the_o rafter_n require_v hip_n 2._o for_o the_o hip_n length_n count_v the_o length_n of_o the_o rafter_n last_o find_v on_o one_o leg_n and_o the_o half_a breadth_n of_o the_o house_n on_o the_o other_o leg_n and_o take_v the_o parallel_a distance_n between_o and_o measure_v it_o from_o the_o centre_n lateral_o and_o it_o shall_v be_v the_o true_a length_n of_o the_o hip_n require_v diagonal_a 3._o for_o the_o diagonal_a line_n count_v the_o half_a breadth_n of_o the_o house_n on_o both_o leg_n and_o take_v the_o parallel_a distance_n between_o and_o measure_v it_o from_o the_o centre_n and_o it_o shall_v be_v the_o length_n of_o the_o diagonal_a line_n from_o the_o corner_n to_o the_o king-post_n length_n 4._o again_o for_o the_o hip_n count_v the_o diagonal_a line_n last_o find_v on_o one_o leg_n and_o the_o perpendicular_a height_n on_o the_o other_o leg_n and_o the_o parallel_a distance_n between_o shall_v be_v the_o hip_n true_a length_n measure_v as_o before_o from_o the_o 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line_n and_o measure_v it_o from_o the_o centre_n and_o it_o shall_v give_v just_a 15_o foot_n the_o length_n of_o the_o rafter_n require_v cf._n 2._o but_o if_o according_a to_o the_o width_n of_o any_o frame_n you_o resolve_v on_o the_o rafter_n length_n and_o will_v have_v the_o perpendicular_a height_n of_o the_o gable_n end_n than_o thus_o count_v the_o length_n of_o the_o rafter_n from_o the_o centre_n and_o take_v the_o lateral_a extent_n thereof_o being_z 15_o between_o your_o compass_n the_o compass_n be_v so_o set_v perpendicular_a set_v one_o point_n in_o 10_o the_o half_a width_n of_o the_o frame_n and_o turn_v the_o other_o point_n parallelly_n to_o the_o common_a line_n and_o there_o it_o shall_v show_v 11_o foot_n 2_o 1_o 7_o inch_n the_o true_a height_n of_o the_o perpendicular_a at_o true_a pitch_n require_v if_o 11_o foot_n 2_o inch_n 1_o 7._o 3._o for_o the_o length_n of_o the_o hip_n count_v the_o half_a breadth_n of_o the_o house_n on_o one_o leg_n and_o the_o rafter_n length_n on_o the_o other_o leg_n and_o take_v the_o parallel_a distance_n between_o and_o it_o shall_v give_v the_o true_a length_n of_o the_o hip_n require_v length_n as_o here_o the_o parallel_a distance_n between_o 15_o and_o 10_o shall_v be_v lateral_a 8_o the_o true_a length_n of_o the_o hip_n require_v in_o a_o square_a frame_n 20_o foot_n wide_o true_a pitch_n cg_n 4._o for_o the_o diagonal_a line_n from_o the_o corner_n to_o the_o king-post_n count_n the_o half_a width_n of_o the_o house_n line_n viz._n 10_o foot_n on_o both_o leg_n and_o take_v the_o parallel_n extent_n between_o and_o it_o shall_v reach_v from_o the_o centre_n to_o 14_o foot_n 1_o inch_n â…_n be_v the_o line_n ce_fw-fr in_o the_o figure_n 5._o otherwise_o for_o the_o hip_n length_n count_v the_o half_a diagonal_a on_o one_o leg_n 24_o 1_o â…_n and_o the_o perpendicular_a 11_o foot_n 2_o in._n inches_n 2_o 2_o 7_o on_o the_o other_o leg_n hip._n and_o the_o parallel_n distance_n between_o measure_v from_o the_o centre_n will_v give_v the_o true_a hip_n length_n 18_o viz._n the_o line_n cg_n thus_o much_o for_o the_o rafter_n and_o hip_n in_o square_a frames_n at_o true_a pitch_n the_o measure_n of_o who_o angle_n and_o length_n be_v as_o follow_v  _fw-fr  _fw-fr  _fw-fr f._n inc._n 180_o part_n f._n 100_o part_n deg_n min._n the_o breadth_n of_o the_o house_n be_v 20_o f._n and_o the_o two_o end_n square_a and_o the_o rafter_n it_o true_a pitch_n the_o length_n and_o angle_n of_o the_o frame_v be_v cf_n rafter_n 15_o 00_o 00_o 15_o 000_o rafter_n top_n foot_n 41_o 50_o cg_n hippolito_n 18_o 00_o 00_o 18_o 000_o 48_o 10_o if_o perpendicular_a 11_o 02_o 17_o 11_o 180_o hip_n top_n foot_n 51_o 38_o be_v ½_o diagonal_a 14_o 01_o 68_o 14_o 140_o 38_o 22_o by_o half_a breadth_n 10_o 00_o 00_o 10_o 000_o  _fw-fr  _fw-fr  _fw-fr bc_n whole_a breadth_n 20_o 00_o 00_o 20_o 000_o difference_n 13_o 16_o kg_n near_o dist._n 16_o 07_o 50_o 16_o 624_o  _fw-fr  _fw-fr  _fw-fr bd_o who_o will_v diagoras_n 28_o 03_o 36_o 28_o 281_o outsid_n ang_fw-mi 116_o 12_o the_o rule_n to_o find_v the_o angle_n of_o the_o rafter_n and_o hip_n 1._o for_o the_o angle_n that_o the_o rafter_n make_v at_o foot_n and_o head_n with_o the_o raising-piece_n and_o king-post_n do_v thus_o when_o the_o rule_n stand_v square_a in_o the_o 30_o scale_n then_o lay_v any_o straight_a piece_n to_o the_o compass_n point_v when_o one_o stand_v in_o the_o half_a breadth_n and_o the_o other_o point_n in_o the_o perpendicular_a then_o if_o you_o apply_v a_o bevel_n several_o to_o that_o straight_a edge_n and_o the_o 30_o scale_n at_o each_o end_n the_o one_o be_v the_o angle_n at_o foot_n 48_o 10_o and_o the_o other_o the_o angle_n at_o head_n viz._n 41_o 50._o 2._o for_o the_o angle_n at_o head_n or_o king-post_n and_o foot_n of_o the_o hip_n do_v thus_o the_o 30_o scale_n be_v set_v square_a set_v one_o point_n of_o the_o compass_n in_o the_o half_a diagonal-line_n on_o one_o 30_o scale_n and_o the_o other_o 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or_o l_o in_o the_o figure_n may_v be_v do_v thus_o count_n the_o length_n of_o the_o hip_n on_o one_o leg_n and_o also_o take_v it_o between_o your_o compass_n and_o count_v the_o breadth_n of_o the_o house_n on_o the_o other_o leg_n and_o set_v one_o point_n of_o the_o compass_n in_o the_o hip_n length_n on_o one_o leg_n and_o the_o other_o point_n in_o the_o breadth_n of_o the_o house_n on_o the_o other_o leg_n alter_v the_o 30_o scale_n but_o not_o your_o compass_n then_o when_o the_o 30_o scale_n be_v so_o set_v one_o represent_v the_o raising-piece_n and_o the_o other_o the_o hip_n set_v up_o then_o the_o near_a distance_n from_o the_o breadth_n
of_o the_o house_n on_o one_o 30_o scale_n to_o the_o common-line_n on_o the_o other_o 30_o scale_n be_v the_o near_a distance_n require_v be_v measure_v from_o the_o centre_n 167½_a then_o take_v the_o whole_a diagonal_a line_n viz._n cl_n or_o bk_n from_o the_o centre_n lateral_o and_o make_v it_o a_o parallel_n in_o the_o near_a distance_n last_o find_v and_o that_o shall_v set_v the_o 30_o scale_n to_o the_o angle_n of_o the_o outside_n of_o the_o hip_n require_v which_o you_o may_v measure_v in_o degree_n thus_o take_v parallel_v 15_o as_o the_o rule_n stand_v and_o lay_v it_o from_o the_o centre_n and_o it_o shall_v reach_v to_o 116_o degree_n on_o the_o chord_n next_o one_o 30_o scale_n the_o angle_n of_o the_o outside_n of_o the_o hip_n require_v example_n and_o more_o brief_o in_o a_o house_n 20_o foot_n broad_a the_o house-end_n be_v 20_o foot_n broad_a the_o whole_a diagonal_a line_n be_v 28_o foot_n 3_o inch_n â…œ_n the_o hip-rafter_n 18_o foot._n take_v 18_o foot_n between_o your_o compass_n and_o set_v one_o point_n in_o 20_o and_o open_a or_o shut_v the_o rule_n till_o the_o other_o fit_v 18_o than_o the_o near_a distance_n from_o 20_o to_o the_o common-line_n will_v be_v 16_o foot_n 7_o inch_n 4_o 8._o then_o take_v 28_o foot_n 3_o inch_n â…_n the_o whole_a diagonal_a line_n and_o make_v it_o a_o parallel_n in_o 16_o foot_n 7_o inch_n ½_o the_o near_a distance_n and_o the_o 30_o scale_n be_v set_v to_o the_o angle_n require_v for_o if_o you_o take_v out_o parallel_v 15_o the_o chord_n of_o 60_o and_o measure_v it_o latteral_o from_o the_o centre_n it_o shall_v reach_v to_o 116_o the_o angle_n in_o degree_n and_o minute_n require_v note_n if_o the_o whole_a breadth_n and_o whole_a diagonal_a line_n be_v too_o large_a for_o your_o compass_n than_o the_o half_a breadth_n and_o half_a diagonal_a will_v do_v as_o well_o take_v the_o half_a length_n of_o the_o hip_n also_o between_o your_o compass_n and_o on_o the_o scale_n also_o and_o that_o shall_v set_v the_o scale_n to_o the_o same_o angle_n as_o before_o use_v xv._n to_o find_v the_o length_n and_o angle_n of_o the_o rafter_n and_o hip_n or_o sleeper_n in_o bevel_v frames_n at_o any_o piton_n 1._o for_o the_o length_n of_o the_o rafter_n set_v the_o 30_o scale_n square_a then_o count_v the_o half_a length_n of_o the_o bevel-end_n on_o one_o leg_n rafter_n be_v always_o more_o there_o than_o the_o half_a breadth_n and_o the_o perpendicular_a resolve_v on_o on_o the_o other_o leg_n then_o the_o parallel_n distance_n between_o measure_v lateral_o shall_v be_v the_o length_n of_o the_o rafter_n require_v and_o a_o ruler_n lay_v to_o the_o two_o point_n of_o the_o compass_n to_o set_v on_o the_o 30_o scale_n and_o a_o bevel_n set_v as_o before_o in_o square_a frames_n be_v show_v shall_v give_v the_o angle_n at_o head_n and_o foot_n require_v 2._o for_o the_o hip_n length_n count_v the_o rafter_n length_n on_o one_o leg_n and_o the_o half_a breadth_n of_o the_o bevel-end_n of_o the_o house_n more_o by_o half_a the_o number_n of_o inches_n bevel_v on_o the_o other_o leg_n and_o take_v the_o parallel_n distance_n between_o hip_n and_o measure_v it_o lateral_o from_o the_o centre_n and_o it_o shall_v be_v the_o length_n of_o the_o long_a hip-rafter_n and_o for_o the_o short_a hip_n count_v less_o than_o the_o bevel-end_n by_o half_a the_o number_n of_o inches_n bevel_v and_o that_o shall_v be_v the_o short_a hip_n require_v 3._o the_o inch_n or_o foot_n and_o inch_n of_o bevel_v be_v give_v to_z and_o how_o much_o one_o corner_n be_v under_o and_o the_o other_o over_o 90_o degree_n or_o just_o square_a open_v the_o 30_o scale_n frame_n and_o take_v the_o breadth_n of_o the_o house_n over_o at_o the_o near_a distance_n between_o your_o compass_n from_o the_o 30_o scale_n from_o the_o centre_n lateral_o and_o make_v it_o a_o parallel_n in_o 15_o and_o 15_o for_o 60_o of_o the_o chord_n then_o take_v the_o foot_n and_o inch_n bevel_v from_o the_o same_o 30_o scale_n lateral_o and_o carry_v it_o parallelly_n till_o it_o stay_v in_o like_a part_n then_o just_a against_o it_o on_o the_o degree_n or_o tangent_n be_v the_o degree_n and_o minute_n require_v that_o one_o corner_n be_v more_o and_o the_o other_o less_o than_o 90_o degree_n 4._o to_o find_v the_o diagonal_a line_n take_v the_o distance_n in_o the_o chord_n to_o the_o degree_n above_o or_o under_o 90_o last_o sound_n from_o the_o centre_n lateral_o and_o make_v it_o a_o parallel_n in_o 15_o and_o 15_o and_o then_o the_o 30_o scale_n be_v set_v to_o the_o angle_n the_o end_n be_v over_o diagonal-line_n or_o under_o 90_o degree_n then_o count_v the_o whole_a or_o half_a bevel-end_n on_o both_o leg_n and_o the_o parallel_n distance_n between_o shall_v show_v the_o length_n of_o the_o whole_a or_o half_a diagonal_a line_n measure_v from_o the_o centre_n note_v that_o when_o the_o rule_n stand_v at_o the_o blunt_a angle_n it_o give_v the_o long_a diagonal_a line_n and_o when_o it_o stand_v at_o the_o sharp_a angle_n it_o give_v the_o short_a diagonal_a line_n 5._o by_o the_o diagonal_a line_n and_o perpendicular_a to_o find_v the_o hip_n length_n and_o the_o angle_n at_o head_n and_o foot_n of_o the_o hip_n or_o sleeper_n count_n the_o half_a diagonal_a on_o one_o leg_n hip_n and_o the_o perpendicular_a height_n on_o the_o other_o leg_n the_o 30_o scale_n be_v square_a than_o the_o parallel_n distance_n between_o shall_v be_v the_o length_n of_o the_o hip_n require_v be_v long_o or_o short_a as_o the_o diagonal_a line_n be_v also_o a_o rule_n lay_v to_o the_o two_o point_n of_o the_o compass_n measure_v the_o parallel_n extent_n hip_n and_o a_o bevel_n lay_v to_o the_o rule_n and_o the_o two_o 30_o scale_n at_o each_o end_n give_v the_o angle_n at_o head_n and_o foot_n of_o hip_n require_v to_o find_v the_o near_a distance_n from_o the_o corner_n of_o the_o rombus_n to_o the_o opposite_a hippolito_n set_v up_o in_o his_o true_a place_n 6._o count_n the_o length_n of_o the_o hip_n on_o one_o 30_o scale_n and_o take_v that_o distance_n also_o between_o your_o compass_n lateral_o count_v also_o on_o the_o other_o 30_o scale_v the_o length_n of_o the_o bevel-end_n and_o there_o set_v one_o point_n of_o the_o compass_n and_o open_a or_o shut_v the_o rule_n till_o the_o other_o point_n fall_v in_o the_o length_n of_o the_o hip-rafter_n first_o count_v then_o one_o 30_o scale_n represent_v the_o raising-piece_n distance_n and_o the_o other_o the_o hip_n set_v up_o then_o the_o near_a distance_n from_o the_o breadth_n of_o the_o frame_n over_o at_o the_o bevel-end_n and_o more_o or_o less_o by_o half_a the_o foot_n and_o inch_n bevel_v to_o the_o common_a line_n of_o the_o other_o 30_o scale_n be_v measure_v from_o the_o centre_n shall_v be_v the_o near_a distance_n require_v to_o find_v the_o angle_n on_o the_o outside_n of_o the_o hip._n 7._o to_o find_v the_o outside_o angle_n of_o the_o long_a hip_n take_v the_o short_a diagonal_a line_n between_o your_o compass_n and_o make_v it_o a_o parallel_n in_o the_o near_a distance_n belong_v to_o that_o hip_n and_o the_o 30_o scale_n will_v be_v set_v to_o the_o angle_n require_v and_o to_o measure_v it_o take_v parallel_v 15_o and_o 15_o and_o measure_v it_o lateral_o from_o the_o centre_n in_o the_o chord_n angle_n and_o you_o shall_v have_v the_o measure_n of_o the_o angle_n require_v example_n in_o a_o house_n of_o 20_o foot_n over_o at_o near_a distance_n and_o 4_o foot_n or_o 48_o inch_n bevel_v out_o of_o square_n see_v fig._n ii_o let_v abcd_n represent_v a_o frame_n 20_o foot_n over_o and_o 4_o foot_n bevel_v the_o bevel_n end_n b_o c_o be_v long_o than_o right_o over_o by_o 5_o inch_n for_o if_o you_o set_v the_o rule_n square_a and_o take_v the_o parallel_n extent_n from_o 20_o the_o measure_n over_o to_z 4_o foot_n the_o measure_n of_o bevel_v and_o measure_v it_o lateral_o you_o shall_v find_v it_o reach_v lateral_o to_o 20_o foot_n and_o 5_o inch_n the_o true_a length_n of_o the_o bevel-end_n the_o bevel-end_n be_v 20_o 5_o inch_n the_o perpendicular_a resolve_v on_o which_o at_o true_a pitch_n ought_v to_o be_v about_o 11_o foot_n 5_o inch_n fere_n then_o first_o for_o the_o rafter_n length_n 1._o set_a the_o 30_o scale_n square_a and_o set_v one_o point_n in_o 11_o 5_o the_o perpendicular_a and_o the_o other_o point_n in_o 10_o foot_n 2_o ½_o the_o half_a bevel-end_n and_o to_o the_o compass-point_n lay_v a_o rule_n and_o to_o the_o rule_n and_o the_o 30_o scale_n at_o both_o end_v set_v a_o bevel_n angle_n and_o one_o shall_v be_v the_o angle_n at_o foot_n and_o the_o other_o at_o the_o angle_n at_o the_o top_n of_o the_o rafter_n
and_o the_o one_o angle_n will_v be_v 42_o degree_n for_o the_o foot_n and_o the_o other_o 48_o for_o the_o top_n of_o the_o rafter_n and_o the_o measure_n between_o the_o compass_n measure_v from_o the_o centre_n shall_v be_v 15_o foot_n 4_o inch_n the_o rafter_n length_n require_v as_o by_o inspection_n on_o the_o 40_o and_o 30_o scale_n you_o may_v see_v 2._o for_o the_o long_a hip_n set_v one_o point_n in_o 12_o foot_n 2_o inch_n and_o ½_o more_o by_o two_o foot_n than_o 10_o foot_n 2_o inch_n ½_o the_o half_a bevel-end_n and_o the_o other_o point_n in_o 15_o 4_o the_o rafter_n length_n and_o measure_v it_o from_o the_o centre_n it_o give_v 19_o foot_n 6_o inch_n the_o long_a hip._n again_o length_n set_v one_o point_n in_o 8_o foot_n 2_o inch_n ½_o 2_o foot_n short_a than_o the_o half_a bevel-end_n by_o 2_o foot_n the_o half_a of_o 4_o foot_n the_o bevel_v and_o the_o other_o point_n in_o 15_o foot_n the_o rafter_n length_n and_o measure_v it_o from_o the_o centre_n it_o give_v 17_o foot_n 4_o inch_n the_o length_n of_o the_o short_a hip._n 3._o for_o the_o length_n of_o both_o diagonal_a line_n set_v the_o scale_n of_o 30_o to_o the_o angle_n of_o the_o frame_n at_o each_o corner_n and_o the_o measure_n from_o the_o half_a or_o the_o whole_a bevel-end_n take_v parallelly_n shall_v be_v the_o length_n require_v of_o the_o half_a or_o whole_a diagonal_a line_n according_a as_o you_o take_v the_o whole_a or_o half_a bevel-end_n as_o here_o in_o our_o example_n the_o blunt-end_n be_v 101_o gr_n 30_o min._n or_o 11_o 30_o more_o than_o 90_o gr_n therefore_o take_v the_o distance_n from_o the_o centre_n to_o 101_o diagonal-line_n 30_o on_o the_o chord_n and_o make_v it_o a_o parallel_n in_o 15_o and_o 15_o the_o chord_n of_o 60_o then_o be_v the_o 30_o scale_n set_v to_o the_o angle_n of_o the_o blunt-end_n of_o the_o frame_n and_o the_o parallel_n distance_n between_o 20-5_a the_o whole_a bevel-end_n give_v 31_o foot_n 6_o inch_n the_o whole_a diagonal_a line_n b_o l_o or_o the_o parallel_n between_o 10_o 2_o ½_o give_v 15-09_a inch_n b_o e_o the_o half_a again_o the_o sharp_a end_n be_v 78_o 30_o 11_o degr_n 30_o less_o than_o 90_o than_o the_o lateral_a chord_n of_o 78_o 30_o make_v a_o parallel_n chord_n of_o 60_o at_o 15_o then_o be_v the_o rule_n set_v to_o the_o sharp_a end_n of_o the_o frame_n for_o the_o short_a diagonal_a line_n and_o the_o parallel_n distance_n between_o 10-2_a ½_o give_v 12._o foot_n 11._o the_o half_a or_o 25_o foot_n 10_o inch_n the_o whole_a diagonal_a line_n c_o f_o who_o half_a be_v c_o e_o the_o short_a whole_a and_o half_o diagonal_a line_n 4._o for_o the_o hip_n length_n and_o angle_n at_o foot_n and_o head._n set_a the_o 30_o scale_n square_a and_o count_v the_o short_a half_a diagonal_a 12_o foot_n 11_o on_o one_o leg_n and_o the_o perpendicular_a 11_o foot_n 5_o on_o the_o other_o leg_n length_n than_o the_o compass_n point_v so_o set_v lay_v a_o rulâ—_n and_o take_v the_o bevel_n at_o both_o end_n and_o it_o shall_v give_v the_o two_o angle_n at_o head_n and_o foot_n of_o the_o short_a hip_n and_o the_o same_o distance_n of_o the_o compass_n point_n shall_v be_v 17_o foot_n 4_o inch_n fere_n angle_n the_o hip-lenght_n as_o before_o and_o the_o angle_n at_o the_o top_n 48_o 30_o and_o at_o foot_n 41_o 30_o his_o compliment_n again_o set_v one_o point_n in_o 15_o foot_n 10_o the_o long_a half_a diagonal_a and_o the_o other_o point_n in_o 11_o foot_n 5_o inch_n the_o perpendicular_a and_o lay_v a_o rule_n to_o they_o and_o set_v the_o bevel_n to_o both_o end_n and_o you_o shall_v find_v 54_o gr_n the_o angle_n at_o the_o top_n and_o 36_o the_o angle_n at_o foot_n and_o the_o distance_n between_o the_o compass_n lay_v from_o the_o centre_n give_v 19_o foot_n 6_o inch_n the_o long_a hip._n 5._o for_o the_o outside_o angle_n of_o both_o hip_n the_o long_a first_o take_v 19_o 6_o between_o your_o compass_n the_o hip_n length_n from_o the_o 30_o scale_n set_v one_o point_n in_o 20_o foot_n 5_o the_o bevel-end_n and_o close_o the_o rule_n till_o the_o other_o point_n touch_v 19_o 6_o the_o hip_n length_n hip._n then_o take_v the_o near_a distance_n from_o 18_o foot_n 5_o 2_o foot_n less_o than_o 20_o foot_n 5_o the_o breadth_n of_o the_o bevel-end_n of_o the_o frame_n to_o the_o other_o 30_o scale_n and_o it_o be_v the_o near_a distance_n from_o the_o point_n of_o the_o rombus_n a_o to_o the_o hip_n bg_n set_v up_o 15_o foot_n 9_o inch_n then_o tâ—ke_v out_o 25_o foot_n 10_o the_o short_a diagonal_a and_o make_v it_o a_o parallel_n in_o 15_o 9_o the_o near_a distance_n and_o then_o the_o 30_o scale_n be_v set_v to_o the_o angle_n require_v for_o the_o outside_o of_o the_o long_a hippolito_n be_v 110_o degree_n for_o parallel_v 15_o measure_v lateral_o on_o the_o chord_n give_v 1100._o 6._o for_o the_o outside_o angle_n of_o the_o short_a hip._n take_v 17_o foot_n 4_o inch_n between_o your_o compass_n and_o set_v one_o point_n in_o 20_o foot_n 5_o the_o bevel-end_n and_o open_a or_o shut_v the_o rule_n till_o the_o other_o point_n reach_v 17_o 4_o on_o the_o other_o 30_o scale_n hip_n then_o the_o near_a distance_n from_o 22_o foot_n 2_o foot_n more_o than_o the_o breadth_n of_o the_o bevel-end_n of_o the_o frame_n to_o the_o common_a line_n on_o the_o other_o 30_o scale_n and_o that_o shall_v be_v the_o near_a distance_n from_o l_o to_o cg_n the_o short_a hip_n set_v up_o which_o be_v 18_o foot_n 9_o inch_n then_o take_v out_o 15_o foot_n 10_o inch_n the_o half_o great_a diagonal_a line_n because_o 31_o foot_n 8_o inch_n be_v more_o than_o the_o scale_n of_o 30_o and_o make_v it_o a_o parallel_n in_o 9_o 00_o the_o half_a of_o 18_o foot_n and_o the_o 30_o scale_n be_v set_v to_o the_o angle_n require_v viz._n 122_o degree_n for_o if_o you_o take_v out_o parallel_v 15_o and_o measure_v it_o in_o the_o chord_n lateral_o it_o shall_v be_v 122_o the_o angle_n require_v note_v here_o by_o the_o way_n the_o length_n of_o the_o bevel-end_n and_o the_o two_o diagonal_a line_n and_o the_o half_n of_o they_o and_o the_o blunt_a and_o sharp_a angle_n of_o the_o frame_n be_v give_v by_o the_o draught_n of_o the_o frame_n and_o they_o be_v first_o know_v the_o work_n be_v half_o do_v but_o if_o not_o give_v then_o use_v these_o direction_n which_o will_v help_v you_o to_o see_v the_o reason_n of_o plain_a triangle_n and_o the_o use_n of_o the_o scale_n use_v xvi_o to_o find_v the_o rafter_n hip_n and_o angle_n in_o bevel_n and_o taper_n frames_n be_v broad_a at_o one_o end_n than_o the_o other_o see_v fig._n iii_o first_o when_o the_o frame_n be_v broad_a at_o one_o end_n than_o the_o other_o than_o the_o middle_a breadth_n be_v to_o be_v the_o guide_n for_o the_o rafter_n length_n and_o the_o perpendicular_a to_o be_v equal_a to_o the_o middle_a rafter_n perpendicular_a on_o both_o end_n though_o one_o pair_n of_o rafter_n be_v long_o than_o another_o and_o the_o roof_n in_o wind_v thereby_o which_o wind_v may_v many_o time_n be_v remedy_v by_o some_o convenient_a artifice_n or_o other_o as_o the_o ingenious_a workman_n will_v soon_o perceive_v as_o thus_o in_o brief_a let_v abcd_n represent_v the_o frame_n of_o a_o house_n bevel_v at_o both_o end_n and_o broad_a by_o 2_o foot_n at_o one_o end_n than_o the_o other_o as_o here_o in_o the_o bevel_a figure_n be_v 20_o foot_n on_o one_o side_n and_o 24_o foot_n on_o the_o other_o side_n at_o one_o bevel-end_n 10_o foot_n 4_o inch_n and_o at_o the_o other_o end_n 8_o foot_n 1_o inch_n ½_o but_o at_o the_o near_a distance_n over_o only_o 10_o foot_n and_o 8_o foot._n first_o for_o your_o more_o apparent_a satisfaction_n draw_v the_o true_a form_n of_o the_o frame_n by_o as_o large_a a_o scale_n as_o you_o convenient_o can_v with_o the_o side_n and_o angle_n as_o exact_v as_o you_o can_v as_o abcd_v then_o draw_v the_o middle_a line_n of_o quite_o through_o the_o length_n and_o gh_a through_o the_o breadth_n of_o the_o frame_n perpendicular_a one_o to_o the_o other_o then_o measure_n gh_o as_o suppose_v 9_o foot_n then_o lay_v off_o the_o half_a of_o gh_o from_o h_n to_o i_o and_o k_o then_o take_v out_o ¾_n of_o gh_a and_o lay_v it_o from_o k_o and_o i_o to_o l_o 6_o foot_n 9_o inch_n for_o a_o pair_n of_o middling_a rafter_n for_o this_o taper-house_n lg_n be_v the_o common_a perpendicular_a at_o the_o middle_n and_o both_o end_n of_o the_o roof_n 5_o foot_n 0_o inch_n â…_n of_o a_o inch._n and_o for_o the_o principal_a rafter_n frame_n or_o other_o rafter_n open_v the_o 30_o scale_v square_a and_o
then_o count_v the_o perpendicular_a 50_o â…_n on_o one_o leg_n and_o half_a the_o distance_n between_o the_o rafter-feet_n or_o half_a breadth_n of_o the_o frame_n at_o that_o place_n on_o the_o other_o leg_n and_o the_o parallel_n distance_n between_o shall_v be_v the_o true_a length_n of_o the_o rafter_n require_v then_o for_o the_o hip_n length_n first_o make_v be_o and_o bm_v equal_a to_o ae_n or_o be_v at_o one_o end_n and_o make_v cn_fw-la and_o dn_n equal_a to_o df_n or_o cf_n and_o draw_v the_o line_n mm_o and_o nn_n at_o both_o end_n also_o make_v ab_n and_o bb_n equal_a to_o ab_fw-la and_o ca_o and_o da_n equal_a to_o cd_o and_o draw_v the_o diagonal_a line_n as_o and_o b_n and_o co_n and_o do_v at_o each_o end_n extend_v and_o set_v down_o the_o measure_n of_o they_o these_o line_n be_v draw_v you_o have_v the_o half_a diagonal_a line_n as_o and_o b_n and_o co_n and_o do_v and_o may_v measure_v they_o by_o your_o scale_n to_o find_v their_o length_n or_o set_v the_o rule_n to_o the_o angle_n ae_z and_o bes_z find_v they_o by_o the_o 30_o scale_n also_o you_o have_v the_o bevel-end_n of_o the_o frame_n and_o the_o near_a distance_n over_o from_o side_n to_o side_n of_o the_o frame_n then_o for_o the_o hip_n length_n and_o angle_n thus_o set_v the_o 30_o scale_n square_a and_o count_v the_o perpendicular_a height_n lg_n on_o one_o leg_n 50_o â…_n and_o each_o half_a diagonal_a line_n etc._n etc._n one_o after_o another_o on_o the_o other_o leg_n and_o the_o parallel_n distance_n between_o shall_v be_v the_o true_a length_n of_o the_o several_a hip_n require_v example_n the_o parallel_n distance_n between_o 5_o foot-o-inche_n â…_n the_o common_a perpendicular_a count_v on_o one_o 30_o scale_n and_o 8_o foot_n 1_o inch_n the_o long_a diagonal_a line_n as_o count_v on_o the_o other_o 30_o scale_n shall_v give_v 9_o foot_n 6_o inch_n for_o the_o length_n of_o one_o hippolito_n ap_n lateral_o and_o the_o parallel_n distance_n between_o 5_o 0-â…_a the_o common_a 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30_o scale_n it_o shall_v give_v the_o true_a angle_n of_o the_o hip_n at_o the_o raising-piece_n and_o king-post_n which_o 8_o angle_n in_o these_o 4_o hip_n be_v express_v by_o the_o line_n and_o letter_n in_o the_o scheme_n thus_o pas_n and_o pb_n pdo_n and_o pco_n the_o 4_o angle_n at_o the_o raising-piece_n and_o spa_n and_o spb_n opc_n and_o opd_v the_o 4_o angle_n at_o the_o king-post_n who_o length_n you_o may_v prove_v by_o mr._n pope_n excellent_a way_n making_z sp_z and_o open_v equal_a to_o lg_n on_o the_o extend_a diagonal_a line_n and_o draw_v the_o line_n ap_n bp_o cp_n dp_n for_o the_o 4_o hip-rafter_n length_n require_v or_o for_o more_o proof_n thus_o also_o by_o the_o rule_n as_o before_o in_o square_a roof_n set_a the_o 30_o scale_n square_a and_o take_v the_o parallel_n extent_n from_o 7_o foot_n 2¾_a the_o rafter_n length_n at_o the_o broad_a end_n on_o one_o 30_o scale_n to_o 6_o foot_n 2_o inch_n more_o than_o ½_o the_o bevel-end_n by_o 1_o foot_n the_o half_a quantity_n of_o bevel_v and_o it_o shall_v give_v 9_o foot_n 6_o inch_n for_o the_o hip_n ap_n and_o from_o 72¾_a to_o 4-2_a one_o foot_n less_o than_o the_o half_a bevel-end_n to_o 8_o foot_n ¼_n the_o hip_n bp_o also_o the_o par._n extent_n from_o 6_o foot_n 5½_a the_o rafter_n length_n at_o the_o lesser_a end_n to_z 5_o foot_n 0¾_a one_o foot_n more_o than_o 4-0-¾_a the_o half_n little_a bevel-end_n shall_v give_v 8_o 1½_a for_o the_o hip_n pc_n and_o the_o extent_n from_o 6-5-4_a 8_o the_o rafter_n length_n to_o 30¾_a 1_o foot_n less_o than_o the_o half_a bevel-end_n give_v 71½_a the_o hip_n dp_n as_o before_o note_v that_o by_o the_o work_a these_o 3_o way_n you_o may_v be_v sure_a to_o prevent_v any_o mistake_n that_o may_v happen_v in_o work_v one_o way_n only_o last_o for_o the_o angle_n on_o the_o outside_n or_o back_n of_o the_o hip_n take_v every_o several_a hip_n length_n lateral_o between_o your_o compass_n and_o set_v one_o point_n in_o the_o length_n of_o the_o bevel-end_n or_o rather_o in_o a_o mean_a between_o ab_fw-la the_o bevel-end_n and_o mm_o at_o the_o great_a end_n or_o cd_o and_o nn_n at_o the_o lesser_a end_n and_o open_a or_o shut_v the_o 30_o scale_n till_o the_o other_o point_n fall_v on_o the_o hip_n length_n that_o you_o work_v for_o then_o for_o the_o long_a hip_n count_v more_o and_o for_o the_o short_a hip_n less_o by_o half_a the_o inch_n bevel_v than_o the_o whole_a breadth_n over_o at_o the_o end_n and_o take_v the_o parallel_n near_a distance_n from_o thence_o to_o the_o 30_o scale_n for_o a_o near_a distance_n which_o near_a distance_n you_o must_v keep_v then_o take_v the_o whole_a diagonal_a line_n perpendicular_a to_o the_o hip_n wrought_v for_o viz._n the_o short_a diagonal_a line_n for_o the_o long_a hip_n at_o each_o end_n between_o your_o compass_n and_o make_v it_o a_o parallel_n in_o the_o near_a distance_n last_o find_v and_o then_o the_o 30_o scale_n be_v set_v to_o the_o angle_n of_o the_o back_n of_o the_o hip_n require_v example_n in_o this_o figure_n for_o the_o long_a hip._n take_v 9_o foot_n 6_o inch_n the_o hip_n length_n ap_n between_o your_o compass_n and_o set_v one_o point_n in_o 10_o foot_n one_o inch_n a_o mean_a between_o ab_fw-la 10_o foot_n 4_o and_o mm_o 9-10_a ½_o and_o open_a or_o shut_v the_o rule_n till_o the_o other_o point_n stand_v in_o 9_o foot_n 6_o the_o hip_n length_n first_o take_v then_o the_o near_a distance_n from_o 9_o foot_n 4_o inch_n one_o foot_n less_o than_o 10_o f._n 4_o inch._n the_o bevel-end_n distance_n over_o to_o the_o other_o 30_o scale_n shall_v give_v 7_o 10_o a_o near_a distance_n from_o the_o point_n b_o to_o ap_n the_o hippolito_n raise_v over_o as_o the_o diagonal_a then_o the_o lateral_a extent_n bb_v of_o the_o whole_a diagonal_a line_n 12_o f._n 7_o inch._n be_v make_v a_o parallel_n in_o 7_o 10_o the_o near_a distance_n last_o find_v shall_v set_v the_o 30_o scale_n to_o the_o angle_n at_o r_o the_o back_n of_o the_o hip_n require_v 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the_o other_o end_n be_v near_o the_o same_o angles_n which_o you_o may_v prove_v by_o m._n will._n pope_n excellent_a way_n thus_o find_v the_o middle_n between_o saint_n and_o a_o or_o saint_n and_o b_o at_o q_n than_o the_o near_a distance_n from_o q_o to_o bp_o or_o ap_n near_o lie_v to_o r_o and_o draw_v the_o line_n re_fw-mi rm_n for_o the_o angle_n at_o r_o the_o back_n of_o the_o hip_n require_v moreover_o if_o you_o raise_v 4_o perpendicular_o cut_v the_o point_n o_o and_o s_o the_o two_o place_n of_o the_o king-post_n be_v perpendicular_a to_o the_o raising-piece_n ac_fw-la end_n bd_o as_o the_o
4_o prick-line_n ♉_o saint_n â™_o s_o ♌_o o_o and_o ♊_o o_fw-fr do_v show_v and_o lay_v the_o length_n of_o each_o hip_n from_o his_o proper_a corner_n abcd_v as_o ap_n from_o a_o to_o ♈_o and_o â™_o bp_o from_o b_o to_o ♈_o and_o ♉_o dp_v from_o d_o to_z ♊_o and_o ♋_o cp_n from_o c_z to_z ♌_o and_o ♋_o then_z draw_z line_n from_o point_n to_o point_n as_o in_o the_o figure_n then_o â™_o ♌_o and_o ♉_o ♊_o be_v the_o two_o ridge_n when_o turn_v right_o over_o os_fw-la and_o c_o ♋_o d_o be_v the_o least_o hip_n and_o a_o ♈_o b_o be_v the_o great_a hip_n as_o mr._n pope_n have_v well_o show_v thus_o much_o for_o hipt_v roof_n use_v xvii_o to_o find_v the_o length_n and_o angle_n of_o every_o principal_a particular_a rafter_n in_o frames_n broad_a at_o one_o end_n than_o the_o other_o the_o perpendicular_a as_o before_o be_v hint_v be_v to_o be_v the_o same_o all_o over_o the_o roof_n therefore_o open_a the_o rule_n square_n and_o take_v from_o the_o perpendicular_a on_o one_o leg_n to_o the_o half_a breadth_n of_o the_o frame_n on_o the_o other_o leg_n measure_v it_o from_o the_o centre_n and_o that_o be_v the_o length_n require_v for_o the_o angle_n lay_v a_o rule_n to_o the_o compass-point_n and_o set_v a_o bevel_n as_o before_o be_v show_v and_o you_o have_v the_o angle_n at_o the_o raising-piece_n and_o ridge_n of_o the_o house_n to_o cut_v the_o rafter_n foot_n by_o the_o same_o rule_n serve_v to_o draw_v out_o a_o pair_n of_o well-stair_n to_o give_v hypothenusaes_n or_o string_n at_o any_o particular_a height_n and_o breadth_n for_o the_o 30_o scale_n set_v square_a and_o the_o perpendicular_a height_n count_v on_o one_o leg_n and_o the_o breadth_n on_o the_o other_o leg_n the_o measure_n between_o be_v always_o the_o hypothenusa_n or_o string_n in_o fly_a stair_n as_o may_v plain_o appear_v use_v xviii_o to_o find_v the_o length_n and_o angle_n of_o collar-beam_n in_o any_o roof_n take_v the_o whole_a breadth_n of_o the_o frame_n between_o your_o compass_n and_o set_v one_o point_n in_o the_o length_n of_o the_o rafter_n on_o one_o leg_n and_o the_o other_o point_n in_o the_o same_o place_n on_o the_o either_o leg_n then_o the_o two_o leg_n represent_v the_o two_o principal_a rafter_n and_o a_o rule_n lay_v to_o the_o compass-point_n represent_v the_o raising-piece_n then_o at_o any_o height_n that_o you_o please_v above_o the_o raising-piece_n apply_v a_o rule_n parallel_n to_o it_o and_o the_o measure_n between_o lay_v from_o the_o centre_n give_v the_o length_n remember_v to_o add_v wood_n for_o the_o tenon_n and_o a_o bevel_n lay_v to_o the_o 30_o scale_n and_o rule_n give_v the_o true_a angle_n to_o cut_v it_o by_o where_o the_o timber_n be_v square_a use_v xix_o to_o find_v the_o length_n and_o angle_n of_o rafter_n and_o purloyn_n in_o bevel_n frames_n the_o length_n of_o the_o rafter_n be_v show_v before_o to_o find_v it_o by_o the_o half_a breadth_n of_o the_o square_a or_o bevel-end_n and_o the_o perpendicular_a answerable_a to_o that_o roof_n as_o afterward_o in_o the_o example_n and_o the_o angle_n of_o the_o foot_n and_o outside_n or_o back_n of_o the_o bevel-end_n rafter_n and_o the_o upright_a of_o the_o gable_n end_n must_v be_v to_o a_o angle_n less_o and_o more_o than_o 90_o degree_n by_o the_o angle_n at_o the_o corner_n of_o the_o frame_n where_o that_o rafter_n be_v to_o stand_v be_v more_o at_o the_o sharp_a angle_n and_o less_o at_o the_o blunt_a angle_n as_o in_o figure_n iv_o you_o may_v see_v the_o true_a quantity_n of_o which_o angle_n be_v thus_o find_v by_o the_o rule_n take_v the_o length_n of_o the_o rafter_n for_o the_o bevel-end_n in_o foot_n and_o inch_n and_o make_v it_o a_o parallel_n in_o 15_o then_o half_a the_o quantity_n of_o foot_n and_o inch_n bevel_v take_v from_o the_o same_o scale_n and_o carry_v parallelly_n till_o it_o stay_v in_o like_a part_n shall_v show_v right_a against_o it_o in_o the_o tangent_n the_o degree_n and_o minute_n require_v and_o this_o be_v the_o angle_n that_o the_o blunt_a corner_n be_v to_o be_v lay_v in_o legement_n more_o than_o a_o square_n and_o the_o sharp_a angle_n less_o than_o a_o square_n or_o 90_o degree_n both_o out_o of_o level_n and_o out_o of_o square_a also_o when_o you_o tumble_v or_o stripe_n in_o the_o tenon_n of_o the_o purloin_v the_o thing_n desire_v example_n let_v ab_fw-la represent_v the_o bevel-end_n of_o a_o frame_n be_v out_o of_o square_n from_o the_o line_n ac_fw-la 6_o foot_n as_o the_o line_n cb_n show_v then_o if_o ac_fw-la be_v 20_o foot_n ab_fw-la will_v be_v 20_o foot_n 10_o inch_n then_o draw_v el_n the_o middle_a line_n of_o the_o frame_n and_o gm_n and_o hk_n the_o line_n at_o three_o quarter_n of_o the_o breadth_n of_o the_o frame_n then_o take_v ed_z the_o half_a bevel_n and_o lay_v it_o from_o g_o to_o f_o and_o from_o h_n to_o i_o and_o draw_v the_o line_n of_o and_o by_o for_o the_o outside_n line_n of_o the_o two_o bevel-end_n rafter_n end_v the_o two_o other_o line_n parallel_v to_o they_o according_a to_o the_o breadth_n or_o scantling_n of_o your_o bevel-end_n rafter_n as_o here_o in_o the_o figure_n 8_o inch_n broad_a thus_o the_o line_n of_o and_o by_o represent_v the_o two_o end_n rafter_n lay_v in_o legement_n to_o fit_v in_o the_o purloin_v as_o for_o their_o lie_v out_o of_o square_n from_o the_o raising-piece_n and_o to_o the_o same_o angle_n they_o be_v to_o be_v lay_v out_o at_o level_n that_o the_o cut_n of_o the_o purloin_v end_n may_v fit_v the_o rafter_n side_n when_o erect_v in_o their_o place_n according_a as_o the_o end_v f_o and_o i_o of_o the_o bevel-end_n rafter_n be_v according_a to_o the_o angel_n afg_n and_o afm_n the_o one_o be_v 11_o degree_n and_o 20_o minute_n under_o and_o the_o other_z 11_o 20_o above_o 90_o degree_n also_o note_v that_o if_o pk_a and_o om_fw-la do_v represent_v a_o pair_n of_o square_a rafter_n at_o any_o intend_a distance_n from_o a_o then_o it_o be_v and_o rq_n will_v give_v the_o true_a length_n of_o the_o purloin_v fit_a for_o those_o place_n rq_n be_v the_o short_a purloin_v and_o it_o be_v the_o long_a purloin_v to_o find_v by_o the_o rule_n only_o how_o long_o the_o purloin_v must_v be_v on_o the_o outside_n more_o or_o less_o than_o the_o distance_n on_o the_o raising-piece_n where_o you_o intend_v the_o two_o square_a rafter_n foot_n shall_v stand_v do_v thus_o set_v the_o 30_o scale_n to_o the_o same_o angle_n that_o the_o bevel-end_n rafter_n lie_v out_o of_o square_a when_o they_o lie_v in_o legement_n to_o frame_v which_o here_o be_v to_o 11_o degree_n and_o 20_o minute_n then_o count_v from_o the_o centre_n the_o quantity_n of_o foot_n and_o inch_n you_o intend_v to_o make_v the_o mortise-hole_n from_o the_o rafter_n foot_n in_o the_o rafter_n for_o the_o tenon_n of_o your_o purloin_v and_o take_v from_o thence_o to_o the_o near_a distance_n to_o the_o other_o line_n and_o that_o shall_v show_v the_o quantity_n that_o the_o one_o purloin_v be_v to_o be_v long_o and_o the_o other_o short_a than_o the_o distance_n between_o the_o rafter-feet_n on_o the_o raise_v piece_n example_n thus_o set_v the_o 30_o scale_n to_o the_o angle_n gaf_n then_o count_v as_o the_o place_n for_o the_o mortise-hole_n from_o a_o on_o the_o rafter_n and_o take_v the_o near_a distance_n from_o thence_o to_o the_o other_o 30_o scale_n that_o shall_v give_v sv_o the_o quantity_n how_o much_o it_o be_v be_v short_a than_o ao_o and_o how_o much_o rq_n be_v long_o than_o pb_n note_v that_o if_o you_o count_v 3_o quarter_n of_o 20_o foot_n 10_o inch_n be_v the_o length_n of_o the_o bevel-end_n that_o then_o you_o will_v make_v the_o rafter_n too_o long_o by_o 4_o inch_n and_o a_o half_a as_o in_o the_o figure_n you_o may_v see_v therefore_o the_o sure_a way_n to_o find_v the_o rafter_n length_n be_v to_o set_v the_o scale_n to_o a_o square_a and_o then_o to_o take_v the_o parallel_n extent_n from_o the_o common_a perpendicular_a to_o the_o ½_o breadth_n between_o the_o place_n for_o the_o rafter-feet_n on_o the_o raising-piece_n so_o that_o the_o length_n of_o the_o rafter_n for_o the_o bevel-end_n at_o true_a pitch_n be_v of_o 15_o foot_n 3_o inch_n and_o not_o awe_o 157½_a which_o be_v just_a 3_o quarter_n of_o ab_fw-la the_o bevel-end_n over_o which_o the_o two_o rafter_n be_v to_o stand_v for_o then_o the_o top_n of_o the_o bevel-end_n rafter_n will_v be_v too_o high_a for_o the_o top_n of_o the_o square_a rafter_n be_v cut_v just_a 15_o foot_n three_o quarter_n of_o 20_o foot_n the_o breadth_n of_o the_o frame_n use_v xx._n the_o use_n of_o the_o scale_n to_o lay_v down_o or_o measure_v out_o on_o paper_n
thereof_o the_o architrave_n have_v 32_o minute_n the_o friese_n 25_o ½_o minute_n the_o cornish_a 38_o ½_o minute_n the_o architrave_n 32_o minute_n divide_v into_o 9_o â…š_n part_n thereof_o stick_v far_o out_o as_o the_o outer-edge_n of_o the_o door-stile_n 7_o â…”_n part_n or_o 8_o ½_o minute_n far_o for_o cornish_v and_o let_v the_o ear_n of_o the_o architrave_n be_v 17_o part_n long_o of_o the_o forgiven_a part_n or_o 55_o ½_o minute_n to_o underneath_o beside_o all_o other_o the_o cornish_n of_o the_o architrave_n as_o you_o may_v see_v in_o the_o figure_n the_o friese_n be_v 25_o ½_o minute_n divide_v in_o 7_o part_n for_o make_v the_o voluta_n or_o scroll_n and_o draw_v one_o line_n up_o the_o four_o part_n or_o 14_o ½_o minute_n from_o above_o off_o right_a parallel_n so_o there_o remain_v 3_o part_n or_o 11_o minute_n for_o the_o stand_v out_o beneath_o and_o the_o eye_n of_o the_o scroll_n be_v 1_o 7_o part_n or_o 3_o minute_n and_o 2_o 14_o of_o the_o height_n of_o the_o friese_n and_o draw_v a_o line_n perpendicular_a from_o above_o to_o the_o underedge_n of_o the_o ear_n of_o the_o architrave_n and_o where_o the_o line_n cut_v cross_v each_o other_o here_o be_v the_o middle_n of_o your_o eye_n strike_v out_o the_o cross_n 4_o part_n 16_o ½_o minute_n near_o to_o the_o outside_n and_o 3_o ½_o part_n or_o 12_o ½_o minute_n to_o the_o inside_n and_o draw_v your_o scroll_n then_o after_o this_o manner_n here_o draw_v the_o scroll_n or_o voluta_n beneath_o be_v â…•_n part_v 5_o ½_o minute_n small_a as_o the_o upper-scrol_a be_v and_o be_v high_a 20_o minute_n and_o the_o breadth_n 12_o ½_o minute_n divide_v the_o height_n in_o 8_o part_n and_o draw_v a_o parallel-line_n of_o 4_o ½_o part_n or_o 11_o ¼_n minute_n from_o beneath_o to_o above_o and_o there_o the_o parallel-line_n cut_v cross_v the_o perpendicular_a be_v the_o middle_n of_o the_o eye_n strikes_z out_z cross_z 3_o ½_o part_n or_o 8_o ¾_n minute_n to_o above_o and_o 4_o part_n or_o 10_o minute_n to_o the_o outside_n and_o there_o remain_v over_o 5_o part_n or_o 12_o ½_o minute_n to_o the_o inside_n far_o all_o that_o belong_v to_o it_o may_v you_o in_o the_o figure_n here_o plain_o see_v as_o for_o the_o breadth_n of_o the_o scroll_n be_v 2_o â…_n part_n of_o the_o cornice_n give_v part_n or_o 19_o minute_n the_o other_o member_n before_o may_v be_v see_v in_o the_o figure_n xxxvi_o here_o be_v show_v two_o chimney-mantils_a with_o their_o prosile_n xxxvii_o here_o be_v show_v the_o ground_n of_o the_o building_n of_o the_o lord_n strozzi_n stand_v at_o florence_n the_o like_a be_v describe_v in_o the_o author_n three_o book_n in_o the_o seven_o chapter_n xxxviii_o the_o half_a of_o the_o building_n on_o the_o ground_n to_o be_v see_v inward_o of_o the_o building_n of_o the_o lord_n strozzi_n thirty-nine_o the_o other_o half_a with_o the_o uprising_n to_o be_v see_v with_o the_o foreside_n of_o the_o foresay_a building_n xl._o here_o we_o have_v the_o under-side_n of_o the_o cornice_n of_o all_o the_o five_o column_n a_o of_o the_o tuscan_a b_o of_o the_o doric_a c_o the_o jonick_a d_o the_o roman_a or_o composita_fw-la e_o the_o corinthian_a finis_fw-la advertisement_n the_o description_n and_o use_v of_o the_o carpenter_n rule_n together_o with_o the_o use_n of_o the_o line_n of_o number_n and_o its_o application_n in_o measure_v all_o superficies_n and_o solid_n gauge_v with_o the_o use_n of_o a_o slide_a rule_n and_o the_o joint_n rule_n by_o john_n browne_n and_o sell_v by_o william_n fisher._n the_o description_n and_o use_v of_o a_o ordinary_a joint-rule_a fit_v with_o line_n for_o the_o ready_a find_v the_o length_n and_o angle_n of_o rafter_n and_o hip_n and_o collar-beam_n in_o any_o square_a or_o bevel_a roof_n at_o any_o pitch_n and_o the_o ready_a draw_v the_o architrave_n friese_n and_o cornice_n in_o any_o order_n with_o other_o useful_a conclusion_n by_o the_o say_a rule_n by_o john_n browne_n london_n print_v in_o the_o year_n mdclxxxvi_o the_o description_n and_o use_v of_o a_o joint-rule_n fit_v with_o line_n for_o the_o ready_a find_v the_o length_n and_o angle_n of_o rafter_n hip_n and_o collar-beam_n in_o any_o square_a or_o bevel_a roof_n at_o any_o pitch_n first_o the_o rule_n be_v a_o ordinary_a joint_a rule_n of_o a_o foot_n long_o when_o shut_v together_o or_o two_o foot_n be_v open_v to_o a_o straight_a line_n and_o the_o line_n delineate_v thereon_o for_o this_o purpose_n be_v 1._o first_o a_o line_n of_o line_n draw_v sectorwise_a from_o a_o centre_n on_o both_o leg_n of_o the_o rule_n but_o continue_v to_o 30_o at_o the_o end_n in_o stead_n of_o 10_o the_o old_a usual_a manner_n and_o every_o single_a integer_fw-la of_o the_o 30_o be_v divide_v into_o 12_o part_n to_o represent_v every_o particular_a inch_n of_o the_o 30_o foot_n according_a to_o the_o common_a reckon_n by_o foot_n and_o inch_n 2._o there_o be_v another_o scale_n of_o equal_a part_n also_o of_o the_o same_o length_n lie_v as_o 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forward_o to_o 20_o towards_o the_o centre_n which_o serve_v to_o divide_v a_o circle_n into_o any_o number_n of_o part_n very_o useful_a and_o ready_a in_o the_o practice_n of_o draw_v or_o architecture_n thus_o much_o for_o description_n the_o use_v follow_v the_o use_v of_o this_o line_n of_o line_n or_o scale_n of_o equal_a part_n to_o 30_o draw_v from_o the_o centre_n be_v of_o a_o general_a and_o manifold_a use_n as_o mr._n gunter_n in_o his_o book_n of_o the_o sector_n have_v show_v a_o brief_a touch_n whereof_o take_v in_o the_o first_o place_n as_o by_o the_o way_n and_o then_o the_o use_n of_o the_o rule_n to_o the_o business_n intend_v and_o for_o the_o better_a do_v hereof_o it_o be_v needful_a to_o explain_v three_o or_o four_o term_n for_o the_o avoid_n of_o many_o word_n and_o needless_a repetition_n in_o this_o brief_a yet_o plain_a discourse_n 1._o first_o by_o the_o word_n lateral_a be_v mean_v any_o distance_n take_v either_o in_o foot_n and_o inch_n on_o the_o 30_o 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number_n on_o the_o other_o leg_n across_o from_o one_o leg_n to_o the_o other_o as_o thus_o the_o rule_n be_v open_v than_o the_o extent_n of_o the_o compass_n from_o 20_o on_o one_o leg_n to_o 20_o on_o the_o other_o leg_n be_v a_o parallel_n extent_n 3._o in_o all_o parallel_n extent_n you_o must_v set_v one_o point_n of_o the_o compass_n in_o the_o common_a line_n on_o one_o leg_n to_o the_o common_a line_n on_o the_o other_o leg_n which_o common_a line_n be_v that_o only_a of_o the_o 30_o scale_n which_o run_v to_o the_o centre_n in_o which_o the_o center-pin_n at_o 15_o and_o 30_o be_v 4._o the_o near_a
whereof_o he_o give_v two_o to_o the_o stair_n and_o two_o to_o the_o vacuity_n which_o have_v all_o their_o light_n from_o above_o and_o this_o in_o exact_a oval_n be_v as_o a_o masterpiece_n you_o have_v here_o insert_v the_o type_n of_o several_a staircase_n with_o their_o ichnography_n one_o whereof_o be_v a_o piece_n of_o rarity_n be_v a_o pair_n of_o double_a stair_n whereon_o two_o person_n the_o one_o ascend_v the_o other_o descend_v shall_v not_o come_v at_o one_o another_o make_v by_o peidro_n deal_v bergo_n and_o jehan_n cousin_n at_o sciamburg_n in_o france_n in_o the_o king_n palace_n describe_v a_o semicircle_n for_o the_o ichnography_n which_o divide_v in_o 12_o equal_a part_n and_o in_o it_o describe_v a_o small_a cycle_n as_o at_o c._n for_o the_o bigness_n of_o the_o newel_n draw_v line_n from_o those_o division_n in_o the_o great_a semicircle_n into_o the_o semicircle_n make_v for_o the_o bigness_n of_o the_o newel_n so_o will_v that_o semicircle_n also_o be_v divide_v into_o 12_o equal_a part_n then_o on_o every_o of_o the_o point_n in_o the_o great_a semicircle_n erect_v perpendicular_o and_o those_o perpendicular_o shall_v show_v the_o end_n of_o each_o respective_a step_n as_o the_o perpendicular_a at_o 11_o bound_n the_o outward_a end_n of_o the_o first_o step_n the_o perpendicular_a at_o 22_o bound_n the_o second_o step_n etc._n etc._n to_o 24_o which_o make_v good_a a_o whole_a circle_n in_o the_o ichnography_n and_o perpendicular_o erect_v from_o the_o inner_a semicircle_n mark_v on_o the_o newel_n the_o end_n of_o the_o same_o step_n work_v the_o same_o way_n with_o the_o step_n on_o your_o right_a hand_n the_o newel_n be_v pierce_v through_o in_o divers_a place_n to_o let_v in_o light_n of_o chimney_n the_o italian_n who_o make_v frugal_a fire_n be_v not_o in_o this_o case_n the_o best_a counsellor_n therefore_o from_o they_o we_o may_v better_o learn_v how_o to_o raise_v fair_a mantle_n within_o and_o how_o to_o disguise_v 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and_o close_o so_o as_o the_o smoke_n can_v issue_v want_v a_o supply_n of_o air_n and_o so_o have_v a_o natural_a reason_n of_o the_o cause_n we_o apply_v suitable_a remedy_n touch_v conduct_n for_o the_o suillage_n and_o other_o necessity_n of_o the_o house_n which_o how_o base_a soever_o in_o use_n yet_o for_o the_o health_n of_o the_o inhabitant_n be_v as_o considerable_a as_o the_o rest_n i_o find_v in_o author_n this_o counsel_n that_o art_n shall_v imitate_v nature_n in_o those_o ignoble_a conveyance_n and_o separate_v they_o from_o sight_n where_o there_o want_v a_o run_a water_n into_o the_o most_o remote_a and_o low_a and_o thick_a part_n of_o the_o foundation_n with_o secret_a vent_n post_v up_o through_o the_o wall_n like_o a_o tunnel_n to_o the_o wiâ—d_a air_n aloft_o thus_o have_v consider_v the_o apertion_n and_o overture_n according_a to_o their_o particular_a requisite_n i_o come_v to_o the_o contexture_n of_o the_o whole_a work_n under_o the_o term_n of_o compartition_n into_o which_o be_v the_o main_a piece_n i_o can_v enter_v without_o a_o few_o general_a precaution_n first_o let_v no_o man_n that_o intend_v to_o build_v settle_v his_o fancy_n upon_o a_o draught_n of_o the_o work_n in_o paper_n how_o exact_o soever_o measure_v or_o neat_o set_v off_o in_o perspective_n without_o a_o model_n or_o type_n of_o the_o whole_a structure_n and_o of_o every_o parcel_n or_o partition_n in_o board_n or_o wood._n next_o that_o the_o say_a model_n be_v as_o plain_a as_o may_v be_v without_o colour_n or_o other_o beautify_v lest_o the_o pleasure_n of_o the_o eye_n preoccupate_v the_o judgement_n last_o the_o big_a this_o type_n be_v the_o better_a not_o that_o i_o will_v persuade_v a_o man_n to_o such_o a_o enormity_n as_o that_o model_n make_v by_o ant._n labaco_n of_o st._n peter_n church_n in_o rome_n contain_v 22_o foot_n in_o length_n 16_o in_o breadth_n and_o 13_o in_o height_n and_o cost_v 4184_o crown_n the_o price_n of_o a_o reasonable_a chapel_n yet_o in_o a_o fabric_n of_o 30_o or_o 40_o thousand_o pound_n 30_o pound_n may_v be_v expend_v in_o a_o exact_a model_n for_o a_o little_a penury_n in_o the_o premise_n may_v easy_o breed_v some_o absurdity_n of_o a_o far_o great_a charge_n in_o the_o conclusion_n now_o after_o these_o premonishment_n i_o come_v to_o the_o compartition_n itself_o by_o which_o be_v understand_v a_o graceful_a and_o useful_a distribution_n of_o the_o whole_a ground-plot_n both_o for_o room_n of_o office_n and_o of_o reception_n or_o entertainment_n as_o far_o as_o the_o capacity_n thereof_o and_o the_o nature_n of_o the_o country_n will_v comport_v the_o gracefulness_n will_v consist_v in_o a_o double_a analogy_n or_o correspondency_n first_o between_o the_o part_n and_o the_o whole_a whereby_o a_o great_a fabric_n shall_v have_v great_a partition_n great_a light_n great_a entrance_n great_a pillar_n or_o pilaster_n in_o sum_n all_o the_o part_n great_a the_o next_o between_o the_o part_n themselves_o not_o only_o consider_v the_o breadth_n and_o length_n as_o before_o when_o we_o speak_v of_o door_n and_o window_n but_o likewise_o their_o height_n a_o point_n hardly_o reducible_a to_o any_o general_a precept_n true_a it_o be_v the_o ancient_n do_v determine_v the_o longitude_n of_o all_o room_n which_o be_v long_o than_o broad_a by_o the_o double_a of_o their_o latitude_n and_o the_o height_n half_a as_o much_o more_o as_o the_o latitude_n which_o dimension_n modern_a architect_n vary_v upon_o discretion_n sometime_o square_n the_o latitude_n and_o then_o make_v the_o diagonal_a or_o overthwart_a line_n from_o angle_n to_o angle_n of_o the_o say_v square_a the_o measure_n of_o the_o height_n sometime_o more_o but_o seldom_o low_o than_o the_o breadth_n itself_o the_o usefulness_n consist_v in_o a_o sufficient_a number_n of_o room_n of_o all_o sort_n and_o their_o apt_a coherence_n without_o distraction_n without_o confusion_n that_o it_o may_v be_v well_o unite_v and_o may_v appear_v airy_a and_o spiritous_a fit_a for_o the_o welcome_a of_o cheerful_a guest_n about_o which_o the_o great_a difficulty_n will_v be_v in_o contrive_v the_o light_n and_o staircase_n in_o which_o respect_n the_o ancient_a architect_n be_v at_o much_o ease_n for_o both_o the_o greek_n and_o roman_n of_o who_o private_a dwelling_n vitruvius_n have_v leave_v some_o description_n have_v common_o two_o cloister_v open_a court_n one_o serve_v for_o the_o woman_n side_n and_o the_o other_o for_o the_o man_n who_o now_o adays_o will_v perchance_o take_v so_o much_o separation_n unkind_o howsoever_o by_o this_o mean_n the_o reception_n of_o light_n into_o the_o body_n of_o the_o building_n be_v very_o prompt_a both_o from_o without_o and_o from_o within_o which_o we_o must_v now_o supply_v by_o some_o open_a form_n of_o the_o fabric_n or_o among_o graceful_a refuge_n by_o tarrase_v any_o story_n which_o be_v in_o danger_n of_o darkness_n or_o last_o by_o perpendicular_a light_n from_o the_o roof_n of_o all_o other_o the_o most_o natural_a for_o the_o second_o difficulty_n which_o be_v cast_v the_o staircase_n which_o be_v no_o hard_a point_n of_o itself_o but_o as_o they_o be_v encumbrance_n of_o room_n for_o other_o use_n i_o have_v mark_v a_o willingness_n in_o the_o italian_a artisan_n to_o distribute_v the_o kitchen_n pantry_n bakehouse_n wash_v room_n and_o even_o the_o buttery_n likewise_o under_o ground_n next_o above_o the_o foundation_n and_o sometime_o level_a with_o the_o floor_n of_o the_o cellar_n raise_v the_o first_o ascent_n into_o the_o house_n fifteen_o foot_n or_o more_o for_o that_o end_n which_o beside_o remove_v annoy_n out_o of_o sight_n and_o gain_v much_o room_n above_o do_v also_o by_o the_o elevation_n of_o the_o front_n add_v majesty_n to_o the_o whole_a aspect_n and_o with_o such_o a_o disposition_n of_o the_o principal_a staircase_n which_o common_o do_v deliver_v we_o into_o the_o plain_a
distance_n from_o a_o point_n to_o a_o line_n be_v only_o thus_o set_v one_o point_n of_o the_o compass_n in_o the_o point_n give_v and_o open_a or_o shut_v the_o other_o be_v turn_v about_o till_o the_o other_o will_v but_o just_a touch_n or_o cleave_v the_o line_n that_o i_o call_v the_o near_a distance_n use_v i._o to_o lay_v down_o a_o line_n that_o shall_v represent_v any_o number_n of_o foot_n and_o inch_n give_v or_o require_v take_v the_o number_n give_v lateral_o from_o the_o 30_o or_o 40_o scale_n from_o the_o centre_n and_o that_o be_v the_o line_n require_v but_o if_o these_o scale_n be_v too_o great_a or_o too_o small_a then_o take_v your_o number_n of_o part_n and_o the_o length_n thereof_o lateral_o as_o for_o example_n suppose_v i_o will_v have_v 3_o inch_n to_o represent_v 30_o foot_n take_v out_o 3_o inch_n between_o your_o compass_n and_o make_v it_o a_o parallel_n in_o 30_o and_o 30_o and_o the_o 30_o scale_n be_v set_v to_o your_o desire_n use_v ii_o to_o increase_n or_o diminish_v a_o line_n to_o any_o proportion_n take_v the_o give_v line_n between_o your_o compass_n and_o make_v it_o a_o parallel_n in_o the_o part_n thereof_o then_o the_o parallel_n extent_n of_o the_o part_n you_o will_v have_v it_o increase_v or_o diminish_v to_o be_v the_o augmentation_n or_o diminution_n which_o be_v require_v example_n let_v 3_o inch_n represent_v 8_o foot_n and_o to_o the_o same_o proportion_n i_o will_v have_v 10_o foot_n or_o 5_o foot_n viz._n more_o or_o less_o take_v 3_o inch_n between_o your_o compass_n and_o make_v it_o a_o parallel_n in_o 8_o and_o 8_o on_o the_o 30_o scale_n then_o the_o parallel_n distance_n between_o 5_o and_o 5_o do_v diminish_v the_o line_n and_o the_o parallel_n between_o 10_o and_o 10_o do_v increase_v the_o line_n to_o the_o proportion_n require_v use_v iii_o to_o divide_v a_o line_n into_o any_o number_n of_o part_n or_o model_n under_o 30._o take_v the_o give_v line_n and_o make_v it_o a_o parallel_n in_o the_o part_n on_o the_o 30_o scale_n into_o which_o you_o will_v have_v it_o divide_v than_o the_o parallel_n extent_n between_o 1_o and_o 1_o shall_v divide_v the_o line_n according_o example_n let_v 4_o inch_n be_v a_o line_n to_o be_v divide_v into_o 9_o part_n take_v 4_o inch_n or_o any_o distance_n whatsoever_o and_o make_v it_o a_o parallel_n in_o 9_o and_o 9_o on_o the_o 30_o scale_n then_o the_o parallel_n distance_n between_o 1_o and_o 1_o shall_v divide_v 4_o inch_n into_o 9_o part_n require_v note_v that_o for_o more_o exactness_n and_o conveniency_n you_o may_v double_v 9_o or_o triple_a 9_o viz._n 18_o or_o 27_o and_o then_o if_o you_o make_v the_o line_n to_o be_v divide_v a_o parallel_n in_o triple_a the_o number_n you_o must_v take_v out_o 3_o in_o stead_n of_o one_o and_o that_o shall_v divide_v the_o line_n into_o the_o part_n require_v example_n i_o will_v have_v 5_o inch_n put_v into_o 10_o part_n take_v 5_o inch_n between_o your_o compass_n and_o make_v it_o a_o parallel_v in_o 30_o and_o 30_o the_o triple_a of_o 10_o then_o take_v out_o parallel_v 3_o and_o 3_o the_o triple_a of_o one_o and_o that_o shall_v divide_v the_o line_n give_v be_v 5_o inch_n into_o 10_o part_n or_o model_n exact_o the_o like_a for_o any_o other_o and_o note_v as_o the_o rule_n stand_v you_o may_v take_v out_o any_o number_n of_o part_n or_o model_n whatsoever_o to_o that_o scale_n use_v iu._n any_o two_o line_n give_v to_o find_v their_o proportion_n one_o to_o another_o according_a to_o any_o other_o number_n take_v the_o line_n several_o and_o lay_v they_o lateral_o from_o the_o centre_n on_o the_o 30_o or_o the_o 40_o scale_n which_o you_o please_v and_o the_o number_n of_o foot_n and_o inch_n to_o which_o they_o reach_v shall_v show_v their_o proportion_n one_o to_o another_o of_o the_o part_n of_o the_o line_n on_o which_o they_o be_v measure_v example_n i_o have_v 2_o line_n suppose_v one_o be_v 2_o inch_n long_o and_o the_o other_o 5_o or_o any_o other_o unknown_a part_n take_v 2_o inch_n the_o measure_n of_o one_o line_n and_o measure_v it_o lateral_o on_o the_o 30_o scale_n and_o it_o give_v 5_o foot_n ½_o a_o inch_n then_o take_v out_o 5_o inch_n the_o suppose_a length_n of_o the_o other_o line_n and_o it_o give_v lateral_o 12_o foot_n 8_o inch_n then_o i_o say_v one_o line_n be_v 5_o foot_n and_o half_a a_o inch_n and_o the_o other_o be_v 12_o foot_n 8_o inch_n of_o a_o scale_n of_o 30_o foot_n in_o 11_o inch_n 3_o quarter_n length_n or_o if_o you_o conclude_v on_o the_o term_n or_o number_n of_o one_o line_n then_o make_v that_o line_n a_o parallel_n in_o the_o part_n thereof_o then_o take_v the_o other_o line_n and_o carry_v it_o parallelly_n till_o it_o stay_v in_o like_a part_n on_o both_o leg_n in_o the_o common_a line_n and_o that_o shall_v be_v the_o denomination_n of_o the_o other_o line_n use_v v._o two_o line_n be_v give_v to_o find_v a_o three_o in_o continual_a proportion_n to_o they_o take_v both_o the_o line_n and_o lay_v they_o lateral_o on_o both_o leg_n and_o note_v the_o foot_n and_o inch_n to_o which_o they_o do_v extend_v as_o in_o the_o last_o then_o take_v out_o the_o lateral_a extent_n of_o the_o second_o line_n and_o make_v a_o parallel_n in_o the_o term_n of_o the_o first_o line_n keep_v the_o common_a line_n at_o that_o open_n than_o the_o parallel_n extent_n from_o the_o term_n of_o the_o second_o line_n shall_v be_v the_o lateral_a 3d_o term_n or_o line_n in_o proportion_n example_n suppose_v i_o have_v one_o line_n 3_o foot_n long_o and_o another_o 5_o foot_n and_o i_o will_v have_v another_o to_o bear_v proportion_n to_o 5_o as_o 3_o do_v to_o 5_o increase_a be_v in_o number_n thus_o as_o 3_o be_v to_o 5_o so_o be_v 5_o to_o what_o here_o note_v that_o 3_o be_v the_o first_o number_n and_o 5_o the_o second_o the_o first_o line_n lay_v from_o the_o centre_n on_o the_o 30_o scale_n extend_v to_o 7_o foot_n 7_o inch_n and_o 5_o inch_n the_o second_o line_n give_v 12_o foot_n 8_o inch_n now_o the_o lateral_a second_o line_n viz._n 5_o or_o 12_o foot_n 8_o inch_n make_v a_o parallel_n 7_o in_o foot_n 7_o inch_n the_o term_n of_o the_o first_o line_n then_o take_v out_o the_o parallel_a extent_n from_o 12_o foot_n 8_o inch_n the_o measure_n of_o 5_o and_o it_o shall_v give_v 21_o foot_n 1_o inch_n lay_v lateral_o from_o the_o centre_n for_o a_o three_o proportional_a require_v which_o measure_v on_o the_o inch_n be_v 8_o inch_n and_o a_o three_o the_o answer_n require_v for_o as_o 3_o be_v in_o proportion_n to_o 5_o so_o be_v 5_o to_o 8_o and_o a_o three_o part_n but_o by_o the_o line_n of_o number_n have_v the_o quantity_n of_o the_o line_n give_v in_o number_n do_v thus_o the_o extent_n of_o the_o compass_n from_o the_o first_o number_n 3_o to_o the_o second_o number_n 5_o shall_v reach_v the_o same_o way_n from_o the_o second_o number_n 5_o to_o 8.33_o the_o three_o proportional_a number_n require_v use_v vi_o to_o divide_v a_o line_n in_o such_o sort_n as_o another_o line_n be_v divide_v take_v the_o whole_a line_n that_o be_v divide_v and_o lay_v it_o lateral_o on_o both_o leg_n and_o fit_v the_o line_n that_o be_v to_o be_v divide_v parallelly_n in_o the_o end_n thereof_o then_o lay_v every_o part_n of_o the_o divide_a line_n lateral_o in_o like_a manner_n as_o the_o whole_a line_n be_v lay_v and_o the_o parallel_a extent_n between_o those_o part_n shall_v divide_v the_o line_n according_o as_o for_o example_n suppose_v i_o will_v divide_v a_o line_n of_o 8_o inch_n ¼_n long_o in_o such_o sort_n as_o the_o line_n of_o circle_n on_o the_o inside_n of_o the_o 30_o scale_n be_v divide_v take_v out_o 8_o inch_n ¾_n and_o make_v it_o a_o parallel_n in_o 2_o and_o 2_o the_o divide_a line_n then_o take_v out_o the_o parallel_a distance_n from_o 3_o and_o 3_o and_o that_o shall_v give_v the_o point_n 3_o from_o the_o end_n of_o the_o line_n you_o will_v divide_v and_o so_o consequent_o all_o the_o rest_n in_o order_n as_o far_o as_o you_o please_v use_v vii_o to_o find_v a_o mean_a proportional_a between_o two_o line_n or_o number_n open_v the_o 30_o scale_n to_o a_o right_a angle_n by_o make_v lateral_a 21_o foot_n 2_o inch_n a_o parallel_n in_o 15_o foot._n then_o find_v the_o sum_n and_o half_a sum_n the_o difference_n and_o half_a difference_n between_o your_o two_o number_n and_o have_v the_o half_a sum_n between_o your_o compass_n set_v one_o point_n to_o the_o half_a difference_n count_v lateral_o on_o one_o leg_n and_o wheresoever_o the_o other_o point_n shall_v touch_v the_o common_a line_n on_o the_o other_o
leg_n be_v the_o mean_a proportional_a require_v example_n suppose_v a_o piece_n of_o timber_n be_v 10_o inch_n one_o way_n and_o 18_o inch_n another_o what_o be_v the_o square_a equal_a which_o be_v the_o mean_a proportional_a between_o they_o the_o sum_n of_o 10_o and_o 18_o be_v 28_o the_o half_a sum_n be_v 14_o the_o difference_n between_o 10_o and_o 18_o be_v 8_o the_o half_a difference_n be_v 4_o now_o the_o 30_o scale_n stand_v square_a take_v 14_o the_o half_a sum_n between_o your_o compass_n and_o then_o set_v one_o point_n in_o 4_o on_o one_o leg_n and_o turn_v the_o other_o point_n of_o the_o compass_n towards_o the_o common_a line_n and_o there_o it_o shall_v show_v 13_o â—_o 12_o near_o the_o square_n equal_a require_v use_v viii_o to_o work_v the_o rule_n of_o three_o by_o the_o line_n of_o line_n to_o 30_o or_o to_o 3_o number_n give_v to_o find_v a_o four_o in_o geometrical_a proportion_n direct_v make_v the_o lateral_a second_o a_o parallel_n in_o the_o first_o than_o the_o parallel_n three_o shall_v give_v the_o lateral_a four_o number_n require_v example_n if_o one_o foot_n of_o timber_n cost_v 10_o d._n what_o shall_v 6_o foot_n cost_n facit_fw-la 60_o d._n make_v lateral_a 10_o a_o parallel_n in_o 10_o count_v as_o 1_o than_o the_o parallel_n extent_n between_o 6_o and_o 6_o shall_v reach_v to_o lateral_a 60_o the_o answer_n require_v in_o penny_n again_o another_o example_n if_o 50_o foot_n or_o a_o load_n of_o timber_n cost_v 44_o s._n what_o shall_v one_o foot_n cost_v take_v the_o lateral_a extent_n from_o 22_o the_o half_a of_o 44_o s._n and_o make_v it_o a_o parallel_n in_o 25_o the_o half_a of_o 50_o than_o the_o parallel_n distance_n between_o 2_o and_o 2_o count_v as_o 4_o foot_n shall_v give_v the_o lateral_a number_n of_o 3_o s._n 6_o d._n the_o price_n of_o 4_o foot_n who_o four_o part_n be_v 10_o d._n ½_o the_o price_n of_o one_o foot._n note_v this_o help_n be_v use_v to_o avoid_v the_o nearness_n to_o the_o centre_n where_o the_o work_n be_v inconvenient_a use_v ix_o to_o measure_v flat_a measure_n by_o the_o scale_n of_o 30._o at_o any_o inch_n broad_a to_o find_v how_o much_o in_o length_n make_v a_o foot._n take_v lateral_a 12_o make_v it_o a_o parallel_n in_o the_o breadth_n give_v then_o take_v out_o parallel_v 12_o again_o and_o it_o shall_v give_v the_o length_n of_o a_o foot_n require_v example_n at_o 9_o inch_n broad_a as_o lateral_a 12_o to_o parallel_v 9_o so_o be_v parallel_v 12_o to_o lateral_a 16_o the_o length_n require_v use_v x._o the_o breadth_n of_o a_o board_n give_v in_o inches_n and_o the_o length_n in_o foot_n to_o find_v the_o content_a in_o foot_n and_o inch_n require_v take_v the_o lateral_a length_n in_o foot_n and_o make_v it_o a_o parallel_n in_o 12_o than_o the_o lateral_a distance_n between_o the_o inch_n broad_a shall_v give_v the_o parallel_n content_a example_n of_o 15_o foot_n 3_o inch_n long_o and_o 9_o inch_n broad_a take_v lateral_a 15_o foot_n 3_o inch_n and_o make_v it_o a_o parallel_n in_o 12_o then_o take_v out_o parallel_v 9_o and_o 9_o and_o it_o shall_v give_v lateral_a 11_o foot_n and_o a_o half_a the_o content_a use_v xi_o to_o measure_v timber_n by_o the_o line_n of_o line_n to_o 30._o at_o any_o inch_n square_a to_o find_v how_o much_o make_v a_o foot_n of_o timber_n if_o the_o piece_n be_v not_o square_a then_o by_o the_o eight_o use_v make_v it_o square_n then_o thus_o take_v the_o lateral_a side_n of_o the_o square_n in_o inches_n make_v it_o a_o parallel_n in_o 12_o then_o take_v out_o the_o parallel_n side_n of_o the_o square_n and_o it_o shall_v give_v a_o lateral_a four_o number_n then_o take_v out_o lateral_a 12_o and_o make_v it_o a_o parallel_n in_o the_o four_o number_n and_o then_o take_v out_o parallel_v 12_o again_o and_o it_o shall_v show_v the_o answer_n in_o inches_n lay_v lateral_o from_o the_o centre_n example_n at_o 9_o inch_n square_a what_o make_v a_o foot_n as_o lat_fw-la 9_o to_o par_fw-fr 12_o so_o be_v par_fw-fr 9_o to_o let_fw-mi 6._o ¾_n again_o as_o lat_fw-la 12_o to_o par_fw-fr four_o viz._n 6_o ¾_n so_o be_v par_fw-fr 12_o to_o 21_o inch_n 1_o â—_o the_o length_n to_o make_v one_o foot_n require_v use_v xii_o the_o inch_n square_n and_o length_n give_v in_o foot_n to_o find_v the_o content_a in_o foot_n and_o inch_n as_o the_o lat._n side_n of_o the_o square_a to_o parallel_v 12_o so_o be_v the_o par_fw-fr length_n to_o lat_fw-la four_o again_o as_o the_o lat._n four_o to_o parallel_v 12_o so_o be_v the_o par_fw-fr side_n of_o the_o square_n to_o lateral_a content_n example_n at_o 9_o inch_n square_a and_o 20_o foot_n long_o as_o lat_fw-la 9_o to_o par_fw-fr 12_o so_o be_v par_fw-fr 20_o to_o let_fw-mi 15_o a_o four_o number_n again_o as_o lat_fw-la 15_o the_o four_o to_o par_fw-fr 12_o so_o be_v parallel_v 9_o to_o lat_fw-la 11_o ¼_n the_o content_a require_v thus_o much_o for_o the_o general_n use_v be_v too_o long_o a_o disgression_n from_o the_o matter_n main_o intend_v use_v xiii_o the_o breadth_n of_o any_o frame_n be_v give_v to_o find_v the_o length_n of_o the_o rafter_n and_o perpendicular_a by_o inspection_n only_o in_o be_v a_o general_n receive_v rule_n that_o the_o length_n of_o the_o rafter_n shall_v be_v three-quarters_o the_o breadth_n of_o the_o house_n or_o frame_n for_o true_a pitch_n and_o 40_o the_o foot_n in_o one_o scale_n be_v equal_a in_o length_n to_o 30_o the_o number_n of_o foot_n in_o another_o scale_n and_o 30_o be_v 3_o quarter_n of_o 40._o therefore_o if_o you_o seek_v for_o the_o breadth_n of_o the_o house_n on_o the_o 40_o scale_n then_o right_o against_o it_o on_o the_o 30_o scale_n be_v the_o length_n of_o the_o rafter_n require_v also_o if_o you_o seek_v the_o length_n of_o the_o rafter_n on_o the_o 40_o scale_n on_o the_o 30_o scale_n right_a against_o it_o be_v the_o height_n of_o the_o perpendicular_a require_v viz._n from_o the_o raising-piece_n to_o the_o top_n of_o the_o gable_n end_n or_o rafter_n require_v example_n if_o a_o house_n be_v 30_o foot_n broad_a the_o rafter_n ought_v to_o be_v 22_o foot_n 6_o inch_n and_o the_o perpendicular_a 16_o foot_n 9_o inch_n and_o a_o ½_o for_o right_a against_o 30_o count_v on_o the_o 40_o scale_n on_o the_o 30_o scale_n be_v 22_o 6_o the_o rafter_n and_o right_a against_o 22_o 6_o on_o the_o 40_o scale_n on_o the_o 30_o be_v 16_o 9_o ½_o the_o perpendicular_a 1._o also_o by_o the_o line_n of_o number_n the_o extent_n of_o the_o compass_n from_o 20_o to_o 15_o will_v reach_v the_o same_o way_n from_o the_o breadth_n of_o any_o house_n to_o his_o proprotionable_a rafter_n at_o true_a pitch_n 2._o and_o the_o extent_n from_o 20_o to_o 18_o turn_v the_o same_o way_n from_o any_o breadth_n of_o a_o house_n to_o his_o proportionable_a hip-rafter_n in_o square_a frames_n 3._o also_o the_o extent_n from_o 20_o to_o 11_o 18_o 100_o will_v reach_v the_o same_o way_n from_o the_o width_n of_o any_o house_n to_o his_o proportionable_a perpendicular_a at_o square_a and_o true_a pitch_n 4._o and_o the_o extent_n from_o 20_o to_o 28_o 28_o will_v reach_v from_o any_o other_o house_n breadth_n to_o his_o proportional_a whole_a diagonal_a line_n require_v at_o square_a and_o true_a pitch_n 5._o and_o the_o extent_n from_o 20_o the_o breadth_n to_o 26_o 63_o the_o near_a distance_n at_o that_o breadth_n shall_v reach_v from_o any_o other_o breadth_n to_o his_o proportional_a near_a distance_n require_v if_o it_o be_v needful_a but_o the_o angle_n in_o all_o roof_n great_a or_o small_a if_o true_a pitch_n and_o square_v be_v the_o same_o in_o all_o frame_v use_v fourteen_o the_o breadth_n of_o the_o house_n and_o the_o height_n of_o the_o perpendicular_a be_v give_v to_o find_v the_o rafter_n length_n the_o hip_n length_n the_o diagonal_a line_n from_o corner_n to_o the_o king-post_n and_o any_o angle_n require_v in_o square_a frames_n what_o the_o perpendicular_a height_n of_o the_o gable_n end_v aught_o to_o be_v at_o true_a pitch_n by_o the_o last_o rule_n you_o may_v ready_o see_v and_o the_o better_o make_v estimate_n of_o the_o quantity_n of_o alteration_n which_o be_v once_o resolve_v on_o then_o thus_o proceed_v first_o open_v the_o two_o 30_o scale_n to_o a_o right_a angle_n by_o make_v lateral_a 21_o foot_n 2_o inch_n ½_o a_o parallel_n in_o 15_o and_o 15_o in_o the_o brass_n center-pin_n 1._o then_o count_v half_a the_o breadth_n of_o the_o house_n on_o one_o leg_n and_o the_o length_n of_o the_o perpendicular_a resolve_v on_o on_o the_o other_o leg_n than_o the_o parallel_n distance_n between_o they_o measure_v lateral_o from_o the_o centre_n rafter_n shall_v give_v the_o true_a length_n of_o