number_n admit_v of_o both_o increase_v by_o addition_n or_o multiplication_n and_o decrease_v by_o subtraction_n or_o division_n as_o 6_o be_v a_o number_n compose_v of_o six_o unit_n and_o admit_v of_o increase_n first_o by_o addition_n as_o 1_o unit_fw-la and_o 6_o make_v 7_o second_o by_o multiplication_n as_o 3_o time_n 6_o make_v 18_o and_o 6_o admit_v likewise_o of_o decrease_v first_o by_o subtraction_n as_o take_v 1_o from_o 6_o and_o there_o remain_v 5_o second_o by_o division_n as_o how_o many_o 2_o can_v i_o have_v in_o 6_o the_o answer_n be_v 3_o time_n numeration_n numeration_n be_v that_o part_n of_o arithmetic_n by_o which_o be_v teach_v right_o and_o just_o to_o value_v declare_v and_o write_v any_o number_n or_o sum_n propound_v all_o number_n and_o sum_n be_v express_v by_o these_o follow_a character_n or_o figure_n which_o be_v in_o number_n ten_o who_o value_n if_o you_o conceive_v each_o figure_n to_o be_v or_o stand_v by_o itself_o you_o may_v take_v notice_n of_o by_o their_o several_a subscription_n 1_o one_o 2_o two_o 3_o three_o 4_o four_z 5_o five_o 6_o six_o 7_o seven_o 8_o eight_o 9_o nine_o 0_o cypher_n nine_o of_o these_o figure_n viz._n 1_o 2_o 3_o 4_o 5_o 6_o 7_o 8_o 9_o be_v significant_a figure_n signify_v each_o figure_n so_o many_o unite_v but_o the_o cypher_n be_v of_o no_o value_n nor_o signification_n as_o as_o it_o stand_v alone_o but_o be_v join_v with_o other_o figure_n it_o increase_v the_o value_n of_o those_o figure_n which_o stand_v to_o the_o left_a hand_n of_o he_o now_o these_o nine_o significant_a figure_n 1_o 2_o 3_o 4_o 5_o 6_o 7_o 8_o 9_o have_v a_o double_a value_n whereof_o the_o one_o be_v certain_a according_a to_o its_o own_o signification_n as_o before_o but_o the_o other_o value_n be_v uncertain_a it_o be_v according_a to_o the_o place_n that_o the_o say_a figure_n do_v stand_v in_o and_o possess_v a_o place_n be_v a_o seat_n or_o room_n that_o a_o figure_n stand_v in_o and_o how_o many_o figure_n there_o be_v in_o any_o sum_n so_o many_o place_n of_o value_n do_v the_o say_a sum_n contain_v and_o that_o be_v the_o first_o place_n of_o any_o sum_n which_o be_v next_o the_o right_a hand_n every_o place_n be_v ten_o time_n the_o value_n of_o the_o next_o right_a hand_n place_n numeration_n table_n c._n million_o x._o million_o million_o c._n thousand_o x._o thousand_o thousand_o hundred_o ten_o unit_n how_o each_o number_n be_v to_o be_v read_v  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 1_o one_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 1_o 2_o twelve_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 1_o 2_o 3_o 1_o hundred_o twenty_o three_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 1_o 2_o 3_o 4_o 1_o thousand_o 234_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 1_o 2_o 3_o 4_o 5_o 12_o thousand_o 345_o  _fw-fr  _fw-fr  _fw-fr 1_o 2_o 3_o 4_o 5_o 6_o 123_o thous_z 456_o  _fw-fr  _fw-fr 1_o 2_o 3_o 4_o 5_o 6_o 7_o 1_o million_o 234567_o  _fw-fr 1_o 2_o 3_o 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 then_o draw_v a_o line_n and_o begin_v at_o the_o bottom_n of_o the_o least_o denomination_n say_v ¾_n and_o ¼_n be_v four_o farthing_n and_o ¾_n be_v seven_o farthing_n and_o ½_n be_v nine_o farthing_n or_o two_o penny_n farthing_n set_v down_o ¼_n under_o the_o farthing_n and_o carry_v 2_o to_o the_o penny_n say_v 2_o as_o i_o carry_v and_o 10_o be_v 12_o and_z 3_o be_v 15_o and_z 8_o be_v 23_o and_o 11_o be_v 34_o penny_n which_o be_v 2_o s._n 10_o d._n therefore_o set_v down_o 10_o under_o the_o penny_n and_o carry_v 2_o to_o the_o shilling_n say_v 2_o as_o i_o carry_v and_o 3_o makes_z 5_o and_z 2_o be_v 7_o and_z 4_o be_v 11_o and_z 6_o be_v 17_o set_v down_o 7_o under_o the_o first_o row_n of_o shilling_n and_o carcarry_v 1_o to_o the_o next_o row_n of_o shilling_n say_v 1_o as_o i_o carry_v and_o 1_o be_v 2_o and_z 1_o be_v 3_o and_o 1_o be_v 4_o and_z 1_o makes_z 5_o which_o be_v odd_a i_o set_v 1_o after_o the_o 7_o but_o under_o the_o last_o row_n of_o shilling_n now_o the_o 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
which_o i_o divide_v by_o 32_o and_o the_o quotient_n give_v 14_o pound_n because_o the_o last_o multiplier_n be_v pound_n but_o of_o this_o last_o division_n there_o do_v remain_v nothing_o find_v by_o the_o operation_n that_o for_o 124_o pound_n i_o can_v buy_v 205_o c._n 1_o qu._n 14_o l._n if_o 53_o hundred_o weight_n cost_v 32_o pound_n be_v the_o answer_n to_o the_o question_v propound_v it_o many_o time_n fall_v out_o in_o question_n of_o the_o rule_n of_o three_o that_o notwithstanding_o the_o first_o and_o three_o number_n be_v of_o one_o kind_a or_o species_n viz._n money_n weight_n measure_n etc._n etc._n yet_o they_o may_v either_o or_o both_o consist_v of_o several_a denomination_n in_o such_o case_n you_o be_v to_o reduce_v both_o number_n into_o the_o low_a denomination_n and_o likewise_o into_o one_o denomination_n also_o if_o your_o second_o number_n be_v of_o several_a denomination_n you_o must_v reduce_v it_o into_o the_o low_a denomination_n name_v or_o low_a if_o you_o please_v which_o be_v do_v then_o multiply_v the_o second_o and_o three_o number_n together_o and_o divide_v by_o the_o first_o according_a to_o the_o former_a direction_n the_o answer_n to_o the_o question_n be_v of_o the_o same_o denomination_n as_o your_o second_o number_n be_v reduce_v unto_o quest_n 5._o if_o 12_o c._n 3_o qu._n of_o sugar_n cost_v 32l_o 14_o s._n 6_o d._n what_o will_v 82_o c._n 1_o qu._n 22l_o cost_v have_v place_v these_o several_a number_n in_o their_o several_a respective_a place_n according_a to_o the_o former_a instruction_n as_o you_o see_v in_o the_o follow_a example_n 12_o c._n 3_o qu._n be_v in_o the_o first_o place_n 32_o l._n 14_o s._n 6_o d._n in_o the_o second_o place_n and_o 82_o c._n 1_o qu._n 22_o l._n in_o the_o three_o place_n now_o i_o perceive_v my_o first_o and_o three_o number_n be_v of_o several_a denomination_n my_o first_o number_n have_v two_o denomination_n as_o hundred_o and_o quarter_n viz._n 12_o c._n 3_o qu._n my_o three_o number_n have_v three_o denomination_n as_o hundred_o quarter_n and_o pound_n viz._n 82_o c._n 1_o qu._n 22_o l._n but_o yet_o the_o first_o and_o three_o number_n be_v of_o one_o kind_n that_o be_v to_o say_v their_o several_a denomination_n be_v of_o weight_n now_o the_o first_o and_o three_o number_n must_v be_v both_o of_o they_o bring_v into_o one_o denomination_n and_o that_o denomination_n must_v be_v the_o low_a name_n either_o in_o the_o first_o or_o three_o number_n which_o here_o in_o this_o example_n be_v pound_n weight_n now_o by_o the_o six_o chapter_n for_o the_o reduction_n of_o averdupoize_n weight_n you_o may_v reduce_v the_o first_o and_o three_o number_n into_o pound_n weight_n the_o first_o number_n produce_v 1428l_o weight_n and_o the_o three_o number_n produce_v 9234_o l._n weight_n next_o i_o consider_v the_o nature_n and_o quality_n of_o the_o second_o number_n which_o be_v money_n but_o it_o likewise_o do_v consist_v of_o several_a denomination_n as_o pound_n shilling_n and_o penny_n viz._n 32_o l._n 14_o s._n 6_o d._n which_o by_o the_o six_o chapter_n of_o reduction_n of_o money_n must_v be_v reduce_v into_o penny_n be_v the_o low_a denomination_n name_v and_o it_o will_v produce_v 7854_o penny_n have_v thus_o reduce_v the_o three_o give_v number_n as_o you_o see_v in_o the_o follow_a example_n i_o proceed_v according_a to_o the_o former_a instruction_n of_o this_o chapter_n multiply_v the_o second_o number_n reduce_v 7854_o by_o the_o three_o number_n reduce_v 9234_o the_o product_n of_o which_o multiplication_n be_v 72523836_o which_o i_o do_v divide_v by_o the_o first_o number_n reduce_v 1428_o by_o the_o instruction_n of_o the_o five_o chapter_n and_o the_o quotient_n make_v 50787_o which_o be_v penny_n because_o the_o second_o number_n 7854_o by_o reduction_n be_v make_v penny_n which_o quotient_a 50787_o be_v the_o four_o proportional_a require_v and_o the_o number_n of_o pence_n answer_v to_o the_o question_n which_o by_o reduction_n make_v 211_o l._n 12_o s._n 3_o d._n and_o so_o much_o will_v 82_o c._n 1_o cue_n 22_o l._n cost_n if_o 12_o c._n 3_o qu._n cost_v 32_o l._n 14_o s._n 6_o d._n as_o be_v require_v to_o prove_v the_o rule_n of_o three_o be_v to_o state_n the_o question_n quite_o backward_o by_o put_v the_o four_o number_n find_v out_o first_o the_o three_o number_n put_v second_o and_o the_o second_o number_n put_v three_o so_o have_v you_o three_o new_a give_v number_n to_o find_v a_o four_o by_o the_o former_a instruction_n which_o four_o number_n when_o it_o be_v find_v will_v be_v the_o same_o as_o the_o first_o number_n in_o the_o question_n first_o state_v the_o proof_n of_o the_o second_o question_n of_o this_o who_o four_o number_n so_o find_v be_v 108._o here_o you_o see_v the_o second_o and_o three_o number_n multiply_v together_o who_o product_n 864_o i_o do_v divide_v by_o the_o first_o number_n 108_o and_o the_o quotient_a 8_o be_v the_o four_o number_n find_v out_o which_o be_v the_o first_o number_n in_o the_o example_n of_o the_o second_o question_n but_o there_o be_v a_o short_a way_n of_o prove_v any_o question_n in_o the_o rule_n of_o three_o thus_o multiply_v the_o first_o number_n by_o the_o four_o number_n find_v likewise_o multiply_v the_o second_o number_n by_o the_o three_o if_o these_o two_o product_n do_v agree_v your_o operation_n be_v without_o any_o error_n else_o not_o as_o you_o may_v see_v by_o the_o proof_n of_o the_o example_n of_o the_o second_o question_n by_o this_o you_o see_v that_o 8_o the_o first_o number_n and_o 108_o the_o four_o number_n multiply_v together_o make_v 864_o and_o the_o second_o number_n 32_o multiply_v by_o the_o three_o number_n 27_o produce_v 864_o as_o before_o the_o five_o question_n prove_v both_o way_n here_o you_o multiply_v your_o first_o number_n 1428_o and_o the_o four_o number_n find_v 50787_o together_o who_o product_n be_v 72523836_o likewise_o multiply_v the_o second_o number_n 7854_o and_o the_o three_o number_n 9234_o together_o and_o the_o product_n be_v 72523836_o as_o before_o chap._n viii_o the_o single_a rule_n of_o three_o backward_o this_o rule_n be_v so_o call_v because_o it_o produce_v and_o require_v a_o proportion_n quite_o backward_o and_o contrary_a to_o the_o rule_n of_o three_o direct_v because_o in_o the_o rule_n of_o three_o direct_v the_o great_a the_o three_o number_n be_v the_o great_a will_v the_o four_o number_n be_v but_o in_o this_o rule_n the_o great_a the_o three_o number_n be_v the_o lesser_a will_v the_o four_o number_n be_v you_o be_v to_o place_v your_o three_o give_v number_n in_o order_n according_a to_o the_o direction_n of_o the_o last_o rule_n but_o in_o this_o rule_n you_o must_v multiply_v the_o first_o and_o second_o number_n together_o and_o the_o product_n of_o that_o multiplication_n divide_v by_o the_o three_o number_n and_o the_o number_n that_o come_v in_o the_o quotient_n shall_v be_v the_o four_o number_n require_v or_o answer_v to_o the_o question_n quest_n 1._o if_o 12_o labourer_n will_v build_v a_o house_n in_o 28_o day_n how_o many_o day_n shall_v 16_o man_n build_v such_o another_o in_o here_o i_o set_v the_o three_o give_v number_n in_o order_n as_o you_o see_v in_o the_o follow_a example_n where_o you_o see_v 12_o in_o the_o first_o place_n 28_o in_o the_o second_o place_n 16_o in_o the_o three_o place_n and_o the_o first_o and_o three_o number_n both_o of_o one_o denomination_n and_o the_o four_o number_n require_v will_v be_v the_o same_o denomination_n as_o the_o second_o number_n be_v of_o according_a to_o the_o former_a instruction_n of_o the_o last_o chapter_n these_o number_n be_v thus_o place_v and_o dispose_v as_o you_o see_v multiply_v the_o first_o number_n 12_o by_o the_o second_o number_n 28_o and_o the_o product_n thereof_o will_v be_v 336_o which_o divide_v by_o 16_o the_o three_o number_n and_o the_o quotient_n give_v you_o 21_o day_n for_o answer_n to_o the_o question_n as_o be_v require_v for_o if_o 12_o man_n can_v do_v the_o work_n in_o 28_o day_n 16_o man_n will_v do_v it_o in_o 21_o day_n quest_n 2._o if_o a_o traveller_n perform_v a_o journey_n when_o the_o day_n be_v 12_o hour_n long_o in_o 12_o day_n in_o how_o many_o day_n shall_v he_o perform_v the_o same_o journey_n when_o the_o day_n be_v 15_o hour_n long_o here_o you_o may_v clear_o perceive_v the_o more_o hour_n be_v in_o a_o day_n the_o few_o day_n will_v he_o be_v in_o perform_v his_o journey_n therefore_o set_v your_o number_n down_o as_o you_o see_v multiply_v the_o second_o number_n 12_o day_n and_o the_o first_o number_n 10_o hour_n together_o and_o the_o product_n 120_o divide_v by_o 15_o hour_n the_o three_o number_n and_o the_o quotient_n will_v give_v you_o 8_o day_n in_o answer_n to_o the_o
quotient_a as_o be_v require_v quest_n 3._o if_o i_o hang_v a_o room_n with_o 36_o yard_n of_o stuff_n at_o 7_o quarter_n wide_a how_o many_o yard_n will_v hang_v the_o same_o room_n at_o 4_o quarter_n or_o yard_n wide_a place_v the_o number_n be_v you_o see_v and_o multiply_v the_o first_o and_o second_o number_n together_o the_o product_n thereof_o will_v be_v 252_o which_o divide_v by_o the_o three_o number_n 4_o and_o the_o quotient_n will_v be_v 63_o yard_n and_o so_o many_o yard_n do_v answer_v or_o be_v equal_a to_o 36_o yard_n of_o 7_o quarter_n wide_a quest_n 4._o if_o when_o the_o bushel_n of_o wheat_n be_v worth_a 3_o s._n a_o penny_n wheaten_a loaf_n weigh_v 8_o ounce_n i_o demand_v how_o many_o ounce_n shall_v the_o same_o loaf_n weigh_v when_o the_o bushel_n be_v worth_a 5_o shilling_n multiply_v the_o first_o and_o second_o number_n together_o the_o product_n be_v 24_o divide_v by_o 5_o the_o three_o number_n the_o quotient_n will_v be_v 4_o ounce_n â…˜_n of_o a_o 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l._n in_o 12_o month_n to_o gain_v 7_o l._n and_o the_o other_o two_o number_n 8_o month_n and_o 3_o 14_o 8_o contain_v the_o demand_n of_o the_o question_n upon_o those_o supposition_n viz._n how_o much_o money_n in_o 8_o month_n will_v gain_v 3_o 14_o 8_o which_o be_v according_a to_o the_o instruction_n of_o the_o last_o chapter_n and_o according_a to_o the_o instruction_n of_o this_o chapter_n i_o have_v make_v the_o three_o number_n 7_o l._n and_o the_o five_o number_n 3_o l._n 14_o s._n 8_o d._n both_o of_o one_o species_n or_o kind_a that_o be_v to_o say_v they_o both_o do_v signify_v money_n gain_v although_o one_o of_o they_o do_v contain_v three_o denomination_n and_o the_o other_o but_o one_o here_o you_o must_v note_v that_o if_o any_o of_o the_o five_o number_n give_v be_v of_o different_a denomination_n you_o must_v reduce_v all_o the_o number_n of_o the_o same_o kind_a or_o species_n into_o the_o low_a denomination_n name_v as_o here_o in_o the_o follow_a example_n the_o 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of_o one_o denomination_n into_o another_o fraction_n that_o be_v of_o the_o same_o value_n 1._o to_o reduce_v mix_v number_n to_o a_o improper_a fraction_n a_o mix_a number_n be_v compose_v of_o two_o part_n or_o number_n whole_a and_o break_a integer_n and_o fraction_n the_o whole_a number_n be_v compose_v of_o integere_fw-la the_o break_a be_v a_o fraction_n annex_v to_o the_o whole_a number_n as_o in_o the_o mix_a number_n 48_o 2_o 86_o 48_o be_v the_o whole_a number_n and_o 12_o 16_o be_v the_o break_a number_n show_v that_o one_o integer_fw-la of_o 48_o be_v divide_v into_o 16_o part_n this_o 12_o 16_o do_v signify_v that_o there_o do_v belong_v to_o 48_o 12_o of_o the_o 16_o part_n the_o rule_n be_v thus_o multiply_v the_o whole_a number_n by_o the_o denominator_fw-la of_o that_o fraction_n annex_v to_o he_o and_o to_o the_o product_n thereof_o add_v the_o numerator_n of_o the_o same_o fraction_n than_o set_v their_o sum_n over_o the_o denominator_fw-la with_o a_o line_n between_o they_o and_o this_o new_a fraction_n though_o improper_a shall_v be_v equal_a to_o the_o mix_a number_n give_v example_n let_v the_o mix_a number_n beforementioned_a 48_o 1_o 16_o be_v require_v to_o be_v reduce_v into_o a_o improper_a fraction_n equal_a thereunto_o multiply_v the_o whol_n number_v 48_o by_o the_o denominator_fw-la pound_n 16_o and_o the_o product_n be_v 768_o to_o which_o add_v the_o numerator_n 12_o and_o they_o do_v make_v 780_o which_o be_v so_o many_o sixteen_n therefore_o i_o set_v down_o 780_o and_o underneath_o 16_o draw_v a_o line_n between_o they_o as_o you_o see_v which_o be_v a_o improper_a fraction_n but_o contain_v 780_o sixteen_n be_v equal_a to_o the_o mix_a number_n 48_o 12_o 16_o as_o be_v require_v 2._o to_o reduce_v a_o whole_a number_n to_o a_o improper_a fraction_n multiply_v the_o whole_a number_n give_v by_o the_o intend_a denominator_fw-la and_o place_v the_o product_n of_o the_o multiplication_n over_o the_o denominator_fw-la and_o draw_v a_o line_n between_o example_n let_v it_o be_v require_v to_o reduce_v the_o whole_a number_n 24_o into_o a_o fraction_n who_o denominator_fw-la be_v 8_o multiply_v the_o whole_a number_n 24_o by_o 8_o and_o pound_n the_o product_n be_v 192_o which_o i_o set_v over_o the_o denominator_fw-la 8_o and_o draw_v a_o line_n between_o so_o 192_o be_v the_o numerator_n and_o 8_o the_o denominator_fw-la make_v 192_o 8_o equal_a to_o 24_o the_o whole_a number_n 3._o to_o reduce_v a_o improper_a fraction_n into_o a_o whole_a or_o mix_a number_n equivalent_a thereunto_o divide_v the_o numerator_n by_o the_o denominator_fw-la and_o the_o quotient_n will_v give_v the_o whole_a number_n equal_a thereunto_o that_o be_v equal_a to_o the_o improper_a fraction_n give_v and_o if_o any_o thing_n remain_v make_v it_o the_o numerator_n and_o make_v the_o divisor_n denominator_fw-la
be_v 3_o and_z 3_o be_v 6_o setting_z down_z 6_o under_o the_o last_o row_n so_o i_o find_v i_o have_v receive_v in_o all_o of_o a_o b_o c_o and_o d_o 671_o l._n 17_o s._n 10_o d._n ¼_n  _fw-fr l._n s._n d._n  _fw-fr  _fw-fr 384_o 16_o 11_o ½_n  _fw-fr 197_o 14_o 08_o ¾_n  _fw-fr 79_o 12_o 03_o ¼_n  _fw-fr 9_o 13_o 10_o ¾_n total_a 671_o 17_o 10_o ¼_n proof_n 287_o 00_o 10_o ¾_n 671_o 17_o 10_o ¼_n for_o the_o proof_n of_o this_o sum_n whether_o it_o be_v cast_v up_o right_a or_o not_o the_o common_a way_n be_v to_o draw_v a_o line_n under_o the_o first_o sum_n and_o then_o sum_n up_o again_o only_o leave_v out_o the_o uppermost_a row_n which_o sum_n be_v add_v to_o the_o uppermost_a row_n or_o line_n then_o if_o the_o sum_n be_v the_o same_o as_o before_o the_o work_n be_v right_o cast_v up_o but_o it_o be_v as_o easy_a or_o better_a to_o cast_v up_o the_o whole_a sum_n again_o and_o if_o you_o think_v by_o do_v so_o you_o may_v commit_v the_o same_o error_n again_o or_o fall_v into_o the_o same_o mistake_v as_o before_o you_o may_v cast_v it_o up_o the_o contrary_a way_n viz._n begin_v at_o top_n and_o go_v downward_o for_o the_o account_n will_v amount_v to_o one_o and_o the_o same_o sum_n if_o it_o be_v right_o do_v but_o tradesman_n and_o merchant_n be_v most_o concern_v herein_o have_v another_o help_n which_o be_v in_o write_v out_o bill_n by_o their_o book_n if_o they_o find_v the_o sum_n in_o both_o account_n do_v not_o agree_v they_o conclude_v there_o must_v be_v a_o mistake_n in_o one_o or_o the_o other_o which_o they_o find_v out_o by_o cast_v the_o account_n over_o again_o in_o cast_v up_o long_a bill_n where_o many_o shilling_n be_v in_o the_o penny_n it_o be_v a_o good_a plain_a way_n to_o make_v a_o prick_n or_o some_o small_a mark_n at_o every_o shilling_n and_o so_o set_v down_o the_o odd_a penâ—e_n at_o last_o count_v over_o how_o many_o prick_v you_o have_v make_v and_o carry_v so_o many_o shilling_n to_o the_o place_n of_o shilling_n but_o such_o as_o be_v ready_a and_o expert_a count_v how_o many_o penny_n be_v in_o the_o whole_a column_n then_o by_o get_v without_o book_n such_o a_o table_n as_o here_o follow_v can_v ready_o tell_v how_o many_o shilling_n and_o odd_a penny_n be_v in_o any_o number_n of_o pence_n d._n  _fw-fr s._n d._n  _fw-fr s._n d._n 12_o be_v 1_o 20_o be_v 1_o 08_o 24_o 2_o 30_o 2_o 06_o 36_o 3_o 40_o 3_o 04_o 48_o 4_o 50_o 4_o 02_o 60_o 5_o 60_o 5_o 00_o 72_o 6_o 70_o 5_o 10_o 84_o 7_o 80_o 6_o 08_o 96_o 8_o 90_o 7_o 06_o 108_o 9_o 100_o 8_o 04_o 120_o 10_o 110_o 9_o 02_o 132_o 11_o 120_o 10_o 00_o 144_o 12_o  _fw-fr  _fw-fr  _fw-fr addition_n of_o flemish_a mony_n flemish_a money_n be_v reckon_v by_o pound_n shilling_n and_o penny_n as_o we_o do_v our_o sterling_n but_o frequent_o they_o do_v reckon_v by_o stivers_n and_o guilder_n or_o stivers_n and_o ducatoon_n 20_o stivers_n be_v 1_o guilder_n and_o 63_o stivers_n be_v 1_o ducatoon_n stiu._n guild_n stiu._n ducat_n stiu._n  _fw-fr 323_o 16_o 321_o 23_o  _fw-fr 129_o 09_o 78_o 34_o  _fw-fr 14_o 18_o 69_o 57_o  _fw-fr 468_o 03_o 469_o 51_o a_o table_n for_o the_o reduce_v flemish_a ducatoon_n into_o guilder_n and_o stivers_n 〈◊〉_d â—uil_n stiu._n duc._n guild_n stiu._n 1_o 3_o 3_o 100_o 315_o 00_o 2_o 6_o 6_o 200_o 630_o 00_o 3_o 9_o 9_o 300_o 945_o 00_o 4_o 12_o 12_o 400_o 1260_o 00_o 5_o 15_o 15_o 500_o 1575._o 00_o 6_o 18_o 18_o 600_o 1890_o 00_o 7_o 22_o 1_o 700_o 2205_o 00_o 8_o 25_o 4_o 800_o 2520_o 00_o 9_o 28_o 7_o 900_o 2835_o 00_o 10_o 31_o 10_o 1000_o 3150_o 00_o 20_o 63_o 00_o 2000_o 6300_o 00_o 30_o 94_o 10_o 3000_o 9450_o 00_o 40_o 126_o 00_o 4000_o 12600_o 00_o 50_o 157_o 10_o 5000_o 15750_o 00_o 60_o 189_o 00_o 6000_o 18900_o 00_o 70_o 220_o 10_o 7000_o 22050_o 00_o 80_o 252_o 00_o 8000_o 25200_o 00_o 90_o 283_o 10_o 9000_o 28350_o 00_o 100_o 315_o 00_o 10000_o 31500_o 00_o addition_n of_o french_a mony_n 4_o quarter_n make_v 1_o solx_n 60_o solx_n make_v one_o french_a crown_n therefore_o for_o 4_o quarter_n carry_v 1_o solx_n to_o the_o solx_n for_o 60_o solx_n carry_v 1_o french_a crown_n as_o you_o may_v plain_o see_v in_o the_o follow_a example_n cr._n solx_fw-fr qr_n 248_o 42_o 3_o 476_o 37_o 2_o 124_o 29_o 3_o 297_o 56_o 1_o 1147_o 46_o 1_o addition_n of_o haverdupoize_n weight_n table_n 16_o ounce_n be_v 1_o pound_n 28_o pound_n be_v 1_o quarter_n 4_o quarter_n be_v 1_o hundred_o weight_n 20_o hundred_o weight_n be_v 1_o tun._n instruction_n therefore_o from_o your_o ounce_n for_o every_o 16_o carry_v 1_o pound_n to_o your_o pound_n from_o your_o pound_n for_o every_o 28_o carry_v 1_o quarter_n to_o your_o quarter_n and_o from_o your_o quarter_n for_o every_o 4_o carry_v 1_o hundred_o to_o your_o hundred_o and_o from_o your_o hundred_o for_o every_o 20_o carry_v 1_o tun_n to_o your_o tun_n as_o you_o perceive_v by_o the_o follow_a example_n example_n tun_n c._n qr_n li._n oz._n 27_o 18_o 2_o 24_o 12_o 15_o 16_o 3_o 26_o 14_o 9_o 12_o 1_o 18_o 09_o 7_o 08_o 3_o 12_o 07_o 60_o 16_o 3_o 26_o 10_o addition_n of_o apothecary_n weight_n table_n 20_o grain_n be_v 1_o scruple_n ℈_o 3_o scruple_n be_v 1_o drachm_n Ê’_n 8_o dram_fw-la be_v 1_o ounce_n â„¥_o 12_o ounce_n be_v 1_o pound_v lb._n instruction_n from_o the_o grain_n for_o every_o 20_o you_o must_v carry_v 1_o scruple_n to_o the_o scruple_n from_o the_o scruple_n for_o every_o 3_o carry_v 1_o drachm_n to_o the_o drachm_n from_o the_o drachm_n for_o every_o 8_o carry_v 1_o ounce_n to_o the_o ounce_n and_o from_o the_o ounce_n for_o every_o 16_o carry_v 1_o pound_n to_o the_o pound_n according_a as_o you_o may_v see_v do_v in_o the_o follow_a example_n example_n lb_n â„¥_o Ê’_n ℈_o gr_n 4_o 12_o 6_o 2_o 16_o 3_o 15_o 5_o 1_o 10_o 1_o 10_o 3_o 1_o 15_o 10_o 07_o 0_o 0_o 01_o addition_n of_o troy_n weight_n table_n 〈◊〉_d grain_n be_v 1_o penny_n weight_n 〈◊〉_d penny_n weight_n be_v 1_o ounce_n 〈◊〉_d ounce_n be_v 1_o pound_n instruction_n for_o 24_o grain_n carry_v 1_o penny_n weight_n to_o the_o penny_n weight_n for_o 20_o penny_n weight_n carry_v 1_o ounce_n to_o the_o ounce_n for_o 12_o ounce_n carry_v 1_o pound_n to_o the_o pound_n example_n li._n oz._n p._n weig_o gr_n 19_o 08_o 16_o 21_o 14_o 09_o 17_o 17_o 9_o 11_o 18_o 22_o 44_o 06_o 13_o 12_o addition_n of_o wine_n measure_n table_n 2_o pint_n be_v 1_o quart_n 2_o quart_n be_v 1_o pottle_n 2_o pottle_n be_v 1_o gallon_n 63_o gallon_n be_v 1_o hogshead_n 4_o hogshead_n be_v 1_o tun._n instruction_n from_o pint_n for_o every_o 2_o carry_v 1_o quart_n to_o the_o place_n of_o quart_n from_o quart_n for_o every_o 2_o carry_v 1_o pottle_n to_o the_o place_n of_o pottle_n from_o the_o place_n of_o pottle_n for_o every_o 2_o carry_v 1_o gallon_n to_o the_o place_n of_o gallon_n and_o from_o the_o place_n of_o gallon_n for_o every_o 63_o carry_v 1_o hogshead_n to_o the_o place_n of_o hogshead_n and_o from_o the_o place_n of_o hogshead_n for_o every_o 4_o carry_v 1_o tun_n to_o the_o place_n of_o tun_n as_o by_o the_o follow_a example_n example_n tun_n hogsh_a gall_n pottl_n qrts._n pint_n 237_o 1_o 38_o 1_o 1_o 1_o 142_o 3_o 47_o 0_o 1_o 1_o 95_o 2_o 54_o 1_o 0_o 1_o 46_o 1_o 29_o 1_o 1_o 0_o 8_o 2_o 12_o 0_o 0_o 1_o 530_o 3_o 56_o 1_o 1_o 0_o addition_n of_o beer_n measure_n table_n 2_o pint_n be_v 1_o quart_n 2_o quart_n be_v 1_o pottle_n 2_o pottle_n be_v 1_o gallon_n 9_o gallon_n be_v 1_o firkin_n 2_o firkins_n be_v 1_o kilderkin_n 2_o kilderkin_n be_v 1_o barrel_n example_n bar._n kill_v firk_v gall_n pottl_n qrts._n pt_n 54_o 1_o 1_o 7_o 1_o 0_o 1_o 32_o 1_o 0_o 6_o 0_o 1_o 0_o 25_o 1_o 1_o 4_o 1_o 1_o 1_o 12_o 1_o 1_o 3_o 0_o 1_o 0_o 9_o 0_o 1_o 5_o 1_o 0_o 1_o 135_o 1_o 1_o 0_o 1_o 0_o 1_o addition_n of_o dry_a measure_n table_n 16_o pint_n be_v 1_o peck_n 4_o peck_v be_v 1_o bushel_n 8_o bushel_n be_v 1_o quarter_n 5_o quarter_n be_v 1_o wey_n 2_o wey_n 1_o last_o example_n quar._n bush_n peck_n pin_n 128_o 5_o 2_o 11_o 342_o 6_o 3_o 12_o 487_o 7_o 1_o 10_o 83_o 4_o 3_o 15_o 1043_o 1_o 0_o 00_o addition_n of_o long_a measure_n table_n 3_o barley_n corn_n make_v 1_o inch._n 12_o inch_n 1_o foot_n 3_o foot_n 1_o yard_n 5_o yard_n ½_n 1_o pole_n or_o perch_n 40_o perch_n 1_o furlong_n 8_o furlong_n 1_o english_a mile_n by_o the_o table_n you_o may_v easy_o
will_v entreat_v the_o learner_n to_o be_v well_o acquaint_v with_o these_o ground_n before_o he_o proceed_v further_o chap._n vi_o of_o reduction_n reduction_n be_v a_o rule_n that_o teach_v to_o bring_v number_n of_o several_a denomination_n into_o one_o particular_a denomination_n whether_o the_o denomination_n do_v signify_v money_n english_a flemish_a or_o french_a also_o weight_n measure_n etc._n etc._n reduction_n be_v perform_v two_o way_n either_o by_o multiplication_n or_o division_n reduction_n by_o multiplication_n be_v a_o reduce_n of_o great_a denomination_n into_o less_o as_o pound_n into_o shilling_n shilling_n into_o penny_n and_o penny_n into_o farthing_n likewise_o hundred_o into_o quarter_n quarter_n into_o pound_n and_o pound_n into_o ounce_n etc._n etc._n which_o be_v do_v by_o multiplication_n reduction_n by_o division_n be_v a_o reduce_n of_o lesser_a denomination_n into_o great_a as_o farthing_n into_o penny_n penny_n into_o shilling_n and_o shilling_n into_o pound_n likewise_o ounce_n into_o pound_n pound_n into_o quarter_n and_o quarter_n into_o hundred_o etc._n etc._n which_o be_v do_v by_o divide_v that_o denomination_n by_o as_o much_o as_o make_v one_o of_o a_o great_a as_o in_o reduce_v farthing_n into_o penny_n i_o divide_v the_o number_n propound_v by_o 4_o because_o 4_o farthing_n make_v 1_o penny_n reduction_n of_o mony_n in_o this_o reduction_n of_o money_n as_o well_o as_o in_o other_o reduction_n you_o must_v consider_v whether_o the_o sum_n propound_v be_v to_o be_v reduce_v into_o a_o great_a or_o lesser_a denomination_n and_o next_o consider_v how_o many_o of_o the_o one_o denomination_n do_v make_v the_o other_o by_o which_o consideration_n you_o will_v know_v when_o to_o multiply_v and_o when_o to_o divide_v and_o what_o to_o multiply_v or_o divide_v by_o as_o for_o example_n quest_n 1._o in_o 374_o pound_n it_o be_v require_v to_o know_v how_o many_o shilling_n here_o i_o do_v consider_v that_o pound_n be_v the_o great_a denomination_n and_o shilling_n be_v the_o lesser_a and_o that_o in_o one_o pound_n be_v contain_v 20_o shilling_n and_o that_o the_o number_n of_o shilling_n in_o 374_o pound_n will_v be_v 20_o time_n as_o much_o as_o 374_o therefore_o i_o multiply_v 374_o by_o 20_o and_o the_o product_n be_v 7480_o and_o so_o many_o shilling_n be_v contain_v in_o 374_o pound_n quest_n 2._o in_o 526_o 18_o how_o many_o shilling_n and_o penny_n in_o this_o example_n you_o have_v two_o denomination_n propound_v to_o find_v out_o the_o denomination_n of_o penny_n here_o in_o multiply_v your_o pound_n by_o 20_o you_o must_v take_v in_o the_o 18_o shilling_n set_v 8_o down_n first_o because_o 0_o can_v multiply_v therefore_o multiply_v by_o the_o next_o 9_o figure_n 2_o say_v 2_o time_n 6_o be_v 12_o and_z 1_o be_v 13_o set_v down_o 3_o and_o carry_v 1_o 2_o time_n 2_o be_v 4_o and_o 1_o be_v 5_o set_z down_z 5_o 2_o time_n 5_o be_v 10_o setting_z 10_o down_z so_o the_o product_n of_o this_o multiplicand_a and_o the_o odd_a shilling_n make_v 10538_o shilling_n now_o be_o i_o to_o reduce_v the_o shilling_n into_o penny_n and_o know_v that_o 12_o penny_n make_v one_o shilling_n i_o therefore_o multiply_v the_o number_n of_o shilling_n by_o 12_o and_o the_o product_n of_o that_o multiplication_n 126456_o will_v be_v so_o many_o penny_n and_o so_o many_o penny_n do_v 526_o pound_n 18_o shilling_n contain_v in_o the_o work_n of_o reduction_n many_o time_n you_o need_v not_o run_v through_o every_o particular_a denomination_n but_o come_v to_o the_o thing_n require_v soon_o as_o for_o example_n quest_n 3._o in_o 398_o l._n 15_o s._n how_o many_o farthing_n first_o multiply_v 398_o by_o 20_o and_o take_v 9_o in_o the_o odd_a 15_o shilling_n the_o product_n of_o shilling_n will_v be_v 7975_o then_o know_v that_o in_o one_o shilling_n be_v 48_o farthing_n i_o do_v not_o reduce_v these_o shilling_n into_o penny_n as_o in_o the_o last_o example_n by_o multiply_v they_o by_o 48._o i_o do_v reduce_v they_o into_o farthing_n at_o once_o and_o the_o product_n of_o that_o multiplication_n be_v 382800_o and_o so_o many_o farthing_n be_v there_o in_o 398_o l._n 15_o s._n as_o be_v require_v rule_n 4._o but_o if_o it_o be_v require_v to_o reduce_v number_n of_o a_o low_a denomination_n into_o a_o great_a in_o such_o case_n you_o must_v divide_v the_o low_a denomination_n propound_v by_o so_o much_o as_o make_v of_o that_o low_a denomination_n one_o unite_v or_o integer_fw-la of_o the_o great_a denomination_n as_o for_o example_n in_o 1360_o shilling_n how_o many_o pound_n and_o know_v that_o 20_o shilling_n of_o the_o low_a denomination_n be_v contain_v in_o a_o unite_n or_o integer_fw-la of_o the_o great_a 9_o denomination_n of_o pound_n i_o therefore_o divide_v the_o low_a denomination_n 1360_o shilling_n by_o 20_o by_o cut_v off_o the_o last_o figure_n and_o take_v the_o half_a of_o the_o remain_a figure_n which_o half_o 68_o be_v the_o quotient_a of_o that_o division_n by_o 20_o and_o the_o number_n of_o pound_n contain_v in_o 1360_o shilling_n as_o be_v require_v rule_n 5._o but_o if_o the_o question_n so_o happen_v in_o reduction_n that_o there_o may_v be_v a_o denomination_n or_o denomination_n between_o the_o denomination_n give_v and_o the_o denomination_n require_v than_o you_o may_v reduce_v your_o denomination_n give_v by_o division_n into_o the_o next_o superior_a or_o great_a denomination_n and_o when_o it_o be_v so_o reduce_v reduce_v it_o again_o into_o the_o next_o above_o that_o and_o so_o until_o you_o have_v bring_v it_o into_o the_o denomination_n require_v as_o for_o example_n rule_n 6._o let_v it_o be_v demand_v in_o 142080_o farthing_n to_o know_v how_o many_o pound_n first_o i_o divide_v the_o give_v number_n farthing_n by_o 4_o to_o bring_v they_o into_o penny_n because_o i_o penny_n do_v contain_v 4_o farthing_n and_o the_o quotient_a thereof_o will_v be_v 35520_o penny_n then_o i_o divide_v 35520_o penny_n by_o 12_o because_o 12_o penny_n make_v 1_o shilling_n and_o the_o quotient_a of_o that_o division_n will_v be_v 2960_o shilling_n and_o then_o i_o divide_v 2960_o by_o 20_o and_o the_o quotient_n give_v 148_o pound_n which_o be_v equal_a in_o value_n to_o 142080_o farthing_n according_a to_o the_o example_n rule_n 7._o when_o the_o number_n give_v to_o be_v reduce_v do_v consist_v of_o divers_a denomination_n as_o pound_n shilling_n penny_n and_o farthing_n hundred_o quarter_n pound_n and_o ounce_n etc._n etc._n then_o you_o must_v reduce_v the_o high_a or_o great_a denomination_n into_o the_o next_o inferior_a or_o low_a take_v in_o the_o odd_a number_n stand_v in_o that_o denomination_n which_o your_o great_a denomination_n be_v reduce_v to_o then_o reduce_v that_o sum_n into_o the_o next_o inferior_a denomination_n add_v thereto_o the_o odd_a number_n stand_v in_o that_o denomination_n and_o so_o do_v until_o you_o have_v bring_v the_o number_n give_v into_o the_o denomination_n require_v as_o for_o example_n let_v it_o be_v require_v to_o reduce_v 137_o 16_o 7_o ½_n into_o farthing_n first_o i_o bring_v 137_o pound_n into_o shilling_n by_o multiply_v by_o 20_o and_o take_v in_o the_o 16_o shilling_n the_o product_n will_v be_v 2756_o shilling_n then_o i_o multiply_v 2756_o shilling_n by_o 12_o to_o bring_v the_o shilling_n into_o penny_n take_v in_o the_o odd_a 7_o penny_n and_o the_o product_n will_v be_v 33079_o penny_n last_o i_o multiply_v 33079_o by_o 4_o to_o bring_v penny_n into_o farthing_n take_v in_o 2_o for_o the_o odd_a half_a penny_n and_o the_o product_n be_v 132318_o farthing_n be_v equal_a in_o value_n with_o 137_o 16_o 7_o ½_n or_o the_o number_n of_o farthing_n contain_v in_o the_o whole_a sum_n as_o be_v require_v rule_n 8._o if_o in_o reduction_n any_o do_v remain_v of_o a_o division_n the_o remainder_n be_v of_o the_o same_o denomination_n as_o the_o dividend_n be_v of_o there_o be_v a_o short_a way_n for_o reduce_v pound_n into_o penny_n and_o penny_n into_o pound_n as_o for_o example_n rule_n 9_o let_v it_o be_v require_v to_o know_v how_o many_o penny_n be_v contain_v in_o 347_o pound_n now_o because_o 20_o shilling_n be_v 1_o pound_n and_o 12_o penny_n be_v 1_o shilling_n 9_o therefore_o 12_o time_n 20_o which_o be_v 240_o be_v the_o number_n of_o penny_n contain_v in_o 20_o shilling_n or_o 1_o pound_n and_o if_o you_o multiply_v your_o pound_n 347_o by_o 240_o the_o product_n thereof_o 83280_o be_v the_o number_n of_o penny_n contain_v in_o the_o sum_n of_o 347_o pound_n as_o be_v require_v rule_n 10._o it_o be_v require_v to_o know_v how_o many_o groat_n be_v comprehend_v or_o contain_v in_o 263_o pound_n the_o way_n of_o reduce_v pound_n into_o groat_n be_v not_o difficult_a for_o multiply_v the_o pound_n by_o 20_o to_o bring_v they_o into_o shilling_n and_o because_o 1_o shilling_n do_v
contain_v 3_o groat_n multiply_v those_o shilling_n by_o 3_o and_o that_o product_n shall_v be_v the_o number_n of_o groat_n in_o so_o many_o pound_n but_o there_o be_v a_o quick_a and_o short_a way_n than_o this_o which_o be_v thus_o because_o 20_o shilling_n be_v 1_o pound_n and_o 3_o 9_o groat_n be_v 1_o shilling_n therefore_o 3_o time_n 20_o which_o be_v 60_o be_v the_o number_n of_o groat_n in_o 20_o or_o 1_o pound_n and_o if_o you_o multiply_v the_o number_n of_o pound_n 263_o by_o 60_o the_o product_n will_v be_v 15870_o the_o number_n of_o groat_n in_o 263_o pound_n which_o be_v a_o short_a way_n than_o to_o reduce_v pound_n into_o shilling_n and_o shilling_n into_o penny_n by_o two_o multiplication_n rule_n 11._o and_o if_o it_o be_v require_v to_o reduce_v penny_n into_o pound_n or_o groat_n into_o pound_n divide_v by_o 240_o for_o reduce_v penny_n into_o pound_n and_o by_o 60_o for_o the_o reduce_v groat_n into_o pound_n and_o the_o quotient_n shall_v be_v the_o number_n of_o pound_n require_v rule_n 12._o let_v it_o be_v require_v to_o reduce_v 83280_o penny_n and_o 15780_o groat_n into_o pound_n for_o experience_n sake_n be_v the_o product_n of_o the_o two_o last_o example_n divide_v 83280_o penny_n into_o pound_n by_o 240_o the_o number_n of_o penny_n in_o 20_o shilling_n or_o one_o pound_n and_o the_o quotient_n will_v be_v 347_o the_o number_n of_o pound_n as_o before_o also_o divide_v 15780_o groat_n by_o 60_o the_o number_n of_o groat_n contain_v in_o 20_o shilling_n or_o one_o pound_n and_o the_o quotient_a thereof_o will_v be_v 263_o pound_n as_o before_o by_o which_o you_o discern_v the_o infallibility_n of_o both_o rule_n for_o divide_v or_o multiply_v by_o 240_o to_o reduce_v penny_n into_o pound_n and_o pound_n into_o penny_n and_o by_o 60_o for_o reduce_v groat_n into_o pound_n and_o pound_n into_o groat_n rule_n 13._o there_o be_v other_o denomination_n of_o english_a money_n beside_o pound_n shilling_n penny_n and_o farthing_n as_o the_o follow_a table_n do_v show_v denomination_n value_v  _fw-fr s._n d._n a_o mark_n 13_o 04_o a_o angel_n 10_o 00_o a_o noble_a 6_o 08_o a_o crown_n 5_o 00_o a_o thirteen_o penny_n half_a penny_n 1_o 01_o ½_n a_o nine_o penny_n 00_o 09_o a_o four_o penny_n half_a penny_n 00_o 04_o piece_n of_o 00_o 03_o 00_o 02_o rule_n 14._o let_v it_o be_v require_v in_o 783_o noble_n to_o know_v how_o many_o mark_n and_o pound_n at_o 20_o s._n by_o this_o table_n you_o find_v the_o value_n of_o a_o mark_n to_o be_v thirteen_o shilling_n and_o four_o penny_n and_o the_o value_n of_o a_o noble_a to_o be_v half_o a_o mark_n that_o be_v 6_o s._n 8_o d._n and_o likewise_o 6_o s._n 8_o d._n be_v one_o three_o of_o 20_o shilling_n therefore_o 20_o shilling_n or_o 1_o pound_n do_v contain_v 3_o mark_n therefore_o to_o resolve_v the_o question_n double_v the_o number_n of_o noble_n give_v 783_o that_o be_v to_o say_v multiply_v 783_o by_o 2_o and_o the_o product_n 9_o 1566_o will_v be_v the_o number_n of_o mark_n contain_v and_o because_o 3_o mark_n viz_o 3_o time_n 6_o s._n 8_o d._n be_v 20_o shilling_n or_o 1_o pound_n i_o therefore_o divide_v the_o number_n of_o mark_n 1566_o by_o 3_o and_o in_o the_o quotient_a i_o do_v find_v 522_o which_o tell_v i_o that_o in_o 1566_o mark_n there_o be_v 522_o pound_n therefore_o in_o 783_o noble_n there_o be_v 1566_o mark_n and_o 522_o pound_n which_o be_v the_o answer_n to_o the_o question_n require_v rule_n 15._o in_o 768_o pound_n how_o many_o mark_n and_o noble_n this_o question_n be_v but_o the_o reverse_n of_o the_o last_o for_o if_o you_o multiply_v your_o pound_n 9_o give_v by_o 3_o the_o product_n 1566_o will_v be_v mark_n and_o the_o half_a of_o that_o number_n will_v be_v 783_o the_o number_n of_o noble_n as_o be_v require_v therefore_o in_o 522_o pound_n there_o be_v contain_v 1566_o mark_n and_o 783_o noble_n as_o be_v require_v rule_n 16._o in_o 538_o pound_n it_o be_v require_v to_o know_v how_o many_o angel_n and_o crown_n by_o the_o forego_n table_n you_o find_v the_o value_n of_o a_o angel_n to_o be_v 10_o shilling_n and_o of_o a_o crown_n 5_o shilling_n therefore_o because_o twice_o 10_o shilling_n be_v 20_o shilling_n and_o twice_o 5_o shilling_n be_v 10_o shilling_n therefore_o i_o multiply_v the_o 9_o number_n of_o pound_n give_v 538_o by_o 2_o the_o product_n thereof_o 1076_o be_v so_o many_o angel_n and_o that_o product_v 1076_o multiply_v again_o by_o 2_o the_o product_n thereof_o 2152_o be_v the_o number_n of_o crown_n therefore_o in_o 538l_o there_o be_v contain_v 1076_o angel_n and_o 2152_o crown_n as_o be_v require_v rule_n 17._o in_o 2152_o crown_n how_o many_o angel_n and_o pound_n this_o be_v the_o reverse_n of_o the_o last_o rule_n and_o whereas_o pound_n 2152_o crown_n 538_o angel_n 1076_o pound_n there_o you_o multiply_v here_o you_o must_v divide_v by_o which_o be_v take_v the_o half_a of_o it_o as_o for_o experience_n sake_n the_o last_o example_n of_o the_o last_o rule_n the_o half_a of_o 2152_o crown_n be_v 1076_o angel_n and_o the_o half_a of_o 1076_o angel_n be_v 538_o pound_n as_o before_o 2152_o crown_n make_v 1076_o angel_n and_o 538_o pound_n as_o be_v require_v rule_n 18._o in_o 294_o pound_n it_o be_v require_v to_o know_v how_o many_o nine_o pence_n and_o four_o penny_n half_a penny_n for_o the_o resolve_v this_o question_n you_o must_v first_o reduce_v your_o pound_n into_o shilling_n than_o your_o shilling_n into_o penny_n by_o the_o seven_o rule_n and_o the_o product_n of_o the_o which_o in_o the_o example_n you_o will_v find_v to_o be_v 70560_o you_o must_v divide_v by_o 9_o to_o bring_v they_o into_o nine_o pence_n and_o the_o quotient_n will_v give_v you_o 7840_o which_o be_v nine_o pence_n and_o the_o double_a thereof_o 15680_o be_v the_o number_n of_o four_o penny_n half_a penny_n as_o be_v require_v rule_n 19_o in_o 15680_o four_o penny_n half_a penny_n how_o many_o nine_o pence_n shilling_n and_o pound_n this_o be_v the_o reverse_n of_o the_o last_o rule_n and_o where_o in_o that_o you_o do_v multiply_v here_o you_o must_v divide_v where_o you_o divide_v here_o you_o must_v multiply_v there_o i_o have_v choose_v the_o same_o example_n for_o your_o better_a experience_n which_o be_v thus_o resolve_v because_o two_o 4_o d._n ½_n make_v 9_o penny_n therefore_o take_v the_o half_a of_o your_o give_a number_n of_o mark_n 15680_o be_v 7840_o nine_o pence_n then_o by_o multiply_v 7840_o by_o 9_o i_o reduce_v they_o into_o penny_n and_o the_o product_n thereof_o be_v 70560_o penny_n by_o the_o instruction_n of_o the_o six_o rule_n and_o you_o will_v find_v the_o product_n of_o shilling_n to_o be_v 5880_o shilling_n and_o the_o pound_n to_o be_v 294._o so_o i_o find_v that_o 15680_o mark_n be_v 7840_o noble_n or_o in_o value_n 5880_o shilling_n and_o 294_o pound_n as_o be_v require_v rule_n 20._o in_o 6748_o thirteen_o penny_n half_a penny_n how_o many_o penny_n shilling_n and_o pound_n you_o must_v first_o compute_v how_o many_o half_a penny_n there_o be_v in_o 13_o d._n ½_n and_o you_o will_v find_v 27_o therefore_o multiply_v 6748_o by_o 27_o and_o the_o product_n 182196_o will_v be_v all_o half_a pence_n and_o the_o half_a thereof_o 91098_o be_v so_o much_o which_o divide_v by_o 12_o the_o quotient_n will_v give_v you_o 7591_o shilling_n and_o 6_o penny_n remain_v 7591_o shilling_n divide_v by_o 20_o give_v 379_o pound_n and_o 11_o shilling_n remain_v so_o that_o i_o find_v 6748_o thirteen_o penny_n half_a penny_n be_v in_o value_n 379l_o 11_n 6d_o as_o be_v require_v rule_n 21._o in_o 436_o l._n 12_o s._n 9_o d._n how_o many_o piece_n of_o 4_o d._n ½_n per_fw-la piece_n by_o the_o seven_o rule_n reduce_v the_o give_v number_n 436_o 12_o 09_o into_o penny_n and_o you_o will_v find_v the_o product_n of_o penny_n to_o be_v as_o by_o the_o example_n 104797_o penny_n which_o because_o there_o be_v a_o odd_a half_a penny_n in_o 4_o d._n ½_n you_o must_v double_v to_o bring_v into_o half_a penny_n and_o the_o product_n than_o will_v be_v 209586_o half_a penny_n now_o by_o reason_n that_o in_o 4_o d._n ½_n there_o be_v 9_o half_a penny_n you_o must_v divide_v these_o number_n of_o half_a penny_n 209586_o by_o 9_o as_o you_o see_v in_o the_o example_n and_o the_o quotient_n will_v be_v 23287_o piece_n of_o 4_o d._n ½_n and_o of_o the_o division_n there_o do_v remain_v 3_o which_o do_v signify_v so_o many_o half_a penny_n over_o and_o above_o 23287_o piece_n of_o 4_o d._n ½_n rule_n 22._o in_o 372_o pound_n how_o many_o piece_n of_o 3_o d._n and_o 2_o d._n of_o each_o equal_a that_o be_v what_o number_n of_o 3_o d._n piece_n and_o
20_o of_o 7393_o be_v 369_o l._n 13_o s._n which_o add_v together_o make_v 2587_o l._n 11_o s._n the_o true_a value_n of_o 7393_o yard_n as_o be_v require_v and_o in_o like_a manner_n be_v the_o other_o example_n operate_v for_o 3767_o yard_n at_o 9_o s._n per_fw-la yard_n proposition_n 9_o if_o the_o price_n of_o a_o unit_fw-la of_o the_o give_a number_n be_v 5_o s._n then_o the_o operation_n although_o it_o be_v a_o odd_a number_n of_o shilling_n may_v by_o take_v the_o 4_o be_v do_v soon_o as_o by_o the_o follow_a example_n do_v more_o plain_o appear_v proposition_n 10._o if_o the_o price_n of_o a_o unite_v of_o the_o give_v number_n be_v shill_n and_o pence_n or_o shill_n penny_n and_o farthing_n if_o the_o shill_n and_o pence_n be_v a_o even_a part_n of_o a_o pound_n divide_v the_o number_n give_v by_o the_o denominator_fw-la of_o that_o fraction_n represent_v the_o say_v even_o part_n as_o by_o the_o follow_a example_n wherein_o it_o be_v require_v to_o know_v how_o much_o 576_o yard_n amount_v to_o at_o 3_o s._n 4_o d._n per_fw-la yard_n first_o by_o the_o table_n of_o the_o 108_o even_a part_n of_o a_o pound_n i_o find_v 3_o s._n 4_o d._n to_o be_v the_o â…™_n of_o a_o pound_n therefore_o i_o divide_v 576_o by_o 6_o which_o be_v the_o denominator_fw-la of_o the_o fraction_n or_o which_o be_v all_o one_o i_o take_v the_o six_o part_n thereof_o which_o be_v 96_o so_o i_o find_v that_o 576_o yard_n at_o 3_o s._n 4_o d._n come_v unto_o 96_o l._n as_o be_v require_v for_o further_a explanation_n sake_n i_o have_v set_v down_o these_o several_a follow_a example_n proposition_n 11._o when_o the_o price_n of_o a_o unit_fw-la of_o the_o number_n give_v be_v shilling_n and_o penny_n but_o not_o the_o even_a part_n of_o a_o pound_n you_o must_v reduce_v they_o into_o even_a part_n as_o 8_o s._n 4_o d._n may_v be_v reduce_v into_o the_o even_a part_n 6_o s._n 8_o d._n and_o 1_o s._n 8_o d._n which_o make_v 8_o s._n 4_o d._n likewise_o 7_o s._n 6_o d._n may_v be_v reduce_v into_o these_o even_a part_n 5_o s._n and_o 2_o s._n 6_o d._n which_o make_v up_o 7_o s._n 6_o d._n add_v together_o the_o several_a product_n of_o such_o reduce_v even_o part_n and_o their_o sum_n be_v the_o answer_n to_o the_o question_n propound_v as_o by_o these_o follow_a example_n may_v appear_v proposition_n 12._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 shilling_n but_o can_v be_v reduce_v to_o even_a part_n then_o in_o such_o case_n multiply_v the_o give_v number_n by_o the_o number_n of_o shilling_n contain_v in_o the_o price_n give_v and_o after_o by_o the_o four_o or_o five_o proposition_n hereof_o then_o add_v the_o several_a product_n find_v together_o their_o sum_n be_v the_o total_a in_o shilling_n as_o by_o this_o example_n follow_v let_v it_o be_v require_v to_o know_v how_o much_o 5734_o yard_n come_v to_o at_o 9_o s._n 9_o d._n per_fw-la yard_n according_a to_o the_o rule_n i_o multiply_v the_o give_v number_n 5734_o by_o 9_o the_o product_n give_v i_o 51606_o shilling_n therefore_o 9_o d._n be_v no_o even_a part_n of_o a_o shilling_n i_o by_o the_o five_o proposition_n divide_v they_o into_o even_a part_n 6_o and_o 3_o take_v the_o ½_n of_o the_o give_v number_n 2867_o and_o the_o ¼_n which_o be_v 1433_o these_o product_n add_v together_o make_v 55906_o shilling_n and_o 6_o penny_n the_o 1_o 20_o thereof_o be_v 2795_o pound_n 6_o shilling_n and_o 6_o penny_n proposition_n 13._o when_o the_o price_n of_o a_o unit_fw-la of_o any_o number_n give_v be_v shill_n penny_n and_o farthing_n then_o tiply_v your_o give_a number_n by_o the_o number_n of_o shilling_n contain_v in_o the_o give_v price_n and_o your_o product_n will_v be_v shilling_n then_o for_o the_o penny_n and_o farthing_n work_v by_o the_o six_o proposition_n of_o this_o chapter_n as_o by_o the_o follow_a example_n do_v appear_v in_o the_o first_o whereof_o it_o be_v require_v to_o know_v how_o much_o 1743_o yard_n come_v to_o at_o 7_o s._n 3_o d._n 3_o â—â—_o first_o i_o multiply_v the_o give_v number_n 1743_o by_o 7_o the_o number_n of_o shilling_n in_o the_o price_n give_v the_o product_n thereof_o be_v 12201_o shilling_n then_o by_o the_o six_o proposition_n i_o find_v the_o product_n for_o 3_o d._n ¾_n add_v they_o together_o i_o find_v they_o do_v make_v 12745_o shilling_n 8_o d._n ¼_n proposition_n 14._o when_o the_o price_n of_o a_o unite_v of_o any_o number_n give_v be_v pound_n multiply_v the_o number_n give_v by_o the_o number_n of_o pound_n contain_v in_o the_o price_n and_o the_o product_n be_v the_o number_n of_o pound_n require_v as_o by_o these_o two_o follow_a example_n you_o may_v discern_v proposition_n 15._o when_o the_o price_n of_o any_o give_a number_n be_v pound_n and_o shilling_n work_v for_o the_o pound_n as_o by_o the_o last_o proposition_n and_o for_o the_o shilling_n as_o by_o the_o 7._o and_o 8._o then_o add_v the_o several_a product_n together_o and_o the_o sum_n be_v the_o value_n seek_v as_o be_v require_v as_o by_o these_o follow_a example_n proposition_n 16._o when_o the_o give_v price_n of_o a_o unite_v of_o the_o number_n give_v be_v pound_n shilling_n penny_n and_o farthing_n first_o find_v out_o the_o whole_a value_n of_o the_o give_v number_n in_o shilling_n penny_n and_o farthing_n by_o the_o instruction_n of_o the_o 13._o proposition_n of_o this_o chapter_n as_o if_o there_o have_v be_v no_o pound_n in_o the_o give_v price_n then_o for_o the_o pound_n work_v as_o by_o the_o direction_n of_o the_o 15._o proposition_n then_o add_v these_o two_o product_n thus_o find_v together_o and_o their_o product_n or_o sum_n shall_v be_v the_o whole_a value_n of_o the_o give_v number_n at_o the_o price_n propound_v proposition_n 17._o if_o the_o give_v number_n who_o value_n be_v require_v be_v of_o several_a denomination_n as_o hundred_o quarter_n and_o pound_n for_o the_o hundred_o follow_v the_o direction_n of_o the_o last_o proposition_n and_o for_o 2_o quarter_n take_v half_a the_o give_v price_n for_o 1_o quarter_n take_v ¼_n for_o 14_o pound_n take_v â…›_n for_o 7_o pound_n take_v 1_o 16_o of_o the_o give_v then_o add_v all_o these_o product_n together_o and_o you_o have_v the_o full_a value_n require_v as_o by_o these_o follow_a example_n do_v appear_v chap._n xix_o the_o rule_n of_o fellowship_n without_o time_n the_o rule_n of_o fellowship_n without_o time_n be_v when_o several_a merchant_n do_v put_v in_o each_o man_n his_o several_a and_o particular_a sum_n of_o money_n without_o any_o respect_n at_o all_o to_o any_o time_n but_o to_o have_v such_o a_o proportion_n of_o the_o gain_n as_o he_o have_v in_o the_o stock_n example_n a_o b_o c_o and_o d_o make_v a_o stock_n of_o 20_o pound_n in_o which_o a_o have_v 5_o pound_n which_o be_v ¼_n  _fw-fr l._n a_o 5_o b_o 10_o c_z 3_o d_o 2_o  _fw-fr 20_o b_o have_v 10_o pound_n which_o be_v ½_n c_o hath_z 3_o l._n which_o be_v 3_o 20_o and_o d_o have_v 2_o pound_n which_o 2_o 20._o by_o this_o 20_o pound_n they_o do_v gain_v 7_o l._n which_o make_v the_o stock_n 27_o pound_n now_o that_o person_n that_o have_v ¼_n in_o the_o first_o stock_n must_v also_o have_v 1_o â—_o of_o the_o profit_n which_o be_v 1_o l._n 15_o s._n and_o he_o that_o have_v ½_n of_o the_o first_o stock_n must_v have_v ½_n of_o the_o profit_n which_o be_v 3_o l._n 10_o s._n and_o he_o that_o have_v and_o he_o that_o have_v 3_o 20_o of_o the_o first_o stock_n must_v likewise_o have_v 3_o 20_o of_o the_o profit_n which_o be_v 1_o l._n 1_o s._n and_o he_o that_o have_v 2_o 20_o of_o the_o first_o stock_n must_v have_v 2_o 20_o of_o the_o profit_n which_o be_v 14_o s._n as_o you_o see_v  _fw-fr  _fw-fr stock_n profit_n a_o 1_o â—_o 5_o 1_o 15_o b_o ½_n 10_o 3_o 10_o c_z 3_o 20_o 3_o 1_o 01_o d_o 2_o 20_o 2_o 14_o  _fw-fr  _fw-fr 20_o 7_o now_o to_o find_v out_o each_o man_n several_a share_n in_o the_o profit_n or_o loss_n you_o must_v collect_v the_o several_a sum_n pay_v into_o stock_n together_o and_o by_o addition_n find_v their_o sum_n then_o by_o the_o rule_n say_v as_o the_o sum_n of_o the_o several_a partner_n share_n be_v to_o the_o profit_n or_o loss_n so_o be_v each_o man_n particular_a share_n in_o stock_n to_o his_o particular_a share_n in_o the_o profit_n or_o loss_n and_o as_o many_o share_n as_o the_o principal_a stock_n do_v contain_v so_o many_o operation_n will_v there_o be_v of_o the_o rule_n of_o three_o the_o four_o proportional_a of_o each_o operation_n be_v the_o respective_a share_n in_o the_o profit_n or_o loss_n belong_v to_o that_o
share_n of_o the_o stock_n which_o be_v the_o three_o number_n in_o the_o same_o operation_n example_n 1._o four_o partner_n viz._n a_o b_o c_o and_o d_o make_v up_o a_o stock_n in_o which_o stock_n they_o have_v each_o different_a and_o unequal_a share_n a_o put_v in_o 160_o l._n b_o put_v in_o 80_o pound_n c_o puts_z in_o 144_o pound_n and_o d_o put_v in_o 96_o l._n now_o there_o be_v gain_v by_o the_o whole_a stock_n 126_o l_o the_o question_n be_v how_o much_o of_o the_o 126_o l._n each_o partner_n to_o be_v have_v according_a to_o his_o share_n in_o the_o stock_n  _fw-fr l._n s._n d._n a_o 160_o  _fw-fr  _fw-fr b_o 80_o  _fw-fr  _fw-fr c_o 144_o  _fw-fr  _fw-fr d_o 96_o  _fw-fr  _fw-fr  _fw-fr 480_o  _fw-fr  _fw-fr accord_n to_o the_o former_a direction_n i_o add_v the_o several_a share_n together_o and_o they_o do_v make_v 480_o pound_n now_o because_o there_o be_v four_o several_a share_n there_o will_v be_v four_o operation_n by_o the_o rule_n of_o three_o which_o be_v as_o follow_v if_o 480_o l._n give_v 126_o l._n what_o will_v 160_o l_o ans_fw-fr 42_o l._n if_o 480_o l._n give_v 126_o l._n what_o will_v 80_o l_o ans_fw-fr 21_o l._n if_o 480_o l._n give_v 126_o l._n what_o will_v 144_o l_o ans_fw-fr 37_o l._n 16_o s._n if_o 480_o l._n give_v 126_o l._n what_o will_v 96_o l_o ans_fw-fr 25_o l._n 04_o s._n and_o these_o four_o proportional_n find_v be_v due_a to_o the_o several_a partner_n over_o and_o above_o their_o respective_a share_n as_o to_o a_o 42_o l._n to_o b_o 21_o l._n to_o c_o 37_o 16_o and_o to_o d_o 25_o l._n 4_o s._n as_o you_o see_v follow_v which_o be_v add_v altogether_o make_v 126_o l._n as_o before_o equal_a to_o the_o sum_n that_o be_v gain_v a_o 42_o b_o 21_o c_z 37_o 16_o d_o 25_o 04_o  _fw-fr 126_o the_o add_v together_o of_o these_o four_o proportional_n find_v be_v the_o proof_n of_o the_o single_a rule_n of_o fellowship_n for_o if_o they_o make_v up_o the_o same_o sum_n as_o be_v gain_v by_o the_o whole_a stock_n or_o lose_v than_o your_o several_a operation_n have_v be_v right_o work_v if_o there_o be_v any_o difference_n you_o may_v certain_o conclude_v you_o have_v commit_v some_o error_n example_n 2._o two_o partner_n join_v together_o and_o be_v resolve_v to_o make_v up_o a_o stock_n viz._n a_o and_o b._n the_o first_o partner_n a_o do_v resolve_v to_o have_v 4_o 7_o of_o the_o profit_n and_o lay_v in_o 1368_o pound_n it_o be_v require_v to_o know_v how_o much_o b_o must_v pay_v into_o stock_n to_o gain_v the_o remain_v 3_o 7_o of_o the_o profit_n by_o the_o rule_n of_o three_o say_v if_o 4_o 7_o of_o the_o gain_n which_o the_o first_o man_n a_o take_v do_v pay_v into_o stock_n 1368_o 1_o how_o much_o must_v 3_o 7_o of_o the_o gain_n lie_v into_o stock_n which_o be_v the_o second_o man_n b_o profit_n which_o by_o multiply_v and_o divide_v you_o will_v find_v to_o be_v 1026l_o and_o so_o much_o must_v b_o lay_v into_o stock_n to_o gain_v 3_o 7_o of_o the_o profit_n if_o a_o gain_v 4_o 7_o by_o put_v in_o 1368l_o example_n 3._o six_o partner_n viz._n a_o b_o c_o d_o e_o and_o f_o build_v a_o ship_n between_o they_o amount_v to_o the_o sum_n of_o 2376_o pound_n the_o several_a partner_n put_v in_o as_o follow_v  _fw-fr l._n s._n a_o put_v in_o 222_o 15_o b_o 271_o 05_o c_o 519_o 15_o d_o 297_o 00_o e_z 816_o 15_o f_o 148_o 10_o  _fw-fr 2376_o  _fw-fr these_o partner_n let_v their_o ship_n out_o to_o freight_n for_o a_o certain_a voyage_n for_o 1250_o l._n it_o be_v require_v to_o know_v how_o much_o of_o the_o say_v freight_n be_v due_a to_o the_o several_a partner_n therefore_o by_o the_o rule_n of_o three_o as_o 2376l_o the_o whole_a value_n of_o the_o ship_n be_v to_o 1250_o l._n the_o freight_n so_o be_v the_o several_a respective_a share_n put_v in_o by_o the_o say_a partner_n to_o their_o respective_a share_n in_o 1250l_o the_o freight_n which_o by_o multiply_v and_o divide_v i_o find_v to_o be_v as_o follow_v answer_n  _fw-fr l._n s._n d._n a_o 117_o 03_o 9_o b_o 195_o 06_o 3_o c_o 273_o 08_o 9_o d_o 156_o 05_o 0_o e_z 429_o 13_o 9_o f_o 78_o 02_o 6_o  _fw-fr 1250_o  _fw-fr  _fw-fr if_o there_o happen_v to_o be_v a_o loss_n the_o several_a partner_n must_v bear_v a_o proportional_a share_n in_o the_o loss_n as_o they_o do_v in_o the_o gain_n which_o be_v to_o be_v find_v out_o after_o the_o same_o manner_n for_o as_o the_o general_a stock_n of_o the_o partner_n be_v to_o the_o general_a loss_n so_o be_v the_o particular_a share_n in_o the_o stock_n to_o the_o particular_a share_n in_o the_o loss_n example_n 4._o three_o merchant_n adventure_n to_o sea_n 794_o pound_n viz._n a_o have_v 148_o 17_o 6_o b_o have_v 198_o 10_o 0_o and_o c_o have_v 446_o 12_o 6._o these_o merchant_n have_v lose_v out_o of_o their_o general_a stock_n 213_o l._n 10_o s._n i_o require_v to_o know_v each_o man_n share_n in_o the_o loss_n as_o 794_o l._n be_v to_o 213_o l._n 10_o s._n so_o be_v 148_o l._n 17_o s._n 6_o d._n to_o 40_o l._n 00_o s._n 7_o d._n ½_n as_o 794_o l._n be_v to_o 213_o l._n 10_o s._n so_o be_v 198_o l._n 10_o s._n 0_o d._n to_o 53_o l._n 7_o s._n 6_o d._n as_o 794_o l._n be_v to_o 213_o l._n 10_o s._n so_o be_v 446_o l._n 12_o s._n 6_o d._n to_o 120_o l._n 1_o s._n 10_o d._n ½_n answer_n a_o have_v lose_v 40_o 00_o 7_o ½_n b_o 53_o 07_o 6_o c_o 120_o 01_o 10_o ½_n  _fw-fr 213_o 10_o  _fw-fr here_n in_o this_o example_n a_o have_v lose_v 40_o l._n 7_o d._n ½_n b_o have_v lose_v 53_o 7_o 6_o and_o c_o have_v lose_v 120_o 1_o 10_o ½_n each_o bear_v such_o a_o proportional_a share_n in_o the_o loss_n as_o they_o have_v in_o the_o general_a stock_n and_o their_o respective_a share_n in_o the_o loss_n make_v up_o the_o just_a sum_n of_o 213_o l._n 10_o s._n the_o general_a loss_n as_o before_o chap._n xx._n the_o rule_n of_o fellowship_n with_o time_n the_o rule_n of_o fellowship_n with_o time_n be_v when_o each_o partner_n share_v in_o the_o stock_n have_v a_o relation_n to_o the_o time_n that_o it_o have_v remain_v in_o stock_n in_o this_o rule_n you_o must_v multiply_v each_o partner_n particular_a share_n by_o the_o time_n it_o have_v continue_v in_o stock_n these_o several_a product_n you_o may_v call_v for_o distinction_n sake_n their_o new_a laying_n in_o then_o by_o the_o rule_n of_o three_o say_v as_o the_o sum_n of_o their_o new_a laying_n in_o be_v to_o the_o profit_n make_v so_o be_v each_o man_n particular_a new_a lay_v in_o to_o his_o particular_a share_n of_o profit_n example_n 1._o two_o partner_n join_v stock_n together_o viz._n a_o lay_v in_o the_o first_o of_o april_n 475_o pound_n and_o b_o lay_v in_o the_o first_o of_o july_n 525_o pound_n and_o by_o the_o last_o of_o december_n they_o have_v gain_v 360_o pound_n now_o i_o desire_v to_o know_v each_o man_n proportion_n of_o the_o profit_n answerable_a to_o his_o share_n in_o stock_n and_o time_n a_o have_v for_o 9_o month_n 475_o b_o have_v for_o 6_o month_n 525_o  _fw-fr 1000_o a_o share_n multiply_v by_o his_o time_n be_v 4275_o b_o share_n multiply_v by_o his_o time_n be_v 3150_o  _fw-fr 7425_o as_o be_v to_o so_o be_v to_o  _fw-fr  _fw-fr  _fw-fr 7425_o 360_o 4275_o 207_o 5_o 5_o ¼_n 6075_o 7425_o 7425_o 360_o 3150_o 152_o 14_o 6_o ½_n 1350_o 7425_o a_o share_n for_o 475_o l._n 9_o mon._n be_v 207_o 5_o 5_o ¼_n 6075_o 7425_o b_o share_n for_o 525_o l._n 6_o mon._n be_v 152_o 14_o 6_o ½_n 1â—25_n 7445_o total_a sum_n be_v 360_o example_n 2._o two_o partner_n be_v resolve_v to_o make_v a_o stock_n together_o viz._n a_o put_v in_o 380_o l._n the_o first_o of_o may_n and_o b_o can_v put_v any_o thing_n in_o till_o the_o first_o of_o august_n next_o i_o demand_v how_o much_o b_o oughts_z to_o put_v into_o receive_v ½_n of_o the_o profit_n at_o the_o year_n end_n multiply_v a_o share_n 380_o by_o 8_o month_n the_o time_n his_o money_n abide_v in_o company_n the_o product_n thereof_o be_v 3040_o l._n for_o his_o new_a lay_n in_o now_o because_o b_o put_v in_o nothing_o until_o the_o first_o of_o august_n his_o money_n will_v lie_v in_o but_o 5_o month_n divide_v 3040_o by_o 5_o and_o thereof_o will_v come_v 608_o l._n and_o so_o much_o must_v b_o lay_v in_o to_o receive_v ½_n of_o the_o profit_n as_o be_v require_v example_n 3._o two_o partner_n join_v together_o in_o a_o stock_n of_o 750_o pound_n by_o which_o stock_n they_o gain_v 240_o pound_n which_o put_v to_o the_o stock_n make_v 990_o l._n
your_o right_a hand_n the_o remainder_n give_v you_o the_o number_n of_o farthing_n contain_v in_o the_o principle_n and_o interest_n upon_o interest_n of_o 200_o l._n for_o 4_o year_n but_o because_o question_n of_o interest_n upon_o interest_n require_v a_o operation_n for_o each_o year_n i_o have_v therefore_o insert_v the_o follow_a table_n a_o table_n show_v the_o principal_a and_o interest_n upon_o interest_n for_o one_o pound_n for_o any_o term_n under_o 31_o year_n year_n l._n s._n d._n f._n 1_o 1_o 1_o 2_o 1_o 2_o 1_o 2_o 5_o 2_o 3_o 1_o 3_o 9_o 3_o 4_o 1_o 5_o 3_o 0_o 5_o 1_o 6_o 9_o 0_o 6_o 1_o 8_o 4_o 2_o 7_o 1_o 10_o 0_o 3_o 8_o 1_o 11_o 10_o 2_o 9_o 1_o 13_o 9_o 2_o 10_o 1_o 15_o 9_o 3_o 11_o 1_o 17_o 11_o 2_o 12_o 2_o 0_o 3_o 0_o 13_o 2_o 2_o 7_o 3_o 14_o 2_o 5_o 2_o 2_o 15_o 2_o 7_o 11_o 1_o 16_o 2_o 10_o 9_o 2_o 17_o 2_o 13_o 10_o 1_o 18_o 2_o 17_o 1_o 0_o 19_o 3_o 0_o 6_o 0_o 20_o 3_o 4_o 1_o 3_o 21_o 3_o 7_o 11_o 3_o 22_o 3_o 12_o 0_o 2_o 23_o 3_o 16_o 4_o 1_o 24_o 4_o 0_o 11_o 1_o 25_o 4_o 5_o 9_o 1_o 26_o 4_o 10_o 11_o 0_o 27_o 4_o 16_o 4_o 1_o 28_o 5_o 2_o 1_o 2_o 29_o 5_o 8_o 3_o 0_o 30_o 5_o 14_o 8_o 3_o 31_o 6_o 1_o 7_o 1_o the_o first_o column_n of_o this_o table_n be_v the_o column_n of_o year_n from_o 1_o to_o 31_o and_o over_o against_o each_o number_n of_o year_n do_v stand_v the_o sum_n that_o 20_o shilling_n or_o one_o pound_n do_v come_v to_o at_o interest_n upon_o interest_n for_o the_o same_o time_n suppose_v it_o be_v require_v to_o know_v by_o this_o table_n the_o increase_n of_o 50_o l._n for_o 12_o year_n at_o interest_n upon_o interest_n look_v in_o the_o table_n over_o against_o 12_o year_n and_o you_o will_v find_v 2_o l._n 0_o s._n 3_o d._n which_o be_v the_o increase_n of_o 1_o pound_n for_o 12_o year_n which_o multiply_v by_o 50_o as_o you_o see_v viz._n  _fw-fr l._n s._n d._n  _fw-fr 2_o 0_o 3_o  _fw-fr  _fw-fr  _fw-fr 50_o 50_o time_n 3_o d._n be_v  _fw-fr 12_o 6_o 50_o time_n 2_o l._n be_v 100_o  _fw-fr  _fw-fr total_a be_v 100_o 12_o 6_o so_o that_o 100_o l._n 12_o s._n 6_o d._n be_v the_o increase_n of_o 50_o l._n for_o 12_o year_n allow_v interest_n upon_o interest_n of_o purchase_n and_o annuty_n if_o you_o will_v purchase_v any_o sum_n of_o money_n to_o be_v pay_v you_o any_o number_n of_o year_n to_o come_v you_o must_v first_o know_v what_o it_o be_v worth_a in_o ready_a money_n allow_v interest_n upon_o innerest_n to_o effect_v this_o say_v as_o 106l_o be_v to_o 100_o l._n so_o 100_o l._n to_o the_o present_a worth_n of_o 100_o l._n to_o be_v pay_v at_o 12_o month_n or_o a_o year_n then_o for_o the_o second_o year_n say_v as_o 106_o l._n be_v to_o 100_o l._n so_o be_v the_o present_a worth_n of_o one_o year_n to_o the_o present_a worth_n for_o two_o year_n and_o in_o like_a manner_n be_v the_o present_a worth_n of_o any_o sum_n of_o money_n give_v find_v out_o for_o any_o number_n of_o year_n to_o come_v as_o by_o the_o follow_a example_n do_v more_o plain_o appear_v example_n let_v it_o be_v require_v to_o know_v how_o much_o 50_o l._n to_o be_v pay_v at_o two_o year_n end_n be_v worth_a in_o ready_a money_n by_o the_o rule_n of_o three_o according_a to_o the_o precede_a instruction_n say_v here_o you_o see_v 50_o l._n to_o be_v pay_v at_o one_o year_n end_n be_v worth_a in_o ready_a money_n 47_o l._n 169_o part_n or_o 3_o s._n 4_o d._n then_o for_o the_o second_o year_n make_v this_o last_o sum_n find_v out_o 47_o 169_o your_o three_o number_n say_v by_o this_o last_o operation_n the_o four_o number_n find_v out_o be_v 44_o 499_o by_o which_o you_o see_v that_o 50_o l._n to_o be_v pay_v at_o the_o end_n and_o expiration_n of_o two_o year_n be_v worth_a no_o more_o than_o 44_o pound_n 10_o shilling_n in_o ready_a money_n and_o in_o like_a manner_n if_o you_o will_v know_v the_o present_a worth_n of_o 50_o l._n at_o the_o end_n and_o ration_n of_o three_o year_n make_v 44_o 499_o your_o three_o number_n say_v as_o 106_o l._n be_v to_o 100_o l._n so_o be_v 44_o 499_o to_o 41_o 980._o but_o to_o avoid_v this_o trouble_n i_o have_v insert_v the_o follow_a table_n show_v the_o present_a worth_n of_o one_o pound_n in_o ready_a money_n to_o be_v pay_v any_o number_n of_o year_n under_o 31_o and_o if_o you_o know_v the_o present_a worth_n of_o one_o pound_n by_o multiplication_n you_o may_v know_v the_o present_a worth_n of_o any_o other_o sum_n of_o mony_n annex_v to_o this_o table_n be_v another_o table_n show_v the_o true_a value_n of_o 1_o l._n annuity_n to_o continue_v 31_o year_n in_o ready_a money_n whereby_o you_o may_v easy_o know_v the_o true_a value_n of_o any_o purchase_n to_o continue_v the_o same_o term_n of_o year_n a_o necessary_a table_n show_v the_o present_a worth_n of_o 1_o l._n to_o be_v pay_v any_o number_n of_o year_n under_o 31_o at_o 6_o l._n per_fw-la cent._n year_n l._n s._n d._n  _fw-fr 1_o 18_o 10_o 2_o 94339_o 2_o 17_o 9_o 2_o 88999_o 3_o 16_o 9_o 2_o 83962_o 4_o 15_o 10_o 0_o 79209_o 5_o 14_o 11_o 1_o 74726_o 6_o 14_o 1_o 1_o 70496_o 7_o 13_o 3_o 2_o 66506_o 8_o 12_o 6_o 2_o 62741_o 9_o 11_o 10_o 0_o 59190_o 10_o 11_o 2_o 0_o 55839_o 11_o 10_o 6_o 2_o 52678_o 12_o 9_o 11_o 1_o 49697_o 13_o 9_o 4_o 2_o 46884_o 14_o 8_o 10_o 0_o 44230_o 15_o 8_o 4_o 1_o 41726_o 16_o 7_o 10_o 2_o 39365_o 17_o 7_o 5_o 0_o 37136_o 18_o 7_o 0_o 0_o 35034_o 19_o 6_o 7_o 1_o 33051_o 20_o 6_o 2_o 3_o 31181_o 21_o 5_o 10_o 2_o 29415_o 22_o 5_o 6_o 2_o 27750_o 23_o 5_o 2_o 3_o 26180_o 24_o 4_o 11_o 1_o 24698_o 25_o 4_o 7_o 2_o 23300_o 26_o 4_o 4_o 3_o 21981_o 27_o 4_o 1_o 3_o 20737_o 28_o 3_o 11_o 0_o 19563_o 29_o 3_o 9_o 1_o 18453_o 30_o 3_o 5_o 3_o 17411_o a_o table_n show_v the_o true_a value_n of_o 1_o l._n annuity_n to_o continue_v any_o number_n of_o year_n under_o 31_o in_o ready_a money_n at_o 6_o l._n per_fw-la cent._n year_n l._n s._n d._n q._n decimal_n 1_o  _fw-fr 18_o 10_o 2_o 0_o 94340_o 2_o 1_o 16_o 08_o 0_o 1_o 83339_o 3_o 2_o 13_o 05_o 2_o 2_o 67301_o 4_o 3_o 09_o 03_o 2_o 3_o 46510_o 5_o 4_o 04_o 03_o 0_o 4_o 21236_o 6_o 4_o 18_o 04_o 1_o 4_o 91732_o 7_o 5_o 11_o 07_o 3_o 5_o 58238_o 8_o 6_o 04_o 02_o 1_o 6_o 20979_o 9_o 6_o 16_o 00_o 1_o 6_o 80169_o 10_o 7_o 07_o 02_o 1_o 7_o 36008_o 11_o 7_o 17_o 08_o 3_o 7_o 88687_o 12_o 8_o 07_o 08_o 0_o 8_o 38384_o 13_o 8_o 17_o 00_o 2_o 8_o 85268_o 14_o 9_o 05_o 10_o 3_o 9_o 29498_o 15_o 9_o 14_o 03_o 0_o 9_o 71224_o 16_o 10_o 02_o 01_o 2_o 10_o 10589_o 17_o 10_o 09_o 06_o 2_o 10_o 47725_o 18_o 10_o 16_o 06_o 2_o 10_o 82760_o 19_o 11_o 03_o 02_o 0_o 11_o 15811_o 20_o 11_o 09_o 04_o 3_o 11_o 46992_o 21_o 11_o 15_o 03_o 1_o 11_o 76405_o 22_o 12_o 00_o 10_o 0_o 12_o 04158_o 23_o 12_o 06_o 00_o 3_o 12_o 30337_o 24_o 12_o 11_o 00_o 0_o 12_o 55035_o 25_o 12_o 15_o 07_o 2_o 12_o 78335_o 26_o 13_o 00_o 00_o 2_o 13_o 00316_o 27_o 13_o 04_o 02_o 2_o 13_o 21053_o 28_o 13_o 08_o 01_o 2_o 13_o 40616_o 29_o 13_o 11_o 10_o 3_o 13_o 59071_o 30_o 13_o 15_o 04_o 2_o 13_o 76482_o the_o use_n of_o the_o forego_n table_n it_o be_v require_v to_o know_v the_o present_a value_n in_o ready_a money_n of_o 36_o l._n annuity_n or_o lease_n that_o be_v to_o continue_v 21_o year_n by_o the_o former_a table_n you_o find_v 1_o l._n annuity_n or_o lease_n to_o continue_v 21_o year_n be_v worth_a 11_o l._n 15_o s._n 3_o d._n 1_o f._n therefore_o the_o answer_n to_o your_o question_n must_v be_v 36_o time_n 11_o l._n 15_o s._n 3_o d._n 1_o f._n  _fw-fr l._n s._n d._n f._n therefore_o 11_o 15_o 3_o 1_o multiply_v by_o  _fw-fr  _fw-fr  _fw-fr 36_o 36_o time_n 1_o farthing_n be_v  _fw-fr  _fw-fr 9_o 0_o 36_o time_n 3_o penny_n be_v  _fw-fr 9_o 0_o 0_o 36_o time_n 15_o shilling_n be_v 27_o 0_o 0_o 0_o 36_o time_n 11_o pound_n be_v 396_o 0_o 0_o 0_o total_a sum_n be_v 423_o 9_o 9_o 0_o by_o decimal_n thus_o look_v for_o the_o decimal_n value_n of_o one_o pound_v annuity_n or_o lease_n for_o 21_o year_n which_o you_o will_v by_o the_o same_o table_n find_v to_o be_v 11_o 76405_o which_o multiply_v by_o 36_o pound_n the_o product_n will_v be_v 423_o pound_n 50580_o which_o in_o value_n be_v ten_o
shilling_n be_v three_o penny_n more_o than_o the_o other_o therefore_o the_o purchase_n of_o 36_o pound_n for_o 21_o year_n be_v worth_a 423_o l._n 9_o s._n 9_o d._n as_o be_v require_v chap._n xxii_o of_o rebate_v or_o discount_n rebate_v or_o discount_n be_v when_o money_n be_v due_a at_o a_o certain_a time_n as_o at_o 2_o 3_o 6_o or_o 12_o month_n and_o the_o person_n to_o who_o the_o money_n be_v payable_a may_v sometime_o have_v such_o occasion_n for_o his_o money_n as_o to_o desire_v it_o before_o it_o be_v due_a the_o person_n that_o be_v to_o pay_v the_o money_n have_v no_o reason_n to_o pay_v his_o money_n before_o it_o be_v due_a without_o some_o consideration_n of_o rebate_v or_o discount_n for_o so_o much_o time_n at_o 6_o 7_o or_o 8_o per_fw-la cent._n as_o they_o do_v agree_v observe_v this_o as_o a_o general_a rule_n that_o upon_o rebatement_n there_o must_v be_v no_o more_o money_n pay_v down_o than_o will_v augment_v itself_o unto_o the_o whole_a sum_n due_a if_o it_o be_v put_v forth_o to_o interest_n for_o so_o much_o time_n as_o it_o be_v pay_v or_o receive_v before_o hand_n example_n 1._o let_v it_o be_v require_v to_o know_v the_o rebate_v of_o 250_o l._n for_o 12_o month_n at_o 6_o per_fw-la cent._n then_o by_o the_o rule_n of_o three_o say_v as_o 106_o be_v to_o 100_o so_o be_v 250_o l._n  _fw-fr l._n s._n d._n  _fw-fr money_n to_o be_v lay_v down_o 235_o 16_o 11_o ¾_n money_n rebate_v or_o discount_v 14_o 03_o 00_o ¼_n total_a 250_o  _fw-fr  _fw-fr  _fw-fr by_o which_o i_o gather_v that_o the_o interest_n of_o 235_o 16_o 11_o ¾_n for_o 12_o month_n at_o 6_o l._n per_fw-la cent._n be_v 14_o 3_o 0_o ¼_n which_o make_v up_o the_o whole_a debt_n 250_o pound_n as_o before_o example_n 2._o i_o demand_v how_o much_o i_o must_v rebate_v or_o discount_n for_o 165_o pound_n for_o 9_o month_n at_o 8_o pound_n per_fw-la cent._n simple_a or_o bare_a interest_n say_v by_o the_o rule_n of_o three_o  _fw-fr l._n s._n d._n total_a sum_n due_a be_v 165_o 00_o 00_o to_o be_v pay_v 155_o 13_o 02_o at_o 8_o l._n per_fw-la cent._n for_o 9_o month_n be_v rebate_v 9_o 6_o 10_o example_n 3._o i_o demand_v the_o discount_n or_o rebate_v of_o 548_o l._n for_o 6_o month_n at_o 7_o per_fw-la cent._n simple_a interest_n say_v by_o the_o rule_n of_o three_o total_a sum_n due_a be_v 548_o  _fw-fr  _fw-fr pay_v down_o 529_o 09_o 04_o rebate_v for_o 6_o month_n at_o 6_o l._n per_fw-la cent._n 18_o 10_o 08_o quest_n let_v it_o be_v require_v to_o know_v the_o rebate_v of_o 500_o l._n for_o 9_o mon._n at_o 6_o l._n per_fw-la cent._n example_n to_o resolve_v this_o question_n you_o must_v find_v out_o the_o interest_n of_o 500_o l._n for_o 9_o month_n the_o interest_n of_o 100_o l._n for_o 9_o month_n or_o three_o quarter_n of_o a_o year_n be_v 4_o l._n 10_o s._n therefore_o the_o interest_n of_o 500_o l._n for_o the_o same_o time_n must_v of_o necessity_n be_v 22_o l._n 10_o s._n now_o i_o say_v if_o 522_o l._n 10_o s._n give_v 500_o l._n what_o will_v 500_o l._n give_v here_o you_o find_v the_o answer_n to_o the_o question_n last_o state_v by_o the_o quotient_a which_o do_v give_v you_o 114832_o penny_n which_o be_v reduce_v as_o follow_v at_o last_o we_o have_v find_v that_o if_o 522_o l._n 10_o s._n give_v 500_o l._n then_o 500_o l._n will_v give_v 478_o l._n 9_o s._n 4_o d._n which_o subtract_v from_o 500_o l._n give_v 21_o l._n 10_o s._n 8_o d._n for_o the_o rebate_v of_o 500_o l._n for_o 9_o month_n at_o 6_o l._n per_fw-la cent._n this_o follow_a table_n will_v be_v of_o very_o great_a use_n for_o the_o ready_a cast_v up_o of_o the_o rebate_v of_o any_o sum_n of_o money_n for_o any_o time_n propound_v a_o table_n of_o rebate_v at_o 6_o per_fw-la cent._n  _fw-fr 1_o month._n 2_o month._n 3_o month_n  _fw-fr l._n s._n d._n l._n s._n d._n l._n s._n d._n 1_o  _fw-fr  _fw-fr 1_o  _fw-fr  _fw-fr 2_o  _fw-fr  _fw-fr 4_o 2_o  _fw-fr  _fw-fr 2_o  _fw-fr  _fw-fr 5_o  _fw-fr  _fw-fr 7_o 3_o  _fw-fr  _fw-fr 3_o  _fw-fr  _fw-fr 7_o  _fw-fr  _fw-fr 11_o 4_o  _fw-fr  _fw-fr 5_o  _fw-fr  _fw-fr 10_o  _fw-fr 1_o 2_o 5_o  _fw-fr  _fw-fr 6_o  _fw-fr 1_o 0_o  _fw-fr 1_o 6_o 6_o  _fw-fr  _fw-fr 7_o  _fw-fr 1_o 2_o  _fw-fr 1_o 9_o 7_o  _fw-fr  _fw-fr 8_o  _fw-fr 1_o 5_o  _fw-fr 2_o 2_o 8_o  _fw-fr  _fw-fr 9_o  _fw-fr 1_o 7_o  _fw-fr 2_o 4_o 9_o  _fw-fr  _fw-fr 11_o  _fw-fr 1_o 9_o  _fw-fr 2_o 8_o 10_o  _fw-fr 1_o 0_o  _fw-fr 2_o 0_o  _fw-fr 2_o 11_o 20_o  _fw-fr 2_o 0_o  _fw-fr 3_o 11_o  _fw-fr 5_o 11_o 30_o  _fw-fr 3_o 0_o  _fw-fr 5_o 11_o  _fw-fr 8_o 10_o 40_o  _fw-fr 4_o 0_o  _fw-fr 7_o 11_o  _fw-fr 11_o 10_o 50_o  _fw-fr 5_o 0_o  _fw-fr 9_o 11_o  _fw-fr 14_o 9_o 60_o  _fw-fr 6_o 0_o  _fw-fr 11_o 11_o  _fw-fr 17_o 9_o 70_o  _fw-fr 7_o 0_o  _fw-fr 13_o 10_o 1_o 0_o 8_o 80_o  _fw-fr 8_o 0_o  _fw-fr 15_o 10_o 1_o 3_o 8_o 90_o  _fw-fr 8_o 11_o  _fw-fr 17_o 10_o 1_o 6_o 7_o 100_o  _fw-fr 9_o 11_o  _fw-fr 19_o 10_o 1_o 9_o 7_o 200_o  _fw-fr 19_o 10_o 1_o 19_o 7_o 2_o 19_o 1_o 300_o 1_o 9_o 11_o 2_o 19_o 5_o 4_o 8_o 8_o 400_o 1_o 19_o 12_o 3_o 19_o 2_o 5_o 18_o 3_o 500_o 2_o 9_o 9_o 4_o 19_o 0_o 7_o 7_o 9_o 600_o 2_o 19_o 8_o 5_o 18_o 10_o 8_o 17_o 4_o 700_o 3_o 9_o 8_o 6_o 18_o 7_o 10_o 6_o 11_o 800_o 3_o 19_o 7_o 7_o 18_o 5_o 11_o 16_o 5_o 900_o 4_o 9_o 7_o 8_o 18_o 2_o 13_o 6_o 0_o 1000_o 4_o 19_o 6_o 9_o 18_o 0_o 14_o 15_o 7_o a_o table_n of_o rebate_v at_o 6_o l._n per_fw-la cent._n  _fw-fr 4_o month_n 5_o month_n 6_o month_n  _fw-fr l._n s._n d._n l._n s._n d._n l._n s._n d._n 1_o  _fw-fr  _fw-fr 5_o  _fw-fr  _fw-fr 6_o  _fw-fr  _fw-fr 7_o 2_o  _fw-fr  _fw-fr 9_o  _fw-fr 1_o 0_o  _fw-fr 1_o 2_o 3_o  _fw-fr 1_o 2_o  _fw-fr 1_o 6_o  _fw-fr 1_o 9_o 4_o  _fw-fr 1_o 7_o  _fw-fr 1_o 11_o  _fw-fr 2_o 4_o 5_o  _fw-fr 1_o 11_o  _fw-fr 2_o 5_o  _fw-fr 2_o 11_o 6_o  _fw-fr 2_o 4_o  _fw-fr 2_o 11_o  _fw-fr 3_o 6_o 7_o  _fw-fr 2_o 9_o  _fw-fr 3_o 5_o  _fw-fr 4_o 1_o 8_o  _fw-fr 3_o 2_o  _fw-fr 3_o 11_o  _fw-fr 4_o 8_o 9_o  _fw-fr 3_o 6_o  _fw-fr 4_o 5_o  _fw-fr 5_o 3_o 10_o  _fw-fr 3_o 11_o  _fw-fr 4_o 11_o  _fw-fr 5_o 10_o 20_o  _fw-fr 7_o 10_o  _fw-fr 9_o 9_o  _fw-fr 11_o 8_o 30_o  _fw-fr 11_o 9_o  _fw-fr 14_o 8_o  _fw-fr 17_o 6_o 40_o  _fw-fr 15_o 8_o  _fw-fr 19_o 6_o 1_o 3_o 4_o 50_o  _fw-fr 19_o 7_o 1_o 4_o 5_o 1_o 9_o 2_o 60_o 1_o 3_o 6_o 1_o 9_o 3_o 1_o 14_o 11_o 70_o 1_o 7_o 5_o 1_o 14_o 0_o 2_o 0_o 9_o 80_o 1_o 11_o 4_o 1_o 19_o 0_o 2_o 6_o 7_o 90_o 1_o 15_o 4_o 2_o 3_o 11_o 2_o 12_o 5_o 100_o 1_o 19_o 3_o 2_o 8_o 9_o 2_o 18_o 3_o 200_o 3_o 18_o 4_o 4_o 17_o 7_o 5_o 16_o 6_o 300_o 5_o 17_o 8_o 7_o 6_o 4_o 8_o 14_o 9_o 400_o 7_o 16_o 11_o 9_o 15_o 1_o 11_o 13_o 0_o 500_o 9_o 16_o 1_o 12_o 3_o 11_o 14_o 11_o 3_o 600_o 11_o 15_o 3_o 14_o 12_o 8_o 17_o 9_o 6_o 700_o 13_o 14_o 6_o 17_o 1_o 6_o 20_o 7_o 9_o 800_o 15_o 13_o 9_o 19_o 10_o 3_o 23_o 6_o 0_o 900_o 17_o 12_o 11_o 21_o 19_o 0_o 26_o 4_o 3_o 1000_o 19_o 12_o 2_o 24_o 7_o 10_o 29_o 2_o 6_o a_o table_n of_o rebate_v at_o 6_o per_fw-la cent._n  _fw-fr 7_o month_n 8_o month_n 9_o month_n  _fw-fr l._n s._n d._n l._n s._n d._n l._n s._n d._n 1_o  _fw-fr  _fw-fr 8_o  _fw-fr  _fw-fr 9_o  _fw-fr  _fw-fr 10_o 2_o  _fw-fr 1_o 4_o  _fw-fr 1_o 6_o  _fw-fr 1_o 8_o 3_o  _fw-fr 2_o 0_o  _fw-fr 2_o 4_o  _fw-fr 2_o 7_o 4_o  _fw-fr 2_o 8_o  _fw-fr 3_o 1_o  _fw-fr 3_o 5_o 5_o  _fw-fr 3_o 4_o  _fw-fr 3_o 10_o  _fw-fr 4_o 4_o 6_o  _fw-fr 4_o 1_o  _fw-fr 4_o 7_o  _fw-fr 5_o 2_o 7_o  _fw-fr 4_o 9_o  _fw-fr 5_o 5_o  _fw-fr 6_o 0_o 8_o  _fw-fr 5_o 5_o  _fw-fr 6_o 1_o  _fw-fr 6_o 11_o 9_o  _fw-fr 6_o 1_o  _fw-fr 6_o 11_o  _fw-fr 7_o 9_o 10_o  _fw-fr 6_o 9_o  _fw-fr 7_o 8_o  _fw-fr 8_o 7_o 20_o  _fw-fr 13_o 6_o  _fw-fr 15_o 5_o  _fw-fr 17_o 3_o 30_o 1_o 0_o 3_o 1_o 3_o 1_o 1_o 5_o 10_o 40_o 1_o 7_o 1_o 1_o 10_o 9_o 1_o 14_o 5_o 50_o 1_o 13_o 10_o 1_o 18_o 6_o 2_o 3_o 1_o 60_o 2_o 0_o 7_o 2_o 6_o 2_o 2_o 11_o 8_o 70_o 2_o 7_o 4_o 2_o 13_o 10_o 3_o 0_o 3_o 80_o 2_o 14_o 1_o 3_o 1_o 6_o 3_o 8_o 11_o 90_o 3_o 0_o 10_o 3_o 9_o 3_o 3_o 17_o 6_o 100_o 3_o
of_o 2_o 8_o by_o the_o 6_o of_o the_o 11_o the_o compound_v fraction_n 7_o 9_o of_o â…—_n of_o â…š_n be_v reduce_v unto_o 105_o 270_o and_o 6_o 7_o of_o ¾_n of_o â…”_n unto_o 36_o 84_o multiply_v these_o two_o simple_a fraction_n numerator_n by_o numerator_fw-la and_o denominator_fw-la by_o denominator_fw-la and_o you_o will_v have_v the_o new_a fraction_n 3750_o 22680_o which_o by_o abbreviation_n be_v 125_o 756_o both_o which_o last_o fraction_n be_v either_o of_o they_o equal_a to_o the_o product_n of_o the_o two_o give_v compound_v fraction_n multiply_v one_o by_o another_o as_o be_v require_v if_o it_o be_v require_v to_o multiply_v a_o fraction_n by_o a_o whole_a number_n make_v that_o whole_a number_n a_o numerator_n and_o set_v 1_o under_o he_o for_o a_o denominator_fw-la so_o the_o fraction_n will_v be_v improper_a but_o multiply_v their_o numerator_n and_o denominator_n together_o as_o before_o example_n it_o be_v require_v to_o multiply_v 16_o by_o there_o efore_o i_o 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divisor_n pound_n i_o place_v they_o as_o you_o see_v the_o divisor_n to_o the_o left_a hand_n and_o the_o dividend_n to_o the_o right_n so_o i_o multiply_v the_o numerator_n of_o the_o dividend_n 4_o by_o the_o denominator_fw-la of_o the_o divisor_n 4_o the_o product_n be_v 16_o for_o a_o new_a numerator_n than_o i_o multiply_v the_o denominator_fw-la of_o the_o dividend_n 5_o by_o the_o numerator_n of_o the_o divisor_n 3_o and_o the_o product_n 15_o be_v the_o new_a denominator_fw-la so_o i_o find_v 16_o 13_o or_o 1_o 1_o 15_o be_v the_o quotient_a seek_v second_o if_o you_o divide_v a_o simple_a fraction_n by_o a_o compound_v or_o a_o compound_v by_o a_o simple_a or_o compound_v by_o compound_v reduce_v such_o compound_v fraction_n to_o simple_a fraction_n then_o proceed_v according_a to_o the_o last_o example_n example_n it_o be_v require_v to_o divide_v 7_o 9_o of_o 12_o 16_o by_o â…”_n of_o â…_n you_o must_v reduce_v 7_o 9_o of_o 12_o 6_o which_o make_v the_o simple_a or_o 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denominator_fw-la 207_o the_o quotient_n give_v 2_o and_o there_o will_v remain_v 189_o which_o be_v the_o numerator_n and_o the_o disor_n 207_o the_o denominator_fw-la so_o the_o mix_a number_n 2_o 189_o 207_o be_v the_o quotient_a require_v and_o in_o like_a manner_n must_v you_o work_v if_o you_o divide_v a_o fraction_n by_o a_o whole_a number_n or_o a_o whole_a number_n by_o a_o fraciion_n as_o you_o see_v in_o this_o last_o example_n chap._n xvi_o the_o rule_n of_o three_o direct_v in_o fraction_n in_o the_o direct_a rule_n of_o three_o in_o fraction_n there_o be_v four_o thing_n to_o be_v observe_v and_o practise_v 1._o that_o the_o fraction_n of_o the_o first_o and_o three_o place_n be_v of_o one_o denomination_n as_o money_n weight_n or_o measure_n 2._o that_o if_o any_o of_o the_o give_v fraction_n be_v compound_v they_o must_v be_v reduce_v to_o simple_a of_o the_o same_o value_n 3._o if_o any_o of_o the_o fraction_n give_v shall_v be_v mix_v number_n reduce_v it_o into_o a_o impro-fraction_n 4._o if_o any_o of_o the_o three_o term_n give_v shall_v be_v a_o whole_a number_n make_v it_o a_o improper_a fraction_n by_o put_v a_o unite_v for_o his_o denominator_fw-la the_o solution_n of_o the_o rule_n of_o three_o direct_v in_o fraction_n be_v perform_v the_o same_o way_n as_o in_o whole_a number_n that_o be_v to_o say_v multiply_v the_o second_o and_o three_o fraction_n together_o by_o the_o 14_o chapter_n and_o the_o product_n thereof_o by_o the_o first_o fraction_n according_a to_o the_o fifteen_o chapter_n and_o the_o quotient_n be_v the_o four_o fraction_n require_v another_o way_n multiply_v the_o numerator_n of_o the_o first_o fraction_n by_o the_o denominator_n of_o the_o second_o and_o three_o fraction_n the_o product_n thereof_o be_v a_o new_a denominator_fw-la then_o multiply_v the_o denominator_fw-la of_o the_o first_o fraction_n by_o the_o numerator_n of_o the_o second_o and_o three_o fraction_n and_o the_o product_n be_v the_o new_a numerator_n and_o this_o fraction_n be_v the_o four_o proportional_a fraction_n require_v and_o answer_v to_o the_o question_n which_o if_o it_o shall_v fall_v out_o to_o be_v a_o improper_a fraction_n must_v be_v reduce_v into_o a_o whole_a or_o mix_a number_n by_o the_o three_o of_o the_o eleven_o quest_n 1._o if_o â…œ_n of_o a_o pound_n weight_n cost_v 5_o 12_o l._n what_o will_v 9_o 21_o of_o a_o pound_n weight_n cost_n have_v dispose_v of_o the_o give_v fraction_n according_a to_o the_o four_o first_o rule_n of_o this_o chapter_n and_o the_o seven_o i_o proceed_v to_o the_o solution_n thus_o multiply_v the_o numerator_n of_o the_o first_o fraction_n which_o be_v 3_o by_o 12_o and_z 12_o the_o denominator_n of_o the_o second_o and_o three_o fraction_n the_o product_n will_v be_v 432_o for_o a_o new_a denominator_fw-la then_o multiply_v 8_o the_o denominator_fw-la of_o the_o first_o fraction_n by_o 5_o and_o 9_o the_o numerator_n of_o the_o second_o and_o three_o fraction_n the_o product_n thereof_o be_v 360_o which_o be_v a_o new_a numerator_n so_o i_o have_v find_v the_o four_o proportional_a fraction_n 360_o 432_o for_o answer_v to_o the_o question_v propound_v and_o by_o abbreviation_n be_v find_v equal_a to_o â…š_n or_o 16_o s._n 8_o d._n chap._n xvii_o the_o rule_n of_o three_o backward_a in_o fraction_n for_o dispose_v of_o the_o give_v fraction_n follow_v the_o four_o rule_n in_o the_o last_o chapter_n and_o the_o way_n of_o resolve_v be_v not_o different_a from_o the_o instruction_n of_o the_o eight_o chapter_n for_o it_o be_v there_o show_v how_o to_o find_v out_o a_o four_o proportional_a to_o three_o give_v number_n when_o you_o have_v a_o question_n to_o be_v resolve_v by_o this_o rule_n than_o the_o three_o term_n be_v the_o divisor_n then_o have_v exact_o reduce_v the_o term_n give_v according_a to_o the_o rule_n of_o the_o last_o chapter_n then_o multiply_v the_o numerator_n of_o the_o three_o fraction_n by_o the_o denominator_n of_o the_o second_o and_o first_o fraction_n and_o the_o product_n give_v a_o new_a denominator_fw-la then_o multiply_v the_o denominator_fw-la of_o the_o three_o fraction_n by_o the_o numerator_n of_o the_o second_o and_o first_o fraction_n and_o the_o product_n give_v a_o new_a numerator_n and_o this_o new_a fraction_n be_v the_o four_o proportional_a fraction_n and_o answer_n to_o the_o question_v propound_v quest_n if_o â…ž_n of_o a_o yard_n of_o cloth_n that_o be_v 1_o yard_n ¾_n will_v make_v a_o garment_n how_o much_o of_o another_o piece_n of_o cloth_n that_o be_v 1_o yard_n â…–_n wide_o will_v make_v the_o same_o garment_n here_o you_o see_v in_o this_o question_n the_o second_o and_o three_o fraction_n be_v mix_v fraction_n there_o you_o see_v they_o be_v reduce_v to_o improper_a fraction_n so_o the_o three_o give_v fraction_n be_v â…ž_n 7_o 4_o and_o 7_o 5._o now_o
according_a to_o the_o former_a instruction_n of_o this_o chapter_n i_o multiply_v the_o numerator_n of_o the_o three_o fraction_n be_v 3_o by_o the_o denominator_n of_o the_o second_o and_o first_o fraction_n which_o be_v 4_o and_o 8_o the_o product_n thereof_o be_v 224_o which_o be_v a_o new_a denominator_fw-la then_o i_o multiply_v the_o devominator_fw-la of_o the_o three_o fraction_n 5_o by_o the_o numerator_n of_o the_o second_o and_o first_o fraction_n which_o be_v 7_o and_o 7_o the_o product_n thereof_o will_v be_v 245_o which_o be_v a_o new_a numerator_n so_o i_o have_v find_v out_o the_o improper_a fraction_n 245_o 224_o which_o reduce_v be_v 1_o 21_o 224_o equal_a to_o 1_o 3_o 32_o which_o be_v the_o answer_n to_o the_o propound_a question_n chap._n xviii_o the_o rule_n of_o practice_n the_o rule_n of_o practice_n be_v so_o call_v because_o it_o be_v the_o practice_n of_o the_o other_o rule_n and_o chief_o of_o the_o rule_n of_o three_o in_o a_o far_o more_o compendious_a and_o short_a way_n be_v by_o some_o call_v the_o brief_a rule_n because_o thereby_o many_o question_n may_v be_v operate_v with_o more_o expedition_n than_o by_o the_o rule_n of_o three_o and_o because_o this_o rule_n be_v so_o expeditious_a in_o find_v a_o resolution_n to_o any_o question_n propound_v it_o be_v therefore_o of_o infinite_a great_a use_n among_o merchant_n tradesman_n and_o other_o it_o be_v very_o convenient_a 108_o 1_o time_n 12_o be_v 12_o 2_o 24_o 3_o 36_o 4_o 48_o 5_o 60_o 6_o 72_o 7_o 84_o 8_o 96_o 9_o 108_o for_o the_o learner_n to_o get_v perfect_o by_o heart_n the_o annex_v table_n contain_v the_o product_n of_o 12_o multiply_v by_o all_o the_o nine_o digit_n for_o the_o speedy_a reduce_v penny_n into_o shilling_n and_o shilling_n into_o penny_n and_o for_o reduce_v shilling_n into_o pound_n i_o refer_v the_o ingenious_a reader_n to_o the_o six_o chapter_n in_o reduction_n of_o mony_n  _fw-fr s._n f._n  _fw-fr  _fw-fr the_o even_a part_n of_o a_o shilling_n 6_o  _fw-fr be_v the_o ½_n 4_o  _fw-fr â…“_n 3_o  _fw-fr ¼_n 2_o  _fw-fr â…™_n 1_o ½_n â…›_n 1_o  _fw-fr 1_o 12_o  _fw-fr ¾_n 1_o 16_o  _fw-fr ½_n 1_o 24_o  _fw-fr ¼_n 1_o 48_o  _fw-fr s._n d._n  _fw-fr  _fw-fr the_o even_a part_n of_o a_o pound_n 10_o  _fw-fr be_v the_o ½_n 6_o 8_o â…“_n 5_o 0_o ¼_n 4_o 0_o â…™_n 3_o 4_o â…›_n 2_o 6_o â…›_n 2_o 0_o 1_o 10_o 1_o 8_o 1_o 12_o 1_o 0_o 1_o 20_o i_o will_v likewise_o advise_v the_o learner_n to_o get_v the_o two_o forego_v table_n by_o heart_n the_o first_o contain_v the_o even_a part_n of_o a_o shilling_n the_o second_o the_o even_a part_n of_o a_o pound_n when_o a_o question_n be_v propound_v to_o be_v resolve_v you_o must_v consider_v whether_o the_o price_n of_o the_o integer_fw-la be_v part_n of_o a_o shilling_n or_o part_n of_o a_o pound_n and_o whether_o the_o say_a price_n be_v either_o the_o even_a part_n of_o a_o shilling_n or_o the_o even_a part_n of_o a_o pound_n if_o it_o be_v neither_o the_o even_a part_n of_o a_o shilling_n nor_o the_o even_a part_n of_o a_o pound_n you_o may_v divide_v the_o say_a price_n into_o so_o many_o part_n that_o each_o part_n may_v be_v the_o even_a part_n either_o of_o a_o shilling_n or_o pound_n as_o 5_o d._n ¾_n may_v be_v divide_v into_o three_o even_a part_n of_o a_o shilling_n viz._n 3_o d._n which_o be_v ¼_n of_o a_o shilling_n 2_o d._n which_o be_v â…™_n and_o ¾_n which_o be_v 1_o 16._o proposition_n 1._o if_o the_o price_n of_o a_o unite_v of_o the_o sum_n propound_v be_v a_o farthing_n i_o find_v by_o the_o table_n a_o farthing_n to_o be_v the_o 1_o 48_o of_o a_o shilling_n but_o because_o the_o 48._o part_n of_o any_o sum_n be_v not_o so_o soon_o take_v as_o the_o ½_n the_o â…“_n the_o ¼_n the_o â…™_n the_o â…›_n and_o the_o like_a therefore_o because_o 8_o farthing_n make_v 2_o d._n i_o divide_v the_o give_v number_n by_o 8_o that_o be_v to_o say_v i_o take_v the_o eight_o part_n and_o if_o any_o thing_n remain_v they_o be_v all_o farthing_n then_o by_o the_o table_n i_o find_v that_o 2_o d._n be_v â…™_n of_o a_o shilling_n therefore_o take_v the_o six_o part_n of_o they_o for_o shilling_n and_o what_o remain_v be_v so_o many_o two_o pence_n now_o these_o shilling_n reduce_v into_o pound_n by_o cut_v off_o the_o first_o figure_n to_o the_o right_a hand_n with_o a_o small_a stroke_n with_o your_o pen_n then_o draw_v a_o line_n underneath_o and_o take_v half_a of_o the_o remain_a figure_n which_o i_o set_v under_o the_o line_n for_o so_o many_o pound_n but_o if_o the_o last_o figure_n you_o be_v to_o halue_fw-mi be_v a_o odd_a figure_n take_v the_o half_a and_o add_v 10_o to_o the_o figure_n cut_v off_o for_o that_o figure_n and_o the_o 10_o add_v together_o make_v so_o many_o shilling_n example_n let_v it_o be_v require_v to_o know_v how_o much_o 9783_o l._n at_o a_o farthing_n per_fw-la pound_n come_v to_o first_o as_o you_o see_v in_o the_o follow_a example_n take_v the_o eight_o part_n of_o 9783_o and_o it_o be_v 1222_o two_o pence_n and_o 7_o farthing_n remain_v which_o be_v 1_o ¾_n i_o set_v a_o little_a distance_n to_o the_o right_a hand_n next_o by_o the_o table_n of_o the_o even_a part_n of_o a_o shilling_n i_o find_v 2_o d._n to_o be_v the_o 1_o 0_o part_n therefore_o i_o draw_v a_o line_n under_o 1222_o and_o take_v the_o â…™_n part_v thereof_o which_o be_v 203_o shilling_n and_o 4_o remain_v which_o be_v so_o many_o two_o pence_n therefore_o i_o set_v down_o 8_o under_o the_o last_o remainder_n i_o draw_v a_o line_n under_o these_o shilling_n 203_o and_o reduce_v they_o into_o pound_n according_a to_o the_o instruction_n hereof_o and_o of_o the_o six_o chapter_n of_o reduction_n of_o money_n by_o cut_v off_o the_o first_o figure_n towards_o your_o right_a hand_n which_o be_v 3_o and_o draw_v a_o line_n i_o take_v the_o half_a of_o the_o remainder_n 20_o which_o be_v 10_o pound_n and_o the_o figure_n 3_o cut_v off_o signify_v so_o many_o shilling_n now_o i_o add_v all_o these_o odd_a remain_v together_o viz._n 1_o ¾_n 8_o d._n unto_o 10_o l._n 3_o s._n so_o the_o whole_a sum_n be_v 10_o 3_o 9_o ¾_n the_o resolution_n of_o the_o propound_a question_n as_o by_o the_o follow_a operation_n for_o the_o more_o clear_a demonstration_n of_o what_o have_v be_v so_o far_o say_v of_o this_o rule_n i_o shall_v set_v down_o more_o example_n in_o the_o first_o example_n it_o be_v propound_v 65937_o l._n at_o a_o farthing_n per_fw-la pound_n the_o â…›_n thereof_o be_v 8242_o two_o pence_n and_o ¼_n farthing_n remain_v the_o â…™_n of_o 8242_o two_o pence_n be_v 1373_o shilling_n and_o 4_o two_o pence_n remain_v be_v 8_o d._n next_o the_o 1_o 20_o of_o 1373_o shilling_n be_v 68_o pound_n and_o 13_o shilling_n remain_v so_o take_v all_o the_o remain_v to_o this_o last_o sum_n it_o make_v 68_o 13_o 8_o ¼_n and_o so_o much_o do_v 65937_o l._n come_v to_o at_o a_o farthing_n per_fw-la pound_n and_o in_o the_o same_o manner_n be_v the_o other_o example_n explain_v the_o reason_n why_o i_o take_v the_o â…›_n and_o â…™_n in_o these_o example_n of_o a_o farthing_n and_o not_o 1_o 48_o be_v because_o the_o â…™_n of_o â…›_n be_v equal_a to_o 1_o 48._o proposition_n 2._o if_o the_o value_n of_o a_o unite_v in_o the_o sum_n of_o the_o propound_a question_n be_v 2_o farthing_n than_o first_o take_v the_o ¼_n and_o afterward_o the_o â…™_n for_o although_o 2_o farthing_n be_v the_o 1_o 24_o of_o a_o shilling_n yet_o ¼_n of_o 1_o â—_o be_v equal_a thereunto_o and_o do_v with_o more_o ease_n and_o less_o charge_n to_o the_o memory_n than_o to_o take_v the_o 1_o 24_o of_o any_o sum_n have_v thus_o take_v the_o ¼_n to_o reduce_v they_o into_o two_o pence_n if_o any_o thing_n remain_v they_o be_v so_o many_o half_a penny_n than_o â…™_n reduce_v they_o into_o shilling_n as_o before_o example_n in_o the_o first_o of_o these_o example_n it_o be_v require_v to_o know_v how_o much_o 57632_o l._n at_o 2_o quarter_n per_fw-la pound_n come_v unto_o knowing_z 4_o half_a penny_n do_v make_v 2_o d._n i_o therefore_o do_v take_v ¼_n of_o 57632_o which_o be_v 14408_o two_o pence_n then_o i_o take_v â…™_n of_o 14408_o which_o be_v 2401_o shilling_n and_o there_o remain_v 2_o two_o pence_n which_o be_v 4_o d._n then_o the_o 1_o 20_o of_o 2401_o shilling_n be_v 120_o pound_n and_o there_o do_v remain_v 1_o shilling_n so_o the_o sum_n make_v 120_o l._n 1_o s._n 4_o d._n in_o the_o second_o example_n the_o ¼_n of_o 76597_o be_v 19149_o two_o pence_n and_o there_o remain_v 1_o half_a penny_n the_o â…™_n of_o 19149_o be_v 3191_o shilling_n and_o there_o
a_o his_o money_n be_v in_o 12_o month_n and_o b_o his_o money_n be_v in_o 8_o month_n when_o they_o divide_v the_o money_n a_o receive_v 671_o l._n 8_o s._n 6_o d._n ¾_n and_o 3_o 7_o and_z b_o receive_v 318_o l._n 11_o s._n 5_o d._n of_o 4_o â—_o i_o require_v to_o know_v how_o much_o each_o man_n stock_n be_v at_o first_o then_o by_o the_o rule_n of_o three_o if_o 12_o month_n give_v 750_o 8_o month_n will_v give_v 500_o there_o the_o stock_n of_o a_o first_o put_v in_o be_v 500_o which_o subtract_v from_o 750_o there_o remain_v the_o stock_n of_o b_o as_o be_v require_v example_n 4._o three_o grazier_n hire_v a_o piece_n of_o ground_n for_o 37_o 10._o a_o put_v into_o the_o say_a ground_n 60_o head_n of_o ox_n 15_o day_n b_o put_v into_o the_o say_a piece_n of_o ground_n 48_o head_n of_o ox_n 21_o day_n and_o c_o put_v in_o 75_o head_n of_o ox_n 12_o day_n i_o desire_v to_o know_v how_o much_o each_o grazier_n must_v pay_v oxen._a day_n a_o 60_o 15_o 900_o b_o 48_o 21_o 1008_o c_o 75_o 12_o 900_o  _fw-fr  _fw-fr  _fw-fr 2808_o if_o give_v what_o will_v  _fw-fr  _fw-fr l._n s._n  _fw-fr l._n s._n d._n  _fw-fr  _fw-fr 2808_o 37_o 10_o 900_o 12_o 0_o 4_o ½_n 1296_o 2808_o 2808_o 37_o 10_o 1008_o 13_o 9_o 2_o ¾_n â—216_n 2808_o 2808_o 37_o 10_o 900_o 12_o 0_o 4_o ½_n 1â—96_n 2808_o  _fw-fr l._n s._n d._n  _fw-fr  _fw-fr at_fw-fr be_v to_o pay_v 12_o 0_o 4_o ½_n 1296_o 2808_o b_o be_v to_o pay_v 13_o 9_o 2_o ¾_n â—â—16_n 28088_o c_o be_v to_o pay_v 12_o 0_o 4_o ½_n 1296_o 2808_o  _fw-fr 37_o 10_o 0_o 0_o  _fw-fr which_o three_o several_a sum_n be_v add_v together_o make_v 37_o l._n 10_o s._n which_o be_v the_o sum_n the_o three_o grazier_n be_v to_o pay_v among_o themselves_o example_n 5._o three_o merchant_n enter_v in_o a_o trade_n of_o company_n as_o a_o b_o c_o and_o put_v in_o several_a sum_n of_o money_n for_o a_o stock_n a_o put_v in_o the_o first_o of_o january_n 250_o l._n and_o the_o first_o of_o july_n follow_v he_o take_v out_o again_o 40_o l._n b._n lay_v in_o the_o first_o of_o april_n 425_o l._n and_o the_o first_o of_o september_n follow_v he_o put_v in_o 75_o l._n c_o lay_v in_o the_o first_o of_o june_n 360_o l._n and_o the_o first_o of_o september_n follow_v he_o take_v out_o again_o 60_o l._n at_o the_o year_n end_v they_o find_v they_o have_v gain_v 275_o l._n i_o require_v to_o know_v how_o much_o each_o partner_n shall_v have_v of_o the_o say_v 275_o l._n gain_v answer_n first_o multiply_v the_o money_n that_o a_o lay_v in_o which_o be_v 250_o l._n by_o 12_o month_n the_o time_n it_o continue_v in_o stock_n the_o product_n thereof_o be_v 3000_o l._n from_o thence_o subtract_v 6_o time_n 40_o l._n which_o be_v 240_o for_o the_o money_n which_o he_o take_v out_o again_o and_o there_o do_v remain_v 2760_o which_o be_v the_o just_a lay_n in_o of_o a._n then_o multiply_v 425_o l._n the_o money_n b_o pay_v by_o 9_o month_n his_o time_n of_o continuance_n the_o product_n thereof_o be_v 3825_o whereto_o add_v 4_o time_n 75_o l._n which_o be_v 300_o for_o the_o money_n he_o lay_v in_o more_o the_o first_o of_o september_n the_o sum_n whereof_o be_v 4125_o the_o second_o man_n b_o his_o laying_n in_o then_o for_o the_o money_n that_o c_z pay_v which_o be_v 360_o l._n multiply_v by_o 7_o month_n his_o time_n the_o product_n thereof_o be_v 2520_o from_o whence_o subtract_v 4_o time_n 60_o l._n for_o the_o money_n c_o take_v out_o the_o first_o of_o september_n which_o be_v 240_o and_o there_o do_v remain_v 2280_o the_o three_o man_n c_o laying_n in_o a_o his_o new_a laying_n in_o 2760_o b_o 4125_o c_o 2280_o  _fw-fr 9165_o then_o according_a to_o the_o instruction_n of_o the_o first_o example_n of_o this_o chapter_n add_v all_o the_o new_a laying_n in_o together_o the_o sum_n whereof_o be_v 9165_o then_o by_o the_o rule_n of_o three_o the_o several_a operation_n be_v as_o follow_v as_o be_v to_o so_o be_v to_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr l._n l._n l._n l._n s._n d._n f._n  _fw-fr 9165_o 275_o 2760_o 82_o 16_o 3_o 2_o 4170_o 9165_o 9165_o 275_o 4125_o 123_o 15_o 5_o 1_o 5535_o 9165_o 9165_o 275_o 2280_o 68_o 08_o 2_o 3_o 8625_o 9165_o a_o be_v to_o have_v 82_o 16_o 3_o 2_o 4170_o 9165_o b_o 123_o 15_o 5_o 1_o 5535_o 9165_o c_o 68_o 08_o 2_o 3_o 8625_o 9165_o  _fw-fr 275_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr which_o share_v aforesaid_a be_v add_v all_o together_o make_v up_o the_o sum_n of_o the_o whole_a gain_n 275._o the_o proof_n of_o this_o rule_n be_v not_o different_a from_o that_o of_o fellowship_n without_o time_n lay_v down_o in_o the_o last_o chapter_n chap._n xxi_o of_o interest_n simple_a and_o compound_v purchase_n and_o valuation_n of_o annuity_n interest_n be_v of_o two_o kind_n simple_a and_o compound_v simple_a interest_n be_v when_o it_o be_v require_v so_o much_o per_fw-la cent._n for_o so_o many_o year_n compound_v interest_n be_v as_o much_o as_o to_o say_v interest_n upon_o interest_n that_o be_v you_o add_v the_o interest_n every_o year_n to_o the_o principal_a and_o the_o next_o year_n you_o account_n interest_n for_o their_o sum_n be_v add_v both_o together_o of_o simple_a interest_n let_v it_o be_v require_v to_o know_v if_o the_o interest_n of_o 100_o l._n for_o 12_o month_n be_v 6_o l._n what_o shall_v the_o interest_n of_o 375_o l._n be_v for_o the_o same_o time_n example_n 1._o for_o the_o effect_n this_o operation_n by_o the_o rule_n of_o practice_n work_v thus_o it_o be_v here_o require_v to_o know_v the_o interest_n of_o 375_o l._n at_o 6_o per_fw-la cent._n i_o therefore_o multiply_v 6l_o by_o 3_o the_o product_n thereof_o be_v 18l_o which_o 108_o be_v the_o interest_n of_o 300_o l._n but_o there_o be_v 75l_o more_o to_o know_v the_o interest_n of_o whichis_fw-la three_o quarter_n of_o a_o hundred_o that_o be_v of_o 100_o the_o half_a whereof_o be_v 50_o l._n the_o quarter_n 25_o l._n which_o make_v up_o 75_o l._n therefore_o under_o 18_o l._n i_o set_v down_o 3_o l._n the_o half_a of_o 6_o l._n and_o 1_o l._n 10_o s._n the_o quarter_n of_o 6_o l._n and_o add_v all_o these_o together_o their_o sum_n be_v 22_o l._n 10_o s._n the_o interest_n of_o 375_o l._n for_o 12_o month_n as_o be_v require_v example_n 2._o i_o desire_v to_o know_v if_o the_o interest_n of_o 100_o l._n for_o 12_o month_n be_v 6_o l._n what_o shall_v the_o interest_n of_o 450_o l._n be_v for_o 9_o month_n this_o question_n may_v be_v answer_v by_o two_o operation_n of_o the_o rule_n as_o follow_v if_o require_v what_o shall_v answer_v 100_o l._n 6_o l._n 450_o l._n 27_o l._n 12_o mon._n 27_o l._n 9_o mon._n 20_o 05_o but_o by_o the_o first_o example_n of_o the_o double_a rule_n of_o three_o you_o do_v this_o and_o such_o like_a question_n at_o one_o operation_n thus_o say_v if_o 100_o l._n for_o 12_o month_n gain_n 6_o l._n what_o shall_v 450_o l._n gain_n for_o 9_o month_n set_a down_o the_o several_a number_n give_v in_o order_n as_o follow_v with_o their_o denomination_n over_o head_n the_o operation_n be_v thus_o you_o have_v here_o five_o number_n give_v to_o find_v out_o a_o six_o proportional_a wherein_o 100_o l._n be_v the_o first_o term_n 12_o the_o second_o 6_o the_o three_o 450_o and_o 9_o the_o five_o term._n therefore_o multiply_v the_o two_o first_o term_n viz._n 100_o and_o 12_o together_o the_o product_n thereof_o be_v 1200_o then_o multiply_v the_o three_o last_o term_n viz._n 60_o 450_o and_o 9_o into_o one_o another_o and_o the_o product_n thereof_o will_v be_v 24300_o which_o be_v the_o dividend_n to_o be_v divide_v by_o the_o divisor_n 1200_o now_o because_o the_o divisor_n and_o dividend_n have_v each_o two_o cipher_n therefore_o i_o cut_v off_o the_o say_a cipher_n and_o there_o remain_v 12_o for_o the_o divisor_n and_o 243_o for_o the_o dividend_n which_o be_v divide_v the_o quotient_n be_v 20_o which_o be_v so_o many_o pound_n but_o there_o remain_v 3_o which_o be_v the_o quarter_n of_o 12_o i_o set_v down_o in_o the_o quotient_a 5_o s._n so_o i_o find_v the_o interest_n of_o 450_o l._n for_o 9_o month_n be_v 20_o l._n 5_o s._n at_o the_o rate_n of_o 6_o l._n per_fw-la 100_o l._n as_o before_o but_o to_o avoid_v fraction_n in_o this_o manner_n of_o work_v and_o to_o find_v out_o the_o true_a and_o exact_a interest_n of_o any_o sum_n of_o money_n propound_v not_o only_o in_o month_n but_o in_o day_n observe_v the_o follow_a direction_n reduce_v your_o interest_n whether_o it_o be_v 6_o l._n 7_o l._n or_o 8_o l._n into_o penny_n as_o you_o see_v
cost_n 13_o l._n what_o shall_v 2704_o l._n cost_n by_o the_o operation_n i_o find_v 2704_o pound_n weight_n to_o be_v worth_a 78_o pound_n sterl_n quest_n 2._o if_o 100_o l._n be_v worth_n 13_o s._n 4_o d._n what_o will_v 2496_o l._n be_v worth_n allow_v 4_o l._n for_o every_o 100_o for_o tret_n divide_v the_o give_v number_n 2496_o by_o 26_o because_o the_o 4_o l._n tret_n be_v the_o 26._o part_n of_o 104_o and_o the_o quotient_n will_v be_v 96_o which_o be_v to_o be_v abate_v for_o the_o tret_n out_o of_o 2496_o and_o there_o will_v remain_v 2400_o l._n net_n at_o 13_o s._n 4_o d._n per_fw-la hundred_o then_o by_o the_o rule_n of_o three_o say_v if_o 100_o cost_n 13_o 4_o what_o will_v 2400_o l._n cost_n the_o answer_n will_v be_v 1600_o l._n the_o answer_n to_o the_o question_n as_o be_v require_v chap._n xxv_o the_o rule_n of_o barter_n barter_n teach_v how_o to_o sell_v ware_n for_o ware_n or_o change_v one_o merchandise_n for_o another_o as_o for_o example_n there_o be_v two_o merchant_n viz._n a_o and_o b_o a_o have_v 24_o c._n weight_n of_o tobacco_n at_o 4_o d._n ½_n per_fw-la pound_n and_o b_o have_v sugar_n at_o 7_o d._n per_fw-la pound_n i_o demand_v how_o much_o sugar_n must_v b_o deliver_v to_o a_o for_o the_o tobacco_n by_o the_o rule_n of_o three_o say_v if_o 1_o l._n of_o tobacco_n cost_v 4_o d._n ½_n what_o will_v 24_o c._n by_o the_o forego_n operation_n you_o find_v that_o 24_o c._n will_v cost_v 50_o l._n 8_o s._n then_o say_v again_o if_o 7d_o buy_v 1_o pound_n of_o sugar_n how_o many_o pound_n will_v 50l_n 8_n by_o multiply_v and_o divide_v you_o will_v find_v that_o 50_o l._n 8_o s._n will_v buy_v 1728_o pound_n of_o sugar_n at_o 7d_o per_fw-la pound_n therefore_o b_o must_v deliver_v 1728_o pound_n of_o sugar_n to_o a_o at_o 7_o d._n per_fw-la pound_n for_o 24_o c._n of_o tobacco_n at_o 4_o d._n ½_n as_o be_v require_v two_o merchant_n barter_n one_o with_o the_o other_o a_o have_v 128_o yard_n of_o broad_a cloth_n at_o 9_o s._n 6_o d._n and_o b_o have_v holland_n cloth_n at_o 3_o s._n 4_o d._n per_fw-la ell._n i_o demand_v how_o much_o holland_n cloth_n b_o must_v deliver_v to_o a_o for_o his_o 128_o yard_n of_o broad_a cloth_n by_o the_o rule_n of_o three_o say_v if_o 1_o yard_n of_o broad_a cloth_n cost_v 9_o 6_o what_o cost_v 128_o yard_n if_o 3_o s._n 4_o d._n buy_v one_o ell_n of_o holland_n cloth_n what_o will_v 60_o l._n 16_o s._n two_o merchant_n barter_n a_o have_v 432_o yard_n of_o canvas_n at_o 14d_o per_fw-la yard_n b_o giveth_z a_o in_o barter_n for_o those_o 432_o yard_n of_o canvas_n at_o 14_o d._n 24_o piece_n of_o cloth_n i_o desire_v to_o know_v how_o much_o a_o give_v for_o one_o piece_n of_o cloth_n by_o the_o rule_n of_o three_o if_o 1_o yard_n cost_v 14_o d._n what_o will_v 432_o yard_n if_o 24_o piece_n cost_v 25_o l._n 4_o s._n what_o cost_v 1_o here_o i_o find_v by_o the_o operation_n a_o give_v 21_o s._n a_o piece_n for_o the_o 24_o piece_n of_o cloth_n as_o be_v require_v two_o merchant_n viz._n a_o and_o b_o do_v barter_v one_o with_o another_o a_o have_v nutmeg_n at_o 5_o s._n per_fw-la pound_n to_o sell_v for_o ready_a money_n but_o in_o barter_n he_o will_v sell_v for_o 6_o s._n per_fw-la pound_n and_o b_o have_v cinnamon_n at_o 4_o s._n 6_o d._n per_fw-la pound_n to_o sell_v for_o ready_a money_n i_o desire_v to_o know_v how_o much_o b_o must_v sell_v his_o cinnamon_n a_o pound_n for_o in_o barter_n that_o he_o may_v not_o be_v a_o loser_n by_o the_o rule_n of_o three_o if_o 5_o s._n give_v 6_o s._n what_o will_v 4_o s._n 6_o do_v answer_v 5_o s._n 4_o d._n ⅔_n two_o merchant_n viz._n a_o and_o b_o do_v barter_v one_o with_o another_o a_o have_v curran_n at_o 35_o s._n per_fw-la hundred_o ready_a money_n which_o he_o barter_n to_o b_o at_o 42_o s._n per_fw-la hundred_o b_o have_v raisin_n of_o the_o sun_n which_o cost_v he_o 28_o shilling_n per_n hundred_o but_o he_o barter_n they_o at_o 33_o shilling_n 3_o penny_n per_fw-la hundred_o i_o desire_v to_o know_v how_o much_o in_o 100_o l._n each_o man_n gain_v by_o the_o rule_n of_o three_o if_o 35_o s._n gain_n 7_o s._n what_o will_v 100_o l._n gain_n answer_v 20_o l._n if_o 28_o s._n gain_n 33_o s._n 3_o d._n what_o will_v 100_o l._n gain_n answer_v 18_o l._n 15_o s._n by_o multiply_v and_o divide_v you_o will_v find_v a_o gain_v 20_o l._n per_fw-la cent._n b_o gain_v 18_o l._n 15_o s._n per_fw-la cent._n chap._n xxvi_o of_o loss_n and_o gain_n this_o rule_n show_v how_o to_o find_v out_o the_o loss_n or_o gain_n upon_o any_o parcel_n of_o good_n sell_v and_o it_o likewise_o show_v how_o to_o find_v what_o price_n you_o must_v sell_v your_o good_n for_o to_o gain_v so_o much_o per_fw-la cent._n quest_n 1._o suppose_v i_o buy_v broad_a cloth_n at_o 7_o s._n 6_o d._n per_fw-la yard_n and_o i_o sell_v the_o same_o cloth_n at_o 8_o s._n 9_o d._n per_fw-la yard_n i_o desire_v to_o know_v how_o much_o be_v gain_v in_o 100_o l._n first_o see_v whether_o there_o be_v gain_n or_o loss_n in_o one_o yard_n and_o how_o much_o it_o be_v  _fw-fr s._n d._n sell_v for_o per_fw-la yard_n 8_o 9_o given_n per_fw-la yard_n 7_o 6_o gain_v per_n yard_n 1_o 3_o by_o the_o rule_n of_o three_o say_v if_o 7_o s._n 6_o d._n gain_n 1_o s._n 3_o d._n what_o will_v 100_o l._n gain_n answer_v 16l_o 13_n 4d_o multiply_v and_o divide_v and_o you_o will_v find_v 16_o l._n 13_o s._n 4_o d._n be_v gain_v per_fw-la 100l_n the_o answer_n to_o the_o question_n as_o be_v require_v quest_n 2._o if_o one_o yard_n of_o broad_a cloth_n be_v worth_a 9_n 6d_o for_o how_o much_o must_v 36_o yard_n be_v sell_v for_o to_o gain_v 20_o per_fw-la cent._n by_o the_o rule_n of_o three_o say_v if_o 100_o l._n give_v 120_o l._n what_o will_v 9_o s._n 6_o d._n give_v answer_v 11_o s._n 4d_o 8_o 10._o multiply_v and_o divide_v and_o you_o will_v find_v 11_n 4d_o 8_o 10._o then_o by_o the_o same_o rule_n again_o say_v if_o 1_o yard_n give_v 11_o 4_o 8_o 10_o what_o will_v 36_o yard_n 20_o 10_o 4_o 8_o 8._o multiply_v and_o divide_v and_o you_o will_v find_v that_o you_o must_v sell_v 36_o yard_n of_o that_o broad_a cloth_n for_o 20_o 10_o 4_o 8_o 10_o to_o gain_n 20l._n per_fw-la cent._n quest_n 3._o if_o a_o piece_n of_o broad_a cloth_n contain_v 34_o yard_n cost_v 18_o l._n 14_o s._n and_o i_o sell_v it_o for_o 10_o s._n 8_o d._n per_fw-la yard_n i_o demand_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 give_v 10_o s._n 8_o d._n what_o will_v 34_o yard_n answ_n 18_o l._n 2_o s._n 8_o d._n which_o be_v less_o than_o the_o price_n it_o cost_v by_o 11_o s._n 4_o d._n therefore_o you_o have_v lose_v now_o to_o find_v how_o much_o you_o you_o have_v lose_v per_fw-la cent._n say_v if_o 18_o l._n 14_o s._n lose_v 11_o s._n 4_o d._n what_o will_v 100_o l._n lose_v 3_o l._n 0_o s._n 7_o d._n ¼_n by_o multiply_v and_o divide_v you_o will_v find_v you_o lose_v 3_o l._n 0s_o 7d_o ¼_n in_o the_o 100_o l._n the_o answer_n to_o the_o question_n as_o be_v require_v quest_n 4._o if_o one_o yard_n of_o broad_a cloth_n cost_v i_o 13_o s._n 4_o d._n and_o i_o sell_v 24_o yard_n of_o the_o same_o cloth_n for_o 14l_o 17_o s._n 6d_o i_o desire_v to_o know_v whether_o i_o gain_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 1_o yard_n cost_v 13_o s._n 4_o d._n what_o will_v 24_o yard_n answer_v 16_o l._n 0_o s._n 0_o d._n by_o multiply_v and_o divide_v i_o find_v 24_o yard_n at_o 13_o s._n 4d_o will_v cost_v 16_o l._n and_o i_o sell_v the_o 24_o yard_n for_o 14_o l._n 17_o s._n 6d_o so_o by_o subtraction_n i_o find_v i_o have_v lose_v upon_o the_o 24_o yard_n 1_o l._n 2_o s._n 6_o d._n now_o to_o know_v how_o much_o per_fw-la cent._n say_v if_o 16_o l._n lose_v 1_o l._n 2._o s._n 6_o d._n what_o will_v 100l_n answer_v 7_o l._n 0_o s._n 7_o d._n ½_n by_o multiply_v and_o divide_v you_o will_v find_v you_o have_v lose_v 7l_o 0_n 7d_o ½_n per_fw-la cent._n the_o answer_n to_o the_o question_n as_o be_v require_v quest_n 5._o if_o i_o give_v for_o 32_o yard_n of_o cloth_n after_o the_o rate_n of_o 7_o s._n 6_o d._n and_o for_o 18_o yard_n 12_o s._n 6_o d._n and_o i_o sell_v one_o yard_n with_o another_o for_o 10_o s._n per_fw-la yard_n i_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