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measure_n agnostus_n and_o lay_v it_o from_o b_o or_o d_o or_o c_o on_o the_o line_n gf_n and_o those_o point_n on_o gf_n shall_v be_v the_o several_a point_n to_o draw_v the_o splay-line_n of_o the_o arch_n and_o key-stone_n by_o chap._n iu._n of_o the_o explanation_n of_o certain_a term_n use_v in_o this_o follow_a book_n 1._o radius_fw-la or_o sine_fw-la of_o 90_o radius_fw-la or_o tangent_fw-la of_o 45_o or_o secant_fw-la of_o 00_o be_v all_o one_o and_o the_o same_o thing_n yet_o take_v respective_o in_o their_o proper_a place_n and_o be_v the_o whole_a line_n of_o sines_n or_o tangent_n to_o 45_o or_o more_o particulary_a
the_o sphere_n inscribe_v and_o to_o the_o circle_n circumscribe_v be_v measure_v by_o compass_n calliper_n and_o line_n of_o line_n very_o careful_o and_o exact_o then_o divide_v the_o circumference_n of_o the_o two_o end_n of_o the_o cillender_n into_o 10_o equal_a part_n and_o draw_v line_n perpendicule_a from_o end_n to_o end_n and_o plain_a all_o away_o between_o the_o line_n flat_a and_o smooth_a so_o that_o the_o two_o plain_n on_o both_o end_n will_v become_v a_o regular_a ten-sided_n figure_n then_o make_v the_o whole_a diameter_n abovesaid_a 10000_o in_o the_o line_n of_o line_n take_v out_o 0-309_a and_o with_o this_o measure_n as_o a_o radius_fw-la on_o the_o centre_n at_o both_o end_n describe_v a_o circle_n and_o if_o you_o draw_v line_n from_o every_o opposite_a line_n of_o the_o 10_o first_fw-mi draw_v you_o shall_v have_v point_n in_o the_o last_o describe_v circle_n to_o draw_v a_o pentagon_n by_o which_o be_v the_o base_a of_o one_o of_o the_o 12_o pentagonal_a pyramid_n contain_v in_o the_o body_n this_o work_n be_v to_o be_v do_v at_o both_o end_n but_o be_v sure_a that_o the_o angle_n of_o the_o pentagon_n at_o one_o end_n be_v opposite_a to_o a_o side_n of_o the_o pentagon_n at_o the_o other_o end_n then_o these_o line_n draw_v the_o two_o end_n be_v full_o mark_v then_o to_o mark_v the_o 10_o side_n do_v thus_o count_v the_o first_o length_n 1000_o viz._n the_o measure_n from_o the_o top_n to_o the_o bottom_n or_o from_o centre_n to_o centre_n and_o fit_a this_o length_n in_o 10_o and_o 10_o of_o the_o line_n of_o line_n the_o sector_n so_o set_v take_v out_o 0-3821_a and_o lay_v it_o from_o the_o two_o end_n and_o either_o draw_v or_o gage_z line_n round_o about_o from_o each_o end_n and_o in_o the_o midst_n between_o the_o two_o line_n will_v remain_v 0-2358_a then_o line_n draw_v diagonal_o on_o the_o 10_o side_n will_v guide_v to_o the_o true_a cut_n of_o the_o dodecahedron_n if_o you_o set_v a_o bevel_n to_o 116_o deg_n 33_o min._n 54_o sec._n and_o apply_v it_o from_o the_o two_o end_n you_o may_v try_v the_o truth_n of_o your_o work_n the_o declination_n and_o reclination_n of_o all_o the_o 10_o pantagonal_a plain_n be_v as_o follow_v first_o you_o have_v 1_o north_n recline_v 26_o deg_n 34_o min_fw-mi and_o 1_o south_n incline_v as_o much_o second_o you_o have_v 2_o north_n decline_v 72_o and_o recline_v 26_o 34_o and_o 2_o south_n decline_v 72_o and_o incline_v 26_o 34._o three_o you_o have_v 2_o north_n decline_v 36_o and_o incline_v 26_o 34_o and_o 2_o south_n decline_v 36_o and_o recline_v 26_o 34_o and_o 1_o horizontal_a plain_n and_o his_o opposite_a base_a to_o stand_v on_o as_o for_o the_o measure_n of_o this_o body_n the_o plain_a and_o natural_a way_n be_v thus_o first_o find_v the_o superficial_a content_n of_o the_o base_a of_o one_o of_o the_o pentagon_n by_o multiply_v the_o measure_n from_o the_o centre_n to_o the_o middle_n of_o one_o of_o the_o side_n which_o be_v the_o contain_v circle_n semi-diameter_n and_o half_o the_o sum_n of_o the_o measure_n of_o all_o the_o side_n put_v together_o and_o then_o to_o multiply_v this_o product_n by_o one_o three_o part_n of_o half_a the_o altitude_n of_o the_o body_n and_o the_o product_n shall_v be_v the_o content_a of_o one_o pentagonal_a pyramid_n be_v one_o twelve_o part_n of_o the_o dodecahedron_n and_o this_o last_o multiply_v by_o 12_o gives_z the_o solid_a content_n of_o the_o dodecahedron_n or_o 12_o time_n the_o superficial_a content_n of_o one_o side_n be_v the_o superficial_a content_a thereof_o example_n suppose_v the_o side_n of_o a_o dodecahedron_n be_v 6_o than_o the_o sum_n of_o the_o side_n measure_v be_v 30_o the_o contain_v circle_n semi-diameter_n be_v 4-12_a then_o 15_o the_o half_a of_o 30_o and_o 4-12_a multiply_v together_o make_v 61-80_a and_o 12_o time_n this_o make_v 741-60_a for_o the_o superficial_a content_n of_o the_o dodecahedron_n then_o for_o the_o solid_a content_a multiply_v 61-80_a the_o superficial_a content_n of_o one_o side_n by_o 2-233_a one_o 6_o part_n of_o 13-392_a the_o whole_a altitude_n of_o the_o body_n the_o product_n be_v 137-99940_a again_o this_o multiply_v by_o 12_o the_o number_n of_o pyramid_n make_v 16â—â—_n 9928_o the_o solid_a content_a as_o near_o as_o may_v be_v in_o such_o a_o decimal_n way_n of_o computation_n 5._o for_o the_o icosahedron_n which_o be_v a_o regular_a solid_a body_n make_v up_o of_o or_o contain_v under_o 20_o triangule_a pyramid_n who_o base_a or_o one_o of_o who_o side_n be_v a_o equilatteral_a triangle_n and_o the_o perpendicule_a altitude_n of_o one_o of_o these_o 20_o pyramid_n be_v equal_a to_o half_a the_o perpendicule_a altitude_n of_o the_o icosahedron_n from_o any_o one_o side_n to_o his_o opposite_a side_n or_o equal_a to_o the_o semi-diameter_n of_o the_o inscribe_v sphere_n to_o cut_v this_o body_n take_v any_o round_a piece_n and_o if_o the_o diameter_n thereof_o be_v 10000_o let_v the_o length_n thereof_o be_v turn_v flat_a and_o even_o to_o 8075_o or_o if_o the_o true_a round_n and_o cillendrical_a form_n in_o diameter_n be_v 4910_o let_v the_o true_a length_n when_o the_o end_n be_v plain_a and_o flat_a be_v 3964_o then_o divide_v the_o cillendrical_a part_n into_o 6_o equal_a part_n and_o plain_a away_o all_o to_o the_o line_n so_o that_o the_o two_o end_n may_v be_v two_o 6-sided-figure_n then_o make_v 5000_o the_o former_a semi-diameter_n 1000_o in_o the_o line_n of_o line_n take_v out_o 616_o and_o on_o the_o centre_n at_o each_o end_n describe_v a_o circle_n and_o by_o draw_v line_n to_o each_o opposite_a point_n make_v a_o triangle_n who_o circumscribe_v circle_n may_v be_v the_o circle_n draw_v at_o each_o end_n but_o be_v sure_a to_o mark_v the_o side_n of_o one_o triangle_n opposite_a to_o the_o point_n of_o the_o other_o triangle_n at_o the_o other_o end_n as_o before_z in_o the_o dodecahedron_n thus_o both_o the_o end_n shall_v be_v full_o and_o true_o mark_v then_o make_v the_o length_n a_o parallel_n in_o 1000_o of_o the_o line_n of_o line_n take_v out_o 379_o and_o 095_o and_o prick_v those_o two_o measure_n from_o each_o end_n and_o by_o those_o point_n draw_n or_o gage_n line_n round_a about_o on_o the_o 6_o side_n then_o diagonal_a line_n draw_v from_o point_n to_o line_n and_o from_o line_n to_o point_v round_o about_o show_v how_o to_o cut_v the_o body_n at_o 12_o cut_n note_v that_o if_o you_o set_v a_o bevel_n to_o 138-11-23_a and_o apply_v it_o from_o each_o end_n it_o will_v guide_v you_o in_o the_o true_a plain_v of_o the_o side_n of_o the_o icosahedron_n and_o a_o bevel_n set_v to_o 100_o degree_n will_v fit_v be_v apply_v from_o the_o midst_n of_o one_o side_n to_o the_o meeting_n of_o two_o side_n the_o reclination_n of_o the_o three_o triangle_n who_o upper_a side_n be_v adjacent_a or_o next_o to_o the_o three_o side_n of_o the_o upper_a horizontal-triangle_n be_v 48_o 11.23_o from_o the_o perpendicule_a or_o 41_o 48_o 37_o from_o the_o horizontal_a and_o when_o one_o corner_n stand_v south_n the_o declination_n of_o one_o of_o these_o 3_o viz._n that_o opposite_a to_o the_o south-corner_n a_o direct_a north_n the_o other_a two_o decline_v 60_o degree_n one_o southeast_n the_o other_o south-west_n the_o other_o 6_o about_o the_o corner_n of_o the_o horizontal-plain_a do_v all_o recline_v 19_o deg_n 28_o min._n 16_o sec._n the_o two_o that_o behold_v the_o south_n decline_v 22_o deg_n 14_o min._n 29_o sec._n and_o those_o two_o that_o behold_v the_o north_n decline_v 37_o deg_n 45_o min._n 51_o sec._n towards_o the_o east_n and_o west_n the_o other_o two_o remain_v recline_v as_o before_o and_o decline_v one_o north-east_n and_o the_o other_o northwest_n 82_o deg_n 14_o min._n 19_o sec._n the_o other_o nine_o under-plain_n opposite_a to_o every_o one_o of_o these_o decline_v and_o incline_v as_o much_o as_o the_o opposite_a do_v recline_v and_o decline_v as_o by_o due_a consideration_n will_v plain_o appear_v for_o the_o measure_n of_o this_o body_n do_v as_o you_o do_v by_o the_o dodecahedron_n find_v the_o area_n of_o one_o triangle_n and_o multiply_v it_o by_o 20_o give_v the_o superficial_a content_a and_o the_o area_n of_o one_o triangle_n multiply_v by_o one_o six_o part_n of_o the_o altitude_n of_o the_o body_n give_v the_o solid_a content_n of_o the_o triangule_a pyramid_n and_o that_o product_v multiply_v by_o 20_o the_o number_n of_o pyramid_n give_v the_o whole_a solid_a content_n of_o the_o icosahedron_n example_n suppose_v the_o side_n of_o a_o icosahedron_n be_v 12_o first_o square_v one_o side_n viz._n 12_o which_o make_v 144_o then_o multiply_v that_o square_n by_o 13_o and_o then_o divide_v the_o product_n by_o 30_o the_o quotient_a and_o his_o remainder_n be_v the_o superficial_a
the_o two_o figure_n note_v two_o and_o iii_o you_o may_v plain_o see_v 15._o all_o angle_n plain_a and_o spherical_a be_v either_o acute_a right_o or_o obtuce_n 17._o a_o right_a angle_n be_v alwaâ—â—â—_n just_a 90_o degree_n as_o you_o may_v 〈◊〉_d in_o the_o figure_n two_o and_o iii_o by_o the_o angle_n at_o a_o in_o both_o of_o they_o 18._o a_o obtuce_n angle_n be_v always_o more_o than_o 90_o degree_n as_o the_o angle_n at_o d_o in_o both_o figure_n show_v 19_o a_o parallel_n line_n be_v any_o line_n draw_v by_o another_o line_n in_o such_o a_o way_n that_o though_o it_o be_v infinite_o produce_v yet_o they_o will_v never_o meet_v or_o cross_a one_o another_o as_o the_o line_n ab_fw-la cd_o 20._o a_o perpendicule_a line_n be_v when_o one_o line_n so_o fall_v on_o another_o line_n that_o the_o angle_n on_o each_o side_n be_v equal_a as_o ca_n fall_v of_o the_o line_n basilius_n figure_n vi._n 21._o all_o triangle_n be_v either_o with_o three_o equal_a side_n as_o figure_n four_o or_o two_o equal_a side_n as_o figure_n v_n or_o all_o unequal_a side_n as_o figure_n vi_o the_o first_o of_o which_o be_v call_v equilateral_a the_o second_o isosceles_n the_o three_o scalenum_n 22._o again_o they_o may_v be_v sometime_o name_v from_o their_o angle_n thus_o orthigonium_fw-la with_o one_o right_a angle_n and_o two_o acute_a angle_n ambligonium_fw-la with_o one_o obtuce_n angle_n and_o two_o acute_a angle_n oxigonium_n with_o three_o acute_a angle_n only_o 23._o the_o three_o angle_n of_o every_o plain_a triangle_n be_v equal_a to_o two_o right_a angle_n 24._o all_o four-sided_n figure_n be_v either_o square_n with_o four_o side_n and_o four_o right_a angle_n all_o equal_a or_o long_a square_n or_o oblong_v with_o the_o two_o opposite_a side_n equal_a or_o the_o same_o crush_v together_o or_o not_o rightangled_n as_o the_o rombus_n and_o rombord_n or_o else_o with_o four_o unequal_a side_n call_v trapeziaes_n 25._o last_o many_o sided-figure_n be_v some_o regular_a have_v every_o side_n alike_o as_o 5_o 6_o 7_o 8_o 9_o 10_o etc._n etc._n or_o else_o unlike_a as_o field_n and_o wood_n and_o meadow_n which_o be_v infinite_a can_v be_v comprehend_v under_o any_o regular_a order_n or_o rule_n 26._o multiplicator_n be_v a_o term_n use_v in_o multiplication_n by_o which_o any_o number_n be_v to_o be_v multiply_v as_o be_v say_v 5_o time_n 6_o 5_o be_v the_o multiplicator_n of_o 6._o 27._o multiplicand_v be_v the_o number_n to_o be_v multiply_v as_o 6_o by_o 5_o as_o above_z named_z 28._o the_o product_n be_v the_o issue_n or_o result_v of_o two_o number_n multiply_v one_o by_o the_o other_o as_o 30_o be_v the_o product_n of_o 6_o multiply_v by_o 5_o for_o 6_o time_n 5_o be_v 30._o 29._o divisor_n be_v a_o term_n use_v in_o division_n and_o be_v the_o number_n by_o which_o another_o number_n be_v to_o be_v divide_v as_o to_o say_v how_o many_o time_n 5_o in_o 30_o 5_o here_o be_v the_o divisor_n 30._o dividend_n be_v the_o number_n to_o be_v divide_v as_o 30_o abovesaid_a 31._o quotient_a be_v the_o answer_n to_o the_o how_o many_o time_n as_o in_o the_o abovesaid_a 5_o be_v in_o 30_o 6_o time_n 6_o then_o be_v the_o quotient_a 32._o square_n be_v the_o product_n of_o two_o number_n multiply_v together_o as_o the_o square_n of_o 6_o multiply_v by_o 6_o be_v 36._o 33._o square-root_n of_o any_o number_n be_v that_o number_n which_o be_v multiply_v by_o itself_o shall_v have_v a_o product_n or_o square_a equal_a to_o the_o give_v number_n thus_o the_o square-root_n of_o 36_o be_v 6_o for_o 6_o multiply_v by_o 6_o be_v 36_o equal_a to_o the_o first_o give_v number_n but_o if_o it_o be_v a_o number_n that_o can_v be_v square_v as_o 72_o the_o content_a of_o half_a a_o foot_n of_o board_n who_o near_a square-root_n be_v 8_o 4852811_o of_o 10000000_o then_o be_v the_o square-root_n to_o be_v express_v as_o near_o as_o you_o may_v or_o care_n for_o as_o here_o the_o square-root_n of_o 72_o which_o be_v call_v a_o fur_v number_n that_o will_v not_o be_v square_v 34._o cube_n be_v a_o second_o product_n or_o power_n of_o two_o number_n increase_v or_o multiply_v together_o as_o thus_o the_o square_a of_o 6_o be_v 36_o the_o first_o power_n and_o the_o cube_n of_o 6_o be_v 216_o that_o be_v to_o say_v 6_o time_n 36_o the_o second_o power_n in_o mr._n windgate_n book_n of_o arithmetic_n be_v the_o way_n of_o do_v it_o by_o number_n or_o figure_n be_v one_o of_o the_o hard_a lesson_n in_o arithmetic_n chap._n iii_o certain_a geometrical_a proposition_n fit_a to_o be_v know_v as_o preparatory_a rudiment_n for_o the_o follow_a work_n 1._o to_o draw_v a_o right_a line_n between_o two_o point_n extend_v a_o thread_n or_o hair_n from_o one_o point_n to_o the_o other_o and_o that_o shall_v be_v the_o line_n require_v but_o if_o you_o use_v a_o rule_n be_v the_o fit_a instrument_n to_o try_v your_o rule_n do_v thus_o apply_v one_o end_n to_o one_o point_v as_o to_o a_o and_o the_o other_o end_n to_o the_o other_o point_n at_o b_o and_o close_o to_o the_o edge_n draw_v the_o line_n require_v then_o turn_v the_o rule_n and_o lay_v the_o first_o end_n to_o the_o last_o point_n yet_o keep_v the_o same_o side_n of_o the_o rule_n towards_o the_o paper_n and_o draw_v the_o line_n again_o and_o if_o the_o two_o line_n appear_v as_o one_o the_o rule_n be_v straight_o or_o else_o not_o note_v the_o figure_n 1._o 2._o to_o draw_v a_o line_n perpendicule_a to_o another_o on_o the_o middle_n of_o a_o line_n on_o the_o point_n e_o on_o the_o line_n ab_fw-la i_o will_v raise_v the_o perpendicule_a line_n ce_fw-fr set_v one_o point_n of_o the_o compass_n in_o e_o and_o open_v they_o to_o any_o distance_n as_o ebb_v and_o ea_fw-la and_o note_v the_o point_n a_o and_o b_o then_o open_a the_o compass_n wide_a and_o set_v one_o point_n in_o a_o make_v the_o part_n of_o the_o arch_n by_o c_o upward_o and_o if_o you_o have_v room_n do_v the_o like_a downward_o near_a d_o then_o the_o compass_n not_o stir_v set_v one_o point_n in_o b_o and_o with_o the_o other_o across_o the_o former_a ark_n near_a c_o &_o d_o a_o rule_n lay_v and_o a_o line_n draw_v by_o those_o two_o cross_n shall_v cut_v the_o line_n ab_fw-la perpendiculer_o just_a in_o the_o point_n e_o which_o be_v require_v 3._o to_o let_v fall_v a_o perpendicule_a from_o a_o point_n to_o a_o line_n but_o if_o the_o point_n c_o have_v be_v give_v from_o whence_o to_o let_v fall_v the_o perpendicule_a to_o the_o line_n ab_fw-la do_v thus_o first_o set_v one_o point_v of_o compass_n in_o c_o open_v the_o other_o to_o any_o distance_n as_o suppose_v to_o a_o and_o b_o and_o then_o if_o you_o have_v room_n upon_o a_o and_o b_o strike_v both_o the_o ark_n by_o d_o which_o find_v the_o point_n d_o if_o not_o the_o middle_a between_o a_o and_o b_o give_v the_o point_n e_o by_o which_o to_o draw_v ce_v the_o perpendicule_a from_o c_z desire_z note_v figure_n 2._o note_v that_o if_o you_o can_v come_v to_o find_v the_o point_n d_o by_o the_o cross_n it_o do_v ready_o and_o exact_o divide_v the_o line_n ab_fw-la in_o two_o equal_a part_n by_o the_o point_n e._n 4._o to_o raise_v a_o perpendicule_a on_o the_o end_n of_o a_o line_n on_o the_o end_n of_o the_o line_n ab_fw-la at_o b_o i_o will_v raise_v a_o perpendicule_a first_o set_v one_o point_v of_o the_o compass_n in_o b_o open_v they_o to_o any_o distance_n as_o suppose_v to_o c_o and_o set_v the_o other_o point_v any_o where_o about_o the_o middle_n between_o d_o and_o e_z as_o suppose_v at_o c_o then_o keep_v that_o point_n fix_v there_o turn_v the_o other_o till_o it_o cut_v the_o line_n as_o at_o d_o and_o keep_v both_o point_n fix_v there_o and_o lay_v a_o straight_a rule_n close_o to_o both_o point_n and_o there_o keep_v it_o then_o keep_v the_o middle-point_n still_o fix_v at_o c_o and_o turn_v the_o other_o neat_o close_a to_o the_o other_o end_n and_o edge_n of_o the_o rule_n to_o find_v the_o point_n e_o then_o a_o rule_n lay_v to_o the_o point_n e_o and_o b_o shall_v draw_v the_o perpendicule_a require_v or_o else_o when_o you_o have_v set_v the_o compass_n in_o the_o point_n c_o prick_v the_o point_n d_o in_o the_o line_n and_o make_v the_o touch_n of_o a_o ark_n near_o to_o e_o then_o a_o rule_n lay_v to_o dc_o cut_n the_o ark_n last_o make_v at_o or_o by_o e_o in_o the_o point_n e_o there_o be_v other_o way_n but_o none_o better_o than_o this_o note_v the_o figure_n 3_o 5._o from_o a_o point_n give_v to_o let_v fall_v a_o perpendicule_a to_o the_o end_n of_o a_o line_n be_v the_o converse_n of_o the_o former_a first_o from_o
right_a ascension_n and_o the_o ascentional-difference_n be_v the_o oblique-ascention_n but_o in_o southern_a declination_n the_o sum_n of_o the_o right_a ascension_n and_o difference_n of_o asscention_n be_v the_o oblique_a ascension_n example_n on_o or_o between_o the_o 25_o and_o 26_o of_o july_n the_o oblique-ascention_n be_v by_o substraction_n 112_o 15_o on_o the_o 30_o of_o october_n the_o oblique-ascention_n be_v 337_o 45_o by_o addition_n use_v viii_o the_o day_n of_o the_o month_n or_o sun_n declination_n and_o altitude_n be_v give_v to_o find_v the_o hour_n of_o the_o day_n take_v the_o sun_n altitude_n from_o the_o particular_a scale_n of_o altitude_n set_v one_o point_n of_o the_o compass_n in_o the_o centre_n at_o the_o begin_n of_o that_o line_n and_o open_v the_o other_o to_o the_o degree_n and_o minute_n of_o the_o sun_n altitude_n count_v on_o that_o line_n then_o lay_v the_o thread_n on_o the_o day_n of_o the_o month_n or_o declination_n and_o there_o keep_v it_o then_o carry_v the_o compass_n set_v at_o the_o former_a distance_n along_o the_o line_n of_o hour_n perpendicule_a to_o the_o thread_n till_o the_o other_o point_n be_v turn_v about_o will_v but_o just_a touch_n the_o thread_n the_o compass_n stand_v between_o the_o thread_n and_o the_o hour_n 12_o than_o the_o fix_a point_n in_o the_o hour-line_n shall_v show_v the_o hour_n and_o minute_n require_v but_o whether_o it_o be_v the_o fore_n or_o afternoon_n your_o judgement_n or_o a_o second_o observation_n must_v determine_v example_n on_o the_o first_o of_o august_n in_o the_o morning_n at_o 20_o degree_n of_o altitude_n you_o shall_v find_v it_o to_o be_v just_a 52_o minute_n past_o 6_o but_o at_o the_o same_o altitude_n in_o the_o afternoon_n it_o be_v 7_o minute_n past_o 5_o at_o night_n in_o the_o latitude_n of_o 51_o 32_o for_o london_n use_v ix_o the_o sun_n declination_n and_o altitude_n give_v to_o find_v the_o sun_n azimuth_n from_o the_o south-part_n of_o the_o horizon_n first_o by_o the_o four_o use_n find_v the_o sun_n declination_n count_v the_o same_o on_o the_o particular_a scale_n and_o take_v the_o distance_n between_o your_o compass_n then_o lay_v the_o thread_n to_o the_o sun_n altitude_n count_v the_o same_o way_n as_o the_o southern-declination_n be_v from_o 600_o towards_o the_o loose-piece_n and_o when_o need_n require_v on_o the_o loose-piece_n then_o carry_v the_o compass_n along_o the_o azimuth-line_n on_o the_o rightside_n of_o the_o thread_n that_o be_v between_o the_o thread_n and_o the_o head_n when_o the_o declination_n be_v northward_o and_o on_o the_o left-side_n of_o the_o thread_n that_o be_v between_o the_o thread_n and_o the_o end_n when_o the_o declination_n be_v southward_o so_o as_o the_o compass_n set_v to_o the_o declination_n as_o before_o and_o one_o point_v stay_v on_o the_o azimuth-line_n and_o the_o other_o turn_v about_o shall_v but_o just_a touch_n the_o thread_n at_o the_o near_a distance_n then_o i_o say_v the_o fixed-point_n shall_v in_o the_o azimuth-line_n show_v the_o suns-azimuth_n require_v example_n 1._o the_o sun_n be_v in_o the_o equinoctial_a and_o have_v no_o declination_n you_o have_v nothing_o to_o take_v with_o your_o compass_n but_o only_o lay_v the_o thread_n to_o the_o altitude_n count_v from_o 600_o towards_o the_o loose-piece_n and_o in_o the_o azimuth-line_n it_o cut_v the_o azimuth_n require_v example_n at_o 25_o degree_n high_a you_o shall_v find_v the_o sun_n azimuth_n to_o be_v 54_o 10_o at_o 32_o degree_n high_a you_o shall_v find_v 38_o 20_o the_o azimuth_n again_o at_o 20_o degree_n of_o declination_n take_v 20_o from_o the_o particular_a scale_n and_o at_o 10_o degree_n of_o altitude_n lay_v the_o thread_n to_o 10_o count_v as_o before_o then_o if_o you_o carry_v the_o compass_n on_o the_o rightside_n for_o north-declination_n you_o shall_v find_v 109_o 30_o from_o south_n but_o if_o you_o carry_v they_o on_o the_o left-side_n for_o south-declination_n you_o shall_v find_v 38_o 30_o from_o south_n the_o rest_n of_o the_o use_v you_o shall_v have_v more_o ample_o afterward_o chap._n vi_o the_o use_n of_o the_o line_n of_o number_n on_o the_o edge_n and_o the_o line_n of_o line_n on_o the_o quadrantal-side_n or_o on_o the_o sector-side_n be_v all_o as_o one_o have_v show_v the_o way_n of_o numeration_n on_o the_o line_n as_o in_o chapter_n the_o first_o also_o to_o add_v or_o subtract_v one_o line_n or_o number_n to_o or_o from_o one_o another_o as_o in_o chapter_n four_o explanation_n the_o 9th_o i_o come_v now_o to_o work_v the_o rule_n of_o multiplication_n and_o division_n and_o the_o rule_n of_o three_o direct_a and_o reverse_v both_o by_o the_o artificial_a and_o natural-line_n and_o first_o by_o the_o artificial_a be_v the_o most_o easy_a and_o then_o by_o the_o natural-line_n both_o on_o the_o sector_n and_o triangule_a quadrant_n be_v alike_o and_o i_o work_v they_o together_o first_o because_o i_o will_v avoid_v tautology_n second_o because_o thereby_o be_v better_o see_v the_o harmony_n between_o they_o and_o which_o be_v best_a and_o speedy_a three_o because_o it_o be_v a_o way_n not_o yet_o as_o i_o know_v of_o go_v by_o any_o other_o and_o last_o of_o all_o because_o one_o may_v explain_v the_o other_o the_o geometrical_a figure_n be_v the_o same_o with_o the_o instrumental-work_n by_o the_o natural_a way_n sect._n i._o to_o multiply_v one_o number_n by_o another_o 1._o by_o the_o line_n of_o number_n on_o the_o edge_n artificial_o thus_o extend_v the_o compass_n from_o 1_o to_o the_o multiplicator_n the_o same_o extent_n apply_v the_o same_o way_n from_o the_o multiplicand_a will_v cause_v the_o other_o point_n to_o fall_v on_o the_o product_n require_v example_n let_v 8_o be_v give_v to_o be_v multiply_v by_o 6_o if_o you_o set_v one_o point_n of_o the_o compass_n in_o 1_o either_o at_o the_o beginning_n or_o at_o the_o middle_n or_o at_o the_o end_n it_o matter_n not_o which_o yet_o the_o middle_n 1_o on_o the_o head-leg_n be_v for_o the_o most_o part_n the_o most_o convenient_a and_o open_v the_o other_o to_o 6_o or_o 8_o it_o matter_n not_o which_o for_o 6_o time_n 8_o and_o 8_o time_n 6_o be_v alike_o but_o yet_o you_o may_v mind_v the_o precept_n if_o you_o will_v the_o same_o extent_n lay_v the_o same_o way_n from_o 8_o shall_v reach_v to_o 48_o the_o product_v require_v which_o without_o these_o parenthesis_n be_v thus_o the_o extent_n from_o 1_o to_o 6_o shall_v reach_v the_o same_o way_n from_o 8_o to_o 48._o or_o the_o extent_n from_o 1_o to_o 8_o shall_v reach_v the_o same_o way_n from_o 6_o to_o 48._o the_o product_v require_v by_o the_o natural-line_n on_o the_o sector-side_n or_o triangule_a quadrant_n with_o a_o thread_n and_o compass_n the_o work_n be_v thus_o 1._o for_o the_o most_o part_n it_o be_v wrought_v by_o change_v the_o term_n from_o the_o artificial_a way_n as_o thus_o the_o former_a way_n be_v as_o 1_o to_o 6_o so_o be_v 8_o to_o 48_o or_o as_o 1_o to_o 8_o so_o be_v 6_o to_o 48_o but_o by_o the_o sector_n it_o be_v thus_o as_o the_o latteral_a 6_o take_v from_o the_o centre_n towards_o the_o end_n be_v to_o the_o parallel_n 10_o &_o 10_o set_v over_o from_o 10_o to_o 10_o at_o the_o end_n count_v as_o 1_o so_o be_v the_o parallel-distance_n between_o 8_o &_o 8_o on_o the_o line_n of_o line_n take_v across_o from_o one_o leg_n to_o the_o other_o to_o the_o latteral-distance_n from_o the_o centre_n to_o 48_o the_o product_v require_v or_o short_a thus_o as_o the_o latteral_a 8_o to_o the_o parallel_n 10_o so_o be_v the_o parallel_n 6_o to_o the_o latteral_a 48._o see_v figure_n i._n 2._o another_o way_n may_v you_o work_v without_o alter_v the_o term_n from_o the_o artificial_a way_n as_o thus_o by_o a_o double_a radius_fw-la take_v the_o latteral-extent_n from_o the_o centre_n to_o 1_o or_o from_o 10_o to_o 9_o if_o the_o beginning_n be_v defective_a make_v this_o a_o parallel_n in_o 6_o &_o 6_o than_o the_o latteral-extent_n from_o the_o centre_n to_o 8_o of_o the_o 10_o part_n between_o figure_n and_o figure_n shall_v reach_v across_o from_o 48_o to_o 48_o as_o before_o see_v fig._n ii_o the_o same_o work_n as_o be_v do_v by_o the_o sector_n be_v do_v by_o the_o line_n of_o line_n and_o thread_n on_o the_o quadrant-side_n that_o if_o your_o sector_n be_v put_v together_o as_o a_o triangule_a quadrant_n you_o may_v work_v any_o thing_n by_o it_o as_o well_o as_o by_o the_o sector_n in_o this_o manner_n or_o by_o the_o scale_n and_o compass_n as_o in_o the_o figure_n i._o and_o first_o as_o above_z sector-wise_a take_v the_o extent_n from_o the_o centre_n to_o 6_o latteral_o between_o your_o compass_n set_v one_o point_n in_o 10_o and_o with_o the_o other_o lie_v the_o thread_n in_o the_o near_a distance_n
large_a and_o plain_a in_o this_o first_o use_n i_o shall_v be_v i_o hope_v as_o plain_a though_o far_o more_o brief_a in_o all_o the_o rest_n for_o if_o you_o look_v back_o to_o chapt._n vi_o probl._n i._o sect._n 3_o you_o shall_v there_o see_v the_o full_a explain_v of_o latteral_a and_o parallel_n and_o nearest-distance_n and_o how_o to_o take_v they_o the_o mark_n for_o latteral_a be_v thus_o the_o mark_n for_o parallel_v thus_o =_o nearest-distance_n thus_o nd_o etc._n etc._n use_v ii_o the_o sine_fw-la of_o any_o ark_n or_o angle_n give_v to_o find_v the_o radius_fw-la to_o it_o take_v the_o sine_fw-la between_o your_o compass_n quadrant_n and_o set_v one_o foot_n of_o the_o compass_n in_o the_o give_v sine_fw-la and_o with_o the_o other_o point_n lie_v the_o thread_n to_o the_o nearest-distance_n and_o there_o keep_v it_o then_o the_o nearest-distance_n from_o the_o sine_fw-la of_o 90_o to_o the_o thread_n shall_v be_v the_o radius_fw-la require_v make_v the_o give_v sine_fw-la a_o parallel_n sine_fw-la sector_n and_o then_o take_v out_o the_o parallel_n radius_fw-la and_o you_o have_v your_o desire_n the_o artificial_a sin_n and_o tangent_n be_v not_o proper_a for_o this_o work_n further_o than_o to_o give_v the_o natural_a number_n thereof_o as_o before_o therefore_o i_o shall_v only_o add_v the_o use_n of_o they_o when_o it_o be_v convenient_a in_o the_o fit_a place_n use_v iii_o the_o radius_fw-la or_o any_o know_a sine_fw-la being_n give_v to_o find_v the_o quantity_n of_o any_o other_o unknown_a sine_fw-la to_o the_o same_o radius_fw-la take_v the_o radius_fw-la or_o know_v sine_fw-la give_v quadr._n and_o make_v it_o a_o parallel_n in_o the_o sine_fw-la of_o 90_o for_o radius_fw-la or_o in_o the_o sine_fw-la of_o the_o know_a angle_n give_v and_o lay_v the_o thread_n to_o nd_o then_o take_v the_o unknown_a sine_fw-la between_o your_o compass_n and_o carry_v one_o point_n along_o the_o line_n of_o sines_n till_o the_o other_o foot_n be_v turn_v about_o will_v but_o just_a touch_n the_o thread_n then_o the_o place_n where_o the_o compass_n stay_v shall_v be_v the_o sine_fw-la of_o the_o unknown_a angle_n require_v to_o that_o radius_fw-la or_o know_v sine_fw-la sector_n make_v the_o give_v radius_fw-la a_o parallel_n radius_fw-la or_o the_o give_v sine_fw-la a_o =_o sine_fw-la in_o the_o answerable_a sine_fw-la thereof_o then_o take_v the_o unknown_a sine_fw-la carry_v it_o parallel_o along_o the_o line_n of_o sines_n till_o it_o stay_v in_o like_a part_n which_o part_n shall_v be_v the_o numerator_n to_o the_o sine_fw-la require_v use_v iu._n the_o radius_fw-la be_v give_v by_o the_o sin_n alone_o to_o find_v any_o tangent_fw-la or_o secant_fw-la to_o that_o radius_fw-la quadrant_n take_v the_o radius_fw-la between_o your_o compass_n and_o set_v one_o point_n in_o the_o sine_fw-la compliment_n of_o the_o tangent_fw-la require_v and_o lay_v the_o thread_n to_o the_o nd_o then_o the_o nd_o from_o the_o sine_fw-la of_o the_o tangent_fw-la require_v to_o the_o thread_n shall_v be_v the_o tangent_fw-la require_v and_o the_o nd_o from_o 90_o to_o the_o thread_n shall_v be_v the_o secant_fw-la require_v make_v the_o give_v radius_fw-la a_o =_o in_o the_o cousin_a of_o the_o tangent_fw-la require_v sector_n then_o the_o =_o sine_fw-la of_o the_o inquire_v ark_n or_o angle_n shall_v be_v the_o tangent_fw-la require_v and_o =_o 90_o shall_v be_v the_o secant_fw-la require_v to_o that_o radius_fw-la use_v v._n any_o tangent_fw-la or_o secant_fw-la be_v give_v to_o find_v the_o answerable_a radius_fw-la and_o then_o any_o other_o proportionable_a tangent_fw-la or_o secant_fw-la by_o sines_n only_o first_o if_o it_o be_v a_o tangent_fw-la that_o be_v give_v quadr._n take_v it_o between_o your_o compass_n and_o set_v one_o foot_n in_o the_o sine_fw-la thereof_o lay_v the_o thread_n to_o nd_o than_o the_o =_o cousin_a thereof_o shall_v be_v radius_fw-la but_o if_o it_o be_v a_o secant_fw-la take_v it_o between_o your_o compass_n and_o set_v one_o foot_n always_o in_o 90_o lay_v the_o thread_n to_o the_o nd_o than_o the_o near_a distance_n from_o the_o cousin_a to_o the_o thread_n or_o the_o =_o cousin_a shall_v be_v the_o radius_fw-la require_v take_v the_o give_v tangent_fw-la sector_n make_v it_o a_o =_o in_o the_o sine_fw-la thereof_o then_o the_o =_o cousin_a thereof_o shall_v be_v radius_fw-la or_o if_o it_o be_v a_o secant_fw-la give_v then_o take_v the_o give_v secant_fw-la make_v it_o a_o =_o in_o 90_o than_o the_o =_o cousin_a thereof_o shall_v be_v the_o radius_fw-la require_v then_o have_v get_v radius_fw-la the_o four_o use_n show_v how_o to_o come_v by_o any_o tangent_fw-la or_o secant_fw-la by_o the_o sin_n only_o use_v vi_o to_o lay_v down_o any_o chord_n to_o any_o radius_fw-la less_o than_o the_o sine_fw-la of_o 30_o degree_n take_v the_o give_v radius_fw-la set_v one_o point_v in_o the_o sine_fw-la of_o 30_o quadr._n lay_v the_o thread_n to_o the_o nd_o and_o for_o your_o more_o ready_a set_n it_o again_o note_n what_o degree_n and_o minuit_fw-la the_o thread_n do_v stay_v at_o on_o the_o degree_n and_o there_o keep_v it_o then_o the_o nd_o from_o the_o sine_fw-la of_o half_a the_o angle_n you_o will_v have_v shall_v be_v the_o chord_n of_o the_o angle_n require_v sector_n take_v the_o give_v radius_fw-la and_o make_v it_o always_o a_o =_o in_o 30_o and_o 30_o of_o sin_n the_o =_o sine_fw-la of_o half_a the_o chord_n shall_v be_v the_o chord_n require_v use_v vii_o to_o lay_v down_o any_o chord_n to_o the_o radius_fw-la of_o the_o whole_a line_n of_o sines_n quadr._n take_v the_o radius_fw-la between_o your_o compass_n and_o set_v one_o point_n in_o 90_o of_o the_o sin_n lay_v the_o thread_n to_o the_o nd_o observe_v the_o place_n there_o keep_v it_o then_o take_v the_o =_o sine_fw-la of_o the_o angle_n require_v with_o it_o set_v one_o point_n in_o the_o line_n to_o which_o you_o will_v draw_v the_o angle_n as_o far_o from_o the_o centre_n as_o the_o radius_fw-la be_v then_o draw_v the_o convexity_n of_o a_o ark_n and_o by_o that_o convexity_n and_o the_o centre_n draw_v the_o line_n for_o the_o angle_n require_v example_n let_v ab_fw-la be_v a_o radius_fw-la of_o any_o length_n under_o or_o equal_v to_o the_o whole_a line_n of_o sines_n take_v ab_fw-la between_o your_o compass_n and_o set_v one_o point_n in_o 90_o lay_v the_o thread_n to_o nd_o then_o take_v out_o the_o =_o sine_fw-la of_o 38_o or_o any_o other_o number_n you_o please_v and_o set_v one_o point_n in_o b_o the_o end_n of_o the_o radius_fw-la from_o a_o the_o centre_n and_o trace_v the_o ark_n dc_o by_o the_o convexity_n of_o which_o ark_n draw_v the_o line_n ac_fw-la for_o the_o angle_n require_v take_v the_o give_v radius_fw-la ab_fw-la sector_n make_v it_o a_o =_o in_o 90_o and_o 90_o of_o sin_n then_o take_v out_o =_o 38_o and_o set_v one_o foot_n in_o b_o draw_v the_o ark_n dc_o and_o draw_v ac_fw-la for_o the_o angle_n require_v or_o else_o work_v thus_o take_v ab_fw-la the_o give_v radius_fw-la have_v draw_v the_o ark_n be_v and_o make_v it_o a_o =_o in_o the_o cousin_a of_o half_a the_o angle_n require_v and_o lay_v the_o thread_n to_o nd_o or_o set_v the_o sector_n then_o take_v the_o =_o nd_o from_o the_o right-sine_a of_o the_o angle_n require_v and_o it_o shall_v be_v be_v the_o chord_n require_v to_o be_v find_v note_v that_o the_o contrary_a work_n find_v radius_fw-la use_v viii_o to_o lay_v off_o any_o angle_n by_o the_o line_n of_o tangent_n or_o secant_v to_o prove_v it_o sector_n have_v draw_v the_o ground-line_n ab_fw-la at_o the_o point_n b_o raise_v a_o perpendicule_a as_o the_o line_n bc_n extend_v at_o length_n then_o make_v ab_fw-la the_o radius_fw-la a_o =_o tangent_fw-la in_o 45_o and_o 45_o then_o take_v out_o the_o =_o tangent_fw-la of_o the_o angle_n require_v and_o lay_v it_o from_o b_o to_z c_z in_o the_o perpendicule_a and_o draw_v the_o line_n ac_fw-la for_o the_o angle_n require_v also_o if_o you_o take_v out_o the_o secant_fw-la of_o the_o angle_n as_o the_o sector_n stand_v and_o lay_v it_o twice_o in_o the_o line_n ae_n it_o will_v reach_v just_a to_o c_o the_o point_n require_v also_o note_v that_o if_o you_o want_v a_o angle_n above_o 45_o degree_n as_o the_o sector_n stand_v take_v the_o same_o from_o the_o small_a tangent_fw-la that_o proceed_v to_o 75_o and_o turn_v that_o extent_n 4_o time_n from_o b_o and_o it_o shall_v give_v the_o point_n require_v in_o the_o line_n bc._n use_v ix_o to_o lay_v down_o or_o protract_v any_o angle_n by_o the_o tangent_fw-la of_o 45_o only_a first_o make_v a_o geometrical_a square_n a_o abcd_a and_o let_v a_o be_v the_o angule_a point_n then_o make_v ab_fw-la radius_fw-la make_v ab_fw-la a_o =_o cousin_a of_o the_o angle_n you_o will_v have_v and_o lay_v the_o thread_n to_o
a_o foot_n shut_v be_v draw_v usual_o just_a 5_o degree_n asunder_o or_o rather_o the_o two_o innermost_a line_n on_o each_o leg_n be_v always_o just_a one_o degree_n from_o the_o inside_n so_o that_o if_o you_o put_v a_o center-pin_n in_o the_o line_n of_o tangent_n just_a against_o the_o sine_fw-la of_o 30_o it_o make_v the_o two_o innermost_a line_n that_o come_v from_o the_o centre_n just_a 2_o degree_n asunder_o which_o be_v easy_a to_o remember_v either_o in_o add_v or_o substract_v as_o follow_v two_o way_n 1._o take_v the_o latteral_a sine_fw-la of_o 30_o viz._n the_o measure_n from_o the_o centre_n to_o 30_o the_o compass_n so_o set_v set_v one_o point_n in_o the_o center-pin_n in_o the_o tangent_n just_a against_o 30_o and_o turn_v the_o other_o till_o it_o cut_v the_o common_a line_n in_o the_o line_n of_o sines_n on_o the_o other_o leg_n and_o there_o it_o shall_v show_v what_o angle_n the_o two_o innermost-line_n make_v count_v from_o the_o end_n towards_o the_o head_n and_o two_o degree_n less_o be_v the_o angle_n the_o sector_n stand_v at_o both_o on_o the_o inside_n and_o outside_n the_o leg_n be_v parallel_n which_o number_n must_v near_o agree_v with_o what_o the_o inside_n of_o the_o leg_n cut_v on_o the_o head-semicircle_n or_o there_o be_v a_o mistake_n as_o thus_o for_o example_n suppose_v i_o open_v the_o rule_n at_o all_o adventure_n and_o take_a the_o latteral_a sine_fw-la of_o 30_o from_o the_o sin_n on_o the_o sector-side_n and_o put_v one_o point_n of_o the_o compass_n in_o the_o centre_n on_o the_o tangent_n right_a against_o the_o sine_fw-la of_o 30_o on_o the_o other_o leg_n or_o the_o begin_n of_o the_o secant_v on_o the_o same_o leg_n and_o turn_v the_o other_o point_n to_o the_o line_n of_o sines_n on_o the_o other_o leg_n it_o cut_v the_o sine_fw-la of_o 60_o on_o the_o innermost_a line_n that_o come_v from_o the_o centre_n then_o i_o say_v that_o the_o line_n of_o sines_n and_o tangent_n be_v just_a 30_o degree_n asunder_o and_o the_o inside_n or_o outside_n of_o the_o leg_n but_o 28_o viz._n two_o degree_n less_o as_o a_o glance_n of_o your_o eye_n to_o the_o head_n will_v plain_o show_v 2._o this_o way_n will_v serve_v very_o well_o for_o all_o angle_n above_o 20_o and_o under_o 80_o but_o for_o all_o under_o 20_o and_o above_o 80_o to_o 120_o this_o be_v a_o better_a way_n open_v the_o rule_n to_o any_o angle_n at_o pleasure_n and_o take_v the_o distance_n parallelly_n that_o be_v across_o from_o one_o leg_n to_o the_o other_o between_o the_o center-pin_n at_o 30_o in_o the_o sin_n and_o that_o in_o the_o tangent_n right_a against_o it_o and_o measure_v it_o latteral_o from_o the_o centre_n and_o it_o shall_v show_v the_o sine_fw-la of_o half_a the_o angle_n the_o sin_n and_o tangent_n stand_v at_o and_o one_o degree_n less_o be_v the_o sine_fw-la of_o half_a the_o angle_n the_o sector_n stand_v at_o example_n suppose_v that_o open_v the_o sector_n at_o adventure_n or_o to_o the_o level_n of_o any_o thing_n i_o will_v know_v the_o angle_n it_o stand_v at_o i_o take_v the_o parallel_n distance_n between_o the_o two_o centre_n and_o measure_v it_o latteral_o from_o the_o centre_n i_o find_v it_o give_v i_o the_o sine_fw-la of_o 51_o degree_n viz._n the_o half_a angle_n the_o line_n stand_v at_o or_o 50_o the_o angle_n the_o rule_n stand_v at_o which_o double_v be_v 102_o for_o the_o line_n or_o 100_o for_o the_o leg_n of_o the_o sector_n as_o a_o glance_n of_o the_o eye_n present_o resolve_v by_o the_o inner-edge_n of_o the_o moving-leg_n and_o the_o divide_a semicircle_n 3._o on_o the_o contrary_a will_v you_o set_v the_o leg_n or_o line_n to_o any_o angle_n take_v the_o half_a thereof_o latteral_o or_o one_o degree_n less_o in_o the_o half_a for_o the_o leg_n and_o make_v it_o a_o parallel_n in_o the_o two_o centre_n and_o the_o sector_n be_v so_o set_v according_o example_n i_o will_v set_v the_o leg_n to_o 90_o degree_n or_o a_o just_a square_n take_v out_o the_o latteral_a sine_fw-la of_o 44_o one_o degree_n less_o than_o 45_o the_o half_a of_o 90_o and_o make_v it_o a_o parallel_n in_o the_o two_o centre_n abovesaid_a and_o you_o shall_v find_v the_o leg_n set_v just_a to_o a_o square_a or_o right-angle_n as_o by_o look_v to_o the_o head_n you_o may_v near_o see_v at_o the_o same_o time_n if_o you_o take_v latteral_a 30_o and_o lay_v it_o from_o the_o centre_n according_a to_o the_o first_o rule_n you_o shall_v see_v a_o great_a deficiency_n therein_o as_o above_o be_v hint_v use_v v._o the_o day_n of_o the_o month_n be_v give_v to_o find_v the_o sun_n declination_n true_a place_n in_o the_o zodiac_n right_a ascention_n ascentional_a difference_n or_o rise_v and_o set_v 1._o lay_v the_o thread_n to_o the_o day_n of_o the_o month_n in_o the_o upper_a line_n of_o month_n where_o the_o length_n of_o the_o day_n be_v increase_v or_o in_o the_o lower-line_n when_o the_o day_n be_v decrease_v according_a to_o the_o time_n of_o the_o year_n then_o in_o the_o line_n of_o degree_n you_o have_v his_o declination_n wherein_o note_n that_o if_o the_o thread_n lie_v on_o the_o right_a hand_n of_o 600_o than_o the_o sun_n declination_n be_v northwards_o the_o contrary-way_n be_v southwards_o also_o on_o the_o line_n of_o the_o sun_n be_v right_a ascension_n you_o have_v his_o right_a ascension_n in_o degree_n and_o hour_n count_v one_o hour_n for_o 15_o degree_n as_o the_o month_n proceed_v from_o march_n the_o 10_o or_o equinoctial_a the_o right_a ascention_n be_v then_o 00_o and_o so_o forward_o to_o 24_o hour_n or_o 360_o degree_n as_o the_o month_n and_o day_n proceed_v again_o on_o the_o line_n oâ—_n the_o sun_n be_v true_a place_n you_o have_v the_o sign_n and_o degree_n of_o his_o place_n in_o the_o ecliptic_a aries_n or_o the_o equinoctial-point_n be_v the_o place_n to_o begin_v and_o then_o proceed_v forward_o as_o the_o month_n and_o day_n go_v last_o on_o the_o hour-line_n you_o have_v the_o ascentional-difference_n in_o degree_n and_o minute_n count_v from_o 6_o or_o the_o sun_n rise_v count_v as_o the_o morning_n hour_n proceed_v or_o his_o set_v count_v as_o the_o afternoon_n hour_n proceed_v of_o all_o which_o take_v two_o or_o three_o example_n 1._o for_o march_v the_o 12_o lay_v the_o thread_n to_o the_o day_n and_o extend_v it_o straight_o then_o on_o the_o line_n of_o degree_n it_o show_v near_o 1_o degree_n or_o 54_o minute_n northward_o 2._o the_o sun_n right_a ascension_n be_v in_o time_n 8_o minute_n and_o better_a or_o in_o degree_n 2_o deg_n 5_o minute_n 3._o the_o sun_n place_n be_v 2_o degree_n and_o 16_o minute_n in_o aries_n ♈_o 4._o the_o ascentional_a difference_n be_v 1_o degree_n and_o 10_o minute_n or_o the_o sun_n rise_v 4_o minute_n before_o and_o set_v 4_o minute_n after_o 6._o again_o for_o may_v the_o 10_o the_o thread_n lay_v thereon_o cut_v in_o the_o degree_n 20_o deg_n 9_o min._n for_o northern_a declination_n and_o 57_o deg_n 24_o min._n or_o 3_o hour_n 52_o min._n right_a ascension_n and_o 29_o 37_o in_o ♉_o taurus_n for_o his_o true_a place_n and_o 27_o 12_o for_o difference_n of_o ascension_n or_o rise_v 11_o minute_n after_o 4_o and_o set_v 49_o minute_n after_o 7._o again_o on_o the_o last_o of_o october_n or_o the_o 21_o of_o january_n near_o the_o declination_n be_v 17_o 22_o southwards_o the_o right_a ascension_n for_o october_n 31_o be_v 225_o 53_o for_o january_n 21_o 314_o 21_o the_o true_a place_n for_o october_n 31_o be_v â™_o scorpio_n 18_o deg_n 22_o min_fw-mi but_o for_o january_n 21_o â™’_o aquarius_n 11_o 52_o according_a as_o the_o month_n go_v to_o the_o end_n at_o ♑_o and_o then_o back_o again_o but_o the_o ascentional_a difference_n and_o rise_v and_o set_v be_v very_o near_o the_o same_o at_o both_o time_n viz._n 23_o 10_o and_o rise_v 32_o minute_n and_o more_o after_z 7_o and_o set_v 28_o minute_n less_o after_o 4._o use_v vi_o the_o declination_n of_o the_o sun_n or_o a_o star_n give_v to_o find_v his_o amplitude_n take_v the_o declination_n be_v count_v on_o the_o particular_a scale_n of_o altitude_n between_o your_o compass_n and_o with_o this_o distance_n set_v one_o foot_n in_o 90_o on_o the_o azimuth-line_n the_o other_o point_v apply_v to_o the_o same_o line_n shall_v give_v the_o amplitude_n count_v from_o 90._o example_n the_o declination_n be_v 12_o north_n the_o amplitude_n be_v 19_o deg_n 15_o min._n northwards_o or_o the_o declination_n be_v 20_o south_n the_o amplitude_n be_v 34_o deg_n 10_o min._n southwards_o use_v vii_o the_o right_a ascention_n and_o ascentional-difference_n be_v give_v to_o find_v his_o oblique-ascention_n when_o the_o declination_n be_v north_n than_o the_o difference_n between_o the_o
from_o a_o but_o if_o you_o remove_v to_o e_o the_o thread_n fall_v on_o 3_o on_o the_o shadow_n the_o altitude_n will_v be_v but_o one_o three_o part_n of_o the_o distance_n ea_fw-la from_o hence_o you_o may_v observe_v that_o observe_v at_o c_o and_o at_z d_o where_o the_o thread_n fall_v on_o 1_o and_o on_o 2_o the_o distance_z between_z c_z and_o d_o be_v equal_a to_o the_o altitude_n so_o likewise_o at_o d_o and_o at_z e_z and_o so_o by_o consequence_n at_o 1_o ½_o and_o 2_o ½_o and_o 3_o ½_o or_o any_o other_o equal_a part_n this_o be_v a_o excellent_a easy_a way_n the_o like_a will_v be_v if_o you_o observe_v at_o d_o and_o c_o look_v up_o to_o f_o where_o the_o altitude_n of_o be_v twice_o the_o distance_n ac_fw-la use_v v._o another_o way_n by_o the_o line_n of_o shadow_n at_o one_o station_n measure_v any_o distance_n as_o foot_n yard_n ii_o or_o the_o like_a from_o any_o object_n as_o suppose_v from_o a_o to_o d_o be_v 200_o foot_n and_o look_v up_o to_o b_o the_o thread_n cut_v the_o stroke_n by_o 2_o on_o the_o line_n of_o shadow_n then_o by_o the_o line_n of_o number_n say_v as_o 2_o the_o part_n cut_v be_v to_o 1_o so_o be_v 200_o the_o distance_n measure_v to_o 100_o the_o height_n or_o suppose_v i_o measure_v any_o other_o uneven_a number_n and_o the_o thread_n fall_v between_o 00_o on_o the_o loose-piece_n and_o 1_o on_o the_o shadow_n common_o call_v contrary_a shadow_n the_o rule_n be_v always_o thus_o as_o the_o part_n cut_v by_o the_o thread_n be_v to_o 1_o so_o be_v the_o measure_a distance_n to_o the_o height_n require_v be_v less_o than_o the_o measure_a distance_n but_o when_o the_o thread_n fall_v between_o 1_o and_o 90_o at_o the_o head_n call_v right_a shadow_n then_o the_o rule_n go_v thus_o as_o 1_o to_o the_o part_n cut_v by_o the_o thread_n so_o be_v the_o measure_a distance_n to_o the_o height_n be_v always_o more_o than_o the_o measure_a distance_n from_o the_o foot_n of_o the_o object_n to_o the_o station_n use_v vi_o another_o way_n by_o the_o line_n of_o shadow_n and_o the_o sun_n shine_v when_o the_o sun_n shine_v find_v his_o altitude_n and_o also_o as_o the_o thread_n lie_v see_v what_o division_n on_o the_o line_n of_o shadow_n be_v cut_v by_o the_o thread_n and_o then_o straightway_o measure_v the_o shadow_n length_n on_o the_o ground_n and_o if_o the_o sun_n be_v under_o 45_o degree_n high_a the_o shadow_n be_v long_o than_o the_o length_n of_o that_o object_n which_o cause_v the_o shadow_n but_o if_o the_o sun_n be_v above_o 45_o degree_n high_a than_o the_o object_n be_v long_o than_o the_o shadow_n and_o the_o operation_n be_v thus_o by_o the_o line_n of_o number_n only_o with_o a_o pair_n of_o compass_n the_o height_n of_o the_o sun_n be_v under_o 45_o say_v as_o the_o part_n cut_v by_o the_o thread_n on_o the_o shadow_n be_v to_o 1_o so_o be_v the_o shadow_n measure_v to_o the_o height_n require_v the_o height_n of_o the_o sun_n be_v above_o 45_o say_v as_o 1_o to_o the_o part_n cut_v by_o the_o thread_n on_o the_o line_n of_o shadow_n so_o be_v the_o measure_n of_o the_o shadow_n to_o the_o height_n in_o the_o same_o part_n use_v vii_o to_o find_v a_o inaccessible_a altitude_n by_o the_o quadrat_fw-la and_o shadow_n otherwise_o observe_v the_o altitude_n at_o both_o station_n and_o count_v the_o observe_v altitude_n at_o both_o station_n on_o the_o quadrat_fw-la or_o shadow_n according_a as_o it_o happen_v to_o be_v either_o above_o or_o under_o 45_o degree_n and_o take_v the_o lesser_a out_o of_o the_o great_a note_v the_o remainder_n for_o the_o first_o term_n and_o the_o divisor_n to_o divide_v the_o distance_n between_o the_o station_n increase_v with_o cipher_n if_o need_v be_v and_o the_o quotient_n be_v the_o answer_v require_v but_o by_o the_o line_n of_o number_n work_v thus_o the_o extent_n from_o the_o difference_n to_o 1_o shall_v reach_v the_o same_o way_n from_o the_o measure_a distance_n to_o the_o height_n require_v example_n figure_n ii_o let_v abcde_v represent_v the_o object_n and_o three_o station_n let_v the_o line_n ac_fw-la represent_v the_o altitude_n the_o point_n b_o one_o station_n 50_o foot_n from_o a_o d_o another_o station_n 100_o foot_n from_o a_o or_o 50_o from_o b_o and_o e_z another_o station_n 73_o foot_n from_o d_o or_o 173_o foot_n from_o a_o all_o which_o measure_v you_o need_v not_o know_v before_o but_o only_o bd_o and_o de_fw-fr also_o the_o angle_n at_o b_o 63-27_a and_o his_o compliment_n count_v the_o other_o way_n be_v the_o angle_n at_o c_o 26_o degree_n 33_o minute_n the_o angle_n at_o d_o 45_o and_o his_o compliment_n so_o also_o the_o angle_n at_o e_o 30_o and_o his_o compliment_n 60._o now_o mind_n the_o operation_n by_o either_o of_o these_o first_o lay_v the_o thread_n on_o 26-33_a and_o in_o the_o quadrat_fw-la it_o cut_v 50_o lay_v the_o thread_n on_o 45_o and_o in_o the_o shadow_n or_o quadrat_fw-la it_o cut_v 100_o or_o 1_o or_o if_o you_o lay_v the_o thread_n to_o 60_o then_o in_o the_o shadow_n it_o cut_v 173._o the_o difference_n between_o 173_o and_o 100_o be_v 73._o then_o as_o 73_o the_o difference_n in_o tangent_n between_o the_o two_o observation_n be_v to_o the_o distance_n in_o foot_n 73_o so_o be_v radius_fw-la 100_o or_o the_o side_n of_o the_o quadrat_fw-la to_o 100_o the_o hight_v require_v again_o for_o the_o two_o near_a observation_n who_o difference_n of_o tangent_n be_v 50._o as_o 50_o the_o difference_n in_o tangent_n to_o 50_o foot_n the_o measure_a distance_n so_o be_v 100_o the_o side_n of_o the_o quadrat_fw-la to_o 100_o the_o height_n again_o last_o by_o the_o observation_n at_o b_o &_o e_o the_o difference_n of_o tangent_n be_v 123._o as_o 123_o the_o difference_n in_o tangent_n to_o 123_o the_o measure_a distance_n so_o be_v 100_o the_o radius_fw-la or_o side_n of_o the_o quadrat_fw-la to_o 100_o the_o height_n require_v or_o in_o the_o first_o figure_n the_o angle_n at_o the_o top_n be_v 33-30_a and_o 48-15_a and_o the_o measure_a distance_n 88_o foot_n and_o a_o half_a the_o difference_n in_o tangent_n will_v be_v 45-8_a then_o as_o 45-8_a to_o 100_o the_o side_n of_o the_o quadrat_fw-la so_o be_v 88_o ½_o the_o measure_a distance_n to_o 194_o the_o altitude_n require_v this_o way_n be_v general_a for_o any_o station_n though_o both_o of_o right_a shadow_n or_o both_o of_o contrary_n or_o mix_v of_o right_a and_o contrary_a and_o do_v by_o the_o line_n of_o number_n or_o by_o multiplication_n and_o division_n also_o note_v that_o you_o may_v find_v this_o difference_n in_o tangent_n or_o secant_v by_o the_o natural_a tangent_n or_o natural_a secant_v on_o the_o sector_n and_o the_o scale_n of_o equal_a part_n belong_v to_o they_o thus_o take_v the_o distance_n between_o the_o compleplement_n of_o the_o two_o observation_n on_o the_o great_a or_o lesser_a line_n of_o tangent_n as_o be_v most_o convenient_a and_o measure_v this_o distance_n in_o the_o line_n of_o line_n or_o equal_a part_n equal_a to_o that_o radius_fw-la and_o that_o shall_v be_v the_o difference_n in_o tangent_n require_v the_o like_a for_o the_o secant_v also_o by_o the_o artificial_a number_n sin_n and_o tangent_n you_o may_v come_v by_o this_o difference_n in_o tangent_n or_o secant_v very_o well_o thus_o just_o right_a against_o the_o tangent_fw-la of_o the_o co-altitude_n count_v on_o the_o line_n of_o tangent_n in_o the_o line_n of_o number_n be_v one_o number_n and_o against_o the_o tangent_fw-la of_o the_o compliment_n of_o the_o other_o angle_n be_v the_o other_o number_n only_o with_o this_o caution_n that_o if_o the_o tangent_fw-la be_v above_o 45_o then_o take_v the_o distance_n from_o 45_o to_o the_o tangent_fw-la as_o it_o be_v count_v backward_o with_o compass_n and_o set_v the_o same_o the_o increase_a way_n from_o 1_o on_o the_o number_n to_o the_o other_o number_n require_v then_o the_o lesser_a take_v from_o the_o great_a leave_v the_o difference_n in_o tangent_n that_o be_v require_v in_o the_o same_o manner_n the_o sin_n count_v from_o 90_o and_o lay_v the_o contrary_a way_n from_o 1_o increase_a will_v give_v the_o difference_n in_o secant_v to_o measure_v the_o baâ—â—_n and_o hypothenusa_n by_o number_n only_o use_v viii_o another_o pretty_a way_n by_o scale_n and_o compass_n without_o arithmetic_n from_o t._n s._n then_o draw_v the_o line_n that_o the_o thread_n make_v on_o the_o board_n then_o measure_v from_o your_o stand_n to_o the_o foot_n of_o the_o object_n and_o take_v the_o number_n of_o foot_n or_o yard_n from_o any_o scale_n and_o lay_v it_o from_o the_o right_a angle_n on_o the_o other_o line_n and_o raise_v a_o perpendicule_a from_o thence_o to_o the_o plumb-line_n make_v by_o the_o thread_n and_o
that_o shall_v be_v the_o altitude_n require_v be_v measure_v on_o the_o same_o scale_n example_n let_v abgd_n represent_v the_o board_n end_n or_o trencher_n and_o on_o that_o let_v ab_fw-la be_v one_o straight_a line_n and_o agnostus_n another_o perpendicule_a to_o it_o in_o the_o point_n a_o knock_v in_o one_o pin_n and_o in_o b_o or_o any_o where_o towards_o the_o end_n another_o on_o the_o pin_n at_o a_o hang_v a_o thread_n and_o plummet_n and_o stand_v at_o ay_o any_o convenient_a station_n look_v up_o by_o the_o two_o pin_n at_o b_o and_o a_o till_o they_o bourn_n in_o a_o right_a line_n with_o the_o point_n h_n the_o object_n who_o height_n be_v to_o be_v measure_v then_o the_o plummet_n play_v well_o and_o even_o make_v a_o point_n just_a therein_o and_o draw_v the_o line_n ad_fw-la as_o the_o thread_n show_v then_o have_v measure_v the_o distance_n from_o g_o the_o foot_n of_o the_o object_n to_o i_o the_o station_n take_v it_o from_o any_o first_o scale_n and_o lay_v it_o from_o a_o to_o g_o then_o on_o the_o point_n g_o raise_v a_o perpendicule_a to_o agnostus_n till_o it_o intersect_v the_o plumb-line_n ad_fw-la then_o i_o say_v the_o distance_n cd_o measure_v on_o the_o same_o scale_v you_o take_v ac_fw-la from_o shall_v be_v equal_a to_o the_o altitude_n gh_o which_o be_v require_v use_v ix_o the_o same_o work_n at_o two_o station_n but_o if_o you_o can_v come_v to_o measure_v from_o i_o the_o first_o station_n to_o g_o v_n then_o measure_v from_o i_o to_o k_o and_o have_v observe_v at_o i_o and_o draw_v the_o plumb-line_n ad_fw-la take_v the_o measure_n between_o i_o and_o k_o the_o two_o station_n from_o any_o fit_a scale_n of_o equal_a part_n and_o lay_v it_o on_o the_o line_n ac_fw-la from_o a_o to_o c_o viz._n 79_o part_n and_o in_o the_o point_n c_o knock_v another_o pin_n and_o hang_v the_o thread_n and_o plummet_n thereon_o and_o observe_v careful_o where_o this_o last_o plumb-line_n do_v cross_v the_o other_o as_o suppose_v at_o e_o then_z from_o e_z let_v fall_v a_o perpendicule_a to_o the_o line_n ac_fw-la which_o line_n ac_fw-la shall_v be_v the_o height_n gh_o require_v or_o thus_o the_o near_a distance_n from_o e_o to_o ac_fw-la be_v the_o height_n require_v viz._n 120_o of_o the_o same_o part_n that_o ik_fw-mi be_v 79_o note_v the_o figure_n and_o behold_v that_o acfe_n the_o small_a figure_n on_o the_o board_n be_v like_a and_o proportional_a to_o aa_n gh_n the_o great_a figure_n vi_o other_o way_n there_o be_v as_o by_o a_o bowl_n of_o water_n or_o a_o glass_n or_o a_o plash_n of_o water_n or_o a_o square_a but_o these_o set_v down_o be_v as_o convenient_a and_o ready_a as_o any_o whatsoever_o as_o in_o the_o next_o figure_n you_o may_v see_v the_o way_n by_o the_o glass_n and_o square_a as_o thus_o let_v c_o represent_v a_o glass_n a_o bowl_n or_o plash_n of_o water_n wherein_o the_o eye_n at_o a_o see_v the_o picture_n or_o reflection_n of_o the_o object_n e._n then_o by_o the_o line_n of_o number_n as_o cb_n the_o measure_n from_o your_o foot_n to_o the_o glass_n be_v to_o ab_fw-la the_o height_n from_o your_o eye_n to_o the_o ground_n at_o your_o foot_n so_o be_v the_o measure_n from_o c_o to_o d_o to_o the_o height_n de._n see_v figure_n vi._n again_o to_o find_v a_o distance_n by_o the_o square_n that_o be_v not_o overlong_a let_v c_o represent_v the_o upper-corner_n of_o a_o square_a hang_v on_o a_o staff_n at_o f_o then_o the_o one_o part_n of_o the_o square_n direct_v to_o e_o and_o the_o other_o to_o a._n the_o proportion_n will_v hold_v by_o the_o line_n of_o number_n as_o favorina_n 11-37_a to_o fc_v 50_o so_o be_v fc_fw-mi 50_o to_o fe_o 220._o that_o be_v so_o many_o time_n as_o you_o find_v of_o in_o fc_n so_o many_o time_n be_v fc_a in_o fe_o and_o the_o like_a note_v that_o you_o must_v conceive_v afe_a to_o be_v the_o ground_n or_o base-line_n in_o this_o operation_n by_o the_o square_a c_o be_v the_o top_n of_o a_o upright_a staff_n 5_o foot_n long_o call_v 50_o for_o fraction_n sake_n use_v x._o to_o find_v a_o distance_n not_o approachable_a by_o the_o triangule_a quadrant_n first_o i_o plant_v my_o triangule_a quadrant_n set_v upon_o a_o three_o legged_a staff_n and_o ball_n socket_n right_a over_o the_o place_n a_o and_o then_o bring_v the_o index_n with_o two_o sight_n in_o it_o lay_v or_o fasten_v to_o the_o centre_n of_o the_o triangule_a quadrant_n right_a over_o the_o line_n of_o sines_n and_o line_n cut_v 90_o at_o the_o head_n the_o index_n and_o sight_n so_o place_v hold_v it_o there_o and_o bring_v it_o and_o the_o instrument_n together_o till_o you_o see_v the_o mark_n at_o c_o through_o the_o two_o sight_n by_o help_n of_o the_o ball-socket_n and_o then_o there_o keep_v it_o then_o remove_v the_o index_n only_o to_o 0-60_a on_o the_o loose-piece_n which_o make_v a_o right_a angle_n and_o set_v up_o a_o mark_n in_o that_o line_n at_o any_o convenient_a distance_n as_o suppose_v at_o b_o 102_o foot_n from_o a_o then_o remove_v the_o instrument_n to_o b_o and_o lay_v the_o index_n on_o the_o centre_n and_o 0-60_a on_o the_o loose-piece_n direct_v the_o sight_n to_o a_o the_o first_o station_n by_o help_n of_o a_o mark_n leave_v there_o on_o purpose_n then_o remove_v the_o sight_n till_o you_o see_v the_o mark_n at_o c_o and_o note_v exact_o on_o what_o degree_n the_o index_n fall_v as_o here_o on_o 60_o count_v from_o 060_o on_o the_o loose-piece_n or_o on_o 30_o count_v from_o the_o head_n which_o be_v the_o angle_n at_o b_o and_o at_o c._n then_o by_o the_o artificial_a number_n sin_n and_o tangent_n on_o the_o edge_n say_v as_o the_o sine_fw-la of_o 30_o the_o angle_n at_o c_o to_o 102_o the_o measure_a distance_n count_v on_o the_o number_n so_o be_v the_o sine_fw-la of_o 60_o the_o angle_n at_o b_o to_o 117_o on_o the_o number_n the_o distance_n require_v so_o also_o be_v 90_o the_o angle_n at_o a_o to_o 206_o the_o distance_n from_o b_o to_o c._n or_o by_o the_o line_n and_o sin_n on_o the_o quadrant-side_n as_o it_o lie_v thus_o as_o the_o measure_n of_o 102_o take_v from_o any_o scale_n as_o the_o line_n of_o line_n double_v to_o the_o =_o sine_fw-la of_o 30_o lay_v the_o index_n or_o a_o thread_n to_o the_o near_a distance_n so_o be_v the_o =_o sine_fw-la of_o 60_o to_o 117_o measure_v latteral_o on_o the_o same_o line_n of_o line_n and_o so_o be_v the_o =_o sine_fw-la of_o 90_o to_o 206_o the_o distance_n from_o b_o to_o c._n so_o also_o if_o you_o observe_v at_o b_o and_o at_z d_o only_o you_o must_v be_v sure_a to_o set_v your_o instrument_n at_o one_o station_n at_o the_o same_o situation_n as_o at_o the_o other_o as_o a_o look_a back_n from_o station_n to_o station_n will_v do_v it_o and_o the_o same_o way_n of_o work_n will_v serve_v for_o as_o the_o sine_fw-la of_o 20_o to_o 110_o so_o be_v the_o sine_fw-la of_o 40_o to_o 206._o and_o so_o be_v the_o sine_fw-la of_o 120_o to_o the_o line_n dc_o 278_o etc._n etc._n use_v xi_o to_o find_v a_o breadth_n and_o a_o distance_n at_o any_o two_o station_n iu._n let_v ab_fw-la be_v two_o mark_n as_o two_o corner_n of_o a_o house_n or_o wall_n and_o let_v the_o breadth_n between_o they_o be_v demand_v and_o their_o distance_n from_o c_o and_o d_o the_o two_o station_n first_o set_v up_o two_o mark_n at_o the_o two_o station_n then_o set_v up_o the_o instrument_n at_o c_o set_v the_o fiducial_a line_n on_o the_o rule_n to_o d_o the_o other_z mark_n then_o direct_v the_o sight_n exact_o to_o b_o and_o to_o a_o observe_v the_o angle_n dcb_n 45_o and_o dca_n 113-0_a as_o in_o the_o figure_n second_o remove_v the_o instrument_n to_o d_o the_o other_z station_n and_o set_v the_o fiducial-line_n of_o the_o quadrant_n viz._n the_o line_n of_o line_n and_o sines_n direct_o to_o c_z then_o fix_v it_o there_o and_o remove_v the_o index_n and_o sight_n to_o a_o and_o to_z b_o to_o get_v the_o angle_n cda_n 42-30_a and_o cdb_v 109-0_a then_o observe_v that_o the_o 3_o angle_n of_o every_o triangle_n be_v equal_a to_o 180_o degree_n have_v get_v the_o angle_n at_o c_o 113_o and_o the_o angle_n at_o d_o 42-30_a by_o consequence_n as_o you_o take_v 155_o the_o sum_n of_o the_o angle_n at_o c_o and_o d_o out_z of_o 180_o then_o there_o remain_v 24-30_a the_o angle_n at_o a._n so_o also_o take_v 109_o and_o 45_o from_o 180_o rest_v 26_o the_o angle_n at_o b_o then_o also_o take_v 45_o the_o angle_n bcd_v out_o of_o 113_o the_o angle_n dca_n rest_v 68_o degree_n the_o angle_n bca_n in_o like_a manner_n take_v 42-30_a from_o 109_o the_o angle_n at_o d_o rest_v