stand_v between_o they_o or_o what_o more_o be_v due_a to_o a._n in_o order_n whereunto_o i_o first_o set_v down_o the_o sum_n which_o a_o lend_v and_o draw_v a_o line_n underneath_o it_o then_o under_o that_o line_n set_v the_o several_a sum_n of_o payment_n as_o you_o see_v in_o the_o margin_n and_o have_v bring_v the_o several_a  _fw-fr l._n s._n d._n lent_n 564_o 13_o 10_o pay_v at_o several_a paym_n 79_o 16_o 08_o 163_o 18_o 11_o 241_o 15_o 08_o pay_v in_o all_o 485_o 11_o 03_o remain_n 79_o 02_o 07_o sum_n of_o payment_n into_o one_o total_a by_o the_o 5_o rule_n of_o the_o four_o chapter_n forego_v i_o find_v their_o sum_n amount_v to_o 485_o l._n 11_o s._n 3_o d._n which_o i_o subtract_v from_o the_o sum_n first_o lend_v by_o a_o by_o the_o 6_o rule_n of_o this_o chapter_n and_o i_o find_v the_o remainder_n to_o be_v 79_o l._n 02_o s._n 07_o d._n and_o so_o much_o be_v still_o due_a to_o a._n when_o the_o learner_n have_v good_a knowledge_n of_o what_o have_v be_v already_o deliver_v in_o this_o and_o the_o forego_n chapter_n he_o will_v with_o ease_n understand_v the_o manner_n of_o work_v the_o follow_a example_n subtraction_n of_o money_n  _fw-fr l._n s._n d._n l._n s._n d._n qr_n borrow_v 374_o 10_o 03_o 700_o 10_o 11_o 2_o pay_v 79_o 15_o 11_o 9_o 03_o 11_o 3_o remain_n 294_o 14_o 04_o 691_o 06_o 11_o 3_o  _fw-fr l._n s._n d._n l._n s._n d._n qr_n borrow_v 1000_o 00_o 00_o 711_o 03_o 00_o 0_o pay_v 19_o 00_o 06_o 11_o 13_o 00_o 1_o rem_fw-la due_a 980_o 19_o 06_o 699_o 09_o 11_o 3_o  _fw-fr l._n s._n d._n qr_n borrow_v 3300_o 00_o 00_o 0_o pay_v at_o several_a payment_n 170_o 10_o 00_o 0_o 361_o 13_o 10_o 1_o 590_o 03_o 04_o 3_o 73_o 04_o 11_o 3_o pay_v in_o all_o 1195_o 12_o 02_o 3_o remain_v due_a 2104_o 07_o 09_o 1_o subtraction_n of_o troy_n weight_n  _fw-fr l._n oz._n p.w._n gr_n buy_v 174_o 00_o 13_o 00_o sould_n 78_o 04_o 16_o 15_o remain_n 95_o 07_o 16_o 09_o  _fw-fr l._n oz._n p.w._n gr_n buy_v 470_o 10_o 13_o 00_o sold_n at_o several_a time_n 60_o 00_o 00_o 00_o 35_o 10_o 18_o 00_o 16_o 07_o 09_o 08_o 48_o 04_o 00_o 00_o 61_o 11_o 19_o 23_o 23_o 00_o 00_o 00_o sold_n in_o all_o 245_o 10_o 07_o 07_o rem_fw-la unsold_a 225_o 00_o 05_o 17_o subtraction_n of_o apothecary_n weight_n  _fw-fr l._n oz._n d_o scr_n gr_n l._n oz._n d_o scr_n gr_n buy_v 12_o 04_o 3_o 0_o 00_o 20_o 00_o 1_o 0_o 07_o sold_n 8_o 05_o 1_o 1_o 15_o 10_o 00_o 1_o 2_o 12_o remain_n 3_o 11_o 1_o 1_o 05_o 9_o 11_o 7_o 0_o 15_o substraction_n of_o averdupois_n weight_n  _fw-fr c._n qr_n l._n tun_n c_o qrs_a l._n oz._n d_o buy_v 35_o 0_o 15_o 5_o 07_o 1_o 10_o 10_o 05_o sold_n 16_o 1_o 20_o 3_o 17_o 1_o 16_o 09_o 13_o rem_fw-la 18_o 2_o 23_o 1_o 09_o 3_o 22_o 00_o 08_o subtraction_n of_o liquid_a measure_n  _fw-fr tun_n hhd_v gall_n tun_n hhd_a gall_n pt_n buy_v 40_o 1_o 30_o 60_o 3_o 42_o 4_o sold_n 16_o 1_o 40_o 15_o 3_o 46_o 6_o remain_n 23_o 3_o 53_o 44_o 3_o 58_o 6_o substraction_n of_o dry_a measure_n  _fw-fr chal._n qr_n bush_n pec_fw-la ch._n qr_n bush_n pec_fw-la buy_v 100_o 0_o 00_o 0_o 73_o 2_o 3_o 2_o sold_n 54_o 1_o 04_o 3_o 46_o 2_o 3_o 3_o remain_n 45_o 2_o 03_o 1_o 26_o 3_o 7_o 3_o substraction_n of_o long_a measure_n  _fw-fr yard_n qrs_fw-fr nails_o yard_n qr_v nail_n buy_v 160_o 1_o 0_o 344_o 0_o 1_o sold_n 64_o 1_o 2_o 177_o 1_o 3_o remain_n 95_o 3_o 2_o 166_o 2_o 2_o subtraction_n of_o land_n measure_n  _fw-fr acre_n rood_n perch_n acre_n rood_n perch_n buy_v 140_o 2_o 13_o 600_o 0_o 00_o sold_n 70_o 3_o 22_o 54_o 0_o 16_o remain_n 69_o 2_o 31_o 545_o 3_o 24_o the_o proof_n of_o subtraction_n 8._o when_o your_o subtraction_n be_v end_v if_o you_o desire_v to_o prove_v your_o work_n whether_o it_o be_v true_a or_o no_o then_o add_v the_o remainder_n to_o the_o minor_a number_n and_o if_o the_o aggregate_v of_o these_o two_o be_v equal_a to_o the_o major_a number_n than_o be_v your_o operation_n true_a otherwise_o false_a thus_o let_v we_o prove_v the_o first_o example_n of_o the_o five_o rule_n of_o this_o chapter_n where_o after_o subtraction_n be_v end_v the_o number_n stand_v as_o in_o the_o margin_n the_o remainder_n or_o difference_n be_v 283676_o now_o to_o prove_v the_o work_n i_o add_v the_o say_a remainder_n 283676_o to_o the_o minor_a number_n 153827_o by_o the_o four_o rule_n of_o the_o forego_n chapter_n and_o i_o find_v the_o sum_n or_o aggregate_v to_o be_v 437503_o equal_a to_o the_o major_a number_n or_o number_n from_o whence_o the_o lesser_a be_v subtract_v behold_v the_o work_n in_o the_o margin_n the_o proof_n of_o another_o example_n may_v be_v of_o the_o first_o example_n of_o the_o six_o rule_n of_o this_o chapter_n where_o it_o be_v require_v to_o subtract_v 57_o l._n 16_o s._n 03_o d._n 2_o qr_n from_o 375_o l._n 13_o s._n 07_o d._n qr_n and_o by_o the_o rule_n i_o find_v the_o remainder_n to_o be_v 317_o l._n 17_o s._n 03_o d._n 3_o qr_n now_o to_o prove_v it_o i_o add_v the_o say_a remainder_n 317_o l._n 17_o s._n l._n s._n d._n qr_n 375_o 13_o 07_o 1_o 57_o 16_o 03_o 2_o 317_o 17_o 03_o 3_o 375_o 13_o 07_o 1_o 03_o d._n 3_o qr_n to_o the_o minor_a number_n 57_o l._n 16_o s._n 03_o d._n 2_o qr_n and_o their_o sum_n be_v 375_o l._n 13_o s._n 07_o d._n 1_o qr_n equal_a to_o the_o major_a number_n which_o prove_v the_o work_n to_o be_v true_a but_o if_o it_o have_v happen_v to_o have_v be_v either_o more_o or_o less_o than_o the_o say_v major_a number_n than_o the_o operation_n have_v be_v false_a 9_o the_o general_a effect_n of_o subtraction_n be_v to_o find_v the_o difference_n or_o excess_n between_o two_o number_n and_o the_o rest_n of_o a_o payment_n make_v of_o a_o great_a sum_n the_o date_n of_o book_n print_v the_o age_n of_o any_o thing_n by_o know_v the_o present_a year_n and_o the_o year_n wherein_o they_o be_v make_v create_v or_o build_v and_o such_o like_a the_o question_n appropriate_v to_o this_o rule_n be_v such_o as_o follow_v quest._n 1._o what_o difference_n be_v there_o between_o one_o thing_n of_o 125_o foot_n long_o and_o another_o of_o 66_o foot_n long_o to_o resolve_v this_o question_n i_o first_o set_v down_o the_o major_a or_o great_a number_n 125_o and_o under_o it_o the_o minor_a or_o lesser_a number_n 66_o as_o be_v direct_v in_o the_o three_o rule_n of_o this_o chapter_n and_o according_a to_o the_o four_o rule_n of_o the_o same_o i_o subtract_v the_o minor_a from_o the_o major_a and_o the_o remainder_n excess_n or_o difference_n i_o find_v to_o be_v 59_o see_v the_o work_n in_o the_o margin_n quest._n 2._o a_o gentleman_n owe_v a_o merchant_n 365_o l._n whereof_o he_o have_v pay_v 278_o l._n what_o more_o do_v he_o owe_v to_o give_v a_o answer_n to_o this_o question_n i_o first_o set_v down_o the_o major_a number_n 365_o l._n and_o under_o it_o i_o place_v 278_o the_o minor_a and_o subtract_v the_o one_o from_o the_o other_o and_o thereby_o i_o discover_v the_o excess_n difference_n or_o remainder_n to_o be_v 87_o and_o so_o much_o be_v still_o due_a to_o the_o creditor_n quest._n 3._o a_o obligation_n be_v write_v book_n print_v a_o child_n bear_v a_o church_n build_v or_o any_o other_o thing_n make_v in_o the_o year_n of_o our_o lord_n 1572_o and_o now_o we_o account_v the_o year_n of_o our_o lord_n 1677_o the_o question_n be_v to_o know_v the_o age_n of_o the_o say_a thing_n that_o be_v how_o many_o year_n be_v pass_v since_o the_o say_a thing_n be_v make_v i_o say_v if_o you_o subtract_v the_o lesser_a number_n 1572_o from_o the_o great_a 1677_o the_o remainder_n will_v be_v 105_o and_o so_o many_o year_n past_a be_v since_o the_o make_n of_o the_o say_a thâ—ngs_n quest._n 4._o there_o be_v 3_o town_n lie_v in_o a_o straight_a line_n viz._n london_n huntingdon_n and_o york_n now_o the_o distance_n between_o the_o fâ—rthest_a of_o these_o town_n viz._n london_n and_o york_n be_v 151_o mile_n and_o from_o london_n to_o huntingdon_n be_v 49_o mile_n i_o demand_v how_o far_o it_o be_v from_o huntingdon_n to_o york_n to_o resolve_v this_o question_n subtract_v 49_o the_o 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ingenious_a cocker_n now_o to_o rest_n thou_o be_v go_v no_n art_n can_v show_v thou_o full_o but_o thy_o own_o thy_o rare_a arithmetic_n alone_o can_v show_v the_o vast_a sum_n of_o thanks_o we_o for_o thy_o labour_n cocker_n arithmetic_n be_v a_o plain_a and_o familiar_a method_n suitable_a to_o the_o mean_a capacity_n for_o the_o full_a understanding_n of_o that_o incomparable_a art_n as_o it_o be_v now_o teach_v by_o the_o able_a schoolmaster_n in_o city_n and_o country_n compose_v by_o edward_n cocker_v late_a practitioner_n in_o the_o art_n of_o write_v arithmetic_n and_o engrave_v be_v that_o so_o long_o since_o promise_v to_o the_o world_n peruse_v and_o publish_v by_o john_n hawkins_n write_v master_n near_o st._n george_n church_n in_o southwark_n by_o the_o author_n correct_v copy_n and_o commend_v to_o the_o world_n by_o many_o eminent_a mathematician_n and_o writing-master_n in_o and_o near_a london_n license_v sept._n 3._o 1677._o roger_n l'_fw-mi estrange_v london_n 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to_o smother_v a_o work_n of_o so_o considerable_a a_o moment_n not_o question_v but_o it_o may_v be_v as_o kind_o accept_v as_o if_o it_o have_v be_v present_v by_o his_o own_o hand_n the_o method_n be_v familiar_a and_o easy_a discover_v as_o well_o the_o theoric_n as_o the_o practic_n of_o that_o most_o necessary_a art_n of_o vulgar_a arithmetic_n and_o thou_o may_v speedy_o expect_v his_o decimal_n logarithmetical_a and_o algebraical_a arithmetic_n concern_v which_o thou_o have_v a_o further_a account_n give_v at_o the_o end_n of_o this_o book_n in_o the_o mean_a time_n judge_v favourable_o of_o the_o present_a undertake_n and_o thou_o will_v oblige_v he_o who_o be_v thou_o to_o serve_v thou_o john_n hawkins_n from_o my_o school_n near_o st._n george_n church_n in_o southwark_n nou._n 29._o 1677._o mr._n edward_n cocker_n proem_n or_o preface_n by_o the_o sacred_a influence_n of_o divine_a providence_n i_o have_v be_v instrumental_a to_o the_o benefit_n of_o many_o by_o virtue_n 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accommodate_v this_o composure_n for_o his_o most_o worthy_a service_n let_v his_o own_o profitable_a experience_n be_v judge_n second_o for_o your_o service_n most_o excellent_a professor_n who_o understanding_n soar_v to_o the_o subliâ—â—â—y_n of_o the_o theory_n and_o practice_n of_o this_o noble_a science_n be_v this_o arithmetical_a tractate_n compose_v which_o you_o may_v please_v to_o employ_v as_o a_o monitor_n to_o instruct_v your_o young_a tyroe_n and_o thereby_o take_v occasion_n to_o reserve_v your_o precious_a moment_n which_o may_v be_v exhaust_v that_o way_n for_o your_o more_o important_a affair_n three_o for_o you_o the_o ingenious_a offspring_n of_o happy_a parent_n who_o will_v willing_o pay_v the_o full_a price_n of_o industry_n and_o exercise_n for_o those_o art_n and_o choice_a accomplishment_n which_o may_v contribute_v to_o the_o felicity_n of_o your_o future_a state_n for_o you_o i_o say_v ingenious_a practitioner_n be_v this_o work_n compose_v which_o may_v prove_v the_o pleasure_n of_o your_o youth_n and_o the_o glory_n of_o your_o age_n last_o for_o you_o the_o pretend_a numerist_n of_o this_o vapour_a age_n who_o be_v more_o disingenuous_o witty_a to_o propound_v unnecessary_a question_n than_o ingenious_o judicious_a to_o resolve_v such_o as_o be_v necessary_a for_o you_o be_v this_o book_n compose_v and_o publish_v if_o you_o will_v deny_v yourselves_o so_o much_o as_o to_o invert_v the_o stream_n of_o your_o ingenuity_n and_o by_o studious_o confer_v with_o the_o note_n name_n order_n progress_n species_n property_n propriety_n proportion_n power_n affection_n and_o application_n of_o number_n deliver_v herein_o become_v such_o artist_n indeed_o as_o you_o now_o only_o seem_v to_o be_v this_o arithmetic_n ingenious_o observe_v and_o diligent_o practise_v will_v turn_v to_o good_a account_n to_o all_o that_o shall_v be_v concern_v in_o account_n all_o who_o rule_n be_v ground_v on_o verity_n and_o deliver_v with_o sincerity_n the_o 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john_n collens_n novemb_n 27_o 1677._o this_o manual_a of_o arithmetic_n be_v recommend_v to_o the_o world_n by_o we_o who_o name_n be_v subscribe_v viz._n mr._n john_n collens_n math._n mr._n james_n atkinson_n math._n mr._n peter_n perkins_n math._n mr._n rich._n noble_a of_o guildford_n mr._n rich._n laurence_n senior_n mr._n eleazar_n wigan_n mr._n benj._n williams_n mr._n luke_n talbot_n mr._n william_n norgate_n mr._n william_n mason_n m._n steph._n thomas_n mr._n peter_n storey_n mr._n benj._n tichbourne_n mr._n joseph_n symmond_n mr._n jerem._n milles_n mr._n josiah_n cuffley_n mr._n john_n hawkins_n a_o table_n of_o the_o content_n of_o this_o book_n  _fw-fr chap._n pag._n notation_n of_o number_n 1_o 1_o of_o the_o natural_a division_n of_o integer_n and_o the_o denomination_n of_o their_o part_n 2_o 18_o of_o the_o species_n or_o kind_n of_o arithmetic_n 3_o 31_o of_o addition_n of_o whole_a number_n 4_o 33_o of_o substraction_n of_o whole_a number_n 5_o 46_o of_o multiplication_n of_o whole_a number_n 6_o 60_o of_o division_n
rule_n descend_v or_o ascend_v viz._n by_o multiplication_n or_o division_n if_o it_o be_v to_o be_v perform_v by_o multiplication_n consider_v how_o many_o part_n of_o the_o denomination_n into_o which_o you_o will_v reduce_v it_o be_v contain_v in_o a_o unit_fw-la or_o integer_fw-la of_o the_o give_a number_n and_o multiply_v the_o say_v give_v number_n thereby_o and_o the_o product_n thereof_o will_v be_v the_o answer_n to_o the_o question_n as_o if_o the_o question_n be_v in_o 438_o l._n pound_n how_o many_o shilling_n here_o i_o consider_v that_o in_o one_o pound_n be_v 20_o shilling_n and_o that_o the_o number_n of_o shilling_n in_o 38_o l._n pound_n will_v be_v 20_o time_n 38_o wherefore_o i_o multiply_v 38_o l._n by_o 20_o and_o that_o product_n be_v 760_o and_o so_o many_o shilling_n be_v contain_v in_o 38_o pound_n but_o when_o there_o be_v a_o denomination_n or_o denomination_n between_o the_o number_n give_v and_o the_o number_n require_v you_o may_v if_o you_o please_v reduce_v it_o into_o the_o next_o inferior_a denomination_n and_o then_o into_o the_o next_o low_o than_o that_o etc._n etc._n until_o you_o have_v bring_v it_o into_o the_o denomination_n require_v as_o for_o example_n let_v it_o be_v demand_v in_o 132_o pound_n how_o many_o farthing_n first_o i_o multiply_v 132_o the_o number_n of_o pound_n give_v by_o 20_o to_o bring_v it_o into_o shilling_n and_o it_o make_v 2643_o shilling_n then_o do_v i_o multiply_v the_o shilling_n 2640_o by_o 12_o to_o bring_v they_o into_o penny_n and_o it_o produce_v 31680_o and_o so_o many_o penny_n be_v contain_v in_o 2640_o shilling_n or_o 132_o pound_n then_o do_v i_o multiply_v the_o penny_n viz._n 31680_o by_o 4_o to_o bring_v they_o into_o farthing_n because_o 4_o farthing_n be_v a_o penny_n and_o i_o find_v the_o product_n thereof_o to_o be_v 126720_o and_o so_o many_o farthing_n be_v in_o equal_a value_n to_o 132_o pound_n the_o work_n be_v manifest_a in_o the_o margin_n and_o if_o the_o number_n propound_v to_o be_v reduce_v be_v to_o be_v divide_v or_o wrought_v by_o the_o rule_n ascend_v consider_v how_o many_o of_o the_o give_v number_n be_v equal_a to_o a_o unit_fw-la or_o integer_fw-la in_o that_o denomination_n to_o which_o you_o will_v reduce_v your_o give_a number_n and_o make_v that_o your_o divisor_n and_o the_o give_v number_n your_o dividend_n and_o the_o quotient_a thence_o arise_v will_v be_v the_o number_n seek_v or_o require_v as_o for_o example_n let_v it_o be_v require_v to_o reduce_v 2640_o shilling_n into_o pound_n here_o i_o consider_v that_o 20_o shilling_n be_v equal_a to_o one_o pound_n wherefore_o i_o divide_v 2640_o the_o give_v number_n by_o 20_o and_o the_o quotient_n be_v 132_o and_o so_o many_o pound_n be_v contain_v in_o 2640_o shilling_n in_o reduction_n descend_v and_o ascend_v the_o learner_n be_v advise_v to_o take_v particular_a notice_n of_o the_o table_n deliver_v in_o the_o second_o chapter_n of_o this_o book_n where_o he_o may_v be_v inform_v what_o multipliars_n or_o divisor_n to_o make_v use_n of_o in_o the_o reduce_n of_o any_o number_n to_o any_o other_o denomination_n whatsoever_o especial_o english_a money_n weight_n measure_n time_n and_o motion_n but_o in_o this_o place_n it_o be_v not_o convenient_a to_o meddle_v with_o foreign_a coin_n weight_n or_o measure_n but_o if_o in_o reduction_n ascend_v it_o happen_v that_o there_o be_v a_o denomination_n or_o denomination_n between_o the_o number_n give_v and_o the_o number_n require_v than_o you_o may_v reduce_v your_o number_n give_v into_o the_o next_o superior_a denomination_n and_o when_o it_o be_v so_o reduce_v bring_v it_o into_o the_o next_o above_o that_o and_o so_o on_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 let_v it_o be_v demand_v in_o 126720_o farthing_n how_o many_o pound_n first_o i_o divide_v my_o give_a number_n be_v farthing_n by_o 4_o to_o bring_v they_o into_o penny_n because_o 4_o farthing_n make_v one_o penny_n and_o they_o be_v 31680_o penny_n than_o i_o divide_v 31680_o penny_n by_o 12_o and_o the_o quotient_n give_v 2640_o shilling_n and_o then_o i_o divide_v 2640_o shilling_n by_o 20_o and_o the_o quotient_n give_v 132_o pound_n which_o be_v equal_a in_o value_n to_o 126720_o farthing_n see_v the_o whole_a work_n as_o it_o follow_v 6._o when_o the_o number_n give_v to_o be_v reduce_v consist_v of_o divers_a denomination_n as_o pound_n shilling_n penny_n and_o farthing_n or_o of_o hundred_o quarter_n pound_n and_o ounce_n etc._n etc._n then_o you_o be_v to_o reduce_v the_o high_a or_o great_a denomination_n into_o the_o next_o inferior_a and_o add_v thereunto_o the_o number_n stand_v in_o that_o denomination_n which_o your_o great_a or_o high_a number_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 number_n stand_v in_o that_o denomination_n do_v so_o until_o you_o have_v bring_v the_o number_n give_v into_o the_o denomination_n propose_v as_o if_o it_o be_v require_v to_o reduce_v 48_o l._n 13_o s._n 10_o d._n into_o penny_n first_o i_o bring_v 48_o l._n into_o shilling_n by_o multiply_v it_o by_o 20_o and_o the_o product_n be_v 960_o shilling_n to_o which_o i_o add_v the_o 13_o shilling_n and_o they_o make_v 973_o than_o i_o multiply_v 973_o by_o 12_o to_o bring_v the_o shilling_n into_o penny_n and_o they_o make_v 11676_o penny_n to_o which_o i_o add_v the_o 10_o penny_n and_o they_o make_v 11686_o penny_n for_o the_o answer_n see_v the_o whole_a work_n do_v 7._o if_o in_o reduction_n ascend_v after_o division_n be_v end_v any_o thing_n remain_v such_o remainder_n be_v of_o the_o same_o denomination_n with_o the_o dividend_n example_n in_o reduction_n of_o coyn._n quest._n 1._o in_o 438_o l._n how_o many_o shilling_n facit_fw-la 8760_o shilling_n for_o multiply_v 438_o by_o twenty_o the_o product_n amount_v to_o so_o much_o quest._n 2._o in_o 467_o l._n how_o many_o penny_n first_o multiply_v the_o give_v number_n of_o pound_n 467_o by_o 20_o to_o bring_v it_o into_o shilling_n and_o it_o make_v 9340_o shilling_n then_o multiply_v the_o shilling_n by_o 12_o and_o it_o produce_v 112080_o penny_n thus_o or_o it_o may_v be_v resolve_v thus_o viz._n multiply_v the_o give_v number_n of_o pound_n 467_o by_o 240_o the_o number_n of_o penny_n in_o a_o pound_n and_o the_o product_n be_v the_o same_o viz._n 112080_o penny_n quest._n 3._o in_o 5673_o l._n how_o many_o farthing_n first_o multiply_v the_o give_v number_n by_o 20_o to_o bring_v it_o into_o shilling_n and_o it_o produce_v 113460_o then_o multiply_v that_o product_n by_o 12_o to_o bring_v it_o into_o penny_n and_o it_o produce_v 1361520_o then_o last_o multiply_v the_o penny_n by_o 4_o and_o it_o produce_v 5446080_o farthing_n see_v the_o operation_n or_o this_o question_n may_v have_v be_v thus_o resolve_v viz._n multiply_v 5673_o the_o give_v number_n of_o pound_n by_o 960_o the_o number_n of_o farthing_n in_o a_o pound_n and_o it_o produce_v the_o same_o effect_n otherwise_o thus_o first_o bring_v the_o give_v number_n 5673_o l._n into_o shilling_n and_o multiply_v the_o shilling_n by_o 48_o the_o number_n of_o farthing_n in_o a_o shilling_n and_o the_o same_o effect_n be_v thereby_o likewise_o produce_v viz._n these_o various_a way_n of_o operate_n be_v express_v to_o inform_v the_o judgement_n of_o the_o learner_n with_o the_o reason_n of_o the_o rule_n more_o way_n may_v be_v show_v but_o these_o be_v sufficient_a even_o for_o the_o mean_a capacity_n quest._n 4._o in_o 458_o l._n 16_o s._n 07_o d._n 3_o qr_n how_o many_o farthing_n to_o resolve_v this_o question_n consider_v the_o 6_o rule_n of_o this_o chapter_n and_o work_v as_o you_o be_v there_o direct_v and_o you_o will_v find_v the_o aforesaid_a give_v number_n to_o amount_v to_o 440479_o farthing_n viz._n this_o last_o question_n or_o any_o other_o of_o this_o kind_n viz._n where_o the_o number_n give_v to_o be_v reduce_v consist_v of_o several_a denomination_n may_v be_v more_o concise_o resolve_v thus_o viz._n when_o you_o multiply_v the_o pound_n by_o 20_o to_o bring_v they_o into_o shilling_n to_o the_o product_n of_o the_o first_o figure_n add_v the_o figure_n stand_v in_o the_o place_n of_o unit_n in_o the_o denomination_n of_o shilling_n but_o because_o the_o first_o figure_n in_o the_o multipliar_a be_v 0_o i_o say_v 0_o time_n 8_o be_v nothing_o but_o 6_o be_v 6_o which_o i_o put_v down_o for_o the_o first_o figure_n in_o the_o product_n then_o because_o this_o multipliar_a be_v 0_o i_o go_v on_o no_o further_a with_o it_o for_o if_o i_o shall_v the_o whole_a product_n will_v be_v 0_o but_o proceed_v and_o when_o i_o come_v to_o multiply_v by_o the_o second_o figure_n in_o the_o multipliar_a to_o the_o product_n of_o
10_o s._n quest._n 28._o if_o 100_o l._n in_o 12_o month_n gain_n 60._o interest_n how_o much_o will_v it_o gain_v in_o 7_o month_n at_o that_o rate_n answer_v 3_o l._n 10_o s._n quest._n 29._o a_o certain_a usurer_n put_v out_o 75_o l._n for_o 12_o month_n and_o receive_v principle_n and_o interest_n 81_o l._n i_o demand_v what_o rate_n per_fw-la cent._n he_o receive_v interest_n answer_v 8_o l._n per_fw-la cent._n quest._n 30._o a_o grocer_n buy_v 2_o chest_n of_o sugar_n the_o one_o weigh_v neat_a 17_o c._n 3_o qr_n 14_o l._n at_o 2_o l._n 6_o s._n 8_o d._n per_fw-la c._n the_o other_o weigh_v neat_a 18_o c._n 1_o qr_n 21_o l._n at_o 4_o d_o ½_o per_fw-la l._n which_o he_o mingle_v together_o now_o i_o desire_v to_o know_v how_o much_o a_o c._n weight_n of_o this_o mixture_n be_v worth_a answer_v 2_o l._n 4_o s._n 3_o d._n 2_o 530_o â—â—â—_o qrs_n quest._n 31._o two_o man_n viz._n a_o and_o b_o depart_v both_o from_o one_o place_n the_o one_o go_v east_n the_o other_o west_n the_o one_o travail_v 4_o mile_n a_o day_n the_o other_o 5_o mile_n a_o day_n how_o far_o be_v they_o distant_a the_o 9th_o day_n after_o their_o departure_n answer_v 91_o mile_n quest._n 32._o a_o fly_v every_o day_n 40_o mile_n be_v pursue_v the_o four_o day_n after_o by_o b_o 7._o post_v 50_o mile_n a_o day_n now_o the_o question_n be_v in_o how_o many_o day_n and_o after_o how_o many_o mile_n travail_n will_v a_o be_v overtake_v answer_v b_o overtake_v he_o in_o 12_o day_n when_o they_o have_v 〈◊〉_d 600_o mile_n 11._o the_o general_n effect_v of_o the_o rule_n of_o three_o direct_v be_v contain_v in_o the_o definition_n of_o the_o same_o that_o be_v to_o find_v a_o four_o number_n in_o proportion_n consist_v of_o two_o equal_a reason_n as_o have_v be_v full_o show_v in_o all_o the_o forego_n example_n the_o second_o effect_n be_v by_o the_o price_n or_o value_n of_o one_o thing_n to_o find_v the_o price_n or_o value_n of_o many_o thing_n of_o like_a kind_n the_o three_o effect_n be_v by_o the_o price_n or_o value_n of_o many_o thing_n to_o find_v the_o price_n of_o 1_o or_o by_o the_o price_n of_o many_o thing_n the_o say_a price_n be_v 1_v to_o find_v the_o price_n of_o many_o thing_n of_o like_a kind_n the_o four_o effect_n be_v by_o the_o price_n or_o value_n of_o many_o thing_n to_o find_v the_o price_n or_o value_n of_o many_o thing_n of_o like_a kind_n the_o five_o effect_n be_v thereby_o to_o reduce_v any_o number_n of_o money_n weight_n or_o measure_n the_o one_o sort_n into_o the_o other_o as_o in_o the_o rule_n of_o reduction_n contain_v in_o the_o 8_o chapter_n forego_v example_n of_o its_o various_a effect_n have_v be_v already_o answer_v 12._o the_o rule_n of_o 3_o direct_v be_v thus_o prove_v viz._n multiply_v the_o first_o number_n by_o the_o four_o direct_v and_o note_v the_o product_n then_o multiply_v the_o second_o number_n by_o the_o three_o and_o if_o this_o product_n be_v equal_a to_o the_o product_n of_o the_o first_o and_o four_o than_o the_o work_n be_v right_o perform_v otherwise_o it_o be_v erroneous_a so_o the_o first_o question_n of_o this_o chapter_n who_o answer_n or_o four_o number_n we_o find_v to_o be_v 18_o s._n be_v thus_o prove_v viz._n the_o first_o number_n be_v 4_o which_o multiply_v by_o 18_o the_o four_o produce_v 72._o and_o the_o second_o and_o three_o number_n be_v 12_o and_o 6_o which_o multiply_v together_o produce_v 72_o equal_a to_o the_o product_n of_o the_o first_o and_o four_o and_o therefore_o i_o conclude_v the_o work_n to_o be_v right_o perform_v always_o observe_v that_o if_o any_o thing_n remain_v after_o you_o have_v divide_v the_o product_n of_o the_o second_o and_o three_o number_n by_o the_o first_o such_o remainder_n in_o prove_v the_o same_o must_v be_v add_v to_o the_o product_n of_o the_o first_o and_o four_o number_n who_o sum_n will_v be_v equal_a to_o the_o product_n of_o the_o second_o and_o three_o the_o second_o number_n be_v of_o the_o same_o denomination_n with_o the_o four_o and_o the_o first_o with_o the_o same_o denomination_n of_o the_o three_o so_o the_o four_o question_n of_o this_o chapter_n be_v again_o repeat_v viz._n if_o 14_o l._n of_o tobacco_n cost_v 27_o s._n what_o will_v 478_o l._n cost_n at_o that_o rate_n the_o answer_v or_o four_o number_n be_v 46_o l._n 01_o s._n 10_o d._n 1_o qr_n 2_o 14_o which_o be_v thus_o prove_v viz._n bring_v the_o four_o number_n into_o farthing_n and_o it_o make_v 44249_o which_o multiply_v by_o the_o first_o number_n 14_o produce_v 619488_o the_o 2_o which_o remain_v be_v add_v thereto_o then_o because_o i_o reduce_v my_o four_o number_n into_o farthing_n i_o reduce_v my_o second_o viz._n 27_o s._n into_o farthing_n and_o they_o be_v 1296_o which_o multiply_v by_o the_o three_o number_n 478_o their_o product_n be_v 619488_o equal_a to_o the_o product_n of_o the_o first_o and_o four_o number_n wherefore_o i_o conclude_v the_o operation_n to_o be_v true_a this_o be_v a_o infallible_a way_n to_o prove_v the_o rule_n of_o 3_o direct_v and_o it_o be_v deduce_v from_o the_o twelve_o sect._n of_o the_o 9th_o chap._n of_o this_o book_n thus_o much_o concern_v the_o single_a rule_n of_o 3_o direct_v and_o i_o question_v not_o but_o by_o this_o time_n the_o learner_n be_v sufficient_o qualify_v to_o resolve_v any_o question_n pertinent_a to_o this_o rule_n not_o rely_v upon_o fraction_n or_o geometrical_a magnitude_n those_o that_o be_v desirous_a to_o see_v the_o demonstration_n of_o this_o rule_n let_v they_o read_v the_o 6_o chapter_n of_o the_o ingenious_a mr._n kersey_n appendix_n to_o wingates_n arithmetic_n or_o the_o 6_o chapter_n of_o mr._n oughtred_n incomparable_a clavis_fw-la mathematicae_fw-la by_o both_o which_o author_n this_o rule_n be_v large_o demonstrate_v be_v ground_v upon_o the_o 19_o prop._n of_o the_o seven_o and_o the_o 19_o prop._n of_o the_o 9th_o of_o euclid_n elem._n chap._n xi_o the_o single_a rule_n of_o three_o inverse_n 1._o the_o golden_a rule_n or_o rule_n of_o 3_o inverse_n be_v when_o there_o be_v 3_o number_n give_v to_o find_v a_o four_o in_o such_o proportion_n to_o the_o 3_o give_v number_n so_o as_o the_o four_o proceed_v from_o the_o second_o according_a to_o the_o same_o rate_n reason_n or_o proportion_n that_o the_o first_o proceed_v from_o the_o three_o or_o the_o proportion_n be_v as_o the_o three_o number_n be_v in_o proportion_n to_o the_o second_o 14._o so_o be_v the_o first_o to_o the_o four_o so_o if_o the_o 3_o number_n give_v be_v 8_o 12_o and_o 16_o and_o it_o be_v require_v to_o find_v a_o four_o number_n in_o a_o invert_v proportion_n to_o these_o i_o say_v that_o as_o 16_o the_o three_o number_n be_v the_o double_a of_o the_o first_o term_n or_o number_n 8_o so_o must_v 12_o the_o second_o number_n be_v the_o double_a of_o the_o four_o so_o will_v you_o find_v the_o four_o term_n or_o number_n to_o be_v 6._o and_o as_o in_o the_o rule_n of_o 3_o direct_v you_o multiply_v the_o second_o and_o three_o together_o and_o divide_v their_o product_n for_o a_o four_o proportional_a number_n so_o 2._o in_o the_o rule_n of_o 3_o inverse_v you_o must_v multiply_v the_o second_o term_n by_o the_o first_o or_o first_o term_n by_o the_o second_o and_o divide_v the_o product_n thereof_o by_o the_o 3d._a term_n so_o the_o quotient_n will_v give_v you_o the_o four_o term_v seek_v in_o a_o invert_v proportion_n the_o same_o order_n be_v observe_v in_o this_o rule_n as_o in_o the_o rule_n of_o 3_o direct_v for_o place_v or_o dispose_n of_o the_o give_v number_n and_o after_o your_o number_n be_v place_v in_o order_n that_o you_o may_v know_v whether_o your_o question_n be_v to_o be_v resolve_v by_o the_o rule_n direct_n or_o inverse_v observe_v the_o general_a rule_n follow_v 3._o when_o your_o question_n be_v state_v and_o your_o number_n orderly_o dispose_v consider_v in_o the_o one_a place_n whether_o the_o four_o term_n or_o number_v seek_v aught_o to_o be_v more_o or_o less_o than_o the_o second_o term_n which_o you_o may_v easy_o do_v and_o if_o it_o be_v require_v to_o be_v more_o or_o great_a than_o the_o second_o term_n than_o the_o lesser_a extreme_a must_v be_v your_o divisor_n but_o if_o it_o require_v less_o than_o the_o big_a extreme_a must_v be_v your_o divisor_n in_o this_o case_n the_o one_a and_o 3d_o number_n be_v call_v extreme_n in_o respect_n of_o the_o second_o and_o have_v find_v out_o your_o divisor_n you_o may_v know_v whether_o your_o question_n belong_v to_o the_o rule_n direct_n or_o inverse_v for_o if_o the_o 3d._n term_v be_v your_o divisor_n than_o it_o be_v inverse_v but_o if_o the_o first_o term_n be_v your_o