that_o when_o you_o have_v measure_v one_o section_n at_o the_o end_n of_o the_o ouall_n you_o have_v also_o the_o content_a of_o the_o other_o section_n at_o the_o other_o end_n because_o they_o be_v equal_a therefore_o you_o need_v but_o to_o double_a the_o one_o and_o so_o you_o have_v the_o content_a of_o they_o both_o in_o like_a sort_n may_v you_o do_v with_o the_o section_n at_o the_o side_n that_o be_v have_v measure_v the_o one_o do_v but_o double_v it_o for_o the_o content_a of_o they_o both_o if_o a_o piece_n of_o timber_n be_v ouall_a fashion_n that_o be_v have_v his_o base_a or_o end_n like_o a_o ouall_n than_o it_o may_v be_v measure_v by_o multiply_v the_o content_a of_o the_o base_a by_o the_o altitude_n or_o length_n of_o the_o piece_n as_o have_v be_v often_o mention_v note_v further_o that_o by_o this_o which_o be_v here_o teach_v and_o by_o that_o which_o be_v afore_o write_v of_o triangle_n and_o mani-sided_n figure_n you_o may_v measure_v any_o kind_n of_o figure_n either_o plain_a or_o solid_a that_o be_v make_v of_o straight_a line_n and_o circular_a line_n together_o if_o you_o do_v but_o use_v diligence_n and_o divide_v or_o imagine_v a_o division_n of_o the_o whole_a figure_n into_o his_o proper_a section_n and_o other_o figure_n as_o become_v and_o so_o measure_v those_o section_n and_o other_o figure_n several_o and_o they_o add_v their_o content_n together_o chap._n 12._o what_o a_o pyramid_n be_v and_o how_o it_o be_v measure_v a_o pyramid_n be_v a_o solid_a figure_n contain_v under_o many_o plain_a superficies_n set_v upon_o one_o plain_a superficies_n and_o gather_v together_o into_o one_o point_n as_o this_o pyramid_n a_o pyramid_n be_v diverse_a according_a as_o their_o base_n be_v diverse_a as_o of_o 3_o 4_o 5_o or_o more_o side_n as_o be_v at_o large_a show_v in_o the_o 10._o definition_n of_o the_o 11._o book_n of_o euclides_n element_n of_o geometry_n but_o of_o what_o sort_v soever_o the_o pyramid_n be_v pyramid_n to_o measure_v the_o solid_a content_n of_o a_o pyramid_n they_o be_v measure_v by_o one_o rule_n which_o be_v thus_o multiply_v the_o altitude_n or_o height_n by_o the_o three_o part_n of_o the_o content_a of_o the_o base_a or_o contrary_o multiply_v the_o content_a of_o the_o base_a by_o the_o three_o part_n of_o the_o altitude_n or_o height_n and_o either_o of_o the_o product_n be_v the_o content_a solid_a of_o the_o pyramid_n here_o note_n that_o the_o altitude_n or_o height_n be_v not_o the_o length_n of_o the_o side_n of_o the_o pyramid_n but_o as_o i_o tell_v you_o in_o the_o first_o chapter_n of_o this_o three_o part_n it_o be_v the_o length_n of_o the_o perpendicular_a or_o plum_n line_n fall_v from_o the_o point_n or_o top_n thereof_o to_o the_o base_a or_o bottom_n but_o if_o you_o will_v measure_v the_o superficies_n or_o outside_n of_o a_o pyramid_n pyramid_n to_o measure_v the_o superficial_a content_n of_o a_o pyramid_n then_o in_o so_o much_o as_o all_o the_o side_n be_v triangle_n measure_v every_o triangle_n by_o itself_o and_o to_o all_o their_o content_n add_v the_o content_a of_o the_o base_a and_o the_o total_a or_o sum_n be_v the_o superficial_a content_n of_o the_o pyramid_n chap._n 13._o how_o to_o measure_v part_n of_o a_o pyramid_n or_o timber_n that_o be_v taper_n grow_v if_o a_o part_n of_o a_o pyramid_n do_v taper_n much_o you_o may_v lay_v it_o on_o a_o paper_n by_o a_o scale_n and_o make_v it_o out_o to_o a_o perfect_a pyramid_n have_v so_o do_v measure_v the_o whole_a pyramid_n measure_v also_o that_o part_n thereof_o which_o be_v add_v which_o subtract_v or_o take_v from_o the_o content_a of_o the_o whole_a pyramid_n and_o the_o remainder_n give_v the_o content_a of_o the_o piece_n of_o a_o pyramid_n this_o way_n be_v not_o convenient_a in_o ordinary_a taper_v timber_n and_o therefore_o take_v rather_o the_o way_n here_o follow_v you_o know_v that_o in_o the_o last_o chapter_n of_o the_o first_o part_n of_o this_o book_n i_o tell_v you_o that_o if_o a_o taper_v piece_n be_v measure_v by_o the_o square_n of_o the_o middle_n there_o be_v lose_v to_o the_o seller_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 which_o have_v for_o his_o breadth_n half_o the_o difference_n of_o the_o breadth_n of_o both_o end_n and_o for_o his_o thickness_n half_o the_o difference_n of_o the_o thickness_n of_o both_o end_n therefore_o have_v measure_v the_o piece_n by_o the_o square_n of_o the_o middle_n deduct_v the_o say_v lose_v piece_n and_o the_o remainder_n be_v the_o content_a of_o the_o taper_v piece_n this_o lose_a piece_n you_o may_v measure_v and_o so_o deduct_v thus_o take_v the_o half_a of_o the_o difference_n of_o the_o breadth_n of_o both_o end_n of_o the_o taper_v piece_n for_o the_o breadth_n of_o your_o lose_a piece_n and_o half_o the_o difference_n of_o the_o thickness_n of_o both_o end_n for_o the_o thickness_n of_o the_o lose_a piece_n &_o 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again_o that_o the_o side_n of_o the_o cone_n be_v not_o the_o height_n plum_n or_o perpendicular_a line_n from_o the_o top_n to_o the_o base_a but_o the_o length_n of_o the_o ridge_n or_o slope_v of_o the_o cone_n there_o be_v many_o other_o kind_n of_o plain_n and_o sollid_n but_o i_o may_v not_o stand_v to_o write_v of_o they_o if_o any_o man_n either_o for_o pleasure_n or_o profit_n shall_v desire_v to_o know_v they_o or_o their_o measure_n let_v he_o look_v into_o euclides_n element_n master_n dig_v his_o pantametria_n master_n lucre_n solace_n and_o other_o good_a book_n of_o geometry_n which_o be_v extant_a in_o english_a finis_fw-la
the_o caâ—â—â—nters_n rule_n or_o a_o book_n show_v many_o 〈◊〉_d way_n true_o to_o measure_v ordinary_a timber_n and_o other_o extraordinary_a sollid_n or_o timber_n with_o a_o detection_n of_o sundry_a great_a error_n general_o commit_v by_o carpenter_n and_o other_o in_o measure_v of_o timber_n tend_v much_o to_o the_o buyer_n great_a loss_n publishâ—â—_a especial_o for_o the_o good_a of_o the_o 〈…〉_o carpenter_n in_o london_n and_o other_o also_o and_o be_v very_a 〈◊〉_d for_o mason_n shipwright_n joiner_n and_o 〈…〉_o to_o measure_n timber_n and_o board_n and_o 〈…〉_o other_o superficies_n and_o sollid_n by_o râ—hard_n more_o carpenter_n at_o london_n imprint_v by_o felix_n kyngston_n 1602._o to_o the_o right_n worshipful_a sir_n henry_n billingsley_n knight_n alderman_n of_o the_o city_n of_o london_n right_o worshipful_a when_o i_o have_v often_o consider_v the_o great_a error_n and_o by_o error_n the_o great_a loss_n come_v to_o this_o city_n in_o measure_v of_o timber_n after_o the_o common_a way_n and_o have_v long_o expect_v some_o man_n endeavour_n for_o redress_n but_o see_v none_o i_o be_v in_o a_o sort_n provoke_v though_o the_o unfit_a of_o a_o number_n to_o attempt_v this_o thing_n and_o because_o it_o be_v not_o otherwise_o likely_a but_o that_o i_o in_o this_o case_n shall_v have_v many_o opposer_n i_o have_v therefore_o embolden_v myself_o humble_o to_o desire_v your_o worship_n protection_n crave_v also_o your_o favourable_a acceptance_n of_o this_o my_o poor_a labour_n that_o so_o it_o may_v be_v the_o better_o accept_v for_o the_o common_a good_a neither_o be_v my_o desire_n only_o to_o entreat_v your_o worship_n favour_n and_o protection_n but_o also_o to_o testify_v my_o dutiful_a thankfulness_n for_o your_o great_a pain_n and_o no_o small_a cost_n in_o publish_v in_o our_o english_a 〈…〉_o euclideâ—_n element_n of_o geometry_n a_o book_n from_o which_o 〈…〉_o well_o may_v so_o myself_o needs_o must_v confess_v that_o i_o have_v receive_v all_o 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of_o a_o heathen_a that_o man_n be_v 〈◊〉_d for_o themselves_o but_o for_o their_o country_n i_o do_v set_v aside_o all_o let_n and_o both_o bold_o and_o rude_o have_v put_v out_o this_o my_o simple_a book_n in_o manner_n as_o you_o see_v the_o book_n i_o have_v divide_v into_o three_o part_n in_o the_o first_o part_n i_o declare_v the_o error_n most_o common_o commit_v and_o take_v for_o truth_n in_o measure_v of_o timber_n in_o the_o second_o part_n i_o show_v how_o ordinary_a timber_n may_v be_v measure_v both_o by_o sundry_a plain_a way_n as_o also_o by_o way_n more_o artificial_a and_o in_o the_o three_o part_n i_o show_v how_o extraordinary_a timber_n and_o solid_a form_n may_v be_v measure_v the_o error_n ordinary_o commit_v in_o measure_v timber_n be_v many_o but_o of_o they_o all_o especial_o two_o bring_v loss_n to_o the_o buyer_n the_o first_o be_v by_o buy_v of_o waynie_a timber_n and_o measure_v it_o as_o square_v the_o other_o be_v by_o take_v half_o the_o breadth_n and_o thickness_n of_o a_o piece_n be_v add_v together_o for_o the_o square_a thereof_o these_o error_n be_v such_o as_o bring_v apparent_a damage_n and_o therefore_o they_o be_v not_o to_o be_v respect_v light_o i_o will_v they_o may_v not_o be_v say_v to_o be_v a_o great_a cause_n if_o not_o of_o the_o overthrow_n yet_o of_o the_o impair_n of_o some_o man_n estate_n for_o as_o for_o wainie_a timber_n who_o know_v not_o that_o as_o it_o be_v often_o measure_v and_o hew_v a_o load_n and_o a_o half_a will_v not_o go_v so_o far_o in_o use_n as_o a_o load_n of_o good_a timber_n be_v well_o hew_v and_o just_o measure_v and_o as_o for_o halue_v the_o sum_n of_o the_o two_o side_n for_o the_o square_n the_o damage_n hereby_o be_v exceed_v much_o not_o only_o to_o those_o that_o buy_v much_o timber_n at_o the_o first_o hand_n but_o also_o and_o that_o especial_o which_o be_v the_o more_o pity_n to_o the_o poor_a sort_n that_o buy_v at_o the_o second_o hand_n for_o myself_o have_v abate_v of_o that_o which_o workman_n themselves_o have_v measure_v a_o piece_n unto_o by_o the_o foresay_a false_a way_n after_z 3_o 4_o 5_o yea_o 6_o foot_n of_o timber_n in_o 20_o and_o yet_o i_o have_v give_v they_o no_o more_o than_o their_o measure_n i_o can_v stand_v to_o amplify_v these_o error_n in_o this_o place_n they_o be_v more_o full_o set_v down_o in_o the_o book_n itself_o by_o which_o if_o they_o be_v well_o weigh_v and_o consider_v upon_o it_o will_v plain_o appear_v to_o be_v true_a as_o i_o have_v say_v namely_o that_o there_o come_v great_a loss_n by_o the_o ordinary_a measure_n of_o timber_n now_o see_v the_o case_n so_o stand_v my_o desire_n and_o request_n be_v even_o to_o every_o man_n but_o especial_o to_o you_o the_o master_n warden_n and_o assistant_n of_o our_o company_n that_o you_o will_v put_v your_o help_a hand_n to_o reform_v these_o error_n many_o reason_n may_v be_v allege_v to_o induce_v you_o hereunto_o but_o for_o some_o reason_n best_o know_v to_o myself_o i_o omit_v they_o all_o not_o doubt_v of_o your_o care_n and_o regard_v hereunto_o i_o have_v hear_v some_o man_n wish_v that_o we_o have_v a_o act_n of_o parliament_n procure_v for_o redress_n of_o false_a measure_n but_o true_o that_o seem_v to_o be_v the_o law_n of_o our_o land_n already_o though_o not_o the_o statute_n law_n for_o the_o law_n intend_v that_o the_o buyer_n shall_v have_v that_o which_o he_o buy_v and_o when_o we_o buy_v a_o load_n of_o timber_n do_v we_o not_o intend_v that_o we_o have_v buy_v 50._o foot_n of_o solid_a timber_n every_o foot_n be_v full_a 12._o inch_n every_o way_n that_o be_v in_o length_n breadth_n &_o thickness_n why_o then_o may_v we_o not_o require_v so_o much_o for_o a_o load_n and_o why_o
be_v not_o the_o seller_n bind_v to_o deliver_v it_o and_o if_o a_o man_n that_o buy_v twenty_o bushel_n of_o wheat_n will_v not_o take_v nineteen_o or_o if_o he_o buy_v a_o yard_n of_o cloth_n he_o will_v not_o take_v three_o quarter_n then_o why_o shall_v we_o buy_v a_o load_n of_o timber_n take_v 40._o foot_n for_o it_o yea_o and_o less_o too_o as_o oft_o time_n it_o fall_v out_o whereas_o we_o shall_v have_v 50._o foot_n i_o know_v that_o many_o man_n will_v object_v many_o thing_n and_o it_o be_v not_o for_o i_o at_o this_o time_n to_o refute_v they_o only_o whereas_o some_o may_v say_v that_o what_o be_v want_v in_o the_o measure_n be_v allow_v in_o the_o price_n i_o answer_v 1._o that_o be_v not_o always_o 2._o but_o where_o allowance_n be_v make_v it_o be_v not_o according_a to_o the_o value_n of_o the_o loss_n come_v by_o the_o false_a measure_n 3._o again_o it_o be_v a_o preposterous_a course_n to_o raise_v or_o let_v fall_v a_o price_n by_o alter_v of_o a_o set_a measure_n to_o a_o uncertainty_n whereas_o we_o use_v in_o all_o trade_n to_o raise_v or_o let_v fall_v the_o price_n according_a to_o the_o goodness_n or_o badness_n of_o the_o ware_n keep_v still_o the_o same_o measure_n for_o they_o both_o and_o sure_o herein_o we_o be_v but_o deceive_v for_o oft_o time_n we_o have_v twelve_o penny_n bate_v in_o the_o price_n of_o a_o load_n and_o lose_v four_o or_o five_o shilling_n in_o the_o measure_n thereof_o therefore_o let_v we_o either_o have_v just_a measure_n if_o we_o buy_v by_o measure_n or_o else_o let_v we_o buy_v it_o by_o guess_n for_o it_o be_v a_o shame_n to_o pretend_v to_o measure_v true_o and_o yet_o do_v nothing_o less_o as_o touch_v myself_o i_o desire_v that_o my_o endeavour_n may_v be_v favourable_o accept_v for_o i_o write_v with_o no_o other_o mind_n then_o as_o tender_v my_o company_n good_a if_o any_o thing_n that_o i_o have_v say_v be_v impugn_a as_o false_a i_o will_v be_v ready_a whensoever_o you_o will_v call_v i_o to_o prove_v my_o affirmation_n if_o any_o man_n of_o knowledge_n shall_v except_v against_o i_o for_o my_o rude_a writing_n and_o gross_a demonstration_n i_o pray_v they_o to_o understand_v that_o i_o write_v not_o for_o they_o but_o for_o the_o simple_a and_o therefore_o i_o demonstrate_v gross_o not_o be_v well_o able_a to_o do_v better_o also_o that_o i_o be_o not_o a_o scholar_n but_o a_o carpenter_n and_o therefore_o can_v not_o but_o write_v rude_o unto_o such_o also_o i_o do_v further_o say_v that_o my_o desire_n be_v that_o they_o will_v take_v knowledge_n that_o this_o have_v be_v one_o cause_n of_o my_o writing_n even_o to_o provoke_v they_o see_v our_o present_a error_n and_o loss_n with_o which_o peradventure_o they_o be_v not_o so_o well_o acquaint_v as_o myself_o to_o take_v some_o pain_n to_o reform_v the_o same_o in_o better_a sort_n then_o either_o i_o have_v or_o can_v do_v while_o this_o book_n be_v in_o print_v i_o come_v to_o the_o sight_n of_o a_o ruler_n sometime_o invent_v by_o one_o master_n bedwel_n which_o as_o it_o be_v easy_a so_o it_o be_v most_o speedy_a and_o not_o less_o certain_a be_v true_o make_v for_o the_o measure_n of_o timber_n and_o board_n which_o i_o expect_v and_o hope_n will_v be_v short_o publish_v for_o the_o common_a good_a but_o i_o will_v not_o trouble_v you_o with_o more_o word_n only_o let_v i_o put_v you_o in_o mind_n of_o this_o one_o thing_n that_o in_o as_o much_o as_o nothing_o be_v more_o fit_a for_o carpenter_n to_o make_v they_o ready_a not_o only_o in_o measure_n but_o also_o in_o other_o thing_n than_o geometry_n that_o therefore_o such_o as_o be_v of_o reasonable_a capacity_n will_v spend_v some_o part_n of_o their_o spare_a time_n to_o study_v the_o same_o in_o some_o measure_n at_o the_o least_o for_o your_o furtherance_n herein_o there_o be_v especial_a good_a help_n both_o by_o the_o lecture_n at_o gresham_n college_n every_o thursday_n in_o the_o term_n time_n if_o you_o be_v but_o a_o little_a enter_v as_o also_o by_o euclides_n element_n of_o geometry_n which_o the_o right_a worshipful_a sir_n henry_n billingsley_n knight_n to_o the_o great_a good_a of_o the_o commonwealth_n though_o to_o his_o own_o great_a travel_n and_o charge_n have_v translate_v and_o publish_v in_o our_o english_a tongue_n but_o i_o be_o over_o tedious_a i_o pray_v you_o accept_v of_o this_o my_o poor_a endeavour_n as_o a_o fruit_n of_o my_o hearty_a good_a will_n to_o my_o company_n and_o other_o who_o it_o may_v concern_v if_o it_o take_v none_o effect_v i_o shall_v be_v sorry_a but_o if_o it_o do_v any_o good_a i_o have_v enough_o for_o my_o labour_n richard_n more_o the_o first_o part_n of_o the_o carpenter_n rule_n show_v diverse_a gross_a error_n general_o commit_v by_o carpenter_n and_o other_o in_o measure_v of_o timber_n arise_v from_o the_o rule_n and_o the_o use_n thereof_o chapter_n 1._o the_o error_n in_o the_o rule_n and_o the_o reason_n thereof_o those_o that_o endeavour_n to_o amend_v thing_n amiss_o must_v first_o of_o all_o labour_n to_o prove_v the_o fault_n especial_o when_o the_o party_n deceive_v be_v not_o yet_o persuade_v that_o they_o be_v out_o of_o the_o way_n and_o because_o man_n little_a regard_n to_o return_v unto_o the_o right_n when_o they_o do_v not_o perceive_v that_o they_o be_v far_o in_o the_o wrong_n i_o have_v therefore_o think_v good_a to_o spend_v this_o first_o part_n of_o my_o book_n in_o show_v and_o declare_v that_o great_a error_n be_v to_o too_o ordinary_o commit_v by_o the_o most_o part_n of_o carpenter_n and_o other_o in_o and_o about_o london_n and_o elsewhere_o in_o measure_v of_o timber_n these_o error_n do_v arise_v either_o by_o mean_n of_o the_o rule_n or_o ruler_n with_o which_o they_o measure_v timber_n or_o else_o by_o the_o misapply_n or_o use_v thereof_o i_o mean_v the_o ordinary_a way_n of_o measure_v timber_n be_v very_o erroneous_a but_o first_o of_o the_o fault_n to_o be_v observe_v in_o the_o ruler_n itself_o the_o ordinary_a rule_n which_o carpenter_n shipwright_n and_o other_o do_v use_v to_o measure_v timber_n withal_o be_v invent_v and_o publish_v by_o master_n leonard_n digger_n tectonicon_fw-la digges_n tectonicon_fw-la now_o those_o rule_n that_o agree_v with_o that_o book_n be_v so_o true_a as_o that_o i_o deem_v they_o overcurious_a that_o except_o against_o they_o and_o they_o will_v serve_v true_o to_o measure_v timber_n withal_o but_o the_o most_o which_o have_v that_o kind_n of_o measure_n on_o they_o which_o master_n digges_n describe_v be_v very_o false_a i_o mean_v those_o division_n or_o strike_v which_o be_v set_v on_o they_o for_o measure_v of_o board_n and_o timber_n be_v not_o in_o their_o right_a place_n and_o as_o those_o strike_v and_o divisson_n agree_v not_o with_o the_o truth_n so_o upon_o diverse_a rule_n you_o shall_v find_v they_o to_o disagree_v one_o from_o another_o yea_o hardly_o shall_v you_o see_v two_o rule_n that_o do_v every_o where_fw-mi agree_v neither_o be_v this_o error_n insensible_a and_o so_o not_o to_o be_v respect_v but_o apparent_o gross_a and_o therefore_o not_o to_o be_v tolerate_v for_o myself_o have_v see_v some_o rule_n that_o in_o some_o of_o their_o division_n have_v err_v from_o the_o truth_n and_o from_o one_o another_o after_o the_o rate_n of_o six_o foot_n in_o a_o hundred_o of_o board_n and_o after_o four_o foot_n in_o a_o load_n of_o timber_n neither_o be_v this_o error_n rare_a and_o in_o some_o alone_a but_o so_o general_a as_o that_o if_o a_o man_n will_v examine_v they_o he_o shall_v be_v force_v to_o say_v that_o true_a rule_n be_v very_o scant_o if_o i_o be_v demand_v the_o cause_n of_o this_o fault_n or_o error_n in_o the_o rule_n i_o shall_v answer_v that_o in_o my_o opinion_n it_o arise_v hence_o many_o will_v take_v upon_o they_o to_o make_v rule_n who_o have_v not_o master_n digges_n his_o book_n to_o make_v they_o by_o or_o if_o they_o have_v it_o understand_v it_o not_o neither_o the_o ground_n from_o whence_o the_o rule_n be_v make_v by_o which_o they_o may_v examine_v the_o rule_n which_o they_o make_v which_o ground_n be_v set_v down_o in_o the_o eleven_o and_o twelve_o chapter_n of_o the_o second_o part_n of_o this_o book_n but_o ordinary_o man_n make_v they_o one_o by_o another_o whereof_o have_v grow_v the_o former_a error_n thus_o much_o for_o the_o rule_n now_o shall_v follow_v to_o show_v the_o error_n in_o measure_v board_n and_o plank_n but_o because_o i_o have_v observe_v no_o main_a error_n in_o measure_v of_o ordinary_a plank_n or_o board_n though_o great_a fault_n in_o buy_v of_o waynie_a board_n and_o measure_v it_o as_o square_v which_o i_o speak_v of_o in_o the_o next_o chapter_n follow_v
i_o will_v therefore_o say_v nothing_o thereof_o now_o but_o pass_v to_o error_n in_o measure_v of_o timber_n chap._n 2._o the_o great_a loss_n that_o come_v in_o buy_v of_o timber_n and_o board_n that_o be_v wainie_a and_o measure_v it_o as_o square_v every_o man_n that_o buy_v board_n or_o timber_n intend_v to_o have_v for_o a_o foot_n as_o follow_v that_o be_v to_o say_v in_o board_n twelve_o ynche_n in_o length_n and_o twelve_o in_o breadth_n and_o in_o timber_n twelve_o ynche_n in_o length_n twelve_o in_o breadth_n and_o twelve_o in_o thickness_n but_o who_o so_o buy_v timber_n or_o board_n that_o be_v waynie_a and_o take_v it_o as_o if_o it_o be_v not_o waynie_a have_v not_o his_o measure_n for_o his_o money_n but_o far_o less_o this_o be_v a_o great_a fault_n and_o general_a throughout_o the_o whole_a company_n and_o among_o other_o also_o yea_o and_o apparent_o know_v and_o note_v by_o every_o man_n and_o yet_o not_o amend_v nor_o endeavour_v to_o be_v amend_v by_o any_o this_o fault_n in_o board_n seem_v to_o come_v from_o carelessness_n and_o in_o timber_n as_o i_o take_v it_o it_o do_v first_o grow_v from_o ignorance_n for_o when_o man_n know_v not_o now_o to_o measure_v a_o waynie_a piece_n of_o timber_n nor_o bow_v to_o deduct_v the_o vein_n have_v measure_v it_o as_o not_o waynie_a then_o they_o do_v careless_o overpasse_v this_o thing_n as_o a_o necessary_a evil_n or_o as_o a_o inconvenience_n that_o can_v not_o be_v avoid_v but_o it_o may_v be_v say_v that_o there_o be_v allowance_n in_o the_o price_n i_o answer_v what_o be_v it_o in_o a_o load_n of_o timber_n or_o in_o a_o persell_a of_o board_n to_o have_v twelve_o penny_n abate_v in_o the_o price_n and_o to_o lose_v four_o or_o five_o shilling_n in_o the_o measure_n this_o be_v to_o get_v in_o the_o hundred_o and_o lose_v in_o the_o shire_n and_o beside_o this_o loss_n that_o come_v by_o waynie_a timber_n there_o be_v also_o another_o great_a loss_n thereby_o not_o to_o be_v forget_v you_o know_v that_o when_o the_o timber_n be_v very_o waynie_a we_o be_v compel_v to_o hew_v away_o a_o great_a part_n of_o it_o after_o it_o be_v saw_v to_o bring_v it_o to_o some_o reasonable_a squarenes_n fit_a for_o use_v if_o then_o you_o shall_v put_v this_o loss_n to_o the_o other_o you_o shall_v find_v that_o it_o be_v no_o small_a damage_n that_o come_v by_o buy_v of_o waynie_a timber_n and_o therefore_o there_o shall_v be_v a_o extraordinary_a care_n and_o respect_n have_v to_o the_o measure_n that_o we_o lose_v not_o by_o it_o see_v so_o great_a loss_n come_v by_o the_o stuff_n itself_o my_o desire_n therefore_o be_v that_o as_o other_o fault_n so_o this_o may_v be_v amend_v not_o that_o i_o will_v have_v timber_n hew_v die_v square_a for_o that_o be_v a_o spoil_n of_o much_o good_a timber_n nor_o that_o i_o will_v have_v gird_v measure_n use_v for_o that_o in_o this_o kind_n be_v very_o false_a as_o appeareth_z afterward_o but_o i_o will_v have_v the_o want_n or_o wainynesse_n deduct_v or_o take_v out_o of_o the_o whole_a piece_n which_o how_o it_o may_v be_v do_v be_v show_v in_o the_o second_o part_n of_o this_o book_n chapter_n 5._o chap._n 3._o that_o it_o be_v very_o false_a to_o take_v for_o the_o square_n of_o a_o piece_n of_o timber_n the_o half_a of_o the_o breadth_n and_o thickness_n add_v together_o by_o which_o square_n shall_v be_v find_v the_o length_n of_o a_o foot_n in_o that_o piece_n it_o be_v a_o common_a practice_n and_o that_o of_o old_a that_o who_o so_o of_o the_o ordinary_a and_o common_a sort_n of_o man_n do_v measure_n timber_n they_o take_v this_o course_n first_o they_o add_v or_o put_v together_o the_o breadth_n and_o thickness_n of_o the_o piece_n of_o timber_n to_o be_v measure_v then_o they_o take_v the_o half_a thereof_o for_o the_o square_n of_o the_o same_o piece_n and_o then_o according_a to_o that_o square_n they_o give_v the_o length_n of_o a_o foot_n by_o the_o rule_n as_o for_o example_n if_o the_o piece_n be_v ten_o ynche_n one_o way_n and_o fourteen_o ynche_n the_o other_o way_n they_o add_v together_o ten_o and_o fourteen_o which_o make_v twenty_o four_o the_o half_a of_o twenty_o four_o be_v twelve_o which_o say_v they_o be_v the_o square_a of_o this_o piece_n of_o timber_n which_o be_v very_o false_a and_o yet_o this_o course_n be_v so_o general_o receive_v and_o so_o common_o repute_v and_o take_v for_o good_a as_o that_o he_o shall_v be_v think_v overcurious_a of_o some_o that_o shall_v but_o except_v against_o it_o howbeit_o if_o you_o will_v but_o mark_v that_o which_o follow_v you_o shall_v plain_o see_v that_o it_o be_v a_o error_n and_o that_o a_o great_a one_o thus_o then_o appear_v the_o error_n if_o you_o will_v know_v the_o greatness_n thereof_o you_o shall_v understand_v that_o in_o the_o former_a example_n and_o so_o in_o all_o timber_n that_o have_v like_o difference_n of_o side_n as_o that_o piece_n have_v there_o be_v loss_n always_o to_o the_o buyer_n a_o quarter_n of_o that_o which_o he_o buy_v or_o one_o load_n of_o timber_n in_o four_o if_o the_o difference_n of_o the_o side_n be_v small_a than_o be_v the_o loss_n small_a but_o if_o it_o be_v great_a than_o be_v the_o loss_n great_a and_o in_o general_a take_v this_o for_o a_o rule_n that_o there_o be_v lose_v by_o this_o kind_n of_o false_a measure_n a_o square_a piece_n of_o timber_n as_o long_o as_o the_o whole_a piece_n to_o be_v measure_v and_o as_o broad_a and_o thick_a as_o half_a the_o difference_n of_o the_o two_o side_n of_o the_o say_a piece_n of_o timber_n to_o be_v measure_v as_o for_o example_n let_v the_o side_n be_v ten_o and_o fourteen_o than_o their_o difference_n be_v four_o for_o fourteen_o be_v more_o than_o ten_o by_o four_o now_o the_o half_a of_o four_o be_v two_o which_o two_o be_v the_o side_n of_o the_o say_v lose_v square_a piece_n of_o timber_n throughout_o the_o piece_n now_o see_v this_o error_n of_o take_v half_o the_o sum_n of_o the_o side_n for_o the_o square_n be_v very_o manifest_a and_o see_v also_o it_o be_v a_o error_n tend_v to_o the_o great_a loss_n of_o the_o buyer_n yea_o to_o the_o loss_n of_o three_o load_n in_o four_o and_o more_o also_o as_o the_o difference_n may_v be_v therefore_o i_o desire_v that_o none_o will_v follow_v that_o corrupt_a custom_n and_o most_o false_a way_n but_o suffer_v themselves_o to_o be_v better_o instruct_v in_o more_o right_a way_n which_o if_o they_o refuse_v to_o do_v and_o shall_v buy_v much_o timber_n after_o that_o rate_n their_o purse_n be_v like_a to_o pay_v for_o it_o but_o some_o may_v say_v unto_o i_o this_o fault_n be_v by_o diverse_a discern_v and_o a_o redress_n not_o altogether_o unthought_a of_o i_o grant_v many_o do_v see_v it_o and_o do_v endeavour_n to_o reform_v it_o thus_o if_o a_o piece_n of_o timber_n be_v eighteen_o ynche_n one_o way_n and_o six_o ynche_n the_o other_o way_n they_o imagine_v it_o to_o consist_v of_o three_o square_n of_o six_o ynche_n a_o piece_n as_o indeed_o it_o do_v the_o which_o they_o measure_v several_o and_o then_o add_v all_o their_o content_n together_o which_o they_o take_v for_o the_o measure_n of_o the_o whole_a piece_n this_o be_v true_a both_o in_o this_o example_n and_o in_o all_o other_o that_o will_v fall_v out_o in_o any_o number_n of_o just_a square_n but_o when_o the_o side_n of_o the_o timber_n to_o be_v measure_v have_v not_o this_o answereablenes_n in_o they_o as_o nine_o ynche_n one_o way_n and_o fourteen_o the_o other_o way_n or_o seven_o and_o nintéene_fw-mi or_o such_o like_a then_o they_o be_v to_o seek_v for_o when_o they_o have_v take_v the_o thickness_n out_o of_o the_o breadth_n as_o often_o as_o they_o may_v then_o be_v the_o remainder_n unsquare_n in_o measure_v whereof_o they_o fail_v and_o err_v as_o a_o foresay_a and_o yet_o they_o profess_v not_o to_o regard_v it_o for_o say_v they_o if_o the_o difference_n of_o the_o side_n be_v not_o past_a three_o or_o four_o ynche_n that_o piece_n may_v be_v measure_v according_a to_o the_o say_v erroneous_a way_n and_o no_o great_a loss_n happen_v thereby_o but_o what_o the_o loss_n be_v i_o have_v show_v before_o which_o although_o it_o seem_v but_o small_a yet_o in_o time_n it_o arise_v to_o no_o small_a matter_n chap._n 4._o the_o error_n in_o measure_v of_o timber_n not_o hew_v square_a but_o bevell_n though_o this_o error_n be_v not_o of_o any_o great_a moment_n because_o timber_n hew_v bevell_a or_o skew_z come_v not_o often_o to_o be_v measure_v yet_o because_o sometime_o there_o be_v such_o timber_n to_o be_v sell_v i_o will_v not_o have_v workman_n to_o be_v ignorant_a that_o it_o be_v a_o apparent_a
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 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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 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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
sure_o i_o be_o that_o no_o carpenter_n can_v have_v measure_v it_o for_o they_o without_o the_o knowledge_n of_o that_o which_o be_v write_v hereafter_o and_o because_o i_o shall_v have_v occasion_n to_o use_v many_o term_n of_o geometry_n by_o which_o i_o may_v with_o more_o ease_n deliver_v and_o you_o with_o more_o plainness_n perceive_v my_o mind_n in_o these_o thing_n i_o have_v therefore_o set_v down_o the_o meaning_n as_o plain_o as_o i_o can_v of_o some_o geometrical_a term_n which_o most_o serve_v for_o our_o present_a purpose_n and_o in_o this_o chapter_n i_o explain_v only_o those_o term_n that_o general_o i_o use_v throughout_o this_o whole_a part_n and_o which_o do_v not_o proper_o belong_v to_o any_o one_o chapter_n the_o rest_n i_o will_v declare_v in_o the_o begin_n of_o every_o chapter_n as_o the_o matter_n thereof_o give_v occasion_n but_o to_o the_o matter_n 1._o a_o angle_n be_v nothing_o else_o but_o a_o corner_n make_v by_o the_o meeting_n of_o two_o line_n for_o 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neither_o high_o nor_o low_a than_o the_o base_a or_o bottom_n chap._n 2._o how_o to_o raise_v and_o let_v fall_v a_o perpendicular_a a_o perpendicular_a line_n be_v that_o which_o stand_v plum_n upright_o upon_o another_o lean_v neither_o the_o one_o way_n nor_o the_o other_o a_o perpendicular_a be_v say_v to_o be_v raise_v when_o a_o point_n be_v give_v in_o a_o line_n from_o which_o it_o must_v rise_v it_o be_v say_v to_o be_v let_v fall_v when_o a_o point_n be_v give_v above_o the_o line_n from_o which_o it_o must_v fall_v now_o beside_o that_o you_o may_v both_o raise_v and_o let_v fall_v a_o perpendicular_a by_o a_o squire_n or_o square_n there_o be_v many_o way_n geometrical_o to_o do_v both_o the_o one_o and_o the_o other_o and_o because_o there_o be_v especial_a use_n in_o this_o three_o part_n of_o let_v fall_v a_o perpendicular_a or_o plum_n line_n from_o a_o point_n give_v as_o also_o from_o a_o angle_n in_o a_o figure_n to_o the_o base_a i_o will_v not_o have_v man_n ignorant_a how_o to_o do_v the_o same_o without_o a_o squire_n which_o be_v not_o always_o at_o hand_n when_o a_o rule_n &_o pair_n of_o compass_n be_v and_o yet_o i_o will_v set_v down_o only_o one_o way_n of_o many_o to_o avoid_v tediousness_n which_o be_v thus_o let_v the_o point_n give_fw-mi be_v a_o the_o line_n give_v bc._n open_v the_o compass_n to_o any_o distance_n convenient_a and_o set_v one_o foot_n in_o the_o point_n a_o make_v a_o ark_n or_o piece_n of_o a_o circle_n with_o the_o other_o foot_n till_o it_o cut_v the_o line_n bc_n twice_o those_o two_o place_n of_o cut_v we_o call_v intersection_n and_o be_v here_o in_o this_o example_n at_o b_o and_z c._n then_o find_v the_o middle_n between_o those_o two_o intersection_n and_o from_o that_o middle_n draw_v a_o line_n to_o the_o point_n a_o which_o be_v the_o point_n give_v and_o that_o line_n shall_v be_v perpendicular_a or_o plumbe_v from_o the_o point_n a_o to_o the_o line_n b_o c_o as_o be_v require_v chap._n 3._o of_o a_o triangle_n and_o a_o prism_n what_o they_o be_v and_o how_o they_o be_v measure_v triangle_n be_v diverse_a both_o in_o respect_n of_o their_o side_n and_o angle_n and_o may_v be_v measure_v diverse_a way_n but_o let_v this_o one_o way_n serve_v for_o all_o multiply_v half_a of_o the_o base_a by_o all_o the_o height_n or_o perpendicular_a or_o which_o be_v all_o one_o multiply_v all_o the_o base_a by_o half_a the_o height_n or_o perpendicular_a and_o either_o of_o the_o product_n give_v the_o content_a of_o the_o triangle_n here_o i_o pray_v you_o remember_v what_o i_o mean_v by_o the_o base_a and_o height_n or_o altitude_n according_a as_o be_v she_o wed_v in_o the_o former_a chapter_n in_o this_o figure_n you_o may_v suppose_v the_o long_a line_n to_o be_v the_o base_a and_o then_o the_o prick_a line_n be_v the_o height_n or_o perpendicular_a now_o note_n that_o a_o prism_n be_v that_o who_o two_o opposite_a plain_n or_o end_n be_v equal_a like_a and_o parallel_v the_o 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of_o the_o way_n teach_v in_o the_o second_o part_n of_o this_o book_n this_o be_v understand_v which_o be_v here_o write_v the_o use_n hereof_o be_v very_o general_a for_o beside_o that_o the_o carpenter_n may_v measure_v hereby_o any_o canted_a piece_n of_o timber_n as_o step_n for_o stair_n and_o cant_v rail_n and_o such_o like_a the_o plasterer_n also_o who_o often_o work_v by_o the_o yard_n may_v hereby_o measure_v gable-end_n and_o such_o like_a form_z the_o glazier_n have_v likewise_o use_v hereof_o and_o also_o it_o may_v stand_v the_o mason_n oft_o in_o stead_n chap._n 4._o what_o a_o parallelogram_n be_v and_o how_o it_o be_v measure_v a_o parallelogram_n be_v a_o figure_n who_o