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price_n value_n buy_v sell_v expense_n wage_n exchange_n interest_n profit_n or_o loss_n of_o any_o one_o thing_n of_o like_a kind_n the_o four_o effect_n be_v to_o aid_v to_o compose_v and_o to_o make_v other_o rule_n but_o principal_o the_o rule_n of_o proportion_n call_v the_o golden_a rule_n or_o rule_n of_o three_o and_o the_o reduction_n of_o money_n weight_n and_o measure_n of_o one_o denomination_n into_o another_o by_z â—t_z also_o fraction_n be_v abbreviate_v by_o find_v a_o common_a measurer_n unto_o the_o numerator_n and_o denominator_fw-la thereby_o discover_v commensurable_a number_n if_o you_o divide_v the_o value_n of_o any_o certain_a quantity_n by_o the_o same_o quantity_n the_o quotient_a 〈◊〉_d the_o rate_n or_o value_n of_o â—he_n integer_fw-la as_o 〈◊〉_d eight_o yard_n of_o cloth_n cost_v 96_o shilling_n here_o if_o you_o divide_v 96_o the_o value_n or_o price_n of_o the_o give_v quantity_n by_o 8_o the_o same_o quantity_n the_o quotient_n will_v be_v 12_o s_o 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follow_v quest._n 1._o if_o 22_o thing_n cost_v 66_o shilling_n what_o will_v 1_o such_o like_a thing_n cost_v facit_fw-la 3_o shilling_n for_o if_o you_o divide_v 66_o by_o 22_o the_o quotient_n be_v 3_o for_o the_o answer_n so_o if_o 36_o yard_n or_o ell_n of_o any_o thing_n be_v buy_v or_o sell_v for_o 108_o l._n how_o much_o shall_v 1_o yard_n or_o ell_n be_v buy_v or_o sell_v for_o facit_fw-la 3_o l._n for_o if_o you_o divide_v 108_o l._n by_o 36_o yard_n the_o quotient_n will_v be_v 3_o l._n the_o price_n of_o the_o integer_fw-la quest._n 2._o if_o the_o expense_n charge_n or_o wage_n of_o 7_o year_n amount_n to_o 868_o l._n what_o be_v the_o expense_n charge_n or_o wage_n of_o one_o year_n facit_fw-la 124_o l._n for_o if_o you_o divide_v 868_o the_o wage_n of_o 7_o year_n by_o 7_o the_o number_n of_o year_n the_o quotient_n will_v be_v 124_o l._n for_o the_o answer_n see_v the_o work_n quest._n 3._o if_o the_o content_a of_o a_o superficial_a foot_n be_v 144_o inch_n and_o the_o breadth_n of_o a_o board_n be_v 9_o inch_n how_o many_o inch_n of_o that_o board_n in_o length_n will_v make_v such_o a_o foot_n facit_fw-la 16_o inch_n for_o by_o divide_v 144_o the_o number_n of_o square_a inch_n in_o a_o square_a foot_n by_o 9_o the_o inch_n in_o the_o breadth_n of_o the_o board_n the_o quotient_a be_v 16_o for_o the_o number_n of_o inch_n in_o length_n of_o that_o board_n to_o make_v a_o superficial_a foot_n quest._n 3._o if_o the_o content_a of_o a_o acre_n of_o ground_n be_v 160_o square_a perch_n and_o the_o length_n of_o a_o furlong_n propound_v be_v 80_o perch_n how_o many_o perch_n will_v there_o go_v in_o breadth_n to_o make_v a_o acre_n facit_fw-la 2_o perch_n for_o if_o you_o divide_v 160_o the_o number_n of_o perch_n in_o a_o acre_n by_o 80_o the_o length_n of_o the_o furlong_n in_o perch_n the_o quotient_a be_v 2_o perch_n and_o so_o many_o in_o breadth_n of_o that_o furlong_n will_v make_v a_o acre_n quest._n 5._o if_o there_o be_v 893_o man_n to_o be_v make_v up_o into_o a_o battle_n the_o front_n consist_v of_o 47_o man_n what_o number_n must_v there_o be_v in_o the_o file_n facit_fw-la 19_o deep_a in_o the_o file_n for_o if_o you_o divide_v 893_o the_o number_n of_o man_n by_o 47_o the_o number_n in_o front_n the_o quotient_n will_v be_v 19_o the_o file_n in_o depth_n the_o work_n follow_v quest._n 6._o there_o be_v a_o table_n who_o superficial_a content_n be_v 72_o foot_n and_o the_o breadth_n of_o it_o at_o the_o end_n be_v 3_o foot_n now_o i_o demand_v what_o be_v the_o length_n of_o this_o table_n facit_fw-la 24_o foot_n long_o for_o if_o you_o divide_v 72_o the_o content_a of_o the_o table_n in_o foot_n by_o 3_o the_o breadth_n of_o it_o the_o quotient_a be_v 24_o foot_n for_o the_o length_n thereof_o which_o be_v require_v see_v the_o operation_n as_o follow_v the_o proof_n of_o multiplication_n and_o division_n multiplication_n and_o division_n interchangeable_o prove_v each_o other_o for_o if_o you_o will_v prove_v a_o sum_n in_o division_n whether_o the_o operation_n be_v right_o or_o no_o multiply_v the_o quotient_a by_o the_o divisor_n and_o if_o any_o thing_n remain_v after_o the_o division_n be_v end_v add_v it_o to_o the_o product_n which_o product_n if_o your_o sum_n be_v right_o divide_v will_v be_v equal_a to_o the_o dividend_n and_o contrariwise_o if_o you_o will_v prove_v a_o sum_n in_o multiplication_n divide_v the_o product_n by_o the_o multipliar_a and_o if_o the_o work_n be_v right_o perform_v the_o quotient_n will_v be_v equal_a to_o the_o multiplicand_a see_v the_o example_n where_o the_o work_n be_v do_v and_o undo_v let_v 7654_o be_v give_v to_o be_v multiply_v by_o 3242_o the_o product_n will_v be_v 24814268_o as_o by_o the_o work_n appear_v and_o than_o if_o you_o divide_v the_o say_a product_n 24814268_o by_o 3242_o the_o multipliar_a the_o quotient_n will_v be_v 7654_o equal_a to_o the_o give_v multiplicand_v in_o like_a manner_n to_o prove_v a_o sum_n or_o number_n in_o division_n if_o 24814268_o be_v divide_v by_o 3242_o the_o quotient_n will_v be_v find_v to_o be_v 7654_o then_o for_o proof_n if_o you_o multiply_v 7654_o the_o quotient_a by_o 3242_o the_o divisor_n the_o product_n will_v amount_v to_o 24814268_o equal_a to_o the_o dividend_n or_o you_o may_v prove_v the_o last_o or_o any_o other_o example_n in_o multiplication_n thus_o viz._n divide_v the_o product_n by_o the_o multiplicand_a and_o the_o quotient_n will_v be_v equal_a to_o the_o multipliar_a see_v the_o work_n from_o whence_o arise_v this_o corollary_n that_o any_o operation_n in_o division_n may_v be_v prove_v by_o division_n for_o if_o after_o your_o division_n be_v end_v you_o divide_v the_o dividend_n by_o the_o quotient_a the_o new_a quotient_n thence_o arise_v will_v be_v equal_a to_o the_o divisor_n of_o the_o first_o operation_n for_o trial_n whereof_o let_v the_o last_o example_n be_v again_o repeat_v for_o proof_n whereof_o divide_v again_o 24814268_o by_o the_o quotient_a 7654_o and_o the_o quotient_a thence_o will_v be_v equal_a to_o the_o first_o divisor_n 3242_o see_v the_o work_n but_o in_o prove_v division_n by_o division_n the_o learner_n be_v to_o observe_v this_o follow_a caution_n that_o if_o after_o his_o division_n be_v end_v there_o be_v any_o remainder_n before_o you_o go_v about_o to_o prove_v your_o work_n subtract_v that_o remainder_n out_o of_o your_o dividend_n and_o then_o work_v as_o before_o as_o in_o the_o follow_a example_n where_o it_o be_v require_v to_o divide_v 43876_o by_o 765_o the_o quotient_a here_o be_v 57_o and_o the_o remainder_n be_v 271_o see_v the_o work_n follow_v now_o to_o prove_v this_o work_n subtract_v the_o remainder_n 271_o out_o of_o the_o dividend_n 43876_o and_o there_o remain_v 43605_o for_o a_o new_a dividend_n to_o be_v divide_v by_o the_o former_a quotient_a 57_o and_o the_o quotient_a thence_o arise_v be_v 765_o equal_a to_o the_o give_v divisor_n which_o prove_v the_o operation_n to_o be_v right_o thus_o have_v we_o go_v through_o the_o four_o species_n of_o arithmetic_n viz._n addition_n 1._o subtraction_n multiplication_n and_o division_n upon_o which_o all_o the_o follow_a rule_n and_o all_o other_o operation_n whatsoever_o that_o be_v possible_a to_o be_v wrought_v by_o number_n have_v their_o immediate_a dependence_n and_o by_o they_o be_v resolve_v therefore_o before_o the_o learner_n make_v a_o further_a step_n in_o this_o art_n let_v he_o be_v well_o acquaint_v with_o what_o have_v be_v deliver_v in_o the_o forego_n chapter_n chap._n viii_o of_o reduction_n 1._o reduction_n be_v that_o which_o bring_v together_o 2_o or_o more_o number_n of_o different_a denomination_n into_o one_o denomination_n or_o it_o serve_v to_o change_v or_o alter_v number_n 13.152_o money_n weight_n measure_n or_o time_n from_o one_o denomination_n to_o another_o and_o likewise_o to_o abridge_v fraction_n to_o their_o low_a term_n all_o which_o it_o do_v so_o precise_o that_o the_o first_o proportion_n remain_v without_o the_o least_o jot_n of_o error_n or_o wrong_n commit_v so_o that_o it_o belong_v as_o well_o to_o fraction_n as_o integer_n of_o which_o in_o its_o proper_a place_n reduction_n be_v general_o perform_v either_o by_o multiplication_n or_o division_n from_o whence_o we_o may_v gather_v that_o 2_o reduction_n be_v either_o descend_v or_o ascend_v 3._o reduction_n descend_v be_v when_o it_o be_v require_v to_o reduce_v a_o sum_n or_o number_n of_o a_o great_a denomination_n into_o a_o lesser_a which_o number_n when_o it_o be_v so_o reduce_v shall_v be_v equal_a in_o value_n to_o the_o number_n first_o give_v in_o the_o great_a denomination_n as_o if_o it_o be_v require_v to_o know_v how_o many_o shilling_n 4._o penny_n or_o farthing_n be_v equal_a in_o value_n to_o a_o hundred_o pound_n or_o how_o many_o ounce_n be_v contain_v in_o 45_o hundred_o weight_n or_o how_o many_o day_n hour_n or_o minute_n there_o be_v in_o 240_o year_n etc._n etc._n and_o this_o kind_n of_o reduction_n be_v general_o perform_v by_o multiplication_n 4._o reduction_n ascend_v be_v when_o it_o be_v require_v to_o reduce_v or_o bring_v a_o sum_n or_o number_n of_o a_o small_a denomination_n into_o a_o great_a which_o shall_v be_v equivalent_a to_o the_o give_v number_n as_o suppose_v it_o be_v require_v to_o find_v out_o how_o many_o penny_n shilling_n or_o pound_n be_v equal_a in_o value_n to_o 43785_o farthing_n or_o how_o many_o hundred_o be_v equal_a to_o or_o in_o 3748_o l._n pound_n etc._n etc._n and_o this_o kind_n of_o reduction_n be_v always_o perform_v by_o division_n 5._o when_o any_o sum_n or_o number_n be_v give_v to_o be_v reduce_v into_o another_o denomination_n you_o be_v to_o consider_v whether_o it_o ought_v to_o be_v resolve_v by_o the_o