6_o 61_o 15_o  _fw-fr 68_o 45_o 7_o 76_o 15_o if_o i_o take_v 15_o the_o quantity_n in_o degree_n of_o one_o hour_n out_o of_o 28-15_a the_o inclination_n of_o meridian_n there_o remain_v 13-45_a for_o the_o first_o hour_n on_o the_o other-side_n of_o the_o substile_a then_o again_o by_o continual_a addition_n of_o 15_o degree_n to_o 13-45_a and_o the_o increase_n thereof_o i_o make_v up_o the_o other_o half_o or_o else_o against_o 12_o set_v 28-45_a and_o add_v 15_o successive_o to_o it_o &_o its_o increase_n till_o it_o come_v to_o 90_o then_o to_o 13-45_a the_o residue_n of_o 15_o take_v from_o 28-45_a add_v 15_o as_o often_o as_o you_o can_v to_o 90_o and_o thus_o be_v the_o table_n make_v to_o draw_v the_o dial._n first_o draw_v a_o perpendicule_a line_n on_o your_o plain_n as_o cb_n by_o cross_v the_o horizontal-line_n at_o right_a angle_n then_o from_o the_o perpendiculer-line_n lie_v off_o from_o the_o upper-end_n towards_o the_o left-hand_a as_o the_o scheam_n direct_v zd_v be_v the_o perpendicule_a and_o zn_o the_o meridian_n and_o ep_n on_o the_o plain_a the_o distance_n between_o be_v towards_o the_o left_a hand_n 20-54_a for_o the_o substile-line_n as_o cd_o then_o on_o that_o line_n any_o where_o draw_v two_o perpendicule_a line_n quite_o through_o the_o plain_a cross_v the_o substile_a at_o right_a angle_n for_o two_o equinoctial-line_n as_o of_o &_o gh_n then_o consider_v what_o hour_n shall_v be_v put_v oâ—_n your_o plain_n as_o here_o be_v convenient_a from_o
then_o to_o any_o one_o whole_a hour_n as_o suppose_v the_o hour-line_n of_o 3_o draw_v two_o =_o line_n equal_o distant_a on_o both_o side_n the_o line_n of_o 3_o as_o ik_fw-mi lm_o then_o count_z any_o way_n 3_o hour_n and_o 6_o hour_n from_o 3_o as_o here_o 12_o and_o 9_o so_o as_o the_o =_o line_n may_v cross_v the_o 3_o remote_a hour_n as_o here_o you_o see_v 9_o and_o 12_o a_o clock_n hour-line_n do_v cross_v the_o =_o line_n at_o i_o and_o k_o then_o take_v the_o distance_n ik_fw-mi and_o lay_v on_o the_o hour-line_n of_o 3_o from_o c_o to_o n_o and_o draw_v inl_n =_o to_o 9_o c_z which_o work_n do_v constitute_v the_o parallellogram_n kilm_n then_o last_o make_v ki_v and_o ni_fw-fr =_o tangent_n of_o 45_o and_o pâ—ick_v off_o every_o hour_n half_a and_o quarter_n and_o minute_n if_o you_o please_v on_o the_o two_o line_n ik_fw-mi and_o il_fw-fr from_o k_o and_o n_o both_o way_n as_o before_o be_v already_o show_v in_o the_o erect_a decliner_n note_v also_o that_o to_o supply_v the_o defect_n on_o the_o other_o side_n when_o the_o point_n m_o falls_z out_z of_o the_o plain_a the_o distance_n from_o i_o to_o the_o hour-point_n from_o 11_o will_v reach_v from_o l_o to_o 7_o and_o from_o i_o to_o 10_o from_o l_o to_o 8._o this_o be_v general_a in_o all_o dial_n also_o note_n if_o you_o like_v not_o to_o lay_v off_o the_o â—irst_n hour_n by_o the_o tangent_n have_v make_v the_o table_n as_o before_o you_o may_v soon_o find_v the_o hour-arks_a on_o the_o plain_a for_o 3_o hour_n as_o â—ere_z 3_o 12_o and_o 9_o or_o 4_o 1_o and_o 8_o which_o â—ould_v have_v make_v the_o parallellogram_n more_o square_a and_o consequent_o more_o better_a and_o â—â—en_o to_o draw_v the_o rest_n by_o the_o sector_n thus_o â—ou_n may_v see_v how_o your_o work_n accord_v the_o â—ay_n by_o the_o table_n and_o contingent-line_n and_o 〈◊〉_d way_n by_o the_o sector_n on_o the_o parallellogram_n 〈◊〉_d by_o calculation_n &_o at_o last_o use_v the_o mystery_n 〈◊〉_d dial_v make_v plain_a and_o ready_a to_o a_o ordinary_a capacity_n of_o north_n decline_a recliner_n the_o other_o kind_n viz._n north_n decline_a recliner_n have_v also_o three_o variety_n as_o those_o â—_o that_o fall_n back_o or_o recline_v between_o the_o zenith_n and_o equinoctial_a 2d_o those_o that_o recline_v to_o the_o equinoctial_a and_o 3d._n those_o that_o recline_v below_o the_o equinoctial_a and_o first_o of_o the_o first_o variety_n recline_v less_o than_o to_o the_o equinoctial_a the_o draw_v the_o scheam_n be_v the_o same_o as_o in_o the_o former_a except_o in_o the_o place_n of_o the_o point_n and_o letter_n for_o first_o these_o plain_n behold_v the_o north-part_n of_o the_o horizon_n and_o then_o when_o you_o look_v on_o the_o plain_a the_o south_n be_v before_o you_o and_o the_o west_n on_o your_o right-hand_a and_o the_o east_n on_o the_o left_a then_o the_o south_n and_o north_n be_v always_o opposite_a and_o the_o point_n p_o represent_v the_o elevate_v pole_n of_o the_o place_n which_o with_o we_o be_v north_n must_v be_v place_v towards_o n_o downward_o as_o before_o in_o south_n recliner_n it_o be_v upward_o also_o it_o be_v necessary_a in_o the_o scheam_n to_o draw_v the_o equinoctial-line_n by_o lay_v the_o half_a tangent_fw-la of_o 51-32_a from_o z_o to_z ae_n then_o the_o secant_fw-la of_o 38-28_a the_o compliment_n of_o see_fw-mi lay_v from_o ae_n on_o the_o line_n sn_a shall_v be_v the_o centre_n to_o draw_v eaew_n for_o the_o equinoctial-circle_n thus_o the_o scheam_n be_v draw_v to_o find_v the_o requisite_n thus_o 1._o for_o the_o meridian_n elevation_n or_o distance_n from_o the_o perpendicule_a agnostus_n or_o ge._n by_o the_o secctor_n as_o sine_fw-la 90_o radius_fw-la zd_v 90-0_a to_o tangent_fw-la declination_n plain_n sd_z 55-0_a so_o sine_fw-la reclination_n plain_n see_fw-mi 20-0_a to_o tangent_fw-la merid._n &_o perpend_v ge_n 26-2_a as_o tangent_fw-la of_o declin_n sd_z 55-0_a to_o =_o sine_fw-la of_o radius_fw-la zd_v 90-0_a so_o =_o sine_fw-la of_o reclination_n see_fw-mi 20-0_a to_o tang._n of_o 12_o from_o perp._n ge_n 26-02_a who_o compliment_n agnostus_n 63-58_a be_v the_o meridian_n elevation_n above_o the_o east-end_n of_o the_o horizon_n by_o the_o scheam_n a_o rule_n lay_v from_o q_o to_o g_z on_o the_o limb_n give_v l_o then_o dl_o and_o all_o be_v the_o ark_v require_v 2._o to_o find_v the_o distance_n on_o the_o meridian_n from_o the_o pole_n to_o the_o plain_a gp_n by_o the_o sector_n as_o sine_fw-la declin_n of_o the_o plain_a gze_n 55-0_a to_o sine_z do_v of_o mer._n &_o perp._n ge_n 26â—02_n so_o sine_fw-la of_o the_o radius_fw-la gez_fw-fr 90â—00_n to_o sine_z of_o do_v on_o merid._n from_o pole_n to_o plain_a gz_n 32-03_a as_o sine_z of_o gez_fw-fr 90-0_a to_o =_o sine_fw-la of_o gze_v 55-0_a so_o =_o sine_fw-la of_o ge_n 26-2_a to_o sine_z of_o gz_n 32-03_a which_o add_v to_o 38-28_a zp_n make_v up_o gp_a to_o be_v 70-31_a or_o by_o the_o scheam_n a_o rule_n lay_v from_o e_o to_o p_o and_o g_o gives_z on_o the_o limb_n ab_fw-la the_o ark_n ab_fw-la be_v 70-31_a 3._o to_o find_v the_o style_n height_n above_o the_o plain_a pf_n by_o the_o sector_n as_o sine_fw-la of_o distance_n on_o mer._n from_o zenith_n to_o the_o plain_a gz_fw-fr 32-03_a to_o sine_fw-la of_o the_o plain_n reclin_n see_fw-mi 20-00_a so_o sine_fw-la of_o do_v on_o mer._n from_o pole_n to_o the_o plain_a gp_n 70-31_a to_o sine_fw-la of_o the_o style_n elevat_fw-la above_o the_o plain_a pf_n 37-01_a as_o the_o sine_fw-la gp_n 70-31_a to_o the_o =_o sine_fw-la gz_fw-fr 32-03_a so_o the_o =_o sine_fw-la see_fw-mi 20-00_a to_o the_o sine_fw-la pf_n 37-01_a by_o the_o scheam_n a_o rule_n lay_v from_o y_o to_o p_o and_o f_o on_o the_o limb_n give_v c_o and_o d_o the_o style_n height_n 4._o to_o find_v the_o distance_n of_o the_o substile_a from_o the_o meridian_n gf_n when_o it_o be_v above_o 90_o deg_n take_v the_o comp_n to_o 108_o deg_n by_o the_o sector_n as_o tangent_fw-la of_o the_o reclin_n see_fw-mi 20-00_a to_z sine_z of_o do_v of_o 12_o from_o perp._n ge_n 26-02_a so_o tang._n of_o the_o style_n elevat_fw-la pf_n 37-01_a to_o sine_fw-la of_o the_o substile_a from_o 12_o gf_n 65-24_a as_o sine_fw-la eglantine_n 26-02_a to_o =_o tangent_fw-la see_fw-mi 20-0_a so_fw-ge =_o tangent_fw-la pf_n 37-01_a to_o sine_z ge_n 65-24_a by_o the_o scheam_n a_o rule_n lay_v from_o q_o to_o g_z and_o f_o give_v on_o the_o limb_n lf_n the_o ark_n require_v 5._o to_o find_v the_o inclination_n of_o meridian_n fpg_n by_o the_o sector_n as_o sine_z do_v on_o merid._n from_o pole_n to_o plain_a gp_n 70-31_a to_o sine_fw-la radius_fw-la opposite_a angle_n gfp_n 90-00_a so_o sine_fw-la do_v on_o plain_a from_o 12_o to_o substile_n gf_n 65-24_a to_o sine_fw-la of_o the_o inclin_n of_o mer._n gpf_n 74-38_a as_o sine_fw-la gf_n 65-24_a to_o =_o sine_fw-la gp_v 70-31_a so_o =_o sine_fw-la gfp_n 90-00_a to_o sine_fw-la gpf_n 74-38_a by_o the_o scheam_n a_o rule_n lay_v from_o p_o to_o y_o on_o the_o limb_n give_v g_o the_o ark_n eglantine_n be_v 74-38_a the_o inclination_n of_o meridian_n or_o a_o rule_n lay_v from_o p_o to_o k_o gives_z h_z shall_z be_v the_o inclination_n of_o meridian_n by_o which_o to_o make_v the_o table_n as_o before_o be_v show_v and_o as_o follow_v to_o draw_v the_o dial._n 3_o 29_o 38_o 2_o 44_o 38_o 1_o 59_o 38_o 12_o 74_o 38_o 11_o 89_o 38_o 10_o 75_o 22_o 9_o 60_o 22_o 8_o 45_o 22_o 7_o 30_o 22_o 6_o 15_o 22_o 5_o 0_o 22_o 4_o 14_o 38_o for_o draw_v the_o dial_n consult_v with_o the_o scheam_n lay_v the_o plain_a aeb_fw-mi and_o his_o perpendicule_a cd_o right_a before_o you_o then_o note_v sn_a be_v the_o meridian-line_n see_fw-mi the_o plain_n perpendicule_a with_o the_o meridian_n g_o on_o the_o left-hand_a and_o the_o subtle_a f_o on_o the_o right-hand_a also_o note_n that_o the_o sun_n be_v in_o the_o south_n as_o saint_n cast_v â—is_n beam_n and_o consequent_o the_o shadow_n of_o â—he_n stile_n into_o the_o north_n so_o that_o though_o g_z be_v the_o true_a meridian_n find_v yet_o it_o be_v the_o north-part_n that_o be_v draw_v as_o a_o hour-line_n â—ut_v the_o substile_a and_o other_o hour_n be_v count_v from_o the_o south-end_n thereof_o as_o the_o tableâ—nd_n â—nd_z the_o figure_n of_o the_o dial_n do_v plain_o make_v manife_a be_v draw_v in_o this_o manner_n first_o draw_v the_o horizontal-line_n ab_fw-la then_o 〈◊〉_d c_o as_o a_o centre_n draw_v a_o semicircle_n equal_a 〈◊〉_d 60_o of_o the_o chord_n and_o lay_v off_o the_o meridian_n substile_n and_o style_v in_o their_o right_a situation_n as_o last_o be_v declare_v then_o draw_v â—â—ose_a line_n and_o to_o the_o substile_n erect_v a_o perâ—endiculer_a as_o de_fw-fr then_o take_v
the_o extent_n or_o near_a distance_n from_o the_o place_n where_o the_o perpendicule_a or_o contingent-line_n last_o draw_v cut_v 12_o and_o the_o stile-line_n and_o make_v it_o a_o =_o tangent_fw-la of_o 45_o then_o be_v the_o sector_n set_v to_o lay_v off_o all_o the_o hour_n by_o the_o =_o tangent_n of_o the_o ark_n in_o the_o table_n except_o 11_o and_o 10_o which_o do_v excur_v for_o if_o you_o prick_v the_o nocturnal-hour_n 12_o 1_o 2_o 3_o and_o draw_v they_o through_o the_o centre_n on_o the_o other_o side_n they_o shall_v be_v the_o hour_n of_o 12_o 1_o 2_o 3_o 4_o etc._n etc._n on_o the_o north-part_n of_o the_o plain_a where_o they_o be_v only_o use_v as_o for_o the_o hour_n of_o 10_o and_o 11_o do_v thus_o draw_v a_o line_n =_o to_o any_o one_o hour_n which_o =_o line_n may_v convenient_o cut_v those_o hour-line_n as_o suppose_v the_o line_n 6_o 12_o which_o be_v =_o to_o the_o hour-line_n of_o 3_o then_o make_v the_o distance_n from_o 9_o to_o 12_o or_o from_o 6_o to_o 9_o in_o that_o line_n last_o draw_v a_o =_o tangent_fw-la of_o 45_o and_o lay_v off_o hour_n and_o quarter_n or_o else_o the_o whole_a hour_n by_o the_o distance_n from_o 9_o to_o 7_o and_o 8_o for_o 10_o and_o 11_o turn_v the_o compass_n the_o other_o way_n from_o 9_o then_o to_o all_o those_o point_n line_n draw_v shall_v be_v the_o hour-line_n require_v or_o have_v only_o the_o hour_n of_o 3_o 6_o &_o 9_o &_o 12_o in_o a_o parallellogram_n design_v the_o rest_n by_o sector_n the_o second_o variety_n of_o north-recliners_a recline_v to_o the_o equinoctial_a by_o the_o bare_a draw_v of_o the_o scheam_n you_o see_v that_o the_o circle_n aeb_fw-mi represent_v the_o recline_a plain_n do_v cut_v the_o meridian_n just_a in_o the_o equinoctial_a now_o to_o try_v by_o arithmetic_n whether_o it_o be_v a_o just_a equinoctial-plain_a or_o no_o say_v 1._o by_o the_o sector_n as_o the_o sine_fw-la of_o 90_o ad_fw-la 90-0_a to_o tang._n of_o the_o reclination_n de_fw-fr 54-10_a so_o cousin_a of_o declin_n plain_o as_o 35-0_a to_o co-tang_n of_o the_o latitude_n sg_n 38-28_a as_o tangent_fw-la reclination_n df_n 54-10_a to_o =_o sine_fw-la 90_o ad_fw-la 90-0_a so_o =_o cousin_a of_o declination_n as_o 35-0_a to_o co-tang_n of_o the_o lat._n sg_n 38-28_a which_o happen_v so_o to_o be_v it_o be_v a_o decline_a equinoctial_a or_o polar_a in_o respect_n of_o its_o pole_n which_o be_v in_o the_o pole_n of_o the_o world_n 2._o if_o the_o declination_n be_v give_v and_o to_o it_o you_o will_v have_v a_o reclination_n to_o make_v it_o equinoctial_a by_o the_o sector_n as_o the_o cousin_a of_o the_o declin_n as_o 35-0_a to_o the_o co-tang_n of_o the_o lat._n sg_n 38-28_a so_o be_v the_o sine_fw-la of_o 90_o ad_fw-la 90-00_a to_o the_o co-tang_n of_o the_o reclin_n de_fw-fr 54-10_a as_o the_o co-tang_n lat._n sg_n 38_o 28_o to_o the_o =_o cousin_a declin_n as_o 35-00_a so_o the_o =_o sine_fw-la radius_fw-la ad_fw-la 90-00_a to_o the_o co-tang_n reclin_n de_fw-fr 54-10_a by_o the_o scheam_n the_o point_n ab_fw-la of_o declination_n be_v give_v and_o the_o point_n g_o on_o the_o meridian_n if_o you_o draw_v the_o recline_a circle_n agb_n it_o will_v intersect_v the_o perpendicule_a at_o e_z then_o the_o measure_n of_o see_fw-mi be_v the_o reclination_n measure_v by_o half-tangents_a or_o by_o chord_n by_o lay_v a_o rule_n from_o a_o to_z e_z on_o the_o limb_n give_v a_o the_o chord_n b_o a_o be_v the_o reclination_n 35-50_a 3._o but_o on_o the_o contrary_a if_o the_o reclination_n be_v give_v and_o a_o declination_n require_v to_o make_v a_o equinoctial_a plain_n then_o contrary_o say_v thus_o by_o the_o sector_n as_o co-tang_n of_o the_o reclin_n ed_z 54-10_a to_o sine_fw-la of_o 90_o ad_fw-la 90-00_a so_o co-tang_n of_o the_o latitude_n sg_n 38-28_a to_o cousin_a of_o the_o declin_n sa_o 35-00_a as_o co-tang_n reclin_n ed_z 54-10_a to_o =_o sine_fw-la ad_fw-la 90-0_a so_n co-tang_n latitude_n sg_n 38-28_a to_o =_o cousin_a declination_n sa_o 35-00_a but_o by_o the_o scheam_n by_o the_o point_n g_o and_o the_o touch_n of_o a_o arch_n about_o e_o draw_v the_o circle_n ge_n to_o cut_v the_o limb_n into_o two_o equal_a part_n and_o you_o have_v the_o point_n ab_fw-la 4._o the_o plain_a thus_o make_v or_o prove_v to_o be_v equinoctial_a to_o find_v the_o meridian_n elevation_n above_o the_o horizon_n agnostus_n or_o his_o distance_n from_o the_o perpendicule_a eglantine_n by_o the_o sector_n as_o sine_fw-la of_o 90_o zeg_v 90-0_a to_o sine_z of_o do_v on_o the_o mer._n from_o z_o to_o the_o plain_a gz_fw-fr 51-30_a so_o sine_fw-la of_o declin_n of_o the_o plain_a gze_n 55-0_a to_o sine_z of_o do_v on_o the_o plain_a from_o perpend_v to_o merid._n ge_n 39-54_a as_o sine_z gze_v 55-0_a to_o =_o sine_fw-la zeg_fw-mi 90-0_a so_o =_o sine_fw-la gz_fw-fr 51-32_a to_o sine_z ge_n 39-54_a who_o compliment_n be_v agnostus_n 50-06_a the_o elevation_n above_o the_o horizon_n by_o the_o scheam_n a_o rule_n lay_v from_o q_o to_o g_z gives_z b_o on_o the_o limb_n db_n be_v 39-54_a as_o before_o 5._o to_o find_v the_o style_n elevation_n above_o the_o substile_a on_o the_o plain_a by_o the_o sector_n as_o sine_fw-la of_o the_o latitude_n gz_fw-fr 51-32_a to_o sine_fw-la of_o the_o reclination_n see_fw-mi 35-50_a so_o sine_fw-la of_o do_v mer._n pole_n to_o plain_a gp_n 90-00_a to_o sine_fw-la of_o the_o style_n elevation_n pf_n 48-24_a as_o sine_fw-la 90_o gp_v 90-0_a to_o =_o sine_fw-la latitude_n gz_n 51-32_a so_o =_o sine_fw-la reclination_n see_fw-mi 35-50_a to_o sine_fw-la stiles_n height_n pf_n 48-24_a by_o the_o scheam_n a_o rule_n lay_v from_o y_o to_o f_o on_o the_o limb_n gives_z c_z nc_n be_v 48-24_a the_o style_n height_n the_o distance_n of_o the_o substile_a from_o 12_o in_o these_o equinoctial_a dial_n be_v always_o 90_o degree_n for_o a_o rule_n lay_v from_o q_n the_o pole_n of_o the_o plain_a to_o g_o on_o the_o limb_n give_v b_o a_o rule_n also_o lay_v from_o q_o to_o f_o the_o substile_a on_o the_o limb_n give_v d_o the_o ark_n bd_v be_v 90_o degree_n both_o for_o the_o distance_n of_o the_o substile_a from_o 12_o and_o also_o for_o the_o inclination_n of_o meridian_n for_o the_o substile_n stand_v on_o the_o hour_n of_o 6_o be_v part_n of_o the_o circle_n epw_o which_o be_v the_o hour_n of_o 6_o 90_o degree_n distant_a from_o the_o hour_n of_o 12._o or_o a_o rule_n lay_v as_o before_o from_o y_z to_o p_o on_o the_o limb_n give_v n_o the_o ark_n en_fw-fr or_o wn_n be_v 90_o for_o the_o inclination_n of_o meridian_n which_o be_v just_a 90_o the_o table_n be_v easy_o make_v viz._n 15_o 30_o 45_o 60_o 75_o 90_o twice_o repeat_v from_o 12_o to_o 6_o both_o way_n s._n to_o draw_v the_o dial._n on_o the_o horizontal-line_n ab_fw-la draw_v a_o obscure_a semicircle_n and_o set_v off_o the_o meridian_n as_o the_o scheam_n show_v viz._n 50_o degree_n 6_o min._n above_o the_o east-end_n of_o the_o horizontal-line_n but_o make_v visible_a only_o the_o north-end_n thereof_o as_o the_o line_n c_o 12_o then_o 90_o degree_n from_o thence_o towards_o the_o right-hand_a as_o the_o scheam_n show_v when_o the_o perpendiculer-line_n be_v right_a before_o you_o draw_v a_o line_n that_o serve_v both_o for_o 6_o and_o the_o substile_a as_o c_z 6._o also_o lay_v off_o the_o chord_n of_o 36-47_a from_o 6_o to_o 9_o and_o draw_v the_o line_n c_o 9_o also_o which_o be_v find_v by_o calculation_n as_o before_o be_v show_v or_o thus_o draw_v a_o line_n =_o to_o 12_o or_o perpendicule_a to_o 6_o be_v in_o this_o dial_n all_o one_o as_o the_o line_n feg_n then_o set_v one_o point_n in_o e_o the_o substile_a take_v the_o near_a distance_n to_o the_o stile-line_n and_o it_o shall_v reach_v from_o e_z to_z g_z the_o point_n for_o 9_o the_o same_o distance_n eglantine_n lay_v also_o on_o the_o line_n 12_o from_o c_z to_o h_n and_o draw_v the_o line_n ghi_n then_o make_v eglantine_n a_o =_o tangent_fw-la of_o 45_o and_o lay_v off_o the_o =_o tangent_n of_o 15-30-45_a both_o way_n from_o e_o as_o have_v be_v often_o show_v also_o make_v the_o distance_n of_o hg_v a_o =_o tangent_fw-la of_o 45_o and_o lay_v the_o same_o =_o tangent_n both_o way_n from_o h_n and_o to_o those_o point_n draw_v the_o hour-line_n require_v the_o three_o variety_n of_o north-recliners_a this_o three_o and_o last_o sort_n of_o north-recliners_a be_v those_o that_o recline_v beyond_o the_o equinoctial_a that_o be_v lie_v between_o the_o equinoctial_a and_o the_o horizon_n and_o it_o differ_v somewhat_o from_o the_o other_o five_o before_o in_o the_o scheam_n and_o operation_n also_o for_o first_o the_o ark_n of_o the_o plain_n be_v extend_v below_o the_o horizon_n till_o it_o meet_v with_o the_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 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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
as_o 12_o &_o 6_o be_v nr_n 60-40_a both_o hour_n and_o quarter_n if_o you_o have_v they_o true_o draw_v on_o a_o large_a general_a scheam_n as_o mr._n lankford_n have_v do_v thus_o much_o for_o direct_v plain_n both_o erect_a and_o recline_a before_o i_o come_v to_o speak_v of_o decliner_n it_o will_v not_o be_v amiss_o to_o show_v how_o to_o find_v the_o declination_n of_o a_o plain_a both_o by_o the_o sunshine_n or_o without_o by_o a_o magnetical-needle_n as_o follow_v as_o sine_z of_o the_o substile_a 41-40_a gf_n to_o =_o sine_fw-la of_o the_o latitude_n 51-32_a np_n so_o be_v =_o sine_fw-la of_o 90_o pfg_n to_o sine_z of_o gpf_n 58-7_a the_o incliner_n chap._n iii_o to_o find_v the_o declination_n of_o any_o plain_a for_o find_v the_o declination_n of_o a_o plain_a the_o most_o easy_a way_n be_v by_o a_o magnetical-needle_n fit_v according_a to_o mr._n fail_v way_n in_o the_o index_n of_o a_o declinatory_n as_o he_o call_v it_o be_v 180_o degree_n of_o a_o semicircle_n divide_v on_o a_o oblong-board_n or_o quadrant_n or_o a_o long_a needle_n in_o a_o square_a box_n or_o fit_v with_o hinge_n and_o a_o cover_v after_o all_o which_o way_n you_o may_v have_v they_o make_v at_o the_o sign_n of_o the_o sundial_n in_o the_o minory_n by_o john_n brown_a or_o of_o any_o other_o manner_n you_o shall_v think_v fit_a but_o to_o our_o triangule_a quadrant_n be_v a_o box_n and_o needle_n also_o to_o be_v fit_v of_o another_o form_n in_o some_o thing_n more_o convenient_a who_o form_n be_v thus_o first_o in_o a_o piece_n of_o box_n 5_o inch_n long_o 2_o ½_o broad_a and_o 6_o ten_o of_o one_o inch_n thick_a be_v a_o hole_n make_v near_o 4_o inch_n long_o 1_o inch_n ¾_n broad_a and_o 4_o ten_o deep_a for_o a_o needle_n to_o play_v in_o about_o 50_o degree_n at_o each_o end_n with_o brass-hinge_n and_o a_o cover_n and_o a_o brace_n to_o keep_v the_o lid_n upright_o &_o a_o axis_n of_o thâ—ed_n and_o a_o plummet_n play_v in_o the_o lid_n and_o a_o horizontal_a and_o a_o south-dial_n draw_v on_o the_o box_n and_o cover_n also_o a_o hasp_v and_o glass_n to_o keep_v the_o needle_n close_o cover_v and_o on_o the_o bottom_n a_o grove_n one_o ten_o of_o a_o inch_n deeâ—_n make_v just_a as_o broad_a as_o one_o leg_n of_o the_o sector_n be_v the_o use_n whereof_o be_v thus_o put_v your_o box_n and_o needle_n on_o that_o leg_n of_o the_o sector_n as_o will_v be_v most_o convenient_a for_o your_o purpose_n the_o north_n or_o cross-end_n of_o the_o needle_n towards_o the_o wall_n when_o it_o be_v a_o south_n decliner_n and_o the_o contrary_a when_o it_o be_v apply_v to_o a_o north_n decliner_n as_o the_o play_v of_o the_o needle_n will_v tell_v you_o better_o than_o many_o word_n then_o open_a or_o close_o the_o rule_n till_o the_o needle_n play_v right_a over_o the_o line_n in_o the_o bottom_n of_o the_o box_n unless_o there_o be_v variation_n than_o you_o must_v allow_v for_o it_o eastward_n or_o westward_n what_o it_o be_v then_o i_o say_v the_o quantity_n of_o the_o angle_n in_o degree_n and_o minute_n the_o sector_n stand_v at_o above_z or_o under_o 90_o be_v the_o degree_n and_o minute_n of_o declination_n be_v count_v from_o 00_o in_o the_o little_a semicircle_n as_o compliment_n to_o the_o angle_n of_o open_v as_o in_o the_o four_o use_n of_o the_o 5_o chapter_n be_v large_o and_o plain_o show_v thus_o you_o have_v the_o quantity_n of_o degree_n and_o minute_n of_o declination_n but_o to_o determine_v which_o way_n consider_v thus_o if_o the_o needle_n will_v stand_v still_o in_o the_o middle_n when_o the_o north-end_n be_v towards_o the_o wall_n than_o the_o first_o denomination_n be_v south_n if_o not_o north._n again_o when_o you_o know_v where_o north_n and_o south_n be_v you_o may_v resolve_v which_o way_n the_o east_n and_o west_n be_v for_o observe_v always_o if_o the_o north_n be_v before_o you_o than_o the_o east_n be_v on_o the_o right-hand_a and_o the_o west_n on_o the_o left_a and_o contrary_o if_o the_o south_n be_v before_o you_o the_o west_n be_v on_o the_o right-hand_a and_o the_o east_n on_o the_o left_a then_o if_o the_o sun_n be_v in_o the_o east-point_n of_o the_o horizon_n can_v look_v on_o the_o plain_a it_o be_v a_o southeast_n plain_a but_o if_o it_o behold_v it_o when_o in_o the_o west-point_n it_o be_v a_o south-west_n plain_a likewise_o if_o the_o cross-end_n of_o the_o needle_n will_v not_o stand_v towards_o the_o wall_n the_o needle_n play_v well_o and_o the_o sun_n be_v due_a east_n behold_v the_o plain_a than_o it_o be_v so_o many_o degree_n north-east_n but_o if_o it_o can_v look_v on_o the_o plain_a be_v due_a east_n than_o it_o be_v a_o northwest_n plain_a decline_v so_o many_o deg_n as_o the_o sector_n stand_v at_o under_z or_o above_o 90_o be_v always_o the_o compliment_n of_o the_o angle_n the_o leg_n of_o the_o sector_n stand_v at_o and_o find_v by_o take_v the_o angle_n the_o leg_n stand_v at_o from_o 90_o when_o the_o angle_n be_v less_o than_o 90._o or_o take_v 90_o out_o of_o the_o angle_n when_o it_o stand_v at_o a_o angle_n above_o 90_o degree_n as_o a_o look_n at_o the_o little_a semicircle_n on_o the_o head_n show_v example_n suppose_v i_o come_v to_o a_o wall_n and_o put_v the_o box_n and_o needle_n on_o the_o leg_n of_o the_o sector_n and_o apply_v the_o other_o leg_n to_o the_o wall_n or_o on_o a_o straight_a piece_n of_o wood_n apply_v to_o the_o wall_n because_o of_o the_o wall_n unevenness_n and_o open_a or_o close_o the_o leg_n till_o the_o needle_n play_v right_a over_o the_o meridian-line_n draw_v on_o the_o bottom_n of_o the_o box_n then_o i_o say_v the_o compliment_n of_o the_o angle_n the_o leg_n of_o the_o sector_n stand_v at_o be_v always_o what_o it_o want_v of_o or_o be_v above_o 90_o degree_n be_v the_o degree_n of_o declination_n and_o the_o coast_n which_o way_n the_o needle_n and_o sun_n be_v east_n and_o west_n tell_v you_o for_o if_o the_o north_n or_o cross-end_n of_o the_o needle_n be_v towards_o the_o wall_n it_o be_v a_o south_n plain_a and_o if_o the_o sun_n be_v in_o the_o east_n can_v behold_v it_o than_o it_o be_v southeast_n if_o not_o a_o south-west_n plain_a a_o ready_a way_n of_o count_v the_o angle_n find_v may_v be_v thus_o take_v the_o =_o distance_n between_o centre_n and_o centre_n in_o the_o middle_n of_o the_o innermost-line_n and_o lay_v it_o latteral_o from_o the_o centre_n and_o coâ—nt_v two_o degree_n more_o than_o the_o point_n show_v after_o the_o manner_n of_o chord_n from_o 90_o at_o the_o sine_fw-la of_o 45_o towards_o the_o compass-point_n and_o that_o shall_v be_v the_o degree_n and_o minute_n require_v example_n suppose_v the_o leg_n be_v so_o open_v that_o the_o =_o distance_n between_o the_o two_o centre_n make_v the_o sine_fw-la of_o 25_o then_o i_o say_v the_o line_n do_v stand_v at_o a_o angle_n of_o 50_o degree_n and_o the_o leg_n at_o 48_o two_o degree_n less_o the_o compliment_n whereof_o be_v 42_o as_o if_o you_o count_v thus_o from_o 45_o you_o will_v find_v 40_o from_o 45_o be_v 10_o 35_o be_v 20_o 30_o be_v 30_o 25_o be_v 40_o and_o 2_o degree_n more_o make_v 42_o the_o thing_n desire_v but_o if_o you_o like_v not_o the_o abate_n of_o two_o degree_n than_o the_o =_o distance_n take_v just_a between_o the_o two_o leg_n right_a against_o the_o centre_n shall_v be_v just_o the_o sine_fw-la of_o 24_o degree_n â—r_o 42_o count_v after_o the_o manner_n of_o chord_n viz._n every_o 5_o degree_n on_o the_o sin_n for_o 10_o on_o â—he_n chord_n backward_o from_o 45_o of_o the_o sin_n which_o be_v 90_o in_o chord_n or_o if_o you_o use_v the_o first_o rule_n of_o the_o four_o useâ—f_n â—f_z the_o 5_o chapter_n viz._n by_o take_v the_o â—ine_z of_o 30_o and_o put_v one_o point_n of_o the_o compass_n in_o the_o middle_a centre_n in_o the_o tangent-â—â—ne_n and_o apply_v the_o other_o to_o the_o line_n of_o â—ines_n you_o shall_v find_v it_o reach_v to_o the_o sine_fw-la compliment_n of_o the_o angle_n the_o line_n stand_v at_o â—iz_o 40_o degree_n and_o 2_o degree_n more_o viz._n â—2_n be_v the_o angle_n or_o thing_n desire_v as_o practise_v with_o consideration_n will_v make_v easy_a thus_o by_o the_o needle_n you_o may_v find_v the_o â—eclination_n of_o a_o wall_n which_o in_o cloudy_a â—eather_n may_v stand_v you_o in_o good_a stead_n or_o 〈◊〉_d prove_v a_o declination_n take_v by_o the_o sun_n to_o prevent_v mistake_n and_o if_o nothing_o draw_v the_o â—eedle_n from_o its_o right_a position_n but_o that_o it_o â—ay_v well_o and_o you_o find_v the_o angle_n true_o â—ou_fw-mi may_v come_v to_o less_o than_o half_a a_o degree_n and_o this_o convenience_n it_o have_v
10_o in_o the_o morning_n to_o 6_o afternoon_n though_o the_o sun_n may_v shine_v on_o it_o from_o 8_o to_o 7_o buâ—_n then_o the_o line_n will_v be_v too_o close_o together_o and_o the_o radius_fw-la too_o small_a and_o also_o when_o you_o will_v have_v those_o two_o utmost_a hour_n 〈◊〉_d be_v as_o at_z e_z and_o f_o on_o the_o upper_a equinoctial-line_n or_o at_z g_z &_o h_n on_o the_o low_a contingent-line_n then_o then_o take_v the_o whole_a distance_n of_o or_o gh_a and_o make_v it_o a_o =_o tangent_fw-la of_o 73-55_a then_o the_o sector_n to_o set_v take_v out_o the_o =_o tangent_fw-la of_o 58-45_a and_o lay_v it_o from_o the_o point_n e_o to_o i_o on_o the_o equinoctial-line_n also_o take_v out_o the_o =_o tangent_fw-la 61-15_a and_o lay_v it_o from_o the_o point_n f_o and_o if_o your_o work_n be_v true_a it_o must_v needs_o meet_v in_o the_o point_n i_o then_o draw_v the_o line_n ik_fw-mi for_o the_o true_a substile_n and_o from_o thence_o lay_v the_o =_o tangent_fw-la of_o 45_o to_o draw_v a_o line_n near_o 5_o for_o the_o style_n elevation_n parallel_n to_o ik_fw-mi the_o substile_a for_o be_v a_o polar-plain_a it_o have_v no_o elevation_n but_o what_o you_o please_v to_o augment_v it_o to_o as_o here_o from_o i_o to_o l._n then_o as_o the_o sector_n stand_v prick_v on_o all_o the_o whole_a hour_n half_n and_o quarter_n according_a to_o the_o number_n in_o your_o table_n at_o least_o those_o that_o be_v above_o 45_o and_o for_o those_o under_o 45_o make_v =_o tangent_fw-la of_o 45_o in_o small_a tangent_n a_o =_o tangent_fw-la of_o 45_o in_o the_o great_a tangent_n and_o then_o the_o sector_n shall_v be_v set_v to_o that_o radius_fw-la which_o be_v most_o convenient_a for_o your_o use_n note_v that_o this_o way_n of_o augment_v the_o style_n be_v general_a in_o all_o dial_n 3._o the_o three_o variety_n of_o south-recliners_a the_o next_o and_o last_o kind_n of_o south_n recliner_n be_v such_o as_o recline_v or_o fall_v from_o you_o below_o the_o pole_n viz_o have_v their_o plain_n lie_v between_o the_o pole_n and_o the_o horizon_n as_o by_o the_o scheam_n be_v more_o apparent_a in_o which_o work_n the_o drawing_z the_o scheam_n and_o the_o thing_n require_v be_v the_o same_o as_o in_o the_o first_o example_n as_o the_o figure_n and_o follow_v word_n do_v make_v make_v manifest_a the_o example_n here_o be_v of_o a_o plain_a that_o decline_v from_o the_o south_n towards_o the_o west_n 35_o degree_n and_o recline_v upon_o its_o proper_a azimuth_n see_fw-mi 60_o degree_n from_o the_o zenith_n 1._o have_v draw_v the_o scheam_n than_o first_o for_o the_o distance_n of_o the_o meridian_n from_o the_o perpendicule_a or_o horizon_n by_o the_o sector_n or_o quadrant_n as_o the_o sine_fw-la of_o zd_a 90-00_a to_o the_o tangent_fw-la of_o declination_n nd_o 35-00_a so_o the_o sine_fw-la of_o reclination_n see_fw-mi 60-00_a to_o the_o tang._n of_o perp._n &_o merid._n eglantine_n 31-12_a as_o tangent_fw-la of_o declination_n nd_o 35-00_a to_o =_o sine_fw-la of_o 90_o zd_v 90-00_a so_o =_o sine_fw-la of_o reclination_n see_fw-mi 60-00_a to_o tang._n of_o perp._n &_o merid._n eglantine_n 31-12_a who_o compliment_n be_v 58-48_a agnostus_n the_o distance_n between_o the_o west-end_n of_o the_o horizontal-line_n and_o the_o meridian_n or_o by_o the_o scheam_n a_o rule_n lay_v from_o q_o to_o g_z cut_v the_o limb_n at_o l_o the_o dl_o and_o all_o be_v the_o ark_v require_v dl_o from_o perpendicule_a and_o all_o from_o the_o horizon_n 2._o to_o find_v pg_n the_o ark_n on_o the_o meridian_n from_o the_o pole_n to_o the_o plain_a by_o the_o sector_n as_o sine_fw-la of_o ad_fw-la 90-0_a to_o co-tang_n of_o the_o reclin_n de_fw-fr 30-0_a so_o cousin_a of_o the_o declination_n a_o 55-0_a to_o tang._n of_o do_v plain_a &_o horiz_n ng_z 25-19_a as_o co-tangent_a reclin_n ed_z 30-0_a to_o =_o sine_fw-la of_o 90_o ad_fw-la 90-0_a so_o =_o sine_fw-la of_o reclination_n a_o 55-0_a to_o tang._n do_v on_o mer._n p._n hor._n ng_z 25-19_a which_o be_v take_v from_o np_n 51-32_a leave_v gp_n 26-13_a the_o distance_n on_o the_o meridian_n from_o the_o pole_n to_o the_o plain_a or_o the_o compliment_n of_o the_o new_a latitude_n or_o a_o rule_n lay_v from_o e_o to_o p_o and_o g_o gives_z on_o the_o limb_n 2_o point_n who_o distance_n between_o be_v ab_fw-la 26-13_a the_o ark_n require_v 3._o to_o find_v the_o style_n elevation_n above_o the_o plain_a by_o the_o sector_n as_o sine_z do_v merid._n horizon_n give_v 58-48_a to_o cousin_a declination_n a_o 55-00_a so_o sine_fw-la do_v pole_n to_o plain_a gp_n 26-13_a to_o sine_fw-la stiles_n elevation_n pf_n 25-02_a as_o sine_z of_o gp_n 26-13_a to_o =_o sine_fw-la of_o give_v 58-48_a so_o =_o sine_fw-la of_o a_o 55-00_a to_o sine_z of_o pf_n 25-02_a be_v find_v by_o the_o scheam_n by_o lay_v a_o rule_n from_o y_o to_o p_o and_o f_o on_o the_o limb_n give_v the_o distance_n between_o be_v 25-02_a the_o style_n elevation_n 4._o to_o find_v the_o substile_a from_o 12._o by_o the_o sector_n as_o co-tang_n of_o the_o declin_n a_o 55-00_a to_o s._n do_v on_o mer._n fr._n pl._n to_o hor._n ng_z 25-19_a so_o tang._n of_o the_o style_n height_n pf_n 25-02_a to_o s._n of_o the_o substile_a from_o 12_o fg_n 8-05_a as_o co-tang_n of_o declin_n plain_o a_o 55-00_a to_o =_o s._n do_v on_o mer._n fr._n pl._n to_o hor._n ng_z 25-19_a so_o tang._n of_o the_o style_n height_n pf_n 25-02_a to_o =_o s._n of_o the_o substile_a from_o 12_o fg_n 08-03_a by_o the_o scheam_n a_o rule_n lay_v from_o q_n to_z g_z and_o f_o on_o the_o limb_n gives_z l_o and_o m_o 8-3_a or_o else_o the_o ark_n md_o be_v the_o distance_n of_o the_o substile_a from_o the_o perpendicule_a 23-19_a 5._o to_o find_v the_o inclination_n of_o meridian_n by_o the_o sector_n as_o the_o sine_fw-la of_o the_o distance_n on_o mer._n from_o pole_n to_o plain_a pg_n 25-19_a to_o the_o sine_fw-la of_o the_o angle_n gfp_n 90-00_a so_o the_o sine_z of_o do_v of_o sub._n fr_n 12_o gf_n 08-03_a to_o the_o sine_fw-la of_o the_o incl._n of_o mer._n gpf_n 18-27_a as_o sine_fw-la gf_n 08-03_a to_o =_o sine_fw-la pg_n 25-19_a so_o =_o sine_fw-la gfp_n 90-00_a to_o sine_fw-la gpf_n 18-27_a by_o the_o scheam_n a_o rule_n lay_v from_o p_o to_o y_o on_o the_o limb_n give_v o_o the_o ark_n eo_fw-la be_v 18-27_a the_o inclination_n of_o meridian_n by_o help_n of_o which_o to_o make_v the_o table_n of_o hour-arks_a at_o the_o pole_n as_o before_o be_v show_v and_o as_o in_o the_o table_n follow_v 12_o 18_o 27_o 8-3_a  _fw-fr 10_o 57_o  _fw-fr 1_o 3_o 27_o 1-27_a  _fw-fr  _fw-fr sub_v  _fw-fr 4_o 03_o  _fw-fr 2_o 11_o 33_o 4-58_a  _fw-fr 18_o 03_o  _fw-fr 3_o 26_o 33_o 11-55_a  _fw-fr 34_o 03_o  _fw-fr 4_o 41_o 33_o 20-35_a  _fw-fr 48_o 03_o  _fw-fr 5_o 56_o 33_o 32-45_a  _fw-fr 64_o 03_o  _fw-fr 6_o 71_o 33_o 51-45_a  _fw-fr 78_o 03_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 7_o 86_o 33_o 81-52_a  _fw-fr 85-57_a  _fw-fr 8_o 78_o 27_o 64-10_a  _fw-fr 70_o 57_o  _fw-fr 9_o 63_o 27_o 40-20_a  _fw-fr 55_o 57_o  _fw-fr 10_o 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general_a and_o particular_a for_o any_o one_o or_o more_o latitude_n the_o figure_n explain_v a_o the_o place_n on_o the_o transum_fw-la for_o the_o glass_n to_o lie_v on_o and_o in_o the_o midst_n thereof_o one_o point_n in_o the_o ray_n of_o the_o quadrant_n be_v to_o play_v ih_o a_o piece_n of_o wood_n to_o be_v nail_v fast_o at_o h_n and_o i_o for_o the_o other_o point_n to_o play_v in_o at_o g_o l_o the_o hole_n for_o the_o plummet_n to_o play_v in_o be_v cut_v through_o the_o thin_a quadrant_n b_o and_o c_z the_o end_n of_o the_o semicircle_n nail_v on_o the_o transum_fw-la or_o stool_n k_o the_o hole_n in_o the_o quadrant_n for_o the_o semi-circular-ring_n to_o pass_v through_o fe_o the_o post_n of_o the_o window_n d_o the_o beginning_n of_o the_o degree_n on_o the_o semicircle_n be_o a_o thread_n extend_v from_o the_o centre_n of_o the_o quadrant_n to_o the_o ceiling_n thus_o you_o have_v the_o usual_a way_n of_o dial_v in_o a_o competent_a measure_n plain_o and_o practical_o handle_v which_o may_v be_v useful_a to_o many_o a_o learner_n and_o i_o hope_v will_v be_v as_o well_o accept_v as_o with_o freewill_n though_o with_o little_a ability_n and_o less_o leisure_n ready_o impart_v a_o table_n of_o the_o sun_n azimuth_n from_o the_o south_n at_o every_o hour_n and_o quarter_n 51-32_a  _fw-fr ♋_o ♊_o ♌_o ♉_o â™_o ♈_o ♎_o ♓_o â™_o â™’_o â™_o ♑_o  _fw-fr d._n m._n d._n m._n d._n m_o d._n m_o d._n m_o d._n m_o d._n m_o 12_o 00_o 00_o 00_o 00_o 00_o 00_o 00_o 00_o 00_o 00_o 00_o 00_o 00_o 00_o  _fw-fr 07_o 10_o 05_o 53_o 5_o 37_o 4_o 55_o 03_o 54_o 03_o 53_o 3_o 52_o  _fw-fr 14_o 22_o 13_o 24_o 11_o 10_o 9_o 40_o 07_o 57_o 07_o 40_o 7_o 10_o  _fw-fr 21_o 27_o 19_o 53_o 16_o 44_o 14_o 13_o 12_o 11_o 11_o 10_o 10_o 37_o 11_o 1_o 27_o 54_o 26_o 00_o 22_o 13_o 18_o 52_o 16_o 22_o 14_o 45_o 14_o 13_o  _fw-fr 34_o 14_o 32_o 01_o 27_o 32_o 23_o 22_o 20_o 15_o 18_o 17_o 17_o 38_o  _fw-fr 40_o 12_o 37_o 40_o 32_o 41_o 27_o 41_o 24_o 06_o 21_o 53_o 20_o 59_o  _fw-fr 45_o 39_o 43_o 04_o 37_o 32_o 32_o 08_o 29_o 44_o 26_o 30_o 24_o 25_o 10_o 2_o 50_o 51_o 47_o 57_o 42_o 05_o 36_o 24_o 31_o 50_o 28_o 52_o 27_o 49_o  _fw-fr 55_o 31_o 52_o 41_o 47_o 04_o 40_o 30_o 35_o 35_o 32_o 18_o 31_o 00_o  _fw-fr 61_o 43_o 57_o 11_o 50_o 51_o 44_o 26_o 39_o 10_o 35_o 39_o 34_o 17_o  _fw-fr 64_o 11_o 61_o 18_o 54_o 33_o 48_o 13_o 42_o 36_o 38_o 50_o 37_o 34_o 9_o 3_o 68_o 10_o 65_o 16_o 58_o 47_o 51_o 56_o 46_o 02_o 42_o 04_o 40_o 36_o  _fw-fr 71_o 52_o 69_o 56_o 62_o 33_o 55_o 33_o 49_o 25_o 45_o 16_o 43_o 40_o  _fw-fr 75_o 26_o 72_o 37_o 66_o 10_o 58_o 59_o 52_o 43_o 48_o 21_o 46_o 42_o  _fw-fr 78_o 48_o 76_o 05_o 69_o 38_o 62_o 22_o 55_o 55_o 51_o 22_o 49_o 40_o 8_o 4_o 82_o 00_o 79_o 20_o 72_o 57_o 65_o 40_o 59_o 00_o 54_o 22_o  _fw-fr  _fw-fr 85_o 08_o 82_o 42_o 76_o 12_o 68_o 53_o 62_o 08_o  _fw-fr  _fw-fr  _fw-fr 88_o 10_o 85_o 38_o 79_o 23_o 72_o 06_o 65_o 12_o  _fw-fr  _fw-fr  _fw-fr 91_o 09_o 87_o 50_o 82_o 28_o 75_o 03_o 68_o 12_o  _fw-fr  _fw-fr 7_o 5_o 94_o 05_o 91_o 34_o 85_o 30_o 78_o 06_o 71_o 10_o  _fw-fr  _fw-fr  _fw-fr 96_o 51_o 94_o 25_o 88_o 27_o 81_o 09_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 99_o 38_o 97_o 16_o 91_o 25_o 84_o 06_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 102_o 25_o 100_o 07_o 94_o 22_o 87_o 04_o  _fw-fr  _fw-fr  _fw-fr 6_o 6_o 105_o 08_o 102_o 54_o 97_o 12_o 90_o 00_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 107_o 52_o 104_o 58_o 100_o 02_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 110_o 36_o 108_o 26_o 103_o 00_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 113_o 18_o 111_o 14_o 105_o 54_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 5_o 7_o 116_o 03_o 114_o 03_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 118_o 50_o 116_o 54_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 121_o 41_o 119_o 47_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 124_o 29_o 122_o 37_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 4_o 8_o 127_o 24_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 130_o 28_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr a_o table_n of_o the_o sun_n altitude_n at_o every_o hour_n and_o quarter_n in_o each_o sign_n for_o 51-32_a  _fw-fr ♋_o ♊_o ♌_o ♉_o â™_o ♈_o ♎_o ♓_o â™_o â™’_o â™_o ♑_o  _fw-fr d._n m_o d._n m_o d._n m_o d._n m_o d._n m_o d._n m_o d._n m_o 12_o 62_o 90_o 58_o 42_o 50_o 00_o 38_o 28_o 27_o 00_o 18_o 18_o 14_o 59_o  _fw-fr 61_o 50_o 58_o 34_o 49_o 52_o 38_o 24_o 26_o 54_o 18_o 13_o 14_o 55_o  _fw-fr 61_o 25_o 58_o 09_o 49_o 31_o 38_o 07_o 26_o 40_o 18_o 00_o 14_o 38_o  _fw-fr 60_o 41_o 57_o 29_o 49_o 00_o 37_o 38_o 26_o 15_o 17_o 37_o 14_o 20_o 11_o 59_o 43_o 56_o 34_o 48_o 12_o 36_o 58_o 25_o 40_o 17_o 06_o 13_o 52_o  _fw-fr 58_o 32_o 55_o 26_o 47_o 10_o 36_o 07_o 24_o 02_o 16_o 26_o 13_o 10_o  _fw-fr 57_o 04_o 54_o 06_o 46_o 02_o 35_o 06_o 23_o 59_o 15_o 38_o 12_o 35_o  _fw-fr 55_o 29_o 52_o 36_o 44_o 38_o 33_o 56_o 22_o 58_o 14_o 49_o 11_o 30_o 10_o 53_o 45_o 50_o 55_o 43_o 12_o 32_o 37_o 21_o 51_o 13_o 38_o 10_o 36_o  _fw-fr 51_o 52_o 49_o 07_o 41_o 33_o 31_o 10_o 20_o 33_o 12_o 27_o 9_o 20_o  _fw-fr 49_o 54_o 47_o 12_o 39_o 46_o 29_o 36_o 19_o 10_o 11_o 09_o 8_o 9_o  _fw-fr 47_o 50_o 45_o 12_o 37_o 56_o 27_o 54_o 17_o 35_o 9_o 44_o 6_o 41_o 9_o 45_o 42_o 43_o 06_o 36_o 00_o 26_o 07_o 15_o 58_o 8_o 13_o 5_o 16_o  _fw-fr 43_o 30_o 40_o 57_o 33_o 55_o 24_o 14_o 14_o 14_o 9_o 49_o 3_o 41_o  _fw-fr 41_o 16_o 38_o 45_o 31_o 50_o 22_o 16_o 12_o 27_o 4_o 54_o 2_o 04_o  _fw-fr 39_o 00_o 36_o 30_o 29_o 40_o 20_o 14_o 10_o 32_o 3_o 07_o 0_o 17_o 8_o 36_o 41_o 34_o 13_o 27_o 31_o 18_o 08_o 8_o 35_o 1_o 15_o  _fw-fr  _fw-fr 34_o 22_o 31_o 55_o 25_o 09_o 15_o 59_o 6_o 30_o  _fw-fr  _fw-fr  _fw-fr 32_o 02_o 29_o 13_o 22_o 56_o 13_o 46_o 4_o 27_o  _fw-fr  _fw-fr  _fw-fr 29_o 42_o 27_o 16_o 20_o 37_o 11_o 33_o 2_o 17_o  _fw-fr  _fw-fr 7_o 27_o 23_o 24_o 56_o 18_o 18_o 09_o 17_o 0_o 06_o  _fw-fr  _fw-fr  _fw-fr 25_o 03_o 22_o 36_o 15_o 58_o 06_o 58_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 22_o 45_o 20_o 16_o 13_o 38_o 04_o 40_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 20_o 28_o 17_o 58_o 11_o 18_o 02_o 20_o  _fw-fr  _fw-fr  _fw-fr 6_o 18_o 11_o 15_o 41_o 09_o 00_o
help_n of_o a_o sector_n with_o sines_n and_o tangent_n to_o 7-5_a such_o as_o be_v usual_o make_v but_o for_o very_o far_o decliner_n use_v that_o help_n as_o direct_v in_o chap._n 4._o the_o like_a work_n serve_v to_o help_v all_o sort_n of_o dial_n with_o low_a style_n polar_a and_o meridian_n dial_n also_o the_o other_o 6_o sort_n yet_o behind_o i_o shall_v demonstrate_v only_o in_o two_o of_o they_o which_o do_v proper_o enough_o comprehend_v they_o all_o and_o the_o work_n of_o one_o be_v as_o easy_a as_o the_o work_n of_o the_o other_o especial_o by_o the_o help_n of_o the_o sphere_n where_o the_o hard_a be_v as_o plain_a as_o the_o horizontal_a therefore_o 7._o of_o decline_a reclining-dials_n 1._o for_o south_n recliner_n they_o may_v recline_v short_a of_o to_z or_o beyond_o the_o pole_n at_o any_o declination_n as_o the_o put_n up_o and_o down_o the_o plain_a do_v plain_o demonstrate_v therefore_o first_o of_o one_o that_o decline_v south-west_n 35_o and_o recline_v 20_o from_o the_o zenith_n set_a the_o notch_n or_o pole_n of_o the_o plain_a to_o the_o declination_n and_o the_o recline_a circle_n to_o its_o reclination_n and_o there_o make_v it_o fast_o then_o extend_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 the_o hour-circle_n exact_o even_o with_o the_o move_a semicircle_n then_o first_o the_o axis_n show_v the_o style_n height_n on_o the_o semicircle_n to_o be_v 12-13_a the_o thread_n bring_v along_o the_o plain_a while_o it_o touch_v the_o meridian_n and_o that_o show_v the_o meridian_n elevation_n above_o the_o horizon_n on_o the_o north_n recliner_n to_o be_v 76-32_a or_o its_o depression_n below_o the_o horizon_n in_o south-recliners_a and_o that_o from_o the_o east-end_n as_o the_o sphere_n show_v then_o 3._o the_o substile_a from_o the_o perpendicule_a line_n of_o the_o plain_a be_v 21-6_a as_o the_o upper_a semicircle_n show_v but_o from_o the_o hour_n 12_o or_o meridian_n 7-58_a and_o stand_v on_o the_o east-side_n of_o the_o meridian_n the_o inclination_n of_o the_o meridian_n be_v 33-29_a as_o the_o degree_n on_o the_o equinoctial_a between_o the_o meridian_n and_o hour-circle_n show_n all_o the_o hour-arks_a be_v easy_o find_v from_o the_o plain_n perpendicule_a eastward_n and_o westward_n by_o apply_v the_o thread_n to_o the_o hour-circle_n and_o plain_n be_v set_v to_o the_o hour_n on_o the_o equinoctial_a the_o south_n pole_n be_v elevate_v in_o the_o south-recline_a and_o the_o north_n on_o the_o north_n incliner_n if_o you_o set_v letter_n to_o the_o side_n and_o angle_n according_a to_o the_o former_a discourse_n you_o will_v see_v how_o all_o the_o canon_n in_o the_o arithmetical_a calculation_n lie_v as_o i_o show_v you_o before_o in_o the_o decline_a dial_n and_o as_o again_o thus_o on_o the_o pole_n set_v p._n on_o the_o zenith_n z._n at_o the_o west-end_n of_o the_o plain_a set_v a._n at_o the_o east-end_n b._n at_o the_o south_n pole_n of_o the_o plain_a c._n at_o the_o north_n pole_n d._n at_o the_o east-end_n of_o the_o horizon_n e._n at_o the_o west-end_n w._n at_o the_o north-end_n of_o the_o meridian_n set_v n._n at_o the_o south-end_n s._n where_o the_o hour-circle_n cut_v the_o plain_a f._n where_o the_o meridian_n cut_v the_o plain_a g._n where_o the_o fix_a semicircle_n cut_v the_o plain_a set_v e._n as_o in_o the_o figure_n before_o then_o these_o canon_n in_o short_a run_v thus_o as_o sine_fw-la base_n zd_v 90-00_a to_o tang._n perpend_v nd_o 35-00_a so_o sine_fw-la of_o base_a see_fw-mi 20-00_a to_o tang._n perpend_v ge_n 13-28_a who_o compliment_n agnostus_n 70-32_a be_v the_o meridian_n elevation_n as_o sine_fw-la of_o the_o side_n ge_n 13-28_a to_o sine_fw-la of_o the_o angle_n cze_v 35-00_a so_o sine_fw-la of_o the_o angle_n gfz_fw-fr 90-00_a to_o sine_fw-la of_o the_o side_n gz_fw-fr 23-57_a which_o take_v from_o zp_n 38-28_a leave_v 14-33_a the_o distance_n of_o the_o meridian_n place_n from_o the_o pole_n to_o the_o plain_a viz._n gf_n as_o sine_fw-la of_o hypothen_n gz_fw-fr 23-57_a to_o sine_fw-la of_o perpend_v see_fw-mi 20-00_a so_o sine_fw-la of_o hypothen_n pg_n 14-33_a to_o sine_fw-la of_o perpend_v pf_n 12-13_a  _fw-fr the_fw-fr style_n as_o tangent_fw-la of_o perpend_v zf_o 20-00_a to_o sine_fw-la of_o base_a ge_n 13-28_a so_o tangent_fw-la of_o perpend_v pf_n 12-13_a to_o sine_fw-la of_o base_a fg_n 7-58_a  _fw-fr the_fw-fr substile_fw-fr to_o 12._o as_o the_o sine_fw-la of_o the_o side_n see_fw-mi 20-00_a to_o the_o sine_fw-la of_o the_o side_n ge_n 13-28_a so_o be_v the_o sine_fw-la of_o the_o angle_n pfg_v 90-00_a to_o the_o sine_fw-la of_o the_o angle_n fpg_n 33-28_a  _fw-fr inclin_n merid._n for_o the_o hour_n in_o all_o dial_n say_v thus_o as_o sine_fw-la of_o 90_o to_o sine_fw-la of_o stiles_n height_n so_o tangent_fw-la of_o the_o angle_n at_o the_o pole_n to_z tangent_fw-la of_o the_o angle_n on_o the_o plain_a 8._o for_o north_n decline_a reclining-dials_n for_o these_o plain_n also_o you_o must_v rectify_v the_o sphere_n to_o the_o latitude_n and_o set_v the_o plain_a to_o his_o declination_n and_o inclination_n which_o be_v give_v and_o for_o which_o you_o be_v to_o make_v a_o north_n decline_a reclining_a dial._n as_o you_o do_v in_o the_o south-recline_a so_o work_v in_o all_o respect_n as_o you_o shall_v bring_v forth_o the_o quesita_n either_o by_o the_o sphere_n or_o arithmetical-calculation_n as_o be_v large_o show_v and_o for_o a_o plain_a that_o decline_v 55_o degree_n from_o the_o north_n towards_o the_o east_n and_o relines_n 20_o from_o the_o zenith_n you_o shall_v find_v the_o requisite_n to_o be_v as_o follow_v 1._o the_o meridian_n elevation_n above_o the_o horizon_n be_v find_v to_o be_v 63_o deg_n 58_o min._n but_o yet_o observe_v you_o must_v make_v use_n of_o that_o part_n of_o it_o which_o be_v below_o the_o horizon_n because_o the_o sun_n be_v elevate_v high_a on_o the_o south-part_n of_o the_o meridian_n must_v needs_o cast_v a_o shadow_n on_o the_o north-part_n thereof_o therefore_o in_o draw_v the_o dial-part_n part_n be_v only_o to_o be_v make_v use_n of_o for_o the_o sun_n to_o shine_v on_o 2._o the_o style_n elevation_n be_v 37_o degree_n 00_o minute_n 3._o the_o substile_a from_o 12_o 65-24_a or_o from_o the_o plain_n perpendicule_a 39-22_a the_o north_n pole_n be_v elevate_v and_o in_o regard_n the_o plain_n decline_v to_o the_o east_n the_o style_n must_v be_v set_v towards_o the_o west_n and_o it_o shine_v on_o the_o plain_a in_o summertime_n from_o the_o rise_n unto_o 12_o but_o in_o the_o wintertime_n but_o a_o few_o hour_n note_v also_o that_o these_o decline_a reclining-plain_n may_v be_v refer_v to_o a_o new_a latitude_n and_o declination_n wherein_o they_o shall_v become_v upright_a decliner_n as_o before_o be_v hint_v the_o poor-mans_n dial-sphear_n or_o another_o way_n to_o demonstrate_v the_o mystery_n of_o dyall_v both_o for_o decline_a and_o incline_v plain_n in_o a_o very_a plain_n easy_a way_n for_o one_o 6_o part_n of_o the_o cost_n of_o the_o other_o brass-sphear_n first_o as_o to_o the_o description_n and_o afterward_o for_o the_o use_n as_o to_o the_o description_n the_o figure_n annex_v and_o a_o few_o word_n shall_v suffice_v wherein_o consider_v first_o the_o plain_a flat-board_n represent_v the_o horizon_n as_o abcd._n second_o the_o two_o upright_a piece_n as_o east_n and_o west-point_n as_o ae_n and_o bf_n to_o support_v the_o move_a plain_n three_o the_o moving-plain_a move_v to_o any_o inclination_n on_o the_o two_o point_n e_o and_o f_o with_o 180_o degree_n upon_o the_o plain_a and_o note_v by_o abef_n four_o also_o a_o brass-circle_n as_o g_o fasten_v to_o the_o plain_a to_o set_v it_o to_o any_o degree_n of_o inclination_n and_o a_o screw_n as_o at_o h_n that_o may_v stay_v it_o steady_a when_o set_v to_o any_o reclination_n five_o on_o the_o middle_n of_o the_o horizontal-board_n be_v fasten_v at_o the_o point_n m_o a_o true_a horizontal-dial_n draw_v fit_a for_o your_o latitude_n and_o to_o turn_v round_o on_o the_o point_n m_o as_o imkl_n six_o a_o thread_n fasten_v in_o l_o the_o centre_n of_o the_o horizontal-dial_n and_o in_o n_o the_o centre_n of_o the_o plain_a to_o be_v both_o a_o style_n for_o the_o horizontal-dial_n and_o to_o represent_v the_o axis_n of_o the_o world_n also_o a_o small_a woodden-quadrant_n will_v be_v useful_a such_o a_o one_o as_o half_a the_o plain_n be_v to_o draw_v perpendiculer_o and_o measure_v angle_n as_o afterward_o in_o the_o use_v the_o use_v follow_v use_v i._o to_o find_v the_o declination_n of_o a_o plain_a by_o the_o sunshining_a apply_v the_o side_n ab_fw-la to_o the_o wall_n and_o hold_v the_o instrument_n level_v as_o by_o help_n of_o a_o point_n plummer_n fasten_v at_o n_o and_o the_o point_n play_v right_o on_o m_n it_o be_v easy_a to_o
30_o s.e._n and_o incline_v 20._o the_o substile_a by_o apply_v the_o square_a you_o shall_v find_v to_o be_v 30_o degree_n on_o the_o left-hand_a of_o the_o perpendicule_a westward_o and_o the_o inclination_n of_o meridian_n 48-20_a the_o style_n height_n 51-36_a and_o the_o meridian_n on_o the_o right-hand_a of_o the_o perpendiculer-line_n 11-30_a eastward_o and_o the_o shadow_n of_o the_o thread_n play_v on_o every_o hour_n and_o quarter_n on_o the_o horizontal-dial_n will_v show_v on_o the_o plain_a the_o quantity_n in_o degree_n from_o the_o perpendiculer-line_n use_v vi_o to_o find_v the_o requisite_n in_o a_o north-east_n reclining-dial_n and_o the_o hour-line_n set_a the_o instrument_n as_o before_o and_o find_v the_o substile_a stile_n and_o inclination_n of_o meridian_n as_n before_o but_o note_n as_o to_o the_o affection_n which_o way_n do_v thus_o turn_v the_o instrument_n the_o bottom_n upward_o and_o as_o near_o as_o you_o can_v guess_v turn_v the_o plain_a to_o its_o situation_n than_o you_o shall_v first_o see_v the_o style_n to_o look_v upward_o in_o the_o north-east_n recliner_n which_o before_o be_v downward_o in_o the_o southeast_n incliner_n also_o the_o substile_a stand_v on_o the_o right-hand_a of_o the_o perpendicule_a 30_o degree_n westward_o for_o observe_v this_o always_o if_o a_o plain_n decline_v eastward_o the_o substile_n will_v stand_v westward_o and_o the_o contrary_a also_o note_n that_o the_o meridian-line_n be_v to_o be_v draw_v quite_o through_o the_o centre_n on_o the_o other-side_n because_o when_o the_o sun_n be_v in_o the_o meridian_n above_o it_o must_v needs_o cast_v the_o shadow_n of_o the_o axis_n or_o style_v the_o contrary_a way_n downward_o use_v vii_o to_o find_v what_o be_v the_o most_o hour_n that_o the_o sun_n can_v shine_v on_o any_o plain_a whatsoever_o first_o on_o all_o south_n direct_v or_o decline_a inclining-dials_n the_o mid-day-meridian_n be_v proper_a to_o it_o unless_o it_o incline_v above_o 75_o degree_n and_o then_o it_o become_v useless_a in_o london_n latitude_n then_o what_o hour_n soever_o you_o can_v make_v the_o sun_n to_o shine_v on_o the_o plain_a and_o horizontal-dial_n both_o together_o the_o sun_n be_v at_o that_o hour_n above_o the_o horizon_n by_o bend_v or_o turn_v the_o instrument_n any_o way_n when_o the_o point_n at_o 12_o be_v first_o set_v to_o the_o declination_n that_o and_o all_o those_o hour_n be_v proper_a to_o that_o plain_a at_o one_o time_n of_o the_o year_n or_o other_o also_o note_n that_o several_a hour_n that_o serve_v for_o the_o south-plain_a do_v at_o some_o time_n of_o the_o year_n belong_v to_o the_o north-plain_a also_o as_o by_o turn_v the_o instrument_n about_o you_o may_v plain_o see_v either_o by_o the_o sunshine_n or_o by_o the_o thread_n and_o your_o eye_n cut_v the_o hour-line_n and_o the_o plain_a also_o observe_v that_o if_o you_o will_v delineate_v a_o south_n recline_v plain_a you_o may_v bring_v the_o plain_a towards_o the_o thread_n till_o it_o become_v a_o polar-plain_a but_o if_o it_o recline_v below_o the_o pole_n then_o conceive_v it_o to_o become_v a_o north_n reclining-dial_n and_o work_v as_o be_v before_o direct_v and_o you_o shall_v obtain_v your_o desire_n for_o the_o dial_n will_v be_v the_o same_o the_o one_o as_o the_o other_o as_o before_o be_v hint_v at_o in_o the_o inclining-plain_n use_v viii_o the_o declination_n of_o any_o plain_n give_v to_o find_v what_o reclination_n will_v make_v it_o a_o polar-dial_n and_o the_o contrary_n set_a the_o north-point_n to_o the_o declination_n and_o bring_v the_o plain_a to_o touch_v the_o thread_n then_o on_o the_o brass_n circle_n be_v cut_v the_o reclination_n require_v or_o contrary_a set_v the_o plain_a to_o the_o reclination_n give_v and_o then_o bring_v the_o thread_n to_o the_o plain_a by_o turn_v the_o horizontal-dial_n and_o the_o point_n at_o 12_o shall_v show_v the_o declination_n require_v to_o make_v it_o polar_a in_o like_a manner_n you_o may_v discover_v a_o decline_a equinoctial_a but_o not_o so_o easy_o when_o the_o substile_a and_o meridian_n be_v 90_o degree_n asunder_o the_o substile_a be_v then_o always_o in_o the_o hour_n of_o 6_o as_o by_o move_v the_o plain_a if_o the_o declination_n be_v give_v or_o by_o move_v the_o thread_n if_o the_o inclination_n be_v give_v till_o the_o square_n touch_v the_o thread_n it_o shall_v shadow_v or_o bourn_n just_a upon_o 6_o on_o the_o horizontal-dial_n note_v also_o that_o east_n and_o west_n recliner_n and_o incliner_n be_v discover_v after_o the_o same_o manner_n so_o also_o direct_v recliner_n and_o incliner_n as_o by_o move_v the_o plain_a to_o and_o fro_o you_o shall_v see_v the_o plain_a and_o true_a reason_n how_o the_o style_n be_v elevate_v or_o depress_v and_o how_o the_o hour-line_n be_v enlarge_v or_o contract_v according_a to_o the_o elevation_n of_o the_o style_n also_o in_o east_n and_o west-dials_n that_o the_o style_n have_v no_o elevation_n but_o be_v parallel_n to_o the_o plain_a and_o how_o the_o meridian_n lie_v in_o the_o horizon_n in_o east_n and_o west_n recliner_n and_o incliner_n many_o more_o uses_n may_v be_v insist_v on_o which_o i_o shall_v leave_v to_o the_o scrutiny_n of_o the_o industrious_a practitioner_n in_o the_o art_n of_o shadow_n chap._n ix_o how_o to_o remedy_v several_a inconvenience_n in_o the_o use_n of_o the_o artificial_a line_n of_o number_n sin_n and_o tangent_n as_o they_o be_v usual_o make_v 1._o if_o the_o term_n require_v happen_v to_o be_v under_o one_o degree_n of_o sines_n and_o tangent_n than_o the_o line_n of_o number_n will_v supply_v it_o have_v due_a respect_n to_o the_o increase_n of_o the_o radius_fw-la or_o caracteristick_n as_o thus_o as_o the_o sine_fw-la of_o 90_o to_o the_o sine_fw-la of_o 23-31_a the_o great_a declination_n so_o be_v the_o sine_fw-la of_o 1_o deg_n 10′_n the_o sun_n distance_n from_o the_o equinoctial_a to_o 0-28_a the_o declination_n which_o fall_v beyond_o the_o end_n of_o the_o rule_n now_o to_o remedy_v this_o the_o 1_o deg_n &_o 10′_n be_v 70_o minute_n therefore_o by_o the_o number_n say_v so_o be_v 70_o minute_n the_o sun_n distance_n from_o the_o equinoctial_a to_o 28_o the_o sun_n declination_n on_o the_o line_n of_o number_n observe_v to_o extend_v the_o same_o way_n as_o from_o the_o first_o to_o the_o second_o term_n 2._o when_o you_o have_v occasion_n to_o use_v a_o sine_fw-la above_o 90_o degree_n than_o you_o must_v count_v the_o sine_fw-la of_o 80_o for_o the_o sine_fw-la of_o 100_o and_o 70_o for_o 110_o and_o 60_o for_o 120._o so_o also_o the_o distance_n from_o 90_o to_o 60_o in_o the_o sin_n be_v the_o secant_fw-la of_o 30_o degree_n and_o the_o distance_n from_o 90_o to_o 50_o be_v the_o secant_fw-la of_o 40_o or_o the_o point_n beyond_o 90_o that_o represent_v the_o secant_fw-la of_o 40._o 3._o if_o the_o extent_n be_v too_o large_a for_o your_o compass_n as_o from_o 45_o or_o 90_o to_o 3_o or_o 4_o degree_n then_o instead_o of_o 90_o or_o 45_o make_v use_n of_o a_o point_n in_o the_o sin_n or_o tangent_n right_a against_o the_o middle_n 1_o in_o the_o line_n of_o number_n where_o you_o may_v have_v two_o brass_n center-pin_n viz._n in_o the_o tangent_fw-la of_o 5-43_a and_o the_o sine_fw-la of_o 5-45_a and_o the_o extent_n from_o thence_o backward_o or_o forward_o shall_v reach_v in_o the_o number_n to_o the_o four_o proportional_a number_n require_v example_n as_o tang._n 45_o to_o 1-61_a in_o the_o number_n so_o be_v tang._n of_o 15-0_a to_o 0-43_a in_o the_o number_n instead_o of_o which_o you_o may_v say_v as_o the_o tang._n of_o 5-43_a to_o 1-61_a on_o the_o number_n so_o be_v the_o tang._n of_o 15_o to_o 0-43_a on_o the_o number_n diminish_v a_o radius_fw-la for_o as_o tang._n 45_o to_o 1-15_a a_o great_a than_o that_o so_o be_v the_o tang._n of_o 15_o to_o a_o great_a than_o 15_o also_o viz._n 0-43_a second_o in_o sines_n &_o tangent_n or_o sin_n only_o where_o there_o be_v another_o caution_n to_o be_v observe_v as_o sine_fw-la 90_o to_o sine_z 10_o so_o be_v sine_fw-la 20_o to_o sine_fw-la of_o 3-24_a ⅓_n to_o work_v this_o with_o small_a compass_n on_o a_o large_a line_n do_v thus_o note_v that_o at_o 10_o on_o the_o line_n of_o number_n or_o sine_fw-la of_o 90_o or_o tang._n of_o 45_o be_v one_o complete_a radius_fw-la but_o at_o the_o middle_n 1_o on_o the_o line_n of_o number_n be_v a_o place_n or_o radius_fw-la less_o wherein_o the_o logarithm_n sines_n the_o characteristic_a be_v 8._o again_o at_o the_o sine_fw-la of_o 0-34_a ½_o the_o characteristic_a be_v 7_o and_o at_o 3_o minute_n it_o be_v 6_o which_o do_v note_v the_o several_a decreasing_n of_o the_o radiuss_n therefore_o set_v the_o distance_n from_o one_o number_n give_v to_o the_o next_o near_a place_n against_o 1_o or_o next_o radius_fw-la as_o far_o