the_o sum_n will_v be_v also_o 6._o and_o further_o whensoever_o the_o erronr_n be_v one_o +_o the_o other_o â_o though_o they_o be_v not_o equal_a yet_o than_o if_o the_o difference_n between_o the_o position_n be_v part_v into_o two_o part_n which_o be_v in_o proportion_n one_o to_o another_o as_o the_o two_o error_n be_v one_o to_o another_o respective_o then_o if_o the_o first_o part_n be_v take_v from_o the_o first_o position_n if_o that_o be_v the_o great_a or_o add_v to_o it_o if_o it_o be_v the_o less_o the_o same_o number_n require_v be_v thereby_o have_v as_o let_v the_o last_o question_n be_v resume_v and_o let_v the_o first_o position_n for_o a_o be_v 15_o then_o the_o first_o error_n will_v be_v â_o 18_o then_o let_v the_o second_o position_n be_v 3_o and_o so_o the_o second_o error_n will_v be_v +6_o and_o the_o difference_n of_o position_n be_v 12_o which_o divide_v into_o two_o part_n 9_o and_o 3_o which_o have_v that_o proportion_n one_o to_o another_o as_o have_v the_o error_n 18_o and_o 6_o then_o if_o the_o first_o part_n 9_o be_v take_v from_o the_o first_o position_n 15_o there_o remain_v the_o true_a number_n 6._o or_o else_o if_o the_o second_o part_n 3_o be_v add_v to_o the_o second_o position_n 3_o thereby_o also_o be_v make_v the_o true_a number_n 6._o the_o way_n of_o part_v 12_o or_o any_o other_o into_o two_o part_n proportional_a with_o the_o error_n be_v easy_o do_v by_o the_o golden_a rule_n thus_o as_o the_o sum_n of_o the_o error_n 24_o be_v to_o the_o difference_n of_o position_n 12_o so_o be_v the_o great_a error_n 18_o to_o the_o great_a part_n require_v namely_o 9_o many_o other_o question_n be_v in_o other_o book_n exemplify_v and_o wrought_v by_o this_o rule_n but_o see_v i_o intend_v not_o to_o write_v a_o great_a book_n and_o also_o because_o some_o of_o those_o question_n may_v be_v easy_o resolve_v without_o this_o rule_n i_o will_v add_v no_o more_o ondy_a mention_n one_o of_o those_o question_n i_o there_o be_v a_o cistern_n with_o 4_o cock_n which_o holl_v 8_o barrel_n of_o water_n and_o the_o first_o cock_n will_v runit_v all_o out_o in_o 6_o hour_n the_o second_o in_o 4_o the_o three_o in_o 3_o and_o the_o last_o in_o 2_o hour_n in_o what_o time_n shall_v all_o of_o they_o run_v it_o out_o if_o the_o first_o in_o 6_o hour_n run_v 8_o the_o second_o in_o the_o same_o time_n will_v âun_v 12_o the_o three_o 16_o the_o last_o 24_o in_o all_o 60_o then_o say_v if_o 60_o require_v 6â_n what_o 8_o the_o answer_n 48_o 60_o that_o be_v 4_o 5_o oâ_n a_o hour_n in_o which_o time_n all_o the_o 4_o cock_n together_o will_v run_v out_o all_o the_o 8_o barrel_n of_o water_n the_o rule_n of_o ceres_n and_o virginum_fw-la this_o be_v the_o most_o uncertain_a and_o unnecessary_a rule_n in_o arithmetic_n be_v seldom_o use_v except_o in_o sport_v question_n to_o puzzle_v young_a beginner_n with_o easy_a problem_n such_o as_o follow_v question_v 1_o a_o caterer_n buy_v 8_o bird_n of_o two_o sort_n as_o goose_n and_o hen_n for_o 20_o s._n the_o goose_n cost_v 4_o s._n a_o piece_n the_o hen_n 2_o s._n a_o piece_n how_o many_o do_v he_o buy_v of_o each_o sort_n this_o may_v be_v do_v by_o the_o rule_n of_o false_a and_o also_o thus_o multiply_v the_o whole_a number_n 8_o into_o the_o least_o price_n 2_o it_o produce_v 16_o which_o take_v from_o the_o whole_a price_n 20_o rest_v 4_o for_o a_o dividend_n which_o divide_v by_o 2_o which_o be_v the_o difference_n of_o the_o particular_a price_n the_o quotient_n be_v 2_o for_o the_o number_n of_o goose_n and_o 6_o must_v be_v for_o the_o hen_n the_o proof_n be_v easy_a question_n 2._o if_o 21_o person_n man_n woman_n and_o child_n spend_v 26_o shilling_n so_o that_o every_o man_n pay_v 2_o s._n every_o woman_n 1_o s._n every_o child_n 6_o d._n how_o many_o be_v there_o of_o each_o sort_n the_o rule_n multiply_v the_o number_n of_o person_n by_o the_o least_o expense_n and_o take_v the_o product_n of_o it_o from_o the_o whole_a expense_n the_o rest_n shall_v be_v the_o dividend_n which_o divide_v by_o the_o difference_n betwixt_o the_o great_a and_o least_o particular_a expense_n the_o quotient_n be_v a_o number_n which_o the_o number_n of_o man_n or_o they_o which_o spend_v most_o come_v near_o to_o but_o can_v exceed_v or_o of_o the_o say_a dividend_n be_v divide_v by_o the_o sum_n of_o the_o great_a and_o least_o expense_n the_o quotient_n be_v a_o number_n then_o which_o the_o number_n of_o man_n or_o those_o which_o spend_v most_o can_v be_v much_o less_o so_o here_o 21_o multiply_v by_o 6_o d._n that_o be_v by_o ½_n the_o product_n be_v 10½_n which_o take_v from_o 26_o rest_v 15½_n for_o the_o dividend_n and_o then_o take_v ½_n from_o 2_o rest_v 1½_n for_o the_o divisor_n and_o the_o quotient_n be_v 3â
_n which_o be_v something_o more_o than_o 10_o the_o number_n of_o man_n therefore_o must_v be_v but_o 9_o then_o turn_v the_o dividend_n and_o the_o divisor_n both_o into_o whole_a number_n by_o multiply_v they_o by_o the_o common_a denominator_fw-la 2_o so_o they_o reduce_v will_v be_v 31_o and_o 3_o as_o before_o be_v to_o be_v see_v in_o the_o quotient_a multiply_v the_o divisor_n 3_o by_z 9_o which_o be_v the_o number_n of_o man_n the_o product_n be_v 27_o which_o take_v from_o 31_o which_o be_v the_o reduce_v dividend_n the_o remain_n be_v 4_o for_o the_o number_n of_o woman_n and_o the_o child_n must_v be_v 8._o example_n 1._o 9_o man_n at_o 2_o s._n each_o 18_o s._n 4_o woman_n at_o 1_o s._n each_o 4_o 8_o child_n at_o 6_o d._n each_o 4_o in_o all_o 21_o in_o all_o 26_o but_o the_o number_n of_o man_n may_v be_v also_o 8_o which_o multiply_v by_o the_o reduce_v divisor_n 3_o product_n be_v 24_o which_o take_v from_o 31_o the_o remain_n be_v 7_o for_o the_o woman_n and_o then_o the_o child_n must_v be_v 6._o example_n 2._o 8_o man_n at_o 2_o s._n each_o 16_o 7_o woman_n at_o 1_o s._n each_o 7_o 6_o child_n at_o 6_o d._n each_o 3_o in_o all_o 21_o in_o all_o 26_o or_o the_o number_n of_o man_n may_v be_v 7_o which_o multiply_v by_o 3_o produce_v 21_o which_o take_v from_o 31_o remain_v 10_o for_o the_o woman_n and_o 4_o child_n example_n 3._o 7_o man_n at_o 2_o s._n each_o 14_o s._n 10_o woman_n at_o 1_o s._n each_o 10_o 4_o child_n at_o 6_o d._n each_o 2_o in_o all_o 21_o in_o all_o 26_o so_o here_o be_v already_o see_v 3_o various_a solution_n of_o this_o question_n which_o make_v this_o rule_n the_o less_o to_o be_v regard_v but_o further_a the_o number_n of_o man_n may_v be_v 10_o and_o not_o more_o for_o if_o you_o put_v they_o 11_o that_o multiply_v by_o 3_o produce_v 33_o which_o be_v great_a than_o 31_o from_o which_o it_o shall_v be_v take_v but_o i_o say_v it_o may_v be_v 10_o and_o then_o there_o be_v only_o one_o woman_n and_z 5_o child_n this_o confirm_v the_o former_a part_n of_o the_o rule_n now_o for_o the_o late_a part_n if_o the_o dividend_n 31_o be_v divide_v by_o the_o sum_n of_o the_o two_o extreme_a expense_n reduce_v by_o double_v as_o the_o dividend_n be_v 4_o the_o quotient_n will_v be_v 7¾_n and_o the_o man_n may_v be_v 7_o as_o have_v be_v show_v but_o they_o may_v be_v also_o but_o 6_o and_o few_o they_o can_v be_v as_o 6_o man_n 13_o woman_n and_o 2_o child_n for_o if_o you_o put_v they_o 5_o that_o multiply_v by_o 3_o produce_v 15_o which_o take_v from_o 31_o there_o remain_v 16_o for_o the_o woman_n and_o so_o there_o shall_v be_v no_o child_n which_o be_v contrary_a to_o the_o supposition_n and_o further_o because_o the_o quotient_n be_v 7¾_n the_o number_n of_o man_n may_v be_v so_o if_o pure_a arithmetical_a division_n be_v only_o regard_v and_o then_o the_o woman_n also_o be_v in_o number_n 7¾_n and_o the_o child_n 5½_n as_o may_v easy_o be_v try_v i_o need_v not_o exemplify_v it_o question_v 3_o if_o there_o be_v a_o exhibition_n of_o 900_o l._n per_fw-la annum_fw-la to_o 30_o person_n some_o clerk_n some_o messenger_n and_o some_o doorkeeper_n at_o 60_o l._n each_o clerk_n 40_o l._n each_o messenger_n and_o 20_o l._n each_o doorkeeper_n how_o many_o must_v there_o be_v of_o each_o sort_n multiply_v according_a to_o the_o rule_n 30_o by_o 20_o the_o product_n be_v 600_o which_o take_v from_o 900_o remain_v 300_o for_o the_o dividend_n and_o 60_o want_v 20_o that_o be_v 40_o for_o the_o divisor_n and_o the_o quotient_n be_v 7½_n and_o more_o the_o clerk_n can_v be_v also_o divide_v by_o 60_o more_o 20_o that_o be_v 80_o quotient_a be_v 3¾_n and_o much_o few_o the_o clerk_n can_v be_v not_o
make_v at_o london_n of_o avoirdupois_n weight_n .82_o lb._n one_o pound_n weight_n in_o venetia_n subtle_a make_v at_o london_n of_o avoirdupois_n weight_n .64_o lb._n one_o pound_n weight_n in_o venetia_n gross_a make_v at_o london_n of_o avoirdupois_n weight_n 1.06_o lb._n one_o pound_n weight_n in_o vienna_n make_v at_o london_n of_o avoirdupois_n weight_n 1.23_o lb._n the_o use_n of_o the_o forego_n table_n in_o 7652_o li._n weight_n at_o mirandola_n how_o many_o pound_n weight_n at_o avoirdupois_n look_v in_o the_o table_n for_o mirandola_n and_o right_a against_o it_o you_o shall_v find_v .75_o which_o show_v that_o one_o pound_n avoirdupois_n be_v equal_a to_o the_o 75_o or_o ¾_n of_o a_o pound_n at_o mirandola_n wherefore_o say_v by_o the_o rule_n of_o three_o if_o 1_o l._n at_o mirandola_n give_v .75_o or_o ¾_n of_o a_o pound_n avoirdupois_n what_o shall_v 7652_o l._n of_o mirandola_n give_v answer_v 5739_o as_o by_o the_o operation_n do_v appear_v a_o table_n reduce_v english_a ell_n to_o the_o measure_n of_o divers_a foreign_a city_n and_o remarkable_a place_n one_o ell_n at_o london_n make_v at_o amsterdam_n 1.6949_o ell_n one_o ell_n at_o london_n make_v at_o antwerp_n 1.6666_o ell_n one_o ell_n at_o london_n make_v at_o bridge_n 1.64_o ell_n one_o ell_n at_o london_n make_v at_o arras_n 1.65_o ell_n one_o ell_n at_o london_n make_v at_o norimberg_n 1.74_o ell_n one_o ell_n at_o london_n make_v at_o colen_n 2.08_o ell_n one_o ell_n at_o london_n make_v at_o lisle_n 1.66_o ell_n one_o ell_n at_o london_n make_v at_o mastrich_n 1.57_o ell_n one_o ell_n at_o london_n make_v at_o frankford_n 2.0866_o ell_n one_o ell_n at_o london_n make_v at_o danzig_n 1.3833_o ell_n one_o ell_n at_o london_n make_v at_o vienna_n 1.45_o auln_n one_o ell_n at_o london_n make_v at_o paris_n .95_o auln_n one_o ell_n at_o london_n make_v at_o rovan_n 1.03_o aulns_n one_o ell_n at_o london_n make_v at_o lion_n 1.0166_o auln_n one_o ell_n at_o london_n make_v at_o 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london_n make_v at_o rome_n .56_o cane_n one_o ell_n at_o london_n make_v at_o barselona_n .7125_o cane_n one_o ell_n at_o london_n make_v at_o valentia_n 1.2125_o cane_n the_o use_n of_o this_o table_n in_o 632_o ell_n at_o london_n how_o many_o brace_n at_o florence_n look_v in_o the_o table_n for_o florence_n and_o right_a against_o it_o you_o shall_v find_v 2.04_o which_o show_v that_o one_o ell_n at_o london_n make_v at_o florence_n 2.204_o brace_n wherefore_o say_v by_o the_o rule_n of_o three_o if_o one_o ell_n at_o london_n give_v 2.04_o brace_n at_o florence_n how_o many_o brace_n shall_v 632_o ell_n give_v answer_v 1289.28_o as_o by_o the_o operation_n follow_v do_v appear_v a_o table_n reduce_v the_o measure_n of_o divers_a foreign_a city_n and_o remarkable_a place_n to_o english_a ells._n one_o ell_n at_o amsterdam_n make_v at_o london_n .59_o ell_n one_o ell_n at_o antwerp_n make_v at_o london_n .6_o ell_n one_o ell_n at_o bridges_n make_v at_o london_n .6097_o ell_n one_o ell_n at_o arras_n make_v at_o london_n .606_o ell_n one_o ell_n at_o norimberg_n make_v at_o london_n .5474_o ell_n one_o ell_n at_o colen_n make_v at_o london_n .4807_o ell_n one_o ell_n at_o lisle_n make_v at_o london_n .6024_o ell_n one_o ell_n at_o mastright_n make_v at_o london_n .6369_o ell_n one_o ell_n at_o frankford_n make_v at_o london_n .4792_o ell_n one_o ell_n at_o danzig_n make_v at_o london_n .7228_o ell_n one_o ell_n at_o vienna_n make_v at_o london_n .9896_o ell_n one_o auln_v at_o paris_n make_v at_o london_n 1.0526_o ell_n one_o auln_v at_o rovan_n make_v at_o london_n .9708_o ell_n one_o auln_v at_o lion_n make_v at_o london_n .9836_o ell_n one_o auln_v at_o callais_n make_v at_o london_n .6369_o ell_n one_o brace_n at_o venice_n linen_n make_v at_o london_n .5555_o ell_n one_o brace_n at_o venice_n silk_n make_v at_o london_n .5102_o ell_n one_o brace_n at_o lucques_n make_v at_o london_n .5_o ell_n one_o brace_n at_o florence_n make_v at_o london_n .4901_o ell_n one_o brace_n at_o milan_n make_v at_o london_n .4347_o ell_n one_o brace_n at_o leghorn_n make_v at_o london_n .5_o ell_n one_o brace_n at_o madera_n isles_n make_v at_o london_n .9681_o ell_n one_o vare_fw-la at_o sivil_a make_v at_o london_n .7409_o one_o vare_fw-la at_o lisbon_n make_v at_o london_n 1_o one_o vare_fw-la at_o castilia_n make_v at_o london_n .7207_o one_o vare_fw-la at_o andolusia_n make_v at_o london_n .7339_o one_o vare_fw-la at_o granado_n make_v at_o london_n .7339_o one_o palm_n at_o genoa_n make_v at_o london_n .2079_o one_o cane_n at_o saragosa_n make_v at_o london_n 1.8181_o one_o cane_n at_o rome_n make_v at_o london_n 1.7857_o one_o cane_n at_o barselona_n make_v at_o london_n 1.4035_o one_o cane_n at_o valentia_n make_v at_o london_n .8247_o the_o use_n of_o this_o table_n in_o 5727_o brace_n at_o ligorn_n how_o many_o ell_n english_a look_v in_o the_o table_n for_o ligorn_n and_o right_a against_o it_o you_o shall_v find_v .5_o which_o show_v that_o one_o brace_n at_o ligorn_n make_v at_o london_n or_o half_o a_o ell_n wherefore_o say_v by_o the_o rule_n of_o three_o if_o one_o brace_n at_o ligorn_n give_v .5_o ell_n at_o london_n what_o shall_v 5727_o brace_n give_v answer_v 2863.5_o as_o by_o the_o work_n appear_v section_n 2._o concern_v interest_n and_o annuity_n the_o first_o table_n show_v what_o one_o pound_n be_v forbear_v any_o number_n of_o year_n under_o 31_o will_v amount_v unto_o account_v interest_n upon_o interest_n after_o the_o rate_n of_o 6_o per_fw-la cent_n y._n 6_o per_fw-la cent_n 1_o 1,06_o 2_o 1,1236_o 3_o 1,19101_o 4_o 1,26247_o 5_o 1,33822_o 6_o 1,41851_o 7_o 1,50363_o 8_o 1,59384_o 9_o 1,68947_o 10_o 1,79084_o 11_o 1,89829_o 12_o 2,01219_o 13_o 2,13292_o 14_o 2,26090_o 15_o 2,39655_o 16_o 2,54035_o 17_o 2,69277_o 18_o 2,85433_o 19_o 3,02559_o 20_o 3,20713_o 21_o 3,29056_o 22_o 3,60353_o 23_o 4,81975_o 24_o 4,04893_o 25_o 4,29187_o 26_o 4,54938_o 27_o 4,82234_o 28_o 5,11168_o 29_o 5,41838_o 30_o 5,74349_o the_o first_o column_n of_o this_o table_n have_v young_a at_o the_o top_n thereof_o beginning_n at_o 1_o and_o so_o proceed_v to_o 30_o signify_v year_n and_o the_o number_n in_o the_o next_o column_n answer_v thereunto_o do_v show_v what_o one_o pound_n be_v worth_a be_v forbear_v any_o number_n of_o year_n under_o 31_o which_o table_n be_v make_v according_a to_o this_o proportion_n as_o 100_o to_o 106_o so_o be_v 1_o to_o 1.06_o and_o again_o as_o 100_o 106_o 106_o 1.1236_o and_o three_o as_o 100_o 106_o 1.1236_o 1.19101_o et_fw-la sic_fw-la ad_fw-la infinitum_fw-la the_o use_n of_o this_o table_n what_o 136_o l._n 15_o s._n 6_o d._n amount_v unto_o be_v forbear_v 20_o year_n after_o the_o rate_n of_o 6_o per_fw-la centum_fw-la interest_n upon_o interest_n look_v in_o the_o table_n for_o 20_o year_n and_o right_a against_o in_o the_o broad_a column_n you_o shall_v find_v 2.20713_o which_o show_v that_o one_o pound_n be_v forbear_v 20_o year_n will_v be_v augment_v to_o 3.20713_o then_o if_o you_o reduce_v your_o 136_o li._n 15_o s._n 6_o d._n into_o a_o decimal_n either_o by_o the_o table_n in_o the_o second_o part_n or_o by_o the_o scale_n in_o the_o three_o part_n of_o this_o book_n you_o shall_v find_v it_o to_o be_v 136.775_o wherefore_o say_v by_o the_o rule_n of_o three_o direct_v if_o one_o pound_n be_v forbear_v 20_o year_n will_v be_v augment_v to_o 3.20713_o to_o how_o much_o will_v 136.775_o li._n be_v augment_v to_o in_o the_o same_o time_n answer_v to_o 438_o li._n 13_o s._n 1_o d._n 1_o q._n as_o by_o the_o operation_n follow_v do_v appear_v or_o 438_o li._n 13_o s._n 1_o d._n 1_o q._n the_o second_o table_n show_v what_o one_o pound_n annuity_n will_v amount_v unto_o be_v forbear_v any_o