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part_n to_o cut_v off_o from_o it_o so_o many_o as_o shall_v be_v require_v as_o let_v ab_fw-la be_v a_o line_n give_v contain_v 52_o part_n upon_o some_o scale_n and_o let_v it_o be_v require_v to_o cut_v off_o from_o it_o 24_o of_o the_o same_o part_n take_v with_o your_o compass_n the_o give_v line_n ab_fw-la and_o set_v that_o in_o 52_o of_o the_o equal_a part_n there_o let_v rest_v the_o scale_n then_o take_v it_o over_o in_o 24_o the_o part_n require_v and_o that_o distance_n set_v from_o a_o to_o c_o so_o be_v ac_fw-la 24_o of_o the_o same_o part_n whereof_o ab_fw-la be_v 52_o which_o
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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 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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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square_a piece_n of_o 16_o inch_n broad_a and_o 10_o inch_n thick_a all_o other_o four_o side_v figure_n beside_o the_o true_a square_n and_o the_o unequal_a square_n in_o the_o ten_o chapter_n and_o the_o rhombus_fw-la in_o the_o last_o chapter_n and_o the_o rhomboide_v in_o this_o be_v call_v trapezias_n or_o tables_n chap._n xv._o how_o to_o measure_v timber_n who_o end_n be_v a_o trapeziam_n a_o trapeziam_n be_v any_o irregular_a four_o side_v figure_n of_o what_o fashion_n soever_o as_o the_o figure_n abcd_n be_v a_o trapeziam_n and_o may_v be_v cast_v into_o two_o triangle_n by_o draw_v the_o diagonall_a line_n ac_fw-la and_o so_o each_o triangle_n measure_v as_o be_v before_o show_v which_o be_v do_v add_v the_o content_n of_o they_o both_o together_o and_o you_o shall_v have_v the_o content_a of_o the_o whole_a trapeziam_n abcd._n or_o you_o may_v more_o ready_o measure_v it_o thus_o take_v one_o half_a the_o diagonall_a line_n ac_fw-la which_o in_o this_o example_n will_v be_v 8_o inch_n for_o one_o side_n of_o your_o piece_n and_o take_v the_o two_o perpendicular_o bf_n and_o de_fw-fr and_o join_v they_o both_o together_o in_o one_o sum_n so_o shall_v you_o have_v in_o this_o example_n 10_o inch_n for_o the_o other_o side_n of_o your_o piece_n with_o which_o two_o side_n as_o if_o it_o be_v a_o unequal_a square_a piece_n of_o timber_n proceed_v as_o before_o in_o the_o former_a part_n of_o the_o ten_o chapter_n chap._n xvi_o how_o to_o measure_v 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 many_o side_v figure_n be_v those_o which_o have_v more_o side_n than_o four_o and_o be_v general_o call_v pollygon_n a_o piece_n
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 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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