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5_o makes_z 6_o and_z 3_o makes_z 9_o and_z 6_o makes_z 15_o and_z 8_o make_v 23_o in_o which_o 23_o ten_o be_v contain_v two_o time_n and_o 3_o remain_v the_o three_o i_o place_n under_o the_o line_n and_o carry_v the_o two_o ten_o to_o the_o next_o row_n say_v 2_o which_o i_o carry_v and_o 8_o makes_z 10_o and_z 5_o makes_z 15_o and_z 7_o make_v 22_o in_o which_o ten_o be_v contain_v two_o time_n and_o 2_o remain_v which_o 2_o i_o set_v under_o the_o line_n and_o because_o there_o be_v never_o another_o row_n to_o be_v add_v to_o which_o i_o shall_v carry_v the_o two_o ten_o i_o therefore_o set_v it_o down_o also_o under_o the_o line_n towards_o the_o left_a hand_n as_o you_o see_v do_v in_o the_o margin_n so_o the_o total_a or_o gross_a sum_n of_o these_o number_n be_v add_v together_o be_v 22364._o example_n 2._o apple_n tree_n 137_o pear_n tree_n 76_o cherry_n tree_n 107_o plum_n tree_n 36_o tree_n in_o all_o 355_o a_o man_n have_v in_o his_o orchard_n 136_o apple_n tree_n 76_o 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in_o england_n be_v pound_n shilling_n penny_n and_o farthing_n of_o which_o coin_n 4_o farthing_n make_v 1_o penny_n thus_o character_v d._n 12_o penny_n make_v 1_o shilling_n thus_o character_v s._n 20_o shilling_n make_v 1_o pound_n thus_o character_v li._n for_o a_o farthing_n we_o use_v q._n the_o rule_n in_o the_o addition_n of_o number_n of_o divers_a denomination_n this_o order_n be_v to_o be_v observe_v viz._n place_v all_o number_n of_o the_o same_o denomination_n one_o direct_o under_o another_o as_o pound_n under_o pound_n shilling_n under_o shilling_n penny_n under_o penny_n and_o farthing_n under_o farthing_n then_o draw_v a_o line_n under_o they_o and_o begin_v your_o addition_n with_o the_o least_o denomination_n first_o observing_z how_o many_o time_n the_o next_o great_a denomination_n be_v contain_v in_o the_o least_o and_o for_o every_o time_n carry_v one_o unite_v to_o the_o next_o denomination_n as_o before_o you_o do_v the_o ten_o set_v down_o the_o remainder_n if_o any_o be_v then_o add_v the_o next_o denomination_n together_o take_v notice_n how_o many_o time_n the_o next_o great_a denomination_n be_v contain_v in_o that_o lesser_a carry_v for_o every_o time_n one_o to_o the_o next_o thus_o proceed_v till_o you_o have_v go_v over_o all_o the_o denomination_n be_v they_o never_o so_o many_o example_n 1._o li._n s._n d._n q._n 37_o 16_o 9_o 3._o 21_o 09._o 8._o 1_o 13_o 12_o 9_o 2_o 72_o 19_o 3_o 2_o let_v the_o number_n to_o be_v add_v together_o be_v 37_o li._n 16_o s._n 9_o d._n 3_o q._n 21_o li._n 9_o s._n 8_o d._n 1_o q._n 13_o li._n 12_o s._n 9_o d._n 2_o q._n place_v the_o number_n as_o in_o
one_o farthing_n be_v 00104167_o and_o the_o reason_n be_v because_o if_o you_o reduce_v 1_o 960_o into_o a_o decimal_n for_o one_o farthing_n be_v the_o 960_o part_n of_o a_o pound_n sterling_n you_o shall_v by_o add_v of_o cipher_n to_o the_o numerator_n find_v the_o quotient_a to_o be_v 104167_o but_o two_o cipher_n must_v be_v place_v before_o it_o because_o divide_v 1000000_o by_o 960_o the_o place_n of_o unite_v in_o the_o divisor_n at_o the_o first_o demand_n extend_v unto_o the_o three_o cypher_n in_o the_o dividend_n for_o in_o reduce_v of_o vulgar_a fraction_n to_o decimal_n this_o be_v a_o general_a rule_n that_o if_o the_o place_n of_o unite_v in_o the_o divisor_n at_o the_o first_o demand_n extend_v but_o unto_o the_o first_o of_o the_o cipher_n annex_v to_o the_o numerator_n of_o the_o fraction_n there_o must_v be_v no_o cypher_n put_v before_o the_o quotient_a but_o if_o the_o place_n of_o unite_v extend_v unto_o the_o second_o cypher_n add_v than_o one_o cypher_n must_v 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03333333_o 7_o 02916667_o 6_o 025_o 5_o 02083333_o 4_o 01666667_o 3_o 0125_o 2_o 00833333_o 1_o 04166667_o f._n 3_o 003125_o 2_o 00208333_o 1_o 00104167_o troy_n weight_n in_o decimal_n o._n 11_o 91666667_o 10_o 83333333_o 9_o 75_o 8_o 66666667_o 7_o 58333333_o 6_o 5_o 5_o 41666667_o 4_o 33333333_o 3_o 25_o 2_o 16666667_o 1_o 08333333_o p._n 19_o 07916667_o 18_o 075_o 17_o 07083333_o 16_o 06666667_o 15_o 0625_o 14_o 05833333_o 13_o 05416667_o 12_o 05_o 11_o 04583333_o 10_o 04166667_o 9_o 0375_o 8_o 03333333_o 7_o 02916667_o 6_o 025_o 5_o 02083333_o 4_o 01666667_o 3_o 0125_o 2_o 00833333_o 1_o 00416667_o gr._n 23_o 00399395_o 22_o 00381944_o 21_o 00364583_o 20_o 00347222_o 19_o 00329861_o 18_o 003125_o 17_o 00295139_o 16_o 00277778_o 15_o 00260417_o 14_o 00243056_o 13_o 00225694_o 12_o 00208333_o 11_o 00190972_o 10_o 00173611_o 9_o 0015625_o 8_o 00138889_o 7_o 00121528_o 6_o 00104166_o 5_o 00086805_o 4_o 00069444_o 3_o 00052083_o 2_o 00044722_o 1_o 00017361_o averdupois_n great_a 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dram_fw-la 15_o 05859375_o 14_o 0546875_o 13_o 05078115_o 12_o 046875_o 11_o 04296875_o 10_o 0390625_o 9_o 03515625_o 8_o 03125_o 7_o 02734375_o 6_o 0234375_o 5_o 01953125_o 4_o 015625_o 3_o 01171875_o 2_o 0078125_o 1_o 00390625_o 3_o qu._n 00292969_o half_a 00195312_o 1_o qu._n 00097656_o liquid_a measure_n in_o decimal_n p._n 7_o 875_o 6_o 75_o 5_o 625_o 4_o 5_o 3_o 375_o 2_o 25_o 1_o 125_o 3_o qu._n 09375_o half_n 0625_o 1_o qu._n 03125_o dry_a measure_n in_o decimal_n bushel_n 7_o 875_o 6_o 75_o 5_o 625_o 4_o 5_o 3_o 375_o 2_o 25_o 1_o 125_o peck_v 3_o 09375_o 2_o 0625_o 1_o 03125_o 3_o qu._n 0234375_o half_n 015625_o 1_o qu._n 0078125_o pintt_n 3_o 0058594_o 2_o 0039063_o 1_o 0019531_o long_a measure_n the-integers_a be_v yard_n and_o ell_n in_o '_o decimal_n qu._n 3_o 75_o 2_o 5_o 1_o 25_o nale_n 3_o 1875_o 2_o 125_o 1_o 0625_o 3_o qu._n 046875_o half_n 03125_o 1_o qu._n 015625_o time_n in_o decimal_n mo._n 11_o 916667_o 10_o 833333_o 9_o 75_o 8_o 666667_o 7_o 833333_o 6_o 5_o 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which_o be_v the_o decimal_n represent_v 7_o penny_n also_o against_o 2_o farthing_n you_o shall_v find_v 00208333_o which_o be_v the_o decimal_n answer_v to_o 12_o farthing_n and_o the_o like_a be_v to_o be_v do_v for_o any_o other_o number_n of_o shilling_n penny_n or_o farthing_n but_o if_o it_o be_v require_v to_o find_v the_o decimal_n of_o divers_a denomination_n of_o coin_n in_o one_o sum_n as_o of_o shilling_n penny_n and_o farthing_n together_o you_o must_v add_v the_o decimal_n of_o all_o the_o particular_n together_o and_o the_o sum_n of_o they_o shall_v be_v the_o decimal_n seek_v example_n if_o you_o will_v know_v the_o decimal_n of_o 13_o s._n 7_o d._n 2_o q._n in_o one_o number_n 65_o 02916667_o 00208333_o 68125000_o you_o must_v first_o look_v in_o the_o table_n for_o the_o decimal_n of_o 13_o s._n which_o be_v 65_o and_o set_v that_o down_o then_o look_v for_o the_o decimal_n of_o 7_o d._n which_o be_v 00916667_o and_o set_v that_o down_o also_o last_o seek_v the_o decimal_n of_o 2_o q._n which_o be_v 00208â—33_n set_v that_o down_o also_o then_o if_o you_o add_v these_o three_o number_n together_o as_o in_o common_a addition_n you_o shall_v find_v the_o sum_n of_o they_o to_o be_v 68125000_o which_o be_v the_o decimal_n belong_v to_o 13_o s._n 7_o d._n 2_o q._n as_o by_o thou_fw-mi work_n in_o the_o margin_n appear_v prop._n ii_o how_o to_o express_a troy_n weight_n in_o decimal_n the_o second_o table_n be_v of_o troy_n weight_n the_o several_a denomination_n whereof_o be_v ounce_n peny-weight_n and_o grain_n so_o that_o by_o the_o table_n you_o shall_v find_v that_o the_o decimal_n belong_v to_o five_o ounce_n be_v 41666667_o the_o decimal_n belong_v to_o 17_o
be_v two_o shilling_n ferâ—_n which_o shall_v be_v two_o shilling_n exact_a but_o it_o want_v somewhat_o viz._n the_o 1000_o part_n of_o a_o farthing_n which_o be_v insensible_a for_o if_o by_o the_o forementioned_a rule_v you_o seek_v the_o value_n of_o the_o decimal_n fraction_n .0999_o you_o shall_v find_v it_o to_o be_v 1_o shilling_n 11_o penny_n 3_o farthing_n and_o the_o 2_o 1000_o part_n of_o a_o farthing_n which_o you_o may_v call_v in_o all_o 2_o shilling_n for_o decimal_a number_n will_v seldom_o happen_v to_o give_v the_o exact_a value_n of_o fraction_n but_o will_v be_v either_o great_a or_o lesser_a than_o they_o ought_v to_o be_v but_o in_o such_o a_o sum_n as_o this_o be_v the_o thousand_o part_n of_o a_o farthing_n be_v not_o to_o be_v regard_v example_n 2._o let_v it_o be_v require_v to_o add_v together_o in_o a_o decimal_n way_n these_o sum_n follow_v viz._n 29_o li._n 18_o s._n 7_o d._n 3_o q._n 63_o li._n 11_o s._n 2_o d._n 1_o q._n 129_o li._n 4_o s._n 0_o d._n 2_o q._n and_o 3_o li_z 7_o s._n 10_o d._n 1_o q._n first_o for_o 29_o li._n 18_o s._n 7_o d._n 3_o q._n set_v down_o 29.93229_o second_o for_o 63_o li._n 11_o s._n 2_o d._n 1_o q._n set_v down_o 63.55937_o three_o for_o 129_o li._n 4_o s._n 2_o q._n set_v down_o 129.20208_o last_o for_o 3_o li._n 7_o s._n 10_o d._n 1_o q._n set_v down_o 3.39271_o as_o you_o see_v here_o down_o in_o the_o margin_n your_o decimal_a number_n thus_o place_v in_o order_n 29.93229_o 63.55937_o 129.20208_o 3.39371_o 226.08645_o add_v they_o together_o as_o if_o they_o be_v whole_a number_n and_o you_o shall_v find_v the_o sum_n of_o they_o to_o contain_v 226.08645_o now_o the_o 226_o which_o stand_v towards_o the_o left_a hand_n of_o the_o comma_n be_v 226_o pound_n and_o the_o other_o figure_n towards_o the_o right_a hand_n viz._n 08645_o be_v the_o fraction_n of_o a_o pound_n sterling_a which_o if_o you_o reduce_v by_o the_o forementioned_a proposition_n you_o shall_v find_v the_o value_n thereof_o to_o be_v 1_o shilling_n 8_o penny_n 3_o farthing_n so_o the_o whole_a sum_n be_v 226_o li._n 1_o s._n 8_o d._n 3_o q._n and_o here_o note_v that_o what_o have_v be_v say_v as_o concern_v money_n the_o same_o be_v also_o to_o be_v understand_v of_o weight_n measure_n time_n etc._n etc._n as_o by_o the_o follow_a example_n will_v appear_v other_o example_n for_o practice_n example_n 1._o in_o money_n 135.8833_o 95.5583_o 3.2875_o 234.7291_o 234_o li._n 14_o s._n 7_o d._n example_n 2._o in_o troy_n weight_n 7.97413_o 6.65330_o 3.62187_o 18.24930_o 18_o li._n 2_o ou_fw-fr 19_o p.w._n 20_o gr_n example_n 3._o in_o averdupois_n little_a w._n 12.7227_o 76.3594_o 32.625_o 91.4883_o 32.8398_o 246.0352_o 246_o li._n 00_o owned_a 9_o d_z example_n 4._o in_o averdup_n great_a weight_n 37.9442_o 9.3053_o 33.6786_o 10.0000_o 12.8142_o 103.7423_o 103_o c._n 2_o q._n 27_o l._n 3_o ow_v subtraction_n of_o decimal_n the_o subtraction_n of_o decimal_n differ_v nothing_o from_o the_o subtract_v of_o one_o whole_a number_n from_o another_o and_o the_o decimal_a number_n to_o be_v subtract_v one_o from_o another_o must_v be_v place_v in_o the_o same_o order_n as_o in_o addition_n of_o decimal_a number_n the_o practice_n of_o subtaction_n shall_v be_v see_v in_o the_o follow_a example_n example_n 1._o let_v it_o be_v require_v to_o subtract_v 31_o li._n 16_o s._n 9_o d._n out_o of_o 36_o li._n 2_o s._n 8_o d._n first_o for_o your_o 36_o li._n 2_o s._n 8_o d._n set_v down_o the_o decimal_n thereof_o which_o be_v 36.1333_o second_o for_o your_o 31_o li._n 16_o s._n 9_o d._n set_v down_o the_o decimal_n thereof_o 31.8375_o this_o do_v draw_v a_o line_n under_o they_o 36_o 1333_o 31_o 8â—75_n 4_o 2958_o &_o subtract_v the_o lesser_a from_o the_o great_a you_o shall_v find_v the_o remainder_n to_o be_v 4._o 2958._o the_o 4_o on_o the_o left_a side_n of_o the_o comma_n be_v four_o pound_n and_o the_o 2958_o which_o stand_v towards_o the_o right_a hand_n be_v the_o fraction_n part_n of_o a_o pound_n the_o value_n whereof_o be_v seek_v will_v be_v find_v to_o be_v 5_o s._n and_o 11_o penny_n so_o that_o if_o you_o subtract_v 31_o li._n 16_o s._n 9_o d._n out_o of_o 36_o li._n 2_o s._n 8_o d._n there_o will_v remain_v 4_o li._n 5_o s._n 1â—_n d._n but_o if_o divers_a sum_n be_v to_o be_v subtract_v out_o of_o one_o great_a sum_n than_o you_o must_v first_o add_v all_o the_o several_a small_a sum_n together_o and_o subtract_v the_o sum_n of_o they_o from_o the_o great_a give_v sum_n so_o shall_v the_o residue_n be_v the_o sum_n desire_v example_n for_o practice_n example_n 1._o in_o money_n lent_n 2684.8375_o pay_v at_o several_a time_n 36.1333_o  _fw-fr 29.0083_o  _fw-fr 31.8375_o  _fw-fr 6.1208_o pay_v in_o all_o 103.0999_o rest_n to_o pay_v 2581.7376_o 2581_o li._n 14_o s._n 9_o d._n example_n 2._o  _fw-fr  _fw-fr in_o averdupois_n great_a weight_n buy_v  _fw-fr 103.7423_o sold_n  _fw-fr 37.0442_o unsold_a  _fw-fr 65.7981_o 65_o c._n 3_o q._n 5_o l._n 7._o owned_a example_n 3._o  _fw-fr in_o troy_n weight_n deliver_v to_o a_o goldsmith_n of_o old_a plate_n 7._o 97413_o receive_v of_o new_a plate_n 5.59670_o rest_n in_o the_o goldsmith_n hand_n 2.7743_o 2_o li._n 4_o owned_a 10_o p_o w._n 14_o gr_n multiplication_n of_o decimal_n multiplication_n of_o decimal_n differ_v nothing_o at_o all_o from_o the_o multiplication_n of_o whole_a number_n for_o make_v the_o great_a number_n the_o multiplicand_a and_o the_o lesser_a number_n the_o multiplyer_n the_o number_n issue_v from_o that_o multiplication_n shall_v be_v call_v the_o product_n now_o in_o the_o multiplication_n of_o decimal_a number_n one_o by_o another_o if_o there_o be_v any_o fraction_n either_o in_o the_o multiplicand_a or_o multiply_o or_o fraction_n in_o both_o so_o many_o figure_n as_o the_o fraction_n contain_v so_o many_o figure_n must_v be_v cut_v off_o from_o the_o product_n towards_o the_o right_a hand_n which_o shall_v be_v the_o fraction_n of_o the_o product_n and_o the_o figure_n towards_o the_o left_a hand_n of_o the_o comma_n in_o the_o product_n shall_v be_v the_o integer_n of_o the_o product_n example_n 1._o let_v it_o be_v require_v to_o multiply_v 34_o pound_n five_o shilling_n three_o penny_n by_o 16_o pound_n six_o shilling_n six_o penny_n first_o seek_v the_o decimal_n of_o 34_o li._n 5_o s._n 3_o d._n which_o you_o shall_v find_v to_o be_v 34._o 2625_o make_v this_o number_n your_o multiplicand_n then_o seek_v the_o decimal_n of_o 16_o li._n 6_o s._n 6_o d._n which_o you_o shall_v find_v to_o be_v 16._o 325_o make_v this_o decimal_n number_v your_o multiplyer_n then_o draw_v a_o line_n and_o multiply_v these_o two_o number_n together_o as_o if_o they_o be_v whole_a number_n and_o you_o shall_v find_v the_o product_n of_o they_o to_o be_v 559._o 3353125._o now_o because_o there_o be_v four_o figure_n in_o the_o multiplicand_a which_o be_v fraction_n namely_o these_o four_o towards_o the_o right_a hand_n viz._n 2625_o and_o there_o be_v also_o three_o figure_n in_o the_o multiplyer_n which_o be_v fraction_n namely_o these_o three_o towards_o the_o right_a hand_n viz._n 325_o that_o be_v in_o all_o seven_o figure_n represent_v fraction_n i_o therefore_o cut_v off_o from_o the_o product_n the_o seven_o figure_n towards_o the_o right_a hand_n by_o make_v of_o a_o comma_n there_o to_o distinguish_v the_o whole_a number_n from_o the_o fraction_n so_o be_v 559_o the_o integer_fw-la or_o whole_a number_n and_o 3353125_o the_o fraction_n of_o this_o multiplication_n example_n 2._o if_o there_o be_v fraction_n in_o the_o multiplicand_a and_o none_o in_o the_o multiplyer_n yet_o that_o work_n be_v still_o the_o same_o for_o you_o must_v cut_v off_o only_o so_o many_o figure_n from_o the_o product_n as_o there_o be_v fraction_n either_o in_o multiplicand_a multiplyer_n or_o both_o so_o if_o it_o be_v require_v to_o multiply_v 5767_o yard_n and_o 3_o quarter_n of_o a_o yard_n by_o 235_o yard_n you_o must_v first_o set_v down_o 5767._o 75_o for_o your_o 5767_o yard_n and_o three_o quarter_n which_o number_n must_v be_v your_o multiplicand_a also_o set_v down_o 235_o yard_n for_o your_o multiplyer_n then_o multiply_v they_o together_o as_o if_o they_o be_v whole_a number_n you_o shall_v find_v the_o product_n to_o be_v 1255421_o 25_o and_o because_o there_o be_v only_o two_o fraction_n figure_n both_o which_o be_v in_o the_o multiplicand_a namely_o the_o two_o last_o thereof_o .75_o and_o none_o in_o the_o multiplyer_n i_o therefore_o cut_v off_o only_o two_o figure_n of_o the_o product_n namely_o the_o two_o last_o which_o be_v .25_o so_o be_v the_o product_n of_o this_o multiplication_n 1355421._o 25_o which_o be_v 1355421_o square_a yard_n and_o one_o quarter_n of_o a_o yard_n and_o
place_n the_o dividend_n be_v the_o lesser_a term_n place_v the_o dividend_n as_o a_o numerator_n and_o the_o divisor_n as_o '_o denominator_fw-la so_o be_v such_o vulgar_a fraction_n the_o quotient_a fight_v but_o if_o the_o term_n give_v consist_v not_o of_o equal_a place_n supply_v the_o place_n or_o place_n want_v in_o either_o of_o the_o term_n by_o annex_v a_o cypher_n or_o cipher_n on_o the_o right_a hand_n and_o then_o proceed_v as_o before_o thus_o if_o .27_o be_v give_v to_o be_v divide_v by_o .93_o the_o quotient_n will_v be_v 27_o 93._o also_o if_o .35_o be_v give_v to_o be_v divide_v by_o .78563_o the_o quotient_a by_o annex_v 3_o cipher_n to_o .35_o the_o lesser_a decimal_n give_v will_v be_v 35000_o 78563_o which_o vulgar_a fraction_n may_v be_v reduce_v into_o decimal_n if_o need_v be_v by_o the_o first_o proposition_n in_o this_o second_o part_n of_o decimal_a arithmetic_n example_n for_o practice_n the_o rule_n of_o three_o in_o fraction_n vulgar_a and_o decimal_a what_o the_o rule_n of_o three_o be_v and_o the_o manner_n of_o work_v be_v already_o show_v in_o the_o first_o part_n that_o which_o we_o here_o intend_v be_v only_o to_o add_v some_o example_n in_o fraction_n vulgar_a as_o well_o as_o decimal_n that_o by_o compare_v the_o work_n in_o both_o the_o excellent_a use_n of_o decimal_a arithmetic_n may_v the_o better_o appear_v and_o how_o to_o convert_v the_o know_a part_n of_o money_n weight_n or_o measure_v english_a into_o decimal_n have_v be_v already_o show_v both_o arithmetical_o and_o by_o table_n yet_o to_o prevent_v the_o several_a addition_n and_o subtraction_n in_o those_o table_n we_o have_v here_o annex_v another_o decimal_a table_n for_o the_o more_o speedy_a reduction_n of_o english_a money_n under_o two_o shilling_n all_o sum_n of_o money_n above_o not_o have_v penny_n or_o farthing_n annex_v be_v as_o easy_o reduce_v by_o memory_n as_o by_o table_n and_o this_o we_o have_v the_o rather_o do_v because_o the_o same_o table_n will_v also_o reduce_v the_o coin_n of_o france_n and_o the_o part_n of_o troy_n weight_n if_o a_o ounce_n be_v make_v the_o integer_fw-la which_o in_o point_n of_o practice_n be_v much_o more_o useful_a than_o the_o pound_n the_o table_n of_o reduction_n penny_n 001042_o  _fw-fr  _fw-fr 002083_o gr._n 1_o  _fw-fr 003125_o  _fw-fr 1_o 004166_o 2_o  _fw-fr 005208_o  _fw-fr  _fw-fr 006250_o 3_o  _fw-fr 007291_o  _fw-fr 2_o 008333_o 4_o  _fw-fr 009375_o  _fw-fr  _fw-fr 010416_o 5_o  _fw-fr 011458_o  _fw-fr 3_o 012500_o 6_o  _fw-fr 013541_o  _fw-fr  _fw-fr 014582_o 7_o  _fw-fr 015625_o  _fw-fr 4_o 016666_o 8_o  _fw-fr 017708_o  _fw-fr  _fw-fr 018750_o 9_o  _fw-fr 019791_o  _fw-fr 5_o 020833_o 10_o  _fw-fr 021874_o  _fw-fr  _fw-fr 022916_o 11_o  _fw-fr 023958_o  _fw-fr 6_o 025000_o 12_o  _fw-fr 026014_o  _fw-fr  _fw-fr 027083_o 13_o  _fw-fr 028125_o  _fw-fr 7_o 029166_o 14_o  _fw-fr 030208_o  _fw-fr  _fw-fr 031250_o 15_o  _fw-fr 032291_o  _fw-fr 8_o 033333_o 16_o  _fw-fr 034375_o  _fw-fr  _fw-fr 035416_o 17_o  _fw-fr 036458_o  _fw-fr 9_o 037500_o 18_o  _fw-fr 038541_o  _fw-fr  _fw-fr 039583_o 19_o  _fw-fr 040625_o  _fw-fr 10_o 041666_o 20_o  _fw-fr 042708_o  _fw-fr  _fw-fr 043750_o 21_o  _fw-fr 044791_o  _fw-fr 11_o 045833_o 22_o  _fw-fr 046875_o  _fw-fr  _fw-fr 047916_o 23_o  _fw-fr 048958_o  _fw-fr 12_o 050000_o 24_o the_o table_n of_o reduction_n  _fw-fr 051042_o  _fw-fr  _fw-fr 052083_o g_z 1_o s.d._n 053125_o  _fw-fr t_o 1_o 054166_o 2_o  _fw-fr 055208_o  _fw-fr  _fw-fr 056250_o 3_o  _fw-fr 057292_o  _fw-fr 2_o 058333_o 4_o  _fw-fr 059375_o  _fw-fr  _fw-fr 060416_o 5_o 3_o 061458_o  _fw-fr  _fw-fr 062500_o 6_o  _fw-fr 063542_o  _fw-fr  _fw-fr 064582_o 7_o  _fw-fr 065625_o  _fw-fr 4_o 066666_o 8_o  _fw-fr 067708_o  _fw-fr  _fw-fr 068750_o 9_o  _fw-fr 069792_o  _fw-fr 5_o 070833_o 10_o  _fw-fr 071874_o  _fw-fr  _fw-fr 072916_o 11_o  _fw-fr 073958_o  _fw-fr 6_o 075000_o 12_o  _fw-fr 076014_o  _fw-fr  _fw-fr 077083_o 13_o  _fw-fr 078125_o  _fw-fr 7_o 079166_o 14_o  _fw-fr 080208_o  _fw-fr  _fw-fr 081250_o 15_o  _fw-fr 082921_o  _fw-fr 8_o 083333_o 16_o  _fw-fr 084375_o  _fw-fr  _fw-fr 085416_o 17_o  _fw-fr 086458_o  _fw-fr 9_o 087500_o 18_o  _fw-fr 088541_o  _fw-fr  _fw-fr 089583_o 19_o  _fw-fr 090625_o  _fw-fr 10_o 091666_o 20_o  _fw-fr 092708_o  _fw-fr  _fw-fr 093750_o 21_o  _fw-fr 094791_o  _fw-fr 11_o 095833_o 22_o  _fw-fr 096875_o  _fw-fr  _fw-fr 097916_o 23_o  _fw-fr 098958_o  _fw-fr 12_o 000000_o 24_o these_o thing_n premise_v we_o will_v now_o show_v the_o use_n of_o the_o table_n in_o some_o practical_a question_n belong_v to_o the_o rule_n of_o three_o direct_v 1_o question_n if_o â…ž_n of_o a_o yard_n of_o cloth_n cost_v 9_o 12_o of_o a_o pound_n what_o shall_v 17_o yard_n cost_v at_o the_o same_o rate_n if_o â…ž_n cost_v 9_o 12_o what_o shall_v 17_o cost_n ans_fw-fr 14_o li._n 4_o 7._o first_o multiply_v 9_o 12_o by_o 17_o 1_o the_o product_n be_v 153_o 12_o then_o divide_v 153_o 12_o by_o â…ž_n the_o quotient_n be_v 1224_o 84_o again_o if_o you_o divide_v 1224_o by_o 84_o the_o quotient_n be_v 14_o â—_o â—4_n or_o in_o the_o least_o term_n 14_o pound_n 4_o 7_o of_o a_o pound_n and_o the_o value_n of_o this_o fraction_n 4_o 7_o of_o a_o pound_n will_v be_v find_v by_o the_o three_o rule_n of_o reduction_n page_n 107_o to_o be_v 11_o shilling_n 5_o penny_n and_o 4_o 7_o of_o a_o penny_n which_o be_v somewhat_o above_o two_o farthing_n for_o it_o be_v 2_o farthing_n and_o 2_o 7_o of_o a_o farthing_n the_o same_o question_n in_o decimal_n if_o â…ž_n of_o a_o yard_n of_o cloth_n cost_v 9_o 12_o of_o a_o pound_n what_o shall_v 17_o yard_n cost_v at_o the_o same_o rate_n to_o answer_v this_o question_n â…ž_n of_o a_o yard_n and_o 9_o 12_o of_o a_o pound_n must_v first_o be_v reduce_v into_o decimal_n either_o by_o division_n or_o by_o the_o table_n of_o reduction_n by_o both_o which_o way_n of_o reduction_n the_o decimal_n of_o â…ž_n will_v be_v 875_o and_o the_o decimal_n of_o 9_o 12_o will_v be_v .75_o and_o 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penny_n and_o farthing_n under_o two_o shilling_n upon_o the_o scale_n unto_o this_o scale_n of_o money_n as_o to_o all_o the_o rest_n of_o the_o scale_n there_o be_v join_v another_o scale_n which_o i_o shall_v always_o hereafter_o call_v the_o scale_n of_o 1000_o the_o use_n of_o which_o scale_n be_v this_o when_o you_o have_v find_v any_o number_n of_o penny_n or_o farthing_n upon_o the_o scale_n of_o money_n you_o shall_v find_v upon_o the_o scale_n of_o 1000_o what_o part_n of_o a_o thousand_o be_v the_o decimal_n of_o those_o penny_n and_o farthing_n thus_o when_o in_o the_o scale_n of_o money_n you_o find_v at_o the_o letter_n a_o 8_o penny_n 3_o farthing_n if_o you_o cast_v your_o eye_n direct_o cross_v to_o the_o scale_n of_o 1000_o you_o shall_v find_v 364_o to_o stand_v direct_o against_o 8_o d._n 3_o q._n which_o 364_o be_v the_o decimal_n of_o 8_o d._n 3_o q._n also_o if_o you_o find_v upon_o the_o scale_n of_o money_n 18_o d._n half_a penny_n which_o be_v at_o the_o letter_n c_o you_o shall_v find_v against_o it_o in_o the_o scale_n of_o 1000_o this_o number_n 771_o which_o be_v the_o decimal_n of_o 18_o d._n half_a penny_n and_o in_o this_o manner_n may_v the_o decimal_n of_o any_o number_n of_o penny_n or_o farthing_n under_o two_o shilling_n be_v most_o easy_o and_o exact_o obtain_v now_o on_o the_o contrary_a suppose_v a_o decimal_n fraction_n be_v give_v represent_v some_o part_n of_o english_a coin_n if_o you_o look_v in_o the_o scale_n of_o 1000_o for_o your_o number_n give_v right_o against_o it_o in_o the_o scale_n of_o money_n you_o shall_v find_v what_o number_n of_o penny_n and_o farthing_n be_v represent_v thereby_o as_o for_o example_n suppose_v .364_o be_v a_o decimal_n give_v and_o it_o be_v require_v to_o find_v what_o part_n of_o coin_n it_o do_v represent_v look_v
4_o decade_n or_o 8_o s._n and_o be_v the_o rest_n to_o the_o right_a hand_n be_v all_o cipher_n they_o signify_v neither_o penny_n nor_o farthing_n so_o be_v the_o total_a of_o this_o addition_n 103_o l._n 8_o s._n 0_o d._n that_o the_o manner_n of_o work_v may_v appear_v more_o plain_a i_o will_v give_v you_o another_o short_a example_n as_o difficult_a as_o i_o can_v invent_v which_o i_o perform_v by_o a_o scale_n of_o wood_n but_o of_o 8_o inch_n long_o let_v the_o sum_n to_o be_v add_v together_o be_v these_o follow_v li._n t._n d._n q_o 332_o 17_o 4_o 1_o 159_o 6_o 8_o 1_o 217_o 5_o 3_o 3_o 709_o 9_o 4_o 1_o first_o set_v down_o your_o several_a sum_n of_o pound_n one_o under_o another_o as_o before_o and_o draw_v a_o line_n by_o the_o side_n of_o they_o 332_o  _fw-fr 159_o  _fw-fr 217_o  _fw-fr and_o another_o under_o they_o so_o will_v they_o stand_v as_o here_o you_o see_v 1_o your_o sum_n of_o pound_n be_v thus_o orderly_o place_v and_o line_n draw_v repair_v to_o your_o scale_n and_o see_v your_o first_o number_n of_o shilling_n penny_n and_o farthing_n be_v 17_o s._n 4_o d._n 1_o q._n for_o your_o 17_o s._n set_v down_o 8_o decade_n which_o be_v 16_o s._n with_o a_o comma_n after_o it_o then_o will_v there_o rest_v to_o be_v set_v down_o 1_o s._n 4_o d._n 1_o q._n or_o 16_o d._n 1_o q._n which_o if_o you_o seek_v in_o your_o scale_n of_o money_n you_o shall_v find_v to_o stand_v against_o it_o in_o the_o scale_n of_o 1000_o this_o number_n 677_o which_o be_v the_o decimal_n of_o 1_o s._n 4_o d._n 1_o q._n 2_o your_o second_o number_n of_o shilling_n penny_n and_o farthing_n be_v 6_o s._n 8_o d._n 1_o q._n for_o your_o 6_o s._n set_v down_o 3_o decade_n which_o be_v 6_o s._n and_o then_o there_o will_v remain_v 8_o d._n 1_o q._n which_o if_o you_o seek_v in_o your_o scale_n of_o money_n you_o shall_v find_v to_o stand_v against_o it_o in_o the_o scale_n of_o 1000_o this_o number_n 344_o which_o be_v the_o decimal_n of_o 8_o d._n 1_o q._n 3_o your_o 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the_o margin_n draw_v a_o line_n under_o they_o and_o begin_v with_o the_o least_o denomination_n which_o in_o this_o example_n be_v farthing_n first_o say_v 2_o q._n and_o 1_o q._n be_v 3_o q._n and_o 3_o q._n be_v 6_o q._n which_o be_v one_o penny_n and_o 2_o q._n remain_v which_o 2_o q._n i_o place_n under_o the_o line_n and_o carry_v the_o one_o penny_n to_o the_o next_o row_n which_o be_v the_o place_n of_o penny_n say_v one_o penny_n and_o 9_o d._n be_v 10_o d._n and_o 8_o d._n be_v 18_o d._n which_o be_v 1_o s._n and_o 6_o d._n now_o against_o the_o 8_o i_o make_v a_o prick_n with_o my_o pen_n for_o my_o better_a remembrance_n to_o signify_v that_o there_o be_v one_o shilling_n to_o be_v carry_v to_o the_o place_n of_o shilling_n then_o go_v on_o and_o say_v 6_o d._n and_o 9_o d._n be_v 15_o d._n which_o be_v 1_o s._n and_o 3_o d._n therefore_o against_o 9_o i_o make_v a_o prick_n with_o my_o pen_n and_o because_o that_o be_v the_o last_o number_n i_o set_v down_o the_o odd_a 3_o d._n under_o the_o place_n of_o penny_n and_o because_o i_o find_v two_o prick_n in_o the_o line_n of_o penny_n therefore_o i_o carry_v 2_o s._n to_o the_o place_n of_o shilling_n say_v 2_o s._n which_o i_o carry_v and_o 12_o s._n be_v 14_o s._n and_o 9_o s._n be_v 23_o s._n which_o be_v one_o pound_n and_o 3_o s._n remain_v i_o make_v a_o prick_n against_o 9_o and_o go_v on_o say_v 3_o s._n and_o 16_o s._n be_v 19_o s._n which_o be_v there_o be_v no_o more_o number_n to_o be_v add_v and_o be_v also_o less_o than_o 20_o s._n i_o set_v under_o the_o line_n and_o find_v one_o prick_n in_o the_o line_n of_o shilling_n i_o therefore_o carry_v one_o to_o the_o place_n of_o pound_n say_v one_o which_o i_o carry_v and_o 3_o be_v 4_o and_z 1_o be_v 5_o and_z 7_o be_v 12._o set_v down_o the_o 2_o under_o the_o line_n as_o in_o addition_n of_o number_n of_o one_o denomination_n and_o carry_v one_o to_o the_o next_o row_n say_v one_o that_o i_o carry_v and_o 1_o be_v 2_o and_z 2_o be_v 4_o and_z 3_o be_v 7_o which_o be_v the_o last_o i_o set_v down_o and_o so_o the_o total_a or_o gross_a sum_n be_v 72_o li._n 19_o s._n 3_o d._n 2_o q._n example_n 2_o li._n s._n d._n 29_o 16._o 8._o 32_o 17._o 9_o 81_o 13_o 11_o 144_o 08_o 4_o let_v the_o number_n to_o be_v add_v be_v 29_o li._n 16_o s._n 8_o d._n 32_o li._n 17_o s._n 9_o d._n 81_o li._n 13_o s._n 11_o d._n and_o let_v it_o be_v require_v to_o find_v the_o total_a or_o gross_a sum_n here_o in_o this_o example_n the_o least_o denomination_n be_v penny_n therefore_o i_o begin_v with_o they_o and_o say_v 11_o d._n and_o 9_o d._n be_v 20_o d._n which_o be_v 1_o s._n and_o 8_o d._n make_v a_o prick_n against_o the_o 9_o and_o say_v 8_o d._n and_o 8_o d._n be_v 16_o d._n that_o be_v 1_o s._n and_o 4_o d._n make_v a_o prick_n against_o the_o 8_o and_o set_v down_o the_o odd_a 4_o d._n then_o because_o there_o be_v two_o prick_n in_o the_o line_n of_o penny_n you_o must_v carry_v 2_o s._n to_o the_o place_n of_o shilling_n say_v 2_o s._n which_o i_o carry_v and_o 13_o s._n be_v 15_o s._n and_o 17_o s._n be_v 32_o s._n which_o be_v 1_o l._n 12_o s._n make_v a_o prick_n agianst_a 17_o and_o say_v 12_o s._n and_o 16_o s._n be_v 28_o s._n make_v a_o prick_n against_o 16_o and_o because_o there_o be_v no_o more_o number_n to_o be_v add_v set_v down_o the_o odd_a 8_o s._n under_o shilling_n and_o be_v there_o be_v two_o prick_n in_o the_o line_n of_o shilling_n carry_v 2_o to_o the_o place_n of_o pound_n say_v 2_o and_o 1_o be_v 3_o and_z 2_o be_v 5_o and_z 9_o be_v 14_o set_z down_z 4_o and_z carry_z 1_o to_o the_o next_o line_n and_o say_v 1_o and_o 8_o be_v 9_o and_z 3_o be_v 12_o and_z 2_o be_v 14_o which_o because_o it_o be_v the_o last_o you_o must_v set_v down_o so_o be_v the_o total_a or_o gross_a sum_n 144_o li._n 8_o s._n 4_o d._n other_o example_n for_o practice_n li._n s._n d._n q._n 29_o 18._o 7_o 3_o 63_o 11._o 2._o 1._o 129_o 4_o 0_o 2_o 3_o 7_o 10_o 1_o 226_o 1_o 8_o 3_o li._n s._n d._n 36_o 2_o 8._o 29_o 0_o 2_o 31_o 16._o 9_o 6_o 2_o 5_o 103_o 2_o 0_o 2_o addition_n of_o troy_n weight_n troy_n weight_n be_v a_o weight_n use_v in_o england_n by_o the_o which_o be_v weigh_v bread_n gold_n silver_n pearl_n etc._n etc._n the_o most_o usual_a denomination_n of_o which_o weight_n be_v pound_n ounce_n penny_n weight_n and_o grain_n of_o which_o 24_o grain_n make_v 1_o peny_n weig_o thus_o character_v pw_o 20_o penny_n weight_n make_v 1_o ounce_n thus_o character_v ou_fw-fr 12_o ounce_n make_v 1_o pound_n thus_o character_v lib_n for_o a_o grain_n we_o write_v gr_n the_o addition_n of_o troy_n weight_n and_o consequent_o of_o any_o other_o weight_n or_o measure_n whatsoever_o either_o domestic_a or_o foreign_a differ_v nothing_o at_o all_o from_o the_o addition_n of_o coin_n last_o teach_v if_o the_o affinity_n of_o one_o denomination_n to_o a_o other_o be_v first_o know_v for_o whereas_o in_o money_n because_o 1â—_n d._n make_v 1_o s._n you_o therefore_o observe_v how_o many_o twelves_o there_o be_v in_o the_o addition_n of_o your_o penny_n and_o for_o every_o 12_o you_o add_v one_o shilling_n to_o the_o place_n of_o shilling_n so_o in_o the_o addition_n of_o troy_n weight_n know_v that_o 24_o gr_n make_v one_o penny_n weight_n you_o must_v therefore_o in_o the_o addition_n of_o grain_n of_o troy_n weight_n observe_v how_o many_o time_n 24_o you_o find_v in_o your_o line_n of_o grain_n and_o for_o every_o 24_o carry_v one_o to_o the_o place_n of_o penny_n weight_n likewise_o in_o the_o addition_n of_o penny_n weight_v troy_n you_o must_v consider_v how_o many_o time_n 20_o be_v contain_v in_o your_o line_n and_o for_o every_o 20_o carry_v one_o to_o the_o place_n of_o ounce_n because_o 20_o penny_n weight_v make_v a_o ounce_n also_o in_o the_o addition_n of_o ounce_n troy_n you_o must_v observe_v how_o many_o time_n 12_o you_o find_v in_o your_o line_n of_o ounce_n and_o for_o every_o 12_o carry_v one_o to_o the_o place_n of_o pound_n than_o last_o add_v your_o pound_n together_o as_o number_n of_o one_o denomination_n example_n li._n ou_fw-fr pw_n gr_n 7_o 11._o 13_o 19_o 6_o 07_o 16._o 19_o 3_o 07_o 09_o 06_o 18_o 02_o 19_o 20_o let_v the_o number_n to_o be_v add_v together_o be_v 7_o li._n 11_o ou_fw-fr 13_o pw_n 19_o gr_n 6_o li_z 7_o ou_fw-fr 16_o pw_n 19_o gr_n 3_o li._n 7_o ou_fw-fr 9_o pw_n 6_o gr_n place_v your_o number_n as_o in_o addition_n of_o money_n each_z under_z other_o according_a to_o their_o respective_a denomination_n as_o in_o the_o margin_n then_o draw_v a_o line_n under_o they_o and_o begin_v your_o addition_n with_o the_o least_o denomination_n first_o viz._n grain_n say_v 6_o gr_n and_o 19_o gr_n be_v 25_o gr_n which_o be_v one_o penny_n weight_n and_o one_o grain_n make_v a_o prick_n against_o 19_o and_o carry_v the_o odd_a grain_n to_o the_o number_n above_o say_v 1_o gr_n and_o 19_o gr_n be_v 20_o gr_n which_o because_o it_o be_v less_o than_o one_o penny_n weight_n i_o set_v under_o the_o line_n then_o find_v one_o prick_n in_o the_o line_n of_o grain_n i_o therefore_o carry_v one_o to_o the_o place_n of_o penny_n weight_n say_v 1_o and_o 9_o be_v 10_o and_o 16_o be_v 26_o which_o be_v one_o ounce_n and_o 6_o pw_n make_v a_o prick_n against_o 16_o and_o say_v 6_o and_o 13_o be_v 19_o which_o be_v less_o than_o a_o ounce_n set_v under_o the_o line_n then_o for_o the_o one_o prick_n carry_v 1_o to_o the_o place_n of_o ounce_n say_v 1_o and_o 7_o be_v 8_o and_z 7_o be_v 15_o which_o be_v one_o pound_n and_o 3_o ou_fw-fr make_v a_o prick_n at_o 7_o and_o say_v 3_o and_o 11_o be_v 14_o which_o be_v one_o pound_n and_o 2_o ounce_n set_v down_o the_o 2_o ounce_n and_o for_o the_o two_o prick_n carry_v 2_o pound_n to_o the_o place_n of_o pound_n say_v 2_o and_o 3_o be_v 5_o and_z 6_o be_v 11_o and_z 7_o be_v 18_o which_o set_v under_o the_o place_n of_o pound_n so_o be_v your_o addition_n end_v and_o the_o sum_n be_v 18_o li._n 2_o ou_fw-fr 19_o pw_n 20_o gr_n other_o example_n for_o practice_n i._o ou_fw-fr pw_n gr_n 32_o 9_o 12_o 16_o 17_o 11._o 6_o 9_o 34_o 8._o 15._o 10_o 8_o 10_o 4_o 7_o 94_o 3_o 18_o 18_o li._n ou_fw-fr pw_n gr_n 0_o 10_o 17._o 11_o 0_o 6._o 0_o 5_o 0_o 0_o 16_o 8._o 0_o 5_o 2_o 19_o 1_o 10_o 16_o 19_o 3_o addition_n
pound_n shilling_n and_o penny_n etc._n etc._n but_o this_o as_o the_o most_o certain_a and_o easy_a i_o embrace_v and_o thus_o much_o for_o addition_n and_o the_o proof_n thereof_o subtraction_n subtrrction_n be_v the_o take_n of_o one_o or_o more_o small_a sum_n out_o of_o a_o great_a as_o 7_o s._n out_o of_o 12_o s._n or_o 37_o li._n out_o of_o 100_o li._n or_o 137_o foot_n out_o of_o 983_o foot_n and_o the_o like_a as_o in_o addition_n the_o sum_n to_o be_v add_v may_v be_v either_o of_o one_o or_o of_o diverse_a denmination_n so_o likewise_o they_o may_v be_v in_o subtraction_n and_o the_o manner_n of_o place_v they_o be_v the_o same_o for_o you_o must_v set_v unite_v under_o unite_v ten_o under_o ten_o hundred_o under_o hundred_o etc._n etc._n example_n 1_o number_n give_v 986_o number_n to_o be_v subtract_v 234_o remainder_n 752_o of_o subtraction_n of_o number_n of_o one_o denomination_n let_v it_o be_v require_v to_o subtract_v 234_o out_o of_o 986_o place_n the_o number_n one_o unde_fw-la the_o other_o as_o you_o see_v do_v in_o the_o margin_n draw_v a_o line_n under_o they_o and_o begin_v with_o the_o first_o figure_n towards_o your_o right_a hand_n which_o be_v 4_o say_v take_v 4_o from_o 6_o and_o there_o remain_v 2_o place_z 2_o under_o the_o line_n and_o go_v to_o the_o next_o figure_n which_o be_v 3_o say_v take_v 3_o from_o 8_o and_o there_o remain_v 5_o place_z 5_o under_o the_o line_n and_o go_v to_o the_o next_o figure_n which_o be_v 2_o say_v take_v 2_o out_o of_o 9_o and_o there_o remain_v 7_o place_z 7_o under_o the_o line_n and_o your_o subtraction_n be_v end_v and_o it_o be_v evident_a by_o the_o work_n that_o if_o you_o take_v 234_o out_o of_o 986_o there_o will_v remain_v 75â—_n which_o you_o may_v thus_o prove_v for_o if_o you_o add_v the_o 234_o to_o 752_o you_o shall_v find_v the_o sum_n of_o that_o addition_n to_o be_v 986_o which_o be_v equal_a to_o the_o whole_a sum_n from_o which_o 234_o be_v subtract_v example_n 2._o 96527_o 2976_o 9355r_n let_v it_o be_v require_v to_o subtact_v 2976_o out_o of_o 96527_o place_n the_o number_n one_o under_o another_o as_o in_o the_o margin_n you_o fee_v do_v then_o draw_v a_o line_n under_o they_o and_o beginning_n with_o the_o first_o figure_n towards_o your_o left_a hand_n say_v take_v 6_o out_o of_o 7_o and_o there_o remain_v 1_o place_z 1_o under_o the_o line_n and_o prodeed_o to_o the_o next_o figure_n say_v 7_o out_o of_o 2_o i_o can_v not_o wherefore_o you_o must_v always_o add_v 10_o to_o the_o number_n above_o which_o in_o this_o example_n be_v 2_o and_o it_o make_v it_o 12_o therefore_o take_v 7_o out_o of_o 12_o and_o there_o remain_v 5_o place_z 5_o under_o the_o line_n and_o because_o you_o add_v 10_o to_o the_o 2_o to_o make_v it_o 12_o you_o must_v carry_v a_o unite_v to_o the_o next_o figure_n say_v one_o which_o i_o carry_v and_o 9_o be_v 10_o take_v ten_o out_o of_o 5_o which_o i_o can_v therefore_o i_o must_v add_v 10_o to_o 5_o and_o it_o make_v 15_o and_o say_v 10_o out_o of_o 15_o and_o there_o remain_v 5_o place_z 5_o under_o the_o line_n and_o because_o you_o add_v 10_o to_o 5_o to_o make_v it_o 15_o you_o must_v therefore_o carry_v a_o unite_v to_o the_o next_o figure_n say_v one_o which_o i_o carry_v and_o 2_o be_v 3_o take_z 3_o out_o of_o 6_o and_o there_o remain_v 3_o place_z 3_o under_o the_o line_n and_o because_o there_o be_v no_o more_o figure_n to_o be_v subtract_v from_o the_o number_n above_o you_o must_v say_v nothing_o from_o 9_o and_o there_o remain_v 9_o set_z the_o 9_o under_o the_o line_n and_o your_o subtraction_n be_v end_v other_o example_n for_o practice_n  _fw-fr li._n ream_n of_o paper_n sheep_n  _fw-fr lent_n 5762_o buy_v 9765_o from_o 1000_o paid_n 378_o sell_v 6529_o take_v 394_o rest_n to_o pay_v 5384_o unsold_a 3236_o remain_v 606_o subtraction_n of_o number_n of_o diverse_a denomination_n 1_o of_o english_a money_n in_o subtraction_n of_o number_n of_o diverse_a denomination_n you_o must_v observe_v the_o same_o order_n as_o in_o addition_n namely_o to_o place_v every_o number_n in_o due_a order_n with_o respect_n to_o its_o denomination_n as_o pound_n under_o pound_n shilling_n under_o shilling_n etc._n etc._n the_o great_a number_n always_o uppermost_a and_o draw_v a_o line_n under_o they_o begin_v with_o the_o least_o denomination_n first_o subtract_v it_o from_o the_o line_n above_o and_o set_v the_o remainder_n under_o the_o line_n as_o in_o whole_a number_n but_o if_o the_o penny_n or_o shilling_n in_o the_o upper_a row_n be_v small_a than_o those_o in_o the_o nether_a row_n you_o must_v add_v 12_o d._n or_o 20_o s._n to_o the_o small_a number_n that_o so_o subtraction_n may_v be_v make_v as_o by_o the_o example_n follow_v will_v appear_v example_n 1._o  _fw-fr li._n s._n d._n lent_n 269_o 18_o 10_o pay_v 38_o 12_o 8_o rest_n 231_o 6_o 2_o let_v it_o be_v require_v to_o subtract_v 38_o li._n 12_o s._n 8_o d._n out_o of_o 269_o l._n 18_o s._n 10_o d._n place_v your_o number_n as_o in_o the_o margin_n then_o begin_v with_o the_o least_o denomination_n first_o which_o in_o this_o example_n be_v penny_n say_v 8_o d._n from_o 10_o d._n and_o there_o remain_v 2_o d._n set_v the_o 2_o d._n under_o the_o line_n and_o proceed_v to_o the_o next_o denomination_n which_o be_v shilling_n say_v take_v 12_o s._n out_o of_o 18_o s._n and_o there_o remain_v 6_o s._n place_n 6_o s_o under_o the_o line_n and_o go_v to_o the_o pound_n say_v 8_o out_o of_o 9_o and_o there_o remain_v 1_o place_z 1_o under_o the_o line_n and_o say_v 3_o out_o of_o 6_o and_o there_o remain_v 3_o than_o because_o there_o be_v no_o more_o figure_n to_o be_v subtract_v say_v nothing_o out_o of_o 2_o and_o there_o remain_v 2_o which_o set_v under_o the_o line_n so_o be_v your_o subtraction_n end_v and_o the_o remainder_n be_v 231_o li._n 6_o s._n 2_o d._n example_n 2._o  _fw-fr li._n s._n p._n lent_n 9320_o 10_o 07_o pay_v 2628_o 16_o 10_o rest_n 6691_o 11_o 8_o let_v it_o be_v require_v to_o subtract_v 2628_o li._n 16_o s._n 10_o d._n out_o of_o 9320_o li._n 10_o s._n 7_o d._n place_n the_o number_n in_o order_n and_o beginning_n with_o the_o penny_n say_v 10_o d._n out_o of_o 7_o d._n i_o can_v therefore_o i_o must_v add_v 12_o d._n which_o be_v one_o shilling_n to_o 7_o d._n and_o it_o make_v 19_o d._n but_o 10_o d._n out_o of_o 19_o d._n and_o there_o remain_v 9_o d._n set_v the_o 9_o d._n under_o the_o line_n and_o because_o i_o add_v 12_o d._n to_o 7_o d._n i_o must_v therefore_o carry_v one_o to_o the_o place_n of_o shilling_n say_v 1_o s._n which_o i_o carry_v and_o 16_o s._n be_v 17._o then_o 17_o s._n from_o 10_o s._n i_o can_v take_v therefore_o i_o must_v add_v 20_o s._n which_o be_v one_o pound_n to_o 10_o s._n and_o it_o make_v 30_o s._n and_o 17_o s._n out_o of_o 30_o s._n and_o there_o remain_v 13_o set_z 13_o under_o the_o line_n and_o carry_v one_o to_o the_o place_n of_o pound_n say_v one_o which_o i_o carry_v and_o 8_o be_v 9_o take_z 9_o of_o o_o i_o can_v but_o 9_o out_o of_o 10_o and_o there_o remain_v 1_o set_z 1_o under_o the_o line_n and_o carry_v a_o unite_v to_o the_o next_o place_n say_v 1_o which_o i_o carry_v and_o 2_o be_v 3_o take_z 3_o out_o of_o 2_o i_o can_v but_o 3_o out_o of_o 12_o and_o there_o remain_v 9_o place_z 9_o under_o the_o line_n and_o carry_v 1_o to_o the_o next_o place_n say_v 1_o which_o i_o carry_v and_o 6_o be_v 7_o take_z 7_o out_z of_o 3_o i_o can_v but_o 7_o out_o of_o 13_o and_o there_o remain_v 6_o place_z 6_o under_o the_o line_n and_o carry_v one_o to_o the_o next_o row_n say_v 1_o and_o 2_o be_v 3_o take_z 3_o from_o 9_o and_o there_o remain_v 6_o place_z 6_o under_o the_o line_n so_o be_v your_o subtraction_n end_v and_o the_o remainder_n be_v 6691_o li._n 13_o s._n 9_o d._n example_n 3._o suppose_v a_o man_n have_v lend_v to_o another_o man_n 1000_o pound_n and_o that_o the_o borrower_n have_v pay_v thereof_o at_o one_o time_n 127_o li._n at_o another_o time_n 430_o li._n 10_o s._n and_o at_o a_o three_o payment_n 50_o li._n and_o the_o creditor_n will_v know_v how_o much_o he_o have_v receive_v and_o how_o much_o be_v owe_v of_o his_o debtor_n place_v the_o number_n as_o here_o you_o see_v  _fw-fr li._n s._n d._n money_n lend_v 1000_o 00_o 00_o  _fw-fr 127_o 00_o 00_o pay_v at_o several_a time_n 430_o 10_o 00_o  _fw-fr 50_o 00_o 00_o pay_v in_o all_o 607_o 10_o 00_o rest_n to_o pay_v 392_o 10_o 00_o
prop._n ix_o how_o to_o express_v dozen_o in_o decimal_n the_o last_o table_n be_v of_o dozen_o the_o integer_fw-la be_v a_o gross_a and_o the_o small_a denomination_n be_v dozen_o and_o part_n of_o dozen_o so_o may_v you_o find_v the_o decimal_n of_o seven_o dozen_o to_o be_v 5833333_o and_o the_o decimal_n of_o five_o part_n of_o a_o dozen_o to_o be_v 0347222_o and_o these_o two_o number_n add_v together_o make_v 6220555_o which_o be_v the_o number_n which_o represent_v 7_o dozen_o and_o 5_o 12_o part_n of_o a_o dozen_o hitherto_o we_o have_v show_v the_o use_n of_o the_o forego_n table_n in_o express_v of_o fraction_n in_o decimal_a number_n it_o rest_v now_o to_o show_v the_o use_n of_o they_o in_o find_v what_o fraction_n either_o of_o money_n weight_n or_o measure_n any_o decimal_a number_n give_v do_v represent_v and_o that_o shall_v be_v make_v evident_a by_o the_o ensue_a proposition_n prop._n x._o a_o decimal_n number_n be_v give_v how_o to_o find_v what_o fraction_n it_o do_v represent_v let_v 02916667_o be_v a_o decimal_n number_n represent_v some_o fraction_n part_n of_o english_a coin_n because_o it_o be_v require_v to_o find_v the_o value_n of_o this_o fraction_n in_o english_a coin_n you_o must_v therefore_o repair_v to_o the_o table_n of_o english_a coin_n in_o the_o second_o column_n of_o which_o table_n seek_v for_o the_o number_n give_v viz._n 02916667_o which_o you_o shall_v find_v to_o stand_v against_o 7_o penny_n and_o so_o much_o be_v the_o value_n of_o the_o decimal_n fraction_n 02916667_o in_o english_a coin_n also_o if_o the_o decimal_a fraction_n 75_o be_v give_v you_o shall_v find_v the_o value_n thereof_o to_o be_v 15_o shilling_n and_o the_o value_n of_o 003125_o to_o be_v three_o farthing_n likewise_o in_o the_o table_n of_o troy_n weight_n if_o 41666667_o be_v give_v it_o will_v signify_v five_o ounce_n and_o 05416667_o will_v express_v 13_o peny-weight_n and_o 00173611_o will_v express_v ten_o grain_n &c_n &c_n after_o this_o manner_n may_v you_o find_v the_o value_n of_o any_o decimal_a number_n give_v either_o in_o money_n weight_n or_o measure_n when_o the_o number_n give_v may_v be_v exact_o find_v in_o the_o table_n but_o if_o the_o number_n give_v can_v be_v find_v exact_o in_o the_o table_n unto_o which_o it_o be_v direct_v than_o you_o must_v find_v in_o the_o same_o table_n the_o near_a number_n you_o can_v less_o than_o the_o give_v number_n and_o take_v the_o number_n that_o answer_v unto_o it_o in_o the_o first_o column_n which_o will_v be_v the_o great_a fraction_n of_o the_o number_n require_v then_o subtract_v the_o decimal_n thus_o find_v out_o of_o the_o decimal_n give_v you_o shall_v have_v a_o remainder_n which_o remainder_n seek_v also_o in_o the_o second_o column_n of_o the_o table_n if_o it_o may_v be_v find_v if_o not_o seek_v the_o near_a less_o and_o the_o number_n answer_v thereunto_o in_o the_o first_o column_n shall_v be_v the_o next_o great_a fraction_n then_o subtract_v this_o decimal_n find_v out_o of_o the_o former_a remainder_n there_o will_v be_v another_o remainder_n which_o also_o seek_v in_o the_o table_n and_o proceed_v as_o in_o the_o former_a a_o example_n or_o two_o will_v make_v all_o plain_a example_n 1._o let_v 68125000_o be_v a_o decimal_n give_v represent_v some_o part_n of_o english_a coin_n if_o you_o look_v in_o the_o table_n of_o english_a coin_n for_o 68125000_o you_o can_v find_v it_o but_o the_o near_a number_n in_o the_o table_n less_o than_o it_o be_v 65_o against_o which_o i_o find_v 13_o s._n so_o that_o 13_o s._n be_v the_o great_a fraction_n part_n of_o english_a coin_n agree_v to_o this_o number_n this_o do_v subtract_v 65_o out_o of_o 68125000_o and_o there_o will_v remain_v 03125000_o which_o number_n also_o you_o must_v seek_v in_o the_o table_n of_o english_a coin_n but_o be_v you_o can_v find_v it_o there_o you_o must_v take_v the_o near_a number_n less_o than_o it_o which_o be_v 02016667_o against_o which_o i_o find_v 7_o penny_n which_o be_v the_o next_o great_a fraction_n part_n of_o english_a coin_n agree_v to_o this_o number_n again_o subtract_v 02916667_o out_o of_o 03125000_o and_o there_o will_v remain_v 00208333_o which_o number_n seek_v in_o the_o table_n and_o you_o shall_v find_v it_o to_o stand_v against_o two_o farthing_n and_o so_o much_o do_v this_o last_o remainder_n signify_v in_o english_a coin_n and_o the_o whole_a give_v number_n 68125000_o do_v represent_v in_o english_a coin_n 13_o shilling_n seven_o penny_n two_o farthing_n as_o by_o the_o operation_n follow_v do_v appear_v 68125000_o number_n give_v 65_o ......_o the_o next_o lesser_o number_v in_o the_o table_n represent_v 13_o s._n 03125000_o first_o remainder_n 02916667_o the_o next_o lesser_o number_v in_o the_o table_n represent_v 7_o d._n 00208333_o second_o remainder_n which_o represent_v two_o farthing_n so_o do_v the_o whole_a number_n represent_v 13_o s._n 7_o d._n 2_o q._n example_n 2._o let_v the_o decimal_n 87426934_o represent_v some_o fraction_n of_o a_o pound_n sterling_a be_v give_v if_o you_o look_v in_o the_o table_n of_o english_a coin_n for_o 87426934_o you_o can_v find_v it_o but_o the_o near_a number_n in_o the_o table_n less_o than_o it_o be_v 85_o against_o which_o i_o find_v 17_o shilling_n so_o that_o 17_o shilling_n be_v the_o great_a fraction_n part_n of_o english_a coin_n agree_v to_o this_o number_n then_o subtract_v 85_o out_o of_o 87426934_o there_o will_v remain_v 02426934_o which_o number_n also_o you_o must_v seek_v in_o the_o table_n of_o english_a coin_n but_o see_v you_o can_v find_v it_o there_o you_o must_v take_v the_o near_a number_n less_o than_o it_o which_o be_v 02083333_o against_o which_o i_o find_v five_o penny_n which_o be_v the_o next_o great_a fraction_n part_n of_o english_a coin_n last_o subtract_v 02083333_o out_o of_o 02426934_o and_o there_o will_v remain_v 00343601_o which_o number_n you_o must_v also_o seek_v in_o the_o table_n of_o english_a coin_n but_o not_o find_v it_o exact_o there_o you_o must_v take_v the_o near_a number_n less_o which_o be_v 003125_o against_o which_o you_o shall_v find_v three_o farthing_n which_o be_v the_o next_o great_a fraction_n part_n of_o english_a coin_n and_o the_o decimal_n 87426934_o do_v in_o value_n signify_v 17_o shilling_n 5_o penny_n 3_o farthing_n and_o something_o more_o for_o 003125_o be_v the_o decimal_n of_o 3_o farthing_n and_o the_o number_n you_o be_v to_o look_v for_o in_o the_o table_n be_v 00343601_o great_a than_o the_o decimal_n of_o 3_o farthing_n wherefore_o if_o you_o subtract_v 003125_o out_o of_o 00343601_o there_o will_v remain_v 31101_o which_o be_v the_o 31101_o 100000_o part_n of_o a_o farthing_n which_o be_v inconsiderable_a see_v the_o follow_a operation_n 87426934_o decimal_n give_v 85_o ......_o decimal_n of_o 17_o s._n 02426934_o first_o remainder_n 02083333_o decimal_n of_o 5_o d._n 00343600_o second_o remainder_n 003125._o decimal_n of_o 3_o q._n 00031101_o decimal_n part_n of_o a_o farthing_n ¶_o and_o here_o note_n that_o whatsoever_o have_v be_v here_o say_v concern_v the_o use_n of_o the_o table_n of_o english_a coin_n the_o same_o order_n be_v to_o be_v observe_v in_o the_o use_n of_o the_o other_o table_n of_o weight_n measure_n time_n etc._n etc._n as_o by_o the_o follow_a example_n if_o you_o make_v trial_n will_v appear_v example_n 1_o if_o this_o decimal_n 48975694_o be_v give_v to_o know_v the_o value_n thereof_o in_o troy_n weight_n you_o shall_v find_v it_o to_o contain_v 15_o ounce_n 17_o peny-weight_n and_o 13_o grain_n 2_o also_o if_o 95075335_o be_v a_o decimal_n give_v and_o it_o be_v require_v to_o find_v the_o value_n thereof_o in_o averdupois_n great_a weight_n you_o shall_v find_v it_o to_o contain_v 3_o quarter_n of_o a_o hundred_o 22_o pound_n 7_o ounce_n and_o 3_o quarter_n of_o a_o ounce_n 3_o likewise_o if_o 70800781_o be_v a_o decimal_n fraction_n give_v you_o shall_v find_v the_o value_n thereof_o in_o averdupois_n little_a weight_n to_o be_v 11_o ounce_n 5_o dram_n and_o one_o quarter_n of_o a_o dram_n 4_o if_o 4375_o be_v a_o decimal_n who_o value_n be_v require_v in_o liquid_a measure_n you_o shall_v find_v it_o to_o contain_v 3_o pint_n and_o a_o half_a 5_o let_v 7148438_o be_v a_o decimal_n give_v who_o value_n be_v require_v in_o dry_a measure_n you_o shall_v find_v it_o to_o contain_v five_o bushel_n 2_o peck_v 3_o quarter_n of_o a_o peck_n and_o 2_o pint_n thus_o have_v i_o show_v you_o the_o use_n of_o these_o decimal_a table_n in_o express_v of_o the_o fraction_n part_n of_o money_n weight_n measure_n etc._n etc._n but_o because_o these_o table_n may_v not_o be_v alwayesat_fw-la hand_n when_o there_o be_v need_n of_o they_o i_o will_v here_o show_v you_o how_o the_o value_n of_o any_o decimal_n give_v may_v