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and_o again_o there_o be_v nothing_o in_o this_o example_n or_o any_o other_o of_o whole_a number_n but_o i_o have_v teach_v you_o the_o rule_n of_o they_o already_o scholar_n then_o i_o trust_v by_o practice_n to_o attain_v the_o use_n of_o it_o and_o be_v this_o all_o that_o i_o shall_v learn_v of_o subtraction_n master_n yea_o save_v that_o as_o you_o have_v see_v in_o addition_n there_o be_v number_n of_o diverse_a denomination_n in_o which_o the_o work_n be_v not_o much_o unlike_a yet_o without_o some_o instruction_n be_v give_v of_o it_o it_o may_v seem_v to_o a_o learner_n more_o difficulte_n then_o in_o deed_n it_o be_v therefore_o i_o will_v brieflye_v show_v you_o the_o use_n of_o it_o only_o by_o one_o example_n or_o two_o a_o certain_a man_n owe_v to_o i_o 14_o lb_n 12_o s_o 8_o d_o of_o which_o he_o pay_v i_o at_o one_o time_n 4_o lb_n 6_o s_o 8_o d_o at_o a_o other_o time_n 3_o lb_n and_o at_o a_o other_o 2_o lb_n 3_o s_o 4_o d_o and_o last_o of_o all_o 6_o s_z 8_o d._n now_o will_v i_o know_v what_o remain_v unpayde_v yet_o therefore_o i_o set_v my_o sum_n thus_o scholar_n sir_n i_o pray_v you_o why_o do_v you_o write_v 2_o lb._n for_o the_o common_a speech_n use_v rather_o to_o say_v 40_o s_o master_n we_o must_v here_o use_v the_o denomination_n that_o be_v great_a in_o any_o sum_n so_o that_o we_o may_v not_o write_v according_a as_o we_o use_v to_o speak_v say_v 16_o d._n 18_o d_o or_o likeways_o 7_o groat_n 8_o groat_n 24_o s_o 40_o s_o 48_o s_o and_o such_o other_o but_o we_o must_v write_v
prove_v it_o but_o now_o i_o thank_v you_o i_o have_v well_o learned_a the_o art_n of_o subtraction_n &_o the_o prove_v of_o it_o both_o by_o 9_o and_o by_o addition_n and_o now_o i_o will_v be_v glad_a to_o know_v how_o i_o may_v prove_v addition_n by_o subtraction_n master_n then_o mark_v you_o this_o subtraction_n the_o proof_n of_o addition_n by_o subtraction_n when_o you_o have_v end_v your_o addition_n take_v the_o number_n all_o that_o you_o do_v add_v to_o the_o high_a sum_n and_o deduct_v or_o subtract_v they_o from_o the_o gross_a sum_n that_o do_v resulte_v and_o if_o the_o remayn_a be_v like_a to_o the_o high_a number_n then_o have_v you_o do_v well_o else_o not_o as_o for_o example_n i_o take_v one_o of_o the_o sum_n that_o i_o do_v add_v before_o which_o be_v this_o that_o follow_v here_o then_o do_v i_o come_v to_o the_o middle_a number_n because_o here_o in_o this_o example_n be_v only_o three_o number_n and_o subtracte_v that_o from_o the_o nether_a number_n begin_v 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noughte_v wherefore_o i_o write_v down_o a_o cypher_n 0._o now_o have_v i_o do_v with_o the_o subtraction_n and_o yet_o in_o the_o gross_a sum_n remain_v 1_o which_o i_o must_v set_v right_a in_o the_o same_o place_n in_o the_o remayner_n and_o so_o the_o remayner_n appear_v to_o be_v like_a unto_o the_o high_a sum_n of_o the_o addition_n as_o here_o appear_v wherefore_o i_o say_v that_o the_o addition_n be_v well_o wrought_v and_o note_v that_o if_o you_o have_v subtract_v the_o uppermost_a from_o the_o product_n or_o total_a sum_n than_o the_o residue_n thereof_o will_v be_v equal_a to_o that_o middlemost_a number_n but_o if_o the_o parcelle_v which_o you_o add_v be_v more_o than_o two_o as_o three_o four_o five_o six_o or_o more_o than_o from_o your_o gross_a or_o total_a sum_n subtracte_v first_o one_o of_o the_o parcel_n and_o note_v that_o new_a residue_n out_o of_o that_o new_a residue_n subtract_v a_o other_o of_o your_o parcel_n which_o you_o will_v and_o note_v that_o 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and_o will_v instruct_v you_o in_o multiplication_n ☞_o ☞_o multiplication_n mvltiplication_n be_v such_o a_o operation_n that_o by_o two_o sum_n produce_v the_o three_o which_o three_o sum_n so_o many_o time_n shall_v contain_v the_o first_o as_o there_o be_v unity_n in_o the_o second_o and_o it_o serve_v in_o the_o stead_n of_o many_o addition_n as_o for_o example_n when_o i_o will_v know_v how_o many_o be_v 30_o time_n 48_o if_o i_o shall_v add_v 48_o thirty_o time_n it_o will_v be_v a_o long_a work_n therefore_o be_v this_o work_n of_o multiplication_n devise_v which_o shall_v do_v that_o at_o once_o that_o addition_n shall_v do_v at_o many_o time_n scholar_n i_o perceive_v the_o commodity_n of_o it_o partly_o but_o i_o shall_v not_o see_v the_o full_a profit_n of_o it_o till_o i_o know_v the_o whole_a use_n of_o it_o therefore_o sir_n i_o beseech_v you_o teach_v i_o the_o work_n of_o it_o master_n so_o i_o judge_v it_o beast_n but_o because_o that_o great_a sum_n can_v not_o be_v 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i_o will_v know_v how_o many_o be_v 7_o time_n 8_o i_o must_v write_v those_o digitte_n thus_o then_o do_v i_o look_v how_o much_o 8_o do_v differ_v from_o 10_o and_o i_o find_v it_o to_o be_v 2_o that_o 2_o do_v i_o write_v at_o the_o right_a hand_n of_o 8_o at_o the_o end_n of_o the_o line_n thus_o after_o that_o i_o take_v the_o difference_n of_o 7_o likewise_o from_o 10_o that_o be_v 3_o and_o i_o write_v that_o at_o the_o right_a side_n of_o 7_o as_o you_o see_v in_o this_o example_n then_o do_v i_o draw_v a_o line_n under_o they_o as_o in_o addition_n thus_o last_o of_o all_o i_o multiply_v the_o two_o difference_n say_v 2_o time_n â—_o make_v 6_o that_o must_v i_o ever_o set_v under_o the_o difference_n beneath_o the_o line_n then_o must_v i_o take_v the_o one_o of_o the_o difference_n which_o i_o will_v for_o all_o be_v like_o from_o the_o other_o digit_fw-la not_o from_o his_o own_o as_o the_o line_n of_o the_o cross_n warn_v i_o and_o that_o that_o be_v leave_v must_v i_o write_v under_o the_o digit_n as_o in_o this_o example_n if_o i_o take_v 2_o from_o 7_o or_o 3_o from_o 8_o there_o remain_v 5_o that_o 5_o must_v i_o write_v under_o the_o digit_n and_o then_o there_o appear_v the_o multiplication_n of_o 7_o time_n 8_o to_o be_v 56._o and_o so_o likewise_o of_o any_o other_o digit_n if_o they_o be_v above_o 5_o for_o if_o they_o be_v under_o 5_o then_o will_v their_o difference_n be_v great_a than_o themselves_o so_o that_o they_o can_v be_v take_v out_o of_o they_o and_o again_o such_o little_a sum_n everye_o child_n can_v multiply_v as_o to_o say_v 2_o time_n 3_o or_o 4_o time_n 5_o and_o such_o like_a scholar_n truth_n it_o be_v and_o see_v i_o seem_v that_o i_o understand_v the_o multiply_a of_o the_o great_a digit_n i_o will_v prove_v by_o a_o example_n how_o i_o can_v do_v it_o i_o will_v know_v how_o many_o be_v 9_o time_n 6._o master_n it_o be_v all_o one_o in_o value_n to_o say_v 9_o time_n 6_o or_o 6_o time_n 9_o but_o yet_o the_o order_n 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it_o by_o 6_o say_v 6_o time_n 1_o make_v 6_o that_o do_v i_o write_v under_o the_o four_o place_n and_o so_o have_v i_o end_v the_o first_o multiplier_n and_o dash_v he_o slight_o with_o my_o pen._n then_o begin_v i_o with_o the_o second_o multiplier_n and_o say_v first_o 3_o time_n 5_o that_o make_v 15_o of_o which_o i_o set_v the_o 5_o under_o the_o second_o place_n because_o that_o the_o multiplier_n be_v there_o and_o the_o 1_o i_o set_v under_o the_o third_o place_n then_o come_v i_o to_o the_o second_o figure_n that_o be_v 6_o and_o multiply_v it_o by_o 3_o which_o make_v 18_o of_o which_o i_o set_v the_o 8_o under_o the_o third_o place_n and_o the_o article_n 1_o in_o the_o four_o place_n than_o come_v i_o to_o the_o three_o figure_n which_o be_v 3_o and_o multiply_v it_o by_o 3_o say_v 3_o time_n 3_o make_z 9_o which_o because_o it_o be_v but_o one_o digit_fw-la i_o set_v under_o the_o four_o place_n and_o then_o come_v to_o the_o last_o figure_n 1_o i_o multiply_v it_o by_o 3_o and_o it_o make_v 3_o which_o i_o set_v in_o the_o five_o place_n and_o then_o have_v i_o end_v two_o of_o the_o multiplyer_n and_o the_o sum_n stand_v thus_o and_o then_o i_o give_v 3_o his_o dash_n then_o come_v i_o to_o the_o third_o multiplier_n and_o multiply_v it_o into_o every_o figure_n of_o the_o high_a sum_n and_o first_o i_o say_v 2_o time_n 5_o make_v 10_o of_o which_o i_o set_v the_o cipher_n under_o the_o multiplyer_n in_o the_o three_o place_n and_o the_o article_n 1_o in_o the_o fourthe_a place_n and_o so_o multiply_v the_o second_o figure_n 6_o by_o that_o same_o 2_o there_o amount_v 12_o whereof_o i_o write_v the_o digitte_n 2_o under_o the_o four_o place_n and_o the_o article_n 1_o under_o in_o the_o five_o place_n now_o do_v i_o multiply_v by_o the_o third_o figure_n of_o the_o high_a sum_n which_o be_v 3_o and_o that_o make_v 6_o which_o i_o set_v under_o the_o fifte_a place_n as_o appeareth_z in_o the_o example_n follow_v than_o come_v i_o to_o the_o last_o 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my_o mind_n and_o it_o make_v 4_o which_o i_o write_v in_o the_o 6_o place_n and_o then_o have_v i_o end_v the_o multiplication_n and_o the_o figure_n stand_v in_o order_n thus_o which_o parcel_n if_o i_o add_v into_o one_o sum_n it_o will_v be_v 562830_o which_o be_v the_o gross_a or_o total_a sum_n of_o all_o that_o multiplication_n scholar_n well_o this_o manner_n of_o multiplication_n i_o perceive_v but_o what_o other_o sort_n have_v you_o mai._n there_o be_v one_o way_n that_o be_v wrought_v by_o a_o chequer_n table_n make_v thus_o look_v how_o many_o place_n your_o sum_n have_v that_o you_o will_v multiply_v so_o many_o square_n must_v you_o make_v in_o your_o table_n from_o the_o right_a side_n to_o the_o left_a multiplication_n another_o way_n of_o multiplication_n and_o so_o many_o from_o the_o high_a part_n to_o the_o low_a as_o there_o be_v place_n in_o your_o multiplier_n then_o set_v down_o your_o great_a sum_n first_o on_o the_o top_n of_o the_o table_n every_o figure_n 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more_o abundantlye_o make_v you_o to_o perceive_v the_o use_n of_o it_o division_n scholar_n well_o sir_n then_o in_o division_n i_o pray_v you_o to_o instruct_v i_o but_o i_o think_v by_o the_o name_n of_o it_o that_o it_o shall_v be_v all_o one_o with_o multiplication_n for_o i_o call_v that_o division_n when_o any_o thing_n be_v part_v into_o diverse_a &_o many_o part_n master_n you_o take_v it_o as_o it_o be_v take_v common_o howbeit_o if_o you_o mark_v well_o you_o shall_v perceive_v that_o it_o be_v quite_o contrary_a to_o multiplication_n and_o do_v not_o part_n one_o thing_n or_o few_o thing_n into_o many_o but_o contrary_a way_n it_o bring_v many_o parcel_n in_o to_o few_o but_o yet_o so_o that_o these_o few_o take_v together_o be_v equal_a in_o valour_n to_o the_o other_o many_o for_o by_o division_n penny_n be_v turn_v into_o shilling_n and_o shilling_n into_o pound_n as_o for_o example_n of_o 1â—0_o shilling_n it_o make_v 6_o pound_n so_o be_v 120_o turn_v into_o 6_o 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must_v be_v first_o write_v and_o the_o second_o so_o set_v under_o it_o that_o the_o last_o figure_n of_o the_o low_a number_n be_v right_a under_o the_o last_o of_o the_o high_a figure_n a_o general_a rule_n for_o place_v the_o figure_n contrary_a way_n to_o the_o work_n of_o the_o other_o kind_n of_o arithmetic_n for_o in_o they_o the_o two_o first_o figure_n be_v set_v ever_o meet_v one_o under_o the_o other_o but_o in_o division_n the_o last_o figure_n must_v be_v set_v meet_a except_o it_o chance_v so_o exception_n a_o exception_n that_o the_o last_o figure_n of_o the_o divisor_n be_v great_a than_o the_o last_v of_o the_o high_a number_n for_o than_o you_o shall_v set_v the_o last_o of_o the_o divisor_n under_o the_o last_o save_o one_o of_o the_o high_a number_n as_o for_o example_n if_o you_o shall_v divide_v 365_o whithe_o be_v the_o sum_n of_o the_o day_n of_o a_o year_n by_o 2d_o which_o be_v the_o day_n of_o a_o common_a month_n then_o shall_v you_o set_v they_o thus_o but_o if_o you_o will_v divide_v those_o 365_o day_n by_o 52._o which_o be_v the_o number_n of_o week_n in_o one_o year_n then_o shall_v you_o set_v they_o thus_o likewayes_n if_o i_o will_v divide_v the_o same_o 365_o by_o 4_o which_o be_v the_o sum_n of_o the_o quarter_n of_o a_o year_n then_o must_v i_o set_v they_o thus_o scholar_n sir_n this_o do_v i_o understande_v but_o how_o now_o shall_v i_o do_v to_o divide_v the_o one_o by_o the_o other_o master_n you_o must_v begin_v with_o the_o last_o figure_n next_o the_o left_a hand_n ☞_o ☞_o and_o see_v how_o many_o time_n the_o last_o figure_n of_o the_o divisor_n may_v be_v take_v out_o of_o the_o last_o figure_n of_o the_o over_o number_n and_o that_o shall_v you_o note_v within_o a_o crooked_a line_n towards_o your_o right_a hand_n as_o for_o example_n i_o will_v divide_v 365_o by_o 28_o then_o set_v i_o those_o two_o sum_n thus_o and_o i_o look_v how_o many_o time_n i_o may_v find_v 2_o which_o be_v the_o last_o figure_n of_o the_o divisor_n in_o 3_o which_o be_v the_o last_o of_o the_o number_n to_o be_v divide_v and_o consider_v that_o i_o can_v take_v 2_o out_o of_o 3_o but_o once_o i_o make_v a_o crooked_a line_n at_o the_o right_a hand_n of_o the_o number_n &_o with_o in_o it_o i_o set_v 1_o and_o that_o be_v call_v the_o quotiente_a number_n as_o i_o tell_v you_o number_n quotient_a number_n then_o because_o that_o when_o 2_o be_v take_v out_o of_o 3_o there_o remain_v 1_o i_o must_v write_v that_o 1_o over_o 3_o and_o deface_v or_o cancel_v the_o 3_o and_o the_o 2_o then_o will_v the_o figure_n stand_v thus_o then_o must_v i_o go_v to_o the_o next_o figure_n of_o the_o divisor_n and_o take_v it_o likeways_o so_o many_o time_n out_o of_o the_o figure_n that_o be_v over_o it_o and_o look_v what_o do_v remain_v that_o i_o must_v write_v over_o they_o and_o cancel_v they_o as_o in_o this_o example_n therefore_o now_o i_o do_v take_v once_o 8_o out_o of_o 16_o and_o there_o remain_v 8_o which_o i_o must_v set_v over_o the_o 6_o and_o cancel_v or_o cross_v out_o the_o 15._o and_o the_o 8_o of_o the_o divisor_n and_o then_o will_v the_o figure_n stand_v thus_o and_o so_o have_v i_o once_o wrought_v scholar_n so_o i_o perceive_v that_o you_o take_v the_o nether_a figure_n not_o only_o out_o of_o the_o other_o that_o be_v right_a over_o he_o but_o out_o of_o that_o with_o the_o other_o also_o that_o remain_v before_o and_o be_v write_v towards_o the_o left_a hand_n master_n so_o must_v you_o do_v for_o you_o must_v so_o take_v the_o divisor_n out_o of_o the_o over_o number_n that_o there_o remain_v not_o over_o it_o so_o great_a a_o sum_n as_o itself_o be_v for_o than_o be_v your_o work_n in_o vain_a but_o yet_o again_o here_o must_v you_o mark_v that_o when_o you_o seek_v how_o many_o time_n the_o last_o figure_n of_o the_o divisor_n may_v be_v find_v in_o the_o number_n over_o he_o note_n note_n that_o you_o look_v also_o whether_o you_o may_v as_o often_o find_v all_o the_o figure_n follow_v in_o those_o that_o be_v above_o they_o consider_v all_o the_o remainder_n if_o there_o be_v any_o if_o not_o take_v your_o quotient_n less_o by_o one_o and_o then_o prove_v again_o and_o so_o still_o till_o you_o find_v a_o moete_n quotient_a and_o by_o that_o moete_n quotient_a must_v you_o always_o multiply_v your_o divisor_n and_o the_o product_v set_v under_o your_o divisor_n so_o that_o his_o first_o figure_n stand_v under_o the_o first_o figure_n of_o your_o divisor_n and_o the_o second_o under_o the_o second_o and_o so_o forth_o and_o then_o subtract_v that_o product_n from_o the_o number_n to_o be_v divide_v that_o stand_v direct_o over_o it_o as_o you_o have_v see_v i_o do_v ☞_o ☞_o when_o you_o have_v thus_o wrought_v once_o than_o must_v you_o begin_v again_o and_o write_v your_o divisour_n a_o new_a near_o toward_o the_o right_a hand_n by_o one_o place_n as_o in_o this_o example_n you_o shall_v set_v 2_o under_o 8_o and_z 8_o under_o 5_o thus_o then_o as_o before_o seek_v how_o many_o time_n you_o may_v take_v your_o divisor_n out_o of_o the_o number_n over_o he_o now_o scholar_n that_o may_v i_o do_v here_o 4_o time_n master_n truth_n it_o be_v that_o you_o may_v find_v 2_o four_o time_n in_o 8_o but_o then_o mark_v whether_o you_o can_v find_v the_o figure_n follow_v so_o many_o time_n in_o the_o other_o that_o be_v over_o he_o can_v you_o find_v 8_o four_o time_n in_o 5_o scholar_n no_o neither_o yet_o once_o master_n therefore_o take_v â—_o out_o of_o â—_o once_o less_o scho._n that_o be_v 3_o time_n ma._n well_o then_o 3_o time_n 2_o
take_v away_o the_o two_o cipher_n from_o the_o number_n that_o shall_v be_v multiply_v but_o also_o i_o may_v take_v away_o the_o one_o cipher_n from_o the_o multiplier_n and_o then_o must_v i_o add_v 3_o cipher_n to_o the_o sum_n that_o amount_v but_o take_v heed_n that_o you_o take_v away_o no_o cipher_n that_o come_v after_o any_o signify_v figure_n as_o in_o this_o last_o example_n you_o may_v not_o take_v away_o that_o in_o the_o four_o place_n of_o the_o high_a number_n neither_o that_o in_o the_o three_o place_n of_o the_o multiplier_n how_o be_v it_o yet_o this_o you_o may_v do_v if_o one_o cipher_n or_o more_o come_v in_o the_o midst_n of_o your_o sum_n you_o may_v multiply_v by_o the_o other_o figure_n and_o overskippe_v they_o but_o so_o that_o you_o give_v everye_o figure_n his_o due_a place_n as_o thus_o i_o will_v multiply_v 3026_o by_o 2004_o therefore_o i_o set_v they_o thus_o and_o thus_o do_v i_o multiply_v then_o first_o 4_o time_n 6_o make_v 24_o i_o set_v the_o 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the_o fraction_n will_v appear_v thus_o so_o that_o both_o fraction_n bring_v to_o one_o denomination_n must_v stand_v thus_o ma._n you_o have_v do_v well_o scholar_n i_o beseech_v you_o let_v i_o examine_v it_o after_o my_o accustom_a form_n by_o common_a part_n of_o coin_n ma._n go_v to_o scholar_n a_o new_a angel_n account_v at_o eight_o shilling_n contain_v 96_o penny_n whereof_o â—_o that_o be_v the_o xuj_o part_n be_v six_o penny_n and_o 1_o 16_o be_v 18_o penny_n that_o be_v 18_o â—6_n again_o â…™_n of_o the_o same_o angel_n be_v 16_o penny_n so_o that_o 4_o 6_o make_v 64_o d_o that_o be_v 64_o â—â—_o and_o so_o i_o find_v the_o sum_n to_o agree_v with_o the_o other_o before_o master_n so_o have_v you_o now_o the_o art_n to_o bring_v such_o two_o fraction_n into_o one_o denomination_n and_o if_o there_o be_v more_o than_o ij_o one_o note_v the_o reduction_n of_o three_o fraction_n or_o more_o to_o one_o then_o must_v you_o multiply_v all_o the_o denominator_n together_o and_o 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&_o so_o have_v i_o these_o ij_o fraction_n 3_o â—2â—_n 8_o â—2_n thus_o short_o reduce_v without_o alter_v the_o one_o fraction_n s_o this_o i_o understande_v ma._n â—arietie_n the_o third_o â—arietie_n then_o mark_v this_o third_o way_n if_o the_o denominator_n do_v not_o happen_v so_o that_o one_o by_o multiplication_n may_v make_v the_o other_o they_o look_v whether_o they_o both_o may_v be_v part_n of_o any_o other_o one_o number_n as_o in_o â—_o 1â—_n and_z â—_o 18_o although_o the_o lesser_a take_v but_o twice_o be_v to_o great_a to_o make_v 18_o yet_o they_o both_o may_v be_v part_n unto_o 36_o therefore_o look_v how_o many_o time_n 12_o be_v in_o 36_o and_o that_o quotient_a be_v multiply_v by_o the_o numeratour_n over_o 12_o the_o total_a shall_v be_v put_v in_o stead_n of_o the_o numerator_n over_o 12_o &_o for_o 12_o put_v 36_o thus_o â—5_n â—6_n so_o likewise_o look_v how_o often_o be_v 18_o in_o â—6_n and_o because_o it_o be_v twice_o therefore_o by_o 2_o multiply_v 7._o which_o be_v over_o 18_o and_o it_o will_v be_v 14_o set_z that_o for_o the_o numerator_n and_o in_o stead_n of_o 18_o put_v 36_o and_o then_o shall_v your_o fraction_n reduce_v stand_v thus_o 1â—_n 36_o 14_o 36_o in_o stead_n of_o 5_o â—2_n and_o 7_o 1â—_n proof_n proof_n and_o if_o you_o will_v prove_v whether_o you_o have_v wrought_v well_o or_o no_o that_o may_v be_v prove_v by_o reduction_n of_o they_o again_o to_o their_o former_a denomination_n which_o art_n shall_v be_v teach_v in_o the_o four_o kind_n of_o reduction_n where_o great_a term_n of_o fraction_n be_v reduce_v into_o small_a in_o number_n but_o no_o small_a in_o proportion_n ☜_o ☜_o and_o if_o in_o such_o reduction_n the_o same_o term_n or_o number_n come_v again_o that_o be_v before_o then_o be_v the_o work_n good_a else_o not_o s_o sir_n i_o hear_v your_o word_n but_o i_o do_v not_o understand_v many_o of_o they_o which_o it_o may_v please_v you_o to_o declare_v ma._n with_o a_o good_a will_n when_o conveniente_a place_n serve_v but_o that_o must_v be_v in_o the_o say_v iiij_o kind_a of_o reduction_n in_o the_o mean_a season_n i_o will_v declare_v the_o second_o form_n of_o reduction_n which_o teach_v how_o to_o reduce_v fraction_n of_o fraction_n into_o one_o fraction_n and_o so_o to_o one_o denomination_n when_o fraction_n of_o fraction_n be_v propon_v denomination_n reduction_n of_o fraction_n of_o fraction_n into_o one_o fraction_n and_o denomination_n you_o shall_v multiply_v the_o numeratour_n of_o each_o into_o other_o and_o set_v the_o total_a for_o the_o new_a numerator_n and_o then_o multiply_v all_o the_o denominatour_n likewaies_o and_o take_v their_o total_a for_o the_o new_a denominator_fw-la and_o so_o be_v they_o speedy_o reduce_v sc._n if_o that_o be_v all_o than_o i_o understand_v it_o already_o as_o by_o this_o example_n i_o will_v declare_v these_o be_v the_o fraction_n ¼_n of_o â…”_n of_o 6_o 7_o of_o 7_o 9_o which_o i_o will_v reduce_v to_o one_o denomination_n therefore_o begin_v i_o with_o the_o numeratour_n and_o multiple_v they_o all_o together_o say_v 3_o into_o 2_o make_v 6_o and_o 6_o by_o 6_o make_v 36_o which_o multiply_v by_o 7_o yield_v 352_o that_o i_o set_v over_o a_o line_n for_o the_o numerator_n thus_o then_o i_o multiply_v the_o denominatour_n 4_o by_o 3_o make_v 12_o &_o that_o by_o 7_o bring_v 84_o which_o multiply_v by_o 9_o yield_v 756_o the_o new_a denominatour_n and_o so_o the_o whole_a reduce_v fraction_n be_v this_o which_o be_v to_o hard_a a_o fraction_n for_o i_o to_o understand_v yet_o mai_n you_o think_v so_o and_o no_o marvel_n but_o anon_o you_o shall_v learn_v to_o judge_v it_o easy_o for_o this_o fraction_n be_v no_o more_o in_o deed_n then_o â…“_n although_o it_o be_v in_o great_a term_n and_o therefore_o more_o
need_v how_o they_o may_v be_v bring_v to_o lesser_a term_n scholar_n to_o write_v any_o thing_n in_o great_a term_n than_o need_v seem_v to_o be_v a_o fault_n reduction_n the_o four_o kind_n of_o reduction_n and_o so_o this_o rule_n seem_v to_o amend_v that_o fault_n na._n it_o be_v a_o fault_n to_o do_v any_o thing_n without_o need_n which_o after_o must_v be_v redress_v but_o in_o this_o case_n it_o be_v not_o so_o neither_o do_v i_o say_v absolute_o as_o you_o do_v that_o it_o need_v not_o to_o express_v those_o fraction_n in_o so_o great_a term_n but_o that_o the_o fraction_n do_v not_o need_v i_o mean_v for_o their_o value_n to_o be_v understand_v but_o yet_o it_o may_v be_v needful_a for_o the_o ease_n of_o those_o work_n whereto_o they_o be_v apply_v as_o for_o example_n in_o the_o first_o kind_n of_o reduction_n this_o be_v your_o own_o example_n 3_o 16_o and_o 4_o â—_o which_o when_o you_o will_v reduce_v you_o be_v fain_o to_o turn_v they_o first_o into_o one_o denomination_n &_o so_o appear_v they_o thus_o 18_o 96_o and_o 6â—_n 96_o where_o the_o fraction_n for_o their_o own_o understanding_n need_v not_o to_o be_v turn_v out_o of_o small_a term_n into_o great_a but_o yet_o the_o easiness_n of_o work_v need_v it_o sch._n sir_n i_o understand_v now_o not_o only_o the_o difference_n of_o this_o need_n for_o the_o fraction_n may_v better_a be_v understand_v as_o fraction_n several_a each_o in_o his_o value_n fraction_n term_n of_o fraction_n when_o they_o be_v in_o lesser_a term_n although_o they_o can_v not_o so_o well_o be_v reduce_v but_o also_o i_o understand_v what_o you_o mean_v by_o great_a term_n and_o lesser_a term_n whereof_o before_o i_o be_v in_o doubt_n for_o i_o see_v you_o call_v the_o numeratour_n and_o denominatour_n the_o term_n of_o the_o fraction_n master_n i_o be_o glad_a you_o understande_v it_o so_o well_o now_o then_o when_o you_o will_v value_v any_o fraction_n because_o that_o may_v best_o be_v do_v when_o the_o term_n be_v small_a you_o shall_v reduce_v they_o to_o the_o small_a that_o you_o can_v which_o thing_n you_o may_v do_v thus_o term_n reduction_n of_o fraction_n into_o their_o small_a term_n divide_v the_o great_a of_o any_o such_o two_o term_n by_o the_o lesser_a and_o if_o any_o thing_n remain_v by_o that_o remainder_n divide_v the_o last_o divisour_n and_o if_o any_o thing_n remain_v now_o by_o that_o divide_v the_o last_o divisour_n which_o be_v before_o the_o remainder_n of_o the_o first_o division_n and_o so_o continue_v still_o till_o nothing_o do_v remain_v in_o the_o division_n and_o then_o mark_v your_o last_o divisour_n for_o it_o be_v the_o number_n that_o will_v easy_o reduce_v your_o fraction_n if_o you_o divide_v both_o the_o numeratour_n and_o the_o denominatour_n by_o the_o same_o number_n and_o put_v for_o the_o numeratour_n the_o quotient_a of_o his_o division_n and_o for_o the_o denominatour_n also_o his_o quotient_n that_o rise_v by_o his_o division_n scho._n i_o take_v for_o example_n 18_o 96_o and_o because_o 96_o be_v the_o great_a number_n i_o divide_v it_o by_o 18_o and_o the_o quotient_n be_v 5_o and_o there_o rest_v 6_o what_o shall_v i_o do_v with_o this_o quotient_a master_n nothing_o in_o this_o work_n but_o now_o see_v there_o remain_v somewhat_o by_o that_o remainder_n must_v you_o divide_v the_o last_o divisor_n sc._n if_o i_o shall_v divide_v 18_o which_o be_v the_o last_o divisour_n by_o 6_o that_o be_v the_o remayner_n so_o be_v the_o quotient_a â—_o and_o nothing_o rest_v ma._n as_o for_o the_o quotient_a i_o omit_v he_o yet_o but_o because_o there_o do_v remain_v nothing_o therefore_o be_v 6_o which_o be_v your_o last_o divisour_n that_o number_n by_o which_o you_o may_v reduce_v the_o fraction_n propon_v sch._n then_o as_o you_o teach_v i_o i_o must_v divide_v the_o numerator_n 18_o by_o 6_o and_o the_o quotient_n be_v 3_o which_o i_o must_v put_v for_o the_o numerator_fw-la over_o a_o line_n thus_o and_o then_o by_o the_o say_v 6_o must_v i_o divide_v also_o the_o denominator_fw-la 96_o and_o the_o quotient_n will_v be_v 16_o which_o i_o must_v take_v for_o the_o denominator_fw-la and_o so_o be_v the_o fraction_n 3_o 16._o and_o so_o i_o think_v this_o rule_n do_v prove_v the_o work_n of_o the_o first_o reduction_n may_v that_o be_v true_a if_o the_o first_o reduction_n be_v make_v of_o fraction_n in_o their_o jest_n term_n and_o else_o not_o without_o some_o help_n as_o the_o second_o number_n in_o that_o place_n will_v declare_v sc._n the_o second_o number_n be_v â—_o 6_o which_o be_v turn_v into_o 64_o 56_o by_o that_o rule_n now_o if_o i_o shall_v by_o this_o rule_n reduce_v it_o again_o into_o the_o jest_n term_n i_o must_v divide_v 96_o by_o 64_o and_o there_o rest_v 32_o by_o which_o 32_o i_o divide_v 64_o &_o there_o remain_v nothing_o wherefore_o i_o must_v take_v that_o 32_o for_o the_o divisour_n to_o reduce_v the_o say_a fraction_n then_o do_v i_o divide_v 64_o by_o 32_o and_o the_o quotient_n be_v 2_o which_o i_o set_v for_o my_o numeratour_n again_o i_o divide_v 96_o by_o 32_o and_o the_o quotient_n will_v be_v 3_o and_o so_o have_v i_o but_o â…”_n ma._n muse_v not_o at_o the_o matter_n for_o you_o have_v do_v well_o enough_o but_o you_o think_v you_o have_v not_o the_o fraction_n that_o you_o look_v for_o that_o be_v 4_o 6_o yet_o have_v you_o one_o equal_a to_o it_o as_o by_o the_o part_n of_o a_o shilling_n you_o may_v prove_v sc._n truth_n it_o be_v for_o each_o of_o they_o will_v bring_v forth_o 8_o penny_n so_o that_o 8_o â—â—_o and_z 4_o 6_o and_o 2_o 7_o be_v all_o three_o equal_a and_o now_o i_o perceive_v that_o because_o 4_o 6_o be_v not_o write_v in_o the_o jest_n term_n that_o it_o may_v be_v therefore_o this_o reduction_n bring_v forth_o not_o it_o but_o that_o other_o which_o be_v write_v in_o the_o jest_n term_n now_o understande_v i_o this_o rule_n well_o but_o be_v there_o any_o other_o way_n to_o work_v this_o reduction_n master_n yes_o but_o first_o note_v this_o reduction_n an_o other_o way_n for_o to_o work_v reduction_n that_o if_o you_o find_v no_o such_o divisor_n to_o reduce_v the_o fraction_n till_o you_o come_v to_o 1_o because_o 1_o do_v make_v no_o division_n therefore_o that_o fraction_n be_v already_o in_o his_o least_o term_n as_o by_o 71_o 100_o you_o may_v prove_v and_o so_o of_o 81_o 98_o and_o many_o other_o like_a but_o now_o for_o your_o better_a aid_n to_o find_v the_o due_a proportion_n in_o least_o term_n with_o more_o ease_n for_o a_o young_a learner_n you_o shall_v mediate_v or_o take_v the_o half_a of_o the_o numerator_n and_o also_o the_o denominator_fw-la as_o long_a as_o you_o may_v upon_o a_o line_n always_o part_v they_o with_o a_o dash_n of_o your_o pen_n as_o you_o work_v which_o may_v easy_o be_v do_v if_o the_o number_n be_v even_o as_o 2_o 4_o 6_o 8_o or_o 10_o but_o if_o they_o be_v odd_a though_o it_o be_v but_o in_o one_o of_o they_o then_o must_v you_o abbreviate_v they_o by_o â—_o by_z 5_o by_z 7_o etc._n etc._n and_o because_o example_n do_v most_o instruct_v i_o have_v in_o the_o page_n follow_v set_v down_o the_o manner_n of_o 2_o or_o 3_o who_o last_o number_n at_o the_o end_n of_o the_o line_n show_v the_o least_o term_n or_o valuation_n of_o that_o fraction_n abbreviate_v first_o by_o 5_o then_o by_o 293._o sc._n sir_n i_o thank_v you_o much_o this_o be_v very_o easy_a and_o good_a for_o a_o young_a learner_n ma._n so_o it_o be_v but_o yet_o notwithstanding_o if_o you_o can_v without_o that_o division_n by_o memory_n espy_v the_o great_a number_n that_o may_v divide_v exact_o both_o term_n of_o your_o fraction_n propon_v then_o need_v you_o not_o to_o use_v that_o division_n as_o in_o this_o fraction_n 6â—_n 96_o i_o see_v that_o 12_o be_v the_o great_a number_n that_o can_v divide_v they_o both_o and_o therefore_o without_o any_o work_n by_o memory_n only_o i_o turn_v that_o into_o â…_n but_o this_o ability_n in_o knowledge_n be_v get_v by_o exercise_n yet_o one_o other_o way_n of_o easy_a reduction_n in_o this_o kind_n there_o be_v when_o your_o fraction_n have_v any_o ciper_n in_o the_o first_o place_n of_o both_o term_n then_o may_v you_o by_o cast_v away_o the_o cipher_n make_v a_o brief_a reduction_n as_o thus_o 300_o 400_o here_o take_v away_o the_o cipher_n and_o it_o will_v be_v ¾_n which_o be_v the_o same_o in_o value_n with_o 300_o 400._o scholar_n and_o so_o if_o i_o have_v 400_o 650_o it_o will_v be_v 4_o 65._o ma._n you_o be_v deceive_v for_o you_o take_v away_o more_o cipher_n from_o the_o numerator_n ☜_o ☜_o than_o you_o do_v take_v from_o the_o
denominator_fw-la which_o you_o may_v not_o do_v sc._n i_o confess_v my_o fault_n which_o come_v of_o too_o much_o haste_n i_o be_v more_o glad_a of_o the_o rule_n than_o wise_a in_o use_v it_o but_o now_o i_o understand_v it_o i_o trust_v ma._n then_o may_v i_o go_v in_o hand_n with_o the_o five_o or_o last_o kind_n of_o reductionâ—_n reduction_n the_o five_o kind_n of_o reduction_n which_o teach_v how_o to_o turn_v any_o fraction_n propon_v into_o any_o other_o denomination_n that_o you_o listen_v or_o into_o any_o part_n of_o common_a coin_n weight_n or_o measure_n or_o such_o like_a for_o declaration_n whereof_o first_o you_o shall_v mark_v whether_o your_o fraction_n be_v a_o simple_a fraction_n either_o else_o a_o fraction_n of_o sundry_a part_n i_o mean_v of_o more_o term_n than_o 2._o and_o if_o your_o fraction_n be_v a_o fraction_n of_o fraction_n or_o otherways_o compound_v you_o must_v reduce_v it_o to_o one_o simple_a fraction_n and_o then_o mark_v well_o the_o denomination_n of_o that_o other_o fraction_n into_o which_o you_o will_v turn_v this_o for_o by_o that_o denominatour_n you_o must_v multiply_v the_o numeratour_n of_o your_o first_o fraction_n and_o the_o total_a producte_v thereof_o shall_v you_o divide_v by_o the_o denominator_fw-la of_o your_o first_o fraction_n and_o that_o quotient_a shall_v be_v the_o numeratour_n to_o the_o denominatour_n propon_v as_o for_o example_n i_o have_v this_o fraction_n â…•_n which_o i_o will_v turn_v into_o ten_o part_n therefore_o i_o multiply_v this_o 10_o by_o 3_o that_o be_v the_o numeratour_n of_o my_o fraction_n and_o there_o rise_v 30_o which_o i_o divide_v by_o 5_o and_o the_o quotient_n be_v 6_o which_o must_v be_v the_o numerator_n to_o 10_o and_o so_o â…—_n will_v be_v 6_o 10._o sc._n this_o be_v easy_a enough_o to_o do_v ma._n then_o shall_v you_o see_v a_o other_o example_n of_o the_o same_o fraction_n that_o be_v not_o so_o easy_a as_o if_o i_o will_v turn_v â…—_n into_o viij_o part_n prove_v you_o that_o work_n sc._n i_o must_v multiply_v 8_o by_o 3_o and_o there_o amount_v 24_o which_o i_o divide_v by_o 5_o and_o the_o quotient_n be_v 4_o then_o be_v the_o new_a fraction_n 4_o 8._o ma._n and_o see_v you_o nothing_o doubtful_a in_o this_o work_n sc._n i_o see_v that_o when_o 24_o be_v divide_v by_o 5_o there_o remain_v 4_o which_o i_o do_v not_o pass_v of_o because_o you_o speak_v nothing_o of_o any_o remayn_a but_o only_o of_o the_o quotient_a ma._n by_o likelihood_n you_o remember_v what_o i_o say_v to_o you_o in_o division_n of_o whole_a number_n that_o you_o shall_v not_o pass_v of_o the_o remayn_a there_o but_o only_o note_v it_o as_o a_o sum_n that_o can_v not_o be_v divide_v without_o knowledge_n of_o fraction_n wherefore_o now_o mark_v this_o that_o in_o all_o division_n of_o whole_a number_n when_o there_o be_v any_o remainder_n you_o shall_v set_v it_o over_o a_o line_n as_o a_o numeratour_n and_o set_v the_o divisour_n for_o the_o denominatour_n and_o that_o fraction_n do_v make_v the_o division_n complete_a and_o be_v part_n of_o the_o quotient_a as_o if_o i_o will_v divide_v 48_o by_o 5_o the_o quotient_n will_v be_v 9_o â…—_n so_o in_o your_o former_a work_n when_o 24_o be_v divide_v by_o 5_o the_o quotient_n shall_v be_v 4_o â…˜_n and_o so_o the_o new_a fraction_n shall_v be_v thus_o that_o be_v 4_o 8_o of_o the_o entire_a number_n and_o â…˜_n of_o 4_o 8_o which_o you_o may_v prove_v be_v example_n of_o some_o coin_n sc._n then_o i_o take_v a_o crown_n who_o â…—_n be_v 3_o s_o now_o if_o i_o will_v prove_v whether_o that_o 3_o s_o be_v 4_o and_o â…˜_n of_o 4_o 8_o i_o shall_v have_v a_o cumbrous_a work_n to_o do_v master_n in_o deed_n for_o whole_a penny_n your_o example_n be_v troublesome_a yet_o tourn_v the_o crown_n into_o half_a penny_n it_o be_v easy_a enough_o sc._n now_o will_v i_o do_v it_o ma._n first_o let_v i_o tell_v you_o a_o easy_a way_n how_o to_o find_v any_o number_n that_o will_v easy_o be_v divide_v into_o such_o part_n as_o you_o desire_v which_o way_n be_v this_o set_a down_o the_o part_n that_o you_o desire_v and_o then_o by_o one_o of_o they_o multiply_v all_o the_o other_o the_o total_a whereof_o shall_v contain_v all_o the_o part_n propon_v as_o if_o i_o will_v have_v a_o number_n that_o may_v be_v divide_v into_o 4_o 5_o 6_o and_z 7_o part_n by_o 4_o multiply_v 5_o and_o there_o rise_v 20_o then_o multiply_v 20_o by_o 6_o &_o it_o will_v make_v 120_o which_o multiply_v by_o 7_o will_v yield_v 840_o and_o so_o of_o any_o other_o number_n sc._n then_o in_o our_o former_a example_n where_o be_v mention_v but_o of_o 5_o part_n and_o 8_o part_n i_o shall_v only_o multiply_v 5_o by_o 8_o which_o make_v 40_o and_o that_o number_n will_v serve_v ma._n so_o will_v it_o sc._n then_o what_o be_v â…•_n of_o 40_o mai._n prove_v by_o the_o same_o rule_n which_o you_o confess_v easy_a enough_o 3_o time_n 40_o be_v 120_o which_o be_v divide_v by_o 5_o make_v 24_o and_o that_o be_v just_a now_o to_o know_v whether_o it_o be_v equal_a to_o 24_o first_o i_o see_v by_o the_o same_o rule_n that_o 4_o 8_o be_v 20_o and_o 2_o 8_o be_v 5_o of_o which_o 5_o i_o must_v take_v â…˜_n and_o that_o by_o the_o same_o rule_n be_v 4._o so_o that_o i_o see_v now_o that_o be_v equal_a to_o â…—_n ma._n and_o by_o the_o way_n note_v this_o form_n of_o fraction_n how_o it_o be_v write_v that_o be_v to_o say_v both_o the_o numerator_n and_o his_o fraction_n above_o the_o line_n although_o i_o know_v it_o may_v be_v write_v otherwise_o as_o thus_o 4_o 8_o and_o â…˜_n of_o 4_o 8_o but_o i_o account_n the_o other_o way_n more_o apt_a a_o great_a deal_n *_o scho._n now_o i_o pray_v you_o sir_n let_v i_o prove_v how_o this_o 4_o 8_o and_o â…˜_n of_o 4_o 8_o of_o a_o crown_n be_v equal_a to_o â…˜_n of_o a_o crown_n our_o first_o proponed_a fraction_n that_o have_v bring_v forth_o these_o hard_a fraction_n to_o my_o think_v yet_o first_o i_o see_v that_o â…—_n of_o a_o crown_n be_v â—_o s_o which_o be_v 36_o do_v or_o 72_o half_a penny_n now_o if_o i_o can_v find_v that_o this_o fraction_n 4_o 8_o and_o â…˜_n of_o 4_o 8_o be_v equal_a unto_o 3_o s_o then_o be_o i_o full_o answer_v because_o i_o can_v take_v 4_o 8_o of_o a_o crown_n i_o turn_v the_o crown_n into_o half_a penny_n as_o you_o will_v i_o which_o make_v 120_o which_o i_o divide_v by_o 8_o my_o quotient_n be_v 15_o which_z taken_z 4_o time_n make_v 60_o now_o rest_v i_o to_o have_v â—_o 5_o of_o the_o â…˜_n whereof_o â…›_n be_v 15_o that_o 15_o be_v part_v into_o 5_o part_n the_o quotient_a be_v 3_o which_o take_v 4_o time_n make_v 12_o which_o with_o my_o 60_o before_o amount_v to_o 72_o which_o be_v then_o equal_a to_o â…•_n my_o desire_n ma._n and_o so_o may_v you_o express_v by_o a_o other_o way_n than_o be_v before_o mention_v all_o fraction_n of_o fraction_n as_o thus_o that_o be_v ¾_n of_o â…_n and_o so_o of_o other_o but_o i_o remit_v these_o form_z to_o the_o arbitrement_n of_o every_o wise_a art_n man_n to_o use_v as_o he_o think_v most_o apt_a and_o ready_a but_o now_o one_o example_n more_o for_o this_o rule_n and_o then_o shall_v we_o end_v it_o if_o i_o have_v â—_o 15_o of_o a_o sovereign_n account_v the_o sovereign_n 20_o shilling_n how_o many_o shilling_n be_v that_o 7_o 15_o sc._n i_o must_v multiply_v 7_o by_o 20_o and_o that_o make_v 140_o which_o i_o shall_v divide_v by_o 15_o and_o the_o quotient_n will_v be_v 9_o 5_o 15_o or_o else_o in_o lesser_a term_n ½_n ma._n that_o be_v 9_o s_o and_o one_o three_o part_n of_o a_o shilling_n that_o be_v 4_o d_o as_o by_o this_o same_o rule_n you_o may_v prove_v and_o this_o for_o this_o time_n shall_v suffice_v for_o reduction_n save_v that_o i_o must_v now_o repeat_v a_o little_a touch_v multiplication_n and_o division_n and_o so_o go_v forward_o multiplication_n in_o multiplication_n it_o happen_v sometime_o that_o there_o be_v whole_a number_n to_o be_v multiply_v with_o fraction_n and_o may_v be_v in_o two_o sort_n for_o either_o the_o whole_a number_n be_v several_a from_o the_o fraction_n and_o be_v the_o multiplyer_n or_o else_o the_o whole_a number_n be_v join_v with_o one_o or_o both_o of_o the_o fraction_n fraction_n reduction_n of_o whole_a number_n into_o fraction_n and_o so_o make_v a_o mix_a number_n thereof_o if_o it_o be_v in_o the_o first_o sort_n then_o need_v there_o no_o reduction_n but_o only_o multiply_v the_o numerator_n of_o the_o fraction_n by_o that_o whole_a number_n and_o the_o total_a thereof_o set_v for_o the_o new_a numerator_n scho._n i_o understand_v you_o thus_o
if_o i_o have_v 6_o 2d_o to_o be_v multiply_v by_o 16_o then_o must_v i_o multiply_v that_o 16_o with_o 6_o which_o be_v the_o numerator_n whereof_o come_v 96_o and_o that_o must_v i_o set_v for_o the_o new_a numerator_n keep_v still_o 23_o for_o the_o denominator_fw-la and_o so_o the_o fraction_n will_v be_v 96_o 2d_o that_o be_v 4_o 4_o 23._o ma._n and_o in_o this_o sort_n of_o work_n you_o may_v abridge_v the_o labour_n thus_o if_o it_o happen_v the_o denominator_fw-la to_o be_v such_o a_o number_n as_o may_v even_o be_v divide_v by_o the_o say_v whole_a number_n propose_v then_o divide_v it_o thereby_o and_o set_v the_o quotient_a of_o that_o division_n for_o the_o former_a denominator_fw-la but_o reserve_v still_o the_o numerator_n and_o so_o be_v the_o multiplication_n end_v scho._n then_o i_o fain_o this_o example_n 7_o 20_o to_o be_v multiply_v by_o 5._o and_o because_o 5_o will_v just_o divide_v 20_o therefore_o i_o take_v the_o quotient_a of_o that_o division_n which_o be_v 4_o and_o set_v in_o stead_n of_o 20_o and_o so_o the_o fraction_n will_v be_v 7_o 4_o that_o be_v 1_o ¼_n master_n which_o be_v all_o one_o with_o 35_o â—0_n that_o will_v have_v follow_v of_o the_o other_o sort_n of_o work_n sch._n i_o perceive_v it_o very_o well_o master_n â—heâ—s_n â—w_v to_o mulâ—ie_v mix_v â—heâ—s_n now_o then_o for_o the_o other_o sort_n where_o the_o number_n be_v mix_v take_v this_o way_n first_o to_o reduce_v the_o say_a whole_a number_n and_o fraction_n into_o one_o fraction_n improper_a as_o i_o show_v you_o in_o reduction_n and_o then_o multiply_v they_o together_o as_o if_o they_o be_v proper_a fraction_n sc._n 13_o â—_o 5_o be_v set_v to_o be_v multiply_v by_o â—_o 9_o first_o i_o must_v reduce_v the_o mix_v number_n as_o appear_v in_o the_o margin_n by_o multiply_v 13_o by_o 5_o â—heâ—s_n and_o that_o make_v 65_o whereto_o i_o must_v add_v the_o numerator_n 3_o and_o so_o the_o fraction_n will_v be_v 68_o 5_o which_o now_o i_o shall_v multiply_v after_o the_o accustom_a form_n and_o it_o will_v be_v 340_o 40._o ma_fw-fr you_o have_v do_v well_o and_o so_o may_v you_o see_v that_o although_o most_o part_n of_o the_o form_n of_o multiplication_n may_v be_v wrought_v without_o reduction_n yet_o some_o can_v not_o as_o name_o mix_v number_n and_o yet_o one_o note_n more_o will_v i_o tell_v you_o of_o multiplication_n before_o we_o leave_v it_o that_o be_v when_o so_o ever_o you_o will_v multiply_v any_o fraction_n by_o 2_o which_o common_o be_v call_v duplation_n you_o may_v do_v it_o not_o only_o by_o double_v the_o numeratour_n but_o also_o by_o part_v the_o denominator_fw-la into_o half_a if_o he_o be_v even_o scholar_n then_o if_o i_o will_v double_v 5_o â—â—_o i_o may_v choose_v whether_o i_o will_v make_v it_o 1â—_n 1â—_n or_o else_o â…š_n and_o in_o deed_n i_o see_v that_o all_o be_v one_o but_o that_o the_o divide_n of_o the_o denominatour_n seem_v the_o better_a way_n to_o make_v small_a term_n of_o the_o fraction_n and_o so_o 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