the_o sun_n azimuth_n be_v the_o declination_n east_n or_o west_n as_o the_o azimuth_n be_v also_o if_o you_o take_v the_o shadow_n when_o the_o sun_n be_v just_a in_o the_o south_n or_o meridian_n of_o the_o place_n the_o shadow_n be_v the_o declination_n if_o it_o be_v pass_v the_o plain_n it_o be_v eastward_o if_o it_o want_v it_o be_v westward_n thus_o i_o have_v i_o hope_v show_v the_o true_a manner_n of_o find_v the_o declination_n of_o a_o wall_n by_o the_o sun_n shine_v on_o the_o plain_a as_o plain_o and_o as_o brief_o as_o the_o matter_n will_v bear_v speak_v to_o young_a tiroe_n therein_o it_o may_v be_v do_v also_o by_o observe_v when_o the_o sun_n just_o begin_v to_o shine_v on_o a_o chimney_n or_o wall_n or_o high_a place_n you_o can_v for_o the_o present_a come_v near_o conceive_v the_o sun_n to_o be_v then_o just_a 90_o degree_n from_o the_o meridian_n of_o the_o place_n want_v or_o just_o when_o it_o leave_v it_o be_v then_o 90_o degree_n past_o the_o plain_n then_o take_v the_o altitude_n and_o azimuth_n and_o work_v according_o to_o the_o former_a rule_n chap._n iv._o to_o draw_v a_o south_n or_o north_n erect_v declining-dial_n for_o better_a illustration_n sake_n i_o will_v draw_v a_o particular_a scheam_n for_o this_o dial_n also_o as_o i_o do_v for_o the_o east_n recliner_n who_o declination_n let_v it_o be_v 20_o degree_n decline_v from_o the_o south_n towards_o the_o west_n in_o the_o latitude_n of_o 51-32_a for_o london_n the_o scheam_n be_v draw_v by_o the_o former_a direction_n the_o pole_n of_o the_o plain_a be_v at_o d_o decline_v 20_o degree_n from_o saint_n towards_o w_n and_o the_o plain_n itself_o be_v represent_v by_o the_o line_n ab_fw-la the_o circular_a prick_v line_n dhpc_n be_v a_o certain_a meridian_n draw_v through_o the_o three_o give_v point_n dpc_n who_o centre_n will_v be_v in_o the_o intersection_n of_o the_o plain_n ab_fw-la and_o the_o tangent_fw-la line_n for_o the_o hour_n which_o be_v draw_v whatsoever_o zh_n be_v in_o the_o half_a tangent_n zq_n be_v the_o compliment_n thereof_o in_o the_o same_o half_a tangent_n the_o scheam_n thus_o draw_v zh_n be_v the_o substile_a ph_n be_v the_o style_n qz_n the_o distance_n of_o 6_o from_o 12_o hpz_n the_o inclination_n of_o meridian_n or_o angle_n between_o the_o two_o meridian_n viz._n of_o the_o place_n pz_n and_o of_o the_o plain_a ph_n find_v by_o the_o follow_a canon_n by_o artificial_a sin_n and_o tangent_n 1._o first_o for_o the_o substile_a from_o 12._o as_o the_o sine_fw-la of_o 90_o zn_n to_o the_o sine_fw-la of_o the_o declination_n nc_n 20_o degree_n so_o be_v the_o co-tangent_a of_o the_o latitude_n pz_fw-fr 38-28_a to_o the_o tangent_fw-la of_o zh_n 15-12_a 2._o for_o the_o style_n elevation_n as_o the_o sine_fw-la of_o 90_o zn_n to_o the_o cousin_a of_o the_o plain_n declination_n na_fw-mi 70-0_a so_o be_v the_o cousin_a of_o the_o latitude_n zp_v 38-28_a to_o the_o sine_fw-la of_o ph_n 35-46_a the_o style_n elevation_n 3._o for_o the_o distance_n between_o 6_o &_o 12._o as_o the_o sine_fw-la of_o 90_o zw_n to_o the_o sine_fw-la of_o the_o plain_n declination_n wa_n 20-0_a so_o be_v the_o tangent_fw-la of_o the_o latitude_n np_v 51-32_a to_o the_o tangent_fw-la of_o aq_n the_o co-tangent_a of_o 6_o from_o 12_o 23-18_a or_o thus_o as_o co-tangent_a latitude_n zp_v 38-28_a to_o the_o sine_fw-la 90_o zpq_n so_o be_v s._n declination_n wza_n 20-0_a to_o the_o tangent_fw-la of_o qa_fw-la 23-18_a 4._o for_o the_o inclination_n of_o meridian_n as_o the_o sine_fw-la of_o the_o latitude_n zae_n 51-32_a to_o the_o sine_fw-la of_o 90_o zs_n so_o be_v the_o tangent_fw-la of_o the_o declination_n sd_z 20-00_a to_o the_o tangent_fw-la of_o aek_v 24-56_a the_o inclination_n of_o meridian_n or_o as_o cousin_a latitude_n 38-28_a pz_n to_o the_o sine_fw-la 90_o phz_n so_o be_v the_o sine_fw-la of_o the_o substile_a zh_n 15-12_a to_o the_o sine_fw-la of_o zph_n 24-56_a in_o 5._o then_o have_v make_v a_o table_n of_o ark_n at_o the_o pole_n by_o this_o canon_n you_o may_v find_v the_o hour-arks_a on_o the_o plain_a thus_o as_o the_o sine_fw-la of_o 90_o pk_n to_o the_o sine_fw-la of_o the_o style_n height_n ph_n 35_o 46_o so_o be_v the_o tangent_fw-la of_o the_o hour_n from_o 12_o 19-56_a for_o i_o aei_n to_o the_o tangent_fw-la of_o the_o hour_n from_o the_o substile_a on_o the_o plain_a h_n 1_o 12-14_a but_o i_o prefer_v the_o way_n by_o tangent_n before_o it_o as_o follow_v all_o these_o requisite_n may_v be_v find_v by_o the_o general_a scale_n and_o sector_n the_o canon_n whereof_o in_o brief_a be_v thus_o by_o the_o trianguler-quadrant_n and_o sector_n substile_n as_o co-tang_n lat._n 38-28_a zp_n to_o =_o sine_fw-la 90_o 90-00_a zn_n so_o =_o sine_fw-la declination_n 20-00_a nc_n to_o i_o substile_o 15-12_a zh_n style_n as_o cousin_a lat._n 38-28_a zp_n to_o =_o sine_fw-la 90_o 90-00_a zn_n so_o =_o cousin_a declin_fw-ge 70-00_a na_n to_o sine_z style_v 35-46_a ph._n distance_n between_o 6_o &_o 12._o as_o sine_fw-la declin_n 20-0_a wa_n to_o =_o sine_fw-la of_o 90_o 90-0_a zw_n so_o be_v =_o c.t._n of_o lat._n 51-32_a np_n to_o c.t._n 6_o &_o 12_o 23-18_a aq_n tangent_fw-la 66-42_a  _fw-fr inclination_n of_o meridian_n as_o i_o declination_n 20-0_a sd_z to_z =_o sine_fw-la latitude_n 51-32_a zae_n so_o =_o sine_fw-la 90_o 90-00_a zs_n to_o t._n inclin_n merid._n 24-56_a aek_v these_o requisite_n be_v also_o find_v by_o the_o particular_a quadrant_n very_o real_o and_o true_o for_o that_o latitude_n the_o rule_n be_v make_v for_o in_o this_o manner_n 1._o first_o for_o the_o substile_a lay_v the_o thread_n to_o the_o compliment_n of_o the_o plain_n declination_n count_v on_o the_o azimuth_n line_n and_o on_o the_o degree_n it_o give_v the_o substile_a from_o 12_o count_v from_o 600_o on_o the_o moveable-leg_n example_n the_o thread_n lay_v to_o 70_o the_o compliment_n of_o 20_o on_o the_o degree_n give_v 15-12_a for_o the_o substile_a 2._o for_o the_o style_n height_n take_v the_o distance_n between_o 90_o and_o the_o plain_n declination_n on_o the_o azimuth-line_n and_o measure_v it_o on_o the_o particular_a scale_n from_o the_o beginning_n and_o it_o shall_v give_v the_o angle_n of_o the_o stiles-elevation_n above_o the_o substile_a 35-46_a 3._o for_o the_o inclination_n of_o meridian_n take_v the_o substile_a from_o the_o particular_a scale_n of_o altitude_n and_o measure_n on_o the_o azimuth-line_n from_o 90_o and_o it_o shall_v give_v the_o compliment_n of_o the_o inclination_n of_o meridian_n or_o the_o angle_n count_v from_o 90._o viz._n here_o 24-56_a 4._o to_o find_v the_o angle_n between_o 12_o &_o 6._o take_v the_o plain_n declination_n from_o the_o particular_a scale_n of_o altitude_n less_o by_o the_o sine_fw-la of_o the_o declination_n to_o a_o radius_fw-la equal_a to_o 45_o minute_n of_o the_o first_o degree_n on_o the_o particular_a scale_n of_o altitude_n and_o lay_v it_o from_o 90_o on_o the_o azimuth_n scale_n and_o to_o the_o compass-point_n lie_v the_o thread_n then_o on_o the_o line_n of_o degree_n the_o thread_n give_v the_o compliment_n of_o 6_o from_o 12_o count_v from_o 60_o towards_o the_o end_n as_o here_o it_o be_v in_o this_o dial_n 23-18_a also_o the_o requisite_n may_v be_v find_v geometrical_o by_o the_o scheam_n thus_o as_o 1._o a_o ruler_n lay_v from_o d_o to_o h_n in_o the_o limb_n give_v f_o the_o ark_n cf_n be_v the_o substile_a 2._o a_o ruler_n lay_v from_o q_o to_o p_o in_o the_o limb_n give_v i_o the_o ark_n ai_fw-fr be_v the_o style_n height_n 3._o a_o rule_n lay_v from_o p_o to_o q_o cut_v the_o limb_n at_o t_o the_o ark_n te_fw-la be_v the_o inclination_n of_o meridian_n or_o a_o rule_n lay_v from_o p_o to_o k_o cut_v the_o limb_n at_o l_o then_o slightall_n be_v the_o inclination_n of_o meridian_n 4._o a_o rule_n lay_v from_o d_o to_o q_o cut_v the_o limb_n at_o 6_o the_o ark_n c_o 6_o be_v the_o angle_n between_o 12_o and_o 6._o 5._o a_o rule_n lay_v from_o d_o to_o the_o intersection_n of_o any_o other_o hour-line_n with_o the_o plain_n ab_fw-la on_o the_o limb_n give_v point_n who_o distance_n from_o c_o be_v their_o angle_n from_o 12_o or_o their_o distance_n from_o f_o or_o their_o angle_n from_o the_o substile_a to_o delineate_v the_o dial_n by_o the_o sector_n thus_o by_o any_o of_o these_o way_n have_v get_v the_o requisite_n proceed_v to_o draw_v the_o dial_n thus_o then_o take_v out_o the_o =_o tangent_fw-la of_o 30_o &_o 15_o and_o the_o respective_a quarter_n and_o &c._n &c._n as_o before_o then_o make_v 6_o g_z a_o =_o tangent_fw-la of_o 45_o and_o do_v likewise_o as_o before_o in_o the_o horizontal_a and_o south_n dial_n and_o to_o those_o point_n draw_v the_o hour-line_n require_v 2._o to_o draw_v
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
show_v also_o 60_o degree_n on_o the_o innermost-edge_n of_o the_o loose-piece_n the_o calendar_n of_o month_n and_o day_n and_o degree_n of_o the_o sun_n place_n and_o right_a ascension_n on_o the_o moveable-leg_n for_o the_o speedy_a and_o ready_a find_v the_o sun_n place_n and_o declination_n which_o you_o may_v do_v to_o a_o minute_n at_o all_o time_n by_o help_n of_o the_o rectify_v table_n and_o astronomical_a caution_n of_o time_n and_o longitude_n also_o on_o the_o head-leg_n be_v the_o general_a scale_n of_o sines_n and_o line_n to_o the_o great_a and_o lesser_a radius_fw-la as_o in_o the_o figure_n and_o thus_o much_o will_v serve_v both_o for_o observation_n and_o operation_n as_o in_o the_o follow_a discourse_n will_v full_o appear_v 4._o to_o this_o instrument_n do_v chief_o belong_v the_o sight_n for_o the_o observation_n at_o sea_n where_o the_o horizon_n be_v make_v use_n of_o in_o the_o take_n the_o sun_n or_o star_n altitude_n and_o to_o this_o instrument_n belong_v the_o index_n and_o square_n that_o make_v it_o a_o most_o complete_a sinical-quadrant_n for_o the_o plain_a and_o easy_a resolve_v of_o all_o plain_a triangle_n also_o a_o weighty_a plummet_n and_o thread_n and_o a_o pair_n of_o large_a wood_n or_o brass_n compass_n for_o operation_n thus_o much_o for_o description_n be_v all_o put_v on_o one_o side_n only_o unless_o you_o shall_v be_v please_v to_o add_v the_o artificial_a number_n sin_n and_o tangent_n on_o the_o outer-edge_n and_o a_o meridian-line_n and_o his_o scale_n on_o the_o inner-edge_n and_o natural_a sin_n and_o natural_a versed-sines_n on_o the_o sector-side_n but_o these_o as_o you_o please_v chap._n ii_o the_o use_n of_o the_o trianguler-quadrant_n in_o observation_n that_o the_o discourse_n may_v be_v plain_a and_o brief_a and_o general_a there_o be_v 10_o term_n to_o be_v name_v and_o describe_v before_o i_o come_v to_o the_o use_v and_o example_n which_o be_v as_o follow_v 1._o first_o the_o head-leg_n of_o the_o instrument_n in_o which_o the_o brass-rivit_a be_v fix_v and_o about_o which_o the_o other_o leg_n turn_v as_o ab_fw-la in_o the_o figure_n on_o which_o leg_n the_o general_a scale_n of_o sines_n and_o line_n be_v usual_o set_v 2._o the_o moveable-leg_n on_o which_o the_o month_n and_o day_n be_v as_o in_o the_o figure_n note_v by_o bd_o which_o leg_n turn_v about_o the_o head-leg_n 3._o the_o loose-piece_n that_o be_v join_v to_o the_o head_n and_o moving-leg_n by_o two_o tennon_n at_o each_o end_n thereof_o note_v by_o da_fw-la in_o the_o figure_n 4._o the_o head-center_n or_o center-pin_n on_o the_o round-part_n of_o the_o head-leg_n be_v centre_n to_o the_o 60_o degree_n on_o the_o inside_n of_o the_o loose-piece_n which_o point_n be_v know_v by_o b_o in_o the_o figure_n 5._o the_o leg-center_n be_v near_o the_o end_n of_o the_o head-leg_n which_o be_v the_o centre_n to_o the_o degree_n on_o the_o moving-leg_n and_o outside_n of_o the_o loose-piece_n be_v in_o all_o 180_o degree_n and_o note_v in_o the_o figure_n by_o the_o letter_n c._n 6._o the_o great_a radius_fw-la or_o great_a line_n of_o sines_n issue_v from_o the_o leg-center_n towards_o the_o head_n have_v the_o tangent_n on_o the_o moveable-leg_n to_o the_o same_o radius_fw-la and_o the_o measure_n from_o the_o leg-center_n to_o the_o tangent_fw-la on_o the_o moving-leg_n a_o secant_fw-la to_o the_o same_o radius_fw-la as_o ce_fw-fr in_o the_o figure_n 7._o the_o little_a radius_fw-la that_o issue_n from_o the_o leg-center_n towards_o the_o end_n have_v the_o tangent_n on_o the_o outside_n of_o the_o loose-piece_n to_o the_o same_o radius_fw-la and_o the_o measure_n from_o the_o centre_n to_o those_o tangent_n for_o secant_v to_o the_o same_o radius_fw-la as_o cf._n 8._o the_o turn_a sight_n always_o to_o be_v skrew_v to_o the_o head_n or_o leg-center_n know_v by_o his_o shape_n and_o skrew-hole_n as_o 9_o the_o slide_a horizon-sight_n to_o slide_v on_o the_o moving-leg_n and_o loose-piece_n note_v with_o its_o bigness_n and_o hole_n to_o look_v through_o as_o 10._o the_o shadow_n sight_n and_o 2_o other_o to_o pin_v the_o instrument_n together_o which_o you_o may_v call_v the_o object-sight_n always_o fix_v in_o the_o two_o hole_n at_o the_o end_n of_o the_o moving-leg_n and_o the_o head-leg_n and_o the_o shadow-sight_n be_v to_o set_v to_o and_o fro_o to_o any_o place_n require_v note_v in_o the_o figure_n with_o 〈◊〉_d and_o the_o other_o two_o with_o 〈◊〉_d and_o thus_o you_o have_v their_o name_n and_o description_n at_o large_a which_o in_o brief_a take_v thus_o for_o easy_a remember_v 1._o the_o head-leg_n 2._o the_o moveable-leg_n 3._o the_o loose-piece_n 4._o the_o head-center_n 5._o the_o leg-center_n 6._o the_o great_a radius_fw-la 7._o the_o less_o radius_fw-la 8._o the_o turning-sight_n 9_o the_o horizon_n sliding-sight_n 10._o the_o shadow-sight_n and_o the_o two_o objest-sight_n the_o open-part_n in_o one_o be_v next_o to_o and_o the_o other_o remote_a from_o the_o rule_n to_o answer_v to_o the_o upper_a or_o lower-hole_n in_o the_o turning-sight_n according_a as_o you_o please_v to_o use_v they_o in_o observation_n thus_o much_o for_o the_o term_n the_o use_v follow_v use_v i._o to_o find_v the_o sun_n or_o a_o star_n altitude_n by_o a_o forward_a observation_n as_o by_o a_o fore-staff_n screw_v the_o turning-sight_n to_o the_o head-center_n and_o put_v the_o object-sight_n into_o the_o hole_n at_o the_o end_n of_o the_o head-leg_n and_o put_v the_o slide_a horizon-sight_n on_o the_o inside_n of_o the_o loose-piece_n then_o set_v the_o turning-sight_n to_o your_o eye_n and_o hold_v the_o loose-piece_n in_o your_o right-hand_a and_o the_o moveable-leg_n towards_o your_o body_n then_o with_o your_o thumb_n on_o the_o right-hand_a thrust_v upward_o or_o pull_v downward_o the_o horizon-sight_n till_o you_o see_v the_o sun_n through_o the_o object-sight_n and_o the_o horizon_n through_o the_o horizon-sight_n then_o the_o degree_n cut_v by_o the_o line_n on_o the_o middle_n of_o the_o horizon-sight_n shall_v show_v the_o true_a altitude_n require_v also_o observe_v that_o if_o you_o like_v to_o use_v the_o upper_a or_o lower-edge_n of_o the_o horizon-sight_n instead_o of_o the_o small_a bar_n across_o the_o open-hole_n after_o the_o manner_n of_o the_o end_n of_o a_o fore-staff_n that_o then_o the_o degree_n and_o minute_n cut_v by_o the_o edge_n of_o the_o brass_n be_v the_o altitude_n require_v to_o be_v count_v as_o it_o be_v figure_v from_o the_o object-sight_n towards_o the_o horizon-sight_n the_o degree_n between_o they_o be_v the_o angle_n require_v note_v also_o that_o if_o the_o altitude_n of_o the_o sun_n or_o star_n be_v above_o 30_o degree_n you_o will_v find_v it_o a_o hard_a matter_n to_o behold_v the_o horizon_n and_o sun_n with_o a_o bare_a roll_v the_o ball_n of_o the_o eye_n only_o and_o a_o stir_v of_o the_o head_n will_v easy_o cause_v a_o stir_v of_o the_o hand_n which_o will_v spoil_v the_o exactness_n of_o observation_n unless_o the_o instrument_n shall_v be_v fix_v to_o a_o ball-socket_n and_o three-legged-staff_n which_o be_v not_o usual_a at_o sea_n therefore_o to_o remedy_v this_o you_o may_v observe_v with_o the_o open_a oval-hole_n in_o the_o turning-sight_n set_v to_o the_o eye_n or_o take_v the_o turning-sight_n quite_o away_o observe_v just_a as_o you_o do_v with_o a_o fore-staffe_n set_v the_o round_a part_n of_o the_o head_n to_o the_o hollow-part_n beside_o your_o eye_n so_o as_o the_o head-center-pin_n may_v be_v as_o near_o the_o very_a sight_n of_o your_o eye_n as_o possible_o as_o you_o can_v which_o centre_n be_v the_o centre_n to_o the_o degree_n now_o use_v in_o a_o forward_a way_n of_o observation_n or_o rather_o use_v this_o way_n when_o the_o wether_n will_v suffer_v by_o a_o thread_n and_o plummet_n which_o i_o shall_v add_v as_o a_o second_o use._n use_v ii_o to_o observe_v the_o sun_n or_o a_o star_n altitude_n by_o a_o forward_a observation_n use_v the_o thread_n and_o plummet_n screw_v the_o turning-sight_n to_o the_o head-center_n as_o before_o and_o put_v the_o two_o object-sight_n into_o the_o two_o hole_n at_o the_o two_o end_n of_o the_o rule_n and_o on_o the_o leg-center-pin_n hang_v the_o thread_n with_o a_o weighty_a plummet_n of_o two_o pound_n or_o above_o a_o pound_n at_o least_o then_o hold_v up_o the_o trianguler-quadrant_n set_v the_o small-hole_n on_o the_o turning-sight_n close_o to_o your_o eye_n and_o if_o the_o sun_n or_o star_n be_v under_o 25_o degree_n high_a then_o look_v to_o the_o sun_n or_o star_n through_o the_o turning-sight_n and_o that_o object-sight_n which_o stand_v in_o the_o end_n of_o the_o moveable-leg_n let_v the_o thread_n and_o plummet_n play_v between_o your_o thumb_n and_o forefinger_n as_o a_o brick-layer_n plummet_n in_o his_o plum-rule_n do_v in_o a_o bendid_a hole_n that_o you_o may_v keep_v it_o in_o order_n whilst_o you_o look_v
horologiographia_fw-la or_o the_o art_n of_o dyall_v be_v the_o second_o book_n of_o the_o use_n of_o the_o trianguler-quadrant_n show_v the_o natural_a artificial_a and_o instrumental_a way_n of_o make_v of_o sun-dials_n on_o any_o flat_a superficies_n with_o plain_a and_o easy_a direction_n to_o discover_v their_o nature_n and_o affection_n by_o the_o horizontal_a projection_n with_o the_o way_n of_o draw_v the_o usual_a ornament_n on_o any_o plain_n also_o a_o familiar_a easy_a way_n to_o draw_v those_o line_n on_o the_o ceiling_n of_o a_o room_n by_o the_o triangule_a quadrant_n also_o the_o use_n of_o the_o same_o instrument_n in_o navigation_n both_o for_o observation_n and_o operation_n perform_v the_o use_n of_o several_a sea-instrument_n still_o in_o use_n by_o john_n brown_n philomath_n london_n print_v by_o john_n derby_n for_o john_n wingfield_n and_o be_v to_o be_v sell_v at_o his_o house_n in_o crutched-fryer_n and_o by_o john_n brown_a at_o the_o sphere_n and_o sundial_n in_o the_o minory_n and_o by_o john_n seller_n at_o the_o hermitage-stair_n in_o wapping_n 1671._o to_o the_o courteous_a reader_n thou_o have_v here_o present_v to_o thy_o view_n courteous_a reader_n in_o this_o second_o part_n a_o plain_a discourse_n of_o dial_v both_o natural_a artificial_a &_o instrumental_a natural_a i_o call_v it_o from_o the_o plain_a illustration_n thereof_o by_o the_o armilary_n sphere_n of_o brass_n herein_o describe_v or_o by_o the_o poor-man_n dial-sphear_n as_o i_o fancy_n to_o call_v it_o be_v only_o a_o move_a horizontal-dial_n and_o a_o move_a plain_n according_a to_o the_o figure_n thereof_o in_o the_o book_n annex_v whereby_o all_o the_o ark_n angle_n situation_n and_o affection_n be_v very_o plain_o represent_v to_o a_o ordinary_a capacity_n artificial_a i_o call_v it_o from_o the_o lively_a delineation_n of_o the_o horizontal-projection_n the_o fit_a in_o my_o opinion_n for_o the_o make_v plain_o the_o mystery_n of_o dial_v instrumental_a i_o call_v it_o from_o the_o apply_v of_o the_o trianguler-quadrant_n to_o the_o ready_a resolve_v all_o the_o arithmetical_a and_o astronomical_a work_n needful_a thereunto_o and_o that_o to_o competent_a exactness_n as_o in_o the_o first_o part_n and_o also_o in_o this_o second_o part_n be_v sufficient_o see_v in_o find_v the_o requisite_n and_o delineat_v the_o hour-line_n to_o small_a part_n exact_o &_o speedy_o by_o the_o natural_a sin_n tangent_n and_o secant_v on_o the_o sector_n and_o quadrant_n also_o the_o ready_a way_n of_o find_v the_o sun_n altitude_n hour_n azimuth_n angle_n of_o the_o plain_a and_o any_o such_o business_n relate_v to_o dyall_v as_o in_o the_o first_o part_n be_v large_o treat_v on_o further_o in_o this_o second_o part_n you_o have_v table_n of_o the_o sun_n declination_n to_o every_o day_n of_o the_o year_n 1_o 2_o &_o 3_o after_o the_o bissextile_a as_o near_o as_o any_o extent_n also_o a_o short_a but_o plain_a direction_n how_o to_o use_v the_o trianguler-quadrant_n at_o any_o manner_n of_o way_n of_o observation_n use_v at_o sea_n as_o backward_o or_o forward_o as_o the_o davis-quadrant_n and_o the_o cross-staff_n be_v use_v also_o as_o gunter_n bow_n be_v use_v both_o for_o the_o sun_n or_o star_n a_o figure_n of_o the_o stereographick_a projection_n pag_n â—_o the_o print_n of_o the_o line_n of_o number_n as_o you_o see_v here_o insert_v be_v in_o part_n according_a to_o mr._n windgates_n as_o to_o a_o single_a and_o break_a line_n of_o number_n but_o the_o addition_n of_o the_o line_n of_o the_o fractional_a part_n of_o a_o pound_n and_o the_o several_a gage-point_n be_v never_o before_o use_v as_o i_o know_v of_o but_o do_v much_o ease_n &_o expedite_v the_o operation_n by_o the_o line_n of_o number_n sin_n and_o tangent_n also_o these_o scale_n of_o reduction_n be_v convenient_a for_o the_o find_v the_o decimal-fraction_n equal_a to_o the_o other_o sexagenary-fraction_n and_o be_v agreeable_a to_o those_o table_n in_o mr._n windgates_n book_n of_o arithmetic_n pag._n 82._o also_o note_n that_o the_o figure_n of_o the_o rule_n at_o the_o begin_n of_o the_o book_n past_v on_o a_o board_n be_v the_o very_a same_o with_o that_o speak_v of_o chap._n xv._n use_v 28._o pag._n 397_o of_o the_o first_o part_n and_o will_v work_v all_o question_n wrought_v by_o the_o trianguler-quadrant_n to_o exercise_v they_o that_o be_v out_o of_o the_o way_n to_o have_v they_o make_v and_o may_v serve_v as_o good_a direction_n to_o the_o young_a instrument-maker_n though_o these_o be_v make_v too_o too_o small_a a_o radius_fw-la to_o arrive_v at_o exactness_n the_o like_a may_v i_o say_v of_o the_o gunters-line_n in_o the_o figure_n annex_v yet_o as_o large_a as_o the_o book_n will_v bear_v thus_o i_o have_v give_v you_o a_o brief_a account_n of_o my_o present_a thought_n about_o this_o matter_n and_o somewhat_o more_o particular_o in_o the_o first_o part_n disclaim_v all_o boast_n or_o vain_a ostentation_n know_v that_o at_o the_o next_o impression_n it_o may_v be_v amend_v in_o many_o place_n i_o shall_v rest_v and_o remain_v ready_a to_o make_v amends_o in_o the_o make_n of_o these_o or_o any_o other_o mathematical_a instrument_n at_o my_o house_n at_o the_o sphere_n and_o sundial_n in_o the_o great_a minories_n john_n browne_n february_n 16._o 1670._o chap._n i._n the_o use_n of_o the_o triangule_a quadrant_n in_o make_v of_o dial_n svn-dials_n may_v be_v make_v on_o any_o plain_a and_o all_o kind_n of_o plain_n be_v either_o flat_a as_o horizontal_a or_o upright_o or_o lean_v the_o horizontal_a have_v two_o face_n the_o one_o behold_v the_o zenith_n call_v the_o horizontal-plain_a the_o other_o behold_v the_o nadir_n as_o the_o ceiling_n of_o a_o room_n be_v the_o upright_a plain_n be_v those_o that_o make_v right_a angle_n with_o the_o horizon_n and_o do_v behold_v neither_o the_o zenith_n or_o nadir_n but_o be_v parallel_n to_o they_o the_o lean_v plain_n be_v of_o two_o sort_n general_o the_o one_o call_v recliner_n behold_v the_o zenith_n the_o other_o sort_n call_v incliner_n behold_v the_o nadir_n as_o the_o outside_n and_o inside_n of_o a_o roof_n of_o a_o house_n may_v represent_v the_o two_o last_o sort_n viz._n upright_a and_o lean_v may_v be_v direct_a or_o decline_a viz._n behold_v the_o south_n or_o north_n or_o east_n or_o west_n point_v of_o the_o horizon_n or_o decline_a therefrom_o viz._n decline_a from_o south_n or_o north_n towards_o the_o east_n or_o west_n all_o which_o plain_n be_v lively_o represent_v by_o a_o sphere_n make_v for_o that_o purpose_n in_o brass_n or_o pasteboard_n or_o by_o the_o projection_n of_o the_o sphere_n in_o plano_n thus_o equal_a to_o the_o radius_fw-la of_o the_o small_a tangent_n describe_v the_o circle_n eswn_n represent_v the_o horizon_n cross_v it_o precise_o in_o the_o the_o centre_n z_o with_o the_o line_n sn_a and_o ewe_n denote_v the_o point_n of_o south_n and_o north_n east_n and_o west_n then_o count_v the_o small_a tangent_fw-la on_o the_o sector-side_n double_o as_o thus_o call_z 5_o 10_o &_o 10_o 20_o &_o 20_o 40_o &_o 30_o 60_o &_o 40_o 80_o &_o 45_o 90_o etc._n etc._n lay_v off_o from_o z_o towards_o saint_n the_o compliment_n of_o the_o sun_n meridian_n altitude_n in_o ♋_o in_o ♈_o and_o ♑_o for_o those_o point_n on_o the_o meridian-line_n between_o z_o and_o s_o and_o consequent_o the_o half_a tangent_fw-la of_o the_o compliment_n of_o the_o sun_n meridian_n altitude_n in_o every_o degree_n of_o declination_n if_o you_o proceed_v so_o far_o then_o for_o the_o intersection_n of_o all_o those_o line_n and_o parallel_n of_o declination_n on_o the_o north-side_n of_o the_o meridian_n observe_v that_o the_o same_o number_n of_o degree_n and_o minute_n that_o any_o point_n be_v above_o the_o horizon_n on_o the_o south_n part_n of_o the_o meridian_n in_o summer_n just_o so_o many_o degree_n and_o minute_n be_v his_o opposite_a parallel_n in_o winter_n below_o the_o horizon_n as_o thus_o for_o example_n the_o sun_n be_v in_o ♋_o or_o 23_o deg_n 31_o min._n of_o declination_n north_n have_v for_o his_o meridian_n altitude_n 62_o degree_n and_o so_o many_o degree_n be_v his_o opposite_a parallel_n of_o 23-31_a or_o ♑_o below_o the_o north_n part_n of_o the_o horizon_n at_o midnight_n as_o thus_o let_v the_o centre_n at_o the_o begin_n of_o the_o line_n of_o tangent_n represent_v the_o centre_n z_o and_o let_v the_o tangent_fw-la of_o 45_o represent_v the_o horizon_n in_o the_o scheam_n viz._n s._n and_o n._n then_o as_o the_o distance_n from_o s._n to_o ♑_o be_v 15_o deg_n take_v from_o 45_o towards_o 0_o and_o lay_v from_o s._n to_o ♑_o inward_o towards_o the_o centre_n z_o as_o the_o distance_n be_v take_v from_o the_o tangent_fw-la of_o 45_o towards_o the_o begin_n of_o the_o line_n of_o tangent_n that_o represent_v the_o centre_n so_o the_o point_n cancer_n from_o n._n
be_v 15_o deg_n count_v beyond_o 45_o towards_o the_o end_n below_z or_o beyond_o the_o horizon_n again_o as_o s._n ♋_o be_v 62_o degree_n from_o 45_o towards_o 00_o so_o be_v the_o other_o point_v 62_o degree_n below_o n_o take_v from_o 45_o viz._n at_o 76_o degree_n which_o be_v lay_v from_o n_o do_v overreach_v this_o little_a page_n so_o that_o to_o draw_v the_o tropic_a of_n ♑_o the_o point_n ♋_o being_n his_o opposite_a be_v 28_o degree_n from_o z_o or_o 62_o deg_n from_o saint_n and_o the_o other_o point_n of_o ♑_o on_o the_o north_n part_n of_o the_o meridian_n be_v 62_o degree_n count_v from_o 45_o double_o also_o or_o 28_o degree_n from_o 90_o the_o suppose_a end_n of_o the_o tangent_fw-la which_o be_v natural_o infinite_a be_v the_o tangent_fw-la of_o 76_o degree_n or_o the_o semi-tangent_a of_o 152_o read_v the_o tangent_n double_o from_o the_o centre_n which_o distance_n from_o the_o centre_n to_o the_o tangent_fw-la of_o 76_o or_o as_o half-tangents_a 152_o lay_v from_o z_o give_v the_o point_n ♑_o on_o the_o north-part_n of_o the_o meridian_n below_o the_o horizon_n the_o midst_n between_o which_o two_o point_n of_o ♑_o on_o the_o south_n and_o north_n part_n of_o the_o meridian_n be_v the_o centre_n to_o draw_v the_o tropic_a of_o capricorn_n again_o to_o illustrate_v this_o difficulty_n to_o draw_v the_o tropic_a of_o cancer_n the_o sun_n meridian-altitude_n in_o ♑_o his_o opposite_a sign_n be_v 15_o degree_n above_o the_o horizon_n on_o the_o south_n part_n of_o the_o meridian_n and_o 15_o degree_n below_o the_o horizon_n on_o the_o north-part_n of_o the_o meridian_n viz._n the_o extent_n from_o the_o centre_n to_o the_o tangent_fw-la of_o 52_o deg_n 30_o min._n or_o the_o semi-tangent_a of_o 105_o read_v it_o double_o be_v lay_v from_o z_o give_v the_o point_n ♋_o below_o the_o horizon_n the_o middle_n between_o which_o two_o point_n be_v the_o centre_n to_o draw_v the_o tropic_a of_o cancer_n again_o for_o the_o equinoctial_a or_o parallel_v of_o ♈_o the_o meridian_n altitude_n in_o ♈_o be_v 38-28_a and_o the_o meridian_n altitude_n likewise_o in_o ♎_o his_o opposite_a parallel_n be_v 38-28_a also_o so_o that_o if_o you_o count_v 38-28_a double_o beyond_o 45_o which_o will_v be_v at_o the_o tangent_fw-la of_o 64_o degree_n and_o 14_o minute_n and_o take_v from_o thence_o to_o the_o centre_n this_o distance_n lay_v from_o z_o shall_v give_v the_o point_n ae_n below_o the_o horizon_n and_o the_o the_o middle_n between_o the_o two_o point_n ae_n be_v the_o centre_n to_o draw_v the_o aequinoctial_a then_o for_o the_o hour-line_n first_o set_v off_o the_o semi-tangent_a of_o 38-28_a from_o z_o to_o p_o and_o the_o secant_fw-la of_o 38-28_a to_o the_o same_o radius_fw-la from_o z_o to_o l_o and_o draw_v the_o line_n l_o 45_o parallel_n to_o ewe_n then_o make_v pl_z a_o tangent_fw-la of_o 45_o degree_n and_o lay_v off_o the_o tangent_n of_o 15-30_a and_o 45_o from_o l_o both-waye_n as_o you_o see_v in_o the_o figure_n also_o as_o the_o sector_n stand_v take_v out_o the_o =_o tangent_n of_o 60_o and_o 75_o several_o and_o turn_v they_o four_o time_n from_o l_o both-waye_n and_o note_v those_o point_n with_o 6_o 7_o 8_o 9_o 10_o 11._o last_o set_v one_o point_n of_o the_o compass_n in_o l_o and_o open_v the_o other_o to_o p_o and_o draw_v the_o line_n wpe_n for_o the_o hour_n of_o 6._o again_o set_v one_o point_n in_o 7-15_a degree_n from_o l_o and_o open_v the_o other_o to_o p_o and_o draw_v the_o hour-line_n 5_o p_o 5_o set_v the_o same_o extent_n also_o in_o 7_o or_o 5_o on_o the_o other_o side_n of_o l_o and_o draw_v the_o hour-line_n 7_o p_o 7_o as_o the_o figure_n show_v then_o set_v one_o point_n of_o the_o compass_n in_o 8_o 30_o degree_n from_o l_o and_o open_v the_o other_o point_n to_o p_o and_o draw_v the_o hour-line_n 8_o p_o 8_o and_o remove_v it_o to_o the_o other_o side_n of_o l_o and_o draw_v the_o hour-line_n 4_o p_o 4_o and_o so_o for_o all_o the_o rest_n in_o order_n thus_o have_v draw_v the_o figure_n to_o draw_v line_n therein_o which_o shall_v true_o represent_v any_o plain_n whatsoever_o observe_v the_o follow_a rule_n 1._o the_o horizontal-plain_a be_v represent_v by_o the_o circle_n e.s.w.n._n 2._o a_o direct_a south_n or_o north-diall_n be_v represent_v by_o the_o line_n e.z.w._n 4._o a_o east_n or_o west_n plain_a be_v represent_v by_o the_o meridian-line_n of_o 12_o viz._n s._n &_o n._n 5._o a_o polar_a plain_n be_v represent_v by_o the_o hour_n of_o 6_o viz._n the_o line_n e.p.w._n 6._o a_o equinoctial_a plain_n be_v represent_v by_o the_o equinoctial-line_n e.ae.w._n 7._o any_o direct_a recline_a or_o inclining-plain_a between_o the_o two_o last_o be_v call_v a_o direct_a recliner_n who_o pole_n be_v always_o in_o the_o meridian_n and_o be_v represent_v by_o any_o recline_a circle_n as_o the_o two_o circle_n w._n ♋_o e._n and_o e._n ☉_o w._n do_v show_v 8._o a_o east_n or_o west_n recliner_n or_o incliner_n represent_v by_o the_o circle_n n.f.s._n 9_o a_o decline_a and_o recline_v or_o incline_v polar-plain_a that_o be_v it_o so_o decline_v and_o recline_v or_o incline_v as_o to_o lie_v parallel_n to_o the_o pole_n as_o the_o circle_n 8_o p_o 8_o do_v represent_v 10._o a_o decline_a reclining-plain_a that_o so_o decline_v and_o recline_v as_o not_o to_o fall_v in_o the_o pole_n or_o equinoctial_a as_o general_o they_o will_v do_v as_o the_o circle_n 60_o g_z 60_o do_v represent_v which_o decline_v from_o the_o south-eastwards_a and_o recline_v 62_o deg_n which_o kind_n of_o plain_n be_v various_a and_o infinite_a yet_o confine_v to_o six_o variety_n as_o afterward_o now_o the_o way_n of_o draw_v these_o scheme_n to_o represent_v these_o variety_n be_v brief_o thus_o by_o the_o sector_n first_o to_o the_o radius_fw-la of_o the_o small_a tangent_n draw_v the_o circle_n n._n e._n s._n w._n observe_v this_o method_n if_o it_o be_v a_o south_n recliner_n to_o set_v the_o letter_n n_o above_o and_o e_z on_o the_o right_a hand_n and_o contrary_o in_o north_n recliner_n for_o we_o meddle_v not_o with_o incliner_n till_o afterward_o and_o always_o observe_v that_o a_o south_n incliner_n be_v the_o same_o with_o a_o north_n recliner_n and_o the_o contrary_a then_o cross_v that_o circle_n with_o two_o diameter_n precise_o in_o the_o centre_n as_o the_o letter_n show_v then_o according_a to_o your_o plain_n declination_n from_o north_n or_o south_n towards_o either_o east_n or_o west_n set_v off_o the_o declination_n with_o a_o line_n of_o chord_n or_o sin_n as_o before_o be_v show_v and_o draw_v that_o line_n for_o the_o perpendicule_a line_n of_o the_o plain_a and_o lay_v the_o same_o distance_n as_o much_o from_o e._n and_o w._n draw_v another_o line_n perpendicule_a to_o the_o former_a represent_v the_o plain_a then_o on_o the_o first_o line_n viz._n the_o plain_n perpendicule_a lay_v off_o from_o z_o the_o half_a tangent_fw-la of_o the_o plain_n reclination_n from_o z_o to_o e_z and_o the_o half_a tangent_fw-la of_o the_o compliment_n thereof_o from_o z_o to_o q_n the_o contrary_a way_n and_o the_o whole_a tangent_fw-la of_o the_o compliment_n thereof_o from_o z_o contrary_a to_o e_o on_o the_o same_o line_n extend_v for_o a_o centre_n to_o draw_v the_o recline_a circle_n that_o represent_v the_o plain_a last_o you_o must_v draw_v a_o circle_n through_o q_o and_o p_o p_o be_v always_o the_o semi-tangent_a of_o the_o compliment_n of_o the_o latitude_n lay_v always_o from_o z_o towards_o n_o for_o the_o north_n pole_n so_o as_o to_o cut_v the_o primitive_a circle_n n.e._n s.w._n into_o two_o equal_a part_n as_o be_v show_v in_o the_o 10_o proposition_n of_o the_o three_o chapter_n part_n of_o which_o line_n do_v represent_v the_o stile-line_n of_o the_o dial_n which_o last_o work_n shall_v be_v again_o show_v in_o the_o example_n example_n to_o draw_v the_o scheam_n for_o a_o plain_a decline_a from_o the_o south_n to_o the_o west_n 35_o degree_n and_o recline_v 20_o degree_n for_o the_o latitude_n of_o 51-30_a first_o to_o the_o radius_fw-la of_o your_o small_a line_n of_o tangent_n be_v the_o latteral_a distance_n from_o the_o centre_n to_o 45_o or_o large_a if_o you_o please_v draw_v the_o circle_n n.e.s.w._n represent_v the_o horizon_n cross_v it_o in_o the_o centre_n with_o the_o line_n n.s._n &_o w.e._n for_o the_o north_n and_o south_n and_o east_n and_o west_n line_n then_o take_v out_o the_o latteral_a tangent_fw-la of_o half_a the_o latitude_n viz._n 19-15_a for_o 38-30_a call_v the_o tangent_fw-la of_o 10_o the_o half_a tangent_fw-la of_o 20_o and_o lay_v it_o from_o z_o at_o the_o centre_n to_o p_o for_o the_o pole-point_n then_o consider_v the_o declination_n of_o your_o plain_n and_o which_o way_n as_o here_o 35_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
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 48_o 27_o 25-36_a  _fw-fr 40_o 57_o  _fw-fr 11_o 33_o 27_o 15-33_a  _fw-fr 25_o 57_o  _fw-fr 12_o 18_o 27_o 8-3_a to_o draw_v the_o dial._n first_o for_o the_o affection_n consult_v the_o scheam_n wherein_o lay_v the_o perpendiculer-line_n cd_o right_a before_o you_o you_o see_v that_o the_o substile_a and_o the_o meridian_n be_v to_o be_v lay_v from_o the_o perpendicule_a towards_o the_o left-hand_a the_o substile_a lie_v between_o the_o perpendicule_a and_o the_o meridian_n and_o the_o style_n or_o cock_n of_o the_o dial_n must_v look_v upward_o the_o north-pole_n be_v elevate_v above_o this_o plain_a which_o will_v guide_v all_o the_o rest_n then_o first_o draw_v the_o horizontal-line_n ab_fw-la and_o on_o c_o as_o a_o centre_n raise_v a_o perpendicule_a and_o set_v off_o by_o chord_n sin_n or_o tangent_n the_o meridian_n or_o 12_o a_o clock_n line_n the_o substile_a and_o style_v as_o exact_o as_o you_o may_v and_o draw_v the_o line_n 12_o c_z substile_n c_o and_o style_v c._n then_o as_o far_o from_o the_o centre_n c_o as_o you_o convenient_o may_v draw_v a_o long_a line_n perpendicule_a to_o the_o substile_a as_o the_o line_n ehf_n then_o set_v one_o point_n of_o a_o pair_n of_o compass_n in_o h_n open_v the_o other_o till_o it_o touch_v the_o stile-line_n at_o the_o near_a distance_n then_o make_v this_o distance_n a_o =_o tangent_fw-la of_o 45_o and_o take_v out_o the_o =_o tangent_n of_o every_o whole_a hour_n as_o in_o the_o table_n as_o far_o as_o the_o tangent_fw-la of_o 76._o will_v give_v leave_n and_o then_o from_o the_o centre_n c_o to_o those_o point_n draw_v line_n for_o the_o even_o whole_a hour_n
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
but_o when_o the_o sun_n be_v in_o the_o equinoctial_a it_o behold_v the_o south-plain_a at_o the_o rise_n be_v at_o 6_o a_o clock_n in_o the_o morning_n and_o shine_v on_o it_o all_o day_n till_o sun_n set_v be_v at_o 6_o at_o night_n and_o then_o the_o north_n dial_n be_v useless_a 2._o for_o a_o declining-plain_a suppose_v 30_o degree_n southeast_n first_o set_v the_o scheam_n in_o his_o right_a situation_n for_o a_o southeast_n plain_a then_o if_o you_o count_v 30_o degree_n from_o saint_n towards_o e_o for_o the_o pole_n of_o the_o plain_a and_o 30_o degree_n from_o w_n towards_o saint_n or_o from_o e_z toward_z n_o and_o draw_v that_o line_n that_o shall_v represent_v the_o plain_a than_o you_o shall_v find_v that_o the_o sun_n be_v in_o cancer_n will_v begin_v to_o shine_v on_o this_o plain_a just_a a_o quarter_n before_o 5_o in_o the_o morning_n and_o continue_v till_o near_o half_a a_o hour_n after_o 2._o but_o about_o the_o middle_n of_o january_n it_o will_v shine_v on_o it_o till_o a_o quarter_n after_o 4_o viz._n till_o sun_n set_v and_o all_o the_o hour_n after_o 2_o belong_v to_o the_o northwest_n plain_a that_o decline_v 30_o degree_n and_o one_o hour_n in_o the_o morning_n also_o viz._n from_o a_o quarter_n before_o till_o three_o quarter_n after_o 4._o the_o like_a work_n serve_v for_o any_o decliner_n whatsoever_o in_o any_o latitude_n 3._o but_o for_o decliner_n and_o recliner_n draw_v a_o long_a line_n as_o ab_fw-la and_o cross_v it_o with_o a_o perpendicule_a in_o the_o centre_n c_o and_o lay_v off_o from_o c_o towards_o a_o and_o b_o the_o tangent_fw-la of_o 45_o or_o the_o semi-tangent_a of_o 90_o equal_a to_o the_o largeness_n of_o your_o scheam_n then_o lay_v off_o the_o semi-tangent_a of_o the_o reclination_n from_o c_o to_o d_o up_z and_o down_o both_o way_n then_o take_v out_o the_o secant_fw-la of_o the_o compliment_n of_o the_o reclination_n which_o will_v be_v a_o radius_fw-la to_o draw_v the_o ark_n adb_n which_o paper_n you_o must_v cut_v out_o and_o apply_v the_o two_o point_n of_o the_o paper_n adbd_v to_o the_o two_o point_n of_o declination_n of_o the_o plain_a note_v in_o the_o scheam_n with_o a_o and_o b_o that_o be_v put_v a_o to_o a_o and_o b_o to_z b_o then_o the_o round_a or_o convex-edge_n of_o the_o paper_n represent_v the_o recline_a plain_n and_o the_o same_o edge_n on_o the_o other_o part_n next_o the_o horizon_n southwards_o represent_v the_o south-west_n incliner_n example_n suppose_v i_o make_v the_o paper_n adb_n to_o recline_v 35-50_a the_o reclination_n of_o the_o equinoctial-plain_a then_o first_o set_v the_o scheam_n right_a before_o you_o in_o its_o right_a situation_n and_o put_v the_o point_v a_o in_o the_o paper_n on_o a_o on_o the_o scheam_n and_o b_o in_o the_o paper_n to_o b_o on_o the_o scheam_n i_o shall_v find_v it_o to_o be_v even_o with_o the_o recline_a circle_n aeb_n then_o follow_v the_o tropic_a of_o cancer_n i_o find_v that_o it_o shine_v on_o the_o north_n recliner_n from_o the_o rise_n till_o near_o 2_o at_o which_o time_n it_o leave_v the_o north-recline_a decline_v eastward_o and_o begin_v to_o shine_v upon_o the_o opposite_a plain_n viz._n the_o south-west_n incliner_n decline_v 55-0_a and_o recline_v 35-50_a and_o so_o continue_v till_o sunset_n but_o note_n that_o if_o the_o line_n that_o represent_v the_o plain_a cut_v the_o tropic_a twice_o as_o the_o line_n ewe_n for_o a_o north-plain_a then_o though_o the_o sun_n leave_v the_o plain_a in_o the_o morning_n it_o will_v shine_v on_o it_o again_o in_o the_o afternoon_n note_v also_o that_o a_o north-east_n recliner_n be_v represent_v by_o the_o other_o convex-edge_n of_o the_o paper_n as_o here_o a_o north-east_n decliner_n 55_o and_o incline_v 35-50_a the_o sun_n will_v shine_v but_o till_o 3_o quarter_n after_o 8_o in_o cancer_n but_o in_o capricorn_n it_o shine_v till_o half_a a_o hour_n after_o 9_o and_o come_v no_o more_o on_o it_o that_o day_n and_o note_v always_o that_o when_o it_o leave_v any_o plain_a that_o then_o it_o begin_v to_o shine_v on_o his_o opposite_a as_o here_o the_o opposite_a to_o this_o north-east_n incliner_n be_v the_o south-west_n recliner_n be_v represent_v by_o the_o same_o line_n or_o circle_n adb_n that_o the_o north_n recliner_n be_v only_o you_o must_v count_v that_o side_n of_o the_o line_n next_o to_o the_o horizon_n the_o inclining-plain_a and_o that_o side_n next_o the_o zenith_n the_o reclining-plain_a for_o the_o line_n that_o represent_v it_o have_v no_o breadth_n can_v be_v no_o otherwise_o distinguish_v unless_o you_o will_v make_v a_o material_a armilary_n sphere_n of_o pasteboard_n or_o brass_n as_o the_o follow_a discourse_n do_v plain_o demonstrate_v in_o these_o several_a operation_n for_o the_o better_a conceive_n of_o these_o mathematical_a excercitation_n thus_o you_o have_v the_o way_n of_o make_v all_o manner_n of_o sun_n dial_n upon_o any_o plain_a superficies_n the_o axis_n of_o the_o world_n be_v the_o suppose_a style_n to_o all_o these_o plain_n as_o for_o those_o curiosity_n of_o upright_a style_n and_o eliptical_a dial_n and_o draw_v of_o dial_n by_o the_o horizontal_a or_o equinoctial_a dial_n you_o have_v they_o in_o the_o work_v of_o mr._n samuel_n foster_n and_o other_o and_o in_o kerkers_n ars_fw-la magna_fw-la etc._n etc._n but_o i_o intend_v not_o a_o volumn_n of_o shadow_n but_o only_o a_o further_a improvement_n of_o the_o trianguler-quadrant_n as_o you_o will_v see_v in_o the_o next_o chapter_n of_o draw_v the_o furniture_n or_o ornament_n of_o dial_n which_o be_v but_o seldom_o use_v i_o shall_v here_o crave_v a_o apology_n for_o the_o brevity_n therein_o fear_v lest_o that_o to_o the_o young_a practitioner_n it_o may_v seem_v somewhat_o hard_a to_o conceive_v though_o to_o the_o exercise_v in_o these_o matter_n it_o may_v be_v plain_a enough_o then_o for_o a_o conclusion_n you_o shall_v have_v a_o easy_a mechanic_n way_n to_o draw_v a_o dial_n on_o the_o ceiling_n of_o a_o room_n that_o lie_v flat_a or_o horizontal_a which_o will_v be_v very_o good_a for_o painter_n or_o plasterer_n to_o ornament_n a_o room_n withal_o and_o be_v not_o yet_o treat_v on_o that_o way_n as_o ever_o i_o read_v of_o chap._n viii_o to_o furnish_v any_o dial_n with_o the_o usual_a mathematical_a ornament_n by_o the_o trianguler-quadrant_n as_o parallel_n of_o the_o sun_n declination_n or_o the_o sun_n place_n or_o length_n of_o the_o day_n to_o find_v the_o horizontal_a and_o virtical_a line_n and_o point_n to_o draw_v the_o azimuth_n and_o almicanter_n the_o jewish_a italian_a &_o babylonish_n hour_n and_o 12_o house_n on_o any_o plain_a before_o mention_v 1._o to_o draw_v the_o tropic_n or_o parallel_n of_o the_o sun_n declination_n or_o the_o length_n of_o the_o day_n artificial_a on_o any_o dial._n but_o note_n that_o if_o it_o be_v a_o perpendicule_a style_n who_o upper_a point_n or_o apex_n be_v to_o be_v the_o nodus_fw-la to_o give_v the_o shadow_n than_o you_o must_v strain_v a_o thread_n very_o hard_o or_o apply_v a_o rule_n for_o the_o present_a whereon_o to_o rest_v the_o moving-leg_n on_o instead_o of_o the_o axis_n or_o else_o you_o may_v do_v it_o thus_o as_o mr._n gunter_n show_v first_o to_o make_v the_o trygon_n if_o the_o rule_n or_o quadrant_n prove_v too_o large_a for_o your_o small_a dial._n on_o a_o sheet_n of_o pasteboard_n or_o slate_n draw_v a_o long_a straight_a line_n as_o ab_fw-la to_o which_o line_n erect_v two_o perpendiculer_o one_o at_o the_o upper_a and_o the_o other_o at_o the_o low_a end_n as_o cd_o and_o of_o then_o make_v ab_fw-la a_o tangent_fw-la of_o 45_o degree_n then_o have_v first_o make_v these_o little_a table_n that_o follow_v by_o the_o trianguler-quadrant_n which_o be_v only_o the_o sun_n declination_n at_o his_o entrance_n into_o the_o whole_a sign_n or_o at_o a_o even_a half-hour_n of_o rise_v lay_v of_o both_o way_n from_o b_o the_o tangent_n of_o the_o sun_n declination_n at_o ♈_o ♉_o ♊_o ♋_o as_o in_o the_o table_n follow_v and_o draw_v line_n to_o these_o point_n from_o the_o centre_n a_o as_o in_o the_o figure_n annex_v and_o then_o set_v the_o mark_n to_o they_o and_o this_o be_v the_o trigon_n figure_n i._n sun_n declination_n for_o the_o parallel_n of_o the_o length_n of_o the_o day_n hour_n declin_n 16-26_a 23-31_a 16-0_a 21-41_a 15-0_a 16-55_a 14_o 11-37_a 13_o 5-53_a 12_o 0-00_a 11_o 5-53_a 10_o 11-37_a 9_o 16-55_a 8_o 21-41_a 7-34_a 23-31_a for_o the_o sign_n of_o the_o zodiac_n sign_n declin_n ♋_o 23-31_a ♌_o ♊_o 20-14_a ♉_o â™_o 11-31_a ♈_o ♎_o 0-00_a ♓_o â™_o 11-31_a â™’_o â™_o 20-14_a ♑_o 23-31_a declination_n 5-0_a 100l_a 15-0_a 20-0_a 23-31_a both_o way_n then_o from_o the_o centre_n a_o any_o way_n on_o the_o line_n cd_o at_o such_o a_o convenient_a distance_n as_o you_o
00_o 00_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 15_o 56_o 13_o 25_o 06_o 41_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 13_o 44_o 11_o 11_o 04_o 23_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 11_o 35_o 8_o 59_o 02_o 08_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 5_o 9_o 32_o 6_o 50_o 00_o 06_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 7_o 23_o 4_o 44_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 5_o 26_o 2_o 41_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 3_o 36_o 0_o 41_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 4_o 1_o 32_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr the_o description_n and_o some_o use_v of_o the_o sphere_n for_o dial_v and_o for_o the_o better_a understanding_n of_o the_o general_a and_o particular_a scheme_n next_o the_o foot_n and_o semicircle_n frame_v for_o support_v of_o it_o you_o may_v consider_v 1._o the_o fix_a horizon_n to_o which_o the_o foot_n be_v fasten_v with_o 4_o screw_n number_v and_o divide_v into_o 360_o degree_n or_o four_o 90_o deg_n who_o count_n begin_v at_o the_o dividee_n side_n of_o the_o meridian-circle_n 2._o the_o meridian_n circle_n who_o fore-side_n at_o the_o nadir-point_n stand_v in_o the_o centre_n of_o the_o foot_n this_o be_v also_o divide_v into_o 4_o 90_o s_o and_o begin_v to_o be_v number_v at_o the_o south_n and_o north_n part_n of_o the_o horizon_n upward_o towards_o the_o zenith_n and_o downward_o towards_o the_o nadir_n which_o circle_n be_v always_o fix_v as_o the_o horizon_n be_v 3._o the_o equinoctial_a circle_n make_v fast_o at_o the_o east_n and_o west_n point_v of_o the_o horizon_n move_v up_o and_o down_o upon_o the_o meridian-circle_n according_a to_o the_o elevation_n of_o the_o equinoctial_a in_o any_o latitude_n this_o be_v divide_v â—â—kewise_o into_o four_o 90_o s_o &_o number_v from_o the_o meridian_n each_o way_n to_o the_o east_n and_o west_n point_v of_o the_o horizon_n 4._o on_o the_o meridian_n circle_n be_v set_v 2_o movable_a pole_n to_o be_v elevate_v or_o depress_v fit_a to_o the_o latitude_n of_o any_o place_n on_o the_o fiducial-edge_n of_o which_o be_v fasten_v the_o thread_n represent_v the_o axis_n of_o the_o world_n at_o any_o elevation_n of_o the_o pole_n 5._o on_o the_o 2_o pole_n point_n be_v fasten_v the_o hour_n circle_n which_o delineate_v or_o represent_v the_o motion_n of_o the_o sun_n or_o any_o fix_a star_n move_v in_o its_o suppose_a diurnal_a motion_n about_o the_o pole_n of_o the_o world_n and_o may_v not_o improper_o be_v call_v the_o movable_a meridian_n circle_n or_o hour_n circle_n divide_v as_o before_o 6._o the_o movable_a horizon_n that_o move_v about_o to_o any_o azimuth_n and_o slide_v or_o move_v in_o the_o fix_a horizon_n 7._o the_o plain_a fix_v in_o 2_o opposite_a point_n to_o the_o move_a horizon_n be_v set_v either_o horizontal_a when_o it_o lie_v parallel_v to_o the_o fix_a horizon_n or_o erect_v when_o perpendicule_a thereunto_o or_o set_v to_o any_o reclination_n or_o inclination_n by_o help_n of_o the_o semicircle_n of_o reclination_n fasten_v to_o the_o backside_n of_o the_o plain_a in_o the_o 2_o pole_n thereof_o 8._o you_o have_v the_o upper_a move_a semicircle_n in_o turn_v about_o of_o which_o whatever_o degree_n the_o fore-side_n of_o the_o semicircle_n cut_v the_o perpendiculer-point_n cut_v the_o compleâ—ment_n thereof_o and_o to_o be_v call_v the_o upper_a semicircle_n or_o circle_n always_o perpendicuâ—ler_n to_o the_o plain_a 9_o there_o aught_o to_o be_v a_o thread_n fasten_v in_o the_o centre_n of_o the_o plain_a to_o be_v extend_v to_o any_o altitude_n or_o azimuth_n require_v thus_o much_o for_o description_n repeat_v again_o in_o short_a thus_o the_o horizon_n the_o meridian_n the_o equinoctial_a circle_n the_o 2_o pole_n point_n and_o axis_n the_o hour_n circle_n or_o movable_a meridian_n the_o movable_a horizon_n the_o plain_a the_o semicircle_n of_o reclination_n the_o upper_a semicircle_n and_o the_o thread_n note_v also_o every_o circle_n be_v divide_v into_o 4_o time_n 90_o and_o number_v the_o most_o useful_a way_n also_o on_o the_o plain_n be_v set_v the_o 12_o month_n and_o every_o single_a day_n on_o which_o every_o respective_a day_n if_o you_o extend_v the_o thread_n then_o in_o the_o degree_n be_v the_o sun_n right_a ascension_n in_o degree_n on_o the_o innermost_a circle_n the_o same_o in_o hour_n and_o quarter_n from_o the_o next_o equinoctial-point_n on_o the_o line_n of_o declination_n his_o mean_a declination_n on_o the_o line_n of_o â—he_n sun_n place_n his_o mean_a true_a place_n sufficient_o true_a for_o any_o illustration_n in_o mathematical_a practice_n the_o use_v whereof_o in_o some_o part_n follow_v 1._o to_o rectify_v the_o sphere_n to_o any_o latitude_n count_v the_o elevation_n of_o the_o pole_n on_o the_o meridian_n circle_n from_o the_o horizon_n upward_o and_o downward_o from_o the_o north_n and_o south_n part_n of_o the_o horizon_n and_o there_o make_v fast_o with_o the_o help_n of_o the_o small_a screw_n the_o fiducial-edge_n of_o the_o pole_n point_n carry_v the_o hour_n circle_v fix_v upon_o they_o than_o the_o pole_n be_v right_o elevate_v 2._o count_n the_o compliment_n of_o the_o pole_n elevation_n on_o the_o meridian_n from_o the_o south_n part_n of_o the_o horizon_n and_o to_o it_o set_v the_o divide_a side_n of_o the_o equinoctial_a circle_n then_o be_v that_o rectify_v also_o in_o the_o northern_a hemisphere_n or_o in_o the_o southern_a if_o you_o call_v the_o north_n pole_n the_o south_n pole_n 3._o extend_v the_o thread_n or_o axis_n pass_v through_o the_o centre_n to_o the_o south_n pole_n and_o there_o make_v it_o fast_o and_o then_o the_o sphere_n be_v rectify_v for_o many_o use_v in_o that_o latitude_n use_v i._o the_o day_n of_o the_o month_n be_v give_v to_o find_v the_o sun_n true_a place_n lay_v the_o thread_n in_o the_o centre_n of_o the_o plain_a on_o the_o day_n of_o the_o month_n and_o in_o the_o line_n of_o the_o sun_n place_n you_o have_v his_o place_n example_n on_o the_o 5_o of_o november_n it_o be_v 23_o degree_n in_o â™_o or_o if_o the_o sun_n place_n be_v give_v look_v for_o that_o and_o just_a against_o it_o in_o the_o month_n be_v the_o day_n require_v example_n the_o sun_n place_n be_v 15_o degree_n ♌_o i_o look_v for_o it_o in_o the_o line_n of_o his_o place_n and_o just_a against_o it_o i_o find_v july_n 28_o day_n use_v ii_o to_o find_v his_o declination_n any_o day_n look_v for_o the_o day_n give_v and_o right_a against_o it_o in_o the_o line_n of_o declination_n be_v his_o due_a declination_n require_v example_n august_n the_o 5_o the_o declination_n be_v 14_o degree_n 5_o minute_n from_o the_o next_o equinoctial-point_n viz._n ♎_o note_v in_o the_o northern_a sin_n or_o summertime_n the_o sun_n have_v north_n declination_n or_o in_o southern_a sin_n or_o winter-month_n the_o sun_n have_v south_n declination_n or_o if_o you_o have_v the_o sun_n declination_n find_v that_o in_o the_o line_n declination_n and_o right_a against_o it_o in_o the_o month_n be_v the_o day_n require_v example_n 21_o degree_n south_n declination_n begin_v from_o the_o equinoctial_a towards_o the_o winter_n solstice_n i_o find_v novemb_n 15._o the_o like_a work_n have_v be_v if_o the_o sun_n place_n have_v be_v give_v to_o find_v his_o declination_n use_v iii_o the_o day_n give_v to_o find_v the_o sun_n rightascention_n this_o be_v usual_o reckon_v from_o ♈_o to_o ♈_o round_a in_o 24_o hour_n but_o twice_o 12_o be_v as_o useful_a and_o then_o it_o be_v thus_o find_v the_o day_n among_o the_o month_n and_o day_n and_o just_a against_o it_o in_o the_o time_n of_o hour_n be_v the_o sun_n right_a ascension_n but_o note_n it_o be_v not_o right_o figure_v for_o this_o use_n count_v onward_o from_o ♈_o or_o the_o 10_o of_o march_n to_o the_o 13_o of_o septemb_n and_o from_o thence_o to_o aries_n again_o likewise_o the_o degree_n be_v to_o be_v reckon_v from_o ♈_o onward_o as_o the_o month_n proceed_v example_n on_o the_o 12_o of_o may_n what_o be_v the_o sun_n right_a ascension_n lay_v the_o thread_n on_o the_o 12_o of_o may_n and_o in_o the_o line_n of_o hour_n it_o cut_v 9-57′_a count_v from_o aries_n onward_o or_o in_o degree_n 59-15_a count_v as_o before_o thus_o if_o any_o one_o of_o these_o 4_o general_a thing_n be_v give_v the_o other_o may_v be_v find_v use_v iu._n the_o sun_n declination_n and_o latitude_n be_v give_v to_o find_v the_o sun_n meridian_n altitude_n the_o sphere_n be_v rectify_v count_v the_o declination_n on_o the_o meridian_n from_o the_o equinoctial_a that_o way_n the_o declination_n be_v either_o north_n or_o south_n and_o where_o the_o count_v end_n there_o be_v the_o meridian_n altitude_n require_v for_o that_o day_n or_o declination_n example_n june_n 11._o declination_n 23-30′_a count_v 23-30_a from_o 38-30_a the_o place_n where_o
sight_n 233_o for_o a_o fore-observation_n with_o thread_n and_o plummet_n 235_o for_o a_o back-observation_n as_o a_o davis_n quadrant_n 237_o to_o find_v the_o sun_n distance_n from_o the_o zenith_n or_o the_o co-altitude_n 238_o to_o find_v the_o altitude_n when_o near_o the_o zenith_n 239_o to_o find_v a_o latitude_n by_o a_o forward_a observation_n as_o with_o a_o gunter_n bow_n 241_o to_o find_v the_o latitude_n by_o a_o back_n observation_n 247_o to_o find_v the_o latitude_n by_o a_o meridian_n observation_n with_o thread_n and_o plummet_n 252_o to_o find_v the_o sun_n declination_n 254_o a_o table_n of_o the_o sun_n declination_n for_o the_o second_o after_o leap-year_n 256_o 257_o a_o table_n of_o the_o sun_n declination_n for_o every_o 5_o day_n the_o intermediate_v year_n 258_o 259_o a_o rectify_v table_n for_o the_o intermediate_v year_n 260_o a_o table_n of_o the_o magnitude_n declination_n and_o right_a ascension_n of_o 33_o fix_a star_n in_o degree_n and_o hour_n and_o minute_n 261_o the_o use_n of_o the_o trianguler-quadrant_n in_o the_o operative_a part_n of_o navigation_n 267_o of_o sail_v by_o the_o arch_n of_o a_o great_a circle_n 300_o finis_fw-la errata_fw-la for_o the_o second_o part._n page_n 6._o line_n 10._o for_o too_o read_z to_z p._n 18._o l._n 10._o f._n h_n r._n the_o end_n of_o the_o arch_a qp_n p._n 22._o l._n 14._o f._n begin_v r._n be_v p._n 15._o l._n 27._o f._n latitude_n r._n co-latitude_n p._n 34._o l._n 8._o f._n sun_n r._n sum_n p._n 39_o l._n 24._o f._n incliner_n r._n inclination_n of_o meridian_n p._n 61._o l._n 23._o f._n place_n r._n plain_a p._n 62._o l._n 20._o f._n ☉_o r._n q._n p._n 66._o l._n 2._o f._n ay_o r._n t._n p._n 69._o l._n 7._o f._n 12._o r._n 7._o p._n 92_o l._n 22._o r._n give_v a_o mark_n near_o e_o who_o measure_n on_o the_o limb_n from_o b._n p._n 87._o l._n 8._o f._n giâ—es_o r._n give_v l._n 11._o add_v at_o r_o near_o c._n p._n 93._o l._n 25._o f._n fe_o r._n pe._n p._n 100_o l._n 21._o add_v cd_o next_o give_n p._n 100l_n l._n 6._o f._n 8-5_a r._n 8-3_a p._n 105._o l._n 19_o f._n use_n r._n have_v p._n 108._o l._n 6._o f._n pole_n r._n zenith_n p._n 112._o l._n 3._o f._n cut_v 12_o r._n cut_v the_o substile_a p_o 113._o l._n 19_o f._n df_n r._n de._n l_o 19_o f._n t._n r._n et_fw-la also_o in_o l._n â—8_o r._n et_fw-la p._n 122._o l._n 6._o f._n e_o r._n f._n p._n 122._o l._n 13_o 14_o 15_o 16_o add_v sine_fw-la p._n 128._o l._n 26._o f._n ay_o r._n l._n p._n 139._o l._n 21._o add_v as_o in_o this_o example_n p._n 140._o l._n 6._o add_v to_o p_o 170._o l._n 10._o f._n divide_v r._n divide_v p._n 181._o l._n 20._o f._n popsition_n r._n proportion_n p._n 119._o l._n 27._o f._n from_o r._n on_o p._n 193._o l._n 6._o f._n be_v r._n bring_v p._n 197_o l._n 4._o f._n elevation_n r._n inclination_n p._n 200_o l._n 24._o f._n c_o r._n g._n p._n 204._o l._n 3._o f._n f_o r._n e._n p_o 209._o add_v in_o the_o last_o line_n or_o by_o the_o upper_a part_n of_o the_o plain_a p._n 124._o l._n 18._o add_v or_o remove_v the_o thread_n to_o turn_v it_o further_o when_o it_o recline_v beyond_o the_o pole_n p._n 238._o l._n 7._o add_v of_o l._n 20_o add_v but._n p._n 247._o l._n 13._o r._n and_o much_o better_a in_o small_a latitude_n p._n 248._o l._n 5._o f._n woe_n r._n two_o p._n 251._o l._n 14._o f._n 20_o r._n 33._o also_o l._n 17._o f._n 40_o r._n 27._o advertisement_n the_o use_n of_o these_o or_o any_o other_o instrument_n concern_v the_o mathematical_a practice_n or_o further_a instruction_n in_o any_o part_n thereof_o be_v teach_v by_o john_n colson_n near_o the_o hermitage-stair_n also_o by_o euclid_n speidwel_n dwell_v near_o to_o white-chappel_n church_n in_o capt._n cane_n rent_n or_o at_o the_o custom-house_n also_o by_o william_n northhall_v mariner_n dwell_v at_o the_o crooked-billet_a in_o meetinghouse_n alley_n on_o green-bank_n near_o wapping_n also_o the_o instrument_n may_v be_v have_v at_o the_o house_n of_o john_n brown_n john_n seller_n or_o john_n wingfield_n as_o in_o the_o title-page_n be_v express_v there_o be_v now_o extant_a a_o large_a treatise_n of_o navigation_n in_o folio_n describe_v the_o seacoast_n cape_n head-land_n the_o bay_n roads_n rivers_n harbour_n and_o sea-mark_n in_o the_o whole_a northern-navigation_n show_v the_o course_n and_o distance_n from_o one_o place_n to_o another_o the_o ebb_a and_o flow_v of_o the_o sea_n with_o many_o other_o thing_n belong_v to_o the_o practic_a part_n of_o navigation_n a_o book_n not_o heretofore_o print_v in_o england_n collect_v from_o the_o practice_n and_o experience_n of_o divers_a able_a and_o experience_a navigator_n of_o our_o english_a nation_n publish_a by_o john_n seller_n hydrographer_n to_o the_o king_n most_o excellent_a majesty_n and_o to_o be_v sell_v by_o he_o at_o the_o sign_n of_o the_o mariner_n compass_n at_o the_o hermitage-stair_n in_o wapping_n and_o by_o john_n wingfield_n right_a against_o st._n olave_n church_n in_o crouched-fryer_n practical_a navigation_n or_o a_o introduction_n to_o that_o whole_a art_n sell_v by_o john_n seller_n and_o john_n wingfield_n aforesaid_a see_v the_o general-scheam_a