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4_o 5_o 6_o 7_o 8_o 12_o mill._n 345678_o 1_o 2_o 3_o 4_o 5_o 6_o 7_o 8_o 9_o 123_o mil._n 456789_o this_o table_n need_v but_o little_a explanation_n for_o thereby_o you_o may_v discern_v the_o first_o place_n next_o the_o right_a hand_n to_o be_v the_o place_n of_o unit_n the_o second_o the_o place_n of_o ten_o the_o â—hird_n the_o place_n of_o hundred_o the_o four_o thousand_o etc._n etc._n so_o admit_v the_o sum_n 6873_o be_v give_v you_o to_o number_n consist_v of_o four_o place_n because_o in_o it_o be_v contain_v four_o figure_n which_o you_o must_v thus_o number_v six_o thousand_o eight_o hundred_o seventy_o three_o and_o in_o like_a manner_n for_o 784395_o which_o you_o must_v thus_o number_v seven_o hundred_o eighty_o four_o thousand_o three_o hundred_o ninety_o five_o chap._n ii_o addition_n addition_n teach_v of_o several_a sum_n to_o make_v one_o which_o shall_v contain_v as_o much_o as_o all_o those_o several_a sum_n as_o suppose_v a_o owe_v unto_o b_o 328_o pound_n c_o 147_o d_o 485_o total_a sum_n 960_o set_v the_o several_a sum_n as_o you_o see_v one_o under_o the_o other_o have_v draw_v a_o line_n begin_v at_o the_o low_a end_n of_o that_o row_n next_o your_o right_a hand_n say_v 5_o and_o 7_o be_v 12_o and_z 8_o be_v 20_o set_v under_o that_o first_o row_n 0_o and_o carry_v 2_o for_o so_o many_o ten_o to_o the_o next_o row_n say_v 2_o as_o i_o carry_v and_o 8_o be_v 10_o and_z 4_o be_v 14_o and_z 2_o be_v 16_o set_v down_o 6_o under_o that_o row_n and_o carry_v 1_o for_o the_o 10_o to_o the_o next_o row_n say_v 1_o as_o i_o carry_v and_o 4_o makes_z 5_o and_z 1_o be_v 6_o and_o 3_o be_v 9_o set_v down_o 9_o under_o that_o row_n so_o you_o have_v under_o the_o line_n these_o figure_n 960_o which_o be_v the_o total_a sum_n of_o those_o three_o so_o that_o a_o owe_v in_o all_o to_o b_o c_o and_o d_o 960_o pound_n when_o you_o have_v any_o sum_n to_o set_v down_o which_o you_o be_v to_o add_v up_o you_o must_v be_v sure_a to_o set_v down_o the_o several_a sum_n so_o orderly_o one_o under_o the_o other_o as_o the_o unit_n may_v stand_v under_o themselves_o ten_o under_o themselves_o hundred_o under_o themselves_o and_o thousand_o under_o themselves_o etc._n etc._n according_a to_o these_o follow_a example_n 3842_o l._n 863219_o 428_o 76824_o 97_o 4386_o 9_o 327_o  _fw-fr 24_o  _fw-fr 6_o addition_n of_o mony_n if_o you_o have_v any_o sum_n which_o be_v compose_v of_o several_a denomination_n as_o pound_n shilling_n penny_n and_o farthing_n or_o any_o other_o kind_n you_o must_v first_o consider_v how_o many_o of_o the_o lesser_a make_v one_o of_o the_o next_o denomination_n as_o in_o sterling_a money_n 4_o farthing_n be_v 1_o penny_n 12_o pence_n be_v 1_o shilling_n 20_o shilling_n be_v 1_o pound_v sterling_n and_o so_o carry_v the_o penny_n from_o the_o farthing_n to_o the_o penny_n the_o shilling_n from_o the_o penny_n to_o the_o shilling_n and_o the_o pound_n from_o the_o shilling_n to_o the_o pound_n as_o you_o may_v plain_o see_v in_o the_o work_n of_o this_o follow_a example_n  _fw-fr l._n s._n d._n  _fw-fr received_n of_o a_o 384_o 16_o 11_o ½_n b_o 197_o 14_o 08_o ¾_n c_o 79_o 12_o 03_o ¼_n d_o 9_o 13_o 10_o ¾_n  _fw-fr 671_o 17_o 10_o ¼_n suppose_v i_o have_v receive_v money_n of_o four_o several_a person_n viz._n of_o a_o 384_o l._n 16_o s._n 11_o d._n ½_n of_o b_o 197_o l._n 14_o s._n 08_o d._n ¾_n of_o c._n 79_o l._n 12_o s._n 03_o d._n ¾_n and_o of_o d_o i_o have_v receive_v 9_o l._n 13_o s._n 10_o d._n ¾_n and_o i_o desire_v to_o know_v how_o much_o the_o four_o sum_n make_v altogether_o set_a down_o the_o say_a sum_n in_o such_o order_n one_o under_o the_o other_o as_o the_o farthing_n may_v stand_v under_o themselves_o the_o penny_n under_o themselves_o the_o shilling_n under_o themselves_o and_o the_o pound_n under_o themselves_o and_o in_o such_o manner_n as_o unit_n ten_o and_o hundred_o may_v stand_v under_o one_o another_o according_a as_o you_o see_v they_o here_o set_v down_o 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half_a of_o 5_o be_v 2_o i_o carry_v 2_o unto_o the_o pound_n say_v 2_o as_o i_o carry_v and_o 9_o be_v 11_o and_z 9_o be_v 20_o and_o 7_o be_v 27_o and_o 4_o be_v 31_o set_v down_o 1_o under_o that_o row_n and_o carry_v three_o to_o the_o next_o row_n say_v 3_o as_o i_o carry_v and_o 7_o be_v â—0_n and_o 9_o be_v 19_o and_o 8_o be_v 27_o set_v 7_o under_o this_o row_n and_o carry_v 2_o to_o the_o next_o say_v 2_o as_o i_o carry_v and_o 1_o
down_o a_o o_o and_o for_o every_o ten_o carry_v so_o many_o unit_v to_o the_o next_o product_n and_o if_o any_o particular_a product_n exceed_v ten_o or_o any_o number_n of_o ten_o set_v down_o the_o excess_n and_o for_o every_o ten_o carry_v so_o many_o unit_v to_o the_o next_o product_n and_o when_o you_o come_v to_o the_o last_o figure_n set_v down_o the_o total_a product_n as_o by_o the_o follow_a example_n will_v appear_v where_o it_o be_v require_v to_o multiply_v 7958_o by_o 7._o first_o set_v down_o 7958_o for_o the_o multiplicand_a and_o under_o it_o in_o the_o place_n of_o unit_v set_v down_o 7_o for_o the_o multiplicator_n 1_o then_o draw_v a_o line_n i_o begin_v find_v by_o the_o former_a multiplication_n table_n that_o 7_o time_n 8_o be_v 56_o i_o set_v down_o 6_o be_v the_o excess_n of_o 5_o ten_o and_o for_o those_o 5_o ten_o i_o carry_v 5_o to_o the_o next_o product_n now_o proceed_n towards_o the_o left_a hand_n to_o the_o next_o figure_n 5_o say_v 7_o time_n 5_o be_v 35_o and_o 5_o as_o i_o carry_v be_v 40_o set_v down_o 0_o and_o for_o the_o 4_o ten_o carry_v 4_o to_o the_o next_o product_n say_v 7_o time_n 9_o be_v 63_o and_o 4_o as_o i_o carry_v be_v 67_o set_v down_o 7_o and_o carry_v 6_o to_o the_o next_o product_n for_o so_o many_o ten_o then_o i_o proceed_v say_v 7_o time_n 7_o be_v 49_o and_o 6_o as_o i_o carry_v be_v 55_o which_o be_v the_o last_o product_n i_o set_v down_o the_o whole_a product_n 55_o have_v finish_v the_o say_a multiplication_n and_o find_v the_o product_n to_o be_v 55706_o as_o be_v require_v in_o multiplication_n if_o both_o the_o multiplicand_a and_o the_o multiplier_n do_v consist_v of_o divers_a place_n begin_v first_o with_o that_o figure_n of_o your_o multiplier_n as_o do_v stand_v in_o the_o place_n of_o unit_n multiply_v it_o into_o all_o the_o figure_n of_o the_o multiplicand_a place_v the_o product_n below_o the_o line_n according_a to_o the_o instruction_n of_o the_o last_o example_n then_o begin_v a_o new_a 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multiplier_n which_o will_v cause_v every_o product_n to_o stand_v one_o figure_n short_a of_o one_o another_o towards_o the_o right_a hand_n according_a to_o the_o forego_n instruction_n the_o undermost_a product_n stand_v one_o figure_n more_o towards_o the_o left_a hand_n than_o his_o undermost_a as_o you_o see_v by_o the_o follow_a example_n it_o be_v require_v to_o multiply_v 486739_o by_o 4387._o i_o set_v 1_o they_o down_o the_o lesser_a under_o the_o great_a according_a to_o the_o instruction_n in_o the_o begin_n of_o this_o chapter_n and_o draw_v a_o line_n under_o they_o i_o begin_v with_o the_o first_o figure_n of_o your_o multiplier_n stand_v in_o the_o place_n of_o unit_n which_o be_v 7_o say_v 7_o time_n 9_o be_v 63_o i_o set_v down_o 3_o and_o carry_v 6._o then_o 7_o time_n 3_o be_v 21_o and_o 6_o as_o i_o carry_v be_v 27_o set_v down_o 7_o and_o carry_v 2._o then_o 7_o time_n 7_o be_v 49_o and_o 2_o as_o i_o carry_v be_v 51_o that_o be_v 1_o and_o carry_v 5._o then_o 7_o time_n 6_o be_v 42_o and_o 5_o as_o i_o carry_v be_v 47_o set_v down_o 7_o and_o carry_v 4._o then_o 7_o time_n 8_o be_v 6_o and_z 4_o as_o i_o carry_v be_v 60_o set_v down_o 0_o and_o carry_v 6._o then_o 7_o time_n 4_o be_v 28_o and_o 6_o as_o i_o carry_v be_v 34_o set_v 4_o and_o 3_o after_o he_o as_o you_o see_v so_o the_o first_o product_n will_v be_v 3407173._o then_o i_o proceed_v to_o the_o next_o figure_n of_o the_o multiplier_n which_o be_v 8_o for_o a_o new_a product_n say_v 8_o time_n 9_o be_v 72_o now_o i_o must_v remember_v the_o former_a instruction_n for_o place_v the_o several_a product_n viz._n to_o place_v the_o first_o figure_n or_o place_n of_o unit_n of_o your_o second_o product_n under_o the_o second_o figure_n or_o place_n of_o ten_o in_o the_o first_o product_n therefore_o for_o 72_o i_o set_v down_o 2_o under_o the_o second_o figure_n of_o the_o first_o product_n be_v 7_o and_o carry_v 7._o then_o 8_o time_n 3_o be_v 24_o and_o 7_o as_o i_o carry_v be_v 31_o set_v down_o 1_o and_o carry_v 3._o then_o 8_o time_n 7_o be_v 56_o and_o 3_o as_o i_o carry_v be_v 59_o set_v down_o 9_o and_o carry_v 5._o then_o 8_o time_n 6_o be_v 48_o and_o 5_o as_o i_o carry_v be_v 53_o set_v down_o 3_o and_o go_v 5._o then_o 8_o time_n 8_o be_v 64_o and_o 5_o as_o i_o carry_v be_v 69_o set_v down_o 9_o and_o carry_v 6._o then_o 8_o time_n 4_o be_v 32_o and_o 6_o as_o i_o carry_v be_v 38_o i_o set_v down_o 8_o and_o 3_o behind_o be_v the_o last_o of_o that_o product_n next_o i_o proceed_v to_o the_o three_o figure_n of_o the_o multiplier_n say_v 3_o time_n 9_o be_v 27_o set_v down_o 7_o under_o the_o 1_o which_o be_v the_o second_o figure_n of_o the_o last_o product_n and_o i_o carry_v 2._o then_o 3_o time_n 3_o be_v 9_o and_z 2_o as_o i_o carry_v be_v 11_o set_v down_o 1_o and_o carry_v 1._o then_o 3_o time_n 7_o be_v 21_o and_o 1_o as_o carry_v be_v 22_o set_v down_o 2_o and_o carry_v 2._o then_o 3_o time_n 6_o be_v 18_o and_o 2_o as_o i_o carry_v be_v 20_o set_v down_o 0_o and_o carry_v 2._o then_o 3_o time_n 8_o be_v 24_o and_o 2_o as_o i_o carry_v be_v 26_o setdown_o 6_o and_o carry_v 2._o then_o 3_o time_n 4_o be_v 12_o and_z 2_o as_o i_o carry_v be_v 14_o i_o set_v down_o 14_o be_v the_o last_o figure_n multiply_v in_o that_o product_n then_o i_o next_o proceed_v to_o the_o four_o figure_n of_o the_o multiplier_n which_o be_v 4._o say_v 4_o time_n 9_o be_v 36_o set_v down_o 6_o under_o 1_o according_a to_o the_o former_a instruction_n and_o i_o carry_v 3._o then_o 4_o time_n 3_o be_v 12_o and_z 3_o as_o i_o carry_v be_v 15_o set_z down_z 5_o and_o carry_v 1._o then_o 4_o time_n 7_o be_v 28_o and_o 1_o as_o i_o carry_v be_v 29_o set_v down_o 9_o and_o carry_v 2._o then_o 4_o time_n 6_o be_v 24_o and_o 2_o as_o i_o carry_v be_v 26_o set_v down_o 6_o and_o carry_v 2._o then_o 4_o time_n 8_o be_v 32_o and_o 2_o as_o i_o carry_v be_v 34_o set_v down_o 4_o and_o carry_v 3_o than_o 4_o time_n 4_o be_v 16_o and_o 3_o as_o carried_z be_v 19_o set_v down_o 19_o be_v the_o last_o figure_n of_o your_o multiplicand_n you_o must_v observe_v the_o same_o order_n in_o place_v the_o respective_a product_n and_o the_o figure_n of_o each_o product_n one_o under_o the_o onther_n as_o you_o see_v in_o the_o example_n and_o draw_v a_o line_n and_o by_o the_o instruction_n of_o the_o second_o chapter_n add_v those_o several_a product_n up_o into_o one_o sum_n under_o the_o line_n which_o will_v be_v 2135323993_o the_o true_a product_n require_v be_v equal_a to_o 4387_o time_n 486739_o or_o 486739_o time_n 4387._o in_o the_o same_o manner_n be_v all_o multiplication_n to_o be_v wrought_v although_o there_o be_v more_o figure_n either_o in_o the_o multiplicand_a or_o multiplier_n another_o way_n of_o multiplication_n the_o carry_v of_o one_o number_n be_v a_o little_a difficult_a to_o young_a learner_n in_o this_o art_n or_o to_o such_o as_o do_v not_o frequent_o exercise_v themselves_o therein_o therefore_o for_o the_o help_n of_o such_o capacity_n i_o show_v you_o a_o plain_a and_o easy_a way_n for_o find_v the_o several_a product_n that_o be_v make_v by_o multiply_v the_o multiplicand_a by_o the_o several_a figure_n of_o the_o multiplier_n when_o you_o have_v two_o number_n give_v to_o be_v multiply_v one_o by_o another_o multiply_v the_o great_a number_n by_o all_o the_o nine_o digit_n by_o continual_a addition_n nine_o time_n over_o set_v the_o several_a sum_n down_o
therefore_o upon_o a_o piece_n of_o waste_a paper_n prepare_v for_o that_o purpose_n i_o multiply_v the_o divisor_n by_o 4_o the_o product_n will_v be_v 984_o which_o can_v be_v subtract_v out_o of_o 978_o therefore_o i_o find_v the_o divisor_n will_v go_v but_o 3_o time_n in_o 976_o i_o set_v down_o 3_o in_o the_o quotient_a make_v a_o separation_n as_o you_o see_v between_o the_o dividend_n and_o the_o quotient_a than_o you_o begin_v to_o multiply_v your_o divisor_n at_o the_o right_a hand_n end_n say_v 3_o time_n 6_o be_v 18_o cancel_v the_o 6._o then_o 8_o from_o 8_o and_o there_o remain_v 0_o and_o 1_o from_o 7_o cancel_v the_o 7_o and_o there_o remain_v 6._o then_o 3_o time_n 4_o be_v 12_o cancel_v the_o 4_o say_v 2_o from_o 6_o and_o there_o remain_v 4_o and_z 1_o from_o 9_o and_o there_o remain_v 8_o setting_z 8_o over_z 9_o and_z 4_o over_z 6_o cancel_v the_o 9_o and_o 6._o then_o 3_o time_n 2_o be_v 6_o cancel_v the_o 2_o and_o say_v 6_o from_z 8_o and_o there_o remain_v 2_o and_o the_o division_n stand_v as_o you_o see_v next_o to_o proceed_v for_o find_v the_o next_o figure_n of_o the_o quotient_a i_o remove_v my_o divisor_n one_o figure_n more_o towards_o the_o right_a hand_n there_o stand_v over_o the_o divisor_n these_o uncancelled_a figure_n 2403._o i_o ask_v how_o many_o time_n 2_o the_o first_o figure_n of_o the_o divisor_n in_o 24_o i_o find_v 9_o time_n by_o multiply_v the_o divisor_n by_o on_o waste_a paper_n therefore_o i_o set_v down_o 9_o in_o the_o 1_o quotient_a after_o the_o 3._o then_o begin_v to_o multiply_v the_o divisor_n say_v 9_o time_n 6_o be_v 54_o 4_o from_o 3_o i_o can_v but_o borrow_v 1_o and_o say_n 4_o from_o 13_o and_o there_o remain_v 9_o cancel_v the_o 6_o and_o 3_o and_o set_v 9_o over_o it_o and_z 1_o as_o i_o borrow_v and_o 5_o be_v 6_o from_o 0_o i_o can_v but_o borrow_v 1_o say_v 6_o from_o 10_o and_o there_o remain_v 4_o and_z 1_o as_o i_o borrow_v from_o 4_o and_o there_o remain_v 3._o then_o 9_o time_n 4_o be_v 36_o 6_o from_o 4_o i_o can_v but_o 6_o from_o 14_o and_o there_o remain_v 8_o cancel_v 4_o at_o bottom_n and_o 4_o above_o setting_z 8_o the_o remainder_n over_o head_n than_o 1_o as_o i_o borrow_v and_o 3_o be_v 4_o from_z 3_o i_o can_v but_o 4_o from_o 13_o and_o there_o remain_v 9_o and_z 1_o as_o i_o borrow_v from_o 2_o and_o there_o remain_v 1._o then_o 9_o time_n 2_o be_v 18_o cancel_v the_o 2_o and_o say_v 8_o from_z 9_o there_o remain_v 1_o and_z 1_o from_o 1_o and_o there_o remain_v 0._o so_o there_o be_v two_o figure_n of_o the_o quotient_a finish_v i_o remove_v the_o divisor_n one_o figure_n more_o towards_o the_o right_a hand_n as_o by_o the_o example_n do_v appear_v then_o over_o the_o first_o figure_n of_o the_o divisor_n towards_o the_o left_a hand_n which_o be_v 2_o 1_o there_o stand_v 18._o so_o i_o demand_v how_o many_o time_n 2_o in_o 18_o answer_v be_v 8_o so_o for_o experience_n i_o multiply_v the_o divisor_n 246_o by_o 8_o the_o product_n will_v be_v 1968_o which_o do_v exceed_v 1894_o the_o number_n stand_v over_o it_o therefore_o i_o do_v conclude_v the_o divisor_n must_v go_v but_o 7_o time_n i_o set_v down_o 7_o for_o the_o three_o figure_n of_o the_o quotient_a and_o proceed_v say_v 7_o time_n 6_o be_v 42_o 2_o from_o 4_o and_o there_o remain_v 2_o and_z 4_o from_o 9_o and_o there_o remain_v 5_o cancel_v the_o 6_o 4_o and_o 9_o set_v the_o remainder_n over_o head_n then_o 7_o time_n 4_o be_v 28_o cancel_v the_o 4_o and_z 8_o from_z 5_o i_o can_v but_o 8_o from_o 15_o and_o there_o remain_v 7_o 1_o as_o i_o borrow_v and_o 2_o be_v 3_o from_o 8_o and_o there_o remain_v 5_o cancel_v your_o figure_n as_o you_o subtract_v from_o then_o 7_o time_n 2_o be_v 14_o 4_o from_z 5_o and_o there_o remain_v 1_o and_z 1_o from_o 1_o and_o there_o remain_v 0_o there_o be_v these_o figure_n uncancel_v 1722._o now_o i_o must_v remove_v the_o divisor_n one_o figure_n more_o towards_o the_o right_a hand_n as_o by_o the_o example_n and_o over_o the_o first_o figure_n of_o your_o divisor_n towards_o the_o left_a hand_n there_o will_v stand_v 17_o i_o demand_v how_o many_o time_n 2_o can_v i_o have_v in_o 17_o i_o find_v but_o 7_o time_n so_o i_o set_v 7_o in_o the_o quotient_a and_o proceed_v in_o multiply_v the_o divisor_n thereby_o say_v 1_o 7_o time_n 6_o be_v 42_o cancel_v the_o 6_o then_o 2_o from_o 2_o and_o there_o remain_v 0_o and_o cancel_v the_o 2_o and_z 4_o from_o 2_o the_o next_o figure_n i_o can_v but_o 4_o from_o 12_o and_o there_o remain_v 8_o and_z 1_o as_o i_o borrow_v from_o 7_o and_o there_o remain_v 6_o cancel_v 2_o and_o 7_o and_o set_v the_o remain_v over_o head_n then_o 7_o time_n 4_o be_v 28_o 8_o from_o 8_o and_o there_o remain_v 0_o and_o 2_o from_o 6_o and_o there_o remain_v 4_o cancel_v 4_o in_o the_o divisor_n and_o 8_o and_o 6_o in_o the_o dividend_n then_o last_o of_o all_o 7_o time_n 2_o be_v 14_o 4_o from_z 4_o and_o there_o remain_v 0_o and_o 1_o from_o 1_o and_o there_o remain_v 0._o the_o division_n be_v 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the_o help_n of_o the_o former_a rule_n example_n it_o be_v require_v to_o divide_v 8748_o by_o 36._o first_o set_v down_o the_o divisor_n 36_o and_o some_o little_a distance_n in_o the_o same_o line_n set_v down_o the_o dividend_n make_v a_o separation_n between_o they_o as_o you_o see_v in_o the_o follow_a example_n so_o i_o demand_v how_o many_o time_n 36_o i_o can_v have_v in_o 1_o 87_o i_o find_v 2_o time_n i_o set_v 2_o in_o the_o quotient_a and_o by_o it_o i_o multiply_v the_o divisor_n say_v 2_o time_n 6_o be_v 12_o setting_z 2_o under_z the_o 7_o which_o be_v the_o second_o figure_n of_o dividend_n then_o proceed_v to_o the_o next_o figure_n of_o the_o divisor_n say_v 2_o time_n 3_o be_v 6_o and_z 1_o as_o i_o carry_v be_v 7_o setting_z down_z the_o 7_o under_z 8_o so_o there_o be_v 72_o the_o product_n of_o the_o divisor_n multiply_v by_o 2_o under_o which_o i_o draw_v a_o line_n and_o subtract_v one_o from_o the_o other_o by_o the_o three_o chapter_n and_o there_o will_v remain_v 15_o which_o place_n under_o the_o line_n at_o which_o time_n the_o operation_n will_v stand_v as_o you_o see_v next_o you_o must_v make_v a_o prick_n under_o the_o next_o figure_n of_o the_o dividend_n be_v 4_o and_o set_v 4_o before_o the_o remainder_n 15_o so_o you_o shall_v have_v 154_o for_o a_o new_a dividend_n as_o you_o see_v now_o i_o demand_v how_o many_o time_n 3_o in_o 15_o i_o find_v 1_o 4_o time_n so_o i_o set_v 4_o for_o the_o second_o figure_n in_o the_o quotient_a and_o i_o multiply_v the_o divisor_n thereby_o and_o the_o product_n 144_o i_o set_v under_o the_o new_a dividend_n 154_o and_o draw_v a_o line_n by_o the_o three_o chapter_n i_o subtract_v one_o from_o the_o other_o and_o there_o will_v remain_v 10._o last_o i_o set_v a_o prick_n under_o the_o next_o figure_n of_o the_o dividend_n which_o be_v the_o last_o being_z 8_o and_o draw_v it_o down_o i_o set_v it_o before_o the_o remainder_n 10_o by_o which_o i_o have_v 108_o for_o a_o new_a dividend_n then_o i_o ask_v how_o many_o time_n 1_o 3_o i_o can_v have_v in_o 10_o i_o find_v 3_o time_n therefore_o i_o set_v down_o 3_o in_o the_o quotient_a and_o multiply_v the_o divisor_n thereby_o i_o set_v the_o product_n which_o be_v 108_o under_o the_o last_o dividend_n and_o subtract_v one_o from_o another_o there_o do_v remain_v 0_o and_o the_o whole_a work_n of_o the_o division_n be_v finish_v but_o if_o it_o do_v fall_v out_o
5._o a_o merchant_n at_o london_n do_v deliver_v for_o frankford_n 140_o l._n sterl_n exchange_n for_o frankford_n at_o 46d_o sterl_n the_o florin_n of_o 66_o kreutrar_n the_o question_n be_v how_o many_o florin_n must_v he_o receive_v at_o 60_o kreutrar_n at_o frankford_n by_o the_o rule_n of_o three_o say_v if_o 46_o d._n give_v i_o 66_o kreutr_n what_o will_v 140_o l_o quest_n 6._o a_o merchant_n in_o antwerp_n take_v up_o money_n by_o exchange_n at_o the_o rate_n of_o 33_o s._n 4_o d._n flemish_n to_o pay_v at_o london_n 20_o s._n sterl_n but_o when_o the_o bill_n of_o exchange_n come_v due_a he_o be_v force_v to_o take_v up_o money_n in_o london_n to_o pay_v the_o say_a bill_n to_o pay_v at_o antwerp_n for_o every_o 20_n sterling_a 33_o s._n 10_o d._n flemish_n i_o desire_v to_o know_v whether_o i_o do_v win_v or_o lose_v and_o how_o much_o in_o the_o 100_o l._n of_o money_n by_o the_o rule_n of_o three_o say_v if_o 33_v 10d_o give_v 33_n 4d_o what_o will_v 100l_n answer_v 98_o l._n 10s_o 5d_o which_o subtract_v from_o 100l_n give_v 1l_o 9_n 7d_o for_o the_o remainder_n and_o so_o much_o be_v lose_v in_o 100_o l._n of_o money_n quest_n 7._o a_o merchant_n at_o cales_n do_v receive_v a_o bill_n of_o exchange_n from_o london_n for_o 1500_o ducat_n which_o be_v the_o value_n of_o 365_o l._n 12_o s._n 6_o d._n sterling_n deliver_v at_o london_n i_o desire_v to_o know_v what_o the_o ducat_n be_v worth_a if_o 1500_o ducat_n cost_v 365l_o 12_n 6d_o what_o cost_v 1_o ducat_n answer_v 4_o l._n 10_o s._n ½_n the_o exchange_n between_o london_n and_o france_n be_v much_o different_a from_o the_o flemish_a exchange_n because_o in_o france_n it_o be_v deliver_v in_o french_a crown_n which_o be_v worth_a 50_o sous_fw-fr tournois_n the_o piece_n for_o in_o france_n they_o do_v account_n by_o denier_n tournois_n account_v 12_o denier_n 1_o sous_fw-fr tournois_n and_o 20_o sous_fw-fr tournois_n 1_o livre_fw-fr or_o frank_n which_o be_v also_o 1_o pound_n tournois_n the_o french_a crown_n in_o commerce_n be_v current_a for_o 51_o sous_fw-fr tournois_n but_o in_o exchange_n it_o will_v pass_v for_o no_o more_o than_o 50_o sous_fw-fr tournois_n which_o be_v 2_o l._n 10_o sous_fw-fr tournois_n the_o crown_n quest_n 8._o a_o merchant_n in_o london_n do_v deliver_v 360_o l._n 2_o s._n 4_o d._n sterling_a exchange_n at_o 5_o s._n 8_o d._n the_o french_a crown_n and_o to_o receive_v at_o paris_n 50_o sous_fw-fr tournois_n for_o every_o french_a crown_n i_o desire_v to_o know_v how_o many_o livre_n i_o shall_v receive_v at_o paris_n for_o the_o 360_o pound_n pay_v in_o london_n by_o the_o rule_n of_o three_o say_v if_o 5_o s._n 8_o d._n give_v 2_o liures_fw-fr 10_o sous_fw-fr what_o will_v 360_o l._n give_v multiply_v and_o divide_v and_o you_o will_v find_v 3177_o livre_n 10_o sous_fw-fr tournois_n and_o so_o much_o must_v i_o receive_v in_o paris_n for_o my_o 360_o pound_n quest_n 9_o a_o merchant_n at_o paris_n do_v deliver_v by_o exchange_n 3784_o livre_n tournois_n at_o 50_o sous_fw-fr tournois_n the_o french_a crown_n and_o for_o each_o french_a crown_n to_o receive_v here_o 5_o s._n 7_o d._n sterling_n in_o london_n i_o desire_v to_o know_v how_o much_o sterling_a money_n i_o shall_v receive_v for_o my_o 3784_o livre_n or_o pound_n tournois_n by_o the_o rule_n of_o three_o say_v if_o 2l_o 10_o sous_fw-fr tournois_n give_v 5s_n 7d_o what_o will_v 3784_o or_o if_o 5_o l._n tournois_n give_v 10_n 2_o d._n sterling_n what_o will_v 3784_o multiply_v and_o divide_v either_o of_o these_o proportion_n and_o you_o will_v find_v the_o four_o proportional_a to_o be_v 422l_o 10_n 11d_o and_o so_o much_o you_o must_v receive_v at_o london_n for_o your_o 3784_o livre_n pay_v or_o deliver_v in_o exchange_n at_o the_o rate_n before_o mention_v chap._n xxx_o of_o gauge_v if_o you_o will_v know_v how_o many_o gallon_n any_o vessel_n contain_v in_o wine_n or_o ale_n measure_n you_o must_v first_o take_v the_o diameter_n of_o the_o head_n of_o the_o say_a vessel_n in_o inch_n than_o the_o diameter_n at_o the_o bung_v withinside_o in_o inch_n then_o in_o the_o respective_a follow_a table_n look_v for_o the_o diameter_n of_o the_o bung_v in_o inches_n before_o take_v which_o you_o will_v find_v in_o the_o respective_a table_n in_o the_o column_n entitle_v inch_n and_o the_o number_n that_o you_o find_v stand_v against_o it_o set_v down_o twice_o then_o in_o the_o same_o column_n entitle_v inch_n look_v for_o the_o diameter_n of_o the_o head_n inches_n and_o the_o number_n stand_v against_o it_o set_v down_o once_o under_o the_o number_n twice_o set_v down_o and_o add_v they_o all_o together_o multiply_v their_o sum_n by_o the_o length_n of_o the_o vessel_n in_o inch_n from_o the_o product_n cut_v off_o 3_o figure_n towards_o the_o right_a hand_n and_o those_o remain_a figure_n towards_o the_o left_a hand_n be_v the_o number_n of_o gallon_n require_v and_o the_o 3_o figure_n cut_v off_o be_v part_n of_o a_o gallon_n either_o of_o ale_n or_o wine_n measure_n according_a to_o the_o table_n from_o whence_o you_o take_v your_o number_n example_n 1._o there_o be_v a_o cask_n or_o vessel_n who_o diameter_n at_o the_o bung_n be_v 26_o inch_n the_o diameter_n at_o the_o head_n be_v 17_o inch_n and_o the_o length_n of_o the_o say_a vessel_n be_v 41_o inch_n i_o desire_v to_o know_v how_o many_o gallon_n of_o wine_n he_o do_v contain_v in_o the_o wine_n table_n over_o against_o 26_o inch_n the_o diameter_n at_o the_o bung_n i_o find_v the_o number_n 0_o 766_o which_o according_a to_o instruction_n i_o set_v down_o twice_o likewise_o against_o the_o number_n 17_o i_o find_v 328_o which_o i_o set_v down_o the_o sum_n of_o all_o these_o three_o be_v 1_o 860_o which_o multiply_v by_o 41_o the_o length_n the_o product_n be_v 76_o 260_o from_o whence_o i_o cut_v off_o the_o three_o figure_n towards_o the_o right_a hand_n and_o there_o will_v remain_v 76_o which_o show_v the_o vessel_n do_v contain_v 76_o gallon_n 260_o 1000_o diameter_n at_o bung_n 26_o 0_o 766_o the_o same_o  _fw-fr 0_o 766_o diameter_n at_o head_n 17_o 0_o 328_o  _fw-fr  _fw-fr 1_o 860_o  _fw-fr  _fw-fr  _fw-fr 41_o  _fw-fr  _fw-fr 1_o 860_o  _fw-fr  _fw-fr 74_o 40_o content_a in_o gallon_n  _fw-fr 76_o 260_o 1000_o example_n 2._o there_o be_v a_o cask_n or_o vessel_n who_o diameter_n at_o bung_n be_v 22_o inch_n his_o diameter_n at_o head_n 16_o inch_n and_o his_o length_n 36_o inch_n i_o do_v desire_n to_o know_v how_o many_o gallon_n of_o ale_n measure_v it_o do_v contain_v out_o of_o the_o respective_a table_n for_o ale_n measure_n i_o find_v the_o diameter_n at_o the_o bung_v 22_o inch_n and_o against_o it_o this_o number_n 450_o which_o i_o set_v down_o twice_o i_o also_o find_v out_o the_o diameter_n at_o head_n 16_o inch_n in_o the_o same_o table_n and_o against_o it_o i_o find_v the_o number_n 238_o which_o i_o set_v down_o as_o you_o see_v add_v all_o these_o together_o and_o their_o sum_n will_v be_v 1138_o which_o multiply_v by_o 36_o the_o length_n of_o the_o cask_n or_o vessel_n the_o product_n will_v be_v 40_o 968_o and_o cut_v off_o three_o figure_n towards_o the_o right_a hand_n there_o remain_v 40_o which_o show_v the_o cask_n do_v contain_v of_o ale_n measure_v 40_o gallon_n 968_o 1000_o diameter_n at_o bung_n 22_o 0_o 450_o the_o same_o again_z  _fw-fr 0_o 450_o diameter_n at_o head_n 16_o 0_o 238_o  _fw-fr  _fw-fr 1_o 138_o  _fw-fr  _fw-fr  _fw-fr 36_o  _fw-fr  _fw-fr 6_o 828_o  _fw-fr  _fw-fr 34_o 14_o content_a in_o gallon_n  _fw-fr 40_o 968_o 1000_o a_o table_n show_v how_o to_o find_v the_o content_a of_o any_o cask_n or_o vessel_n in_o gallon_n etc._n etc._n inc_n ale_n inc_n measure_n inc_n wine_n inc_n measure_n 1_o 0_o 001_o 31_o 0_o 892_o 1_o 0_o 001_o 31_o 1_o 089_o 2_o 0_o 004_o 32_o 0_o 951_o 2_o 0_o 005_o 32_o 1_o 160_o 3_o 0_o 008_o 33_o 1_o 011_o 3_o 0_o 010_o 33_o 1_o 234_o 4_o 0_o 015_o 34_o 1_o 073_o 4_o 0_o 016_o 34_o 1_o 310_o 5_o 0_o 023_o 35_o 1_o 137_o 5_o 0_o 028_o 35_o 1_o 388_o 6_o 0_o 032_o 36_o 1_o 203_o 6_o 0_o 041_o 36_o 1_o 469_o 7_o 0_o 045_o 37_o 1_o 271_o 7_o 0_o 056_o 37_o 1_o 551_o 8_o 0_o 059_o 38_o 1_o 341_o 8_o 0_o 072_o 38_o 1_o 636_o 9_o 0_o 075_o 39_o 1_o 412_o 9_o 0_o 092_o 39_o 1_o 724_o 10_o 0_o 093_o 40_o 1_o 485_o 10_o 0_o 113_o 40_o 1_o 813_o 11_o 0_o 112_o 41_o 1_o 561_o 11_o 0_o 137_o 41_o 1_o 904_o 12_o 0_o 134_o 42_o 1_o 638_o 12_o 0_o 163_o 42_o 2_o 000_o 13_o 0_o 157_o 43_o 1_o 717_o 13_o 0_o 192_o 43_o 2_o 096_o 14_o 0_o 182_o 44_o 1_o 797_o
14_o 0_o 221_o 44_o 2_o 194_o 15_o 0_o 208_o 45_o 1_o 880_o 15_o 0_o 255_o 45_o 2_o 295_o 16_o 0_o 238_o 46_o 1_o 965_o 16_o 0_o 296_o 46_o 2_o 398_o 17_o 0_o 264_o 47_o 2_o 051_o 17_o 0_o 328_o 47_o 2_o 504_o 18_o 0_o 301_o 48_o 2_o 139_o 18_o 0_o 367_o 48_o 2_o 611_o 19_o 0_o 335_o 49_o 2_o 219_o 19_o 0_o 409_o 49_o 2_o 721_o 20_o 0_o 371_o 50_o 2_o 321_o 20_o 0_o 453_o 50_o 2_o 833_o 21_o 0_o 409_o 51_o 2_o 415_o 21_o 0_o 500_o 51_o 2_o 948_o 22_o 0_o 450_o 52_o 2_o 510_o 22_o 0_o 548_o 52_o 3_o 065_o 23_o 0_o 491_o 53_o 2_o 608_o 23_o 0_o 600_o 53_o 3_o 184_o 24_o 0_o 535_o 54_o 2_o 707_o 24_o 0_o 653_o 54_o 3_o 305_o 25_o 0_o 580_o 55_o 2_o 808_o 25_o 0_o 708_o 55_o 3_o 428_o 26_o 0_o 628_o 56_o 2_o 911_o 26_o 0_o 766_o 56_o 3_o 554_o 27_o 0_o 677_o 57_o 3_o 016_o 27_o 0_o 826_o 57_o 3_o 682_o 28_o 0_o 728_o 58_o 3_o 123_o 28_o 0_o 888_o 58_o 3_o 813_o 29_o 0_o 781_o 59_o 3_o 232_o 29_o 0_o 933_o 59_o 3_o 945_o 30_o 0_o 836_o 60_o 3_o 341_o 30_o 1_o 020_o 60_o 4_o 080_o chap._n xxxi_o the_o extraction_n of_o the_o square_a root_n it_o be_v necessary_a to_o insert_v the_o table_n of_o the_o square_n of_o all_o the_o nine_o digit_n as_o follow_v root_n square_n 1_o 1_o 2_o 4_o 3_o 9_o 4_o 16_o 5_o 25_o 6_o 36_o 7_o 49_o 8_o 64_o 9_o 81_o example_n it_o be_v require_v to_o extract_v the_o square_a root_n of_o 22429696_o set_v a_o mark_n or_o prick_v with_o your_o pen_n under_o the_o first_o figure_n towards_o your_o right_a hand_n and_o so_o under_o every_o second_o figure_n as_o you_o see_v so_o will_v your_o give_a number_n be_v divide_v into_o four_o part_n or_o point_n whereby_o you_o must_v note_v that_o the_o root_n will_v admit_v of_o four_o figure_n for_o the_o square_a root_n of_o the_o give_v number_n do_v always_o admit_v of_o as_o many_o figure_n as_o the_o give_v number_n do_v admit_v point_n then_o proceed_v to_o the_o extraction_n thus_o beginning_n at_o the_o left_a hand_n the_o first_o point_n be_v 22_o by_o the_o former_a table_n of_o square_n i_o find_v 16_o to_o be_v the_o great_a square_a number_n contain_v therein_o who_o square_a root_n be_v 4_o therefore_o i_o set_v down_o 4_o in_o the_o quotient_a and_o the_o square_a thereof_o 16_o i_o set_v underneath_o 22_o and_o i_o subtract_v one_o from_o the_o other_o and_o there_o remain_v 6_o which_o i_o set_v underneath_o to_o this_o remainder_n 6_o i_o draw_v down_o the_o next_o point_n 42_o which_o do_v make_v the_o number_n 642_o next_o i_o double_v the_o quotient_a 4_o which_o be_v 8_o which_o i_o set_v down_o one_o figure_n short_a of_o the_o right_a hand_n as_o you_o see_v then_o do_v i_o seek_v how_o many_o time_n 8_o will_v go_v in_o 64_o which_o be_v 7_o time_n set_v down_o 7_o under_o that_o vacant_a figure_n towards_o your_o right_a hand_n 2_o and_o likewise_o set_v down_o 7_o in_o the_o quotient_a and_o multiply_v 87_o by_o 7_o who_o product_n 609_o set_v under_o the_o line_n and_o subtract_v it_o from_o the_o number_n make_v of_o the_o last_o remainder_n and_o the_o point_n last_o bring_v down_o 642_o and_o the_o remainder_n of_o this_o subtraction_n will_v be_v 33_o to_o which_o remainder_n draw_v down_o the_o next_o point_n 96_o and_o it_o make_v the_o number_n 3396_o next_o double_v the_o quotient_a 47_o it_o make_v 94_o which_o set_v under_o the_o number_n 3396_o that_o it_o may_v stand_v one_o figure_n short_a towards_o the_o right_a hand_n as_o you_o see_v in_o the_o follow_a example_n then_o ask_v how_o many_o time_n 94_o be_v contain_v in_o the_o number_n or_o figure_n stand_v over_o they_o 339_o answer_v be_v three_o time_n therefore_o i_o set_v down_o 3_o to_o the_o right_a hand_n of_o 94_o also_o i_o set_v down_o 3_o in_o the_o quotient_a then_o do_v i_o multiply_v 943_o by_o 3_o the_o last_o figure_n in_o the_o quotient_a and_o the_o product_n of_o the_o multiplication_n 2829_o i_o set_v underneath_o the_o line_n and_o subtract_v it_o from_o the_o number_n make_v of_o the_o last_o remainder_n and_o the_o point_n last_o bring_v down_o which_o be_v 3396_o and_o of_o this_o subtraction_n there_o do_v remain_v 567_o last_o to_o this_o remainder_n i_o draw_v down_o the_o next_o point_n 96_o and_o it_o make_v the_o number_n 56796_o now_o double_a the_o quotient_a 473_o which_o make_v 946_o and_o set_v it_o under_o the_o number_n 56796_o that_o it_o stand_v one_o figure_n short_a towards_o your_o right_a hand_n as_o you_o see_v and_o ask_v how_o many_o time_n 946_o be_v contain_v in_o the_o figure_n stand_v over_o he_o 5679_o answer_v be_v 6_o time_n set_v down_o 6_o to_o the_o right_a hand_n of_o 946_o and_o also_o in_o the_o quotient_a and_o multiply_v 9466_o by_o 6_o the_o last_o figure_n set_v in_o the_o quotient_a and_o the_o product_n of_o such_o multiplication_n i_o set_v down_o under_o the_o line_n be_v 56796_o which_o i_o subtract_v from_o the_o number_n compose_v of_o the_o last_o remainder_n and_o last_o point_n bring_v down_o which_o be_v 56796_o and_o there_o will_v remain_v 0_o and_o have_v no_o 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8_o 3_o 27_o 4_o 64_o 5_o 125_o 6_o 216_o 7_o 343_o 8_o 512_o 9_o 729_o example_n let_v it_o be_v require_v to_o extract_v the_o cube_n root_n of_o the_o give_v number_n 42144192._o first_o point_v the_o give_v number_n as_o you_o see_v set_v a_o prick_n under_o the_o first_o figure_n towards_o your_o right_a hand_n and_o so_o under_o every_o three_o figure_n as_o you_o see_v every_o prick_n except_o the_o last_o towards_o the_o left_a hand_n contain_v three_o figure_n and_o that_o contain_v the_o two_o figure_n 42_o therefore_o in_o the_o forego_n table_n find_v out_o the_o great_a cube_n number_n in_o 42_o which_o i_o find_v to_o be_v 27_o who_o cube_n root_n be_v 3_o which_o place_n in_o the_o quotient_a and_o subtract_v the_o cube_n number_n 27_o from_o 42_o and_o there_o will_v remain_v 15_o which_o place_n under_o neath_a to_o this_o remainder_n bring_v down_o the_o next_o point_n 144_o so_o have_v you_o the_o number_n 15144_o which_o call_v your_o resolve_v draw_v a_o line_n under_o square_v the_o quotient_a 3_o which_o be_v 9_o multiply_v the_o say_v spuare_fw-la 9_o by_o 300_o and_o the_o product_n thereof_o 2700_o place_n under_o the_o resolvend_n and_o call_v it_o the_o treble_a square_n again_o multiply_v the_o quotient_a 3_o by_o 30_o which_o make_v 90_o place_n 90_o under_o the_o treble_a square_n and_o call_v it_o the_o treble_a quotient_n add_v the_o treble_a square_n and_o treble_a quotient_n together_o into_o one_o sum_n and_o it_o make_v 2790_o which_o call_v your_o divisor_n then_o examine_v how_o often_o you_o can_v take_v your_o divisor_n in_o your_o resolvend_n which_o be_v four_o time_n set_v 4_o in_o the_o quotient_a then_o multiply_v the_o treble_a square_a 2700_o by_o the_o 4_o last_v place_v in_o the_o quotient_a and_o subscribe_v the_o product_n underneath_o your_o divisor_n square_v the_o last_o say_v figure_n in_o the_o quotient_a 4_o which_o be_v 16_o thereby_o multiply_v the_o treble_a quotient_a 90_o and_o the_o product_n thereof_o 1440_o place_n under_o the_o last_o product_n 10800_o cube_fw-la the_o figure_n 4_o last_v place_v in_o the_o quotient_a which_o by_o the_o forego_n table_n be_v 64_o and_o place_n it_o under_o the_o precede_a product_n then_o add_v these_o three_o product_n into_o one_o sum_n and_o subtract_v the_o sum_n thereof_o 12304_o from_o your_o resolve_v and_o there_o will_v remain_v 2840_o to_o this_o remainder_n draw_v down_o the_o next_o point_n 192_o and_o the_o number_n 2840192_o be_v a_o new_a resolvend_n under_o which_o draw_v a_o line_n then_o square_a the_o quotient_a 34_o which_o be_v 1156_o which_o square_a multiply_v by_o 300_o and_o the_o product_n 346800_o set_v under_o the_o resolvend_n and_o call_v it_o the_o treble_a square_n as_o before_o then_o multiply_v the_o quotient_a 34_o by_o 30_o and_o the_o product_n thereof_o 1020_o set_v under_o the_o treble_a square_n and_o call_v it_o the_o treble_a quotient_n and_o the_o sum_n of_o the_o treble_a square_n and_o treble_a quotient_n be_v 347820_o which_o call_v your_o divisor_n and_o examine_v how_o often_o you_o can_v take_v your_o last_o divisor_n in_o your_o last_o resolvend_n which_o will_v be_v 8_o time_n therefore_o set_v 8_o in_o the_o quotient_a multiply_v your_o last_o treble_a square_n by_o the_o last_o figure_n in_o your_o quotient_a 8_o the_o product_n thereof_o 2774400_o subscribe_v under_o your_o last_o divisor_n square_v the_o last_o figure_n in_o your_o quotient_a 8_o which_o be_v 64_o by_o which_o multiply_v the_o last_o treble_a quotient_n the_o product_n 65280_o set_v under_o the_o last_o product_n then_o cube_fw-la the_o last_o figure_n of_o your_o quotient_a 8_o which_o by_o the_o forego_n table_n you_o will_v find_v to_o be_v 512_o which_o place_n under_o the_o precede_a product_n and_o add_v all_o these_o three_o product_n into_o one_o sum_n which_o make_v 2840192_o which_o if_o you_o subtract_v from_o your_o last_o resolvend_n there_o will_v remain_v 0_o and_o in_o such_o manner_n must_v you_o proceed_v by_o reiterate_v the_o work_n by_o square_n the_o quotient_a until_o all_o the_o figure_n be_v bring_v down_o but_o in_o this_o example_n the_o work_n be_v finish_v for_o there_o be_v no_o more_o figure_n to_o draw_v down_o and_o 0_o remains_o so_o the_o cube_n root_n of_o 42144192_o be_v 348_o as_o be_v require_v to_o prove_v the_o extraction_n of_o the_o cube_n root_n multiply_v the_o cube_n root_n find_v by_o itself_o then_o multiply_v the_o product_n of_o the_o multiplication_n by_o the_o root_n find_v and_o the_o product_n of_o this_o second_o multiplication_n be_v the_o give_v number_n who_o cube_n root_n be_v require_v example_n it_o be_v require_v to_o prove_v this_o example_n of_o the_o extraction_n of_o the_o cube_n root_n wherein_o the_o cube_n root_n find_v be_v 348_o which_o multiply_v by_o 348_o and_o the_o product_n of_o the_o multiplication_n will_v be_v 121104_o which_o multiply_v again_o by_o 348_o the_o root_n find_v produce_v the_o give_v number_n to_o be_v extract_v 42144192_o whereby_o it_o be_v conclude_v the_o operation_n be_v right_a finis_fw-la there_o be_v new_o publish_v by_o the_o same_o author_n the_o accomptant_n guide_v or_o merchant_n book-keeper_n contain_v a_o explanation_n of_o all_o the_o most_o useful_a and_o necessary_a rule_n of_o arithmetic_n that_o the_o mean_a capacity_n thereby_o may_v attain_v to_o the_o knowledge_n thereof_o with_o table_n for_o the_o reduce_n of_o flemish_a ell_n into_o english_a and_o english_a into_o flemish_n also_o for_o the_o ready_a and_o exact_a compute_v of_o the_o custom_n of_o holland_n cloth_n tobacco_n and_o reduce_v uncertain_a cask_n of_o oil_n by_o the_o weight_n in_o tun_n and_o gallon_n and_o table_n of_o exchange_n for_o the_o ready_a and_o exact_a compute_v of_o any_o sum_n of_o money_n remit_v from_o england_n to_o holland_n flanders_n france_n spain_n and_o italy_n et_fw-la contra._n instruction_n for_o the_o methodical_a keep_n of_o 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do_v remain_v 3_o two_o pence_n which_o be_v 6_o penny_n and_o the_o 1_o 20_o of_o 3191_o be_v 159_o pound_n and_o 11_o shilling_n remain_v so_o the_o whole_a sum_n do_v amount_v 10_o 159_o l._n 11_o s._n 6_o d._n 2_o quarter_n proposition_n 3._o if_o the_o price_n of_o a_o unite_v in_o sum_n propound_v be_v 3_o farthing_n then_o take_v the_o ¼_n of_o sum_n propound_v which_o will_v be_v three_o pence_n and_o if_o any_o thing_n remain_v it_o will_v be_v so_o many_o three_o farthing_n then_o the_o ¼_n of_o the_o three_o pence_n be_v shilling_n and_o what_o do_v remain_v be_v so_o many_o three_o pence_n and_o the_o 1_o 20_o of_o those_o shilling_n be_v pound_n as_o before_o example_n in_o the_o last_o of_o these_o example_n you_o find_v it_o require_v for_o to_o know_v how_o much_o 769327_o l._n at_o 3_o farthing_n per_fw-la pound_n come_v to_o the_o ¼_n of_o 769327_o be_v 192331_o three_o pence_n and_o there_o remain_v three_o time_n three_o farthing_n which_o be_v 2_o d._n 1_o qu._n 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shilling_n the_o 1_o 20_o of_o 3547_o shilling_n be_v 177_o pound_n and_o 7_o shilling_n remain_v as_o by_o the_o follow_a operation_n of_o every_o even_a part_n of_o a_o shilling_n above_o the_o value_n of_o 3_o farthing_n i_o have_v demonstrate_v by_o these_o follow_a example_n which_o need_v little_a or_o no_o explanation_n be_v so_o plain_a that_o at_o first_o sight_n they_o may_v be_v understand_v example_n proposition_n 5._o if_o the_o price_n of_o a_o unite_v of_o the_o propound_a sum_n be_v penny_n and_o not_o the_o even_a part_n of_o a_o shilling_n than_o you_o must_v divide_v the_o price_n give_v into_o even_a part_n as_o 7_o d._n be_v not_o even_o part_n of_o a_o shilling_n yet_o may_v be_v divide_v into_o even_a part_n as_o 4_o d._n and_o 3_o d._n make_v 7_o d._n and_o be_v both_o even_a part_n of_o a_o shilling_n in_o which_o case_n work_v thus_o first_o take_v â…“_n and_o then_o the_o 1_o â—_o of_o the_o give_v number_n and_o add_v the_o â…“_n and_o ¼_n of_o the_o number_n give_v together_o and_o you_o have_v the_o true_a number_n of_o shilling_n the_o 1_o 20_o whereof_o be_v pound_n as_o before_o likewise_o 9_o d._n be_v ½_n and_o ¼_n or_o three_o time_n ¼_n 11_o d._n be_v ½_n and_o 1_o â—_o and_o â…™_n or_o else_o it_o be_v 1_o â—_o and_o â…“_n and_o ¼_n of_o a_o shilling_n as_o by_o the_o follow_a operation_n do_v more_o plain_o appear_v where_o you_o have_v a_o example_n of_o every_o uneven_a part_n of_o a_o shilling_n the_o price_n be_v any_o number_n of_o penny_n only_o proposition_n 6._o when_o the_o price_n of_o a_o unite_v of_o the_o give_v number_n be_v pence_n and_o farthing_n and_o if_o it_o be_v a_o even_a part_n of_o a_o shilling_n work_v as_o in_o the_o four_o proposition_n but_o if_o it_o be_v uneven_a part_n of_o a_o shilling_n as_o 1_o ¼_n 1_o ¾_n 2_o 1_o â—_o 2_o ¾_n or_o the_o like_a first_o find_v out_o some_o part_n of_o the_o price_n that_o be_v a_o equal_a part_n of_o a_o shilling_n then_o consider_v what_o part_n the_o remainder_n of_o the_o price_n be_v of_o that_o even_a part_n and_o divide_v that_o even_a part_n thereby_o then_o take_v their_o sum_n which_o be_v the_o true_a number_n of_o shilling_n the_o 1_o 20_o whereof_o be_v pound_n as_o before_o example_n it_o be_v require_v to_o know_v how_o much_o 28762_o l._n be_v worth_n at_o 1_o ¼_n first_o i_o take_v the_o 1_o 12_o which_o be_v 2396_o shilling_n and_o there_o remain_v 10_o d._n now_o 2396_o shilling_n 10_o d._n be_v the_o value_n of_o the_o say_a number_n at_o 1_o d._n per_fw-la pound_n and_o 1_o farthing_n be_v ¼_n of_o a_o penny_n therefore_o the_o ¼_n of_o the_o value_n at_o 1_o d._n per_fw-la pound_n 2396_o shilling_n and_o 10_o which_o be_v 599_o shilling_n 2_o ½_n be_v the_o value_n of_o the_o say_a number_n at_o 1_o farthing_n per_fw-la prove_v which_o add_v together_o give_v 2996_o shilling_n one_o half_a penny_n the_o 1_o 20_o whereof_z 149_o 16_o 0_o 2_o qu._n be_v the_o whole_a sum_n require_v in_o the_o forego_n example_n you_o may_v perceive_v how_o the_o several_a example_n be_v wrought_v by_o divide_v the_o give_v price_n into_o so_o many_o even_a part_n as_o will_v make_v the_o complete_a price_n although_o it_o may_v consist_v of_o 3_o 4_o or_o 5_o division_n as_o in_o the_o 10._o example_n the_o price_n be_v 11_o d._n 3_o qu._n which_o be_v make_v up_o with_o the_o ½_n and_o 1_o â—_o and_o ¼_n of_o the_o â…“_n and_o the_o ½_n of_o the_o ¼_n and_o the_o ½_n of_o that_o ½_n as_o 6_o 4_o 1_o ½_n and_o ¼_n which_o all_o put_v together_o make_v 11_o ¾_n proposition_n 7._o if_o the_o price_n of_o a_o unit_fw-la of_o the_o give_a number_n be_v 2_o shilling_n cut_v off_o the_o figure_n towards_o the_o right_a hand_n of_o the_o give_v number_n and_o double_v it_o the_o product_n will_v be_v shilling_n and_o the_o remain_a figure_n towards_o the_o left_a hand_n be_v pound_n example_n let_v it_o be_v require_v to_o know_v how_o much_o 1283_o yard_n be_v worth_a at_o 2_o shilling_n per_fw-la yard_n the_o figure_n towards_o the_o right_a hand_n which_o be_v 3_o be_v cut_v off_o and_o double_v make_v 6_o shilling_n and_o the_o remain_a figure_n 128_o be_v pound_n so_o 108_o the_o true_a worth_n of_o 1283_o yard_n at_o 2_o shilling_n per_fw-la yard_n come_v to_o 128_o pound_n 6_o shilling_n as_o by_o the_o annex_v example_n may_v appear_v be_v the_o answer_n and_o solution_n of_o the_o question_n as_o be_v require_v by_o this_o proposition_n we_o gather_v that_o when_o the_o price_n of_o any_o number_n of_o yard_n pound_n etc._n etc._n be_v a_o even_a number_n of_o shilling_n with_o the_o half_a of_o the_o even_a number_n multiply_v the_o give_v number_n but_o double_a the_o first_o figure_n of_o the_o product_n and_o set_v it_o apart_o for_o shilling_n and_o the_o rest_n of_o the_o product_n shall_v be_v pound_n example_n let_v it_o be_v require_v to_o know_v how_o much_o 5783_o ell_n of_o linen_n come_v unto_o at_o 14_o s._n per_fw-la ell_n for_o the_o solution_n whereof_o i_o take_v 108_o half_a of_o the_o price_n give_v which_o be_v 7_o and_o therewith_o i_o do_v multiply_v the_o give_v number_n 5783_o say_v 7_o time_n 3_o be_v 21_o now_o according_a to_o the_o rule_n i_o double_v the_o first_o figure_n 1_o which_o make_v 2_o shilling_n set_v it_o apart_o and_o i_o carry_v 2_o to_o the_o next_o figure_n say_v 7_o time_n 8_o be_v 56_o and_o 2_o as_o i_o carry_v be_v 58_o set_v down_o 8_o and_o carry_z 5_o proceed_v according_a to_o the_o instruction_n of_o the_o 4._o chapter_n and_o you_o will_v find_v the_o remain_a part_n of_o the_o product_n to_o be_v 4048._o so_o i_o find_v that_o 5783_o yard_n ell_n or_o pound_n at_o 14_o be_v worth_a 4048_o l._n 2_o s._n as_o by_o the_o annex_v example_n do_v appear_v proposition_n 8._o if_o the_o price_n of_o a_o unit_fw-la of_o the_o give_a number_n be_v any_o odd_a number_n of_o shilling_n work_v the_o even_a number_n of_o shilling_n by_o the_o last_o example_n of_o the_o 7._o proposition_n and_o for_o the_o odd_a shilling_n take_v the_o 1_o 20_o of_o the_o give_v number_n and_o add_v these_o two_o together_o and_o you_o will_v find_v your_o desire_n as_o by_o these_o follow_a example_n do_v appear_v where_o in_o the_o first_o towards_o your_o left_a hand_n it_o be_v require_v to_o know_v how_o much_o 7393_o yard_n come_v unto_o at_o 7_o s._n per_fw-la yard_n for_o the_o even_a number_n of_o 6_o s._n per_fw-la yard_n by_o the_o second_o example_n of_o the_o 7._o proposition_n 7393_o yard_n come_v to_o 2217_o l._n 18_o s._n then_o the_o 1_o
of_o long_a measure_n in_o the_o second_o chapter_n will_v inform_v you_o of_o the_o several_a denomination_n and_o their_o content_n and_o the_o way_n of_o subtract_v by_o the_o follow_a example_n example_n engl._n mile_n furl_n pole_n yard_n foot_n inch_n b._n corn._n  _fw-fr 156_o 5_o 33_o 4_o 3_o 11_o 2_o  _fw-fr 98_o 7_o 17_o 5_o 2_o 07_o 1_o  _fw-fr 57_o 6_o 15_o 4½_n 1_o 04_o 1_o subtraction_n of_o cloth_n measure_n here_o it_o will_v be_v convenient_a to_o let_v you_o know_v as_o by_o the_o say_a table_n in_o the_o second_o chapter_n of_o addition_n you_o may_v discern_v that_o in_o cloth_n measure_v there_o be_v three_o sort_n of_o measure_n as_o broad_a cloth_n be_v measure_v by_o yard_n quarter_n and_o nail_n linen_n cloth_n in_o england_n by_o ell_n quarter_n and_o nail_n and_o linen_n cloth_n in_o holland_n by_o flemish_a ell_n quarter_n and_o nail_n in_o each_o of_o which_o it_o will_v be_v convenient_a to_o give_v a_o example_n and_o to_o note_v that_o whereas_o by_o the_o table_n of_o cloth_n measure_n in_o addition_n you_o find_v 4_o quarter_n be_v 1_o yard_n 5_o quarter_n 1_o english_a ell_n and_o 3_o quarter_n 1_o flemish_a ell_n it_o be_v to_o be_v 5_o such_o quarter_n as_o one_o yard_n do_v contain_v viz._n 1_o quarter_n more_o make_v a_o ell_n english_a and_o 3_o quarter_n of_o our_o english_a yard_n make_v 1_o ell_n flemish_n  _fw-fr example_n 1._o example_n 2._o  _fw-fr yard_n qr_n na_fw-fr ells._n qr_n n._n buy_v in_o england_n 215_o 3_o 1_o 163_o 4_o 2_o sold_n 127_o 2_o 2_o 86_o 4_o 3_o remain_v 88_o 0_o 3_o 76_o 4_o 3_o example_n 3._o  _fw-fr flem._n ells._n qr_n nail_n buy_v 479_o 1_o 2_o sold_n 247_o 2_o 3_o remain_v 231_o 1_o 3_o subtraction_n of_o time_n you_o will_v find_v by_o the_o table_n of_o time_n that_o 60_o minute_n make_v a_o hour_n 24_o hour_n one_o natural_a day_n 365_o day_n one_o year_n by_o the_o follow_a example_n of_o subtraction_n you_o more_o plain_o understand_v how_o to_o work_v all_o such_o like_a example_n example_n year_n day_n hour_n min._n 348_o 340_o 16_o 45_o 179_o 285_o 12_o 25_o 169_o 55_o 04_o 20_o proof_n of_o subtraction_n when_o your_o subtraction_n be_v end_v if_o you_o desire_v to_o prove_v your_o work_n whether_o you_o have_v do_v right_a or_o wrong_n add_v the_o remainder_n to_o the_o number_n that_o be_v to_o be_v subtract_v and_o if_o the_o sum_n of_o those_o two_o number_n be_v equal_a to_o the_o great_a number_n or_o number_n from_o whence_o the_o subtraction_n be_v to_o be_v make_v than_o your_o subtraction_n be_v true_a otherwise_o false_a thus_o let_v we_o prove_v the_o second_o example_n of_o this_o chapter_n where_o after_o subtraction_n be_v end_v the_o number_n stand_v as_o you_o see_v the_o remainder_n or_o difference_n be_v 3311_o l._n 16_o s._n 09_o d._n ½_n now_o to_o prove_v the_o work_n i_o add_v this_o remainder_n 3311_o 16_o 1_o l._n s._n d._n f._n 7836_o 14_o 7_o 1_o 4524_o 17_o 9_o 3_o 3311_o 16_o 9_o 2_o 7836_o 14_o 7_o 1_o 9_o 2_o to_o the_o number_n that_o be_v to_o be_v subtract_v which_o be_v 4524_o 17_o 9_o 3_o and_o the_o sum_n of_o these_o two_o number_n be_v 7836_o l._n 14_o s._n 7_o d._n ½_n be_v equal_a to_o the_o number_n from_o whence_o the_o subtraction_n be_v to_o be_v make_v therefore_o i_o do_v conclude_v the_o subtraction_n be_v true_a chap._n iu._n multiplication_n mvltiplication_n be_v a_o rule_n which_o teach_v by_o two_o number_n give_v to_o produce_v a_o three_o number_n which_o shall_v contain_v one_o of_o the_o give_v number_n so_o often_o as_o there_o be_v unit_v in_o the_o other_o and_o it_o serve_v instead_o of_o many_o addition_n be_v a_o compound_v of_o many_o equal_a number_n into_o one_o sum_n by_o multiply_v one_o sum_n into_o another_o for_o it_o increase_v one_o number_n so_o often_o as_o there_o be_v unit_v in_o the_o other_o 2._o multiplication_n do_v consist_v of_o three_o part_n or_o number_n that_o be_v to_o say_v the_o multiplicand_a the_o multiplicator_n and_o the_o 1_o product_n the_o multiplicand_n be_v the_o number_n to_o be_v multiply_v the_o multiplicator_n be_v the_o number_n give_v by_o which_o the_o multiplicand_a be_v to_o be_v multiply_v and_o the_o product_n be_v the_o number_n which_o come_v of_o the_o multiplication_n as_o you_o see_v in_o the_o margin_n 384_o be_v the_o multiplicand_a or_o number_n to_o be_v multiply_v 23_o be_v the_o multiplicator_n or_o number_n by_o which_o the_o multiplicand_a be_v to_o be_v multiply_v and_o 8732_o be_v the_o product_n or_o number_n that_o arise_v and_o come_v by_o the_o say_a multiplication_n contain_v the_o multiplicand_a so_o often_o as_o there_o be_v unit_v in_o the_o multiplier_n that_o be_v 23_o time_n for_o the_o product_n contain_v the_o multiplicand_a as_o many_o time_n as_o there_o be_v unit_v in_o the_o multiplicator_n it_o make_v no_o difference_n which_o of_o the_o two_o give_v number_n you_o make_v the_o multiplicand_a or_o the_o multiplicator_n for_o 8_o multiply_v by_o 6_o be_v as_o much_o as_o 6_o multiply_v by_o 8_o but_o common_o the_o great_a number_n be_v make_v the_o multiplicand_a stand_v uppermost_a and_o the_o lesser_a number_n the_o multiplicator_n stand_v under_o the_o multiplicand_a the_o learner_n must_v get_v the_o follow_a table_n complete_o by_o heart_n before_o he_o can_v proceed_v any_o further_a in_o arithmetic_n because_o there_o be_v no_o rule_n in_o arithmetic_n but_o have_v a_o great_a dependence_n upon_o multiplication_n and_o division_n multiplication_n table_n 1_o 2_o 3_o 4_o 5_o 6_o 7_o 8_o 9_o 10_o 11_o 12_o 2_o 4_o 6_o 8_o 10_o 12_o 14_o 16_o 18_o 20_o 22_o 24_o 3_o 6_o 9_o 12_o 15_o 18_o 21_o 24_o 27_o 30_o 33_o 36_o 4_o 8_o 12_o 16_o 20_o 24_o 28_o 32_o 36_o 40_o 44_o 48_o 5_o 10_o 15_o 20_o 25_o 30_o 35_o 40_o 45_o 50_o 55_o 60_o 6_o 12_o 18_o 24_o 30_o 36_o 42_o 48_o 54_o 60_o 66_o 72_o 7_o 14_o 21_o 28_o 35_o 42_o 49_o 56_o 63_o 70_o 77_o 84_o 8_o 16_o 24_o 32_o 40_o 48_o 56_o 64_o 72_o 80_o 88_o 96_o 9_o 18_o 27_o 36_o 45_o 54_o 63_o 72_o 81_o 90_o 99_o 108_o 10_o 20_o 30_o 40_o 50_o 60_o 70_o 80_o 90_o 100_o 110_o 120_o 11_o 22_o 33_o 44_o 55_o 66_o 77_o 88_o 99_o 110_o 121_o 132_o 12_o 24_o 36_o 48_o 60_o 72_o 84_o 96_o 108_o 120_o 132_o 144_o the_o use_n of_o this_o table_n be_v not_o difficult_a in_o the_o top_n of_o the_o table_n you_o have_v these_o number_n 1_o 2_o 3_o 4_o 5_o 6_o 7_o 8_o 9_o 10_o 11_o 12_o and_o likewise_o down_o the_o first_o column_n towards_o your_o left_a hand_n you_o have_v the_o same_o figure_n 1_o 2_o 3_o 4_o 5_o 6_o 7_o 8_o 9_o 10_o 11_o 12_o and_o in_o their_o respective_a column_n you_o have_v all_o those_o number_n multiply_v by_o one_o another_o so_o that_o if_o you_o will_v know_v the_o product_n of_o any_o two_o give_v number_n from_o 1_o to_o 12_o multiply_v together_o look_v for_o either_o of_o the_o two_o give_v number_n in_o the_o top_n or_o uppermost_a column_n and_o for_o the_o other_o in_o the_o side_n column_n guide_v your_o eye_n in_o the_o same_o until_o you_o come_v under_o 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desire_v to_o know_v whether_o i_o gain_v or_o lose_v and_o how_o much_o per_fw-la cent._n by_o the_o rule_n of_o three_o say_v if_o 1_o yard_n cost_v 7_o s._n 6_o d._n what_o cost_v 32_o yard_n answer_v 12_o 0_o 0_o if_o 1_o yard_n cost_v 12_o 6_o what_o cost_v 18_o yard_n answer_v 11_o 5_o 0_o 50_o 23_o 5_o 0_o so_o i_o find_v the_o two_o piece_n contain_v 50_o yard_n and_o cost_v i_o 23_o l._n 5_o s._n 0_o d._n but_o i_o sell_v they_o round_o for_o 10_o s._n per_fw-la yard_n and_o by_o the_o rule_n of_o three_o say_v if_o 1_o yard_n sell_v for_o 10_o s._n what_o will_v 50_o yard_n sell_v for_o answer_v 25_o l._n by_o multiply_v and_o divide_v you_o will_v find_v it_o to_o amount_v unto_o 25_o l._n so_o that_o i_o have_v gain_v 1_o l._n 15_o s._n now_o to_o know_v how_o much_o per_fw-la cent._n i_o have_v gain_v by_o the_o rule_n of_o three_o say_v if_o 23_o l._n 5_o s._n gain_n 1_o l._n 15_o s._n what_o will_v 100_o l._n gain_n answer_v 7_o l._n 10_o s._n 6_o d._n ¼_n multiply_v and_o divide_v and_o you_o will_v find_v you_o have_v gain_v 7_o 10_o 6_o ¼_n in_o 100_o l._n which_o be_v the_o answer_n to_o the_o question_n as_o be_v require_v quest_n 6._o if_o i_o buy_v 100_o of_o orange_n at_o 2_o a_o penny_n and_o another_o at_o 3_o a_o penny_n and_o sell_v they_o 5_o for_o two_o penny_n i_o require_v to_o know_v how_o much_o be_v lose_v or_o gain_v by_o the_o rule_n of_o three_o say_v if_o 2_o or._n cost_n 1_o d._n what_o cost_v 100_o ans_fw-fr 4_o 2_o if_o 3_o or._n cost_n 1_o d._n what_o cost_v 100_o ans_fw-fr 2_o 9â…“_n 5_o 200_o 6_o 11â…“_n if_o 5_o orange_n cost_v 2_o d._n what_o cost_v 200_o answer_v 80_o d._n or_o 6_o s._n 8_o d._n so_o i_o find_v by_o multiply_v and_o divide_v the_o several_a operation_n that_o there_o be_v 3_o d._n â…“_n of_o a_o penny_n lose_v be_v the_o answer_n to_o the_o question_n as_o be_v require_v chap._n xxvii_o allegation_n medial_a teach_v how_o to_o find_v out_o a_o common_a or_o medium_fw-la rate_n or_o price_n in_o a_o 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be_v 2160_o penny_n and_o 120_o gallon_n by_o 40_o penny_n or_o 3_o s._n 4_o d._n the_o product_n thereof_o be_v 4800_o the_o sum_n of_o these_o several_a product_n be_v 9024_o which_o if_o you_o divide_v by_o 250_o gallon_n the_o sum_n of_o the_o several_a quantity_n the_o quotient_n will_v be_v 36_o d._n 24_o 250_o or_o 3_o s._n 0_o d._n 24_o 250_o which_o be_v the_o medium_fw-la or_o common_a price_n as_o be_v require_v quest_n 2._o a_o mealman_n have_v 230_o bushel_n of_o meal_n at_o 9_o d._n 368_o bushel_n at_o 14_o d._n and_o 485_o bushel_n at_o 16_o d._n he_o be_v intend_v to_o mix_v all_o these_o together_o and_o desire_n to_o know_v the_o common_a price_n the_o common_a price_n here_o find_v out_o be_v 13_o d._n ¾_n as_o be_v require_v and_o in_o like_a manner_n for_o all_o other_o question_n of_o this_o nature_n chap._n xxviii_o alligation_n alternate_a alligation_n alternate_a teach_v how_o to_o mix_v divers_a sort_n and_o price_n together_o in_o such_o manner_n that_o you_o may_v make_v they_o of_o what_o price_n or_o quantity_n you_o please_v quest_n 1._o a_o goldsmith_n have_v four_o sort_n of_o gold_n the_o first_o sort_n be_v worth_a 36_o crown_n the_o pound_n weight_n the_o second_o sort_n be_v worth_a 38_o crown_n the_o pound_n the_o three_o sort_n be_v worth_a 42_o crown_n the_o pound_n and_o the_o four_o sort_n be_v worth_a 45_o crown_n the_o pound_n and_o with_o these_o it_o be_v require_v to_o make_v a_o mixture_n worth_a 41_o crown_n the_o pound_n i_o desire_v to_o know_v how_o much_o of_o each_o sort_n he_o must_v take_v first_o set_v down_o the_o number_n of_o which_o the_o alligation_n be_v to_o be_v make_v one_o under_o the_o other_o viz._n 36_o 38_o 42_o and_o 45_o in_o such_o order_n as_o you_o see_v in_o the_o follow_a example_n and_o the_o common_a price_n unto_o which_o you_o will_v reduce_v they_o to_o the_o left_a hand_n which_o in_o this_o example_n be_v 41_o then_o observe_v which_o of_o the_o four_o number_n before_o set_v down_o be_v great_a than_o the_o common_a number_n 41_o and_o which_o be_v less_o and_o with_o a_o semicircle_n link_v a_o great_a and_o a_o lesser_a number_n together_o for_o two_o great_a or_o two_o small_a number_n than_o the_o common_a number_n may_v not_o be_v couple_v together_o after_o these_o number_n be_v according_a to_o the_o former_a direction_n link_v or_o couple_v together_o next_o observe_v how_o much_o each_o of_o the_o lesser_a number_n differ_v from_o the_o common_a number_n 41_o and_o set_v that_o difference_n against_o his_o respective_a number_n to_o which_o he_o be_v couple_v as_o here_o 36_o differ_v 5_o from_o the_o common_a number_n 41_o which_o i_o do_v not_o set_v down_o against_o 36_o but_o against_o 45_o the_o number_n to_o which_o he_o be_v couple_v so_o likewise_o 38_o do_v differ_v 3_o from_o the_o common_a number_n 41_o which_o i_o do_v not_o set_v against_o 38_o but_o against_o 42_o the_o number_n to_o which_o he_o be_v couple_v likewise_o you_o must_v observe_v how_o much_o each_o of_o the_o great_a number_n do_v exceed_v the_o common_a number_n 41_o as_o 42_o do_v exceed_v the_o common_a number_n 41_o but_o 1_o which_o i_o set_v against_o the_o number_n 38_o to_o which_o he_o be_v couple_v and_o 45_o do_v exceed_v the_o common_a number_n 41_o but_o 4_o which_o i_o set_v against_o the_o number_n 36_o to_o which_o he_o be_v couple_v the_o sum_n of_o these_o difference_n which_o be_v 13_o show_v the_o number_n of_o pound_n the_o composition_n or_o mixture_n must_v weigh_v and_o the_o several_a difference_n do_v show_v how_o many_o pound_n of_o each_o sort_n you_o must_v take_v as_o 4_o sheweth_z you_o must_v take_v 4_o pound_n of_o 36_o crown_n fine_a 1_o pound_n of_o 38_o crown_n fine_a 3_o pound_n of_o 42_o crown_n and_o 5_o pound_n of_o 45_o crown_n fine_a each_o pound_n of_o this_o mixture_n contain_v 13_o l._n be_v worth_n 40_o crown_n as_o be_v desire_v the_o proof_n  _fw-fr  _fw-fr crown_n 4_o l._n of_o 36_o crown_n fine_a be_v 144_o 1_o l._n of_o 38_o 38_o 3_o l._n of_o 42_o 126_o 5_o l._n of_o 45_o 225_o  _fw-fr  _fw-fr 533_o so_o likewise_o 13_o l._n of_o 41_o crown_n 533_o but_o suppose_v it_o be_v require_v to_o make_v a_o mixture_n of_o a_o certain_a weight_n as_o well_o as_o a_o certain_a fineness_n as_o let_v it_o be_v require_v to_o make_v a_o mixture_n of_o 8_o pound_n weight_n of_o the_o several_a former_a fineness_n and_o to_o the_o former_a common_a price_n of_o 41_o crown_n how_o much_o must_v be_v take_v of_o each_o sort_n then_o by_o the_o rule_n of_o three_o say_v as_o the_o sum_n of_o the_o several_a difference_n which_o be_v 13_o be_v to_o the_o weight_n propound_v 8_o pound_n so_o be_v each_o particular_a difference_n to_o the_o weight_n desire_v as_o follow_v as_o 13_o be_v to_z 8_o so_o be_v 4_o to_o 26_o 13._o as_o 13_o be_v to_z 8_o so_o be_v 1_o to_o 8_o 13._o as_o 13_o be_v to_z 8_o so_o be_v 3_o to_o 11_o â—â—_o as_o 13_o be_v to_z 8_o so_o be_v 5_o to_o 3_o â—â—_o  _fw-fr 8_o l._n so_o there_o must_v be_v 2_o l._n 6_o 13_o of_o the_o fineness_n of_o 36_o crown_n 8_o 13_o part_n of_o a_o pound_n of_o 38_o crown_n 1_o pound_n 11_o 13_o of_o 42_o crown_n and_o 3_o pound_n 1_o 13_o of_o 45_o crown_n which_o add_v all_o together_o make_v 8._o to_o prove_v the_o work_n 2_o 6_o 13_o of_o 36_o crown_n be_v 88_o 8_o 13_o 8_o 13_o of_o 38_o 23_o 5_o 13_o 1_o 11_o 13_o of_o 42_o 77_o 7_o 13_o 3_o 1_o 13_o of_o 45_o 138_o 6_o
13_o  _fw-fr  _fw-fr 328_o 8_o pound_n of_o 41_o crown_n be_v 328_o therefore_o you_o may_v certain_o conclude_v you_o have_v commit_v no_o error_n in_o your_o work_n quest_n 2._o a_o vintner_n have_v several_a sort_n of_o wine_n viz._n he_o have_v wine_n of_o 14_o d._n the_o gallon_n wine_n of_o 19d_o the_o gallon_n wine_n of_o 23d_o the_o gallon_n and_o he_o have_v wine_n of_o 28d_o the_o gallon_n now_o he_o do_v intend_v to_o make_v a_o mixture_n of_o 48_o gallon_n now_o it_o be_v require_v to_o know_v how_o many_o gallon_n of_o each_o price_n he_o must_v take_v to_o make_v one_o gallon_n with_o another_o worth_n 21_o d._n  _fw-fr d._n gal._n s._n d._n 21_o 14_o 2_o at_o 14_o 2_o 4_o 19_o 7_o at_o 19_o 11_o 1_o 23_o 7_o at_o 23_o 13_o 5_o 28_o 2_o at_o 28_o 4_o 8_o  _fw-fr  _fw-fr 18_o at_z 21_o 1_o 11_o 6_o say_v by_o the_o rule_n of_o three_o as_o 18_o to_o 48_o so_o 2_o to_o 5_o gallon_n 6_o 18_o as_o 18_o to_o 48_o so_o 7_o to_o 18_o gallon_n 1_o 18_o as_o 18_o to_o 48_o so_o 7_o to_o 18_o gallon_n 12_o 18_o as_o 18_o to_o 48_o so_o 2_o to_o 5_o gallon_n 6_o 18_o  _fw-fr 48_o the_o proof_n be_v as_o follow_v  _fw-fr  _fw-fr d._n 5_o gallon_n 6_o 18_o of_o 14_o penny_n be_v 74_o â—â—_o 18_o 18_o gallon_n 12_o 18_o of_o 19_o 354_o 12_o 18_o 18_o gallon_n 12_o 18_o of_o 23_o 429_o 6_o 18_o 5_o gallon_n 6_o 18_o of_o 28_o 149_o 6_o 18_o  _fw-fr  _fw-fr 1008_o d._n 48_o gallon_n of_o 21_o penny_n be_v 1008_o d._n therefore_o you_o may_v conclude_v your_o operation_n be_v without_o error_n quest_n 3._o a_o drugster_n have_v three_o sort_n of_o drug_n the_o first_o sort_n at_o 3_o s._n the_o pound_n the_o second_o at_o 7_o s._n and_o the_o three_o at_o 15_o s._n per_fw-la pound_n of_o these_o sort_n he_o be_v to_o make_v 3_o parcel_n contain_v each_o 24_o pound_n one_o parcel_n to_o be_v reckon_v 11_o s._n per_fw-la pound_n the_o other_o 12_v and_o the_o other_o 13_v how_o much_o must_v be_v take_v of_o each_o sort_n to_o make_v up_o each_o parcel_n the_o common_a price_n propound_v be_v 11_o shilling_n 12_o shilling_n and_o 13_o shilling_n likewise_o the_o price_n give_v of_o which_o the_o mixture_n be_v to_o be_v make_v be_v 3_o shilling_n 7_o shilling_n and_o 15_o shilling_n and_o because_o two_o of_o the_o three_o give_v price_n be_v less_o than_o the_o common_a price_n i_o couple_v the_o two_o lesser_a with_o the_o great_a as_o you_o see_v and_o the_o difference_n of_o the_o 2_o less_o i_o place_n against_o the_o great_a and_o the_o difference_n of_o the_o great_a against_o the_o lesser_a then_o proceed_v as_o before_o say_v as_o 20_o the_o whole_a difference_n be_v to_o 24_o the_o whole_a quantity_n of_o each_o parcel_n so_o be_v each_o particular_a difference_n to_o its_o respective_a quantity_n inquire_v after_o as_o follow_v 1._o as_o 20_o to_o 24_o so_o 4_o to_o 4_o â…˜_n as_o 20_o to_o 24_o so_o 4_o to_o 4_o â…˜_n as_o 20_o to_o 24_o so_o 12_o to_o 14_o â…–_n  _fw-fr 24_o 2._o as_o 20_o to_o 24_o so_o 3_o to_o 3_o â…—_n as_o 20_o to_o 24_o so_o 3_o to_o 3_o â…—_n as_o 20_o to_o 24_o so_o 14_o to_o 16_o â…˜_n  _fw-fr 24_o 3._o as_o 20_o to_o 24_o so_o 2_o to_o 2_o â…–_n as_o 20_o to_o 24_o so_o 2_o to_o 2_o â…–_n as_o 20_o to_o 24_o so_o 16_o to_o 19_o â…•_n  _fw-fr 24_o here_o you_o see_v in_o the_o first_o parcel_n that_o be_v to_o be_v 11_o s._n per_fw-la pound_n to_o make_v a_o mixture_n of_o 24_o l._n you_o must_v take_v 4_o pound_n â…˜_n of_o 3_o s._n per_fw-la pound_n 4_o l._n â…˜_n of_o 7_o s._n per_fw-la pound_n and_o 14_o l._n â…–_n of_o 15_o s._n per_fw-la pound_n and_o in_o the_o second_o parcel_n of_o 12_o s._n the_o common_a price_n round_o you_o must_v take_v 3_o l._n â…—_n of_o 3_o s._n per_fw-la pound_n 3_o l._n â…—_n of_o 7_o s._n per_fw-la pound_n and_o 16_o l._n â…˜_n of_o 15_o s._n per_fw-la pound_n and_o in_o the_o three_o parcel_n of_o 13_o s._n round_o you_o must_v take_v 2_o l._n â…–_n of_o 3_o s._n and_o 2_o l._n â…–_n of_o 7_o s._n and_o 19_o l._n â…•_n of_o 15_o s._n per_fw-la pound_n and_o if_o you_o add_v up_o each_o parcel_n find_v out_o they_o will_v each_o amount_v unto_o 24_o l._n quest_n 4._o a_o goldsmith_n have_v five_o sort_n of_o gold_n one_o be_v 15_o carrect_v fine_a 17_o carrect_v fine_a 20_o carrect_v fine_a 23_o carrect_v fine_a and_o 26_o carrect_v fine_a all_o these_o five_o sort_n he_o do_v intend_v to_o mix_v with_o such_o a_o allay_n as_o that_o a_o mixture_n of_o 124_o ounce_n shall_v be_v but_o 12_o carrect_v fine_a i_o desire_v to_o know_v how_o much_o of_o either_o sort_n of_o gold_n must_v be_v take_v to_o make_v up_o 124_o l._n to_o answer_v this_o and_o all_o other_o question_n of_o this_o nature_n set_v down_o their_o several_a and_o particular_a fineness_n one_o under_o another_o as_o you_o see_v in_o the_o follow_a example_n and_o set_v down_o the_o common_a fineness_n of_o the_o gold_n which_o be_v demand_v viz._n 12_o carrect_v towards_o the_o left_a hand_n also_o set_v down_o a_o cypher_n under_o the_o particular_n for_o a_o alloy_n set_v the_o alloy_v difference_n which_o be_v 12_o against_o all_o the_o other_o sum_n as_o in_o the_o example_n you_o may_v see_v be_v do_v and_o set_v the_o difference_n of_o all_o the_o other_o sum_n against_o the_o alloy_n as_o 3_o 5_o 8_o 11_o and_o 14._o then_o by_o the_o rule_n of_o three_o say_v as_o 101_o the_o whole_a difference_n be_v to_o 124_o the_o whole_a quantity_n so_o be_v each_o particular_a difference_n to_o each_o particular_a quantity_n seek_v  _fw-fr oz._n  _fw-fr as_o 101_o to_o 124_o so_o 12_o to_o 14_o 74_o 101_o as_o 101_o to_o 124_o so_o 12_o to_o 14_o 74_o 101_o as_o 101_o to_o 124_o so_o 12_o to_o 14_o 74_o 101_o as_o 101_o to_o 124_o so_o 12_o to_o 14_o 74_o 101_o as_o 101_o to_o 124_o so_o 12_o to_o 14_o 74_o 101_o as_o 101_o to_o 124_o so_o 41_o to_o 50_o 34_o 101_o  _fw-fr 124_o  _fw-fr chap._n xxix_o of_o exchange_n exchange_n be_v the_o way_n of_o remit_v money_n from_o one_o place_n or_o country_n to_o another_o by_o pay_v money_n in_o one_o place_n and_o receive_v the_o like_a value_n in_o another_o with_o allowance_n sometime_o of_o profit_n and_o sometime_o of_o loss_n it_o will_v be_v of_o little_a or_o no_o consequence_n to_o give_v you_o the_o name_n of_o the_o particular_a coin_n of_o several_a country_n because_o with_o we_o in_o england_n they_o sometime_o rise_v and_o sometime_o fall_v in_o value_n according_a as_o the_o exchange_n run_v i_o therefore_o do_v only_o intend_v to_o lay_v down_o some_o necessary_a question_n as_o follow_v quest_n 1._o a_o merchant_n pay_v at_o london_n or_o any_o other_o sea_n port_n town_n of_o england_n 256_o l._n sterling_n to_o receive_v the_o value_n thereof_o at_o amsterdam_n exchange_n at_o 33_o s._n 9_o d._n flemish_n for_o 20_o s._n sterling_n i_o desire_v to_o know_v how_o much_o flemish_a money_n i_o must_v receive_v at_o amsterdam_n by_o the_o rule_n of_o three_o say_v if_o 1_o l._n sterl_n give_v 33_o s._n 9_o d._n fl._n what_o will_v 256_o l_o quest_n 2._o a_o merchant_n at_o amsterdam_n do_v deliver_v 432_o l._n flemish_n to_o receive_v the_o value_n thereof_o at_o london_n exchange_n 33_o s._n 9_o d._n for_o 20_o s._n sterling_n i_o desire_v to_o know_v how_o much_o sterling_a money_n i_o must_v receive_v at_o london_n by_o the_o rule_n of_o three_o say_v if_o 33_o s._n 9_o d._n fl._n give_v 1_o l._n stir_v what_o will_v 432_o l._n fl._n multiply_v and_o divide_v and_o you_o will_v find_v he_o must_v receive_v 256_o l._n sterling_n these_o two_o question_n do_v prove_v one_o another_o as_o you_o may_v plain_o see_v quest_n 3._o a_o merchant_n at_o london_n deliver_v 374_o l._n 2_o s._n sterling_a to_o be_v receive_v in_o paris_n the_o like_a value_n exchange_n at_o 58d_o per_fw-mi french_a crown_n i_o demand_v how_o many_o french_a crown_n must_v i_o receive_v in_o paris_n by_o the_o rule_n of_o three_o say_v if_o 58_o d._n give_v 1_o fr._n cr._n what_o will_v 374_o l._n 2_o s_o by_o multiply_v and_o divide_v you_o will_v find_v you_o must_v receive_v at_o paris_n 1548_o french_a crown_n quest_n 4._o a_o merchant_n at_o paris_n do_v deliver_v 2870_o french_a crown_n the_o like_a value_n to_o be_v receive_v in_o london_n exchange_n at_o 57d_o ½_n per_fw-la crown_n i_o desire_v to_o know_v how_o much_o sterling_a money_n i_o must_v receive_v at_o london_n by_o the_o rule_n of_o three_o say_v if_o 1_o fr._n cr._n give_v 57_o d._n ½_n how_o much_o will_v 2870_o quest_n