declination_n of_o 12_o principal_a fix_a star_n in_o the_o heaven_n most_o of_o which_o be_v insert_v on_o the_o rule_n or_o if_o room_n will_v allow_v all_o of_o they_o  _fw-fr r._n asc._n declina_fw-la star_n name_n h._n m._n deg._n m._n pleyade_n or_o 7_o star_n 03_o 24_o 23_o 20_o bulls-eye_n 04_o 16_o 15_o 48_o orion_n girdle_n 05_o 18_o 01_o 195_o little_a dog_n 07_o 20_o 06_o 08_o lion_n heart_n 09_o 50_o 13_o 40_o lion_n tail_n 11_o 30_o 16_o 30_o arcturus_n 14_o 00_o 21_o 04_o vulture_n heart_n 19_o 33_o 08_o 00_o dolphin_n head_n 20_o 30_o 14_o 52_o pegasus_n mouth_n 21_o 27_o 08_o 19_o fomahant_n 22_o 39_o 31_o 17_n pegasus_n lower_v wing_n 23_o 55_o 13_o 19_o  _fw-fr 1_o  _fw-fr 3_o  _fw-fr 5_o 7_o 4_o  _fw-fr  _fw-fr 6_o  _fw-fr 8_o  _fw-fr  _fw-fr  _fw-fr month_n 9_o  _fw-fr 11_o  _fw-fr 2_o 10_o 12_o  _fw-fr 1_o 2_o 3_o 4_o 5_o 6_o 7_o  _fw-fr 8_o 9_o 10_o 11_o 12_o 13_o 14_o day_n 15_o 16_o 17_o 18_o 19_o 20_o 21_o  _fw-fr 22_o 23_o 24_o 25_o 26_o 27_o 28_o  _fw-fr 29_o 30_o 31_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr weekday_n s_o m_o t_o w_n t_o f_o sat_n dom._n letter_n d_o c_o b_o a_o g_o f_o e_o leap_n year_n 68_o 80_o 64_o 76_o 60_o 72_o 84_o exact_v 26_o 9_o 12_o 25_o 28_o 11_o 23_o the_o description_n and_o use_v of_o a_o joynt-rule_a chap._n i._n the_o description_n of_o the_o line_n on_o the_o rule_n as_o it_o be_v make_v only_o for_o one_o latitude_n and_o for_o the_o find_v the_o hour_n of_o the_o day_n only_o first_o open_v the_o joint_a of_o the_o rule_n then_o upon_o the_o head-leg_n be_v next_o to_o your_o right_a hand_n you_o have_v a_o line_n beginning_n at_o the_o hole_n which_o be_v the_o centre_n of_o the_o quadrantal_a line_n and_o divide_v from_o thence_o downward_o towards_o the_o head_n into_z as_o many_o degree_n as_o the_o sun_n great_a altitude_n in_o that_o latitude_n will_v be_v which_o with_o we_o at_o london_n be_v to_o 62_o degree_n which_o line_n i_o call_v the_o scale_n of_o altitude_n divide_v to_o whole_a half_n and_o sometime_o quarter_n of_o degree_n 2._o second_o on_o the_o other_o leg_n and_o next_o to_o the_o inside_n be_v the_o line_n of_o hour_n usual_o divide_v into_o hour_n quarter_n and_o every_o five_o minute_n begin_v at_o the_o head_n with_o 4_o and_o so_o proceed_v to_o 5_o 6_o 7_o 8_o 9_o 10_o 11_o and_o 12_o at_o the_o end_n and_o then_o back_o again_o with_o 1_o 2_o 3_o 4_o 5_o 6_o 7_o 8_o for_o the_o morning_n and_o afternoon_n hour_n 3._o next_o to_o this_o be_v a_o calendar_n of_o month_n and_o day_n in_o two_o line_n the_o uppermost_a contain_v that_o half_a year_n the_o day_n lengthen_v in_o and_o the_o lowermost_a the_o shorten_n day_n as_o by_o the_o name_n of_o the_o month_n may_v appear_v the_o name_n of_o every_o month_n stand_v in_o the_o month_n and_o at_o the_o begin_n of_o the_o month_n and_o all_o but_o the_o two_o month_n that_o have_v the_o long_a and_o the_o short_a day_n viz._n june_n and_o december_n be_v divide_v into_o single_a day_n the_o ten_o day_n have_v a_o figure_n 10_o or_o a_o point_n or_o prick_v on_o the_o head_n of_o the_o stroke_n and_o the_o five_o only_o a_o long_a stroke_n without_o a_o prick_n and_o the_o beginning_n of_o every_o month_n a_o long_a stroke_n and_o every_o single_a day_n all_o alike_o of_o one_o shortness_n according_a to_o the_o usual_a manner_n of_o distinguish_v on_o line_n 4._o and_o last_o you_o have_v a_o line_n of_o degree_n for_o so_o they_o be_v most_o proper_o call_v and_o they_o be_v the_o same_o with_o the_o equal_a limb_n on_o quadrant_n and_o serve_v for_o the_o same_o use_n viz._n for_o take_v of_o altitude_n or_o horizontal_a angle_n and_o be_v divide_v usual_o to_o whole_a and_o half_a degree_n of_o the_o quadrant_a and_o figure_v with_o 30_o 40_o 50_o 600_o 7010_o 8020_o and_o 90_o just_a on_o the_o head_n cut_v the_o centre_n or_o point_n where_o the_o scale_n of_o altitude_n and_o the_o line_n of_o hour_n meet_v which_o point_n for_o distinction_n sake_n i_o call_v the_o rectify_v point_n and_o the_o reckon_n on_o this_o line_n as_o to_o take_v of_o altitude_n be_v thus_o at_o the_o number_n 600_o be_v the_o beginning_n then_o towards_o the_o head_n count_v 10_o 20_o 30_o where_o the_o 90_o be_v then_o begin_v at_o the_o end_n again_o &_o count_v as_o the_o figure_n show_v you_o to_o 90_o at_o the_o head_n as_o before_z chap_n ii_o the_o use_v of_o the_o rule_n follow_v 1._o to_o rectify_v or_o set_v the_o rule_n to_o his_o true_a angle_n open_v the_o rule_n to_o 60_o degree_n which_o be_v do_v thus_o indifferent_o make_v the_o line_n on_o the_o head_n and_o the_o line_n on_o the_o other_o leg_n meet_v in_o a_o straight_a line_n then_o be_v the_o scale_n of_o altitude_n and_o the_o line_n of_o hour_n set_v to_o a_o angle_n of_o 60_o degree_n the_o rectify_v point_n be_v the_o centre_n of_o that_o angle_n or_o to_o do_v it_o more_o exact_o do_v thus_o put_v one_o point_n of_o a_o pair_n of_o compass_n into_o the_o rectify_v point_n then_o open_a the_o other_o to_o 10_o 20_o 30_o or_o 40_o on_o the_o scale_n of_o altitude_n the_o compass_n so_o open_v and_o the_o point_n yet_o remain_v in_o the_o rectify_v point_n turn_v the_o other_o to_o that_o margenal_a line_n in_o the_o line_n of_o hour_n that_o cut_v the_o rectify_v point_n and_o there_o stay_v it_o then_o remove_v the_o point_n that_o be_v fix_v in_o the_o rectify_v point_n and_o open_a or_o shut_v the_o rule_n till_o the_o point_n of_o the_o compass_n will_v touch_v 10_o 20_o 30_o or_o 40_o be_v the_o point_n you_o set_v the_o compass_n too_o in_o the_o scale_n of_o altitude_n in_o the_o innermost_a line_n that_o cut_v the_o centre_n and_o the_o rectify_v point_n then_o be_v it_o set_v exact_o to_o 60_o degree_n and_o fit_v for_o observation_n 2._o to_o find_v the_o sun_n altitude_n at_o any_o time_n put_v a_o pin_n in_o the_o centre_n hole_n at_o the_o upper_a end_n of_o the_o scale_n of_o altitude_n and_o on_o the_o pin_n hang_v a_o thread_n and_o plummet_n then_o if_o the_o sun_n be_v low_a that_o be_v to_o say_v under_o 25_o degree_n high_a as_o in_o the_o winter_n it_o will_v always_o be_v then_o lift_v up_o the_o movable_a leg_n where_o the_o month_n and_o the_o degree_n be_v till_o the_o shadow_n of_o the_o end_n fall_v just_a on_o the_o meeting_n of_o that_o leg_n with_o the_o head_n than_o the_o thread_n shall_v show_v the_o sun_n altitude_n count_v from_o 600_o towards_o the_o head_n either_o 10_o 20_o 25_o or_o any_o degree_n between_o but_o if_o the_o sun_n be_v above_o 25_o or_o 30_o degree_n high_a lift_v up_o the_o head_n leg_n till_o the_o shadow_n of_o that_o play_n as_o before_o or_o make_v the_o shadow_n of_o the_o pin_n in_o the_o centre_n hole_n play_v on_o the_o innermost_a line_n of_o the_o scale_n of_o altitude_n where_o the_o pin_n stand_v than_o the_o thread_n will_v fall_v on_o the_o degree_n and_o part_n of_o a_o degree_n that_o his_o true_a altitude_n shall_v be_v but_o if_o the_o sun_n be_v in_o a_o cloud_n and_o can_v not_o be_v see_v so_o as_o to_o give_v a_o shadow_n then_o look_v up_o along_o by_o the_o head-leg_n or_o movable_a leg_n just_a against_o the_o middle_n of_o the_o round_a body_n of_o the_o sun_n and_o the_o thread_n play_v even_o by_o the_o degree_n shall_v show_v the_o true_a altitude_n require_v the_o like_a must_v you_o do_v for_o a_o star_n or_o any_o other_o object_n who_o altitude_n you_o will_v find_v 3._o have_v find_v the_o sun_n altitude_n and_o the_o day_n of_o the_o month_n to_o find_v the_o hour_n of_o the_o day_n whatsoever_o you_o find_v the_o altitude_n to_o be_v take_v the_o same_o off_o from_o the_o line_n of_o altitude_n from_o the_o centre_n downward_o with_o a_o pair_n of_o compass_n then_o lay_v the_o thread_n be_v put_v over_o the_o pin_n on_o the_o day_n of_o the_o month_n than_o put_v one_o foot_n of_o the_o compass_n in_o the_o line_n of_o hour_n in_o that_o line_n that_o cut_v the_o rectify_v point_n and_o carry_v it_o further_o off_o or_o nigh_o till_o the_o other_o foot_n of_o the_o compass_n be_v turn_v about_o will_v just_o touch_v the_o thread_n at_o the_o near_a distance_n than_o the_o point_n of_o the_o compass_n on_o the_o line_n of_o hour_n shall_v show_v the_o true_a hour_n and_o minute_n of_o the_o day_n require_v example_n on_o the_o 2._o of_o july_n 1._o i_o observe_v the_o altitude_n in_o the_o morning_n and_o i_o find_v it_o to_o be_v 30_o degree_n high_a then_o lay_v the_o thread_n on_o the_o day_n of_o
the_o amplitude_n from_o the_o east_n or_o west_n count_v from_o 90._o example_n may_v the_o ten_o it_o be_v 33._o 37._o chap._n v._n have_v the_o sun_n declination_n or_o day_n of_o the_o month_n to_o find_v the_o azimuth_n at_o any_o altitude_n require_v for_o that_o day_n first_o find_v the_o sun_n declination_n by_o the_o first_o proposition_n of_o the_o four_o chapter_n then_o take_v that_o out_o of_o the_o particular_a scale_n of_o altitude_n or_o scale_v to_o 62_o degree_n than_o whatsoever_o the_o altitude_n shall_v happen_v to_o be_v count_v the_o same_o on_o the_o degree_n from_o 60_o towards_o the_o end_n of_o the_o rule_n according_a to_o the_o second_o manner_n of_o count_v in_o the_o three_o proposition_n of_o the_o three_o chapter_n and_o thereunto_o lie_v the_o thread_n than_o the_o compass_n set_v to_o the_o declination_n carry_v one_o point_n along_o the_o line_n of_o hour_n on_o the_o same_o side_n of_o the_o thread_n the_o declination_n be_v that_o be_v to_o say_v if_o the_o day_n of_o the_o month_n or_o declination_n be_v on_o the_o right_a side_n the_o aequinoctial_a then_o carry_v the_o compass_n on_o the_o right_a side_n but_o if_o the_o declination_n be_v on_o the_o south_n side_n that_o be_v towards_o the_o end_n count_v from_o the_o ten_o of_o march_n or_o aries_n or_o libra_n then_o carry_v the_o compass_n along_o the_o line_n of_o hour_n and_o azimuth_n on_o the_o left_a side_n of_o the_o thread_n as_o all_o winâ—er_a time_n it_o will_v be_v and_o have_v set_v the_o compass_n to_o the_o least_o distance_n to_o the_o thread_n it_o shâ—ll_v stay_v at_o the_o sun_n true_a azimuth_n from_o the_o south_n require_v count_v as_o the_o figure_n be_v number_v or_o from_o east_n or_o west_n count_v from_o 90._o example_n 1._o on_o the_o ten_o of_o july_n i_o desire_v to_o find_v the_o sun_n azimuth_n at_o any_o altitude_n first_o on_o that_o day_n i_o find_v the_o sun_n declination_n to_o be_v 20._o 45_o which_o number_n count_v from_o the_o begin_n of_o the_o particular_a scale_n of_o altitude_n towards_o 62_o and_o that_o distance_n take_v between_o your_o compass_n then_o be_v they_o set_v for_o all_o that_o day_n then_o suppose_v the_o sun_n height_n to_o be_v ten_o degree_n lay_v the_o thread_n on_o 10_o count_v from_o 60_o towards_o the_o left_a end_n then_o carry_v the_o compass_n on_o the_o right_a side_n of_o the_o thread_n because_o it_o be_v summer_n or_o north_n declination_n on_o the_o line_n of_o azimuth_n it_o shall_v show_v 110._o 40_o the_o azimuth_n from_o the_o south_n require_v but_o if_o you_o count_v from_o 90_o it_o be_v but_o 20._o 40._o from_o the_o east_n or_o west_n point_v northward_o according_a to_o the_o time_n of_o the_o day_n either_o morning_n or_o evening_n example_n 2._o again_o on_o the_o 14._o of_o november_n or_o the_o 6._o of_o january_n when_o the_o sun_n have_v the_o same_o declination_n southward_o and_o the_o same_o altitude_n to_o work_v this_o you_o must_v lay_v the_o rule_n down_o on_o something_o then_o lay_v the_o thread_n on_o the_o altitude_n count_v from_o 60_o towards_o the_o end_n as_o before_o and_o carry_v the_o compass_n on_o the_o southside_n of_o the_o aequinoctial_a along_o the_o azimuth-line_n till_o the_o other_o point_n do_v but_o just_a touch_n the_o thread_n and_o it_o shall_v stay_v at_o 36._o 45_o the_o azimuth_n from_o south_n require_v if_o it_o be_v morning_n it_o want_v of_o come_v to_o south_n if_o it_o be_v afternoon_n it_o be_v pass_v the_o south_n example_n 3._o but_o if_o the_o sun_n be_v in_o the_o aequinoctial_a and_o have_v no_o declination_n than_o it_o be_v but_o lay_v the_o thread_n to_o the_o altitude_n and_o in_o the_o line_n of_o azimuth_n the_o thread_n shall_v show_v the_o true_a azimuth_n require_v as_o for_o instance_n at_o 00_o degree_n of_o altitude_n the_o azimuth_n be_v 90_o at_o 10_o degree_n it_o be_v 77._o 15_o at_o 20_o degree_n 62._o 45_o at_o 30_o degree_n high_a 43._o 15_o at_o 35_o degree_n high_a 28._o 10_o at_o 38_o degree_n 28_o '_o high_z it_o be_v just_a south_n as_o by_o practice_n may_v plain_o appear_v but_o if_o the_o sun_n altitude_n be_v above_o 45_o than_o the_o degree_n will_v go_v beyond_o the_o end_n of_o the_o rule_n to_o supply_v this_o defect_n do_v thus_o subtract_v 45_o out_o of_o the_o number_n you_o will_v have_v and_o double_a the_o remainder_n then_o lay_v the_o rule_n down_o with_o some_o piece_n of_o the_o same_o thickness_n in_o a_o straight_a line_n with_o the_o movable_a leg_n then_o take_v the_o distance_n from_o the_o tangent_fw-la of_o the_o remainder_n double_v count_v from_o 60_o to_o the_o end_n of_o the_o rule_n in_o the_o line_n next_o the_o edge_n to_o the_o centre_n lay_v that_o distance_n in_o the_o same_o straight_a line_n from_o the_o tangent_fw-la double_v and_o that_o shall_v be_v the_o tangent_fw-la of_o the_o angle_n above_o 45_o whereunto_o you_o must_v lay_v the_o thread_n for_o the_o find_v the_o azimuth_n when_o the_o sun_n be_v above_o 45_o degree_n high_a chap._n vi_o to_o find_v the_o hour_n of_o the_o night_n by_o the_o moon_n first_o by_o the_o help_n of_o a_o almanac_n get_v the_o true_a time_n of_o the_o new_a moon_n then_o compute_v her_o true_a place_n at_o that_o time_n which_o be_v always_o the_o place_n of_o the_o sun_n very_o nigh_o at_o the_o hour_n and_o minute_n of_o conjunction_n then_o compute_v how_o many_o day_n old_a the_o moon_n be_v then_o by_o the_o line_n of_o number_n say_v if_o 29_o day_n 13_o hour_n or_o on_o the_o line_n 29._o 540_o require_v 860_o degree_n or_o 12_o sign_n what_o shall_v â—ny_v less_o number_n of_o day_n and_o part_n of_o a_o day_n require_v the_o answer_n will_v be_v the_o moon_n true_a place_n at_o that_o age_n have_v â—ound_v her_o true_a place_n then_o take_v her_o altitude_n and_o lay_v the_o thread_n on_o the_o moon_n place_v find_v and_o work_v as_o you_o do_v for_o the_o sun_n and_o note_v what_o hour_n you_o find_v then_o consider_v if_o it_o be_v new_a moon_n the_o hour_n you_o find_v be_v thentrue_a hour_n likewise_o in_o the_o full_a but_o if_o it_o be_v before_o or_o after_o you_o must_v subtract_v by_o the_o line_n of_o number_n thus_o if_o 29_o day_n 540_o part_n require_v 24_o hour_n what_o shall_v any_o number_n of_o day_n and_o part_n require_v the_o answer_n be_v what_o you_o must_v take_v away_o from_o the_o moon_n hour_n find_v to_o make_v the_o true_a hour_n of_o the_o night_n which_o be_v require_v but_o for_o more_o plainness_n sake_n i_o will_v reduce_v these_o operation_n to_o so_o many_o proposition_n before_o i_o come_v to_o a_o example_n prop._n 1._o to_o find_v the_o moon_n age._n first_o it_o be_v most_o ready_o and_o exact_o do_v by_o a_o ephemerides_n such_o a_o one_o as_o you_o find_v in_o mr._n lilly_n almanac_n or_o as_o to_o her_o age_n only_o in_o any_o book_n or_o sheet-almanack_n but_o you_o may_v do_v it_o indifferent_o by_o the_o epact_n thus_o by_o the_o rule_n of_o the_o 152_o page_n in_o the_o appendix_n to_o the_o carpenter_n rule_n add_v the_o epact_n the_o month_n and_o the_o day_n of_o the_o month_n together_o and_o the_o sum_n if_o under_o 30_o be_v the_o moon_n age_n but_o if_o above_o consider_v if_o the_o month_n have_v 30_o or_o 31_o day_n then_o subtract_v 29_o or_o 30_o out_o and_o the_o remainder_n be_v the_o moon_n age_n in_o day_n example_n august_n 2._o 1660._o epact_n 28._o month_n 6._o day_n 2._o add_v make_n 36._o now_o august_n or_o six_o month_n have_v 31_o day_n therefore_o 30_o being_n take_v away_o 6_o day_n remain_v for_o the_o moon_n age_n require_v prop._n 2._o to_o find_v the_o moon_n place_n by_o the_o ephemerides_n aforesaid_a in_o mr._n lilly_n almanac_n you_o have_v it_o ser_fw-mi down_o every_o day_n in_o the_o year_n but_o to_o find_v it_o by_o the_o rule_n do_v thus_o count_n six_o day_n back_o from_o august_n 2._o viz._n to_o july_n 27._o there_o lay_v the_o thread_n and_o in_o the_o line_n of_o the_o sun_n place_n you_o have_v the_o moon_n place_v require_v be_v then_o near_o alike_o then_o in_o regard_n the_o moon_n go_v fast_a than_o the_o sun_n that_o be_v to_o say_v in_o 29_o day_n 13_o hour_n 12_o sign_n or_o 360_o degree_n in_o 3_o day_n 1_o sign_n 6_o degr_n 34_o min._n 20_o sec._n in_o one_o day_n o_o sign_n 12_o degr_n 11_o min._n 27_o sec._n in_o one_o hour_n 30_o min._n 29_o sec._n or_o half_o a_o minute_n add_v the_o sign_n and_o degree_n and_o minute_n the_o moon_n have_v go_v in_o so_o many_o day_n and_o hour_n if_o you_o know_v they_o together_o and_o the_o sun_n shall_v be_v the_o moon_n true_a place_n be_v add_v to_o what_o she_o have_v on_o
day_n in_o this_o latitude_n will_v be_v find_v to_o be_v 109_o degree_n want_v of_o south_n or_o pole_n of_o the_o place_n therefore_o unlike_o sign_n and_o to_o be_v add_v and_o they_o make_v up_o 119_o degree_n who_o compliment_n to_o 180_o be_v 61_o for_o 61_o and_o 119_o add_v make_v up_o 180_o therefore_o this_o plain_n decline_v 61_o degree_n from_o the_o north_n towards_o the_o east_n again_o the_o same_o day_n in_o the_o afternoon_n i_o find_v the_o azimuth_n past_o the_o south_n or_o meridian_n of_o the_o place_n 30_o degree_n and_o at_o the_o same_o time_n the_o sun_n want_v in_o come_v to_o the_o meridian_n or_o pole_n of_o the_o plain_a 10_o degree_n here_o by_o addition_n i_o find_v the_o declination_n to_o be_v 40_o degree_n south-west_n note_v what_o i_o have_v say_v in_o these_o three_o example_n be_v general_a at_o all_o time_n but_o if_o it_o be_v a_o fair_a day_n and_o time_n and_o opportunity_n serve_v to_o come_v either_o just_a at_o 12_o a_o clock_n when_o the_o sun_n be_v the_o meridian_n or_o pole_n of_o the_o place_n or_o just_o when_o the_o sun_n be_v in_o the_o meridian_n or_o pole_n of_o the_o plain_a than_o your_o work_n be_v only_o thus_o first_o if_o you_o come_v to_o observe_v at_o 12_o then_o apply_v your_o rule_n to_o the_o wall_n and_o hold_v up_o the_o thread_n and_o plummet_n how_o much_o so_o ever_o the_o sun_n want_v or_o be_v past_o the_o pole_n of_o the_o plain_a that_o be_v the_o declination_n if_o it_o be_v pass_v it_o be_v east-ward_n if_o it_o want_v it_o be_v south-west-ward_n if_o neither_o a_o just_a south_n plain_a and_o then_o the_o pole_n or_o meridian_n of_o place_n and_o plain_n be_v the_o same_o but_o second_o if_o you_o come_v when_o the_o sun_n be_v just_a in_o the_o pole_n of_o the_o plain_a than_o whatsoever_o you_o find_v the_o sun_n azimuth_n to_o be_v that_o be_v the_o declination_n if_o it_o want_v of_o south_n it_o decline_v east-ward_n if_o it_o be_v past_a it_o decline_v westward_n thus_o i_o have_v copious_o and_o yet_o very_o brief_o show_v you_o the_o most_o artificial_a way_n of_o get_v the_o declination_n of_o any_o wall_n howsoever_o situate_v note_v if_o the_o sun_n be_v above_o 15_o degree_n want_v of_o the_o meridian_n of_o the_o plain_a your_o rule_n will_v prove_v defective_a in_o take_v the_o plain_n meridian_n when_o the_o centre_n leg_n be_v next_o the_o wall_n than_o you_o must_v turn_v the_o other_o leg_n to_o the_o wall_n and_o then_o you_o find_v a_o supply_n for_o all_o angle_n to_o 45_o degree_n past_o the_o plain_a but_o for_o the_o supply_n of_o the_o rest_n which_o be_v 45_o degree_n do_v thus_o open_v the_o rule_n till_o the_o great_a line_n of_o tangent_n &_o the_o outside_n of_o the_o leg_n make_v a_o right_a angle_n for_o which_o on_o the_o head_n you_o may_v make_v a_o mark_n for_o the_o ready_a set_n then_o make_v the_o inside_n of_o the_o leg_n at_o the_o end_n of_o 45_o as_o a_o centre_n the_o tangent_n on_o the_o other_o leg_n supply_v very_o large_o the_o defect_n of_o the_o otherside_n or_o if_o you_o set_v on_o the_o box_n and_o needle_n on_o the_o rule_n and_o open_a or_o shut_v the_o rule_n till_o the_o shadow_n of_o the_o thread_n show_v just_a 12_o than_o the_o angle_n the_o sector_n stand_v at_o be_v the_o compliment_n of_o what_o the_o sum_n want_v or_o be_v past_o the_o meridian_n or_o pole_n of_o the_o plain_a chap._n fourteen_o to_o draw_v a_o vertical_a decline_a plain_n to_o any_o declination_n first_o draw_v a_o perpendicular-line_n for_o 12_o as_o a_o b_o then_o design_v a_o point_n in_o that_o line_n for_o the_o centre_n as_o c_o at_o the_o upper_a end_n if_o it_o be_v a_o south_n plain_a or_o contrary_a if_o it_o be_v a_o north_n plain_a then_o on_o that_o centre_n describe_v a_o arch_n of_o a_o circle_n on_o that_o side_n of_o 12_o which_o be_v contrary_a to_o the_o plain_n declination_n as_o d_o e_z and_o in_o that_o arch_n lie_v off_o from_o 12_o the_o substile_a and_o on_o that_o the_o style_n height_n and_o the_o hour_n of_o 6_o be_v find_v by_o the_o ten_o chapter_n and_o draw_v those_o line_n from_o c_o the_o centre_n then_o draw_v two_o parallel_n to_o 12_o as_o in_o the_o direct_a south_n then_o fit_a the_o distance_n of_o the_o parallel_n in_o the_o secant_fw-la of_o the_o declination_n and_o take_v the_o secant_fw-la of_o the_o latitude_n and_o set_v it_o from_o the_o centre_n c_o on_o the_o line_n of_o 12_o to_o f_o and_o on_o the_o parallel_n from_o 6_o to_z g_z and_o draw_v a_o line_n by_o those_o two_o point_n f_o and_o g_o to_o cut_v the_o other_o parallel_n in_o h_n then_o have_v you_o find_v 6_o 3_o and_o 9_o then_o fit_a 6_o g_o in_o the_o tangent_fw-la of_o 45_o and_o prick_v off_o 15_o 30_o and_o the_o respective_a quarter_n both_o way_n from_o 6_o for_o the_o morning_n and_o afternoon_n hour_n then_o fit_a f_o g_o in_o 45_o and_o lay_v off_o the_o same_o point_n from_o f_o both_o way_n for_o 10_o 11_o 1_o and_o 2_o and_o the_o quarter_n also_o if_o you_o please_v and_o those_o shall_v be_v point_n to_o draw_v the_o hour-line_n by_o the_o stile_n must_v be_v set_v perpendicular_a over_o the_o substile_a to_o the_o angle_n find_v by_o the_o rule_n in_o the_o ten_o chapter_n and_o then_o the_o dial_n shall_v show_v the_o true_a hour_n of_o the_o day_n be_v draw_v fit_a to_o his_o proper_a declination_n another_o way_n to_o perform_v this_o geometrical_o for_o all_o erect_a dial_n with_o centre_n when_o you_o have_v draw_v a_o line_n of_o 12_o and_o appoint_v a_o centre_n make_v a_o geometrical_a square_n on_o that_o side_n 12_o as_o the_o stile_n must_v stand_v on_o as_o a_o b_o c_o d_o the_o perpendicular_a side_n of_o which_o square_a may_v also_o be_v the_o parallel_n as_o before_o again_o fit_v the_o side_n of_o the_o square_n in_o the_o cousin_n of_o the_o latitude_n and_o take_v out_o the_o sine_fw-la of_o the_o latitude_n and_o fit_a that_o over_o in_o the_o sine_fw-la of_o 90_o then_o take_v out_o the_o 〈◊〉_d sine_fw-la of_o the_o declination_n and_o lay_v it_o from_o d_o to_z g_z for_o the_o hour_n of_o 6_o and_o draw_v the_o line_n a_o g_o for_o the_o 6_o a_o clock_n hour_n line_n then_o again_o fit_v the_o side_n of_o the_o square_n or_o the_o distance_n of_o the_o parallel_n in_o the_o other_o way_n when_o you_o want_v a_o secant_fw-la or_o your_o secant_fw-la too_o little_a in_o the_o sine_fw-la of_o 90_o and_o take_v out_o the_o cousin_n of_o the_o declination_n fit_a that_o in_o the_o cousin_n of_o the_o latitude_n then_o take_v out_o the_o sine_fw-la of_o 90_o and_o lay_v it_o from_o the_o centre_n on_o the_o line_n of_o 12_o and_o 〈◊〉_d 6_o in_o the_o side_n of_o the_o square_n and_o by_o those_o two_o point_n draw_v the_o contingent_a line_n and_o then_o fit_a those_o point_n or_o distance_n in_o the_o tangent_fw-la of_o 45_o and_o lay_v down_o the_o hour_n as_o in_o the_o former_a part_n of_o this_o chapter_n but_o if_o you_o want_v the_o hour_n before_o 9_o in_o west-decliners_a or_o the_o hour_n after_o 3_o in_o east-decliners_a and_o the_o 6_o fall_v too_o high_a above_o the_o horizontal_a line_n on_o that_o side_n you_o may_v supply_v this_o defect_n thus_o take_v the_o measure_n with_o your_o compass_n from_o 3_o to_o 4_o and_o 5_o upward_o in_o the_o west-decliners_a or_o from_o 9_o to_o 7_o and_o 8_o in_o east-decliners_a and_o lay_v it_o upward_o from_o 9_o or_o 3_o on_o the_o deficient_a side_n in_o the_o parallel_n as_o it_o shall_v have_v be_v from_o 6_o downward_o in_o south_n or_o upward_o in_o north_n plain_n and_o you_o shall_v see_v all_o your_o defective_a point_n to_o be_v complete_o supply_v whereunto_o draw_v the_o hour-line_n according_o chap._n xv_o to_o draw_v the_o hour-line_n on_o a_o upright_a decline_a dial_n decline_v above_o 60_o degree_n in_o all_o erect_a decliner_n the_o way_n of_o find_v the_o stile_n substile_a 6_o and_o 12_o and_o inclination_n of_o meridian_n be_v the_o same_o but_o when_o you_o come_v to_o protract_v or_o lay_v down_o the_o hour-line_n you_o shall_v find_v they_o come_v so_o close_o together_o as_o they_o will_v be_v useless_a unless_o the_o stile_n be_v augment_v the_o usual_a way_n for_o do_v of_o which_o be_v to_o draw_v the_o dial_n on_o a_o large_a floor_n and_o then_o cut_v off_o so_o much_o and_o at_o such_o a_o distance_n as_o best_o serve_v your_o turn_n but_o this_o be_v not_o always_o to_o be_v affect_v for_o want_v of_o conveniency_n and_o large_a instrument_n it_o may_v very_o artificial_o be_v do_v by_o a_o natural_a tangent_fw-la of_o 75_o or_o 80_o degree_n fit_v on_o the_o leg_n of_o a_o
the_o month_n and_o take_v 30_o degree_n from_o the_o scale_n of_o altitude_n and_o put_v one_o point_n in_o the_o line_n of_o hour_n till_o the_o other_o point_n turn_v about_o will_v but_o just_a touch_n the_o thread_n and_o i_o find_v it_o to_o 23_o minute_n past_o 7_o but_o if_o it_o have_v be_v in_o the_o afternoon_n it_o will_v have_v be_v 37_o minute_n past_o 4._o 2._o again_o on_o the_o ten_o of_o august_n in_o the_o afternoon_n at_o 20_o degree_n high_a i_o take_v 20_o degree_n from_o the_o scale_n of_o altude_n and_o lay_v the_o thread_n on_o the_o day_n of_o the_o month_n viz._n the_o ten_o aforesaid_a count_v from_o the_o name_n at_o the_o begin_n of_o august_n towards_o september_n and_o carry_v the_o compass_n in_o the_o line_n of_o hour_n till_o the_o other_o point_n do_v but_o just_a touch_n the_o thread_n and_o you_o shall_v find_v it_o to_o be_v 54_o minute_n past_o 4_o a_o clock_n 3._o again_o on_o the_o 11._o of_o december_n at_o 15_o degree_n high_a work_v as_o before_o and_o you_o shall_v find_v it_o to_o be_v just_a 12_o a_o clock_n but_o to_o work_v this_o you_o must_v lay_v the_o rule_n down_o on_o something_o and_o extend_v the_o thread_n beyond_o the_o rule_n for_o the_o nigh_a distance_n will_v happen_v on_o the_o outside_n of_o the_o rule_n 4._o again_o on_o the_o 11_o of_o june_n at_o noon_n i_o find_v the_o altitude_n to_o be_v 62_o degree_n high_a then_o lay_v the_o thread_n on_o the_o 10_o the_o or_o 11_o the_o of_o june_n for_o then_o a_o day_n be_v unsensible_a and_o work_v as_o before_o you_o shall_v find_v the_o point_n of_o the_o compass_n to_o stay_v at_o just_a 12_o a_o clock_n the_o time_n require_v for_o that_o altitude_n 4._o to_o find_v the_o sun_n rise_v any_o day_n in_o the_o year_n lay_v the_o thread_n on_o the_o day_n of_o the_o month_n and_o in_o the_o line_n of_o hour_n it_o show_v the_o true_a hour_n and_o minute_n of_o the_o sun_n rise_v or_o set_v for_o the_o rise_n count_v the_o morning_n hour_n and_o for_o the_o set_n count_v the_o evening_n hour_n 5._o to_o find_v if_o any_o place_n lie_v level_a or_o nor_o open_v the_o rule_n to_o his_o true_a angle_n of_o 60_o degree_n than_o set_v the_o movable_a leg_n upon_o the_o place_n you_o will_v make_v level_a and_o if_o the_o thread_n play_v just_a on_o 60_o degree_n it_o be_v a_o true_a level_a place_n or_o else_o not_o 6._o to_o try_v if_o any_o thing_n be_v upright_o or_o not_o hang_v a_o thread_n and_o plummet_n on_o the_o centre_n than_o ap_o the_o head_n leg_n of_o the_o rule_n to_o the_o wall_n or_o post_n and_o if_o it_o be_v upright_o the_o thread_n will_v play_v just_a on_o the_o innermost_a line_n of_o the_o scale_n of_o altitude_n or_o else_o not_o chap._n iii_o a_o further_a description_n of_o the_o rule_n to_o make_v it_o to_o show_v the_o sun_n azimuth_n declination_n true_a place_n right_a ascention_n and_o the_o hour_n of_o day_n or_o night_n in_o this_o or_o any_o other_o lattitude_n 1._o first_o in_o stead_n of_o the_o scale_n of_o altitude_n to_o 62_o degree_n there_o be_v one_o put_v to_o 90_o degree_n in_o that_o place_n and_o that_o of_o 62_o be_v put_v by_o in_o some_o other_o place_n where_o it_o may_v serve_v as_o well_o 2._o the_o line_n of_o hour_n have_v a_o double_a margin_n viz_o one_o for_o hour_n and_o the_o other_o for_o azimuth_n &_o then_o every_o 5_o the_o minute_n be_v more_o proper_o make_v 4_o or_o else_o every_o 2_o minute_n and_o in_o a_o large_a rule_n to_o every_o quarter_n of_o a_o degree_n of_o azimuth_n or_o to_o every_o single_a minute_n of_o time_n 3._o the_o degree_n ought_v to_o be_v reckon_v after_o 3_o manner_n of_o way_n first_o as_o before_o be_v express_v second_o from_o 60_o towards_o the_o end_n with_o 10_o 20_o 30_o 40_o 50_o 60_o etc._n etc._n to_o be_v so_o account_v in_o find_v the_o azimuch_o for_o a_o particular_a latitude_n and_o and_o three_o from_o the_o head_n or_o 90_o towards_o the_o end_n with_o 10_o 20_o 30_o 40_o 50_o 60_o 70_o 80_o etc._n etc._n for_o the_o general_a find_v of_o hour_n and_o azimuth_n in_o any_o latitude_n and_o many_o other_o problem_n of_o the_o sphere_n beside_o to_o which_o may_v be_v add_v where_o room_n will_v allow_v a_o line_n of_o hour_n begin_v at_o 6_o at_o the_o head_n and_o 12_o at_o the_o end_n but_o reckon_v 15_o degree_n for_o a_o hour_n and_o 4_o minute_n for_o every_o degree_n it_o may_v do_v as_o well_o without_o it_o 4._o to_o the_o calendar_n of_o month_n and_o day_n be_v add_v a_o line_n of_o the_o sun_n true_a place_n in_o the_o zodiac_n or_o where_o room_n fail_v the_o character_n of_o the_o twelve_o sign_n put_v on_o that_o day_n of_o the_o month_n the_o sun_n enter_v into_o it_o and_o count_v every_o day_n for_o a_o degree_n may_v indifferent_o serve_v for_o the_o use_v it_o be_v chief_o intend_v for_o 5._o under_o that_o be_v a_o line_n of_o the_o sun_n right_a ascension_n to_o hour_n and_o quarter_n at_o least_o or_o rather_o every_o five_o minute_n number_v thus_o 12_o and_o 24_o right_n under_o ♈_o and_o ♎_o or_o the_o ten_o of_o march_n and_o so_o forward_o to_o the_o ten_o of_o june_n or_o ♋_o where_o stand_v 6_o then_o backward_o to_o 12_o where_o you_o begin_v then_o backward_o still_o to_o the_o eleven_o of_o december_n with_o 13_o 14_o 15_o 16_o 17_o 18_o to_o ♑_o then_z from_o thence_o forward_o to_o 24_o where_o you_o first_o begin_v but_o when_o you_o be_v straighten_v for_o room_n as_o on_o most_o ordinary_a rule_n you_o will_v be_v than_o it_o may_v very_o well_o suffice_v to_o have_v a_o point_n or_o stroke_n show_v when_o the_o sun_n shall_v gradual_o get_v a_o hour_n of_o right_a ascension_n and_o from_o that_o for_o every_o day_n count_v four_o minute_n of_o time_n till_o it_o have_v increase_v to_o a_o hour_n more_o and_o this_o computation_n will_v serve_v very_o well_o and_o in_o stead_n of_o say_v 13_o 14_o 15_o hour_n of_o right_a ascension_n say_v 1_o 2_o 3_o etc._n etc._n which_o will_v perform_v the_o work_n as_o well_o and_o reduce_v the_o time_n to_o more_o proper_a term_n 6._o there_o be_v fit_v two_o line_n one_o contain_v 24_o hour_n and_o the_o other_o 29_o day_n and_o about_o 13_o hour_n and_o they_o serve_v to_o find_v the_o time_n of_o the_o moon_n come_v to_o the_o south_n before_o or_o after_o the_o sun_n and_o by_o that_o the_o time_n of_o high-water_n at_o london-bridge_n or_o any_o other_o place_n as_o be_v ordinary_a chap._n iu._n the_o use_v follow_v in_o order_n 1._o to_o find_v the_o sun_n declination_n lay_v the_o thread_n on_o the_o day_n of_o the_o month_n then_o in_o the_o line_n of_o degree_n you_o have_v the_o declination_n from_o march_v the_o ten_o towards_o the_o head_n be_v the_o declination_n northward_o the_o other_o way_n be_v southward_o as_o by_o the_o time_n of_o the_o year_n be_v discover_v example_n on_o the_o ten_o of_o april_n it_o be_v 11_o 48_o '_o toward_z the_o north_n but_o on_o the_o ten_o of_o october_n it_o be_v 10_o 30_o '_o toward_z the_o south_n 2._o as_o the_o thread_n be_v so_o lay_v on_o the_o day_n of_o the_o month_n in_o the_o line_n of_o the_o sun_n place_n it_o show_v that_o and_o in_o the_o line_n of_o the_o sun_n right_a ascension_n his_o right_a ascension_n also_o only_o you_o must_v give_v it_o its_o due_a order_n of_o reckon_n as_o thus_o it_o begin_v at_o ♈_o aries_n and_o so_o proceed_v to_o ♋_o then_z back_o again_o to_o ♑_o at_o the_o eleven_o of_o december_n then_o forward_o again_o to_o ♈_o aries_n where_o you_o begin_v 3._o to_o find_v the_o sun_n right_a ascension_n in_o hour_n and_o minute_n lay_v the_o thread_n as_o before_o on_o the_o day_n of_o the_o month_n and_o in_o the_o line_n of_o right_a ascension_n you_o have_v the_o hour_n and_o minute_n require_v compute_v right_o according_a to_o the_o time_n of_o the_o year_n that_o be_v begin_v at_o the_o ten_o of_o march_n or_o ♈_o aries_n and_o so_o reckon_v forward_o and_o backward_o as_o the_o month_n go_v example_n on_o the_o ten_o of_o april_n the_o sun_n place_n be_v 1_o degree_n in_o ♉_o taurus_n and_o the_o sun_n right_a ascension_n 1_o hour_n 55_o minute_n on_o the_o ten_o of_o october_n 27_o 1_o 4_o in_o ♎_o libra_n and_o his_o right_a ascension_n be_v 13_o hour_n and_o 42_o minute_n 4._o to_o find_v the_o sun_n amplitude_n at_o rise_v or_o set_v take_v the_o sun_n declination_n out_o of_o the_o particular_a scale_n of_o altitude_n and_o lay_v it_o the_o same_o way_n as_o the_o declination_n be_v from_o 90_o in_o the_o azimuth_n scale_n and_o it_o shall_v show_v
not_o the_o time_n in_o common_a hour_n but_o be_v thus_o find_v add_v the_o compliment_n of_o the_o sun_n ascension_n and_o the_o star_n right_a ascension_n and_o the_o star_n hour_n last_o find_v together_o and_o the_o sun_n if_o less_o than_o 12_o or_o the_o remain_z 12_o be_v substract_v shall_v be_v the_o time_n of_o his_o rise_n in_o common_a hour_n but_o for_o his_o set_n add_v the_o star_n set_v last_o find_v to_o the_o other_o number_n and_o the_o sum_n or_o difference_n shall_v be_v the_o set_n example_n for_o the_o bulls-eye_n on_o the_o 23_o of_o december_n it_o rise_v at_o 2_o in_o the_o afternoon_n and_o set_v at_o 4._o 46_o in_o the_o morning_n 4._o to_o find_v the_o time_n of_o the_o sothe_v of_o any_o star_n on_o the_o rule_n or_o any_o other_o who_o right_a ascension_n and_o declination_n be_v know_v subtract_v the_o sun_n right_a ascension_n from_o the_o star_n increase_v by_o 24_o when_o you_o can_v do_v without_o and_o the_o remainder_n if_o less_o than_o 12_o be_v the_o time_n require_v in_o the_o afternoon_n or_o night_n before_o 12_o but_o if_o there_o remain_v more_o than_o 12_o subtract_v 12_o and_o the_o residue_n be_v the_o time_n from_o midnight_n to_o midday_n follow_v example_n lyons-heart_n on_o the_o ten_o of_o march_n the_o sun_n ascension_n be_v 0_o 2_o '_o lyons-heart_n whole_a right_a asc_n be_v 9_o 50_o '_o time_z of_o sothe_v be_v 9_o 48_o '_o at_o night_n 5._o to_o find_v how_o long_o any_o star_n will_v be_v above_o the_o horizon_n lay_v the_o thread_n to_o the_o star_n and_o in_o the_o hour-line_n it_o show_v the_o ascensional_a difference_n count_v from_o 90_o then_o note_n if_o the_o star_n have_v north_n declination_n add_v that_o to_o 6_o hour_n and_o the_o sum_n be_v half_a the_o time_n if_o south_n subtract_v it_o from_o 6_o and_o the_o residue_n be_v half_a the_o time_n and_o the_o compliment_n of_o each_o to_o 24_o be_v double_v be_v the_o whole_a nocturnal_a arch_n under_o the_o horizon_n example_n for_o the_o bulls-eye_n his_o ascensional_a difference_n will_v be_v find_v to_o be_v one_o hour_n 23_o minute_n which_o add_v to_o 6_o hour_n and_o double_a make_v 14._o 46_o the_o diurnal_a ark_n of_o the_o star_n and_o the_o residue_n from_o 24_o be_v 9_o 14._o for_o the_o nocturnal_a ark_n or_o the_o time_n of_o its_o be_v under_o the_o horizon_n chap._n ix_o to_o perform_v the_o foregoing_a work_n in_o any_o latitude_n as_o rise_v amplitude_n ascensional_a difference_n latitude_n hour_n and_o azimuth_n wherein_o i_o shall_v give_v only_o the_o rule_n and_o leave_v out_o the_o example_n for_o brevity_n sake_n 1._o for_o the_o rise_n and_o set_v and_o ascensional_a difference_n be_v all_o one_o do_v thus_o take_v the_o sun_n declination_n out_o of_o the_o general_a scale_n of_o altitude_n than_o set_v one_o foot_n of_o the_o compass_n in_o the_o colatitude_n on_o the_o same_o scale_n and_o with_o the_o other_o lie_v the_o thread_n to_o the_o nigh_a distance_n then_o the_o thread_n so_o lay_v take_v the_o nigh_a distance_n from_o the_o latitude_n to_o the_o thread_n with_o that_o distance_n set_v one_o foot_n in_o the_o sun_n declination_n count_v from_o 90_o towards_o the_o centre_n and_o the_o thread_n lay_v to_o the_o near_a distance_n shall_v in_o the_o degree_n show_v the_o ascensional_a difference_n require_v count_v from_o 90_o at_o the_o head_n towards_o the_o end_n of_o the_o rule_n and_o if_o you_o reduce_v those_o degree_n and_o minute_n to_o time_n you_o have_v the_o rise_n and_o set_v before_o and_o after_o 6_o according_a to_o the_o declination_n and_o time_n of_o the_o year_n 2._o to_o find_v the_o sun_n amplitude_n take_v the_o sun_n declination_n and_o set_v one_o foot_n in_o the_o colatitude_n with_o the_o other_o lie_v the_o thread_n to_o the_o near_a distance_n and_o on_o the_o degree_n it_o show_v the_o sun_n amplitude_n at_o rise_v or_o set_v count_v as_o beâ—ore_v from_o 90_o to_o the_o left_a end_n of_o the_o rule_n 3._o have_v amplitude_n and_o declination_n to_o find_v the_o latitude_n take_v the_o declination_n from_o the_o general_a scale_n and_o set_v one_o foot_n in_o the_o amplitude_n the_o thread_n lay_v to_o the_o near_a distance_n in_o the_o line_n of_o degree_n it_o show_v the_o compliment_n of_o the_o latitude_n require_v or_o the_o converse_n 4._o have_v latitude_n sun_n declination_n and_o altitude_n to_o find_v the_o height_n at_o 6_o and_o then_o at_o any_o other_o time_n of_o the_o day_n and_o year_n count_n the_o declination_n in_o the_o degree_n from_o 90_o towards_o the_o end_n thereto_o lay_v the_o thread_n the_o least_o distance_n from_o which_o to_o the_o latitude_n in_o the_o general_a scale_n shall_v be_v the_o sun_n height_n at_o 6_o in_o the_o summer_n or_o his_o depression_n in_o the_o winter_n the_o compass_n stand_v at_o this_o distance_n take_v measure_n on_o the_o general_a scale_n of_o altitude_n from_o the_o begin_n at_o the_o pin_n towards_o 90_o keep_v one_o point_n there_o open_v the_o other_o to_o the_o sun_n altitude_n thus_o have_v you_o substract_v the_o height_n at_o 6_o out_o of_o the_o sun_n altitude_n but_o in_o winter_n you_o must_v add_v the_o depression_n at_o 6_o which_o be_v all_o one_o at_o the_o same_o declination_n with_o his_o height_n at_o 6_o in_o summer_n and_o that_o be_v do_v thus_o put_v one_o point_n of_o the_o compass_n so_o set_v in_o the_o general_a scale_n to_o the_o sun_n altitude_n then_o turn_v the_o other_o outward_n towards_o 90_o there_o keep_v it_o then_o open_a the_o compass_n to_o the_o begin_n of_o the_o scale_n then_o have_v you_o add_v it_o to_o the_o sun_n altitude_n have_v this_o distance_n set_v one_o foot_n in_o the_o colatitude_n on_o the_o general_a scale_n lay_v the_o thread_n to_o the_o near_a distance_n the_o thread_n so_o lay_v take_v the_o near_a distance_n from_o 90_o to_o the_o thread_n than_o set_v one_o foot_n in_o the_o declination_n count_v from_o 90_o and_o on_o the_o degree_n it_o show_v the_o hour_n from_o 6_o reckon_v from_o the_o head_n or_o from_o 12_o count_v from_o the_o end_n of_o the_o rule_n i_o shall_v make_v all_o more_o plain_a by_o make_v three_o proposition_n of_o it_o thus_o prop._n 1._o to_o find_v the_o hour_n in_o the_o aequinoctial_a take_v the_o altitude_n from_o the_o begin_n of_o the_o general_a scale_n of_o altitude_n and_o set_v one_o foot_n in_o the_o colatitude_n the_o thread_n lay_v to_o the_o near_a distance_n with_o the_o other_o foot_n in_o the_o degree_n shall_v show_v the_o hour_n from_o 6_o count_v from_o 90_o and_o allow_v for_o every_o 15_o 1_o hour_n and_o 4_o min_fw-mi for_o every_o degree_n prop._n 2._o to_o find_v it_o at_o just_a 6._o be_v before_o express_v by_o the_o converse_n of_o the_o first_o part_n of_o the_o four_o which_o i_o shall_v again_o repeat_v prop._n 3._o to_o find_v it_o at_o any_o time_n do_v thus_o count_n the_o sun_n declination_n in_o the_o degree_n thereunto_o lay_v the_o thread_n the_o least_o distance_n to_o which_o from_o latitude_n in_o the_o general_a scale_n shall_v be_v the_o sun_n altitude_n at_o 6_o which_o distance_n in_o summer_n you_o must_v subtract_v from_o but_o in_o winter_n you_o must_v add_v to_o the_o sun_n present_a altitude_n have_v that_o distance_n set_v one_o foot_n in_o the_o coaltitude_n with_o the_o other_o lie_v the_o thread_n to_o the_o near_a distance_n take_v again_o the_o near_a distance_n from_o 90_o to_o the_o thread_n than_o set_v one_o foot_n in_o the_o sun_n diclination_n count_v from_o 90_o and_o lay_v the_o thread_n to_o the_o near_a distance_n and_o in_o the_o degree_n it_o shall_v show_v the_o hour_n require_v example_n at_o 10_o declination_n north_n and_o 30_o high_a latitude_n 51._o 32_o the_o hour_n be_v find_v to_o be_v 8._o 25_o count_v 90_o for_o 6_o and_o so_o forward_o again_o at_o 20_o degree_n of_o declination_n south_n and_o 10_o degree_n of_o altitude_n i_o find_v the_o hour_n in_o the_o same_o latitude_n to_o be_v 17_o minute_n past_o 9_o have_v latitude_n delination_n and_o altitude_n to_o find_v the_o sun_n azimuth_n take_v the_o sine_fw-la of_o the_o declination_n put_v one_o foot_n in_o the_o latitude_n the_o thread_n lay_v to_o the_o near_a distance_n in_o the_o degree_n it_o show_v the_o sun_n height_n at_o due_a east_n or_o west_n which_o you_o must_v in_o summer_n subtract_v from_o the_o sun_n altitude_n as_o before_o on_o the_o general_a scale_n of_o altitude_n with_o which_o distance_n put_v one_o foot_n in_o the_o colatitude_n and_o lay_v the_o thread_n to_o the_o near_a distance_n then_o take_v the_o near_a distance_n from_o the_o sine_fw-la of_o the_o latitude_n fit_a that_o again_o in_o the_o colatitude_n and_o the_o thread_n lay_v to_o the_o heere_v
distance_n in_o the_o degree_n shall_v show_v the_o sun_n azimuth_n require_v 6._o but_o in_o winter_n you_o must_v do_v thus_o by_o the_o second_o proposition_n of_o the_o nine_o chapter_n find_v the_o sun_n amplitude_n for_o that_o day_n then_o take_v the_o altitude_n from_o the_o general_a scale_n of_o altitude_n and_o put_v one_o point_n in_o colatitude_n lay_v the_o thread_n to_o the_o near_a distance_n than_o the_o near_a distance_n from_o the_o latitude_n must_v be_v add_v to_o the_o sun_n amplitude_n this_o distance_n so_o add_v must_v be_v set_v from_o the_o coaltitude_n and_o the_o thread_n lay_v to_o the_o high_a distance_n and_o in_o the_o line_n of_o degree_n it_o give_v the_o azimuth_n from_o south_n count_v from_o the_o end_n of_o the_o rule_n or_o from_o the_o east_n or_o west_n count_v from_o the_o head_n or_o 90_o degree_n example_n at_o 15_o degree_n of_o declination_n and_o 10_o altitude_n latitude_n 51._o 32._o the_o azimuth_n be_v 49._o 20._o from_o the_o south_n or_o 40_o degree_n and_o 40_o '_o from_o east_n or_o west_n chap._n x._o to_o find_v all_o the_o necessary_a quesita_fw-la for_o any_o erect_a decline_a sundial_n both_o particular_o and_o general_a by_o the_o line_n on_o the_o dial_n side_n also_o by_o number_n sin_n and_o tangent_n artificial_a be_v logarithm_n on_o a_o rule_n 1._o first_o a_o particular_a for_o the_o substile_a count_n the_o plain_n declination_n on_o â—he_n azimuth_n scale_n from_o 90_o towards_o the_o end_n and_o thereunto_o lie_v the_o thread_n in_o the_o line_n of_o degree_n it_o show_v the_o distance_n of_o the_o substile_a from_o 12._o example_n at_o 10_o degree_n declination_n i_o find_v 7._o 51._o for_o the_o substile_a 2._o for_o the_o height_n of_o the_o stile_n above_o the_o substile_a take_v the_o plain_n declination_n from_o 90_o in_o the_o azimuth_n line_n but_o count_v from_o the_o south_n end_n between_o your_o compass_n and_o measure_v it_o in_o the_o particular_a scale_n of_o altitude_n and_o it_o shall_v give_v the_o height_n of_o the_o stile_n require_v example_n at_o 30_o declination_n be_v 32._o 35._o 3._o for_o the_o inclination_n of_o meridian_n count_v the_o substile_a on_o the_o particular_a scale_n of_o altitude_n and_o take_v that_o distance_n between_o your_o compass_n measure_v this_o distance_n on_o the_o azimuth_n line_n from_o 90_o towards_o the_o end_n and_o count_v that_o way_n it_o show_v the_o inclination_n of_o meridian_n require_v example_n at_o 15_o the_o substile_a the_o inclination_n of_o meridian_n will_v be_v find_v to_o be_v 24._o 36._o 4._o to_o find_v the_o angle_n of_o 6_o from_o 12._o take_v the_o plain_n declination_n from_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_n point_v lay_v the_o thread_n then_o on_o the_o line_n of_o degree_n you_o have_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 note_v this_o rule_n as_o this_o line_n be_v draw_v do_v not_o give_v this_o angle_n exact_o neither_o will_v it_o be_v worth_a the_o while_n to_o delineate_v another_o line_n for_o this_o purpose_n but_o if_o it_o be_v require_v it_o may_v be_v do_v but_o i_o rather_o prefer_v this_o help_n the_o great_a error_n be_v about_o the_o space_n of_o 45_o minute_n of_o the_o first_o degree_n in_o the_o particular_a scale_n of_o altitude_n so_o that_o if_o you_o conceive_v those_o 45_o minute_n to_o be_v divide_v as_o the_o particular_a scale_n of_o altitude_n be_v like_o a_o natural_a sine_fw-la and_o if_o your_o declination_n be_v 30_o then_o take_v half_a the_o space_n of_o the_o 45_o minute_n less_o and_o that_o shall_v be_v the_o true_a distance_n to_o lay_v on_o the_o azimuth_n line_n from_o 90_o whereunto_o to_o lay_v the_o thread_n example_n a_o plain_a decline_v 30_o degree_n the_o angle_n will_v be_v find_v to_o be_v 32._o 21._o who_o compliment_n 57_o 49._o be_v the_o angle_n require_v 5._o to_o perform_v the_o same_o general_o by_o the_o general_a scale_n of_o altitude_n and_o first_o for_o the_o stile_n lay_v the_o thread_n to_o the_o compliment_n of_o the_o latitude_n count_v in_o the_o degree_n from_o the_o head_n towards_o the_o end_n than_o the_o night_a distance_n from_o the_o compliment_n of_o the_o plain_n declination_n to_o the_o thread_n take_v and_o measure_v on_o the_o general_a scale_n from_o the_o centre_n shall_v be_v the_o style_n height_n require_v 6._o to_o find_v the_o inclination_n of_o meridian_n take_v the_o plain_n declination_n from_o the_o general_a scale_n and_o fit_v it_o in_o the_o compliment_n of_o the_o style_n elevation_n and_o lay_v the_o thread_n to_o the_o near_a distance_n and_o on_o the_o degree_n it_o show_v the_o inclination_n of_o meridian_n require_v 7._o for_o the_o substile_a count_n in_o the_o inclination_n of_o meridian_n on_o the_o degree_n from_o 90_o and_o thereto_o lie_v the_o thread_n then_o take_v the_o least_o distance_n from_o the_o latitude_n compliment_n to_o the_o thread_n set_v one_o foot_n of_o that_o distance_n in_o 90_o and_o lay_v the_o thread_n to_o the_o near_a distance_n and_o in_o the_o degree_n it_o shall_v show_v the_o substile_a from_o 12_o require_v 8._o for_o the_o angle_n of_o 6_o from_o 12._o take_v the_o side_n of_o the_o square_n or_o the_o measure_n of_o the_o parallel_n from_o 12_o and_o fit_v it_o in_o the_o cousin_n of_o the_o latitude_n and_o lay_v the_o thread_n to_o the_o nigh_a distance_n then_o take_v out_o the_o near_a distance_n from_o the_o sine_fw-la of_o the_o latitude_n to_o the_o thread_n then_o fit_a that_o over_o in_o the_o sine_fw-la of_o 90_o and_o to_o the_o near_a distance_n lay_v the_o thread_n then_o take_v the_o near_a distance_n from_o the_o sine_fw-la of_o the_o plain_n declination_n to_o the_o thread_n and_o it_o shall_v reach_v on_o the_o parallel_a line_n or_o side_n of_o the_o square_n from_o the_o horizon_n to_o 6_o a_o clock_n line_v require_v four_o canon_n 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degree_n on_o the_o other_o side_n of_o the_o rule_n and_o lay_v off_o 15_o 30_o and_o 45_o for_o every_o whole_a hour_n or_o every_o 3_o degree_n and_o 45_o minute_n for_o every_o quarter_n from_o d_o and_o e_z toward_z f_o and_o g_o for_o 7_o 8_o 9_o and_o for_o 3_o 4_o and_o 5_o a_o clock_n hour_n point_v last_o set_v c_o d_o or_o b_o e_z in_o the_o tangent_fw-la of_o 45_o and_o lay_v the_o same_o point_n of_o 15_o 30_o 45_o both_o way_n from_o b_o or_o 12_o for_o 10_o 11_o and_o 1_o 2_o and_o to_o all_o those_o point_n draw_v line_n for_o the_o true_a hour-line_n require_v for_o lay_v down_o the_o style_v height_n if_o you_o take_v the_o latitude_n compliment_n out_o of_o the_o tangent-line_n as_o the_o sector_n stand_v to_o prick_v the_o noon_n hour_n and_o set_v it_o on_o the_o line_n d_o f_o or_o e_o g_o from_o d_o or_o e_z downward_o from_o d_o to_o h_n it_o will_v show_v you_o where_o to_o draw_v c_o h_n for_o the_o style_n then_o to_o those_o line_n set_v figure_n and_o plant_v the_o dial_n horizontal_a and_o the_o style_v perpendicular_a and_o right_a north_n and_o south_n and_o it_o shall_v show_v when_o the_o sun_n shine_v the_o true_a hour_n of_o the_o day_n note_v well_o the_o figure_n follow_v chap._n xii_o to_o draw_v a_o vertical_a direct_v south_n or_o north_n dyal_n first_o draw_v a_o perpendicular_a line_n for_o 12_o a_o clock_n then_o in_o that_o line_n at_o the_o upper_a end_n in_o the_o south_n plain_a and_o at_o the_o low_a end_n in_o a_o north_n plain_a appoint_v a_o place_n for_o the_o centre_n through_o which_o point_n across_o it_o at_o right_a angle_n a_o horizontall_a dial_n a_o south_n dial_n for_o 6_o and_o 6_o as_o you_o do_v in_o the_o horizontal_a plain_n as_o the_o line_n a_o b_o and_o c_o d_o on_o each_o side_n 12_o make_v two_o parallel_n as_o in_o the_o horizontal_a then_o take_v a_o d_o the_o parallel_n and_o fit_v it_o in_o the_o sine_fw-la of_o the_o latitude_n compliment_n and_o take_v out_o the_o sine_fw-la of_o 90_o 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or_o west_n dial_n the_o distance_n from_o six_o to_o nine_o or_o from_o six_o to_o three_o in_o the_o west_n be_v the_o height_n of_o the_o stile_n in_o the_o east_n and_o west_n dial_n and_o must_v stand_v in_o the_o six_o a_o clock_n line_n and_o parallel_v to_o the_o plain_a chap._n xiii_o to_o find_v the_o declination_n of_o any_o plain_a for_o the_o find_n of_o the_o declination_n of_o a_o plain_a the_o most_o usual_a and_o easy_a way_n be_v by_o a_o magnetical_a needle_n fit_v according_a to_o mr._n fail_v way_n in_o the_o index_n of_o a_o declinatory_n or_o in_o a_o square_a box_n with_o the_o 90_o degree_n of_o a_o quadrant_a on_o the_o two_o side_n or_o by_o a_o needle_n fit_v on_o the_o index_n of_o a_o quadrant_a after_o all_o which_o way_n you_o may_v have_v they_o at_o the_o sign_n of_o the_o sphere_n and_o sundial_n in_o the_o minory_n make_v by_o john_n brown_n but_o the_o work_n may_v be_v very_o ready_o and_o exact_o perform_v by_o the_o rule_n either_o by_o the_o sun_n or_o needle_n in_o this_o manner_n follow_v of_o which_o two_o way_n that_o by_o the_o sun_n be_v always_o the_o best_a and_o most_o exact_a and_o artificial_a and_o the_o other_o not_o to_o be_v use_v if_o i_o may_v advise_v but_o when_o the_o other_o fail_v by_o the_o sun_n not_o shine_v or_o as_o a_o proof_n or_o confirmation_n of_o the_o other_o and_o first_o by_o the_o needle_n because_o the_o easy_a for_o this_o purpose_n you_o must_v have_v a_o needle_n well_o touch_v with_o the_o loadstone_n of_o about_o three_o or_o four_o inch_n long_o and_o fit_v into_o a_o box_n somewhat_o broad_a than_o one_o of_o the_o leg_n of_o the_o sector_n with_o a_o lid_n to_o open_v and_o shut_v and_o on_o the_o inside_n of_o the_o lid_n may_v be_v draw_v a_o south_n erect_v dial_n and_o a_o wire_n to_o set_v the_o lid_n upright_o and_o a_o thread_n to_o be_v the_o gnomon_n or_o stile_n to_o that_o dial_n it_o will_v not_o be_v a_o miss_n also_o to_o extend_v the_o line_n on_o the_o horizontal_a part_n for_o the_o same_o thread_n be_v a_o stile_n for_o that_o also_o also_o on_o the_o bottom_n let_v there_o be_v a_o rabbit_n or_o grove_n make_v to_o fit_v the_o leg_n of_o the_o rule_n or_o sector_n so_o as_o be_v press_v into_o it_o it_o may_v not_o fall_v off_o from_o the_o rule_n if_o your_o hand_n shall_v shake_v or_o you_o cease_v to_o hold_v it_o there_o this_o be_v so_o fit_v the_o use_n follow_v in_o their_o order_n put_v your_o box_n and_o needle_n on_o that_o leg_n of_o the_o rule_n that_o will_v be_v most_o fit_a for_o your_o purpose_n and_o also_o the_o north_n end_n of_o the_o needle_n towards_o the_o wall_n if_o it_o be_v a_o south_n wall_n and_o the_o contrary_a if_o a_o north_n as_o the_o play_v of_o the_o needle_n will_v direct_v you_o better_a than_o the_o way_n how_o in_o a_o thousand_o word_n then_o open_a or_o close_o the_o rule_n till_o the_o needle_n play_v right_a over_o the_o north_n and_o south-line_n in_o the_o bottom_n of_o the_o box_n then_o the_o compliment_n of_o the_o angle_n that_o the_o sector_n stand_v at_o which_o may_v always_o be_v under_o 90_o degree_n be_v the_o declination_n of_o the_o plain_a but_o if_o it_o happen_v to_o stand_v at_o any_o angle_n above_o 90_o than_o the_o quantity_n thereof_o above_o 90_o be_v the_o declination_n of_o the_o wall_n to_o find_v the_o quantity_n of_o the_o angle_n the_o sector_n stand_v at_o may_v be_v do_v two_o way_n first_o by_o protraction_n by_o lay_v down_o the_o
rule_n so_o set_v on_o a_o board_n and_o draw_v two_o line_n by_o the_o leg_n of_o the_o sector_n and_o find_v the_o angle_n by_o a_o line_n of_o chord_n second_o more_o speedy_o and_o artificial_o thus_o by_o the_o line_n of_o sines_n be_v draw_v to_o 2._o 4_o or_o 6_o degree_n asunder_o the_o sector_n so_o set_v take_v the_o parallel_n sine_fw-la of_o 30_o and_o 30_o and_o measure_v it_o on_o the_o lateral_a sin_n from_o the_o centre_n and_o it_o shall_v reach_v to_o the_o sine_fw-la of_o half_a the_o angle_n the_o line_n of_o sin_n stand_v at_o be_v more_o by_o 2_o 4_o or_o 6_o degree_n then_o the_o sector_n stand_v at_o because_o it_o be_v draw_v one_o two_o or_o three_o degree_n from_o the_o inside_n or_o else_o take_v the_o latteral_a sine_fw-la of_o 30_o from_o the_o centre_n and_o keep_v one_o foot_n fix_v in_o 30_o turn_v the_o other_o till_o it_o cross_v the_o line_n of_o sin_n on_o that_o line_n next_o the_o inside_n and_o count_v from_o 90_o it_o shall_v touch_v at_o the_o 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labour_n may_v be_v save_v i_o take_v the_o parallel_n sine_fw-la of_o 30_o and_o measure_v it_o from_o the_o centre_n it_o reach_v suppose_v to_o the_o sine_fw-la of_o 20_o then_o be_v the_o line_n of_o sin_n at_o a_o angle_n of_o 40_o degree_n but_o the_o sector_n at_o two_o degree_n less_o viz._n 38_o degree_n who_o compliment_n 52_o be_v the_o declination_n then_o to_o consider_v which_o way_n mind_n thus_o first_o it_o be_v south_n because_o the_o sun_n be_v in_o the_o south_n shine_v on_o the_o wall_n second_o consider_v the_o sun_n be_v in_o the_o east_n it_o shine_v also_o on_o the_o wall_n therefore_o it_o be_v east_n plain_a thus_o have_v you_o get_v the_o denomination_n which_o way_n and_o also_o the_o quantity_n how_o much_o that_o way_n or_o if_o you_o take_v the_o latteral_a sine_fw-la of_o 30_o from_o the_o centre_n and_o turn_v the_o point_n of_o the_o compass_n from_o 30_o towards_o 90_o on_o the_o other_o leg_n you_o shall_v find_v it_o to_o reach_v to_o the_o sine_fw-la of_o 50_o degree_n who_o compliment_n count_v from_o 90_o be_v 40_o or_o rather_o 38_o for_o the_o reason_n before-said_a or_o else_o add_v 2_o to_o 50_o and_o you_o have_v the_o angle_n require_v without_o complement_n of_o it_o be_v the_o true_a declination_n seek_v for_o thus_o by_o the_o needle_n you_o may_v get_v the_o declination_n of_o any_o wall_n which_o in_o cloudy_a weather_n may_v stand_v you_o in_o good_a stead_n or_o to_o examine_v a_o observation_n by_o the_o sun_n as_o to_o the_o mis-counting_a or_o mistake_v therein_o but_o for_o exactness_n the_o sun_n be_v always_o the_o best_a because_o the_o needle_n though_o never_o so_o good_a may_v be_v draw_v aside_o by_o iron_n in_o the_o wall_n and_o also_o by_o some_o kind_n of_o brick_n therefore_o not_o to_o be_v too_o much_o trust_v unto_o to_o find_v a_o declination_n by_o the_o sun_n first_o open_v the_o rule_n to_o a_o angle_n of_o 60_o degree_n as_o you_o do_v to_o find_v the_o hour_n of_o the_o day_n and_o put_v a_o pin_n in_o the_o hole_n and_o hang_v the_o thread_n and_o plummet_n on_o the_o pin_n also_o you_o must_v have_v another_o thread_n somewhat_o long_o and_o grosser_n than_o that_o for_o the_o hour_n in_o a_o readiness_n for_o your_o use_n then_o apply_v the_o head_n leg_n to_o the_o wall_n if_o the_o sun_n be_v come_v on_o the_o plain_a and_o hold_v the_o rule_n horizontal_a or_o level_a then_o hold_v up_o the_o long_a thread_n till_o the_o shadow_n fall_v right_a over_o the_o pin_n or_o the_o centre_n hole_n at_o the_o same_o instant_n the_o shadow_n shall_v show_v on_o the_o degree_n how_o much_o the_o sun_n want_v of_o come_v to_o be_v just_a against_o the_o plain_a which_o i_o call_v the_o meridian_n or_o pole_n of_o the_o plain_a which_o number_n you_o must_v write_v down_o thus_o as_o suppose_v it_o fall_v on_o 40_o write_v down_o 40-00_a want_n then_o as_o soon_o as_o may_v be_v take_v the_o sun_n true_a altitude_n and_o write_v that_o down_o also_o with_o which_o you_o must_v find_v the_o sun_n azimuth_n then_o subtract_v the_o great_a out_o of_o the_o less_o and_o the_o remainder_n be_v the_o declination_n require_v but_o for_o a_o general_a rule_n take_v this_o if_o the_o sun_n do_v want_n of_o come_v to_o the_o meridian_n of_o the_o place_n and_o also_o want_v of_o come_v to_o the_o meridian_n of_o the_o plain_a than_o you_o must_v always_o subtract_v the_o great_a number_n out_o of_o the_o less_o whether_o it_o be_v forenoon_n or_o afternoon_n so_o likewise_o when_o the_o sun_n be_v pass_v the_o meridian_n and_o past_o the_o plain_a also_o but_o if_o the_o sign_n be_v unlike_a that_o be_v to_o say_v one_o past_o the_o plain_n or_o meridian_n and_o the_o other_o want_n either_o of_o the_o plain_a or_o meridian_n than_o you_o must_v add_v they_o together_o and_o the_o sum_n be_v the_o declination_n from_o the_o south_n which_o rule_n for_o better_a tenaciousness_n sake_n take_v in_o this_o homely_a rhyme_n sign_n both_o alike_o substraction_n do_v require_v but_o unlike_a sign_n addition_n do_v desire_v the_o further_a illustration_n by_o two_o or_o three_o example_n suppose_v on_o the_o first_o of_o may_n in_o the_o forenoon_n i_o come_v and_o apply_v the_o rule_n be_v open_v to_o his_o angle_n of_o 60_o degree_n to_o the_o wall_n viz._n the_o head_n leg_n or_o the_o leg_n where_o the_o centre_n be_v and_o hold_v up_o my_o thick_a thread_n and_o plummet_n so_o as_o the_o shadow_n of_o it_o cross_v the_o centre_n and_o at_o the_o same_o instant_n also_o on_o 60_o degree_n than_o i_o say_v the_o sun_n want_v 60_o deg_n of_o come_v to_o the_o meridian_n of_o the_o plain_a at_o the_o same_o instant_n or_o as_o soon_o as_o possible_a i_o can_v i_o take_v the_o sun_n altitude_n as_o before_o be_v show_v and_o set_v that_o down_o which_o suppose_v it_o to_o be_v 20_o degree_n then_o by_o the_o rule_v before_o get_v the_o sun_n azimuth_n for_o that_o day_n and_o altitude_n which_o in_o our_o example_n will_v be_v find_v to_o be_v 94_o degree_n from_o the_o south_n or_o meridian_n then_o in_o regard_n the_o sign_n be_v both_o alike_o i._n e._n want_n if_o you_o subtract_v one_o out_o of_o the_o other_o there_o remain_v 34_o the_o declination_n require_v but_o for_o the_o right_a denomination_n which_o way_n either_o north_n or_o south_n towards_o either_o east_n or_o west_n observe_v this_o plain_a rule_n first_o if_o the_o sun_n come_v to_o the_o meridian_n or_o pole_n of_o the_o plain_a before_o it_o come_v to_o the_o meridian_n or_o pole_n of_o the_o place_n than_o it_o be_v always_o a_o east-plain_a but_o if_o the_o contrary_a it_o be_v a_o west-plain_a that_o be_v to_o say_v if_o the_o sun_n come_v to_o the_o meridian_n or_o pole_n of_o the_o place_n before_o it_o come_v to_o the_o meridian_n or_o pole_n of_o the_o plain_a than_o it_o be_v a_o west-plain_a also_o if_o the_o sum_n or_o remainder_n after_o addition_n or_o substraction_n be_v under_o 90_o it_o be_v a_o south-plain_a but_o if_o it_o be_v above_o 90_o it_o be_v a_o north-plain_a also_o note_n that_o when_o the_o sum_n or_o remainder_n be_v above_o 90_o than_o the_o compliment_n to_o 180_o be_v always_o the_o declination_n from_o the_o north_n towards_o either_o east_n or_o west_n so_o that_o according_a to_o these_o rule_n in_o our_o example_n it_o be_v 34_o degree_n southeast_n again_o in_o the_o morning_n june_n 13._o i_o apply_v my_o rule_n to_o the_o wall_n and_o i_o find_v the_o sun_n be_v pass_v the_o pole_n or_o meridian_n of_o the_o plain_a 10_o degree_n and_o the_o altitude_n at_o the_o same_o time_n 15_o degree_n the_o azimuth_n at_o that_o altitude_n and_o
to_o add_v the_o height_n of_o your_o eye_n from_o the_o ground_n at_o the_o time_n of_o take_v the_o angle_n to_o the_o altitude_n find_v for_o the_o operation_n of_o this_o extend_v the_o compass_n from_o the_o sine_fw-la of_o the_o compliment_n of_o the_o angle_n find_v to_o the_o number_n of_o the_o measure_a side_n on_o the_o line_n of_o number_n that_o distance_n apply_v the_o same_o way_n from_o the_o sine_fw-la of_o the_o angle_n find_v shall_v reach_v on_o the_o line_n of_o number_n to_o altitude_n require_v example_n at_o one_o station_n i_o open_v my_o rule_n and_o hang_v on_o the_o thread_n and_o plummet_n on_o the_o centre_n and_o observe_v the_o angle_n at_o c_o i_o find_v it_o to_o be_v 41._o 45_o and_o the_o angle_n at_o b_o the_o compliment_n of_o it_o 48._o 15_o and_o the_o measure_n from_o c_o to_o a_o 271_o foot_n then_o the_o work_n be_v so_o prepare_v be_v thus_o as_o the_o sine_fw-la of_o 48._o 15_o be_v to_o 271_o the_o measure_n of_o the_o side_n opposite_a to_o it_o so_o be_v the_o sine_fw-la of_o the_o angle_n 41._o 45_o to_o 242_o the_o measure_n of_o the_o side_n a_o b_o opposite_a to_o the_o angle_n at_o c_o the_o height_n require_v again_o at_o the_o station_n d_o 160_o foot_n from_o a_o i_o observe_v and_o find_v the_o angle_n d_o to_o be_v 56._o 30_o the_o angle_n at_o a_o be_v the_o compliment_n thereof_o viz._n 33._o 30._o this_o be_v prepare_v i_o extend_v my_o compass_n from_o the_o sine_fw-la of_o 33._o 30_o to_o 160_o on_o the_o line_n of_o number_n the_o same_o extent_n will_v reach_v from_o the_o sine_fw-la of_o 56._o 30_o to_o 242_o on_o the_o line_n of_o number_n lack_v a_o small_a fraction_n with_o which_o i_o shall_v not_o trouble_v you_o a_o example_n at_o two_o station_n as_o the_o sine_fw-la of_o the_o difference_n which_o be_v the_o angle_n c_o b_o d_o 14._o 45_o be_v to_o the_o side_n measure_v viz._n d_o c_o 111_o foot_n on_o the_o number_n so_o be_v the_o sine_fw-la of_o the_o angle_n at_o c_o 41._o 45_o to_o the_o measure_n of_o the_o side_n b_o c_o the_o hypothenusa_fw-la or_o measure_n from_o your_o eye_n to_o the_o top_n of_o the_o object_n viz._n 290_o foot_n again_o for_o the_o second_o operation_n as_o the_o sine_fw-la of_o 90_o the_o right_a angle_n at_o a_o be_v to_o 290_o the_o hypothenusa_fw-la b_o d_o so_o be_v the_o sine_fw-la of_o 56._o 30_o the_o angle_n at_o the_o first_o station_n d_o to_z 242_o the_o altitude_n b_o a_o the_o thing_n require_v so_o also_o be_v the_o sine_fw-la of_o the_o angle_n at_o b_o 33._o 70_o the_o compliment_n of_o 56_o 30._o to_o 160_o the_o distance_n from_o d_o to_z a._n to_o perform_v the_o same_o by_o the_o line_n of_o sin_n draw_v from_o the_o centre_n on_o the_o flat-side_n and_o the_o line_n of_o line_n or_o equal_a part_n or_o inch_n in_o ten_o part_n to_o work_v these_o or_o any_o other_o question_n by_o the_o line_n of_o natural_a sin_n and_o tangent_n on_o the_o flat-side_n draw_v from_o the_o centre_n it_o be_v but_o change_v the_o term_n thus_o as_o the_o measure_a distance_n take_v out_o of_o the_o line_n of_o line_n or_o any_o scale_n of_o equal_a part_n be_v to_o the_o sine_fw-la of_o the_o angle_n opposite_a to_o that_o measure_a side_n fit_v across_o from_o one_o leg_n to_o the_o other_o the_o sector_n so_o stand_v take_v out_o the_o parallel_n sine_fw-la of_o the_o angle_n opposite_a to_o the_o inquire_v side_n and_o that_o measure_n shall_v reach_v on_o the_o line_n of_o equal_a part_n to_o the_o measure_n of_o the_o altitude_n requiâ—â—â—_n example_n as_o before_o take_v out_o of_o the_o line_n or_o inch_n 2._o 71_o and_o fit_v it_o in_o the_o sine_fw-la of_o 48._o 15_o across_o from_o one_o leg_n to_o the_o other_o which_o i_o call_v a_o parral_n sine_fw-la but_o when_o you_o measure_n from_o the_o centre_n onward_o the_o end_n i_o call_v it_o a_o latteral_a sine_fw-la then_o take_v out_o the_o parallel_n sine_fw-la of_o 41._o 45_o and_o measure_v it_o on_o the_o line_n of_o inch_n or_o equal_a part_n and_o it_o shall_v reach_v to_o 2_o inch_n 42_o part_n or_o 242_o the_o altitude_n require_v after_o the_o same_o manner_n may_v question_n be_v wrought_v on_o the_o line_n of_o line_n sin_n or_o tangent_n alone_o or_o any_o one_o with_o the_o other_o by_o change_v the_o logarithmetical_a canon_n from_o the_o first_o to_o the_o second_o or_o three_o and_o the_o second_o or_o three_o to_o the_o first_o to_o second_o as_o the_o case_n shall_v require_v from_o a_o great_a to_o a_o less_o and_o the_o contrary_a for_o the_o four_o be_v always_o the_o same_o of_o which_o in_o the_o use_n of_o the_o sector_n by_o edmund_n gunter_n you_o may_v find_v many_o example_n to_o which_o i_o refer_v you_o also_o without_o the_o line_n of_o sin_n either_o natural_a or_o artificial_a you_o may_v find_v altitude_n by_o put_v the_o line_n of_o quadrat_fw-la or_o shadow_n on_o the_o rule_n as_o in_o a_o quadrant_a than_o the_o direction_n in_o the_o use_n of_o the_o quadrat_fw-la page_n 146_o of_o the_o carpenter_n rule_n will_v serve_v your_o turn_n which_o run_v thus_o as_o 100_o or_o 50_o according_a as_o it_o be_v divide_v to_o the_o part_n cut_v by_o the_o thread_n so_o be_v the_o distance_n measure_v to_o the_o height_n require_v which_o work_n be_v perform_v by_o the_o line_n of_o number_n only_o or_o again_o as_o the_o part_n cut_v to_o 100_o or_o 50_o so_o be_v the_o height_n to_o the_o distance_n require_v but_o when_o the_o thread_n fall_v on_o the_o contrary_a shadow_n that_o be_v make_v a_o angle_n above_o 45_o than_o the_o work_n be_v just_a the_o contrary_n to_o the_o former_a what_o be_v speak_v here_o of_o take_v of_o altitude_n may_v be_v apply_v to_o the_o take_n of_o distance_n for_o if_o the_o sector_n be_v fit_v with_o a_o staff_n and_o a_o ball-socket_n you_o may_v turn_v it_o either_o horizontal_a or_o perpendicular_a and_o so_o take_v any_o angle_n with_o it_o very_o convenient_o and_o ready_o by_o the_o same_o rule_n and_o direction_n as_o be_v give_v for_o the_o find_n of_o altitude_n chap._n xvii_o the_o use_n of_o certain_a line_n for_o the_o mensuration_n of_o superficial_a and_o solid_a body_n usual_o insert_v on_o joynt-rule_n for_o the_o use_n of_o workman_n of_o several_a sort_n and_o kind_n first_o the_o most_o general_a and_o receive_a line_n for_o mensuration_n of_o magnitude_n be_v a_o foot_n divide_v into_o 12_o inch_n and_o those_o inch_n into_o 8_o 10_o 12_o or_o more_o part_n but_o this_o be_v not_o so_o apt_a for_o application_n to_o the_o number_n i_o shall_v not_o insist_v of_o it_o here_o but_o rather_o refer_v you_o to_o the_o carpenter_n rule_n yet_o nevertheless_o those_o inch_n lay_v by_o a_o line_n of_o foot_n measure_n do_v by_o ocular_a inspection_n only_o serve_v to_o reduce_v foot_n measure_n to_o inch_n and_o inch_n likewise_o to_o foot_n measure_n and_o some_o other_o conclusion_n also_o 1._o as_o first_o the_o price_n of_o any_o commodity_n at_o five_o score_n to_o the_o hundred_o either_o tale_n or_o weight_n be_v give_v to_o find_v the_o price_n of_o one_o in_o number_n or_o one_o pound_n in_o weight_n as_o suppose_v at_o two_o penny_n halfpenny_n a_o pound_n or_o one_o i_o demand_v to_o what_o come_v the_o hundred_o weight_n or_o fivescore_o count_v so_o many_o pound_n to_o the_o hundred_o weight_n if_o you_o look_v for_o two_o inch_n and_o a_o half_a represent_v two_o penny_n two_o farthing_n right_a against_o it_o on_o the_o foot_n measure_n you_o have_v 21_o very_o near_o for_o if_o you_o conceive_v the_o space_n between_o 20_o and_o 21_o to_o be_v part_v into_o 12_o part_n this_o will_v be_v find_v to_o contain_v ten_o of_o they_o for_o the_o odd_a ten_o penny_n but_o for_o the_o more_o certain_a computation_n of_o the_o odd_a penny_n look_v how_o many_o farthing_n there_o be_v in_o the_o price_n of_o one_o pound_n twice_o so_o many_o shilling_n and_o once_o so_o many_o penny_n be_v the_o remainder_n which_o if_o it_o be_v above_o 12_o the_o 12_o or_o 12_n be_v substract_v the_o remainder_n be_v the_o precise_a number_n of_o penny_n above_o the_o shilling_n there_o express_v and_o on_o the_o contrary_a at_o any_o price_n the_o c_o hundred_o or_o 5_o score_n to_o find_v the_o price_n of_o one_o or_o 1l_o as_o suppose_v at_o 40_n the_o c._n or_o 5_o score_n look_v for_o 40_o in_o the_o foot_n measure_n and_o right_a against_o it_o in_o the_o inch_n you_o have_v 4_o inch_n 3_o quarter_n and_o 1_o 4_o of_o a_o quarter_n which_o in_o this_o way_n of_o account_n be_v 4_o penny_n 3_o farthing_n and_o about_o a_o quarter_n of_o one_o farthing_n thus_o by_o the_o line_n as_o they_o be_v
divide_v it_o proceed_v to_o 12_o penny_n a_o pound_n but_o if_o you_o conceive_v the_o inch_n to_o be_v double_v and_o the_o foot_n measure_n also_o you_o shall_v have_v it_o to_o 24_o d._n or_o 48_o d._n the_o pound_n or_o one_o in_o tale_n of_o any_o commodity_n as_o at_o 18_o d._n a_o piece_n or_o pound_n the_o price_n come_v to_o 7l_o 10_n the_o c._n for_o then_o every_o ten_o stroke_n be_v 20_n in_o the_o foot_n measure_n and_o every_o inch_n be_v 2_o penny_n and_o every_o eight_o one_o farthing_n 2._o second_o for_o the_o buy_n of_o timber_n at_o 50_o foot_n to_o a_o load_n at_o any_o price_n the_o load_n how_o much_o a_o foot_n here_o in_o resolve_v this_o the_o inch_n be_v to_o be_v double_v and_o the_o foot_n measure_v take_v as_o it_o be_v as_o at_o 40_o shilling_n the_o load_n 40_o in_o the_o foot_n measure_n stand_v right_a against_o 4_o inch_n 3_o quarter_n and_o better_a which_o be_v double_v be_v 9d_o 2_o far_o 1_o 2_o far_a near_o for_o the_o price_n of_o one_o foot_n and_o on_o the_o contrary_a at_o 5d_o a_o foot_n be_v 41_n 8_o d._n a_o load_n etc._n etc._n 3._o for_o the_o great_a hundred_o of_o 112l_o to_o the_o hundred_o let_v the_o space_n of_o 12_o inch_n be_v divide_v into_o 112_o part_n than_o the_o like_a rule_n hold_v for_o that_o also_o for_o the_o inch_n be_v divide_v into_o quarter_n every_o quarter_n be_v a_o farthing_n and_o every_o eight_o half_a a_o farthing_n and_o every_o division_n of_o the_o 112_o be_v a_o shilling_n and_o every_o alteration_n of_o a_o farthing_n in_o the_o price_n of_o a_o pound_n make_v a_o groat_n in_o the_o hundred_o as_o thus_o at_o 3_o penny_n a_o pound_n be_v 28_n the_o c._n at_o 3d._n 1_o q._n a_o pound_n 30_n and_o 4d_n the_o c._n at_o 3d._n 1_o 2_o the_o pound_n 32_n 8_o d._n the_o c._n at_o 3_o d._n 3_o farthing_n 35_n the_o c._n thus_o you_o see_v that_o every_o fraction_n at_o a_o farthing_n advance_v be_v 4_o penny_n in_o the_o hundred_o but_o for_o any_o other_o account_n as_o 3_o penny_n farthing_n half_a farthing_n then_o count_v the_o fraction_n as_o 1_o 12_o part_n of_o a_o shilling_n and_o near_o you_o can_v come_v by_o a_o bare_a ocular_a inspection_n but_o the_o price_n of_o the_o hundred_o be_v give_v the_o price_n of_o the_o pound_n you_o have_v as_o near_o by_o this_o ocular_a inspection_n as_o any_o usual_a coin_n be_v reducable_a viz._n to_o the_o 32_o part_n of_o a_o penny_n or_o nigh_a if_o you_o please_v again_o note_v here_o also_o you_o may_v double_v or_o quadruple_a the_o price_n as_o to_o 24d_o or_o 48d_o the_o pound_n or_o any_o price_n between_o as_o for_o example_n at_o 13d_o a_o pound_n be_v 6l_o 1_n 4d_o the_o c._n at_o 32d_o or_o 2s_n 8d_n the_o pound_n be_v 14l_o 19_n the_o c._n and_o the_o like_a by_o duple_v and_o quadruple_v the_o inch_n and_o the_o 112_o part_n that_o lay_v by_o it_o 4._o these_o line_n of_o equal_a part_n serve_v as_o scale_n for_o the_o protract_n of_o any_o draught_n of_o house_n or_o field_n or_o the_o like_a also_o for_o addition_n or_o substraction_n of_o any_o small_a number_n 5._o note_v that_o the_o line_n of_o foot_n measure_n may_v be_v apply_v for_o the_o reduce_n of_o any_o odd_a fraction_n to_o a_o decimal_n fraction_n as_o you_o may_v fee_v it_o in_o page_n 64._o of_o mr._n windgat_n arithmetic_n make_v easy_a 2._o the_o use_n of_o the_o line_n of_o decimal_a timber_n and_o board_n measure_n the_o line_n of_o decimal_a timber_n and_o board_n measure_n be_v fit_v to_o agree_v with_o the_o ten_o or_o foot_n measure_n as_o those_o line_n in_o the_o first_o chapter_n of_o the_o carpenter_n rule_n be_v fit_v to_o the_o inch_n and_o the_o use_n of_o they_o be_v thus_o and_o first_o for_o the_o decimal_n board_n measure_n suppose_v a_o board_n be_v 1_o foot_n 50_o broad_a i_o look_v for_o 150_o on_o that_o line_n and_o from_o that_o place_n to_o the_o end_n of_o the_o rule_n forward_o towards_o 100_o so_o much_o in_o length_n must_v you_o have_v to_o make_v a_o foot_n of_o superficial_a or_o board_n measure_n 2._o or_o else_o thus_o if_o you_o apply_v the_o end_n of_o the_o rule_n next_o 100_o to_o one_o edge_n of_o the_o breadth_n of_o a_o board_n or_o glass_n then_o right_o against_o the_o other_o edge_n of_o the_o board_n on_o that_o line_n of_o decimal_a board_n measure_n you_o shall_v find_v the_o 10th_n and_o 100_n or_o foot_n 10th_n &_o 100_o part_v of_o a_o foot_n that_o you_o must_v have_v in_o length_n to_o make_v a_o foot_n superficial_a at_o that_o breadth_n example_n i_o come_v to_o a_o board_n and_o apply_v the_o upper_a end_n next_o 100_o even_o to_o one_o edge_n of_o the_o board_n the_o other_o reach_v to_o 0._o 8_o ten_o than_o i_o say_v that_o 8_o ten_o of_o a_o foot_n length_n at_o that_o breadth_n make_v a_o foot_n 3._o the_o use_n of_o decimal_a timber_n measure_n the_o use_n of_o this_o be_v much_o like_o the_o board_n measure_n only_o here_o you_o must_v have_v a_o respect_n to_o the_o squareness_n of_o the_o piece_n and_o not_o to_o the_o breadth_n only_o for_o after_o you_o know_v how_o much_o the_o piece_n of_o timber_n or_o stone_n be_v square_a in_o foot_n and_o 100_o part_n then_o look_v that_o number_n on_o the_o line_n of_o decimal_a timber_n measure_n and_o from_o thence_o to_o the_o end_n of_o the_o rule_n be_v the_o length_n that_o go_v to_o make_v a_o foot_n of_o timber_n example_n at_o 14_o or_o 1._o 40._o part_n of_o a_o foot_n square_a look_v the_o same_o on_o the_o rule_n and_o from_o thence_o to_o the_o end_n where_o 40_o be_v be_v the_o length_n of_o a_o foot_n of_o timber_n at_o that_o squareness_n be_v about_o 51_o part_n of_o a_o foot_n divide_v into_o a_o 100_o part_n 5._o the_o use_n of_o the_o line_n of_o decimal_a yard_n measure_n also_o run_v yard_n measure_n according_a to_o the_o inch_n or_o decimal_a part_n of_o a_o foot_n the_o decimal_a yard_n measure_n be_v nothing_o else_o but_o a_o yard_n or_o 3_o foot_n divide_v into_o a_o 100_o part_n and_o use_v in_o the_o same_o manner_n as_o the_o foot_n measure_n be_v for_o if_o you_o take_v the_o length_n and_o the_o breadth_n in_o that_o measure_n and_o multiply_v it_o together_o you_o shall_v have_v the_o content_n in_o yard_n and_o 100_o part_n of_o a_o yard_n example_n suppose_v a_o piece_n of_o plaster_v be_v 4_o yard_n 78_o part_n one_o way_n and_o 7._o 35_o part_n another_o way_n be_v multiply_v together_o make_v 35_o yard_n and_o 9954._o of_o 10000_o which_o be_v very_o near_o 36_o yard_n 5._o but_o the_o decimal_n run_v yard_n measure_n be_v fit_v to_o the_o foot_n measure_n and_o the_o use_n be_v thus_o suppose_v a_o room_n be_v to_o be_v measure_v that_o be_v 7_o foot_n 8_o ten_o high_a and_o i_o will_v know_v how_o much_o make_v a_o yard_n at_o that_o breadth_n or_o height_n look_v forth_o 7f_o 8_o 10th_n on_o the_o line_n of_o decimal_n run_v yard_n measure_n and_o the_o space_n on_o the_o rule_n from_o thence_o to_o the_o end_n next_o 100_o be_v the_o true_a length_n that_o go_v to_o make_v up_o a_o yard_n of_o superficial_a measure_n at_o that_o breadth_n or_o height_n but_o if_o the_o piece_n be_v between_o 4_o foot_n 5_o 10_o broad_a and_o 2_o foot_n than_o the_o table_n at_o the_o end_n of_o the_o line_n will_v supply_v the_o defect_n or_o you_o may_v change_v the_o term_n and_o call_v the_o length_n the_o breadth_n and_o the_o contrary_n but_o if_o it_o be_v under_o 2_o foot_n broad_a then_o if_o you_o do_v as_o you_o do_v with_o the_o board_n measure_n you_o shall_v have_v your_o desire_n example_n at_o 1_o foot_n 3_o 10_o broad_a 6_o foot_n 9_o 10th_n make_v a_o yard_n 6._o but_o if_o the_o run_a yard_n measure_n be_v make_v to_o agree_v with_o the_o inch_n then_o measure_v the_o height_n of_o the_o room_n in_o foot_n and_o inch_n and_o if_o you_o take_v a_o pair_n of_o compass_n and_o measure_n from_o that_o place_n to_o the_o end_n of_o the_o rule_n then_o turn_v the_o compass_n set_v at_o that_o distance_n as_o many_o time_n as_o you_o can_v about_o the_o room_n so_o many_o yard_n be_v there_o in_o the_o room_n 7._o the_o use_n of_o the_o line_n of_o decimal_n round_a measure_n common_o call_v girt-measure_n which_o be_v when_o the_o circumference_n of_o a_o round_a cillender_n or_o pillar_n give_v in_o inch_n or_o ten_o part_n of_o a_o foot_n first_o for_o girt-measure_n according_a to_o inch_n be_v the_o most_o usual_a measure_n now_o much_o the_o pillar_n be_v about_o then_o look_v for_o the_o same_o number_n on_o the_o line_n of_o girt-measure_n and_o from_o thence_o to_o
the_o end_n of_o the_o rule_n be_v the_o length_n that_o go_v to_o make_v a_o foot_n of_o timber_n but_o if_o it_o be_v under_o 30_o inch_n about_o than_o you_o must_v have_v above_o two_o foot_n in_o length_n and_o then_o a_o table_n at_o the_o end_n of_o the_o line_n or_o a_o repetition_n in_o another_o line_n will_v supply_v the_o defect_n but_o if_o the_o line_n of_o girt-measure_n be_v divide_v according_a to_o foot_n measure_n then_o use_v it_o as_o before_o seek_v the_o decimal_n part_n on_o the_o line_n and_o from_o thence_o to_o the_o end_n be_v a_o foot_n 8._o the_o use_n of_o a_o line_n of_o solid_a measure_n by_o have_v the_o diameter_n of_o a_o round_a piece_n give_v in_o inch_n or_o foot_n measure_n take_v the_o diameter_n with_o a_o rule_n or_o a_o pair_n of_o calliper_n and_o learn_v the_o measure_n either_o in_o inch_n or_o foot_n measure_n according_a as_o your_o line_n of_o diameter_n be_v divide_v then_o look_v for_o the_o same_o number_n on_o the_o line_n of_o diameter_n and_o from_o thence_o to_o the_o end_n of_o the_o rule_n forward_o be_v the_o length_n that_o make_v a_o foot_n of_o timber_n at_o that_o diameter_n or_o measure_v cross_v the_o end_n of_o the_o round_a piece_n of_o timber_n or_o stone_n the_o table_n of_o all_o the_o under_o measure_n for_o all_o these_o line_n follow_v decimal_n superficial_a under_o m._n  _fw-fr 10_o f._n 1000_o  _fw-fr 10_o f._n 1000_o p._n  _fw-fr 1_o 100_o 00_o  _fw-fr  _fw-fr 3._o 848_o  _fw-fr 2_o 50._o 000_o  _fw-fr  _fw-fr 3._o 706_o  _fw-fr 3_o 33._o 300_o  _fw-fr  _fw-fr 3._o 570_o  _fw-fr 4_o 25._o 000_o  _fw-fr  _fw-fr 3._o 450_o  _fw-fr 5_o 20._o 000_o 3_o 3_o 3._o 332_o  _fw-fr 6_o 16._o 600_o  _fw-fr  _fw-fr 3._o 217_o  _fw-fr 7_o 14._o 300_o  _fw-fr  _fw-fr 3._o 115_o  _fw-fr 8_o 12._o 500_o  _fw-fr  _fw-fr 3._o 025_o  _fw-fr 9_o 11._o 120_o  _fw-fr  _fw-fr 2._o 940_o 1_o 1_o 10._o 000_o  _fw-fr 5_o 2._o 850_o  _fw-fr 1_o 9_o 100_o  _fw-fr 6_o 2._o 780_o  _fw-fr 2_o 8._o 340_o  _fw-fr 7_o 2._o 700_o  _fw-fr 3_o 7._o 720_o  _fw-fr 8_o 2._o 628_o  _fw-fr 4_o 7._o 150_o  _fw-fr 9_o 2._o 560_o  _fw-fr 5_o 6._o 670_o  _fw-fr 4_o 2._o 500_o  _fw-fr 6_o 6._o â—60_n  _fw-fr  _fw-fr â—_o 440_o  _fw-fr 7_o 5._o 888_o  _fw-fr  _fw-fr 2._o 382_o  _fw-fr 8_o 5._o 5â—5_n  _fw-fr  _fw-fr 2._o 336_o  _fw-fr 9_o 5._o 260_o  _fw-fr  _fw-fr 2._o 273_o 2_o 2_o 5._o 000_o  _fw-fr  _fw-fr 2._o 213_o  _fw-fr  _fw-fr 4._o 760_o  _fw-fr  _fw-fr 2._o 173_o  _fw-fr  _fw-fr 4._o 5â—6_n  _fw-fr  _fw-fr 2._o 127_o  _fw-fr  _fw-fr 4._o 350_o  _fw-fr  _fw-fr â—_o 083_o  _fw-fr  _fw-fr 4._o 170_o  _fw-fr  _fw-fr 2._o 042_o  _fw-fr 5_o 4_o 000_o  _fw-fr 5_o 2._o 000_o decimall_n superficial_a m._n  _fw-fr f._n 1000_o p._n 01_o f._n 1000_o p._n  _fw-fr 1._o 962_o  _fw-fr 1._o 320_o  _fw-fr 1._o 923_o  _fw-fr 1._o 304_o  _fw-fr 1._o 816_o  _fw-fr 1._o 286_o  _fw-fr 1._o 850_o  _fw-fr 1._o 268_o  _fw-fr 1._o 820_o 8_o 1._o 250_o  _fw-fr 1._o 785_o  _fw-fr 1._o 237_o  _fw-fr 1._o 756_o  _fw-fr 1._o 220_o  _fw-fr 1._o 726_o  _fw-fr 1._o 207_o  _fw-fr 1._o 697_o  _fw-fr 1._o 192_o 6_o 1._o 669_o  _fw-fr 1._o 178_o  _fw-fr 1._o 640_o  _fw-fr 1._o 164_o  _fw-fr 1._o 615_o  _fw-fr 1._o 151_o  _fw-fr 1._o 589_o  _fw-fr 1._o 138_o  _fw-fr 1._o 563_o  _fw-fr 1._o 125_o  _fw-fr 1._o 538_o 9_o 1._o 112_o  _fw-fr 1._o 516_o  _fw-fr 1._o 100_o  _fw-fr 1._o 493_o  _fw-fr 1._o 087_o  _fw-fr 1._o 472_o  _fw-fr 1._o 076_o  _fw-fr 1._o 450_o  _fw-fr 1._o 063_o 7_o 1._o 430_o  _fw-fr 1._o 052_o  _fw-fr 1._o 409_o  _fw-fr 1._o 041_o  _fw-fr 1._o 391_o  _fw-fr 1._o 030_o  _fw-fr 1._o 373_o  _fw-fr 1._o 020_o  _fw-fr 1._o 353_o  _fw-fr 1._o 011_o  _fw-fr 1._o 337_o 10_o 1._o 000_o decimal_n solid_a under_o measure_n  _fw-fr f._n 1000_o p._n 10_o f._n 1000_o p._n 1_o 10000_o 000_o  _fw-fr 14._o 805_o 2_o 2500._o 000_o  _fw-fr 13._o 735_o 3_o 1100._o 000_o  _fw-fr 12._o 780_o 4_o 630._o 000_o  _fw-fr 11._o 916_o 5_o 400._o 000_o 3_o 11._o 125_o 6_o 277._o 900_o  _fw-fr 10._o 415_o 7_o 200._o 430_o  _fw-fr 9_o 760_o 8_o 150._o 660_o  _fw-fr 9_o 125_o 9_o 120._o 350_o  _fw-fr 8._o 625_o 1_o 100_o 0000_o  _fw-fr 8._o 150_o  _fw-fr 82._o 800_o  _fw-fr 7._o 700_o  _fw-fr 96._o 500_o  _fw-fr 7._o 310_o  _fw-fr 59_o 390_o  _fw-fr 6._o 900_o  _fw-fr 51._o 100_o  _fw-fr 6._o 565_o  _fw-fr 44._o 500_o 4_o 6._o 250_o  _fw-fr 39_o 150_o  _fw-fr 5._o 945_o  _fw-fr 34._o 650_o  _fw-fr 5._o 664_o  _fw-fr 30._o 850_o  _fw-fr 5._o 404_o  _fw-fr 27._o 750_o  _fw-fr 5._o 465_o 2_o 25._o 000_o  _fw-fr 4._o 938_o  _fw-fr 22._o 700_o  _fw-fr 4._o 720_o  _fw-fr 20._o 675_o  _fw-fr 4._o 530_o  _fw-fr 18._o 920_o  _fw-fr 4._o 342_o  _fw-fr 17._o 400_o  _fw-fr 4._o 162_o  _fw-fr 16._o 000_o 5_o 4._o 000_o decimall_n solid_a under_o measure_n  _fw-fr f._n 1000_o p._n 01._o f._n 100_o p._n  _fw-fr 3._o 825_o  _fw-fr 1._o 738_o  _fw-fr 3._o 7â—0_n  _fw-fr 1_o 694_o  _fw-fr 3._o 524_o  _fw-fr 1._o 651_o  _fw-fr 3._o 430_o  _fw-fr 1._o 608_o  _fw-fr 3._o 310_o 8_o 1._o 568_o  _fw-fr 3._o 188_o  _fw-fr 1._o 528_o  _fw-fr 3._o 078_o  _fw-fr 1._o 493_o  _fw-fr 2._o 968_o  _fw-fr 1._o 458_o  _fw-fr 2._o 873_o  _fw-fr 1._o 420_o 6_o 2._o 780_o  _fw-fr 1._o 390_o  _fw-fr 2._o 688_o  _fw-fr 1._o 356_o  _fw-fr 2._o 602_o  _fw-fr 1._o 323_o  _fw-fr 2._o 521_o  _fw-fr 1._o 297_o  _fw-fr 2._o 442_o  _fw-fr 1._o 266_o  _fw-fr 2._o 366_o 9_o 1._o 236_o  _fw-fr 2._o 294_o  _fw-fr 1._o 208_o  _fw-fr 2._o 227_o  _fw-fr 1._o 185_o  _fw-fr 2._o 160_o  _fw-fr 1._o 160_o  _fw-fr 2._o 100_o  _fw-fr 1._o 131_o  _fw-fr 2._o 043_o  _fw-fr 1._o 109_o 7_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 1._o 985_o  _fw-fr 1._o 084_o  _fw-fr 1._o 93â—_n  _fw-fr 1_o 061_o  _fw-fr 1._o 878_o  _fw-fr 1._o 041_o  _fw-fr 1._o 830_o  _fw-fr 1._o 021_o  _fw-fr 1._o 781_o 10._o 1._o 000_o under_o yard-measure_n for_o foot_n and_o inch_n from_o one_o inch'to_fw-la four_o foot_n six_o inch_n f._n f._n 1000_o f._n f._n 1000_o in._n  _fw-fr in._n  _fw-fr 1_o 108.000_o  _fw-fr 3._o 850_o 2_o 54._o 000_o  _fw-fr 3._o 720_o 3_o 36._o 000_o  _fw-fr 3._o 600_o 4_o 27._o 000_o 6_o 3._o 482_o 5_o 21._o 600_o  _fw-fr 3._o 373_o 6_o 18._o 000_o  _fw-fr 3._o 271_o 7_o 15._o 420_o  _fw-fr 3._o 175_o 8_o 13._o 520_o  _fw-fr 3._o 085_o 9_o 12._o 000_o 3_o 3._o 000_o 10_o 10._o 300_o  _fw-fr 2._o 922_o 11_o 9_o 820_o  _fw-fr 2._o 842_o 1._o 9_o 000_o  _fw-fr 2._o 769_o  _fw-fr 8._o 320_o  _fw-fr 2._o 710_o  _fw-fr 7._o 740_o  _fw-fr 2._o 633_o  _fw-fr 7._o 201_o 6_o 2._o 572_o  _fw-fr 6._o 760_o  _fw-fr 2._o 512_o  _fw-fr 6._o 350_o  _fw-fr 2._o 455_o 6_o 6._o 000_o  _fw-fr 2._o 400_o  _fw-fr 5._o 680_o  _fw-fr 2._o 345_o  _fw-fr 5._o 400_o  _fw-fr 2._o 298_o  _fw-fr 5._o 140_o 4_o 2._o 250_o  _fw-fr 4._o 906_o 1_o 2._o 203_o  _fw-fr 4._o 695_o 2_o 2._o 160_o 2_o 5._o 500_o 3_o 2._o 119_o  _fw-fr 4._o 320_o 4_o 2._o 073_o  _fw-fr 4._o 160_o 5_o 2._o 037_o  _fw-fr 4._o 000_o 9_o 2._o 000_o under_o yard_n measure_n according_a to_o decimal_n or_o foot_n measure_n f._n 10._o f._n 1000_o p._n  _fw-fr f._n 1000_o p._n 1_o 90._o 000_o 4_o 3._o 7â—0_n 2_o 45._o 000_o 5_o 3._o 600_o 3_o 30._o 000_o 6_o 3._o 461_o 4_o 22._o 500_o 7_o 3._o 332_o 5_o 18._o 000_o 1_o 3._o 211_o 6_o 15._o 000_o 9_o 3._o 104_o 7_o 12._o 880_o 3_o 3._o 000_o 8_o 11._o 200_o 1_o 2._o 903_o 9_o 10._o 000_o 2_o 2._o 812_o 1_o 9_o 000_o 3_o 2._o 728_o 1_o 8._o 190_o 4_o 2._o 648_o 2_o 7._o 510_o 5_o 2._o 572_o 3_o 6._o 930_o 6_o 2._o 502_o 4_o 6._o 430_o 7_o 2._o 435_o 5_o 6._o 000_o 8_o 2._o 370_o 6_o 5._o 625_o 9_o 2._o 310_o 7_o 5._o 290_o 4_o 2._o 250_o 8_o 5._o 000_o 1_o 2._o 195_o 9_o 4._o 735_o 2_o 2._o 142_o 1_o 4._o 500_o 3_o 2._o 093_o 1_o 4._o 285_o 4_o 2._o 046_o 2_o 4._o 092_o 5_o 2._o 000_o 3_o 3912_o  _fw-fr  _fw-fr under_o girt-measure_n inc._n about_o f._n in_o 100_o  _fw-fr f._n in_o 100_o 1_o 1809.6.81_o 24_o 3.1.87_o 2_o 452._o 4._o 74_o 25_o 2._o 10._o 74_o 3_o 201._o 0._o 77_o 26_o 2._o 8._o 12_o 4_o 113._o 1._o 18_o 27_o 2._o 5._o 87_o 5_o 72._o 4._o 60_o 28_o 2._o 3._o 70_o 6_o 50._o 3._o 19_o 29_o 2._o 1._o 83_o 7_o 39_o 3._o 22_o 30_o 2._o 0._o 13_o 8_o 28._o 4._o 00_o 31_o 1._o 10._o 60_o 9_o 22._o 4._o 09_o 32_o 1._o 9_o 21_o 10_o 18._o 1._o 15_o 33_o 1._o 7_o 94_o 11_o 14._o 11._o 46_o 34_o 1._o 6._o 78_o 12_o 12._o 6._o 80_o 35_o 1._o
1_o 2_o then_o look_v for_o 17_o 3_o 4_o on_o the_o first_o line_n where_o 15_o 1_o 2_o be_v find_v and_o right_a against_o it_o on_o the_o second_o line_n be_v near_o 42_o the_o fraction_n be_v all_o decimal_n and_o you_o must_v reduce_v they_o to_o proper_a fraction_n according_o to_o work_v the_o rule_n of_o 3_o reverse_n 4._o set_a the_o first_o term_n seek_v out_o on_o the_o first_o line_n to_o the_o second_o be_v of_o the_o same_o denomination_n or_o kind_n to_o the_o second_o line_n or_o side_n then_o seek_v the_o three_o term_n on_o the_o second_o side_n and_o on_o the_o first_o you_o shall_v have_v the_o answer_v require_v example_n 5._o if_o 300_o mason_n build_v a_o edifice_n in_o 28_o day_n how_o many_o man_n must_v i_o have_v to_o perform_v the_o same_o in_o six_o day_n the_o answer_n will_v be_v find_v to_o be_v 1400._o 6._o to_o work_v the_o double_a rule_n of_o 3_o direct_v this_o be_v do_v by_o two_o work_n as_o thus_o for_o example_n if_o 112_o l._n or_o 1_o c._n weight_n cost_v 12_o penny_n the_o carraiage_n for_o 20_o mile_n what_o shall_v 6_o c_z cost_n 100_o mile_n say_v first_o by_o the_o three_o rule_n last_o mention_v as_o 1_o c._n weight_n to_o 12_o so_o be_v 6_o c._n weight_n to_o 72._o penny_n second_o say_v if_o 6_o c._n cost_n 72_o penny_n or_o rather_o 6_n for_o 20_o mile_n what_o shall_v 100_o mile_n require_v the_o answer_n be_v 30_o s._n for_o if_o you_o set_v 20_o against_o 6_o then_o right_a against_o 100_o be_v 30_o the_o answer_n require_v the_o use_n of_o mr._n whites_n rule_v in_o measure_v timber_n round_o or_o square_a the_o square_a or_o gird_v be_v give_v in_o inch_n and_o the_o length_n in_o foot_n and_o inch_n 1._o the_o inch_n that_o a_o piece_n of_o timber_n be_v square_a be_v give_v to_o find_v how_o much_o in_o length_n make_v a_o foot_n of_o timber_n look_v the_o number_n of_o inch_n square_a on_o that_o side_n of_o the_o timber_n line_n which_o be_v number_v with_o single_a figure_n from_o 1_o to_o 12_o and_o set_v it_o just_a against_o 100_o on_o the_o other_o or_o second_o side_n then_o right_o against_o 12_o at_o the_o low_a or_o some_o time_n the_o upper_a end_n on_o the_o first_o line_n in_o the_o second_o you_o have_v the_o number_n of_o foot_n and_o inch_n require_v example_n at_o 4_o 1_o 2_o inch_n square_a you_o must_v have_v 7_o foot_n 1_o inch_n 1_o 3_o to_o make_v a_o foot_n of_o timber_n but_o if_o it_o be_v above_o 12_o inch_n square_a then_o use_v the_o six_o problem_n of_o the_o 5_o chapter_n of_o the_o carpenter_n rule_n with_o the_o double_a figure_a side_n and_o compass_n 2._o but_o if_o it_o be_v a_o round_a smooth_a stick_n of_o above_o 12_o inch_n about_o and_o to_o it_o you_o will_v know_v how_o much_o in_o length_n make_v a_o true_a foot_n then_o do_v thus_o set_a the_o one_o at_o the_o begin_n of_o the_o double_a figure_a side_n next_o your_o left_a hand_n to_o the_o foot_n and_o inch_n about_o count_v in_o the_o other_o side_n number_v with_o single_a figure_n from_o 1_o to_o 12_o then_o right_o against_o three_o foot_n six_o 1_o 2_o inch_n in_o the_o single_a figure_n side_n next_o the_o right_a hand_n you_o have_v in_o the_o first_o side_n the_o number_n of_o foot_n and_o inch_n require_v example_n a_o piece_n of_o 12_o inch_n about_o require_v 11_o f_z 7_o in_o fere_n to_o make_v a_o foot_n again_o a_o piece_n of_o 15_o inch_n about_o must_v have_v 8_o foot_n 1_o 2_o a_o inch_n in_o length_n to_o make_v a_o foot_n of_o timber_n 3._o but_o if_o you_o will_v have_v it_o to_o be_v equal_a to_o the_o square_n make_v by_o the_o four_o part_n of_o a_o line_n gird_v about_o the_o piece_n than_o instead_o of_o three_o foot_n 6_o 1_o 2_o inch_n make_v use_v of_o four_o foot_n and_o you_o shall_v have_v your_o desire_n 4._o the_o side_n of_o a_o square_n be_v give_v in_o inch_n and_o the_o length_n in_o foot_n to_o find_v the_o content_n of_o a_o piece_n of_o timber_n if_o it_o be_v under_o 12_o inch_n square_v then_o work_v thus_o set_v 12_o at_o the_o beginning_n or_o end_n of_o the_o right_a hand_n side_n to_o the_o length_n count_v on_o the_o other_o side_n then_o right_o against_o the_o inch_n square_a on_o the_o right_a side_n be_v the_o content_a on_o the_o left_a side_n example_n at_o 30_o foot_n long_o &_o 9_o inch_n square_a you_o shall_v find_v 16_o foot_n 11_o inch_n for_o the_o work_a this_o question_n 12_o at_o the_o end_n must_v be_v use_v but_o if_o it_o be_v above_o 12_o inch_n square_a then_o ser_fw-mi one_o at_o the_o beginning_n or_o 10_o at_o the_o end_n of_o the_o right_a hand_n side_n to_o the_o length_n count_v on_o the_o other_o side_n than_o the_o number_n of_o inch_n or_o rather_o foot_n and_o inch_n count_v on_o the_o first_o side_n shall_v show_v on_o the_o second_o the_o foot_n and_o part_n require_v example_n at_o 1_o f._n 6_o inch_n square_n and_o 30_o foot_n long_o you_o shall_v find_v 67_o foot_n and_o about_o a_o 1_o 2._o 5._o to_o measure_v a_o round_a piece_n by_o have_v the_o length_n and_o the_o number_n of_o inch_n about_o be_v a_o smooth_a piece_n and_o to_o measure_v true_a and_o just_a measure_n then_o proceed_v thus_o set_v 3_o f._n 6_o 1_o 2_o inch_n on_o the_o right_a side_n to_o the_o length_n on_o the_o other_o side_n than_o the_o foot_n and_o inch_n about_o on_o the_o first_o side_n shall_v show_v on_o the_o second_o or_o leave_v the_o content_a require_v as_o at_o 20_o inch_n about_o and_o 20_o foot_n long_o the_o content_n will_v be_v find_v to_o be_v about_o 4_o foot_n 5_o inch_n but_o if_o you_o give_v the_o usual_a allowance_n that_o be_v make_v by_o duple_v the_o string_n 4_o time_n that_o girt_n the_o piece_n than_o you_o must_v set_v 4_o foot_n on_o the_o right_a side_n to_o the_o length_n on_o the_o other_o then_o at_o 1_o foot_n 8_o inch_n about_o the_o last_o example_n you_o shall_v find_v but_o three_o foot_n 6_o inch_n 6._o â—_o astly_a if_o the_o rule_n be_v make_v fit_a for_o foot_n measure_n only_o than_o the_o point_n of_o 12_o be_v altogether_o neglect_v and_o one_o only_o make_v use_n of_o as_o a_o stand_a number_n and_o the_o point_n at_o three_o foot_n 6_o 1_o 2_o will_v be_v at_o three_o foot_n 54_o part_n and_o the_o four_o will_v be_v the_o same_o and_o the_o same_o direction_n in_o every_o respect_n serve_v the_o turn_n and_o because_o i_o call_v it_o mr._n whites_n rule_n be_v the_o contriver_n thereof_o according_a to_o foot_n and_o inch_n i_o have_v therefore_o fit_v these_o direction_n according_o and_o there_o be_v sufficient_a to_o the_o ingenious_a practitioner_n chap._n xix_o certain_a proposition_n to_o find_v the_o hour_n and_o the_o azimuth_n by_o the_o line_n on_o the_o sector_n prop._n 1._o have_v the_o latitude_n and_o compliment_n of_o the_o declination_n and_o sun_n altitude_n and_o the_o hour_n from_o noon_n to_o find_v the_o sun_n azimuth_n 〈◊〉_d that_o time_n take_v the_o right_n sine_fw-la of_o the_o compliment_n of_o the_o sun_n altitude_n and_o make_v 〈◊〉_d it_o a_o parallel_n sine_fw-la in_o the_o sine_fw-la of_o the_o 〈◊〉_d hour_n from_o noon_n count_v 15_o degree_n 〈◊〉_d for_o a_o hour_n and_o 1_o degree_n for_o for_o minute_n count_v from_o the_o centre_n the_o sector_n so_o set_v take_v the_o right_a sine_fw-la of_o the_o compliment_n of_o the_o declination_n and_o carry_v it_o parallel_n till_o the_o compass_n stay_v in_o like_a sin_n and_o the_o sine_fw-la wherein_o they_o stay_v shall_v be_v the_o sine_fw-la of_o the_o azimuth_n require_v or_o else_o thus_o take_v the_o right_n sine_fw-la of_o the_o declination_n make_v it_o a_o parallel_n in_o the_o cousin_n of_o the_o sun_n altitude_n then_o take_v the_o parallel_n sine_fw-la of_o the_o hour_n from_o noon_n and_o it_o shall_v be_v the_o latteral_a or_o right_a sine_fw-la of_o the_o azimuth_n from_o the_o south_n require_v if_o it_o be_v between_o six_o in_o the_o morning_n and_o 6_o at_o night_n or_o from_o the_o north_n if_o it_o be_v before_o or_o after_o six_o and_o so_o likewise_o be_v the_o azimuth_n prop._n 2._o have_v the_o azimuth_n from_o south_n or_o north_n the_o compliment_n of_o the_o sun_n altitude_n and_o declination_n to_o find_v the_o hour_n take_v the_o latteral_a or_o right_a sine_fw-la of_o the_o compliment_n of_o the_o sun_n altitude_n make_v it_o a_o gaâ—â—llel_n in_o the_o cousin_n of_o the_o declination_n the_o sector_n so_o set_v ache_v out_o the_o parallel_n sine_fw-la of_o the_o azimuth_n and_o measure_v it_o from_o the_o centre_n and_o it_o shall_v reach_v to_o the_o right_n sine_fw-la of_o the_o hour_n from_o noon_n require_v or_o
in_o the_o cousin_n of_o the_o latitude_n than_o the_o parallel_n sine_fw-la of_o the_o declination_n take_v and_o measure_v in_o the_o line_n of_o sin_n from_o the_o centre_n shall_v give_v the_o amplitude_n require_v prop._n 10._o to_o find_v the_o sun_n height_n at_o six_o in_o any_o latitude_n take_v the_o lateral_a or_o right_a sine_fw-la of_o the_o declination_n and_o make_v it_o a_o parallel_n in_o the_o sine_fw-la of_o 90_o then_o take_v out_o the_o parallel_n sine_fw-la of_o the_o latitude_n and_o measure_v it_o in_o the_o line_n of_o sin_n from_o the_o centre_n and_o it_o shall_v reach_v to_o the_o altitude_n require_v note_v in_o work_v of_o any_o of_o these_o proposition_n if_o the_o sin_n draw_v from_o the_o centre_n prove_v too_o large_a for_o your_o compass_n or_o to_o make_v a_o parallel_n sine_fw-la or_o tangent_fw-la to_o a_o small_a number_n of_o degree_n than_o you_o may_v use_v the_o small_a sine_fw-la or_o tangent_fw-la adjoin_v that_o be_v set_v on_o the_o rule_n and_o it_o will_v answer_v your_o desire_n and_o note_v also_o in_o these_o proposition_n the_o word_n right_a or_o latteral_a sine_fw-la or_o tangent_fw-la be_v to_o be_v take_v right_o on_o from_o the_o centre_n or_o beginning_n of_o the_o line_n of_o sin_n or_o tangent_n and_o the_o word_n parallel_v always_o across_o from_o one_o leg_n to_o the_o other_o prop._n 11._o to_o find_v the_o sun_n height_n at_o any_o time_n in_o any_o latitude_n as_o the_o right_a sine_fw-la of_o 90_o be_v to_o the_o parallel_n cotangent_fw-la of_o the_o latitude_n so_o be_v the_o latteral_a or_o right_a sine_fw-la of_o the_o hour_n from_o 6_o to_o the_o parallel_n tangent_fw-la of_o a_o four_o ark_n which_o you_o must_v subtract_v from_o the_o sun_n distance_n from_o the_o pole_n and_o note_v the_o difference_n then_o as_o the_o right_n of_o the_o latitude_n to_o the_o parallel_a cousin_n of_o the_o four_o ark_n so_o be_v the_o parallel_a cousin_n of_o the_o remainder_n to_o the_o latteral_a sine_fw-la of_o the_o altitude_n require_v prop._n 12._o to_o find_v when_o the_o sun_n shall_v come_v to_o due_a east_n or_o west_n take_v the_o tangent_fw-la of_o the_o latitude_n from_o the_o small_a tangent_n make_v it_o a_o parallel_n in_o the_o sine_fw-la of_o 90_o then_o take_v the_o latteral_a tangent_fw-la of_o the_o declination_n from_o the_o small_a tangent_n and_o carry_v it_o parallel_v in_o the_o sin_n till_o it_o stay_v in_o like_a sin_n and_o that_o sine_fw-la shall_v be_v the_o sine_fw-la of_o the_o hour_n require_v from_o 6._o prop._n 13._o to_o find_v the_o sun_n altitude_n at_o east_n or_o west_n or_o vertical_a circle_n as_o the_o latteral_a sine_fw-la of_o declination_n be_v to_o the_o parallel_n sine_fw-la of_o the_o latitude_n so_o be_v the_o parallel_n sine_fw-la of_o 90_o to_o the_o latteral_a sine_fw-la of_o the_o altitude_n require_v prop._n 14._o to_o find_v the_o style_n height_n in_o upright_a decline_a dial_n as_o the_o right_a sine_fw-la of_o the_o compliment_n of_o the_o latitude_n to_o the_o parallel_n sine_fw-la of_o 90_o so_o the_o parallel_n sine_fw-la compliment_n of_o the_o plain_n declination_n to_o the_o right_a sine_fw-la of_o the_o style_n elevation_n prop._n 15._o to_o find_v the_o substiles_a distance_n from_o the_o meridian_n as_o the_o lateral_a tangent_fw-la of_o the_o colatitude_n to_o the_o parallel_n sine_fw-la of_o 90_o so_o the_o parallel_n sine_fw-la of_o the_o declination_n to_o the_o latteral_a tangent_fw-la of_o the_o substile_a from_o the_o meridian_n prop._n 16._o to_o find_v the_o inclination_n of_o meridian_n as_o the_o latteral_a tangent_fw-la of_o the_o declination_n to_o the_o parallel_n sine_fw-la of_o 90_o so_o be_v the_o parallel_n sine_fw-la of_o the_o latitude_n to_o the_o latteral_a cotangent_fw-la in_o the_o inclination_n of_o meridian_n prop._n 17._o to_o find_v the_o hour_n distance_n from_o the_o substile_a in_o all_o plain_n as_o the_o latteral_a tangent_fw-la of_o the_o hour_n from_o the_o proper_a meridian_n to_o the_o parallel_n sine_fw-la of_o 90_o so_o be_v the_o parallel_n sine_fw-la of_o the_o style_n elevation_n to_o the_o latteral_a tangent_fw-la of_o the_o hour_n from_o the_o substile_a prop._n 18._o to_o find_v the_o angle_n of_o 6_o from_o 12_o in_o erect_a decliner_n as_o the_o latteral_a tangent_fw-la of_o the_o compliment_n of_o the_o latitude_n to_o the_o parallel_n sine_fw-la of_o the_o declination_n of_o the_o plain_a so_o be_v the_o parallel_n sine_fw-la of_o 90_o to_o the_o latteral_a tangent_fw-la of_o the_o angle_n between_o 12_o and_o 6._o thus_o you_o see_v the_o natural_a sin_n and_o tangent_n on_o the_o sector_n may_v be_v use_v to_o operate_v any_o of_o the_o canon_n that_o be_v perform_v by_o logarithm_n or_o the_o artificial_a sin_n and_o tangent_n by_o change_v the_o term_n from_o the_o first_o to_o the_o three_o and_o the_o second_o to_o the_o first_o and_o the_o three_o to_o the_o second_o and_o the_o four_o must_v always_o be_v the_o four_o in_o 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