rather_o to_o use_v some_o of_o the_o way_n follow_v but_o if_o their_o readiness_n in_o cast_v up_o a_o stock_n of_o board_n shall_v cause_v they_o to_o accept_v of_o this_o way_n i_o will_v not_o be_v their_o let_n now_o the_o way_n be_v this_o suppose_v the_o piece_n of_o timber_n to_o be_v measure_v to_o be_v a_o stock_n of_o board_n consist_v of_o so_o many_o board_n as_o there_o be_v inch_n in_o the_o thickness_n of_o the_o piece_n then_o measure_v one_o of_o those_o suppose_a board_n that_o do_v cast_v up_o the_o whole_a stock_n now_o this_o be_v perform_v you_o be_v to_o know_v that_o every_o twelve_o foot_n of_o board_n be_v a_o foot_n of_o timber_n as_o every_o man_n may_v perceive_v and_o six_o foot_n of_o board_n be_v half_a a_o foot_n of_o timber_n and_o three_o foot_n be_v a_o quarter_n of_o a_o foot_n of_o timber_n also_o every_o thréeskore_n foot_n of_o board_n be_v five_o foot_n of_o timber_n and_o so_o sixeskore_n foot_n of_o board_n be_v ten_o foot_n of_o timber_n nineskore_n foot_n of_o board_n be_v fifteen_o foot_n of_o timber_n twelueskore_n be_v twenty_o foot_n fiftéeneskore_n or_o three_o hundred_o be_v twenty_o and_o five_o foot_n six_o hundred_o foot_n of_o board_n be_v fifty_o foot_n of_o timber_n and_o so_o forth_o now_o if_o this_o be_v observe_v it_o be_v easy_a for_o any_o man_n to_o cast_v up_o the_o content_a of_o any_o ordinary_a piece_n of_o timber_n true_o there_o be_v far_a to_o be_v note_v that_o if_o there_o be_v any_o odd_a half_a ynche_n in_o the_o thickness_n of_o the_o piece_n to_o be_v measure_v that_o then_o it_o be_v account_v as_o half_a of_o one_o of_o the_o suppose_a board_n of_o the_o stock_n and_o if_o there_o be_v a_o quarter_n of_o one_o inch_n than_o it_o be_v a_o quarter_n of_o a_o board_n and_o if_o there_o be_v a_o odd_a three_o quarter_n of_o a_o inch_n it_o be_v three_o quarter_n of_o a_o board_n and_o if_o there_o be_v any_o other_o odd_a part_n of_o a_o inch_n it_o be_v the_o same_o part_n of_o a_o board_n and_o must_v be_v count_v with_o the_o whole_a stock_n this_o way_n be_v so_o plain_a that_o it_o need_v no_o example_n i_o suppose_v the_o simple_a may_v understand_v it_o and_o therefore_o i_o will_v say_v no_o more_o of_o it_o only_o this_o you_o may_v observe_v that_o you_o may_v measure_v the_o piece_n by_o imagine_v it_o to_o be_v divide_v into_o two_o inch_n three_o inch_n or_o four_o inch_n plank_n so_o that_o you_o search_v out_o how_o many_o foot_n of_o such_o plank_n be_v contain_v in_o a_o foot_n of_o timber_n chap._n 4._o how_o timber_n may_v be_v measure_v after_o the_o ordinary_a way_n by_o deduct_v the_o lose_a square_n it_o be_v observe_v in_o the_o three_o chapter_n of_o the_o first_o part_n of_o this_o book_n that_o when_o any_o piece_n of_o timber_n be_v measure_v after_o the_o most_o common_a way_n which_o be_v by_o add_v the_o breadth_n and_o thickness_n together_o and_o take_v the_o half_a thereof_o for_o the_o square_n of_o the_o piece_n etc._n etc._n that_o then_o there_o be_v always_o lose_v a_o square_a piece_n of_o timber_n of_o the_o whole_a length_n of_o the_o piece_n to_o be_v measure_v who_o square_a be_v half_a the_o difference_n of_o the_o two_o side_n of_o the_o piece_n now_o by_o observe_v of_o this_o lose_a square_n any_o ordinary_a piece_n of_o timber_n may_v be_v true_o measure_v as_o follow_v measure_v the_o piece_n by_o take_v for_o the_o square_a thereof_o the_o half_a of_o the_o sum_n or_o total_a of_o the_o two_o side_n as_o be_v aforesaid_a and_o as_o be_v usual_o accustom_v this_o do_v note_v the_o difference_n of_o the_o two_o side_n then_o take_v the_o half_a of_o that_o difference_n for_o the_o side_n of_o the_o lose_a square_n which_o be_v all_o the_o length_n of_o the_o piece_n then_o measure_v that_o suppose_a or_o lose_v square_a and_o what_o it_o amount_v unto_o deduct_v out_o of_o the_o measure_n of_o the_o whole_a piece_n be_v measure_v after_o the_o say_v common_a way_n and_o the_o remainder_n be_v the_o true_a content_n of_o the_o piece_n and_o because_o the_o lose_a square_n may_v have_v in_o it_o a_o odd_a half_a inch_n as_o some_o time_n it_o have_v as_o three_o inch_n and_o ahalfe_n or_o such_o like_a i_o have_v therefore_o add_v unto_o the_o common_a rule_n what_o length_n make_v a_o foot_n of_o timber_n from_o a_o inch_n to_o ten_o inch_n note_v still_o every_o half_a inch_n as_o you_o may_v behold_v in_o the_o table_n of_o timber_n measure_v hereafter_o follow_v in_o the_o latter_a end_n of_o this_o second_o part_n for_o to_o take_v half_a the_o difference_n betwixt_o the_o two_o next_o adjoin_v number_n of_o inch_n add_v to_o the_o lesser_a of_o they_o as_o common_o man_n do_v be_v not_o true_a as_o for_o example_n at_o a_o inch_n square_a one_o hundred_o forty_o four_o foot_n in_o length_n make_v a_o foot_n of_o timber_n at_o two_o inch_n thirty_o six_o foot_n do_v it_o so_o that_o if_o the_o half_a betwixt_o thirty_o six_o and_o one_o hundred_o and_o forty_o four_o be_v take_v and_o add_v to_o thirty_o six_o for_o the_o length_n of_o a_o foot_n at_o a_o inch_n and_o a_o half_a square_n it_o will_v be_v nintie_a foot_n whereas_o in_o truth_n it_o be_v but_o sixty_o four_o foot_n so_o in_o this_o example_n it_o err_v twenty_o six_o foot_n in_o length_n of_o a_o piece_n of_o timber_n of_o a_o inch_n and_o a_o half_a square_n and_o how_o so_o ever_o it_o be_v not_o so_o much_o in_o other_o number_n above_o two_o inch_n square_a yet_o it_o always_o err_v more_o or_o less_o chap._n 5._o how_o wainie_n or_o canted_a timber_n may_v be_v measure_v although_o there_o be_v diverse_a way_n to_o measure_v wainie_a or_o canted_a timber_n yet_o i_o will_v observe_v only_o this_o one_o plain_a way_n measure_v then_o the_o piece_n as_o if_o it_o be_v not_o wainie_a out_o of_o which_o deduct_v the_o wane_v and_o the_o remainder_n be_v the_o true_a content_n of_o the_o piece_n how_o to_o deduct_v the_o wane_v be_v better_a teach_v by_o a_o example_n then_o by_o a_o precept_n and_o therefore_o suppose_v the_o figure_n a_o be_v the_o end_n of_o a_o piece_n of_o timber_n of_o ten_o inch_n square_a have_v one_o corner_n thereof_o wainie_a this_o piece_n measure_n as_o if_o it_o be_v not_o wainie_a that_o do_v measure_v what_o the_o wain_n be_v either_o way_n from_o the_o corner_n which_o i_o call_v the_o want_n because_o the_o piece_n want_v so_o much_o of_o square_n which_o want_n in_o this_o example_n be_v four_o inch_n either_o way_n as_o you_o may_v see_v by_o the_o two_o prick_a line_n with_o the_o figure_n of_o four_o stand_v by_o either_o of_o they_o this_o measure_n as_o if_o it_o be_v a_o piece_n of_o timber_n of_o four_o inch_n either_o way_n and_o as_o long_o as_o the_o whole_a piece_n that_o do_v take_v half_a the_o content_a thereof_o the_o which_o half_o deduct_v out_o of_o the_o measure_n of_o the_o whole_a piece_n as_o it_o be_v before_o measure_v and_o the_o remainder_n will_v be_v the_o true_a content_n thereof_o and_o as_o you_o do_v with_o this_o corner_n so_o must_v you_o do_v with_o the_o rest_n if_o they_o be_v wainie_a also_o and_o here_o i_o will_v have_v you_o note_n that_o where_o i_o bid_v the_o half_a of_o the_o content_a of_o the_o say_v square_a to_o be_v deduct_v that_o the_o reason_n hereof_o be_v for_o that_o in_o geometry_n all_o paralletogram_n and_o parallelipipidon_n be_v divide_v into_o two_o equal_a part_n by_o their_o diameter_n as_o it_o be_v demonstrate_v in_o euclid_n book_n 1._o proposition_n 34._o and_o book_n 11._o proposition_n 18._o that_o be_v to_o say_v in_o plain_a term_n for_o our_o purpose_n a_o board_n or_o a_o piece_n of_o timber_n which_o have_v their_o opposite_a or_o contrary_a side_n equal_o distant_a be_v cut_v into_o two_o piece_n by_o a_o straight_a line_n pass_v by_o the_o opposite_a corner_n as_o you_o may_v see_v in_o the_o figure_n b_o i_o say_v that_o board_n or_o piece_n of_o timber_n be_v cut_v into_o two_o equal_a part_n so_o that_o it_o be_v manifest_a by_o this_o that_o the_o say_a wain_n be_v half_a so_o much_o as_o the_o piece_n who_o side_n be_v equal_a to_o the_o say_a want_n chap._n 6._o how_o round_a timber_n may_v be_v measure_v i_o tell_v you_o before_o that_o i_o will_v not_o trouble_v you_o with_o geometrical_a work_n and_o howsoever_o i_o do_v hereafter_o set_v down_o some_o more_o artificial_a way_n to_o measure_v by_o yet_o my_o endeavour_n especial_o be_v to_o correct_v the_o common_a error_n by_o that_o knowledge_n which_o most_o man_n have_v already_o and_o therefore_o you_o may_v measure_v round_a timber_n plain_o in_o this_o sort_n gird_a the_o
at_o the_o left_a side_n and_o the_o inch_n and_o part_n of_o a_o inch_n in_o a_o c_o d_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr ½_n 1_o 12_o  _fw-fr 8_o  _fw-fr 2_o 6_o  _fw-fr 4_o 9_o ⅗_n 3_o 4_o  _fw-fr 3_o 5_o 1_o 7_o 4_o 3_o  _fw-fr 2_o 8_o 5_o 2_o 4_o ⅘_n 2_o 2_o 2_o 11_o 6_o 2_o  _fw-fr 1_o 10_o 1_o 7_o 7_o 1_o 8_o 4_o 7_o 1_o 7_o ⅕_n 8_o 1_o 6_o 1_o 4_o 16_o 17_o 9_o 1_o 4_o 1_o 3_o 3_o 19_o 10_o 1_o 2_o ⅖_n 1_o 2_o ¾_n 11_o 1_o 1_o 1_o 11_o 1_o ½_n 12_o 1_o  _fw-fr  _fw-fr 11_o ½_n 13_o  _fw-fr 11_o 1_o 13_o  _fw-fr 10_o ⅔_n 14_o  _fw-fr 10_o 2_o 7_o  _fw-fr 9_o ⅞_n 15_o  _fw-fr 9_o ⅗_n  _fw-fr 9_o 2_o 7_o 16_o  _fw-fr 9_o  _fw-fr 8_o ¾_n 17_o  _fw-fr 8_o ½_n  _fw-fr 8_o ⅕_n 18_o  _fw-fr 8_o  _fw-fr 7_o ⅘_n 19_o  _fw-fr 7_o 4_o 7_o  _fw-fr 7_o ⅓_n 20_o  _fw-fr 7_o ⅕_n  _fw-fr 7_o 1_o 41_o 21_o  _fw-fr 6_o 6_o 7_o  _fw-fr 6_o 5_o 7_o 22_o  _fw-fr 6_o ½_n  _fw-fr 6_o ⅜_n 23_o  _fw-fr 6_o ¼_n  _fw-fr 6_o ⅛_n 24_o  _fw-fr 6_o  _fw-fr 5_o ⅞_n 25_o  _fw-fr 5_o ¾_n  _fw-fr 5_o 11_o 17_o 26_o  _fw-fr 5_o ½_n  _fw-fr 5_o 3_o 7_o 27_o  _fw-fr 5_o ⅓_n  _fw-fr 5_o 2_o 9_o 28_o  _fw-fr 5_o 1_o 7_o  _fw-fr 5_o 1_o 10_o 29_o  _fw-fr 5_o  _fw-fr 4_o ⅞_n 30_o  _fw-fr 4_o ⅘_n  _fw-fr 4_o 5_o 7_o the_o broad_a row_n at_o the_o right_a side_n thereof_o note_v also_o that_o where_o as_o you_o see_v in_o the_o fraction_n sometime_o one_o prick_n sometime_o two_o prick_v that_o when_o one_o prick_n stand_v before_o the_o fraction_n it_o signify_v a_o littellesse_a and_o two_o prick_v a_o little_a more_o now_o if_o that_o the_o breadth_n of_o the_o board_n be_v a_o certain_a number_n of_o inch_n and_o one_o half_a inch_n then_o be_v the_o length_n of_o a_o foot_n over_o against_o those_o number_n of_o inch_n in_o the_o colum_fw-la under_o d._n but_o because_o a_o example_n will_v give_v more_o light_a than_o many_o word_n otherwise_o therefore_o suppose_v the_o board_n to_o be_v 11_o inch_n broad_a then_o find_v 11_o in_o the_o row_n ab_fw-la and_o over_o against_o it_o in_o the_o colum_fw-la c_o you_o shall_v see_v 1.1_o and_o 1_o 11_o which_o be_v one_o foot_n one_o inch_n and_o one_o eleven_o part_n of_o a_o inch_n but_o if_o the_o board_n be_v 11_o inch_n and_o ½_n broad_a then_o seek_v the_o length_n of_o a_o foot_n over_o against_o that_o 11_o in_o the_o colum_fw-la d_o and_o it_o be_v 12_o inch_n and_o ½_n so_o if_o the_o breadth_n of_o the_o board_n be_v 25_o inch_n and_o ½_n look_v for_o 25_o in_o the_o row_n ab_fw-la and_o over_o against_o it_o in_o the_o colum_fw-la d_o you_o shall_v see_v five_o inch_n and_o five_o seven_o part_n of_o a_o inch_n and_o let_v this_o suffice_v for_o the_o table_n of_o boord-measure_n the_o table_n of_o timber-measure_n in_o the_o row_n ab_fw-la be_v set_v down_o the_o square_n of_o timber_n from_o one_o inch_n to_o 30_o inch_n over_o against_o every_o one_o of_o these_o in_o the_o colum_fw-la under_o c_o be_v set_v down_o the_o length_n of_o a_o foot_n in_o foot_n and_o inch_n and_o part_n of_o a_o inch_n the_o foot_n be_v set_v down_o in_o the_o row_n at_o the_o left_a hand_n of_o this_o columas_fw-la far_o as_o the_o square_n do_v yield_v a_o foot_n and_o the_o inch_n and_o part_n of_o a_o inch_n be_v set_v down_o in_o the_o row_n towards_o the_o left_a hand_n of_o the_o same_o colum_fw-la but_o if_o the_o square_n of_o the_o piece_n of_o timber_n be_v any_o number_n of_o inch_n between_o 1_o and_o 10_o and_o a_o odd_a half_a inch_n more_o then_o over_o against_o those_o number_n of_o inch_n in_o the_o colum_fw-la under_o d_o you_o shall_v find_v the_o length_n of_o a_o foot_n in_o foot_n inch_n and_o part_n of_o a_o inch_n the_o foot_n stand_v as_o in_o the_o other_o colum_fw-la in_o the_o row_n at_o the_o left_a side_n thereof_o and_o the_o inch_n &_o part_n of_o a_o inch_n in_o the_o row_n at_o the_o right_a side_n the_o reason_n why_o i_o add_v those_o half_a inch_n from_o 1_o to_o 10_o be_v because_o in_o measure_v of_o timber_n by_o deduct_v the_o lose_a square_n as_o be_v set_v down_o in_o the_o four_o chapter_n of_o this_o second_o part_n of_o this_o book_n you_o shall_v have_v occasion_n oft_o time_n to_o seek_v out_o the_o length_n of_o a_o foot_n for_o a_o square_a of_o one_o inch_n and_o a_o half_a two_o inch_n and_o ½_n three_o inch_n and_o ½_n and_o so_o forth_o to_o ten_o inch_n here_o far_o it_o be_v to_o be_v note_v that_o whereas_o you_o shall_v find_v for_o the_o most_o part_n before_o the_o numerafor_a of_o the_o fraction_n sometime_o one_o prick_n sometime_o two_o prick_v that_o one_o prick_n do_v signify_v somewhat_o less_o and_o two_o prick_v do_v signify_v somewhat_o more_o this_o i_o have_v note_v as_o master_n digges_n have_v also_o do_v though_o it_o matter_n not_o whether_o such_o more_o or_o less_o be_v observe_v or_o not_o see_v no_o sensible_a error_n come_v by_o omit_v they_o a_o c_o d_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr ½_n 1_o 144_o  _fw-fr 64_o  _fw-fr 2_o 36_o  _fw-fr 23_o ½_n 3_o 16_o  _fw-fr 11_o 9_o 1_o 16_o 4_o 9_o  _fw-fr 7_o 1_o ⅓_n 5_o 5_o 9_o 3_o 25_o 4_o 9_o ⅛_n 6_o 4_o  _fw-fr 3_o 4_o 8_o 9_o 7_o 2_o 11_o 2_o 7_o 2_o 4_o ¾_n 8_o 2_o 3_o 1_o 11_o 12_o 13_o 9_o 1_o 9_o ⅓_n 1_o 7_o 1_o 7_o 10_o 1_o 5_o 2_o 7_o  _fw-fr  _fw-fr 11_o 1_o 2_o 2_o 7_o  _fw-fr  _fw-fr 12_o 1_o  _fw-fr  _fw-fr  _fw-fr 13_o  _fw-fr 10_o ⅕_n  _fw-fr  _fw-fr 14_o  _fw-fr 8_o 13_o 16_o  _fw-fr  _fw-fr 15_o  _fw-fr 7_o ⅔_n  _fw-fr  _fw-fr 16_o  _fw-fr 6_o ¾_n  _fw-fr  _fw-fr 17_o  _fw-fr 6_o  _fw-fr  _fw-fr 18_o  _fw-fr 5_o ⅓_n  _fw-fr  _fw-fr 19_o  _fw-fr 4_o 25_o 32_o  _fw-fr  _fw-fr 20_o  _fw-fr 4_o 5_o 16_o  _fw-fr  _fw-fr 21_o  _fw-fr 3_o 11_o 12_o  _fw-fr  _fw-fr 22_o  _fw-fr 3_o 4_o 7_o  _fw-fr  _fw-fr 23_o  _fw-fr 3_o ¼_n  _fw-fr  _fw-fr 24_o  _fw-fr 3_o  _fw-fr  _fw-fr 25_o  _fw-fr 2_o ¾_n  _fw-fr  _fw-fr 26_o  _fw-fr 2_o 9_o 16_o  _fw-fr  _fw-fr 27_o  _fw-fr 2_o ⅜_n  _fw-fr  _fw-fr 28_o  _fw-fr 2_o ⅕_n  _fw-fr  _fw-fr 29_o  _fw-fr 2_o 1_o 16_o  _fw-fr  _fw-fr 30_o  _fw-fr 1_o 11_o 12_o  _fw-fr  _fw-fr a_o example_n or_o two_o in_o this_o case_n shall_v not_o be_v unnecessary_a if_o the_o square_a of_o the_o piece_n give_fw-mi be_v five_o inch_n find_v five_o in_o the_o row_n ab_fw-la and_o over_o against_o it_o in_o the_o colum_fw-la of_o c_o you_o shall_v find_v five_o foot_n nine_o inch_n and_o three_o twenty_o five_o part_n of_o a_o inch_n if_o the_o square_a give_v be_v thirtéene_fw-mi then_o over_o against_o thirtéene_n you_o shall_v find_v on_o the_o right_a side_n of_o the_o colum_fw-la c_o 10⅕_n which_o be_v 10_o inch_n and_o somewhat_o more_o than_o one_o five_o part_n of_o a_o inch_n if_o the_o square_n give_v be_v six_o inch_n and_o a_o half_a then_o over_o against_o six_o you_o shall_v find_v the_o colum_fw-la d_o for_o the_o length_n of_o a_o foot_n three_o foot_n four_o inch_n and_o somewhat_o less_o than_o eight_o nine_o part_n of_o a_o inch_n more_o example_n needs_o not_o enough_o have_v be_v say_v to_o any_o that_o be_v but_o of_o mean_a capacity_n and_o desirous_a to_o learn_v the_o end_n of_o the_o second_o part_n the_o three_o part_n of_o the_o carpenter_n rule_n contain_v sundry_a true_a way_n to_o measure_v superficies_n and_o sollid_n or_o as_o we_o call_v they_o board_v and_o timber_n of_o extraordinary_a form_n chapter_n 1._o the_o meaning_n of_o certain_a term_n of_o geometry_n general_o use_v in_o this_o three_o part_n when_o i_o have_v write_v the_o former_a part_n of_o this_o book_n concern_v measure_v of_o ordinary_a timber_n and_o board_n and_o do_v consider_v that_o beside_o the_o pleasure_n there_o will_v come_v some_o good_a to_o carpenter_n if_o they_o can_v also_o measure_v extraordinary_a form_z i_o have_v therefore_o think_v good_a to_o add_v this_o part_n unto_o the_o other_o two_o true_a it_o be_v that_o master_n dig_v in_o his_o tectonicon_fw-la have_v not_o be_v silent_a of_o the_o most_o of_o these_o thing_n but_o because_o he_o apply_v they_o to_o measure_v of_o land_n few_o or_o none_o do_v think_v that_o they_o belong_v also_o to_o measure_v of_o timber_n and_o therefore_o my_o labour_n i_o hope_n be_v not_o unnecessary_a though_o i_o shall_v but_o have_v repeat_v the_o same_o thing_n and_o apply_v they_o to_o our_o use_n without_o add_v any_o other_o thing_n i_o have_v know_v some_o that_o will_v buy_v whole_a frame_n ready_o wrought_v by_o measure_n but_o
of_o such_o a_o taper_v piece_n that_o be_v take_v for_o the_o breadth_n of_o the_o lose_a péce_n half_o the_o difference_n of_o the_o breadth_n of_o both_o end_n and_o for_o the_o thickness_n of_o the_o lose_a péce_n half_o the_o difference_n of_o the_o thickness_n of_o both_o end_n as_o for_o example_n if_o the_o piece_n be_v twenty_o ynche_n broad_a and_o sixtéene_a ynche_n thick_a at_o one_o end_n and_o fifteen_o ynche_n broad_a and_o twelve_o ynche_n thick_a at_o the_o other_o end_n and_o twenty_o four_o foot_n long_o then_o the_o last_o piece_n be_v four_o foot_n long_o two_o ynche_n and_o a_o half_a broad_a and_o two_o ynche_n thick_a for_o two_o and_o a_o half_a be_v the_o half_a of_o five_o which_o be_v the_o difference_n of_o the_o breadth_n of_o both_o end_n and_o two_o be_v the_o half_a of_o four_o which_o be_v the_o difference_n of_o the_o thickness_n of_o both_o end_n the_o loss_n that_o come_v by_o this_o error_n be_v to_o the_o seller_n and_o yet_o in_o truth_n it_o be_v such_o as_o yield_v no_o profit_n to_o the_o buyer_n for_o we_o lose_v more_o by_o such_o timber_n be_v employ_v to_o any_o ordinary_a use_n than_o that_o advantage_n by_o the_o measure_n do_v come_v unto_o but_o yet_o i_o will_v not_o have_v workman_n to_o take_v that_o way_n for_o a_o true_a measure_n which_o be_v false_a neither_o to_o be_v ignorant_a how_o such_o timber_n be_v to_o be_v measure_v if_o occasion_n do_v offer_v or_o if_o man_n shall_v require_v it_o in_o the_o second_o and_o three_o part_n of_o this_o book_n where_o i_o show_v how_o to_o measure_v timber_n i_o will_v show_v how_o taper_v timber_n may_v be_v measure_v from_o which_o i_o will_v no_o long_o detain_v you_o take_v that_o to_o be_v sufficient_a which_o i_o have_v write_v already_o to_o show_v the_o gross_a of_o the_o error_n general_o commit_v by_o carpenter_n and_o other_o in_o measure_v of_o timber_n the_o end_n of_o the_o first_o part_n the_o second_o part_n of_o the_o carpenter_n rule_n wherein_o be_v set_v down_o sundry_a plain_a way_n true_o to_o measure_v ordinary_a timber_n and_o board_n chapter_n 1._o how_o board_n and_o plank_n be_v ordinary_o measure_v in_o the_o former_a part_n of_o this_o book_n i_o tell_v you_o that_o i_o have_v not_o observe_v any_o main_a error_n in_o measure_v of_o ordinary_a board_n and_o plank_n though_o great_a fault_n in_o buy_v of_o wainie_a board_n and_o plank_n and_o measure_v it_o as_o square_v and_o therefore_o it_o shall_v not_o be_v needful_a to_o invent_v or_o set_v down_o any_o new_a way_n of_o measure_v of_o they_o only_o it_o shall_v suffice_v to_o repeat_v the_o way_n already_o in_o use_n ordinary_o which_o be_v three_o of_o which_o the_o first_o be_v troublesome_a and_o therefore_o rather_o to_o be_v know_v for_o variety_n then_o use_v in_o measure_v the_o second_o be_v true_a but_o long_o in_o do_v then_o the_o three_o and_o therefore_o i_o will_v advise_v the_o three_o to_o be_v follow_v and_o use_v only_o look_v that_o your_o rule_n be_v true_o make_v and_o that_o diligence_n be_v use_v in_o measure_v therewith_o else_o there_o will_v follow_v error_n of_o necessity_n be_v the_o way_n to_o measure_n by_o never_o so_o exact_a board_n the_o first_o way_n to_o measure_v board_n the_o first_o way_n let_v be_v this_o and_o first_o note_n that_o for_o this_o purpose_n i_o call_v a_o inch_n that_o which_o be_v a_o inch_n broad_a and_o twelve_o ynche_n long_o of_o which_o ynche_n twelve_o do_v make_v a_o foot_n now_o if_o the_o board_n to_o be_v measure_v be_v under_o a_o foot_n in_o breadth_n then_o reckon_v how_o many_o time_n twelve_o of_o the_o say_a ynche_n you_o can_v have_v in_o the_o whole_a board_n and_o so_o many_o foot_n be_v there_o in_o it_o if_o the_o board_n be_v just_a a_o foot_n broad_a than_o it_o contain_v so_o many_o foot_n as_o it_o be_v foot_n in_o length_n but_o if_o it_o be_v more_o than_o a_o foot_n broad_a then_o measure_v it_o as_o a_o foresay_a as_o if_o it_o be_v two_o board_n the_o one_o of_o a_o foot_n broad_a the_o other_o so_o broad_a as_o the_o odd_a inch_n remain_v then_o add_v their_o content_n together_o for_o the_o content_a of_o the_o whole_a board_n this_o rule_n to_o they_o that_o understand_v it_o may_v be_v fitly_o set_v down_o in_o other_o word_n thus_o multiply_v the_o number_n of_o inch_n in_o the_o breadth_n by_o the_o number_n of_o foot_n in_o the_o length_n then_o divide_v the_o product_n by_o twelve_o and_o the_o quotient_n show_v the_o number_n of_o foot_n in_o the_o board_n the_o second_o way_n be_v thus_o measure_v the_o length_n of_o the_o board_n board_n the_o second_o way_n to_o measure_v board_n then_o if_o the_o same_o board_n be_v under_o a_o foot_n broad_a draw_v or_o set_v the_o breadth_n thereof_o so_o many_o time_n on_o the_o board_n as_o it_o conntayn_v foot_n in_o length_n and_o there_o make_v a_o prick_n and_o then_o so_o many_o foot_n as_o there_o be_v from_o the_o begin_n to_o that_o prick_n so_o many_o foot_n do_v the_o board_n contain_v and_o if_o the_o board_n be_v above_o a_o foot_n broad_a than_o you_o may_v take_v out_o the_o even_a foot_n and_o measure_v the_o remainder_n as_o aforesaid_a and_o then_o add_v both_o those_o together_o for_o the_o content_a of_o the_o whole_a the_o three_o way_n be_v this_o take_v the_o breadth_n of_o the_o board_n board_n the_o three_o way_n to_o measure_v board_n then_o find_v by_o the_o rule_n what_o length_n make_v a_o foot_n at_o that_o breadth_n and_o then_o see_v how_o many_o time_n that_o length_n be_v in_o the_o board_n and_o so_o many_o foot_n be_v in_o it_o these_o i_o stand_v not_o upon_o because_o they_o be_v well_o enough_o know_v to_o all_o man_n chap._n 2._o how_o to_o measure_v timber_n by_o a_o certain_a way_n call_v drawght-measure_n this_o way_n may_v fall_v out_o so_o tedious_a as_o that_o i_o will_v not_o have_v trouble_v either_o myself_o to_o write_v it_o or_o you_o to_o read_v it_o have_v it_o not_o be_v that_o i_o will_v not_o have_v you_o ignorant_a of_o that_o way_n which_o some_o do_v use_v in_o some_o place_n of_o this_o land_n the_o way_n be_v thus_o this_o rule_n aforesaid_a will_v hold_v true_a for_o any_o timber_n that_o be_v under_o a_o foot_n square_n but_o if_o it_o be_v above_o a_o foot_n square_a and_o not_o above_o two_o foot_n square_a then_o must_v you_o imagine_v that_o one_o quarter_n thereof_o be_v to_o be_v measure_v and_o therefore_o take_v but_o half_a of_o each_o of_o the_o two_o side_n and_o when_o you_o have_v so_o cast_v it_o up_o as_o if_o it_o be_v but_o a_o quarter_n account_n four_o time_n so_o much_o for_o the_o content_a of_o the_o whole_a piece_n but_o if_o the_o piece_n of_o timber_n be_v above_o two_o foot_n square_a and_o not_o above_o four_o foot_n square_a then_o may_v you_o imagine_v that_o a_o sixtéenth_fw-mi part_n thereof_o be_v to_o be_v measure_v which_o do_v account_n sixtéene_a time_n somuch_o for_o the_o content_a of_o the_o whole_a piece_n now_o to_o take_v the_o sixtéenth_fw-mi part_n you_o may_v take_v a_o quarter_n of_o the_o breadth_n and_o a_o quarter_n of_o the_o thickness_n but_o this_o kind_n of_o measure_n if_o it_o fall_v out_o in_o a_o piece_n of_o timber_n above_o a_o foot_n square_n be_v so_o tedious_a as_o that_o i_o do_v wonder_n any_o man_n will_v content_v himself_o with_o it_o and_o yet_o because_o i_o have_v set_v it_o down_o take_v one_o note_n more_o which_o be_v this_o if_o the_o piece_n to_o be_v measure_v have_v any_o odd_a ynche_n in_o the_o length_n either_o at_o the_o first_o or_o second_o work_v then_o must_v you_o have_v draw_v the_o want_n so_o many_o time_n as_o there_o be_v foot_n in_o length_n add_v thereunto_o such_o part_n of_o the_o want_n as_o the_o odd_a measure_n of_o the_o length_n be_v part_n of_o a_o foot_n and_o thus_o much_o of_o drawght-measure_n chap._n 3._o how_o timber_n may_v be_v measure_v by_o board_n measure_v only_o when_o i_o consider_v the_o readiness_n of_o many_o man_n in_o measure_v of_o board_n by_o one_o of_o the_o three_o former_a way_n and_o how_o speedy_o they_o will_v cast_v up_o the_o whole_a stock_n have_v measure_v one_o board_n by_o the_o observe_n of_o score_n ten_o and_o five_o therein_o and_o withal_o consider_v the_o great_a error_n that_o those_o man_n run_v into_o in_o measure_v of_o timber_n this_o move_v i_o to_o think_v of_o some_o course_n how_o these_o man_n that_o be_v so_o expert_a in_o measure_v of_o board_n may_v by_o the_o same_o way_n measure_v any_o square_a piece_n of_o timber_n this_o way_n though_o it_o be_v true_a yet_o it_o be_v troublesome_a and_o therefore_o i_o will_v wish_v they_o
piece_n about_o with_o a_o line_n or_o thread_n then_o take_v a_o quarter_n thereof_o for_o the_o square_n of_o that_o piece_n though_o indeed_o it_o be_v not_o the_o square_a and_o so_o measure_v it_o after_o the_o common_a way_n but_o now_o note_v that_o which_o i_o tell_v you_o in_o the_o first_o part_n of_o this_o book_n namely_o that_o this_o piece_n be_v more_o than_o it_o be_v thus_o measure_v to_o be_v 10._o see_v a_o more_o exact_a way_n in_o the_o three_o part_n of_o this_o book_n chap._n the_o 10._o and_o therefore_o to_o find_v the_o true_a content_n add_v to_o that_o which_o you_o have_v measure_v the_o piece_n to_o be_v a_o quarter_n thereof_o and_o also_o after_o the_o rate_n of_o a_o foot_n in_o a_o load_n and_o then_o the_o total_a will_v show_v the_o content_a of_o the_o piece_n though_o not_o exact_o yet_o so_o near_o as_o that_o the_o loss_n will_v not_o bring_v any_o damage_n to_o any_o man_n that_o be_v worth_a look_v after_o take_v a_o example_n for_o more_o plainness_n suppose_v the_o tree_n be_v measure_v after_o the_o former_a way_n to_o contain_v twenty_o foot_n then_o must_v you_o add_v thereto_o a_o quarter_n thereof_o which_o be_v 5_o and_o that_o make_v 25_o foot_n then_o add_v to_o that_o half_o a_o foot_n which_o be_v after_o a_o foot_n in_o a_o load_n and_o the_o content_a of_o the_o piece_n will_v amount_v to_o 25_o foot_n and_o a_o half_a and_o here_o be_v to_o be_v note_v that_o if_o the_o piece_n be_v not_o exact_o round_a that_o then_o this_o measure_n will_v not_o hold_v as_o be_v show_v in_o the_o seven_o chapter_n of_o the_o former_a part_n of_o this_o book_n but_o how_o such_o timber_n be_v to_o be_v measure_v see_v in_o the_o latter_a end_n of_o the_o eleven_o chapter_n of_o the_o three_o part_n chap._n 7._o how_o timber_n may_v be_v measure_v by_o arithmetic_n though_o the_o former_a way_n for_o measure_v of_o timber_n be_v sufficient_a yet_o because_o variety_n give_v pleasure_n and_o these_o that_o follow_v admit_v of_o less_o error_n in_o the_o work_n then_o some_o of_o the_o former_a i_o have_v therefore_o think_v good_a to_o set_v they_o down_o as_o follow_v and_o if_o any_o man_n shall_v object_v that_o i_o spend_v this_o labour_n in_o vain_a because_o carpenter_n common_o have_v not_o arithmetic_n i_o answer_v that_o some_o have_v more_o knowledge_n therein_o than_o they_o know_v how_o to_o apply_v to_o the_o present_a purpose_n for_o who_o chief_o i_o have_v write_v this_o chapter_n and_o some_o other_o follow_v as_o also_o i_o can_v wish_v that_o other_o which_o have_v not_o will_v learn_v which_o they_o may_v do_v by_o book_n which_o be_v extant_a or_o at_o least_o forbear_v to_o be_v common_a rule-maker_n until_o they_o have_v knowledge_n therein_o or_o well_o understand_v the_o table_n which_o be_v for_o that_o purpose_n here_o first_o i_o shall_v have_v show_v how_o to_o measure_v board_n by_o arithmetic_n but_o because_o it_o little_o differ_v from_o measure_v of_o paralellogram_n i_o will_v therefore_o refer_v it_o to_o the_o three_o part_n of_o this_o book_n where_o it_o be_v teach_v how_o to_o measure_v they_o now_o to_o measure_v timber_n by_o arithmetic_n do_v thus_o reduce_v the_o length_n of_o the_o piece_n to_o be_v measure_v into_o inch_n by_o multiply_v the_o number_n of_o foot_n therein_o contain_v by_o twelve_o then_o multiply_v the_o breadth_n by_o the_o thickness_n and_o the_o product_n or_o sum_n thereof_o multiply_v by_o the_o length_n be_v also_o reduce_v into_o inch_n as_o aforesaid_a then_o divide_v that_o product_n or_o of_o come_v by_o 1728_o which_o be_v the_o number_n of_o inch_n in_o a_o foot_n of_o timber_n and_o the_o quotient_n will_v give_v you_o the_o number_n of_o foot_n contain_v in_o that_o piece_n of_o timber_n here_o it_o shall_v not_o be_v unnecessary_a to_o give_v two_o example_n the_o one_o where_o the_o lenge_v breadth_n and_o thickness_n be_v even_o inch_n and_o the_o other_o where_o they_o have_v odd_a part_n of_o a_o inch_n suppose_v the_o piece_n of_o timber_n to_o be_v measure_v to_o be_v nine_o foot_n in_o length_n eighteen_o inch_n in_o breadth_n and_o six_o inch_n in_o thickness_n now_o multiply_v nine_o foot_n the_o length_n by_o twelve_o and_o that_o yield_v 108._o inch_n which_o be_v multiply_v by_o 18._o the_o breadth_n make_v 1944._o and_o that_o be_v multiply_v by_o six_o the_o thickness_n yield_v 11664._o which_o be_v the_o content_a of_o the_o whole_a piece_n in_o inch_n then_o divide_v this_o 11664._o by_o 1728._o and_o the_o quotient_n will_v be_v six_o foot_n and_o 1296_o 1728_o part_n of_o a_o foot_n which_o be_v reduce_v to_o his_o low_a denomination_n be_v ¾_n of_o a_o foot_n so_o that_o the_o whole_a piece_n be_v six_o foot_n and_o three_o quarter_n and_o if_o you_o will_v know_v how_o many_o quarter_n of_o a_o foot_n be_v in_o any_o such_o fraction_n you_o may_v divide_v it_o by_o 432_o the_o number_n of_o inch_n in_o a_o quarter_n of_o a_o foot_n of_o timber_n &_o the_o quotient_n will_v tell_v you_o but_o suppose_v the_o piece_n have_v in_o the_o breadth_n or_o thickness_n a_o odd_a quarter_n or_o half_a or_o three_o quarter_n of_o a_o inch_n then_o reduce_v the_o length_n breadth_n and_o thickness_n into_o quarter_n of_o inch_n after_o that_o multiply_v they_o be_v so_o reduce_v one_o into_o another_o that_o be_v the_o length_n by_o the_o breadth_n and_o that_o of_o come_v or_o product_v by_o the_o thickness_n then_o divide_v that_o total_a by_o 110592_o which_o be_v the_o number_n of_o quarter_n of_o inch_n contain_v in_o a_o foot_n of_o timber_n and_o the_o quotient_n will_v show_v you_o how_o many_o foot_n be_v contain_v in_o the_o piece_n as_o for_o example_n let_v the_o piece_n be_v 20_o foot_n long_o 8_o inch_n and_o a_o half_a broad_a and_o 11_o inch_n and_o three_o quarter_n thick_a first_o i_o reduce_v 20_o foot_n the_o length_n into_o quarter_n of_o inch_n by_o multiply_v 20_o by_o 12_o which_o be_v 240_o which_o bring_v 20_o foot_n into_o inch_n then_o i_o multiply_v that_o 240_o by_o 4_o to_o bring_v they_o into_o quarter_n of_o inch_n which_o be_v 960._o second_o reduce_v 8_o inch_n and_o a_o half_a the_o breadth_n into_o quarter_n of_o inch_n which_o be_v 34._o three_o reduce_v 11._o inch_n and_o three_o quarter_n the_o thickness_n into_o quarter_n of_o inch_n which_o be_v 47._o then_o multiply_v 960_o and_o 34_o and_o 47_o together_o and_o they_o make_v 1534080._o last_o divide_v these_o by_o 110592_o and_o the_o quotient_n will_v be_v 13_o and_o 96384_o odd_a quarter_n of_o inch_n which_o be_v divide_v by_o 27648_o the_o number_n of_o quarter_n of_o a_o inch_n in_o a_o quarter_n timber_n quarter_n note_v here_o that_o i_o mean_v not_o by_o a_o quarter_n of_o a_o foot_n a_o square_a of_o 3._o inch_n which_o be_v a_o quarter_n of_o a_o foot_n one_o way_n but_o the_o four_o part_n of_o a_o square_a foot_n of_o timber_n of_o a_o foot_n of_o timber_n the_o quotient_n will_v be_v three_o quarter_n of_o a_o foot_n and_o 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mvltiplie_v the_o breadth_n in_o the_o thickness_n and_o by_o the_o product_n or_o ofcome_v thereof_o divide_v 1728_o and_o the_o quotient_n will_v show_v you_o how_o much_o in_o length_n make_v a_o foot_n of_o that_o piece_n according_a to_o which_o you_o must_v measure_v the_o whole_a piece_n and_o if_o there_o be_v any_o odd_a quarter_n or_o half_a inch_n in_o the_o breadth_n or_o thickness_n then_o reduce_v the_o two_o side_n into_o quarter_n of_o inch_n as_o be_v teach_v in_o the_o last_o chapter_n then_o have_v reduce_v they_o multiply_v the_o breadth_n by_o the_o thickness_n and_o by_o their_o product_n divide_v 27648._o and_o the_o quotient_n show_v you_o the_o length_n of_o the_o foot_n in_o
error_n to_o measure_v it_o as_o if_o it_o be_v hew_v square_a when_o the_o corner_n of_o the_o timber_n be_v hew_v unsquare_n i_o do_v not_o mean_v waynie_a for_o of_o that_o i_o have_v speak_v before_o in_o the_o second_o chapter_n but_o when_o it_o be_v hew_v bevell_a or_o diamond_n wise_a as_o sometime_o it_o be_v by_o the_o carelessness_n or_o unskilfulnes_n of_o the_o hewer_n then_o to_o take_v the_o square_a of_o such_o timber_n according_a to_o the_o breadth_n of_o the_o side_n thereof_o be_v untrue_a for_o the_o side_n be_v long_o than_o if_o it_o be_v square_a and_o so_o give_v the_o piece_n to_o be_v big_a than_o it_o be_v how_o great_a this_o error_n be_v i_o stand_v not_o to_o show_v at_o this_o time_n only_a note_n that_o it_o do_v increase_v and_o decrease_v according_a as_o the_o corner_n of_o the_o timber_n do_v swerve_v from_o square_a but_o how_o such_o timber_n be_v to_o be_v measure_v see_v in_o the_o three_o part_n chapter_n she_o sixth_o chap._n 5._o the_o error_n in_o the_o ordinary_a measure_n of_o round_a timber_n the_o former_a error_n do_v always_o bring_v loss_n to_o the_o buyer_n but_o these_o that_o follow_v do_v always_o bring_v loss_n to_o the_o seller_n and_o though_o such_o round_a timber_n come_v not_o often_o to_o be_v measure_v here_o in_o london_n the_o worse_a for_o the_o buyer_n yet_o will_v i_o have_v carpenter_n know_v the_o error_n which_o be_v use_v in_o measure_v the_o same_o which_o be_v this_o they_o gird_v the_o timber_n round_o about_o with_o a_o line_n or_o thread_n and_o then_o take_v one_o quarter_n thereof_o for_o the_o square_n as_o we_o call_v it_o of_o the_o piece_n to_o be_v measure_v and_o so_o find_v out_o as_o they_o think_v the_o length_n of_o a_o foot_n in_o that_o piece_n of_o timber_n or_o tree_n this_o be_v a_o gross_a error_n and_o yield_v not_o the_o content_n of_o the_o piece_n or_o tree_n by_o one_o five_o part_n of_o it_o and_o more_o but_o how_o round_a timber_n be_v to_o be_v measure_v be_v teach_v in_o the_o sixth_o chapter_n of_o the_o second_o part_n and_o in_o the_o nine_o chapter_n of_o the_o three_o part_n of_o this_o book_n which_o when_o you_o have_v learned_a and_o try_v than_o you_o will_v tell_v yourself_o that_o in_o measure_v round_a timber_n after_o the_o former_a way_n be_v very_o erroneous_a and_o intolerable_a chap._n 5._o error_n in_o measure_v of_o timber_n not_o full_o round_a but_o somewhat_o flat_o call_v ouall_n fashion_n so_o that_o to_o measure_v oual_n by_o the_o former_a way_n be_v so_o uncertain_a that_o you_o may_v have_v peradventure_o more_o than_o you_o shall_v and_o peradventure_o less_o than_o you_o shall_v by_o a_o five_o part_n a_o four_o part_n a_o three_o part_n and_o so_o forth_o but_o because_o ordinary_o tree_n or_o timber_n that_o be_v dual_a fashion_n do_v not_o much_o vary_v from_o a_o round_a therefore_o the_o loss_n be_v always_o to_o the_o seller_n be_v measure_v as_o a_o foresay_a here_o i_o have_v purpose_v to_o have_v somewhat_o digress_v from_o my_o general_a purpose_n and_o to_o have_v show_v the_o great_a loss_n that_o come_v by_o buy_v of_o faggot_n that_o be_v bind_v flat_a but_o the_o statute_n for_o fuel_n in_o the_o last_o parliament_n have_v prevent_v i_o where_o it_o be_v enact_v that_o band_n of_o faggot_n shall_v be_v round_o but_o yet_o because_o i_o fear_v all_o man_n understand_v not_o what_o be_v mean_v by_o the_o word_n round_o or_o if_o they_o do_v yet_o they_o will_v not_o regard_v to_o redress_v it_o i_o pray_v you_o therefore_o take_v knowledge_n that_o where_o as_o man_n do_v common_o buy_v the_o flat_a faggot_n for_o the_o great_a they_o be_v deceive_v for_o indeed_o they_o be_v less_o than_o the_o round_a by_o far_o and_o evermore_o the_o flatter_v they_o be_v the_o lesser_a they_o be_v and_o to_o speak_v no_o more_o than_o myself_o have_v try_v i_o have_v take_v four_o faggot_n indeed_o of_o the_o flat_a and_o have_v put_v the_o wood_n of_o they_o all_o into_o three_o of_o their_o own_o band_n without_o strain_v lo_o than_o the_o great_a loss_n that_o come_v to_o folk_n by_o this_o error_n that_o which_o i_o say_v of_o faggot_n i_o intend_v also_o to_o be_v speak_v of_o billet_n for_o the_o flatter_v they_o be_v the_o lesser_a they_o be_v be_v no_o more_o in_o compass_n then_o the_o statute_n require_v i_o need_v not_o stand_v to_o demonstrate_v that_o this_o be_v a_o error_n if_o i_o be_v persuade_v you_o understand_v that_o which_o be_v say_v before_o of_o oual_n but_o for_o far_a proof_n take_v a_o quart_n pot_n of_o pewter_n that_o be_v round_o and_o make_v it_o more_o flat_a by_o crush_a in_o the_o side_n thereof_o and_o you_o shall_v find_v that_o it_o will_v not_o hold_v a_o quart_n of_o water_n as_o before_o it_o do_v and_o yet_o the_o compass_n of_o the_o pot_n be_v as_o much_o as_o it_o be_v before_o you_o may_v also_o prove_v the_o same_o by_o a_o board_n thus_o the_o faggot_n band_n ought_v to_o be_v by_o the_o statute_n twenty_o four_o ynche_n about_o so_o than_o a_o boards_n end_n of_o a_o foot_n broad_a will_v hardly_o go_v into_o one_o of_o those_o band_n but_o if_o you_o cleave_v that_o boards_n end_n into_o a_o dozen_o or_o more_o piece_n you_o shall_v well_o perceive_v that_o you_o may_v put_v four_o and_o more_o of_o such_o board_n be_v so_o cle_v into_o that_o band_n be_v round_o this_o have_v i_o write_v not_o carp_o but_o as_o desirous_a that_o the_o buyer_n will_v not_o deceive_v themselves_o by_o their_o eye_n neither_o that_o they_o shall_v be_v deceive_v by_o other_o chap._n 7._o the_o error_n in_o measure_v timber_n that_o be_v waynie_a i_o tell_v you_o before_o in_o the_o second_o chapter_n that_o there_o come_v great_a loss_n to_o carpenter_n in_o buy_v of_o waynie_a timber_n after_o the_o ordinary_a way_n but_o here_o i_o show_v the_o loss_n that_o come_v indeed_o not_o to_o the_o buyer_n but_o the_o seller_n in_o measure_v of_o waynie_a timber_n it_o have_v be_v use_v as_o i_o be_o inform_v that_o if_o timber_n be_v waynie_a the_o buyer_n will_v measure_v it_o as_o by_o gird_v it_o about_o and_o take_v one_o quarter_n of_o the_o comqasse_n for_o the_o square_n as_o in_o the_o case_n of_o round_a timber_n before_o show_v chapter_n the_o six_o but_o it_o seem_v to_o i_o that_o the_o seller_n grow_v weary_a of_o this_o way_n so_o that_o in_o my_o time_n to_o my_o knowledge_n it_o have_v not_o be_v use_v in_o or_o about_o this_o city_n how_o much_o this_o loss_n be_v do_v not_o appear_v by_o this_o demonstration_n but_o in_o this_o figure_n if_o you_o will_v take_v my_o word_n there_o be_v lose_v a_o sixth_o part_n full_a but_o i_o have_v rather_o you_o will_v try_v the_o loss_n yourselves_o by_o the_o rule_n teach_v in_o the_o five_o chapter_n of_o the_o second_o part_n of_o this_o book_n then_o to_o believe_v i_o in_o this_o case_n chap._n 8._o that_o in_o measure_v of_o timber_n that_o be_v taper_n grow_v it_o be_v false_a to_o take_v the_o square_a of_o the_o middle_n thereof_o and_o so_o to_o give_v up_o the_o content_a by_o the_o common_a rule_n it_o be_v so_o usual_a a_o thing_n in_o measure_v of_o timber_n that_o be_v taper_n grow_v or_o narrow_a at_o one_o end_n then_o at_o another_o to_o take_v the_o square_a of_o the_o middle_n of_o the_o piece_n and_o so_o to_o measure_v it_o by_o the_o common_a rule_n as_o that_o i_o shall_v be_v not_o only_o not_o beléeve_v but_o also_o repute_v to_o have_v apparent_o err_v in_o affirm_v the_o contrary_a for_o it_o will_v be_v say_v that_o that_o which_o it_o have_v too_o much_o in_o the_o great_a half_n it_o want_v in_o the_o lesser_a half_n indeed_o this_o be_v true_a in_o board_n or_o other_o superficies_n that_o taper_n who_o side_n be_v straight_o but_o in_o a_o solid_a or_o piece_n of_o timber_n it_o be_v simple_o false_a how_o to_o demonstrate_v the_o error_n on_o a_o paper_n so_o as_o that_o it_o may_v be_v easy_o conceive_v be_v very_o hard_a but_o in_o a_o solid_a it_o may_v plain_o be_v declare_v to_o the_o understanding_n of_o the_o simple_a if_o a_o pyramid_n that_o be_v a_o piked_a piece_n of_o timber_n sharp_a at_o one_o end_n like_o a_o piked_a steeple_n be_v so_o measure_v there_o will_v be_v lose_v very_o much_o and_o always_o the_o lesser_a the_o piece_n do_v taper_n the_o lesser_a be_v the_o loss_n in_o general_n there_o be_v lose_v by_o certain_a pyramid_n a_o piece_n of_o timber_n who_o length_n be_v the_o sixth_o part_n of_o the_o length_n of_o the_o whole_a piece_n and_o who_o end_n or_o base_a be_v contain_v under_o half_a the_o difference_n of_o the_o side_n of_o both_o the_o end_n
opposite_a side_n be_v equal_a also_o note_v that_o whereas_o i_o say_v all_o right_a angle_n it_o be_v but_o to_o distinguish_v betwixt_o this_o figure_n and_o the_o two_o next_o follow_v for_o they_o be_v parallellogram_n also_o and_o who_o angle_n or_o corner_n be_v all_o right_a or_o square_a angle_n such_o as_o be_v the_o figure_n b._n it_o be_v measure_v thus_o multiply_v the_o length_n by_o the_o breadth_n and_o the_o product_n or_o ofcome_v give_v the_o content_a the_o prism_n or_o piece_n of_o timber_n who_o base_n or_o end_n be_v parallellogram_n as_o be_v the_o say_a figure_n b_o you_o may_v measure_v thus_o multiply_v the_o content_a of_o the_o base_a by_o the_o length_n and_o the_o product_n yield_v the_o solid_a content_n as_o be_v teach_v in_o the_o seven_o chapter_n of_o the_o second_o part_n of_o this_o book_n chap._n 5._o what_o a_o rombus_n be_v and_o how_o it_o be_v measure_v a_o rombus_n other_o wise_a call_v a_o diamond_n form_n be_v a_o figure_n of_o four_o equal_a side_n &_o oblique_a angle_n or_o the_o side_n be_v all_o of_o one_o length_n and_o none_o of_o the_o angle_n be_v square_a such_o as_o be_v the_o figure_n b._n the_o measure_n of_o a_o rombus_n be_v thus_o multiply_v the_o length_n of_o one_o of_o the_o side_n by_o the_o perpendicular_a plum_n line_n draw_v from_o that_o side_n to_o the_o opposite_a side_n which_o in_o this_o figure_n be_v the_o prick_a line_n and_o the_o product_n yield_v the_o content_a 1._o the_o prism_n or_o piece_n of_o timber_n who_o base_n be_v a_o rombus_n be_v measure_v thus_o multiply_v the_o content_a of_o the_o base_a or_o end_n by_o the_o length_n and_o the_o product_n give_v your_o desire_n 2._o or_o else_o as_o in_o the_o three_o chapter_n of_o this_o part_n take_v all_o the_o perpendicular_a for_o one_o side_n of_o a_o square_a piece_n and_o one_o side_n of_o the_o figure_n b_o for_o the_o other_o side_n of_o the_o square_a piece_n and_o so_o measure_v it_o by_o any_o of_o the_o way_n teach_v in_o the_o second_o part_n of_o this_o book_n chap._n 6._o what_o a_o romboide_n be_v and_o how_o it_o be_v measure_v a_o romboide_n call_v a_o diamondlike_a figure_n be_v that_o who_o opposite_a side_n and_o opposite_a angle_n be_v equal_a but_o all_o the_o side_n be_v not_o equal_a neither_o be_v any_o of_o the_o angle_n right_a such_o be_v this_o figure_n c._n the_o measure_n differ_v nothing_o from_o the_o measure_n of_o a_o rombus_n in_o the_o former_a chapter_n and_o may_v well_o have_v be_v soyn_v together_o so_o that_o he_o that_o can_v measure_v one_o can_v measure_v both_o but_o to_o the_o former_a way_n you_o may_v add_v this_o if_o you_o please_v first_o divide_v it_o into_o two_o triangle_n as_o here_o this_o figure_n be_v by_o the_o prick_a line_n then_o measure_v one_o of_o those_o triangle_n by_o the_o way_n set_v down_o in_o the_o three_o chapter_n of_o this_o part_n the_o double_a whereof_o be_v the_o content_a of_o this_o figure_n the_o like_a be_v also_o to_o be_v do_v with_o a_o rombus_n or_o a_o parallelogram_n the_o prism_n or_o piece_n of_o timber_n who_o base_n be_v a_o romboide_n be_v measure_v as_o a_o piece_n who_o base_a be_v a_o rombus_n as_o in_o the_o former_a chapter_n but_o if_o you_o measure_v the_o base_a or_o end_n by_o two_o triangle_n as_o in_o this_o chapter_n then_o take_v as_o for_o the_o side_n of_o a_o square_a piece_n of_o timber_n all_o the_o perpendicular_a of_o one_o of_o the_o triangle_n and_o all_o the_o base_a of_o the_o same_o triangle_n and_o so_o measure_v it_o by_o any_o of_o the_o way_n teach_v in_o the_o second_o part_n chap._n 7._o what_o a_o trapezium_fw-la be_v and_o how_o it_o be_v measure_v a_o trapezium_fw-la be_v a_o figure_n of_o four_o side_n not_o have_v all_o the_o side_n and_o angle_n equal_a as_o be_v the_o figure_n d._n it_o be_v measure_v thus_o first_o divide_v it_o into_o two_o triangle_n by_o draw_v a_o line_n from_o one_o angle_n to_o the_o opposite_a angle_n as_o here_o the_o figure_n d_o be_v divide_v by_o the_o prick_a line_n then_o measure_v by_o the_o way_n teach_v in_o the_o three_o chap._n of_o this_o 3._o part_n both_o those_o triangle_n several_o and_o add_v both_o their_o content_n for_o the_o content_a of_o the_o whole_a trapezium_fw-la 1._o the_o prism_n or_o piece_n of_o timber_n who_o end_n or_o base_a be_v a_o trapezium_n as_o the_o trapezium_n d_o may_v be_v thus_o measure_v multiply_v the_o content_a of_o the_o base_a or_o end_n by_o the_o length_n of_o the_o piece_n and_o the_o product_n give_v the_o content_a thereof_o 2._o or_o else_o take_v the_o square_a root_n of_o the_o content_a of_o the_o hase_fw-mi or_o end_n d_o and_o so_o measure_v it_o by_o any_o of_o the_o wase_v teach_v in_o the_o second_o part_n 3._o orel_n suppose_v the_o piece_n to_o be_v cut_v into_o two_o cant_n according_a as_o the_o base_a or_o end_n thereof_o d_o be_v divide_v then_o measure_v both_o those_o cant_n by_o the_o way_n teach_v in_o the_o three_o chapter_n of_o this_o part_n and_o take_v the_o sum_n of_o those_o two_o cant_n for_o the_o content_a of_o the_o whole_a piece_n chap._n 8._o what_o a_o regular_a mani-sided_n figure_n be_v and_o how_o it_o be_v measure_v a_o mani-sided_n figure_n be_v that_o which_o have_v more_o side_n than_o four_o they_o be_v either_o regular_a or_o irregular_a a_o regular_a mani-sided_n figure_n be_v that_o who_o side_n and_o angle_n be_v all_o equal_a as_o be_v this_o figure_n mark_v with_o a._n a_o irregular_a be_v that_o who_o side_n or_o angle_n be_v unequal_a a_o regular_a mani-sided_n figure_n be_v thus_o measure_v first_o draw_v a_o perpendicular_a from_o the_o centre_n of_o the_o figure_n to_o the_o middle_n of_o one_o of_o that_o side_n as_o be_v the_o short_a prick_a line_n in_o the_o say_a figure_n a._n then_o seek_v the_o length_n or_o compass_v about_o of_o all_o the_o side_n the_o half_a whereof_o you_o must_v multiply_v by_o the_o length_n of_o the_o say_v perpendicular_a and_o the_o product_n give_v the_o content_a of_o the_o figure_n now_o the_o centre_n of_o a_o regular_a mani-sided_n figure_n be_v thus_o find_v raise_v a_o perpendicular_a upon_o the_o middle_n of_o any_o two_o of_o the_o side_n not_o be_v direct_o opposite_a and_o where_o they_o intersect_v or_o cut_v one_o another_o there_o be_v the_o centre_n of_o the_o figure_n by_o this_o may_v you_o find_v the_o centre_n of_o a_o circle_n or_o of_o any_o piece_n of_o a_o circle_n namely_o if_o you_o draw_v any_o two_o right_a line_n either_o equal_a or_o unequal_a in_o the_o circle_n or_o piece_n of_o the_o circle_n and_o from_o their_o middle_n do_v raise_v perpendicular_o i_o say_v the_o meeting_n of_o those_o perpendicular_o be_v the_o centre_n of_o the_o circle_n or_o piece_n of_o a_o circle_n but_o if_o the_o figure_n have_v a_o even_a number_n of_o side_n as_o 6_o 8_o 10_o and_o so_o forth_o than_o you_o need_v but_o draw_v a_o line_n from_o any_o two_o opposite_a angle_n and_o another_o line_n from_o any_o two_o 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thus_o measure_v divide_v the_o figure_n into_o triangle_n as_o here_o i_o have_v divide_v the_o figure_n b_o by_o certain_a prick_v line_n then_o measure_v each_o triangle_n by_o itself_o as_o be_v teach_v in_o the_o three_o chapter_n of_o this_o part_n and_o add_v the_o content_n of_o all_o the_o triangle_n together_o and_o their_o sum_n or_o total_a be_v the_o content_a of_o the_o figure_n 1._o the_o prism_n or_o piece_n of_o timber_n who_o base_a or_o end_n be_v the_o figure_n b_o or_o any_o other_o unequal_a mani-sided_n figure_n be_v measure_v by_o multiply_v the_o content_a of_o the_o base_a or_o end_n in_o the_o length_n of_o the_o piece_n and_o the_o product_n give_v the_o
solid_a content_n 2._o or_o else_o take_v the_o square_a root_n of_o the_o number_n of_o inch_n in_o the_o content_a of_o the_o base_a and_o so_o measure_v it_o by_o any_o of_o the_o way_n teach_v in_o the_o second_o part_n of_o this_o book_n 3._o and_o because_o for_o the_o measure_n of_o every_o sort_n of_o timber_n i_o have_v use_v to_o set_v down_o some_o way_n by_o which_o it_o may_v be_v do_v without_o arithmetic_n therefore_o for_o a_o three_o way_n as_o every_o triangle_n in_o the_o figure_n b_o be_v measure_v so_o measure_v so_o many_o sollid_n whereof_o the_o triangle_n be_v the_o base_n and_o who_o length_n be_v that_o length_n of_o the_o irregular_a piece_n of_o timber_n as_o be_v teach_v in_o the_o three_o chapter_n of_o this_o three_o part_n and_o then_o add_v all_o their_o content_n for_o the_o content_a of_o the_o whole_a piece_n chap._n 10._o what_o a_o circle_n a_o semicircle_n and_o a_o sector_n be_v and_o how_o they_o be_v measure_v 1._o a_o circle_n be_v a_o figure_n plain_a and_o round_o 2._o the_o round_a line_n the_o make_v the_o circle_n be_v call_v the_o circumference_n 3._o the_o point_n in_o the_o middle_n of_o the_o circle_n be_v call_v that_o centre_n 4._o the_o line_n and_o indeed_o every_o line_n pass_v by_o the_o centre_n to_o both_o side_n of_o the_o circumference_n be_v call_v the_o diameter_n as_o that_o black_a line_n in_o this_o circle_n c._n 5._o half_n the_o diameter_n and_o indeed_o every_o line_n pass_v from_o the_o centre_n to_o the_o circumference_n be_v call_v the_o semidiameter_n 6._o all_o line_n in_o the_o circle_n except_o the_o diameter_n which_o be_v draw_v from_o side_n to_o side_n be_v call_v cord_n such_o be_v the_o prick_a line_n in_o the_o circle_n c._n 7._o the_o diameter_n cut_v the_o circle_n into_o two_o equal_a part_n each_o of_o which_o part_n be_v call_v a_o semicircle_n 8._o a_o cord_n cut_v the_o circle_n into_o two_o unequal_a part_n each_o of_o which_o part_n be_v call_v a_o section_n of_o a_o circle_n the_o one_o be_v call_v the_o great_a section_n because_o it_o be_v great_a than_o that_o semicircle_n the_o other_o be_v call_v the_o lesser_a section_n because_o it_o be_v less_o than_o the_o semicircle_n 9_o a_o sector_n be_v any_o part_n of_o a_o circle_n either_o great_a or_o lesser_a than_o a_o semicircle_n contain_v under_o two_o semidiameter_n meeting_n in_o the_o centre_n and_o a_o piece_n of_o the_o circumference_n 10_o note_v that_o the_o circumference_n of_o a_o circle_n be_v triple_a the_o diameter_n and_o almost_o one_o seven_o part_n more_o but_o we_o count_v it_o as_o just_a triple_a and_o one_o seven_o part_n or_o as_o 22_o be_v to_o 7._o therefore_o to_o find_v the_o circumference_n the_o diameter_n be_v know_v multiply_v your_o diameter_n by_o 22._o and_o divide_v the_o product_n by_o 7_o and_o the_o quotient_a she_o wes_z you_o the_o circumference_n now_o to_o measure_v a_o circle_n do_v thus_o circle_n to_o measure_v a_o circle_n multiply_v half_o the_o diameter_n by_o half_a the_o circumference_n or_o all_o the_o diameter_n by_o a_o quarter_n of_o the_o circumference_n or_o all_o the_o circumference_n by_o a_o quarter_n of_o the_o diameter_n and_o any_o of_o the_o product_n give_v the_o content_a of_o the_o circle_n the_o semicircle_n be_v thus_o measure_v semicircle_n to_o measure_v a_o semicircle_n multiply_v half_o the_o diameter_n in_o half_a the_o ark_n or_o arch_n thereof_o or_o all_o the_o diameter_n in_o a_o quarter_n of_o the_o ark_n thereof_o etc._n etc._n and_o either_o of_o the_o product_n give_v the_o content_a of_o the_o semicircle_n a_o sector_n be_v measure_v as_o a_o semicircle_n sector_n to_o measure_v a_o sector_n namely_o by_o multiply_v half_o the_o semidiameter_n in_o half_a the_o ark_n or_o arch_n thereof_o etc._n etc._n the_o product_n whereof_o be_v the_o content_a of_o the_o sector_n 1_o the_o solid_a or_o piece_n of_o timber_n who_o end_n or_o base_a be_v a_o circle_n a_o semicircle_n or_o a_o sector_n may_v be_v thus_o measure_v multiply_v the_o content_a of_o the_o base_a or_o end_n in_o the_o length_n of_o the_o piece_n and_o the_o product_n give_v the_o solid_a content_n 2_o or_o take_v the_o semidiameter_n for_o one_o side_n of_o a_o square_a piece_n of_o timber_n and_o half_o the_o ark_n be_v it_o of_o a_o circle_n semicircle_n or_o sector_n for_o the_o other_o side_n and_o so_o measure_v it_o by_o any_o of_o the_o way_n teach_v in_o the_o second_o part_n here_o it_o be_v not_o unnecessary_a to_o show_v how_o to_o find_v the_o quantity_n of_o a_o ark_n or_o piece_n of_o a_o circle_n but_o of_o the_o diverse_a way_n that_o be_v find_v you_o may_v use_v this_o first_o have_v take_v the_o length_n of_o your_o semidiameter_n in_o any_o measure_n which_o let_v be_v for_o more_o conveniency_n in_o work_n in_o for_o the_o great_a measure_n the_o great_a error_n in_o this_o kind_n of_o work_n inch_n then_o open_a your_o compass_n to_o a_o inch_n and_o see_v how_o many_o of_o they_o be_v contain_v in_o your_o ark_n chap._n 11._o how_o to_o measure_v section_n of_o a_o circle_n i_o tell_v you_o in_o the_o last_o chapter_n that_o there_o be_v two_o sort_n of_o section_n a_o great_a which_o be_v more_o than_o a_o semicircle_n and_o a_o lesser_a which_o be_v not_o so_o much_o as_o a_o semicircle_n they_o be_v measure_v diverse_o a_o great_a section_n be_v thus_o measure_v section_n to_o measure_v a_o great_a section_n draw_v two_o semidiameter_n from_o either_o end_n of_o the_o ark_n to_o the_o centre_n as_o the_o two_o prick_a line_n in_o the_o figure_n a._n then_o multiply_v half_o the_o ark_n in_o the_o semidiameter_n and_o to_o the_o product_n thereof_o add_v the_o content_a of_o the_o say_a triangle_n make_v of_o the_o cord_n and_o the_o two_o semidiameter_n and_o the_o total_a will_v be_v the_o content_a of_o the_o whole_a section_n the_o solid_a or_o piece_n of_o timber_n who_o base_a be_v the_o figure_n a_o or_o any_o great_a section_n of_o a_o circle_n be_v find_v as_o before_o be_v oft_o say_v by_o multiply_v the_o content_a of_o the_o base_a in_o the_o length_n of_o the_o piece_n or_o take_v half_a the_o ark_n as_o one_o side_n of_o a_o square_a piece_n of_o timber_n and_o the_o semidiameter_n as_o the_o other_o side_n and_o so_o measure_v it_o by_o any_o of_o the_o way_n in_o the_o second_o part_n then_o add_v thereunto_o the_o content_a of_o the_o solid_a whereof_o the_o triangle_n before_o name_v be_v the_o base_a and_o the_o total_a will_v be_v the_o content_a of_o the_o solid_a who_o end_n be_v the_o say_a section_n the_o solid_a or_o piece_n of_o timber_n who_o base_a or_o end_n be_v the_o figure_n b_o or_o any_o lesser_a section_n of_o a_o circle_n may_v be_v measure_v as_o before_o be_v teach_v by_o multiply_v the_o content_a of_o the_o figure_n in_o the_o length_n of_o the_o solid_a or_o else_o take_v half_a the_o ark_n as_o one_o side_n of_o a_o square_a piece_n of_o timber_n and_o the_o semidiameter_n for_o the_o other_o side_n and_o so_o measure_v it_o by_o the_o way_n in_o the_o second_o part_n of_o this_o book_n then_o deduct_v out_o of_o the_o content_a thereof_o the_o content_a of_o the_o solid_a or_o piece_n of_o timber_n whereof_o the_o triangle_n make_v of_o the_o cord_n and_o the_o two_o semidiameter_n be_v the_o base_a or_o end_n and_o the_o remainder_n be_v the_o content_a of_o the_o solid_a make_v upon_o the_o say_a lesser_a section_n b._n in_o the_o 6._o chapter_n of_o the_o second_o part_n of_o this_o book_n ouall_n to_o measure_v a_o ouall_n i_o tell_v you_o that_o i_o will_v show_v you_o in_o the_o end_n of_o this_o chapter_n how_o to_o measure_v a_o ouall_a which_o in_o a_o word_n be_v thus_o first_o find_v by_o that_o which_o be_v teach_v in_o the_o 8._o chapter_n of_o this_o part_n the_o four_o centre_n of_o the_o four_o arke_n or_o piece_n of_o circle_n whereof_o the_o ouall_n be_v make_v for_o every_o ouall_n be_v make_v by_o join_v together_o four_o several_a arke_n or_o piece_n of_o circle_n whereof_o those_o at_o the_o two_o end_n be_v equal_a and_o those_o at_o the_o two_o side_n be_v also_o equal_a then_o have_v find_v those_o arke_n draw_v their_o cord_n under_o they_o so_o shall_v you_o see_v the_o whole_a ouall_n to_o be_v divide_v into_o four_o lesser_a section_n of_o a_o circle_n and_o a_o parallelogram_n therefore_o measure_v all_o those_o four_o section_n as_o afore_o be_v teach_v in_o this_o chapter_n and_o measure_v also_o the_o parallelogram_n by_o the_o way_n teach_v in_o the_o three_o chapter_n of_o this_o three_o part_n and_o the_o content_a of_o they_o all_o that_o be_v of_o those_o four_o section_n and_o the_o parailelogram_n be_v the_o content_a of_o the_o ouall_n neat_a