both_o end_n together_o and_o take_v half_a thereof_o for_o a_o mean_a breadth_n so_o find_v you_o 18_o then_o be_v it_o all_o one_o as_o if_o your_o board_n be_v 18_o inch_n and_o you_o will_v know_v how_o much_o in_o length_n make_v a_o foot_n take_v 12_o and_o fit_v it_o in_o 18_o and_o take_v it_o over_o in_o 12_o and_o so_o much_o make_v a_o foot_n let_v a_o board_n be_v broad_a at_o one_o end_n ten_o inch_n and_o a_o quarter_n and_o at_o the_o other_o seven_o and_o a_o half_a now_o the_o desire_n be_v to_o know_v how_o much_o in_o length_n make_v a_o foot_n add_v both_o the_o number_n together_o and_o take_v half_a which_o make_v 8_o inch_n and_o seven_o eight_o part_n of_o a_o inch_n for_o the_o common_a breadth_n then_o bring_v 8_o inch_n and_o seven_o eight_o of_o a_o inch_n &_o 12_o inch_n into_o eight_o and_o it_o make_v 71_o eight_o and_o 96_o eight_o take_v then_o 96_o in_o some_o scale_n and_o fit_a that_o in_o 71_o then_o let_v the_o scale_n rest_n then_o take_v it_o over_o in_o 12_o and_o that_o apply_v to_o the_o same_o scale_n where_o the_o 96_o be_v take_v and_o it_o show_v 16_o and_o a_o quarter_n and_o so_o many_o inch_n in_o length_n make_v one_o foot_n of_o board_n chap._n xiii_o to_o find_v how_o many_o square_a foot_n any_o whole_a board_n contain_v without_o find_v how_o much_o in_o length_n make_v a_o foot_n imagine_v a_o board_n be_v 15_o foot_n long_o and_o 16_o inch_n broad_a and_o it_o be_v require_v to_o find_v how_o many_o square_a foot_n of_o board_n it_o contain_v take_v the_o length_n of_o 15_o on_o some_o scale_n of_o equal_a part_n and_o fit_a that_o in_o 12_o the_o inch_n in_o a_o foot_n always_o there_o let_v the_o scale_n rest_n then_o take_v it_o over_o in_o 16_o the_o breadth_n and_o apply_v it_o to_o the_o same_o scale_n where_o the_o length_n be_v take_v it_o show_v 20_o and_o so_o many_o square_a foot_n be_v find_v to_o be_v therein_o contain_v let_v a_o board_n be_v 17_o foot_n and_o a_o quarter_n long_o and_o 16_o inch_n and_o a_o half_a broad_a and_o the_o desire_n be_v to_o know_v how_o many_o foot_n it_o contain_v take_v 17_o and_o a_o quarter_n the_o length_n and_o fit_v it_o in_o 12_o and_o take_v it_o over_o in_o 16_o and_o a_o half_a and_o that_o apply_v to_o the_o same_o scale_n when_o 17_o and_o a_o quarter_n the_o length_n be_v take_v it_o show_v 23_o and_o two_o three_o and_o so_o many_o foot_n it_o contain_v or_o you_o may_v bring_v 17_o and_o a_o quarter_n into_o quarter_n make_v 69_o and_o in_o like_a manner_n 12_o into_o quarter_n make_v 48_o and_o take_v it_o over_o in_o 16_o and_o a_o half_a the_o breadth_n so_o find_v you_o 23_o and_o two_o three_o as_o before_o chap._n fourteen_o to_o measure_v board_n that_o be_v broad_a at_o the_o one_o end_n then_o at_o the_o other_o in_o the_o same_o manner_n suppose_v a_o board_n be_v broad_a at_o the_o one_o end_n 18_o inch_n and_o at_o the_o other_o end_n 14_o and_o long_o 21_o foot_n i_o demand_v how_o many_o square_a foot_n it_o contain_v add_v the_o breadth_n at_o both_o end_n together_o make_v 32_o inch_n who_o half_a be_v 16_o inch_n for_o a_o mean_a breadth_n then_o proceed_v as_o before_o take_v 21_o and_o fit_a it_o in_o 12_o and_o take_v it_o over_o in_o 16_o or_o fit_v it_o in_o five_o time_n 12_o and_o take_v it_o over_o in_o five_o time_n 16_o so_o find_v you_o 28_o for_o the_o area_n require_v again_o let_v a_o board_n be_v broad_a at_o the_o one_o end_n 11_o inch_n and_o a_o half_a and_o at_o she_o other_o 7_o and_o three_o quarter_n and_o 15_o foot_n and_o three_o quarter_n long_o now_o the_o area_n be_v require_v first_o add_v they_o both_o together_o and_o take_v half_a make_v 9_o five_o eight_o part_n for_o the_o mean_a breadth_n then_o take_v 15_o three_o quarter_n the_o length_n on_o any_o scale_n and_o fit_a in_o 12_o and_o take_v it_o over_o in_o 9_o five_o eight_o and_o that_o apply_v to_o the_o same_o scale_n where_o the_o length_n be_v take_v and_o it_o show_v how_o many_o foot_n it_o contain_v or_o bring_v 12_o and_o 9_o five_o eight_o into_o eight_o make_v 96_o and_o 77_o then_o fit_a fifteen_o three_o quarter_n the_o length_n in_o 96_o and_o take_v it_o over_o in_o 77_o and_o that_o show_v on_o the_o same_o scale_n where_o the_o 15_o three_o quarter_n be_v take_v twelve_o two_o three_o the_o area_n desire_v chap._n xv._o to_o measure_n timber_n suppose_v a_o piece_n of_o timber_n be_v 18_o inch_n broad_a and_o deep_a 16_o inch_n it_o be_v require_v to_o find_v how_o much_o in_o length_n do_v make_v a_o foot_n take_v twelve_o the_o inch_n in_o a_o foot_n on_o any_o scale_n of_o equal_a part_n &_o fit_a that_o in_o the_o breadth_n eighteen_o and_o take_v that_o over_o in_o twelve_o always_o again_o set_v that_o distance_n in_o sixteen_o the_o depth_n and_o take_v it_o over_o in_o twelve_o still_o and_o that_o apply_v to_o the_o same_o scale_n where_o the_o twelve_o be_v take_v show_v six_o and_o so_o many_o inch_n in_o length_n make_v a_o foot_n the_o thing_n require_v again_o let_v a_o piece_n of_o timber_n be_v broad_a sixteen_o inch_n and_o deep_a thirteen_o and_o a_o half_a and_o it_o be_v require_v to_o find_v how_o much_o in_o length_n make_v one_o foot_n as_o before_o fit_a twelve_o in_o sixteen_o and_o take_v it_o over_o in_o 12_o still_o &_o that_o apply_v to_o the_o same_o scale_n where_o the_o twelve_o be_v take_v show_v eight_o inch_n and_o so_o many_o inch_n in_o length_n make_v one_o foot_n again_o let_v a_o piece_n of_o timber_n be_v fifteen_o three_o quarter_n broad_a and_o eleven_o three_o quarter_n deep_a i_o demand_v how_o much_o shall_v make_v a_o foot_n bring_v fifteen_o three_o quarter_n and_o twelve_o into_o quarter_n make_v sixty_o three_o and_o forty_o eight_o then_o take_v twelve_o on_o some_o scale_n of_o equal_a part_n and_o fit_v it_o in_o sixty_o three_o and_o take_v it_o over_o in_o 48_o and_o that_o distance_n fit_a in_o eleven_o one_o quarter_n and_o take_v it_o over_o in_o 12_o or_o as_o before_o bring_v eleven_o one_o quarter_n and_o twelve_o both_o into_o quarter_n make_v forty_o eight_o and_o forty_o five_o then_o fit_v it_o in_o forty_o five_o and_o take_v it_o over_o in_o forty_o eight_o and_o that_o apply_v to_o the_o same_o scale_n where_o the_o first_o twelve_o be_v take_v show_v nine_o four_o fifth_n and_o so_o many_o inch_n in_o length_n will_v make_v one_o foot_n if_o a_o piece_n of_o timber_n be_v seven_o one_o quarter_n broad_a and_o five_o &_o a_o half_a deep_a it_o be_v require_v to_o find_v how_o much_o in_o length_n shall_v make_v a_o foot_n bring_v seven_o one_o quarter_n and_o five_o a_o a_o half_a into_o quarter_n make_v twenty_o nine_o eight_o hundred_o twenty_o two_o likewise_o twelve_o make_v 48_o then_o take_v twelve_o on_o any_o scale_n of_o equal_a part_n and_o fit_v it_o on_o twenty_o nine_o and_o take_v it_o over_o in_o forty_o eight_o which_o distance_n fit_v again_o in_o twenty_o two_o and_o take_v it_o over_o in_o forty_o eight_o and_o that_o apply_v to_o the_o same_o scale_n where_o the_o twelve_o be_v take_v show_v forty_o three_o one_o three_o part_n and_o so_o many_o inch_n in_o length_n make_v a_o foot_n which_o be_v require_v to_o be_v do_v chap._n xvi_o to_o measure_v timber_n that_o be_v broad_a at_o one_o end_n than_o at_o the_o other_o suppose_v a_o piece_n be_v broad_a at_o the_o one_o end_n than_o at_o the_o other_o be_v give_v to_o be_v measure_v first_o take_v some_o place_n near_o the_o big_a end_n for_o a_o mean_a part_n then_o take_v the_o breadth_n and_o depth_n thereabouts_o which_o suppose_v to_o be_v twenty_o and_o fifteen_o then_o proceed_v as_o before_o so_o find_v you_o 5_o three_o quarter_n and_o so_o many_o inch_n in_o length_n make_v a_o foot_n chap._n xvii_o how_o perpendicular_a height_n may_v be_v find_v without_o either_o instrument_n or_o arithmetic_n take_v a_o trencher_n or_o any_o simple_a board_n end_n of_o what_o fashion_n soever_o such_o as_o you_o can_v get_v &_o draw_v thereon_o a_o line_n towards_o one_o of_o the_o side_n as_o the_o line_n ab_fw-la and_o on_o the_o point_n a_o raise_v a_o perpendicular_a as_o ad_fw-la then_o in_o the_o line_n ab_fw-la knock_v in_o two_o pin_n one_o at_o a_o and_o the_o other_o at_o b_o then_o on_o the_o point_n or_o pin_n at_o a_o hang_v a_o three_o with_o a_o plummet_n then_o lift_v up_o this_o board_n with_o the_o end_n a_o towards_o the_o height_n require_v till_o you_o bring_v the_o two_o pin_n into_o one_o straight_a line_n with_o your_o eye_n and_o the_o top_n of_o the_o height_n
of_o timber_n who_o end_n shall_v have_v more_o side_n than_o four_o may_v be_v measure_v after_o this_o manner_n add_v all_o their_o side_n together_o and_o take_v half_a that_o number_n for_o one_o side_n of_o a_o unequal_a square_a piece_n of_o timber_n then_o let_v fall_v a_o perpendicular_a from_o the_o centre_n or_o midst_n of_o the_o figure_n to_o the_o midst_n of_o some_o one_o side_n and_o take_v that_o length_n for_o the_o other_o side_n of_o the_o same_o piece_n with_o which_o two_o side_n proceed_v as_o before_o be_v show_v suppose_v the_o figure_n a_o to_o be_v the_o end_n of_o a_o piece_n of_o timber_n of_o five_o side_n be_v all_o equal_a and_o each_o side_n contain_v 12_o inch_n which_o be_v add_v together_o into_o one_o sum_n will_v make_v 60_o the_o half_a whereof_o will_v be_v 30_o for_o the_o breadth_n of_o your_o piece_n then_o take_v the_o length_n of_o the_o perpendicular_a fall_v from_o the_o centre_n a_o to_o the_o midst_n of_o one_o of_o the_o side_n which_o here_o be_v 8_o inch_n for_o the_o thickness_n of_o the_o same_o piece_n with_o which_o breadth_n and_o thickness_n proceed_v in_o all_o thing_n according_a to_o the_o former_a part_n of_o the_o ten_o chapter_n this_o rule_n be_v general_a in_o all_o kind_n of_o regular_a polygon_n how_o many_o side_n soever_o they_o have_v here_o i_o may_v have_v proceed_v to_o have_v show_v by_o what_o mean_v pyramidal_a or_o pick_a timber_n or_o steeple_n may_v be_v measure_v but_o consider_v how_o little_a this_o appertain_v to_o carpenter_n and_o how_o sufficient_o they_o be_v handle_v by_o master_n diggs_n in_o his_o geometrical_a work_n i_o forbear_v here_o to_o write_v of_o they_o chap._n xvii_o how_o to_o find_v the_o length_n of_o a_o foot_n of_o board_n at_o any_o breadth_n give_v the_o breadth_n of_o a_o board_n be_v give_v with_o the_o number_n of_o 12_o the_o side_n of_o a_o square_a foot_n of_o board_n you_o may_v by_o the_o sixth_o chapter_n find_v how_o much_o in_o length_n will_v make_v a_o foot_n at_o any_o give_v breadth_n by_o find_v a_o three_o proportional_a number_n which_o shall_v be_v to_o 12_o as_o 12_o be_v to_o the_o give_v breadth_n as_o suppose_v a_o board_n to_o be_v 16_o inch_n broad_a and_o i_o will_v know_v how_o much_o in_o length_n will_v make_v a_o foot_n thereof_o chap._n xviii_o the_o breadth_n and_o thickness_n of_o a_o piece_n of_o timber_n give_v to_o find_v how_o much_o in_o length_n shall_v make_v a_o foot_n of_o square_a timber_n at_o that_o breadth_n and_o thickness_n suppose_v a_o piece_n of_o timber_n to_o be_v 18_o inch_n broad_a and_o 14_o inch_n thick_a first_o make_v any_o angle_n as_o dfb_v and_o place_v 18_o inch_n from_o f_o to_o a_o this_o be_v the_o suppose_a breadth_n of_o your_o piece_n then_o place_v 12_o the_o side_n of_o a_o cubicall_a foot_n of_o timber_n from_o f_o to_o e_z and_o draw_v the_o line_n ae_n so_o likewise_o place_n 12_o from_o f_o to_o g_z from_o which_o point_n g_z draw_v the_o line_n gh_a parallel_n to_o ae_n till_o it_o cut_v fd_v in_o h_n so_o shall_v hf_n be_v the_o length_n of_o asquare_n foot_n of_o flat_a measure_n at_o the_o former_a breadth_n give_v thus_o far_o according_a to_o the_o last_o chapter_n now_o to_o proceed_v place_n 14_o the_o thickness_n of_o your_o piece_n from_o f_o to_o c_o and_o draw_v the_o line_n cg_n and_o last_o from_o the_o point_n h_n draw_v the_o line_n he_o parallel_n to_o cg_n till_o it_o cut_v fb_n in_o i_o so_o shall_v if_o be_v the_o length_n of_o a_o foot_n require_v which_o be_v apply_v to_o your_o scale_n will_v reach_v almost_o unto_o 7_o inch_n it_o want_v but_o one_o seven_o part_n of_o a_o inch_n and_o such_o be_v the_o length_n of_o a_o foot_n of_o timber_n who_o breadth_n be_v 18_o inch_n and_o thickness_n 14_o inch_n chap._n xix_o of_o the_o table_n for_o board_n and_o square_a timber_n and_o also_o for_o round_a timber_n concern_v the_o use_n of_o these_o table_n i_o will_v have_v you_o to_o understand_v that_o i_o have_v suppose_v the_o inch_n to_o be_v divide_v into_o 10_o equal_a part_n and_o each_o part_n divide_v into_o 10_o equal_a part_n and_o so_o the_o whole_a inch_n will_v contain_v 100_o equal_a part_n a_o table_n for_o board_n measure_n inches_n foot_n inches_n 10_o part_n of_o in_o 10_o part_n of_o a_o 10_o part_n 1_o 12_o 00_o 0_o 0_o 2_o 06_o 00_o 0_o 0_o 3_o 04_o 00_o 0_o 0_o 4_o 03_o 00_o 0_o 0_o 5_o 02_o 04_o 8_o 0_o 6_o 02_o 00_o 0_o 0_o 7_o 01_o 08_o 5_o 7_o 8_o 01_o 06_o 0_o 0_o 9_o 01_o 04_o 0_o 0_o 10_o 01_o 02_o 4_o 0_o 11_o 01_o 01_o 0_o 9_o 12_o 01_o 00_o 0_o 0_o 13_o  _fw-fr 11_o 0_o 7_o 14_o  _fw-fr 10_o 2_o 8_o 15_o  _fw-fr 09_o 6_o 0_o 16_o  _fw-fr 9_o 0_o 0_o 17_o  _fw-fr 8_o 4_o 7_o 18_o  _fw-fr 8_o 0_o 0_o 19_o  _fw-fr 7_o 5_o 7_o 20_o  _fw-fr 7_o 2_o 0_o 21_o  _fw-fr 6_o 8_o 5_o 22_o  _fw-fr 6_o 5_o 4_o 23_o  _fw-fr 6_o 2_o 6_o 24_o  _fw-fr 6_o 0_o 0_o 25_o  _fw-fr 5_o 7_o 6_o 16_o  _fw-fr 5_o 5_o 3_o 27_o  _fw-fr 5_o 3_o 3_o 28_o  _fw-fr 5_o 1_o 4_o 29_o  _fw-fr 4_o 9_o 6_o 30_o  _fw-fr 4_o 8_o 0_o a_o table_n of_o square_a timber_n measure_n inches_n foot_n inches_n 10_o part_n of_o in_o 10_o part_n of_o a_o 10_o part_n 1_o 144_o 00_o 0_o 0_o 2_o 36_o 00_o 0_o 0_o 3_o 16_o 00_o 0_o 0_o 4_o 9_o 00_o 0_o 0_o 5_o 5_o 09_o 1_o 2_o 6_o 4_o 00_o 0_o 0_o 7_o 2_o 11_o 2_o 6_o 8_o 2_o 03_o 0_o 0_o 9_o 1_o 09_o 3_o 3_o 10_o 1_o 05_o 2_o 8_o 11_o 1_o 02_o 2_o 8_o 12_o 1_o 00_o 0_o 0_o 13_o  _fw-fr 10_o 2_o 2_o 14_o  _fw-fr 08_o 8_o 1_o 15_o  _fw-fr 07_o 6_o 8_o 16_o  _fw-fr 6_o 7_o 5_o 17_o  _fw-fr 5_o 9_o 7_o 18_o  _fw-fr 5_o 3_o 3_o 19_o  _fw-fr 4_o 7_o 8_o 20_o  _fw-fr 4_o 3_o 2_o 21_o  _fw-fr 3_o 9_o 1_o 22_o  _fw-fr 3_o 5_o 7_o 23_o  _fw-fr 3_o 2_o 6_o 24_o  _fw-fr 3_o 0_o 0_o 25_o  _fw-fr 2_o 7_o 6_o 26_o  _fw-fr 2_o 5_o 5_o 27_o  _fw-fr 2_o 3_o 7_o 28_o  _fw-fr 2_o 2_o 0_o 29_o  _fw-fr 2_o 0_o 5_o 30_o  _fw-fr 1_o 9_o 2_o a_o table_n of_o round_a timber_n measure_n inches_n foot_n inches_n 10_o part_n of_o in_o 10_o part_n of_o a_o 10_o part_n 1_o 113_o 01_o 7_o 1_o 2_o 28_o 03_o 4_o 2_o 3_o 12_o 06_o 8_o 5_o 4_o 7_o 00_o 8_o 5_o 5_o 4_o 06_o 3_o 0_o 6_o 3_o 01_o 7_o 1_o 7_o 2_o 03_o 7_o 0_o 8_o 1_o 09_o 2_o 3_o 9_o 1_o 04_o 7_o 6_o 10_o 1_o 01_o 5_o 7_o 11_o  _fw-fr 11_o 2_o 2_o 12_o  _fw-fr 09_o 4_o 2_o 13_o  _fw-fr 08_o 0_o 3_o 14_o  _fw-fr 06_o 9_o 2_o 15_o  _fw-fr 06_o 0_o 3_o 16_o  _fw-fr 5_o 3_o 0_o 17_o  _fw-fr 4_o 6_o 9_o 18_o  _fw-fr 4_o 1_o 9_o 19_o  _fw-fr 3_o 7_o 6_o 20_o  _fw-fr 3_o 3_o 9_o 21_o  _fw-fr 3_o 1_o 1_o 22_o  _fw-fr 2_o 8_o 0_o 23_o  _fw-fr 2_o 5_o 6_o 24_o  _fw-fr 2_o 3_o 5_o 25_o  _fw-fr 2_o 1_o 7_o 26_o  _fw-fr 2_o 0_o 0_o 27_o  _fw-fr 1_o 8_o 6_o 28_o  _fw-fr 1_o 7_o 3_o 29_o  _fw-fr 1_o 6_o 1_o 30_o  _fw-fr 1_o 5_o 1_o the_o first_o column_n towards_o the_o left_a hand_n do_v contain_v any_o number_n of_o inch_n from_o one_o to_o 30._o in_o each_o of_o these_o table_n be_v set_v down_o the_o length_n of_o a_o foot_n in_o foot_n &_o inch_n &_o the_o ten_o part_n of_o a_o inch_n and_o so_o to_o the_o ten_o part_n of_o one_o ten_o part_n of_o a_o inch_n that_o be_v to_o the_o hundred_o part_n of_o a_o inch_n of_o board_n measure_n a_o example_n upon_o each_o table_n will_v give_v more_o light_a than_o many_o word_n and_o therefore_o first_o of_o board_n suppose_v a_o board_n to_o be_v 7_o inch_n broad_a then_o find_v 7_o in_o the_o first_o column_n towards_o the_o left_a hand_n and_o over_o against_o it_o under_o the_o title_n of_o board_n measure_n you_o shall_v find_v one_o foot_n 8_o inch_n 5_o ten_o of_o a_o inch_n and_o 7_o ten_o of_o one_o ten_o part_n of_o a_o inch_n and_o such_o be_v the_o length_n of_o a_o foot_n of_o board_n at_o that_o breadth_n and_o so_o if_o a_o board_n be_v 14_o inch_n broad_a look_v 14_o in_o the_o column_n towards_o the_o left_a hand_n and_o against_o it_o under_o the_o title_n of_o board_n measure_n you_o shall_v find_v 10_o inch_n two_o ten_o of_o a_o inch_n and_o eight_o part_n of_o one_o ten_o part_n of_o a_o inch_n for_o the_o length_n of_o a_o foot_n at_o that_o breadth_n and_o the_o like_a be_v to_o be_v observe_v for_o timber_n of_o square_a timber_n suppose_v a_o piece_n of_o
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show_v 72_o inch_n and_o so_o many_o in_o length_n be_v a_o foot_n of_o board_n the_o board_n be_v two_o inch_n broad_a let_v a_o board_n be_v three_o inch_n and_o three_o quarter_n broad_a now_o you_o desire_v to_o know_v how_o much_o in_o length_n make_v a_o foot_n bring_v three_o inch_n and_o a_o quarter_n into_o quarter_n and_o it_o make_v 13_o quarter_n then_o multiply_v 12_o the_o inch_n in_o a_o foot_n into_o quarter_n and_o it_o make_v 48_o take_v then_o 48_o part_n of_o some_o small_a scale_n and_o fit_a that_o in_o 13_o then_o let_v the_o scale_n rest_n and_o take_v it_o over_o in_o 12_o and_o apply_v that_o to_o the_o same_o scale_n where_o the_o 48_o be_v take_v show_v 44_o and_o one_o three_o part_n and_o so_o many_o inch_n in_o length_n be_v require_v to_o make_v a_o foot_n but_o have_v take_v your_o 48_o on_o some_o small_a scale_n and_o be_v to_o fit_v it_o on_o 13_o now_o if_o it_o open_v your_o scale_n too_o wide_a you_o may_v fit_v it_o over_o in_o two_o or_o three_o time_n 13_o and_o take_v it_o over_o in_o so_o many_o time_n 12_o as_o fit_v 48_o in_o four_o time_n 13_o that_o be_v in_o 52_o and_o take_v it_o over_o in_o four_o time_n 12_o that_o be_v in_o 48_o and_o it_o show_v 44_o and_o one_o three_o as_o before_z be_v apply_v to_o the_o same_o scale_n where_o the_o 48_o be_v take_v again_o let_v a_o board_n be_v 5_o inch_n and_o three_o eight_o part_n of_o a_o inch_n broad_a and_o it_o be_v require_v to_o find_v how_o many_o inch_n in_o length_n make_v a_o foot_n bring_v five_o and_o three_o eight_o into_o eight_o make_v 43_o and_o 12_o into_o eight_o make_v 96_o then_o take_v 96_o and_o fit_a it_o in_o 43_o or_o in_o twice_o 43_o there_o let_v the_o scale_n rest_n and_o take_v it_o over_o in_o 12_o and_o also_o apply_v it_o to_o the_o same_o scale_n where_o 96_o be_v take_v and_o it_o show_v 26_o and_o three_o quarter_n and_o so_o much_o in_o length_n make_v a_o foot_n of_o board_n the_o breadth_n be_v 5_o inch_n and_o three_o eight_o part_n of_o a_o inch_n which_o be_v the_o thing_n desire_v chap._n xii_o to_o measure_v board_n that_o be_v broad_a at_o one_o end_n then_o at_o the_o other_o suppose_v a_o board_n be_v broad_a at_o one_o end_n 20_o inch_n and_o at_o the_o other_o 16_o now_o it_o be_v require_v to_o find_v how_o much_o in_o length_n make_v one_o foot_n throughout_o the_o whole_a board_n add_v the_o breadth_n at_o
the_o artificer_n plain_a scale_n or_o the_o carpenter_n new_a rule_n in_o two_o part_n the_o first_o show_v how_o to_o measure_v all_o superficies_n and_o solid_n as_o timber_n stone_n board_n glass_n etc._n etc._n geometrical_o without_o the_o help_n of_o arithmetic_n it_o be_v a_o new_a way_n not_o heretofore_o practise_v the_o second_o show_v how_o to_o measure_v board_n and_o timber_n instrumental_o upon_o the_o scale_n itself_o without_o arithmetic_n or_o geometry_n but_o what_o be_v common_a to_o every_o man_n also_o how_o to_o take_v height_n and_o distance_n several_a way_n and_o to_o draw_v the_o plot_n of_o a_o town_n or_o city_n by_o thomas_n stirrup_n philomat_n london_n print_v by_o r._n &_o w._n leybourn_n for_o thomas_n pirrepont_n at_o the_o sun_n in_o paul_n church_n yard_n 1651._o to_o the_o reader_n gentle_a reader_n although_o many_o excellent_a both_o in_o arithmetic_n &_o geometry_n upon_o infallible_a ground_n have_v put_v forth_o divers_a most_o certain_a and_o sufficient_a rule_n for_o the_o measure_n of_o board_n &_o timber_n yet_o very_a few_o of_o our_o common_a artificer_n have_v be_v further_v thereby_o because_o they_o have_v not_o the_o art_n of_o arithmetic_n upon_o which_o most_o of_o their_o rule_n depend_v the_o consideration_n of_o which_o with_o the_o aptness_n which_o i_o see_v in_o some_o of_o they_o for_o the_o raise_n of_o a_o perpendicular_a and_o the_o draw_v of_o a_o parallel_n line_n upon_o which_o most_o of_o this_o book_n depend_v this_o i_o say_v have_v be_v the_o cause_n which_o have_v move_v i_o to_o give_v they_o some_o rule_v geometrical_a whereby_o they_o may_v measure_v both_o board_n &_o timber_n without_o the_o help_n of_o arithmetic_n therefore_o to_o thy_o view_n gentle_a reader_n that_o want_v the_o art_n of_o arithmetic_n do_v i_o prefer_v this_o short_a and_o plain_a treatise_n wherein_o &_o in_o the_o beginning_n be_v declare_v the_o infallible_a ground_n upon_o which_o the_o whole_a work_n do_v depend_v &_o then_o do_v follow_v the_o apply_v of_o those_o rule_n to_o the_o present_a purpose_n with_o the_o declaration_n of_o three_o table_n one_o for_o board_n and_o one_o for_o square_a timber_n and_o the_o three_o for_o round_a timber_n very_o fit_a for_o all_o such_o as_o stand_v in_o need_n thereof_o and_o yet_o want_v both_o instrument_n and_o arithmetic_n whereby_o to_o use_v the_o same_o in_o the_o second_o part_n of_o this_o book_n be_v show_v a_o second_o way_n whereby_o you_o may_v measure_v board_n and_o timber_n by_o rule_n and_o compass_n only_o without_o draw_v of_o line_n &_o also_o how_o to_o take_v height_n and_o distance_n several_a way_n without_o instrument_n all_o which_o be_v ground_v upon_o infallible_a principle_n geometrical_a thus_o desire_v thou_o to_o accept_v of_o this_o little_a book_n as_o a_o taste_n of_o my_o good_a will_n towards_o thou_o which_o i_o wish_v even_o so_o to_o further_o thou_o as_o i_o know_v it_o sufficient_a for_o the_o true_a measure_v both_o of_o board_n and_o timber_n farewell_n the_o content_n the_o meaning_n of_o certain_a term_n of_o geometry_n use_v in_o this_o book_n page_z 1_o how_o to_o raise_v a_o perpendicular_a on_o any_o part_n of_o a_o right_a line_n give_v page_z 5_o how_o to_o let_v fall_v a_o perpendicular_a from_o a_o point_n assign_v to_o a_o line_n give_v page_z 7_o to_o a_o line_n give_v to_o draw_v a_o parallel_n line_n at_o any_o distance_n require_v page_z 8_o to_o perform_v the_o former_a proposition_n at_o a_o distance_n require_v and_o by_o a_o point_n limit_v page_z 10_o have_v two_o line_n give_v to_o find_v a_o three_o proportional_a line_n to_o they_o page_z 12_o have_v three_o line_n give_v to_o find_v a_o four_o proportional_a line_n to_o they_o page_z 14_o the_o make_n of_o a_o rule_n or_o scale_n for_o the_o measure_n of_o board_n and_o timber_n page_n 17_o how_o any_o board_n may_v be_v measure_v geometrical_o page_n 20_o how_o timber_n may_v be_v measure_v geometrical_o page_n 26_o of_o round_a timber_n page_n 33_o how_n triangle_v timber_n or_o timber_n which_o have_v but_o three_o side_n may_v be_v measure_v page_n 42_o how_o timber_n who_o end_n be_v a_o rhombus_fw-la be_v to_o be_v measure_v page_n 45_o how_o timber_n who_o end_n be_v a_o rhomboiades_n be_v measure_v page_n 47_o how_o to_o measure_n timber_n who_o end_n be_v a_o trapesiam_n page_n 49_o how_o to_o measure_n timber_n who_o side_n be_v many_o as_o 5_o 6_o 7_o 8_o 9_o 10_o or_o more_o so_o they_o be_v all_o equal_a page_n 51_o how_o to_o find_v the_o length_n of_o a_o foot_n of_o board_n at_o any_o breadth_n give_v page_n 54_o the_o breadth_n and_o thickness_n of_o a_o piece_n of_o timber_n give_v to_o find_v how_o much_o in_o length_n shall_v make_v a_o foot_n of_o square_a timber_n at_o that_o breadth_n and_o thickness_n page_n 56_o how_o to_o find_v a_o mean_a proportional_a line_n between_o two_o line_n give_v page_n 66_o the_o second_o part._n of_o the_o scale_n and_o the_o graduation_n or_o division_n thereof_o and_o how_o they_o be_v to_o be_v use_v page_n 71_o to_o divide_v a_o line_n give_v into_o any_o number_n of_o equal_a part_n page_n 73_o to_o take_v any_o part_n or_o part_n of_o a_o line_n page_n 74_o a_o line_n contain_v any_o part_n or_o part_n of_o a_o line_n thereby_o to_o find_v the_o whole_a line_n page_n 75_o a_o line_n be_v give_v contain_v any_o number_n of_o equal_a part_n to_o cut_v off_o from_o it_o so_o many_o as_o shall_v be_v require_v page_n 77_o to_o lay_v down_o sudden_o two_o three_o or_o more_o line_n in_o proportion_n require_v page_n 78_o in_o a_o map_n or_o plot_n the_o length_n of_o any_o line_n be_v know_v thereby_o to_o find_v the_o length_n of_o all_o or_o any_o of_o the_o rest_n page_n 80_o unto_o two_o line_n give_v to_o find_v a_o three_o in_o proportion_n page_n 82_o unto_o three_o line_n give_v to_o find_v a_o four_o in_o proportion_n that_o be_v to_o perform_v the_o rule_n of_o three_o in_o line_n page_n 84_o to_o divide_v a_o line_n give_v into_o two_o such_o part_n bearing_z proportion_n one_o to_o the_o other_o as_o two_o number_n give_v page_n 86_o to_o measure_v flat_a measure_n page_n 87_o to_o measure_n board_n that_o be_v broad_a at_o one_o end_n than_o at_o the_o other_o page_n 91_o to_o find_v how_o many_o square_a foot_n any_o whole_a board_n contain_v without_o find_v how_o much_o in_o length_n make_v a_o foot_n page_n 93_o to_o measure_n board_n that_o be_v broad_a at_o the_o one_o end_n then_o at_o the_o other_o in_o the_o same_o manner_n page_n 95_o to_o measure_n timber_n page_n 97_o to_o measure_n timber_n that_o be_v broad_a at_o one_o end_n than_o at_o the_o other_o page_n 100_o how_o perpendicular_a height_n may_v be_v find_v without_o either_o instrument_n or_o arithmetic_n page_n 101_o how_o to_o take_v the_o altitude_n or_o height_n of_o a_o build_n by_o a_o bowl_n of_o water_n page_n 105_o how_o to_o take_v the_o altitude_n of_o a_o building_n by_o a_o line_n and_o plummet_n the_o sun_n shine_v page_n 107_o how_o to_o find_v the_o altitude_n of_o a_o building_n by_o two_o stick_n join_v in_o a_o right_a angle_n page_n 109_o to_o find_v a_o distance_n by_o the_o two_o stick_n join_v square_a page_n 112_o how_o to_o describe_v a_o town_n or_o city_n according_a to_o chorographicall_a proportion_n by_o the_o help_n of_o a_o plain_a glass_n page_n 116_o a_o advertisement_n to_o the_o reader_n forasmuch_o as_o throughout_o this_o whole_a book_n there_o be_v mention_v make_v of_o rule_n and_o scale_n the_o make_v whereof_o be_v different_a from_o those_o which_o be_v vulgar_o make_v and_o sell_v if_o any_o therefore_o be_v desirous_a to_o have_v any_o particular_a rule_n mention_v in_o this_o book_n or_o one_o rule_n to_o perform_v all_o the_o work_n in_o general_a he_o may_v have_v they_o exact_o make_v by_o master_n anthony_n thompson_n in_o hosier_n lane_n near_o smithfield_n the_o artificer_n plain_a scale_n chap._n i._n the_o meaning_n of_o certain_a term_n of_o 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to_o the_o 9th_o chapter_n as_o if_o it_o have_v be_v a_o board_n this_o chapter_n will_v i_o have_v you_o well_o to_o consider_v because_o i_o do_v not_o intend_v to_o repeat_v what_o i_o have_v hear_v deliver_v but_o only_o describe_v unto_o you_o the_o end_n of_o some_o piece_n according_a to_o their_o form_n and_o so_o give_v you_o some_o rule_n for_o to_o measure_v they_o by_o this_o chapter_n chap._n xi_o of_o round_a timber_n here_o first_o i_o will_v have_v you_o to_o understand_v what_o the_o circumference_n the_o centre_n and_o diameter_n of_o a_o circle_n be_v the_o circumference_n be_v the_o line_n encompass_v the_o circle_n the_o centre_n be_v the_o point_n in_o the_o midst_n thereof_o the_o diameter_n be_v a_o right_a line_n pass_v by_o the_o centre_n through_o the_o whole_a circle_n and_o divide_v the_o same_o into_o two_o equal_a part_n either_o half_a of_o which_o diameter_n be_v call_v the_o semidiameter_n now_o have_v find_v the_o circumference_n of_o a_o round_a 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and_o so_o measure_v it_o by_o the_o former_a part_n of_o the_o ten_o chapter_n in_o all_o respect_n as_o there_o be_v show_v let_v the_o triangle_n abc_n be_v the_o end_n of_o a_o piece_n of_o timber_n to_o be_v measure_v which_o have_v but_o only_o three_o side_n chap._n xiii_o how_o timber_n who_o end_n be_v a_o rhombus_fw-la or_o diamond_n form_n be_v to_o be_v measure_v a_o rhombus_fw-la or_o diamond_n be_v a_o figure_n of_o four_o equal_a side_n but_o no_o right_a angle_n such_o as_o be_v the_o figure_n abcd_n for_o the_o measure_n whereof_o observe_v this_o example_n let_v the_o say_a figure_n abcd_v be_v the_o end_n of_o a_o piece_n of_o timber_n to_o be_v measure_v now_o take_v the_o length_n of_o the_o side_n or_o base_a ab_fw-la which_o be_v 14_o inch_n for_o one_o of_o the_o side_n of_o a_o square_a piece_n of_o timber_n and_o the_o length_n of_o the_o perpendicular_a de_fw-fr which_o will_v be_v find_v to_o be_v 12_o and_o something_o better_a than_o the_o eight_o part_n 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require_v and_o direct_o where_o the_o three_o fall_v there_o mark_v it_o with_o a_o prick_n of_o your_o compass_n as_o at_o e_o and_o draw_v the_o line_n ae_n now_o measure_v the_o distance_n between_o your_o stand_n and_o the_o base_a of_o your_o altitude_n which_o here_o we_o will_v suppose_v to_o be_v 36_o foot_n as_o from_o f_o to_o g_z and_o take_v 36_o from_o your_o scale_n &_o set_v it_o down_o from_o a_o to_o d_o from_o which_o point_n d_o raise_v a_o perpendicular_a to_o cut_v the_o plumbe-line_n ae_n in_o e_z so_o shall_v de_fw-fr be_v the_o height_n require_v which_o be_v apply_v unto_o your_o scale_n will_v reach_v unto_o 32_o and_o so_o many_o foot_n be_v the_o altitude_n gh_o here_o note_n that_o the_o altitude_n thus_o find_v be_v from_o the_o level_n of_o the_o eye_n upward_o and_o therefore_o the_o height_n from_o the_o eye_n downward_o be_v to_o be_v add_v thereto_o to_o make_v it_o complete_a chap._n xviii_o how_o to_o take_v the_o altitude_n or_o height_n of_o a_o 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port_n harbour_n bay_n gate_n fort_n and_o such_o other_o notable_a place_n as_o you_o intend_v to_o describe_v which_o place_n be_v choose_v provide_v a_o plain_a glass_n which_o in_o the_o midst_n of_o the_o platform_n hang_v parallel_n to_o the_o horizon_n in_o the_o do_n of_o which_o you_o must_v be_v very_o careful_a so_o that_o move_v up_o and_o down_o the_o platform_n you_o may_v in_o the_o centre_n of_o the_o glass_n see_v all_o those_o notable_a place_n the_o foundation_n be_v lay_v let_v we_o now_o proceed_v to_o the_o work_n and_o first_o of_o all_o on_o your_o platform_n you_o must_v draw_v a_o meridian_n line_n which_o must_v pass_v just_a under_o the_o glass_n so_o that_o if_o a_o perpendicular_a line_n be_v let_v fall_n from_o the_o centre_n of_o the_o glass_n to_o the_o platform_n it_o may_v cut_v the_o meridian_n line_n at_o right_a angle_n and_o by_o have_v this_o line_n draw_v you_o may_v draw_v the_o line_n of_o east_n and_o west_n at_o right_a angle_n to_o the_o 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