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end_n low_a part_n upper_a 1,487 5 9.1326 5 false
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ID Title Author Corrected Date of Publication (TCP Date of Publication) STC Words Pages
A77649 The description and use of the carpenters-rule: together with the use of the line of numbers (inscribed thereon) in arithmetick and geometry. And the application thereof to the measuring of superficies and solids, gaging of vessels, military orders, interest and annuities: with tables of reduction, &c. : To which is added, the use of a (portable) geometrical sun-dial, with a nocturnal on the backside, for the exact and ready finding the hour of the day and night: and other mathematical conclusions. Also of a universal-dial for the use of seamen or others. With the use of a sliding or glasiers-rule and Mr. White's rule for solid measure. / Collected and fitted to the meanest capacity by J. Browne. Brown, John, philomath.; Gaywood, Richard, fl. 1650-1680. 1667 (1667) Wing B5039D; ESTC R173095 73,644 256

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the_o true_a diameter_n of_o a_o round_a solid_a body_n at_o a_o inch_n further_o be_v 12_o set_v which_o i_o call_v small_a 12_o be_v in_o small_a figure_n again_o at_o 1_o foot_n 3_o inch_n better_o be_v another_o mark_n and_o right_a against_o it_o the_o word_n diameter_n for_o the_o diameter_n of_o a_o piece_n of_o timber_n according_a to_o the_o usual_a english_a allowance_n then_o again_o at_o 3_o foot_n 6_o inch_n ½_n near_o be_v t_n r_n for_o the_o true_a circumference_n of_o a_o round_a cillender_n
last_o at_o 4_o foot_n be_v the_o word_n round_o note_v the_o circumference_n according_a to_o the_o usual_a allowance_n who_o use_n follow_v note_v also_o if_o you_o put_v on_o the_o gage-point_n for_o ale_n or_o wine_n with_o the_o mean_a diameter_n and_o length_n you_o may_v gauge_v any_o wine_n or_o beer-vessel_n the_o wine_n at_o 17_o inch_n ¼_n the_o ale_n or_o beer_n at_o 18.95_o four_o the_o figure_n on_o the_o left_a side_n be_v not_o much_o unlike_o the_o right_n for_o 1_o at_o the_o beginning_n be_v one_o inch_n and_o so_o it_o proceed_v by_o quarter_n of_o inch_n to_o one_o foot_n then_o by_o figure_n at_o the_o foot_n and_o the_o division_n all_o whole_a inch_n to_o 10_o foot_n than_o every_o whole_a foot_n and_o half_a and_o quarter_n or_o 10_o to_o 100_o or_o 140_o or_o 150_o foot_n and_o this_o i_o call_v the_o left-side_n the_o other_o the_o right_a side_n so_o that_o from_o one_o inch_n at_o the_o low_a end_n to_o one_o foot_n every_o inch_n have_v a_o figure_n from_o one_o foot_n to_o 10_o foot_n every_o foot_n have_v a_o figure_n and_o from_o 10_o foot_n to_o a_o 100_o every_o 10_o foot_n only_o be_v figure_v i_o have_v be_v very_o plain_a in_o explain_v this_o because_o i_o will_v avoid_v vain_a repetition_n in_o the_o follow_a use_n wherein_o you_o shall_v have_v first_o the_o most_o ordinary_a and_o easy_a question_n and_o then_o the_o more_o hard_a and_o critical_a and_o less_o useful_a the_o use_v follow_v prob._n 1._o a_o piece_n of_o timber_n be_v not_o square_a to_o make_v it_o square_n set_a the_o breadth_n on_o the_o left_a side_n to_o the_o breadth_n on_o the_o right_n then_o right_o against_o the_o inch_n and_o quarter_n thick_o find_v on_o the_o left_a side_n on_o the_o right_n be_v the_o inch_n square_v require_v example_n at_o 18_o broad_a and_o 6_o thick_a you_o shall_v find_v 10_o inch_n ⅜_n the_o side_n of_o the_o square_n require_v for_o if_o you_o set_v 6_o inch_n against_o 6_o inch_n on_o the_o right_n and_o left-side_n then_o right_a against_o 18_o inch_n or_o 1_o foot_n 6_o inch_n on_o the_o left_a on_o the_o right_n you_o have_v 10_o inch_n 1_o quarter_n and_o half_a a_o quarter_n for_o the_o side_n of_o the_o square_a equal_a to_o 18_o one_o way_n and_z 6_o the_o other_o way_n prob._n 2._o the_o side_n of_o the_o square_n give_v to_o find_v how_o much_o make_v a_o foot_n for_o all_o piece_n between_o 3_o or_o 4_o inch_n and_o 42_o inch_n square_a which_o be_v the_o most_o usual_a this_o be_v the_o best_a way_n set_v the_o inch_n or_o foot_n and_o inch_n square_a find_v out_o on_o the_o rightside_n to_o one_o foot_n on_o the_o left_a then_o right_o against_o one_o foot_n on_o the_o right_n on_o the_o left_a be_v the_o inch_n or_o foot_n and_o inch_n require_v to_o make_v a_o foot_n of_o timber_n example_n at_o 8_o inch_n square_v set_v 8_o on_o the_o right_n to_z 1_o foot_n on_o the_o left_a then_o right_o against_o 1_o foot_n on_o the_o right_n on_o the_o left_a be_v 2_o foot_n 3_o inch_n the_o length_n require_v to_o find_v how_o much_o be_v in_o a_o foot_n long_o just_o as_o the_o rule_n stand_v even_o look_v for_o the_o inch_n the_o piece_n be_v square_a on_o the_o right_n and_o on_o the_o left_a be_v the_o inch_n or_o foot_n and_o inch_n require_v example_n at_o 17_o inch_n square_a there_o be_v 2_o foot_n of_o timber_n in_o one_o foot_n long_o which_o if_o you_o multiply_v by_o the_o length_n you_o shall_v have_v the_o true_a content_n a_o very_a good_a way_n for_o large_a piece_n and_o very_o exact_a prob._n 3._o the_o side_n of_o the_o square_a and_o length_n give_v to_o find_v the_o content_a for_o all_o piece_n between_o one_o inch_n or_o 8_o 12_o part_n of_o a_o foot_n and_o 100_o foot_n this_o be_v the_o easy_a way_n set_a the_o word_n square_a or_o 1_o foot_n to_o the_o length_n on_o the_o left_a then_o right_o against_o the_o inch_n or_o foot_n and_o inch_n square_a on_o the_o right_n on_o the_o leave_v you_o have_v the_o content_a example_n at_o 9_o inch_n square_a and_o 20_o foot_n long_o set_v the_o long_a stroke_n by_o the_o word_n square_v to_o 20_o foot_n on_o the_o left_a then_o right_o against_o 9_o inch_n on_o the_o right_a side_n on_o the_o left-side_n you_o have_v 11_o foot_n and_o a_o quarter_n the_o content_a require_v but_o if_o it_o be_v a_o very_a great_a piece_n as_o above_o 100_o foot_n then_o call_v one_o foot_n on_o the_o left_a side_n 10_o foot_n and_o 2_o foot_n 20._o etc._n etc._n then_o 10_o shall_v be_v 100_o and_o 100_o a_o 1000_o that_o will_v supply_v to_o 1500_o foot_n in_o a_o piece_n but_o if_o you_o will_v go_v to_o a_o big_a piece_n then_o call_v 2_o foot_n on_o the_o leave_v 200_o etc._n etc._n then_o you_o shall_v have_v it_o to_o 150000_o foot_n in_o a_o piece_n such_o as_o i_o never_o see_v but_o for_o all_o small_a piece_n under_o 3_o inch_n square_a and_o above_o 1_o quarter_n of_o a_o inch_n do_v thus_o set_v 12_o on_o the_o top_n or_o the_o small_a 12_o when_o it_o be_v most_o convenient_a to_o use_v to_o the_o length_n on_o the_o left-side_n then_o right_o against_o the_o inch_n or_o 12_o s._n of_o one_o inch_n square_n sound_v on_o the_o rightside_n on_o the_o left_a be_v the_o true_a content_a require_v example_n at_o 2_o inch_n 3_o twelve_o or_o 1_o quarter_n square_a and_o 10_o foot_n long_o you_o shall_v find_v 4_o inch_n and_o a_o quarter_n ferè_fw-la but_o note_v when_o you_o use_v the_o small_a 12_o the_o answer_n be_v give_v in_o decimal_n of_o a_o foot_n therefore_o the_o top_n 12_o be_v best_a prob._n 4._o the_o square_a of_o a_o small_a piece_n of_o timber_n give_v to_o find_v how_o much_o make_v a_o foot_n for_o all_o piece_n from_o 12_o inch_n to_o 1_o inch_n square_a do_v thus_o set_v the_o inch_n and_o 12_o s._n or_o quarter_v square_a count_v one_o foot_n on_o the_o right_a side_n for_o one_o inch_n and_o 2_o foot_n for_o 2_o inch_n etc._n etc._n find_v out_o on_o the_o rightside_n to_o 100_o on_o the_o left_a then_o right_a against_o the_o upper_a or_o small_a 12_o on_o the_o right_n on_o the_o left_a be_v the_o length_n require_v to_o make_v a_o foot_n of_o timber_n example_n at_o 2_o inch_n ¼_n square_a you_o must_v have_v 28_o foot_n 4_o inch_n to_o make_v a_o foot_n prob._n 5._o under_o 1_o inch_n square_a to_o find_v the_o length_n of_o a_o foot_n set_a 1_o foot_n 9_o inch_n 6_o inch_n or_o 3_o inch_n find_v on_o the_o rightside_n for_o one_o inch_n ¾_n ½_n or_o ¼_n of_o a_o inch_n against_o 10_o on_o the_o left-side_n count_v for_o 100_o then_o right_a against_o the_o small_a 12_o you_o have_v the_o foot_n in_o length_n require_v example_n at_o 1_o inch_n square_a you_o find_v 144_o foot_n at_o ¾_n square_v 256_o foot_n at_o ½_n a_o inch_n square_a 576_o foot_n at_o ¼_n or_o a_o inch_n square_a you_o find_v 2034_o foot_n in_o length_n to_o make_v one_o foot_n of_o timber_n or_o if_o you_o set_v the_o former_a number_n 12_o 9_o 6_o 1_o against_o 1_o inch_n on_o the_o left_a then_o right_o against_o the_o upper_a 12_o be_v a_o number_n which_o multiply_v by_o 12_o be_v the_o number_n of_o foot_n require_v prob._n 6._o a_o great_a piece_n above_o 3_o foot_n ½_n square_a to_o find_v the_o length_n of_o a_o foot_n set_a the_o foot_n and_o inch_n on_o the_o right_n to_o 100_o on_o the_o left_a then_o right_a against_o small_a 12_o be_v the_o inch_n and_o 12_o s_o or_o 12_o s_o of_o a_o 12_o that_o go_v to_o make_v a_o foot_n example_n at_o 4_o foot_n square_a you_o have_v 9_o 12th_n or_o ¾_n of_o a_o inch_n to_o make_v a_o foot_n of_o timber_n at_o 5_o foot_n square_a 5._o 12th_n and_o 10._o 12th_n of_o a_o 12_o to_o make_v a_o foot_n thus_o you_o see_v the_o rule_n as_o now_o contrive_v resolve_v from_o 1_o quarter_n square_a to_o 12_o foot_n square_a the_o content_a or_o quantity_n of_o a_o foot_n of_o timber_n in_o length_n at_o any_o squareness_n without_o pen_n or_o compass_n chap._n v._o for_o round_a timber_n prob._n 1._o the_o number_n of_o inch_n that_o a_o piece_n of_o timber_n be_v about_o be_v give_v to_o find_v how_o much_o make_v a_o foot_n first_o for_o all_o ordinary_a piece_n set_v one_o foot_n on_o the_o left_a to_o the_o inch_n or_o foot_n and_o inch_n above_o on_o the_o right_n then_o right_o against_o tr_z for_o true_a measure_n or_o round_o for_o the_o usual_a measure_n be_v the_o foot_n or_o foot_n and_o inch_n require_v to_o make_v a_o foot_n of_o timber_n at_o that_o circumference_n about_o example_n at_o 4_o inch_n about_o 113_o foot_n 2_o inch_n be_v