in_o yard_n of_o that_o pane_n which_o be_v almost_o 5_o yard_n a_o quarter_n and_o a_o half_a or_o rather_o 5_o yard_n and_o one_o three_o part_n of_o a_o yard_n problem_n v._o the_o breadth_n of_o any_o superficies_n be_v give_v in_o inch_n or_o foot_n to_o find_v how_o much_o in_o length_n will_v make_v a_o superficial_a foot_n the_o rule_n be_v thus_o as_o the_o breadth_n in_o inch_n to_o 144_o so_o be_v 1_o to_o the_o length_n in_o inch_n to_o make_v a_o foot_n example_n let_v the_o breadth_n give_v be_v 30_o inch_n and_o the_o length_n to_o make_v a_o foot_n at_o that_o breadth_n be_v require_v set_a 30_o on_o the_o first_o to_o 144_o on_o the_o second_o and_o then_o against_o 1_o on_o the_o first_o be_v 4,8_o on_o the_o second_o so_o much_o in_o length_n make_v a_o foot_n at_o 30_o inch_n broad_a but_o if_o the_o breadth_n be_v give_v in_o foot_n then_o as_o the_o breadth_n in_o foot_n be_v to_o 1_o so_o be_v 1_o to_o the_o length_n to_o make_v a_o foot_n therefore_o set_v 2,5_o on_o the_o first_o to_z 1_o on_o the_o second_o and_o then_o against_o 1_o on_o the_o first_o side_n be_v 4_o on_o the_o second_o which_o 4_o signify_v four_o ten_o part_n of_o a_o foot_n so_o much_o in_o length_n make_v a_o foot_n at_o that_o breadth_n problem_n vi_o the_o length_n and_o breadth_n of_o a_o plot_n of_o land_n be_v give_v in_o chain_n to_o find_v the_o content_a in_o acre_n have_v a_o chain_n of_o 4_o perch_n long_o divide_v into_o 100_o link_n that_o be_v 25_o in_o the_o perch_n measure_v the_o length_n and_o breadth_n of_o the_o land_n to_o be_v measure_v in_o chain_n and_o link_n and_o then_o cast_v up_o the_o content_a into_o acre_n thus_o as_o 10_o to_o the_o breadth_n in_o chain_n so_o be_v the_o length_n in_o chain_n to_o the_o content_a in_o acre_n example_n let_v the_o breadth_n give_v be_v 7_o chain_n 50_o link_n and_o the_o length_n 45_o chain_n 75_o link_n and_o the_o content_a in_o acre_n seek_v set_a 10_o on_o the_o first_o to_o 7,5_o on_o the_o second_o and_o then_o against_o 45,75_o on_o the_o first_o be_v 34,31_o on_o the_o second_o which_o be_v the_o content_a in_o acre_n of_o that_o plat_n of_o land_n or_o have_v the_o breadth_n be_v 15_o chain_n 25_o link_n and_o the_o breadth_n 22_o chain_n 50_o link_n then_o set_v 10_o or_o 1_o on_o the_o first_o to_o 15,5_o on_o the_o second_o and_o then_o against_o 22,50_o on_o the_o first_o be_v 34,31_o on_o the_o second_a the_o content_a in_o acre_n seek_v for_o which_o fraction_n 31_o above_o the_o 34_o acre_n contain_v 1_o rood_n 10_o perch_n so_o that_o the_o true_a content_n be_v 34_o acre_n 1_o rood_n and_o 10_o pole_n if_o the_o plot_n of_o land_n be_v of_o a_o triangle_n form_n or_o any_o other_o figure_n whatsoever_o the_o analogy_n be_v this_o as_o 10_o be_v to_o one_o of_o the_o two_o number_n of_o chain_n that_o be_v to_o be_v multiply_v together_o so_o be_v the_o other_o of_o they_o to_o the_o content_a in_o acre_n as_o if_o the_o half_a perpendicular_a of_o a_o triangle_n be_v 3,75_o chain_n and_o the_o base_a 45,75_o the_o content_a will_v be_v find_v to_o be_v 17,15_o acre_n for_o set_v 10_o on_o the_o first_o to_o 3,75_o on_o the_o second_o and_o then_o against_o 45_o 75_o on_o that_o first_o be_v 17,15_o the_o content_a or_o else_o have_v the_o whole_a base_a and_o whole_a perpendicular_a say_v thus_o as_o 20_o to_o the_o whole_a perpendicular_a 7,50_o so_o be_v the_o whole_a base_a 45,75_o to_o 17,15_o the_o content_a in_o acre_n as_o before_o for_o set_v 20_o on_o the_o first_o to_o 7,50_o on_o the_o second_o and_o then_o against_o 45,75_o on_o the_o first_o be_v 17,15_o on_o the_o second_o or_o if_o the_o base_a of_o a_o triangle_n be_v 36,83_o chain_n and_o the_o perpendicular_a 17,59_o chain_n the_o content_n will_v be_v find_v by_o either_o way_n of_o work_v to_o be_v 32,39_o which_o be_v 32_o acre_n 1_o rood_n 22_o perch_n problem_n vii_o the_o content_a of_o a_o piece_n of_o land_n be_v measure_v by_o one_o kind_n of_o perch_n to_o find_v the_o content_a thereof_o after_o another_o kind_n of_o perch_n these_o kind_n of_o proportion_n be_v wrought_v by_o the_o rule_n of_o three_o reverse_n after_o a_o duplicate_v proportion_n and_o the_o analogy_n be_v thus_o as_o the_o length_n of_o the_o second_o perch_n be_v to_o the_o length_n of_o the_o first_o perch_n so_o the_o content_a in_o acre_n give_v to_o a_o four_o number_n and_o so_o be_v that_o four_o number_n to_o a_o five_o number_n which_o be_v the_o content_n seek_v suppose_v a_o piece_n of_o land_n measure_v by_o the_o 16½_n foot-pole_n do_v contain_v 34,3_o acre_n and_o it_o be_v demand_v how_o much_o it_o will_v contain_v if_o it_o be_v measure_v by_o a_o 18_o foot-pole_n note_v that_o i_o call_v the_o 16½_n foot-perch_n the_o first_o perch_n because_o by_o it_o the_o land_n be_v measure_v and_o the_o 18_o foot-perch_n i_o call_v the_o second_o perch_n because_o according_a to_o it_o the_o content_n be_v seek_v for_o wherefore_o set_v the_o second_o perch_n 18_o on_o the_o first_o to_o 16,5_o on_o the_o second_o the_o perch_n first_o use_v and_o then_o against_o 34,3_o the_o content_a in_o acre_n give_v on_o the_o first_o be_v 31,45_o on_o the_o second_o and_o then_o against_o that_o 31,45_o on_o that_o first_o be_v 28,8_o on_o the_o second_o so_o much_o be_v the_o content_a in_o acre_n by_o the_o 18_o foot-pole_n which_o be_v demand_v in_o like_a manner_n be_v the_o content_a give_v 5_o acre_n 2_o rood_n 20_o pole_n or_o 5,62_o set_v 18_o on_o the_o first_o to_o 16,5_o on_o the_o second_o and_o then_o against_o 5,62_o on_o the_o first_o be_v 5,15_o on_o the_o second_o and_o last_o against_o that_o 5,15_o on_o that_o first_o be_v near_o about_o 4,7_o on_o the_o second_o so_o much_o be_v the_o content_a of_o that_o close_a by_o the_o 18_o foot-pole_n problem_n viii_o the_o one_o side_n of_o any_o piece_n of_o land_n be_v give_v to_o find_v how_o much_o in_o breadth_n the_o other_o way_n will_v make_v a_o acre_n of_o land_n let_v the_o side_n of_o a_o close_o be_v 20_o pole_n and_o it_o be_v require_v how_o much_o in_o breadth_n will_v make_v a_o acre_n of_o land_n at_o that_o length_n set_a the_o breadth_n give_v 20_o on_o the_o first_o to_o 160_o on_o the_o second_o and_o then_o against_o 1_o or_o 10_o on_o that_o first_o be_v 8_o on_o the_o second_o so_o much_o in_o breadth_n make_v a_o acre_n at_o 20_o pole_n long_o or_o if_o the_o side_n measure_v be_v 25_o than_o set_v 25_o to_o 160_o and_o against_o 1_o on_o that_o first_o be_v 6,4_o on_o the_o second_o the_o breadth_n seek_v for_o and_o if_o the_o length_n be_v 32_o pole_n the_o breadth_n to_o make_v a_o acre_n will_v be_v 5_o pole_n problem_n ix_o a_o plot_n of_o land_n be_v lay_v down_o and_o cast_v up_o by_o any_o scale_n to_o find_v how_o much_o it_o will_v contain_v by_o any_o other_o scale_n either_o great_a or_o lesser_a suppose_v a_o plot_n of_o land_n be_v lay_v down_o and_o cast_v up_o by_o a_o scale_n of_o 10_o in_o the_o inch_n do_v contain_v 28,5_o acre_n and_o it_o be_v require_v to_o know_v how_o many_o acre_n it_o will_v contain_v shall_v it_o be_v cast_v up_o by_o a_o scale_n of_o 12_o in_o the_o inch_n here_o because_o 12_o the_o scale_n to_o be_v use_v be_v lesser_a than_o 10_o the_o scale_n former_o use_v and_o so_o by_o consequence_n the_o content_a of_o the_o give_v plot_n by_o the_o scale_n of_o 12_o will_v be_v more_o acre_n than_o it_o be_v by_o the_o scale_n of_o 10_o in_o the_o inch_n therefore_o set_v the_o scale_n use_v 10_o on_o the_o first_o to_o the_o scale_n to_o be_v use_v 12_o on_o the_o second_o and_o then_o against_o the_o content_a know_v 28,5_o on_o the_o first_o be_v 34,2_o acre_n or_o near_o thereabouts_o on_o the_o second_o so_o much_o be_v the_o content_a by_o the_o scale_n of_o 12_o in_o the_o inch_n but_o if_o the_o plot_n have_v be_v lay_v down_o and_o cast_v up_o by_o a_o scale_n of_o 12_o and_o the_o content_a require_v by_o a_o scale_n of_o 10_o in_o the_o inch_n which_o be_v the_o great_a scale_n and_o therefore_o the_o content_n be_v the_o lesser_a then_o set_v 12_o on_o the_o first_o to_z 10_o on_o the_o second_o which_o do_v right_o against_o the_o content_a in_o acre_n by_o the_o scale_n of_o 12_o on_o the_o first_o be_v the_o content_a by_o the_o scale_n of_o 10_o on_o the_o second_o as_o if_o the_o content_a by_o the_o scale_n of_o 12_o be_v 34,2_o acre_n than_o the_o content_a by_o the_o scale_n of_o 10_o will_v be_v find_v to_o be_v 28,5_o acre_n near_o for_o
vi_o the_o rule_n of_o proportion_n inverse_v three_o number_n be_v give_v to_o find_v a_o four_o in_o a_o inversed_a proportion_n it_o be_v to_o be_v note_v in_o this_o inverse_n rule_n of_o proportion_n that_o if_o the_o three_o number_n be_v great_a than_o the_o first_o then_o will_v the_o four_o number_n be_v less_o than_o the_o second_o and_o contrariwise_o if_o the_o three_o number_n be_v less_o than_o the_o first_o than_o the_o four_o number_n be_v to_o be_v great_a than_o the_o second_o but_o in_o the_o rule_n of_o proportion_n direct_v if_o the_o second_o number_n or_o term_n be_v more_o than_o the_o first_o than_o the_o four_o term_n be_v also_o more_o than_o the_o three_o and_o if_o the_o second_o term_n be_v less_o than_o the_o first_o then_o be_v the_o four_o term_n less_o than_o the_o three_o this_o inverse_n rule_n may_v be_v wrought_v two_o way_n on_o our_o double_a line_n one_o way_n be_v thus_o set_v the_o first_o term_n on_o the_o first_o to_o the_o other_o term_n of_o the_o same_o denomination_n on_o the_o second_o and_o then_o against_o the_o other_o term_n of_o contrary_a denomination_n seek_v out_o on_o that_o second_o be_v the_o four_o number_n seek_v for_o on_o the_o first_o or_o else_o set_v the_o three_o term_n on_o the_o first_o to_o the_o first_o term_n on_o the_o second_o and_o then_o against_o the_o second_o term_n on_o the_o first_o be_v the_o answer_n on_o the_o second_o example_n 1._o if_o 60_o pioner_n can_v make_v a_o trench_n in_o 45_o hour_n in_o how_o long_a time_n can_v 40_o pioner_n make_v it_o set_a 40_o on_o the_o first_o to_o 60_o on_o the_o second_o the_o two_o number_n of_o the_o same_o denomination_n and_o then_o against_o 45_o on_o that_o first_o the_o number_n of_o contrary_a denomination_n be_v 67,5_o on_o the_o second_o which_o 67,5_o be_v the_o four_o term_n in_o reciprocal_a proportion_n to_o the_o other_o three_o and_o of_o the_o same_o denomination_n with_o 45_o viz._n hour_n and_o be_v the_o answer_n to_o the_o question_n demand_v show_v that_o 40_o man_n can_v do_v as_o much_o in_o 67,5_o hour_n as_o 60_o man_n can_v do_v in_o 45_o hour_n or_o set_v 60_o on_o the_o first_o to_o 40_o on_o the_o second_o and_o then_o against_o 45_o on_o that_o second_o be_v 67,5_o on_o the_o first_o another_o way_n be_v thus_o set_v 40_o the_o three_o term_n on_o the_o first_o to_o 45_o on_o the_o second_o which_o be_v the_o term_n of_o contrary_a denomination_n to_o the_o other_o two_o and_o then_o right_a against_o 60_o on_o the_o first_o which_o be_v the_o number_n of_o the_o same_o denomination_n with_o the_o 40_o be_v 67,5_o on_o the_o second_o the_o number_n seek_v thus_o one_o way_n of_o work_v prove_v the_o other_o example_n 2._o if_o 45_o man_n do_v a_o work_n in_o 30_o day_n in_o how_o many_o day_n will_v 270_o man_n do_v it_o set_a 270_o on_o the_o first_o to_o 45_o on_o the_o second_o and_o then_o against_o 30_o on_o the_o first_o be_v 5_o on_o the_o second_o or_o set_v 270_o on_o the_o first_o to_o 30_o on_o the_o second_o and_o then_o against_o 45_o on_o the_o first_o be_v 5_o on_o the_o second_o and_o therefore_o the_o four_o number_n seek_v for_o be_v 5_o show_v that_o 270_o man_n will_v do_v as_o much_o work_n in_o 5_o day_n as_o 45_o man_n can_v do_v in_o 30_o day_n this_o rule_n be_v prove_v by_o multiply_v together_o the_o first_o and_o second_o term_n and_o also_o the_o three_o and_o four_o and_o if_o the_o two_o product_n be_v equal_a the_o work_n be_v true_o wrought_v or_o else_o not_o by_o the_o line_n it_o be_v thus_o prove_v set_v 1_o on_o the_o first_o to_o 30_o on_o the_o second_o and_o then_o against_o 45_o on_o the_o first_o be_v 1350_o on_o the_o second_o this_o do_v set_v 1_o on_o the_o first_o to_o 5_o on_o the_o second_o and_o then_o against_o 270_o on_o the_o first_o be_v 1650_o on_o the_o second_o here_o both_o product_n be_v equal_a declare_v the_o work_n to_o be_v true_o wrought_v problem_n vii_o of_o duplicate_v proportion_n three_o number_n be_v give_v to_o find_v the_o four_o in_o a_o duplicate_v proportion_n this_o rule_n chief_o concern_v the_o proportion_n of_o line_n to_o superficies_n or_o of_o superficies_n to_o line_n 1_o of_o the_o proportion_n of_o line_n to_o superficies_n example_n 1._o if_o the_o diameter_n of_o a_o circle_n be_v 14_o inch_n and_o its_o content_a 154_o inch_n what_o will_v the_o content_a be_v of_o another_o circle_n that_o be_v 28_o inch_n in_o diameter_n set_a 14_o on_o the_o first_o to_o 28_o on_o the_o second_o they_o be_v the_o term_n of_o one_o denomination_n viz._n line_n and_o then_o against_o 154_o on_o the_o first_o the_o content_a of_o the_o circle_n give_v be_v 308_o on_o the_o second_o this_o 308_o seek_v on_o the_o first_o and_o against_o it_o on_o the_o second_o be_v 616_o which_o 616_o be_v the_o content_a of_o that_o other_o circle_n of_o 28_o inch_n diameter_n example_n 2._o let_v the_o diameter_n of_o one_o circle_n be_v 7_o foot_n and_o the_o area_n of_o it_o 38,5_o foot_n and_o let_v it_o be_v demand_v what_o the_o superficial_a area_n of_o another_o circle_n be_v who_o diameter_n be_v 18_o foot_n because_o 7_o and_o 18_o be_v term_n of_o one_o denomination_n viz._n line_n set_v 7_o the_o diameter_n of_o the_o the_o circle_n who_o content_a be_v know_v on_o the_o first_o to_o 18_o on_o the_o second_o be_v the_o diameter_n of_o the_o other_o circle_n who_o content_a be_v seek_v and_o then_o against_o 38,5_o the_o content_a know_v on_o the_o first_o be_v 99_o on_o the_o second_o and_o then_o seek_v this_o 99_o on_o the_o first_o and_o against_o it_o be_v 254,5_o ten_o on_o the_o second_o which_o be_v the_o superficial_a area_n or_o content_a in_o foot_n of_o that_o other_o circle_n which_o be_v demand_v example_n 3._o if_o a_o piece_n of_o land_n that_o be_v 20_o pole_n square_a be_v worth_a 30_o pound_n what_o be_v a_o piece_n of_o land_n of_o the_o same_o goodness_n worth_n that_o be_v 35_o pole_n square_a set_a 20_o on_o the_o first_o to_o 35_o on_o the_o second_o and_o then_o against_o 30_o on_o the_o first_o be_v 52,5_o on_o the_o second_o and_o last_o against_o 52,5_o on_o the_o first_o be_v 91,8_o on_o the_o second_o that_o be_v 91_o pound_n and_o eight_o ten_o of_o a_o pound_n or_o 16_o shilling_n so_o much_o be_v the_o worth_n of_o that_o piece_n of_o land_n of_o 35_o pole_n square_a example_n 4._o how_o many_o acre_n of_o land_n of_o our_o english_a measure_n of_o 16,5_o foot_n to_o the_o pole_n be_v contain_v in_o 30_o irish_a acre_n of_o 21_o foot_n to_o the_o pole_n place_n 16,5_o on_o the_o first_o to_o 21_o on_o the_o second_o and_o then_o against_o 30_o on_o the_o first_o be_v 38,2_o on_o the_o second_o and_o against_o 38,2_o on_o the_o first_o be_v 48,6_o on_o the_o second_o so_o many_o english_a acre_n be_v in_o 30_o irish_a acre_n 2_o of_o the_o proportion_n of_o superficies_n to_o line_n if_o the_o two_o term_n of_o like_a denomination_n be_v of_o superficial_a content_n and_o a_o diameter_n or_o a_o line_n seek_v for_o example_n let_v two_o circle_n be_v give_v the_o content_a of_o the_o one_o be_v 154_o and_o its_o diameter_n 14_o the_o area_n of_o the_o other_o circle_n be_v 616_o and_o its_o diameter_n be_v require_v set_a the_o area_n of_o the_o circle_n know_v viz._n 154_o on_o the_o first_o to_o its_o diameter_n 14_o on_o the_o second_o and_o then_o against_o 616_o on_o the_o first_o be_v 56_o on_o the_o second_o the_o half_a whereof_o viz._n 28_o be_v the_o diameter_n of_o that_o other_o circle_n who_o content_a be_v 616_o which_o 28_o be_v foot_n or_o inch_n or_o any_o other_o measure_n such_o as_o the_o diameter_n of_o the_o other_o circle_n be_v measure_v by_o problem_n viii_o of_o triplicate_v proportion_n three_o number_n be_v give_v to_o find_v a_o four_o in_o a_o triplicate_v proportion_n this_o rule_n concern_v the_o proportion_n betwixt_o line_n and_o solid_n example_n 1._o there_o be_v a_o bullet_n who_o diameter_n be_v 4_o inch_n weigh_v 9_o pound_n what_o will_v another_o bullet_n weigh_v who_o diameter_n be_v 8_o inch_n and_o of_o the_o same_o metal_n set_a 4_o on_o the_o first_o to_z 8_o on_o the_o second_o rhat_o be_v the_o one_o diameter_n to_o the_o other_o and_o then_o against_o 9_o on_o the_o first_o which_o be_v the_o weight_n of_o the_o bullet_n of_o 4_o inch_n diameter_n be_v 18_o on_o the_o second_o and_o against_o 18_o on_o the_o first_o be_v 36_o on_o the_o second_o and_o three_o against_o 36_o on_o the_o first_o be_v 72_o on_o the_o second_o this_o three_o sum_n find_v be_v the_o four_o proportional_a number_n which_o be_v
pay_v 224_o pound_n be_v 16_o which_o be_v 16_o pound_n so_o much_o be_v the_o yearly_a rent_n seek_v a_o man_n borrow_v 666_o pound_n 13_o shilling_n and_o 4_o penny_n for_o 2_o year_n and_o covenant_v that_o he_o will_v repay_v at_o the_o 12_o year_n end_n 1333_o pound_n 6_o shilling_n and_o 8_o penny_n it_o be_v desire_v to_o know_v after_o what_o rate_n of_o interest_n by_o the_o 100_o he_o pay_v for_o his_o money_n borrow_v set_a 1333â—_n on_o the_o first_o the_o sum_n of_o money_n to_o be_v pay_v to_o 666â—_n on_o the_o second_o the_o sum_n lend_v and_o then_o against_o 12_o on_o the_o second_o the_o term_n of_o year_n it_o be_v lend_v be_v 5,95_o which_o be_v 5_o pound_n 19_o shilling_n so_o much_o by_o the_o 100_o do_v he_o pay_v for_o the_o money_n lend_v a_o sum_n of_o money_n be_v due_a at_o a_o certain_a time_n to_o come_v to_o find_v what_o it_o be_v worth_a in_o present_a money_n to_o take_v in_o there_o be_v 402_o pound_n 2_o shilling_n due_a at_o the_o end_n of_o 5_o year_n to_o come_v i_o will_v know_v what_o it_o be_v worth_a in_o ready_a money_n abate_v interest_n for_o the_o money_n receive_v in_o before_o due_a after_o the_o rate_n of_o 8_o in_o the_o 100_o first_o set_v 108_o on_o the_o first_o to_o 100_o on_o the_o second_o and_o then_o against_o 402,1_o on_o the_o first_o be_v 37,1_o on_o the_o second_o second_o against_o 37,1_o on_o the_o first_o be_v 34,46_o on_o the_o second_o three_o against_o 34,46_o on_o the_o first_o be_v 31,95_o on_o the_o second_o four_o against_o 31,95_o on_o the_o first_o be_v 29,71_o on_o the_o second_o five_o against_o 29,71_o on_o the_o first_o be_v 373_o on_o the_o second_o so_o much_o namely_o 373_o pound_n may_v be_v receive_v in_o present_a money_n for_o the_o 402_o pound_n and_o 2_o shilling_n due_a five_o year_n hence_o as_o be_v the_o present_a worth_n thereof_o here_o take_v notice_n that_o as_o the_o principal_a and_o interest_n of_o money_n forbear_v for_o many_o year_n increase_v in_o a_o proportion_n direct_v so_o in_o this_o case_n where_o money_n be_v pay_v many_o year_n before_o due_a it_o decrease_v in_o the_o like_a proportion_n chap._n iii_o the_o use_n of_o the_o double_a scale_n of_o number_n in_o superficial_a measure_n as_o board_n glass_n land_n and_o the_o like_a problem_n i._o the_o length_n and_o breadth_n of_o any_o square_n or_o long_o square_a superficies_n be_v give_v to_o find_v the_o content_a thereof_o if_o the_o length_n and_o breadth_n be_v give_v in_o inch_n then_o as_o 1_o to_o the_o breadth_n in_o inch_n so_o be_v the_o length_n in_o inch_n to_o the_o content_a in_o inch_n example_n let_v a_o plain_a superficies_n as_o a_o board_n or_o plank_n be_v give_v to_o be_v measure_v the_o breadth_n be_v find_v 30_o inch_n and_o its_o length_n 183_o and_o the_o content_v require_v set_a 1_o on_o the_o first_o to_o 30_o on_o the_o second_o and_o then_o against_o 183_o on_o the_o first_o be_v 5490_o the_o content_a seek_v in_o inch_n if_o the_o superficies_n give_v be_v a_o piece_n of_o land_n 30_o perch_n broad_a and_o 183_o long_a the_o content_a be_v 5490_o perch_n again_o let_v a_o piece_n of_o wainscot_n be_v 2,5_o foot_n in_o breadth_n and_o 15,25_o foot_n in_o length_n the_o content_a will_v be_v find_v 38,12_o foot_n for_o set_v 1_o on_o the_o first_o to_o 2,5_o on_o the_o second_o and_o then_o against_o 15,25_o on_o the_o first_o be_v 38,12_o foot_n the_o content_a seek_v problem_n ii_o the_o breadth_n and_o length_n of_o any_o superficies_n be_v give_v in_o one_o kind_n of_o measure_n to_o find_v the_o content_a in_o another_o kind_n of_o measure_n let_v the_o length_n and_o breadth_n be_v give_v in_o inch_n and_o the_o content_v require_v in_o foot_n the_o rule_n be_v thus_o as_o 144_o to_o the_o breadth_n in_o inch_n so_o be_v the_o length_n in_o inch_n to_o the_o content_a in_o foot_n example_n let_v the_o breadth_n be_v 30_o inch_n and_o the_o length_n 183_o inch_n and_o the_o content_a in_o foot_n require_v in_o this_o case_n because_o 144_o inch_n make_v a_o foot_n of_o superficial_a measure_n set_v 144_o on_o the_o first_o to_o 30_o the_o breadth_n on_o the_o second_o and_o then_o against_o 183_o the_o length_n on_o that_o first_o be_v 38_o foot_n and_o a_o fraction_n of_o a_o foot_n be_v a_o little_a more_o than_o one_o ten_o part_n of_o a_o foot_n so_o many_o foot_n be_v in_o that_o board_n or_o what_o other_o platform_n it_o be_v that_o be_v give_v to_o be_v so_o measure_v if_o the_o platform_n be_v a_o piece_n of_o land_n 30_o perch_n broad_a and_o 183_o perch_n long_o than_o the_o analogy_n be_v thus_o as_o 160_o the_o perch_n make_v a_o acre_n to_o the_o breadth_n in_o perch_n so_o be_v the_o length_n in_o perch_n to_o the_o content_a in_o acre_n and_o therefore_o in_o this_o case_n of_o land_n measure_n set_v 160_o on_o the_o first_o to_o 30_o the_o breadth_n on_o the_o second_o and_o then_o against_o 183_o the_o length_n on_o that_o first_o be_v 34,31_o on_o the_o second_o so_o many_o acre_n of_o land_n be_v contain_v in_o that_o ground_n if_o the_o place_n who_o content_a be_v to_o be_v cast_v up_o be_v a_o triangle_n a_o trapezia_n or_o of_o any_o other_o form_n whatsoever_o the_o analogy_n in_o general_n be_v this_o as_o 144_o or_o 160_o etc._n etc._n be_v to_o one_o of_o the_o number_n give_v to_o be_v multiply_v together_o so_o be_v the_o other_o of_o they_o to_o the_o content_a in_o foot_n or_o acre_n etc._n etc._n there_o be_v a_o piece_n of_o wainscot_n that_o be_v 3,5_o foot_n broad_a and_o 21_o foot_n long_o how_o many_o yard_n be_v in_o it_o see_v that_o in_o a_o yard_n be_v contain_v 9_o foot_n therefore_o set_v 9_o on_o the_o first_o to_o 3,5_o on_o the_o second_o and_o then_o against_o 21_o on_o the_o first_o be_v 8,16_o on_o the_o second_o so_o many_o yard_n be_v in_o that_o piece_n problem_n iii_o the_o breadth_n of_o a_o superficies_n be_v give_v in_o one_o kind_n of_o measure_n and_o the_o length_n in_o another_o to_o find_v the_o content_a in_o the_o great_a measure_n let_v the_o breadth_n of_o a_o superficies_n give_v be_v in_o inch_n and_o the_o length_n in_o foot_n and_o the_o content_a in_o foot_n require_v here_o the_o analogy_n be_v as_o 12_o to_o the_o breadth_n in_o inch_n so_o the_o length_n in_o foot_n to_o the_o content_a in_o foot_n so_o that_o if_o the_o breadth_n be_v 30_o inch_n and_o the_o length_n 15,25_o foot_n the_o content_a will_v be_v 38,12_o foot_n for_o set_v 12_o on_o the_o first_o to_o 30_o on_o the_o second_o and_o then_o against_o 15,25_o on_o the_o first_o be_v 38,12_o on_o the_o second_o be_v the_o content_a seek_v for_o or_o else_o set_v 12_o to_o 15,25_o and_o then_o against_o 30_o on_o that_o first_o be_v 38,12_o on_o the_o second_o by_o this_o rule_n also_o if_o the_o breadth_n of_o a_o plot_n of_o land_n be_v give_v in_o perch_n and_o the_o length_n in_o chain_n be_v measure_v by_o a_o chain_n of_o 4_o perch_n long_o the_o content_a in_o acre_n be_v ready_o have_v example_n let_v a_o piece_n of_o land_n be_v in_o breadth_n 30_o perch_n and_o in_o length_n 15,25_o chain_n measure_v by_o a_o chain_n of_o 4_o perch_n in_o length_n in_o this_o case_n the_o analogy_n be_v thus_o as_o 4_o be_v to_o the_o breadth_n in_o pole_n so_o be_v the_o length_n in_o chain_n to_o the_o content_a in_o acre_n therefore_o set_v 4_o to_o 30_o and_o then_o against_o 15,25_o on_o that_o first_o side_n whereon_o the_o 4_o be_v you_o shall_v have_v 11,4_o on_o the_o second_o side_n so_o much_o be_v the_o content_a in_o acre_n of_o that_o piece_n of_o land_n again_o let_v a_o piece_n of_o land_n be_v 36_o pole_n broad_a and_o the_o length_n 23_o chain_n and_o a_o half_a to_o find_v the_o content_a set_a 4_o on_o the_o first_o to_o 36_o on_o the_o second_o and_o then_o against_o 23,5_o on_o that_o first_o be_v 21,1_o and_o better_o on_o the_o second_o the_o content_a seek_v problem_n iu._n the_o length_n and_o breadth_n of_o a_o superficies_n be_v give_v in_o foot_n to_o find_v the_o content_a in_o yard_n take_v this_o for_o a_o general_a rule_n as_o 9_o be_v to_o the_o breadth_n in_o foot_n so_o be_v the_o length_n in_o foot_n to_o the_o content_a in_o yard_n example_n let_v the_o breadth_n of_o a_o pane_n of_o wainscot_n be_v 4_o foot_n and_o the_o length_n 12_o foot_n and_o the_o content_a in_o yard_n be_v seek_v for_o here_o be_v no_o more_o to_o be_v do_v but_o to_o set_v 9_o on_o the_o first_o to_z 4_o on_o the_o second_o and_o then_o against_o 12_o on_o the_o first_o be_v 5,35_o on_o the_o second_o the_o content_a
so_o express_v be_v all_o decimal_n fraction_n who_o denominator_fw-la be_v a_o unite_v with_o so_o many_o cipher_n as_o there_o be_v fraction_n figure_n as_o the_o denominator_fw-la of_o the_o fraction_n figure_n of_o the_o 75_o belong_v to_o the_o whole_a number_n 46_o be_v 100_o be_v a_o unite_v with_o two_o cypher_n because_o two_o figure_n and_o the_o denominator_fw-la to_o 5_o be_v 10_o be_v a_o unite_v with_o one_o cypher_n because_o but_o one_o figure_n and_o when_o a_o fraction_n be_v to_o be_v express_v alone_o without_o a_o whole_a number_n than_o the_o numerator_n be_v first_o express_v and_o after_o it_o the_o denominator_fw-la right_o on_o in_o the_o line_n with_o a_o comma_n betwixt_o as_o 75_o 100_o and_o 5_o 10_o be_v thus_o express_v 75,100_o 5,10_o and_o so_o of_o other_o the_o like_a problem_n iv_o of_o continual_a proportional_n two_o number_n be_v give_v to_o find_v a_o three_o a_o four_o a_o five_o or_o many_o number_n in_o continual_a proportion_n geometrical_a to_o they_o two_o example_n let_v the_o two_o number_n give_v be_v 2_o and_o 4_o and_o it_o be_v require_v to_o find_v several_a number_n in_o continual_a geometrical_a proportion_n to_o they_o two_o set_a 2_o on_o the_o first_o to_z 4_o on_o the_o second_o and_o then_o against_o 4_o on_o that_o first_o be_v 8_o on_o the_o second_o which_o be_v the_o three_o number_n in_o continual_a proportion_n geometrical_a to_o they_o two_o and_o then_o against_o 8_o on_o the_o first_o be_v 16_o on_o the_o second_o which_o 16_o be_v the_o four_o number_n in_o continual_a proportion_n to_o they_o two_o and_o against_o 16_o on_o the_o first_o be_v 32_o on_o the_o second_o the_o five_o continual_a proportional_a and_o against_o 32_o on_o the_o first_o be_v 64_o on_o the_o second_o the_o six_o continual_a proportional_a and_o against_o 64_o on_o the_o first_o be_v 128_o on_o the_o second_o the_o seven_o continual_a proportional_a and_o against_o 128_o on_o the_o first_o be_v 256_o on_o the_o second_o which_o be_v the_o eight_o proportional_a to_o the_o two_o propose_a number_n wherefore_o 8_o 16_o 32_o 64_o 128_o and_o 256_o be_v a_o rank_n of_o number_n in_o continual_a geometrical_a proportion_n to_o 2_o and_o 4_o the_o thing_n that_o be_v require_v example_n 2._o let_v it_o be_v require_v to_o find_v a_o rank_n of_o number_n in_o continual_a proportion_n as_o 2_o to_o 3._o here_o set_v 2_o on_o the_o first_o to_o 3_o on_o the_o second_o and_o then_o without_o move_v the_o instrument_n against_o 3_o on_o the_o first_o you_o have_v 4,5_o on_o the_o second_o and_o against_o the_o same_o 4,5_o find_v on_o the_o first_o be_v 6,75_o on_o the_o second_o and_o against_o 6,75_o on_o the_o first_o be_v 10,125_o on_o the_o second_o therefore_o 4,5_o 6,75_o and_o 10,125_o be_v a_o rank_n of_o number_n in_o continual_a proportion_n to_o 2_o and_o 3_o as_o be_v require_v if_o it_o be_v require_v to_o find_v such_o a_o rank_n of_o proportional_n to_o the_o number_n 2_o and_o 4_o which_o may_v bear_v the_o same_o proportion_n to_o one_o another_o as_o 2_o bears_z to_z 4_o set_v 4_o to_o 2_o and_o then_o against_o 2_o on_o that_o first_o side_n whereon_o the_o 4_o be_v you_o have_v 1_o on_o the_o second_o side_n which_o be_v the_o three_o proportional_a to_o 4_o and_o 2_o bearing_z the_o same_o proportion_n to_o 2_o as_o 2_o do_v to_o 4._o and_o against_o 1_o on_o the_o first_o be_v 5,10_o on_o the_o second_o the_o four_o proportional_a and_o against_o 5,10_o on_o the_o first_o be_v 25,100_o on_o the_o second_o which_o be_v the_o five_o number_n in_o continual_a proportion_n inverse_v or_o backward_o if_o the_o two_o number_n give_v be_v 10_o and_o 9_o and_o a_o rank_n of_o number_n to_o they_o in_o a_o inverse_n proportion_n geometrical_a be_v require_v set_v 10_o on_o the_o first_o to_z 9_o on_o the_o second_o and_o then_o against_o 9_o on_o the_o first_o be_v 8,1_o on_o the_o second_o which_o be_v the_o three_o proportional_a and_o then_o against_o 8,1_o be_v 7,29_o the_o four_o proportional_a wherefore_o 10,9_o 8,1_o and_o 7,29_o be_v number_n in_o a_o continual_a proportion_n but_o if_o the_o number_n give_v be_v 1_o and_o 9_o and_o a_o three_o and_o four_o number_n in_o proportion_n to_o they_o as_o 9_o be_v to_o 1_o be_v require_v then_o must_v the_o number_n find_v be_v account_v 81_o and_o 729_o they_o be_v the_o three_o and_o four_o number_n in_o a_o geometrical_a proportion_n to_o 1_o and_o 9_o in_o like_a manner_n if_o the_o two_o number_n give_v be_v 10_o and_o 12_o then_o if_o you_o set_v 10_o to_o 12_o you_o shall_v see_v on_o the_o first_o against_o 12_o 14,4_o which_o be_v the_o three_o proportional_a and_o against_o 14,4_o on_o the_o first_o be_v 17,28_o on_o the_o second_o which_o be_v the_o four_o proportional_a but_o have_v the_o two_o number_n give_v be_v 1_o and_o 12_o then_o bring_v 1_o on_o the_o first_o to_z 12_o on_o the_o second_o and_o you_o shall_v have_v against_o 13_o on_o the_o first_o 144_o on_o the_o second_o for_o the_o three_o proportional_a and_o the_o four_o will_v be_v 1728_o and_o so_o of_o all_o other_o problem_n v._o of_o the_o rule_n of_o proportion_n direct_v three_o number_n be_v give_v to_o find_v a_o four_o the_o analogy_n stand_v thus_o as_o the_o first_o number_n be_v to_o the_o second_o so_o be_v the_o three_o number_n to_o a_o four_o therefore_o work_v thus_o set_v the_o first_o number_n in_o the_o proportion_n on_o the_o first_o side_n to_o the_o second_o number_n in_o the_o proportion_n on_o the_o second_o side_n and_o then_o against_o the_o three_o number_n on_o the_o first_o be_v the_o four_o number_n seek_v for_o on_o the_o second_o example_n 1._o let_v the_o diameter_n of_o a_o know_a circle_n be_v 7_o and_o its_o circumference_n 22_o and_o it_o be_v require_v to_o know_v what_o the_o circumference_n of_o another_o circle_n be_v who_o diameter_n be_v 14._o to_o resolve_v this_o quaere_fw-la set_v 7_o on_o the_o first_o to_o 22_o on_o the_o second_o and_o then_o against_o 14_o the_o diameter_n of_o the_o other_o circle_n find_v on_o the_o first_o be_v 44_o on_o the_o second_o this_o 44_o be_v the_o circumference_n of_o that_o other_o circle_n who_o diameter_n be_v 14._o example_n 2._o if_o 45_o yard_n of_o stuff_n cost_v 30_o pound_n what_o will_v 84_o yard_n of_o it_o cost_n set_a 45_o the_o first_o number_n in_o the_o rule_n on_o the_o first_o to_o 30_o the_o second_o number_n on_o the_o second_o and_o then_o against_o 84_o the_o three_o number_n in_o the_o rule_n on_o the_o first_o be_v 56_o on_o the_o second_o which_o 56_o be_v the_o four_o number_n and_o show_v that_o 84_o yard_n will_v cost_v 56_o pound_n or_o if_o 45_o acre_n of_o land_n be_v worth_a 30_o pound_n a_o year_n what_o will_v 84_o acre_n be_v worth_a by_o the_o year_n the_o answer_n be_v as_o before_o 56_o pound_n and_o if_o 26_o of_o any_o thing_n give_v 64_o what_o will_v 36_o of_o the_o same_o give_v set_a 26_o to_o 64_o and_o then_o against_o 36_o on_o the_o first_o be_v 88,615_o the_o answer_n to_o the_o question_n demand_v on_o the_o second_o note_v that_o general_o in_o the_o rule_n of_o direct_a proportion_n if_o the_o three_o number_n be_v great_a than_o the_o first_o then_o will_v the_o four_o number_n be_v great_a than_o the_o second_o but_o if_o the_o three_o number_n be_v less_o than_o the_o first_o than_o the_o four_o number_n will_v be_v less_o than_o the_o second_o example_n 3._o if_o the_o circumference_n of_o a_o circle_n be_v 22_o and_o its_o diameter_n 7_o what_o will_v the_o diameter_n of_o another_o circle_n who_o circumference_n be_v 44_o here_o set_v 22_o on_o the_o first_o to_z 7_o on_o the_o second_o and_o then_o against_o 44_o on_o the_o first_o be_v 14_o on_o the_o second_o which_o 14_o be_v the_o diameter_n of_o that_o circle_n who_o circumference_n be_v 44_o be_v their_o measure_n take_v in_o inch_n foot_n or_o any_o other_o measure_n whatsoever_o to_o make_v proof_n of_o the_o work_n whether_o true_o wrought_v or_o not_o multiply_v the_o first_o term_n in_o the_o rule_n and_o the_o four_o term_n new_o find_v the_o one_o by_o the_o other_o and_o likewise_o the_o second_o and_o three_o term_n and_o if_o the_o two_o product_n be_v equal_a the_o work_n be_v true_o wrought_v or_o else_o not_o to_o prove_v the_o last_o question_n by_o the_o line_n set_v 1_o on_o the_o first_o to_o 22_o on_o the_o second_o and_o then_o against_o 14_o on_o the_o first_o be_v 308_o on_o the_o second_o next_o set_v 1_o to_o 7_o and_o then_o against_o 44_o on_o that_o first_o be_v 308_o on_o the_o second_o here_o both_o product_n be_v equal_a prove_v the_o work_n to_o be_v true_o wrought_v problem_n
length_n know_v it_o be_v require_v to_o make_v another_o pentagonal_a fort_n who_o quantity_n or_o content_a in_o land_n shall_v be_v the_o just_a four_o part_n of_o the_o propose_v pentagonal_a fort_n propound_v where_o note_n that_o the_o half_a of_o the_o side_n and_o line_n of_o the_o fort_n make_v will_v make_v another_o fort_n that_o will_v contain_v the_o four_o part_n of_o the_o ground_n in_o that_o fort_n make_v and_o that_o you_o may_v ready_o have_v half_a of_o all_o the_o line_n of_o the_o fort_n make_v do_v thus_o set_v 2_o on_o the_o first_o to_z 1_o on_o the_o second_o and_o then_o against_o the_o number_n of_o any_o line_n on_o the_o first_o be_v its_o half_a on_o the_o second_o as_o against_o 662_o the_o length_n of_o the_o side_n of_o the_o pentagon_n give_v be_v 331_o the_o length_n of_o the_o pentagons_n side_n to_o be_v make_v the_o line_n thus_o remain_v without_o any_o move_a against_o 119_o on_o the_o first_o the_o length_n of_o the_o gorge-line_n in_o the_o 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first_o be_v its_o match-line_n in_o the_o fort_n to_o be_v make_v as_o against_o dn_n the_o curtain_n in_o the_o make_a fort_n 424_o yard_n be_v 565â—_n so_o many_o yard_n will_v the_o curtain_n be_v in_o that_o fort_n to_o be_v make_v and_o so_o of_o all_o other_o line_n and_o if_o a_o fort_n be_v to_o be_v make_v who_o side_n and_o line_n must_v be_v half_a so_o much_o more_o in_o length_n as_o be_v the_o side_n and_o line_n of_o the_o propose_a fort_n then_o take_v the_o half_a of_o any_o number_n and_o add_v it_o to_o the_o same_o number_n and_o so_o proceed_v as_o before_o note_v that_o the_o line_n in_o the_o type_n or_o diagram_n annex_v may_v be_v account_v in_o their_o length_n there_o set_v down_o either_o so_o many_o foot_n or_o so_o many_o yard_n or_o so_o many_o perch_n or_o what_o other_o measure_n you_o be_v to_o use_v and_o so_o the_o side_n of_o the_o pentagon_n 662_o may_v be_v account_v 662_o yard_n or_o 662_o foot_n or_o 662_o perch_n thus_o by_o suppose_v a_o 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