ought_v to_o receive_v 2817_o â…—_n ducat_n at_o naples_n for_o the_o 587_o l._n flemish_a deliver_v at_o amsterdam_n quest._n 3._o a_o merchant_n at_o florence_n deliver_v 3478_o ducatoon_n to_o receive_v the_o value_n at_o london_n in_o penny_n the_o exchange_n 53_o 1_o â—_o penny_n sterling_n per_fw-la ducatoon_n i_o demand_v how_o much_o sterling_a he_o ought_v to_o receive_v the_o proportion_n for_o resolution_n be_v as_o be_v to_o so_o be_v to_o which_o be_v equal_a to_o 775_o l._n 6_o 1_o 12_o for_o the_o answer_n i_o may_v here_o according_a to_o the_o custom_n of_o arithmetical_a writer_n lay_v down_o table_n for_o the_o reduction_n of_o foreign_a coin_n to_o english_a but_o by_o reason_n of_o their_o instability_n for_o they_o continue_v not_o at_o a_o constant_a standard_n as_o our_o sterling_a money_n do_v but_o be_v sometime_o raise_v and_o sometime_o depress_v i_o shall_v forbear_v 4._o when_o there_o be_v a_o comparison_n make_v between_o more_o than_o two_o different_a coin_n weight_n or_o measure_n there_o arise_v ordinary_o two_o different_a case_n from_o such_o a_o comparison_n 1._o when_o it_o be_v require_v to_o know_v how_o many_o piece_n of_o the_o first_o coin_n weight_n or_o measure_n be_v equal_a in_o value_n to_o a_o know_a number_n of_o piece_n of_o the_o last_o coin_n weight_n or_o measure_n 2._o when_o it_o be_v require_v to_o find_v out_o how_o many_o piece_n of_o the_o last_o coin_n weight_n or_o measure_n be_v equal_a in_o value_n to_o a_o give_v number_n of_o the_o first_o sort_n of_o coin_n weight_n or_o measure_n a_o example_n of_o the_o first_o case_n may_v be_v this_o viz._n quest._n 4._o if_o 150_o penny_n at_o london_n be_v equal_a to_o 3_o ducat_n at_o naples_n and_o 4_o 4_o â—_o ducat_n at_o naples_n make_v 34_o ½_o shilling_n at_o brussels_n then_o how_o many_o penny_n at_o london_n be_v equal_a to_o 138_o shilling_n at_o brussels_n facit_fw-la 960_o d._n this_o question_n may_v be_v resolve_v at_o two_o single_a rule_n of_o three_o for_o first_o i_o say_v if_o 3_o 1_o ducat_n at_o naples_n make_v 150_o penny_n at_o london_n how_o many_o penny_n will_v 4_o â…˜_n ducat_n make_v answ._n 240_o penny_n by_o the_o foregoing_a proportion_n we_o have_v discover_v that_o 4_o â…˜_n ducat_n at_o naples_n make_v 240_o penny_n at_o london_n and_o by_o the_o tenor_n of_o the_o question_n we_o see_v that_o 4_o â…˜_n ducat_n at_o venice_n make_v 34_o ½_o shilling_n at_o brussels_n therefore_o 240_o penny_n at_o london_n be_v equal_a to_o 34_o ½_o shilling_n at_o brussels_n for_o the_o thing_n that_o be_v equal_a to_o one_o and_o the_o same_o thing_n be_v also_o equal_a to_o one_o another_o wherefore_o we_o have_v a_o way_n lay_v open_a to_o give_v a_o solution_n to_o this_o question_n by_o another_o single_a rule_n of_o three_o who_o proportion_n be_v as_o 34_o ½_o shilling_n at_o brussels_n be_v to_o 240_o penny_n at_o london_n so_o be_v 138_o shilling_n at_o brussels_n to_o 960_o penny_n at_o london_n which_o be_v the_o answer_n to_o the_o question_n a_o example_n of_o the_o second_o case_n may_v be_v this_o viz._n quest._n 5._o if_o 40_o l._n averdupoize_n weight_n at_o london_n be_v equal_a to_o 36_o l._n weight_n at_o amsterdam_n and_o 90_o l._n at_o amsterdam_n make_v 116_o l._n at_o dantzick_n then_o how_o many_o pound_n at_o dantzick_n be_v equal_a to_o 112_o l._n of_o averdupois_n weight_n at_o london_n answer_n 129_o 23_o 25_o pound_n at_o dantzick_n this_o question_n be_v likewise_o answer_v at_o two_o single_a rule_n of_o three_o viz._n first_o i_o say_v as_o 36_o l._n at_o amsterdam_n be_v to_o 40_o l._n at_o lond._n so_o be_v 90_o l._n at_o amsterdam_n to_o 100_o l._n at_o lond._n and_o by_o the_o question_n you_o find_v that_o 90_o l._n at_o amsterdam_n be_v 116_o l._n at_o dantzick_n and_o therefore_o 100_o l._n at_o london_n be_v likewise_o equal_a thereunto_o wherefore_o again_o i_o say_v as_o 100_o l._n at_o london_n be_v to_o 116_o l._n at_o dant_fw-la so_o be_v 112_o l._n at_o london_n to_o 129_o 23_o 25_o at_o dant_fw-la by_o which_o i_o find_v that_o 112_o 23_o 25_o l._n at_o dantzick_n be_v equal_a to_o 112_o l._n averdupois_n weight_n at_o london_n 5._o there_o be_v a_o more_o speedy_a way_n to_o resolve_v such_o question_n as_o be_v contain_v under_o the_o two_o case_n before_o mention_v lay_v down_o by_o mr._n kersey_n in_o the_o three_o chapter_n of_o his_o appendix_n to_o mr._n wingates_n arithmetic_n where_o he_o have_v give_v two_o rule_n for_o the_o resolution_n of_o the_o question_n pertinent_a to_o the_o two_o say_a case_n 6._o but_o i_o shall_v lay_v down_o a_o general_a rule_n for_o the_o solution_n of_o both_o case_n and_o first_o let_v the_o learner_n observe_v the_o follow_a direction_n in_o place_v of_o the_o give_v term_n viz._n 7._o let_v there_o be_v make_v two_o collume_n and_o in_o these_o collume_n so_o place_v the_o give_v term_n one_o over_o the_o other_o as_o that_o in_o the_o same_o collume_n there_o may_v not_o be_v find_v two_o term_n of_o the_o same_o kind_a one_o with_o the_o other_o have_v thus_o place_v the_o term_n the_o general_n rule_n be_v observe_v which_o of_o the_o say_a collume_n have_v the_o most_o term_n place_v in_o it_o and_o multiply_v all_o the_o term_n therein_o continual_o and_o place_v the_o last_o product_n for_o a_o dividend_n then_o multiply_v the_o term_n in_o the_o other_o collume_n continual_o and_o let_v the_o last_o product_n be_v a_o divisor_n then_o divide_v the_o say_a dividend_n by_o the_o say_a divisor_n and_o the_o quotient_a thence_o arise_v be_v the_o answer_n to_o the_o question_n so_o the_o example_n of_o the_o first_o of_o the_o say_a case_n be_v again_o repeat_v viz._n if_o 150_o penny_n at_o london_n make_v 3_o ducat_n at_o naples_n and_o 4_o â…˜_n ducat_n at_o naples_n make_v 34_o ½_o shill_n at_o brussels_n then_o how_o many_o penny_n at_o london_n be_v equal_a to_o 138_o shilling_n at_o brussels_n the_o term_n be_v place_v according_a to_o the_o 7_o rule_n will_v stand_v as_o follow_v  _fw-fr a_o b_o  _fw-fr pence_n at_o lond._n 150_o 3_o duc._n at_o na._n ducat_n at_o na._n 4_o 4_o â—_o 34_o ½_o shill_n at_o bruss_n shiâ—l_n at_o bruss_n 138_o  _fw-fr  _fw-fr having_z thus_o place_v the_o term_n that_o in_o neither_o collume_n there_o be_v 2_o term_n of_o one_o kind_n than_o i_o observe_v that_o the_o collume_n under_o a_o have_v most_o term_n in_o it_o therefore_o they_o must_v be_v multiply_v together_o for_o a_o dividend_n viz._n 150_o mult_fw-la by_z 4_o 4_o â—_o produce_v 3600_o 5_o which_o multiply_v by_o 138_o produc_n 106800_o 5_o for_o a_o dividend_n then_o in_o the_o collume_n under_o b_o there_o be_v 3_o and_o 34_o ½_o which_o multiply_v together_o produce_v 207_o 2_o for_o a_o divisor_n then_o have_v divide_v 496800_o â—_o by_o 207_o 2_o the_o quotient_n be_v 960_o penny_n for_o the_o answer_n as_o before_o again_o let_v the_o example_n of_o the_o second_o case_n be_v again_o repeat_v viz._n if_o 40_o l._n averdupois_n weight_n at_o london_n make_v 36_o l_o weight_n at_o amsterdam_n and_o 90_o l._n at_o amsterdam_n make_v 116_o l._n at_o dantzick_n then_o how_o many_o pound_n at_o dantzick_n be_v equal_a to_o 112_o l._n averdupois_n weight_n at_o london_n the_o term_n be_v dispose_v according_a to_o the_o 7_o rule_n forego_v will_v stand_v thus_o  _fw-fr a_n b_o  _fw-fr l._n at_o lond._n 40_o 36_o l._n at_o amsterdam_n l._n at_o amst._n 90_o 116_o l._n at_o dantzick_n  _fw-fr  _fw-fr 112_o l._n at_o london_n whereby_o i_o find_v that_o the_o term_n under_o b_o multiply_v together_o produce_v 467712_o for_o a_o dividend_n and_o the_o term_n under_o a_o viz._n 40_o and_o 90_o produce_v 3600_o for_o a_o divisor_n and_o division_n be_v finish_v the_o quotient_n give_v 129_o 3312_o 3600_o pound_n at_o dantzick_n for_o the_o answer_n chap._n xxxi_o single_a position_n 1._o negative_a arithmetic_n call_v the_o rule_n of_o false_a be_v that_o by_o which_o we_o find_v out_o a_o truth_n by_o number_n invent_v or_o suppose_v and_o this_o be_v either_o single_a or_o double_a 2._o the_o rule_n of_o single_a position_n be_v when_o at_o once_o viz._n by_o one_o false_a position_n or_o feign_a number_n we_o find_v out_o the_o true_a number_n seek_v 3._o in_o the_o single_a rule_n of_o false_a when_o you_o have_v make_v choice_n of_o your_o position_n work_v it_o according_a to_o the_o tenor_n of_o the_o question_n as_o if_o it_o be_v the_o true_a number_n seek_v and_o if_o by_o the_o order_n of_o your_o position_n you_o find_v the_o result_n either_o too_o much_o or_o too_o little_a you_o may_v then_o find_v out_o the_o number_n seek_v by_o this_o proportion_n follow_v viz._n as_o the_o result_n of_o your_o
give_v the_o high_a or_o superior_a number_n be_v call_v the_o major_a number_n and_o the_o low_a or_o inferior_a be_v call_v the_o minor_a number_n and_o the_o operation_n of_o subtraction_n be_v finish_v the_o rest_n or_o remainder_n be_v call_v the_o difference_n of_o the_o number_n give_v 3._o in_o subtraction_n place_n the_o number_n give_v respective_o the_o one_o under_o the_o other_o in_o such_o sort_n as_o like_a degree_n place_n or_o denomination_n may_v stand_v in_o the_o same_o series_n viz._n unit_v under_o unit_n ten_o under_o ten_o etc._n etc._n pound_n under_o pound_n etc._n etc._n foot_n under_o foot_n and_o part_n under_o part_n etc._n etc._n this_o be_v do_v draw_v a_o line_n underneath_o as_o in_o addition_n 4._o have_v place_v the_o number_n give_v as_o be_v before_o direct_v and_o draw_v a_o line_n under_o they_o subtract_v the_o low_a number_n which_o in_o this_o case_n must_v always_o be_v lesser_a than_o the_o uppermost_a out_o of_o the_o high_a number_n and_o subscribe_v the_o difference_n or_o remainder_n respective_o below_o the_o line_n and_o when_o the_o work_n be_v finish_v the_o number_n below_o the_o line_n will_v give_v you_o the_o remainder_n as_o for_o example_n let_v 364521_o be_v give_v to_o be_v subtract_v from_o 795836_o i_o set_v the_o lesser_a under_o the_o great_a as_o in_o the_o margin_n and_o draw_v a_o line_n under_o they_o then_o begin_v at_o the_o right_a hand_n i_o say_v 1_o out_o of_o 6_o and_o there_o remain_v 5_o which_o i_o set_v in_o order_n under_o the_o line_n then_o i_o proceed_v to_o the_o next_o say_v 2_o from_o 3_o rest_n 1_o which_o i_o note_v also_o under_o the_o line_n and_o thus_o i_o go_v on_o until_o i_o have_v finish_v the_o work_n and_o then_o i_o find_v the_o remainder_n or_o difference_n to_o be_v 431315._o 5._o but_o if_o it_o so_o happen_v as_o common_o it_o do_v that_o the_o lowermost_a number_n or_o figure_n be_v great_a than_o the_o uppermost_a then_o in_o this_o case_n add_v ten_o to_o the_o uppermost_a number_n and_o subtract_v the_o say_v lowermost_a number_n from_o their_o sum_n and_o the_o remainder_n place_n under_o the_o line_n and_o when_o you_o go_v to_o the_o next_o figure_n below_o pay_v a_o unit_fw-la by_o add_v it_o thereto_o for_o the_o 10_o you_o borrow_v before_o and_o subtract_v that_o from_o the_o high_a number_n or_o figure_n and_o thus_o go_v on_o until_o your_o subtraction_n be_v finish_v as_o for_o example_n let_v 437503_o be_v give_v from_o whence_o it_o be_v require_v to_o subtract_v 153827_o i_o dispose_v of_o the_o number_n as_o be_v before_o direct_v and_o as_o you_o see_v in_o the_o margin_n then_o i_o begin_v say_v 7_o from_o 3_o i_o can_v but_o add_v 10_o thereto_o i_o say_v 7_o from_o 13_o and_o there_o remain_v 6_o which_o i_o set_v under_o the_o line_n in_o order_n then_o i_o proceed_v to_o the_o next_o figure_n say_v 1_o that_o i_o borrow_v and_o 2_o be_v 3_o from_o 0_o i_o can_v but_o 3_o from_o 10_o and_o there_o remain_v 7_o which_o i_o likewise_o set_v down_o as_o before_o then_o one_o that_o i_o borrow_v and_o eight_o be_v nine_o from_o five_o i_o can_v but_o nine_o from_o fifteen_o and_o there_o remain_v six_o then_o one_o i_o borrow_v and_o three_o be_v four_o from_o seven_o and_o there_o remain_v three_o then_o five_o from_o three_o i_o can_v but_o five_o from_o thirteen_o and_o there_o remain_v eight_o then_o one_o i_o borrow_v and_o one_o be_v two_o from_o four_o and_o there_o rest_v two_o and_o thus_o the_o work_n be_v finish_v and_o after_o these_o number_n be_v subtract_v one_o from_o another_o the_o inequality_n remainder_n excess_n or_o difference_n be_v find_v to_o be_v 283676._o example_n for_o thy_o further_a experience_n may_v be_v these_o that_o follow_v from_o 3475016_o from_o 3615746_o take_v 738642_o take_v 5864_o rest_n 2736374_o rest_n 3609882_o 6._o if_o the_o sum_n or_o number_n to_o be_v subtract_v be_v of_o several_a denomination_n place_v the_o lesser_a sum_n below_o the_o great_a and_o in_o the_o same_o rank_a and_o order_n as_o be_v show_v in_o addition_n of_o the_o same_o number_n then_o begin_v at_o the_o right_a hand_n and_o take_v the_o low_a number_n out_o of_o the_o uppermost_a if_o it_o be_v lesser_a but_o if_o it_o be_v big_a than_o the_o uppermost_a then_o borrow_v a_o unit_fw-la from_o the_o next_o great_a denomination_n and_o turn_v it_o into_o the_o part_n of_o the_o lesser_a denomination_n and_o add_v those_o part_n to_o the_o uppermost_a number_n and_o from_o their_o sum_n subtract_v the_o lowermost_a note_v the_o remainder_n below_o the_o line_n then_o proceed_v and_o pay_v 1_o to_o the_o next_o denomination_n for_o that_o which_o you_o borrow_v before_o and_o proceed_v in_o this_o order_n until_o the_o work_n be_v finishâ—ed_v a_o example_n of_o this_o rule_n may_v be_v thiâ—_n that_o follow_v let_v 375_o l._n 13_o s._n 07_o d._n 1_o qr_n be_v give_v from_o whence_o let_v it_o be_v require_v to_o subtract_v 57_o l._n 16_o s._n 03_o d._n 2_o qr_n in_o order_n whereunto_o i_o place_v the_o number_n as_o you_o see_v iâ—_n the_o margin_n and_o thus_o i_o begin_v at_o the_o leasâ—_n denomination_n say_v l._n s._n d._n qrâ—_n 375_o 13_o 07_o 1_o 57_o 16_o 03_o 2_o 317_o 17_o 03_o â—3_n two_o from_o one_o i_o can_v therefore_o i_o borrow_v one_o penny_n from_o the_o next_o denomination_n and_o turn_v it_o into_o farthing_n which_o be_v four_o and_o add_v four_o 〈◊〉_d one_o which_o be_v five_o i_o say_v but_o two_o from_o fiuâ—_o and_o there_o remain_v three_o which_o i_o put_v undâ—â—_n the_o line_n then_o go_v on_o i_o say_v one_o that_o i_o borrow_v and_o three_o be_v four_o from_o 7_o and_o there_o rest_v three_o then_o go_v on_o i_o say_v sixteen_o from_o thirteen_o i_o can_v but_o borrow_v one_o pound_n and_o turn_v it_o into_o twenty_o shilling_n i_o add_v it_o to_o thirteen_o and_o that_o be_v thirty_o three_o wherefore_o i_o say_v sixteen_o from_o thirty_o three_o and_o there_o remain_v seventeen_o which_o i_o set_v under_o the_o line_n and_o go_v on_o say_v one_o that_o i_o borrow_v and_o seven_o be_v eight_o from_o five_o i_o can_v but_o eight_o from_o fifteen_o and_o there_o remain_v seven_o then_o one_o that_o i_o borrow_v and_o five_o be_v six_o from_o seven_o there_o rest_v one_o and_o nothing_o from_o three_o rest_n three_o and_o the_o work_n be_v do_v and_o i_o find_v the_o remainder_n or_o difference_n to_o be_v 317_o l._n 17_o s._n 03_o d._n 3_o qr_n another_o example_n of_o troy_n weight_n may_v be_v this_o i_o will_v subtract_v 17_o l._n 10_o oz._n 11_o p.w._n 20_o gr_n from_o 24_o l._n 05_o oz._n 00_o p.w._n 08_o gr_n i_o place_v the_o number_n according_a to_o rule_n and_o begin_v say_v twenty_o l._n oz._n p.w._n gr_n 24_o 05_o 00_o 08_o 17_o 10_o 11_o 20_o 06_o 06_o 08_o 12_o from_o eight_o i_o can_v but_o borrow_v one_o penny_n weight_n which_o be_v twenty_o four_o grain_n and_o add_v they_o to_o eight_o and_o they_o be_v thirty_o two_o wherefore_o i_o say_v twenty_o from_o thirty_o two_o rest_n twelve_o then_o one_o that_o i_o borrow_v and_o eleven_o be_v twelve_o from_o 00_o i_o can_v but_o twelve_o from_o twenty_o borrow_v a_o ounce_n which_o be_v twenty_o penny_n weight_n and_o there_o remain_v eight_o then_o one_o that_o i_o borrow_v and_o ten_o be_v eleven_o from_o five_o i_o can_v but_o eleven_o from_o seventeen_o and_o there_o rest_v six_o then_o one_o that_o i_o borrow_v and_o seven_o be_v eight_o from_o four_o i_o can_v but_o eight_o from_o fourteen_o and_o there_o rest_v six_o then_o one_o that_o i_o borrow_v and_o one_o be_v two_o from_o two_o and_o there_o rest_v nothing_o so_o that_o i_o find_v the_o remainder_n or_o difference_n to_o be_v 6_o l._n 6_o oz._n 8_o p.w._n 12_o gr_n 7._o it_o many_o time_n happen_v that_o you_o have_v many_o sum_n or_o number_n to_o be_v subtract_v from_o one_o number_n as_o suppose_v a_o man_n shall_v lend_v his_o friend_n a_o certain_a sum_n of_o money_n and_o his_o friend_n have_v pay_v he_o part_v of_o his_o debt_n at_o several_a time_n then_o before_o you_o can_v convenient_o know_v what_o be_v still_o owe_v you_o be_v to_o add_v the_o several_a number_n or_o sum_n of_o payment_n together_o and_o subtract_v their_o sum_n from_o the_o whole_a debt_n and_o the_o remainder_n be_v the_o sum_n due_a to_o the_o creditor_n as_o suppose_v a_o dare_v to_o b_o 564_o l._n 13_o s._n 10_o d._n and_o b_o have_v repay_v he_o 79_o l._n 16_o s._n 08_o d._n at_o one_o time_n and_o 163_o l._n 18_o s._n 11_o d._n at_o another_o time_n and_o 241_o l._n 15_o s._n 08_o d._n at_o another_o time_n and_o you_o will_v know_v how_o the_o account_n
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