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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 10-2½_a 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 than_o the_o
compass_n point_v so_o set_v lay_v a_o rule_n length_n hip_n length_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 the_o hip_n angle_n hip_n length_n and_o angle_n length_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_n angle_n of_o both_o 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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 fig._n iii_o 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_v that_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 a_o the_o ingenious_a workman_n will_v soon_o perceive_v as_o thus_o in_o brief_a let_v a_o b_o c_o d_o represent_v the_o frame_n of_o a_o house_n bevel_v at_o both_o end_n and_o 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foot_n 9_o inch_n for_o a_o pair_n of_o middling_a rafter_n for_o this_o taper_n house_n l_o g_o 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 o_o inch_n â…_n of_o a_o inch_n and_o for_o the_o principal_a rafter_n or_o other_o rafter_n open_v the_o frame_n to_o find_v the_o length_n of_o the_o very_a principal_n or_o single_a rafter_n in_o a_o taper_n frame_n 30_o scale_v square_a and_o then_o count_v the_o perpendicular_a 5._o 0._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 a_o m_n and_o b_o m_o equal_a to_o a_o e_o or_o b_o e_o at_o one_o end_n and_o make_v c_o n_n and_o d_o n_o equal_a to_o d_o f_o or_o c_o f_o and_o draw_v the_o line_n m_o m_n and_o n_o n_n at_o both_o end_n also_o make_v a_o b_o and_o b_o b_o equal_a to_o a_o b_o and_z c_z a_o and_z d_o a_o equal_a to_z c_o d_o and_o draw_v the_o diagonal_a line_n a_o s_n and_o b_o s_o and_o c_o o_o and_o d_o o_o 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 a_o s_n and_o b_o s_o and_o c_o o_o and_o d_o o_o 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 a_o e_o s_o and_o b_o e_o s_o find_v they_o by_o the_o 30_o scale_n also_o you_o have_v the_o bevel_n end_v 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 l_o g_z on_o one_o leg_n 5_o 0_o â…_n and_o each_o half_a diagonal_a line_n etc._n etc._n one_o after_o another_o 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and_o the_o 30_o scale_n at_o each_o end_n a_o bevel_n and_o set_v it_o according_a to_o the_o rule_n and_o 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 &_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 scheam_n thus_o p_o a_o s_o and_o p_o b_o s_o p_o d_o o_o and_o p_o c_o o_o the_o 4_o angle_n at_o the_o raise_v piece_n and_o s_o p_o a_n and_o s_o p_o b_o o_o p_o c_o and_o o_o p_o d_o 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 make_v s_n p_o and_z o_o p_o equal_a to_o l_o g_z on_o the_o extend_a diagonal_a line_n and_o draw_v the_o line_n a_o p_o b_o p_o c_o p_o d_o p_o 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 2_o ¾_n 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_n 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 a_o p_o and_o from_o 7_o 2_o ¾_n to_o 4_o 2_o one_o foot_n less_o than_o the_o half_a bevel-end_n to_o 8_o foot_n ¾_n the_o hip_n b_o p._n also_o the_o par._n extent_n from_o 6_o foot_n 5_o ½_n the_o rafter_n length_n at_o the_o lesser_a end_n to_o 5._o foot_n 0_o ¾_n one_o foot_n more_o than_o 4._o 0_o ¾_n the_o half_a little_a bevel-end_n shall_v give_v 8_o 1_o ½_n for_o the_o hip_n p_o c._n and_o the_o extent_n from_o 6_o 5_o 4_o 8_o the_o rafter_n length_n to_o 3_o 0_o ¾_n 1_o foot_n less_o than_o the_o half_a bevel-end_n give_v 7_o 1_o ½_n the_o hip_n d_o p_o as_o before_z 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 a_o b_o the_o bevel-end_n and_o m_o m_o at_o the_o great_a end_n or_o c_z d_o and_z n_z n_z 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_o 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_o 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 a_o p_o 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 a_o b_o 10_o foot_z 4_o and_o m_o m_o 9-10½_a 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 inc_fw-la the_o bevel-end_n distance_n over_o to_o the_o other_o 30_o scale_n shall_v give_v 7-10_a a_o near_a distance_n from_o the_o point_n b_o to_o a_o p_o the_o hip_n raise_v over_o a_o s_o the_o diagonal_a then_o the_o lateral_a extent_n b_o b_o of_o 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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 scale_n or_o degree_n and_o minute_n on_o the_o chord_n take_v and_o count_v from_o the_o centre_n in_o the_o midst_n of_o the_o head_n of_o the_o joynt-rule_n a_o long_a any_o one_o leg_n as_o thus_o suppose_v i_o will_v take_v out_o 15_o foot_n lateral_o set_v on_o point_n of_o the_o compass_n in_o the_o centre_n at_o the_o head_n and_o open_v the_o other_o to_o 15_o on_o any_o one_o leg_n on_o the_o 30_o scale_n this_o extent_n i_o call_v a_o lateral_a extent_n of_o 15_o foot_n also_o if_o you_o takethe_v lateral_a chord_n of_o 60_o degree_n you_o shall_v find_v the_o extent_n of_o the_o compass_n from_o the_o centre_n to_o 60_o to_o be_v the_o same_o as_o from_o the_o centre_n to_o 15_o foot_n on_o the_o 30_o scale_n of_o foot_n and_o inch_n 2._o by_o the_o word_n parallel_n i_o mean_v any_o distance_n take_v by_o set_v one_o point_n of_o the_o compass_n in_o any_o number_n of_o foot_n and_o inch_n on_o one_o leg_n and_o the_o other_o point_n in_o the_o same_o or_o any_o other_o 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 then_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 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._n 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_v 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_z 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 &_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_n 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_z 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
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_z let_fw-mi 6_o ¾_n agair_n as_o lat_fw-la 12_o to_z 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 ¼_n the_o length_n to_o make_v one_o foot_n require_v use_v xii_o the_o inch_n square_a 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_n to_o parallel_v 12_o so_o be_v the_o parlength_n to_o a_o let_fw-mi four_o again_o as_o the_o laâ—_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 lateral_a 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_z let_fw-mi 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 digression_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 it_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_o quarter_n 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_n 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_n 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 proportionable_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_n rafter_n in_o square_a frame_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 16_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 perpendicule_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_n a_o parallel_n in_o 15_o &_o 15_o in_o the_o brass_n centre_n 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 shall_v give_v the_o true_a length_n of_o the_o rafter_n require_v rafter_n rafter_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 hip_n hip_n 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 3._o for_o the_o diagonal_a line_n count_v the_o half_a breadth_n of_o the_o diagonal_a diagonal_a 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 4._o again_o for_o the_o hip_n count_v the_o diagonal_a line_n last_o find_v length_n hip_n length_n 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 we_o before_o from_o the_o centre_n example_n in_o a_o house_n of_o 20_o foot_n wide_a at_o true_a pitch_n see_v fig._n 1._o let_v a_o b_o c_o d_o represent_v a_o frame_n of_o a_o house_n 20_o foot_n wide_a b_o i_o the_o half_a width_n b_o a_o and_o c_o d_o equal_a to_o b_o c_o the_o whole_a width_n be_v 2_o point_n to_o draw_v the_o diagonal_a line_n by_o i_o e_o be_v equal_a to_o i_o b_o and_o the_o half_a e_o i_o lay_v from_o e_z to_z g_z gives_z i_o g_z the_o true_a length_n of_o the_o rafter_n and_o g_z b_o or_o g_o c_o the_o length_n of_o the_o hip_n or_o thus_o three_o quarter_n of_o c_o b_o viz._n c_o h_n gives_z c_o f_o and_o b_o f_o the_o rafter_n length_n the_o same_o extent_n also_o lay_v upon_o the_o middle_a line_n from_o i_o to_o g_o gives_z cg_n and_o bg_n the_o hip_n length_n if_o be_v the_o perpendicular_a height_n e_z be_v the_o point_n of_o the_o diagonal_a line_n or_o king-post_n perpendicular_o opposite_a to_o or_o right_n under_o the_o meeting_n point_n of_o the_o 2_o hip_n and_o the_o two_o rafter_n when_o raise_v and_o set_v in_o their_o place_n thus_o much_o for_o illustration_n what_o to_o do_v now_o for_o application_n how_o to_o do_v the_o width_n of_o the_o house_n be_v always_o give_v the_o length_n of_o the_o rafter_n or_o the_o height_n of_o the_o perpendicular_a be_v next_o resolve_v on_o which_o in_o our_o example_n be_v true_a pitch_n be_v also_o resolve_v on_o either_o by_o inspection_n as_o before_o or_o else_o by_o operation_n in_o this_o manner_n 1._o the_o breadth_n of_o the_o house_n be_v 20_o foot_n and_o the_o perpendicular_a resolve_v on_o to_o be_v 11_o foot_n 2_o inch_n ½_n to_o find_v the_o rafter_n length_n work_v thus_o open_v the_o 30_o scale_n to_o a_o right_a angle_n by_o use_v the_o 7_o count_v 10_o the_o half_a breadth_n of_o the_o house_n on_o one_o leg_n and_o the_o length_n for_o the_o rafter_n length_n perpendicular_a height_n 11_o 2_o ½_n on_o the_o other_o leg._n viz._n both_o on_o the_o 30_o scale_n from_o the_o centre_n and_o take_v the_o parallel_a distance_n between_o they_o on_o the_o common_a 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 c_o f._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
proportion_n one_o to_o another_o according_a to_o any_o other_o number_n that_o 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_n 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._n 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 3._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 in_o 7_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._o 33_o the_o three_o proportional_a number_n require_v use_v vi._n 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 yond_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 ¾_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 fetch_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 5_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_v 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_o 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_o 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_n 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 8_o use_v make_v it_o square_n then_o thus_o take_v the_o lateral_a