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38_o 5._o 120._o and_o the_o product_n of_o they_o be_v 45_o 60_o 5_o which_o be_v divide_v by_o 73_o â—_o the_o product_v of_o the_o number_n in_o the_o second_o column_n the_o quotient_n be_v 62_o â—4_n â—â—_o as_o before_o but_o if_o the_o question_n have_v be_v how_o many_o piece_n of_o the_o last_o coin_n be_v equal_a in_o value_n to_o a_o give_v number_n of_o the_o first_o that_o be_v how_o many_o crown_n genoa_n be_v equal_a to_o 120_o spanish_a pistolet_n the_o last_o number_n 120_o pistolet_n must_v have_v be_v place_v in_o the_o second_o column_n as_o here_o you_o see_v 1._o column_n 2._o column_n 1_o spanish_a pistolet_n =_o â—3_n â—_o shilling_n sterling_a 3_o â—_o â—_o shilling_n sterling_a =_o 1_o crown_n genoa_n crown_n genoa_n =_o 1â—0_o spanish_a pistolet_n and_o then_o to_o resolve_v this_o question_n by_o two_o rule_n of_o three_o in_o the_o ordinary_a way_n the_o first_o in_o the_o second_o column_n must_v be_v the_o first_o term_n in_o the_o first_o rule_n and_o the_o first_o and_o second_o number_n in_o the_o first_o column_n must_v be_v the_o second_o and_o three_o term_n as_o before_o and_o the_o four_o proportional_a arise_v from_o those_o three_o number_n give_v must_v be_v one_o of_o the_o first_o term_n in_o the_o second_o to_o which_o the_o second_o number_n in_o the_o second_o column_n must_v be_v one_o of_o the_o middle_a term_n in_o the_o last_o proportion_n stir_v pistolet_n stir_v pistolet_n â—â—_o â—_o 1_o 38_o 5_o 38_o 75_o  _fw-fr pistolet_n crown_n genoa_n pistolet_n crown_n genoa_n 2._o 78_o â—3_n 1_o 120_o â—_o 23._o â—0_n 38_o note_n that_o when_o the_o same_o number_n happen_v to_o be_v multiplicator_n in_o the_o dividend_n and_o also_o in_o the_o divisor_n such_o multiplicator_n may_v be_v neglect_v in_o both_o and_o much_o
denominator_n than_o one_o which_o kind_n of_o break_a number_n be_v common_o set_v down_o with_o the_o particle_n of_o between_o they_o as_o five_o twelfth_n of_o one_o third_n be_v to_o be_v write_v thus_o 5_o 12_o of_o 1_o â—â—_o three_o fourth_n of_o seven_o eighth_n thus_o ¾_n of_o 7_o â—_o and_o so_o of_o any_o other_o 11._o the_o thing_n to_o be_v express_v by_o break_a number_n be_v chief_o the_o part_n or_o fraction_n of_o money_n weight_n measure_n time_n motion_n and_o thing_n account_v by_o the_o dozen_o of_o the_o three_o first_o of_o these_o there_o be_v infinite_a kind_n and_o variety_n according_a to_o the_o law_n and_o custom_n of_o particular_a country_n those_o use_v in_o this_o kingdom_n be_v most_o proper_a for_o we_o to_o know_v and_o the_o knowledge_n of_o they_o will_v be_v sufficient_a to_o direct_v we_o in_o the_o use_n of_o those_o in_o foreign_a nation_n if_o at_o any_o time_n there_o be_v a_o occasion_n for_o they_o 12._o the_o several_a piece_n of_o coin_n or_o denomination_n of_o money_n use_v in_o england_n in_o reference_n to_o account_v be_v pound_n shilling_n penny_n and_o farthing_n who_o particular_a value_n be_v as_o follow_v 4._o farthing_n make_v 1._o penny_n 12._o penny_n make_v 1._o shilling_n 20._o shilling_n make_v 1._o pound_n sterling_n and_o according_a to_o these_o value_n a_o pound_n sterling_n be_v esteem_v a_o integer_fw-la and_o may_v be_v divide_v into_o 20_o part_n call_v shilling_n and_o therefore_o one_o shilling_n be_v a_o break_a number_n of_o a_o pound_n sterling_n &_o by_o the_o former_a direction_n be_v to_o be_v write_v thus_o 1_o â—â—_o l._n that_o be_v one_o twenty_o of_o a_o pound_n again_o a_o shilling_n may_v be_v divide_v into_o twelve_o equal_a part_n call_v penny_n and_o so_o one_o penny_n be_v a_o fraction_n of_o a_o shilling_n and_o be_v to_o be_v write_v thus_o â—_o 12_o s._n that_o be_v one_o twelve_o of_o a_o shilling_n last_o a_o penny_n may_v be_v divide_v into_o four_o equal_a part_n call_v farthing_n and_o so_o one_o farthing_n be_v a_o fraction_n of_o a_o penny_n and_o write_v thus_o ¼_n d._n that_o be_v one_o four_o of_o a_o penny_n or_o thus_o ¼_n of_o 1_o 12_o s._n that_o be_v one_o four_o of_o one_o twelve_o of_o a_o shilling_n or_o thus_o ¼_n of_o 1_o 12_o of_o 1_o 20_o l._n that_o be_v one_o four_o of_o one_o twelve_o of_o one_o twenty_o of_o a_o pound_n sterling_n 13._o now_o than_o though_o the_o true_a and_o natural_a way_n of_o express_v break_a number_n be_v by_o their_o numerator_n and_o denominator_n as_o have_v be_v show_v yet_o the_o break_a number_n or_o know_v part_n of_o money_n weight_n measure_n and_o such_o like_a be_v for_o more_o convenient_a operation_n common_o express_v like_o integer_n so_o that_o if_o 12_o shilling_n seven_o penny_n half_a penny_n farthing_n be_v to_o be_v express_v in_o figure_n the_o ordinary_a &_o most_o usual_a way_n be_v thus_o 12_n −_o 07d_o 03_o f._n but_o the_o say_v twelve_o shilling_n seven_o penny_n half_a penny_n farthing_n be_v distinct_o consider_v as_o fraction_n of_o a_o pound_n sterling_n the_o way_n to_o write_v they_o proper_o be_v thus_o 12_o shilling_n be_v twelve_o twentieth_n of_o a_o pound_n sterling_n and_o write_v thus_o 12_o 2d_o l._n 7_o penny_n be_v seven_o twelfth_n of_o one_o twenty_o of_o a_o pound_n sterling_n and_o write_v thus_o 7_o 12_o of_o 1_o 20_o l._n 3_o farthing_n be_v three_o fourth_n of_o one_o twelve_o of_o one_o twenty_o of_o a_o pound_n and_o write_v thus_o ¾_n of_o 1_o 12_o of_o 1_o 20_o l._n 14._o the_o weight_v use_v in_o england_n be_v of_o two_o sort_n troy_n weight_n and_o averdupois_n 15._o the_o several_a piece_n or_o denomination_n of_o troy_n weight_n be_v pound_n ounce_n penny_n weight_n and_o grain_n who_o particular_a value_n be_v as_o follow_v 24_o grain_n make_v 1_o peny_n weight_n 20_o penny_n weight_n make_v 1_o ounce_n 12_o ounce_n make_v 1_o pound_n troy_n 16._o the_o weight_v use_v by_o apothecary_n be_v derive_v from_o a_o pound_n troy_n the_o which_o be_v subdivide_v as_o in_o the_o follow_a table_n lb_v a_o pound_n troy_n be_v equal_a to_o 12_o ounce_n â„¥_o a_o ounce_n be_v equal_a to_o 8_o dram_fw-la Ê’_n a_o dram_n be_v equal_a to_o 3_o scruple_n ℈_o a_o scruple_n be_v equal_a to_o 20_o grain_n 17._o but_o beside_o troy_n weight_n there_o be_v another_o kind_n of_o weight_n use_v in_o england_n call_v averdupois_n weight_n a_o pound_n whereof_o be_v equal_a unto_o 14_o ounce_n and_o twelve-peny_n weight_n troy_n 18._o this_o averdupois_n weight_n be_v either_o great_a or_o small_a 19_o the_o great_a averdupois_n weight_n be_v when_o a_o hundred_o consist_v of_o 112_o pound_n averdupois_n be_v the_o integer_fw-la and_o subdivide_v into_o half_n and_o quarter_n each_o quarter_n contemn_v 28_o pound_n 20._o the_o small_a averdupois_n weight_n be_v when_o a_o pound_n be_v the_o integer_fw-la each_o pound_n be_v subdivide_v into_o 16_o ounce_n each_o ounce_n into_o 16_o dram_n and_o each_o dram_n into_o 4_o quarter_n and_o because_o many_o person_n have_v occasion_n to_o use_v both_o and_o be_v perhaps_o furnish_v but_o with_o one_o i_o have_v here_o exhibit_v a_o table_n for_o the_o speedy_a convert_n of_o the_o part_n of_o a_o pound_n troy_n into_o the_o part_n of_o a_o pound_n averdupois_n and_o the_o contrary_a dram_fw-la averdupois_n  _fw-fr peny-weight_n troy_n grain_n decimal_n of_o a_o grain_n  _fw-fr ounce_n averdupois_n ounce_n troy_n peny-weight_n grain_n 1_o  _fw-fr 01_o 03_o 375_o  _fw-fr 1_o 00_o 18_o 06_o 2_o  _fw-fr 2_o â—6_n â—50_n  _fw-fr 2_o 01_o 16_o 12_o 3_o  _fw-fr 3_o 10_o 125_o  _fw-fr 3_o 2_o 14_o 18_o 4_o dram_n averdupois_n 4_o 13_o 500_o  _fw-fr 4_o 3_o 13_o  _fw-fr 5_o  _fw-fr 5_o 16_o 875_o  _fw-fr 5_o 4_o 11_o 06_o 6_o  _fw-fr 6_o 20_o 250_o  _fw-fr 6_o 5_o 9_o 12_o 7_o  _fw-fr 7_o 23_o 625_o  _fw-fr 7_o 6_o 7_o 18_o 8_o weight_n be_v equal_a to_o 9_o 03_o 000_o  _fw-fr 8_o 7_o 06_o  _fw-fr 9_o  _fw-fr 10_o 06_o 375_o  _fw-fr 9_o 8_o 04_o 06_o 10_o  _fw-fr 11_o 19_o 750_o  _fw-fr 10_o 9_o 02_o 12_o 11_o  _fw-fr 12_o 03_o 125_o  _fw-fr 11_o 10_o 00_o 18_o 12_o  _fw-fr 13_o 16_o 500_o  _fw-fr 12_o 10_o 19_o 00_o 13_o  _fw-fr 14_o 19_o 875_o  _fw-fr 13_o 11_o 17_o 06_o 14_o  _fw-fr 15_o 23_o 250_o  _fw-fr 14_o 12_o 15_o 12_o 15_o  _fw-fr 17_o 02_o 625_o  _fw-fr 15_o 13_o 13_o 18_o 16_o  _fw-fr 18_o 06_o 000_o  _fw-fr 16_o 14_o 12_o 00_o 21._o the_o measure_v use_v in_o england_n be_v of_o two_o sort_n capacity_n or_o length_n 22._o the_o measure_n of_o capacity_n be_v produce_v from_o weight_n and_o be_v also_o of_o two_o sort_n liquid_a or_o dry_a 23._o the_o liquid_a measure_n be_v those_o in_o which_o all_o kind_n of_o liquid_a substance_n be_v measure_v and_o be_v express_v in_o the_o table_n follow_v 1_o pound_n of_o wheat_n troy_n weight_n make_v 1_o pint._n 2_o pint_n make_v 1_o quart_n 2_o quart_n make_v 1_o pottle_n 2_o pottle_n make_v 1_o gallon_n 8_o gallon_n make_v 1_o firkin_n of_o ale_n soap_n herring_n 9_o gallon_n make_v 1_o firkin_n of_o beer_n 10½_n gallon_n make_v 1_o firk_v of_o salmon_n or_o eel_n 2_o firkins_n make_v 1_o kilderkin_n 2_o kilderkin_n make_v 1_o barrel_n 42_o gallon_n make_v 1_o tierce_n of_o wine_n 63_o gallon_n make_v 1_o hogshead_n 2_o hogshead_n make_v 1_o pipe_n or_o but._n 2_o pipe_n or_o butt_n make_v 1_o tau_n of_o wine_n 24._o dry_a measure_n be_v those_o in_o which_o all_o kind_n of_o dry_a substance_n be_v measure_v as_o grain_n sea-coal_n salt_n and_o such_o like_a and_o be_v express_v in_o the_o table_n follow_v 1_o pint_n make_v 1_o pint._n 2_o pint_n make_v 1_o quart_n 2_o quart_n make_v 1_o pottle_n 2_o pottle_n make_v 1_o gallon_n 2_o gallon_n make_v 1_o peck_n 4_o peck_v make_v 1_o bushel_n land_n measure_n 5_o peck_v make_v 1_o bushel_n water_n measure_n 8_o bushel_n make_v 1_o quarter_n 4_o quarter_n make_v 1_o chalder_n 5_o quarter_n make_v 1_o wey_n 25._o long_o measure_n be_v as_o follow_v 3_o barley_n corn_n in_o length_n make_v 1_o inch._n 12_o inch_n make_v 1_o foot_n 3_o foot_n make_v 1_o yard_n 3_o foot_n 9_o inch_n make_v 1_o ell._n 6_o foot_n make_v 1_o fathom_n 5_o yard_n and_o ½_o make_v 1_o pole_n or_o perch_n 40_o pole_n make_v 1_o furlong_n 8_o furlong_n make_v 1_o english_a mile_n 26._o in_o superficial_a or_o square_a measure_n 40_o square_a pole_n or_o perch_n make_v 1_o rood_n or_o quarter_n of_o a_o acre_n and_o 4_o rood_n a_o acre_n 27._o a_o table_n of_o time_n be_v this_o that_o follow_v 1_o minute_n make_v 1_o minute_n 60_o minute_n make_v 1_o hour_n 24_o hour_n make_v 1_o day_n 7_o day_n
multiplication_n and_o after_o the_o multiplication_n be_v finish_v to_o reduce_v the_o product_n into_o the_o former_a denomination_n if_o need_v be_v for_o example_n if_o 283_o man_n be_v to_o receive_v 28_o pound_n 13_o shilling_n 9_o penny_n a_o man_n how_o much_o money_n must_v be_v pay_v to_o the_o 283_o man_n before_o i_o begin_v the_o multiplication_n i_o must_v reduce_v the_o 28_o pound_n 13_o shilling_n 9_o penny_n into_o penny_n which_o according_a to_o the_o rule_n of_o reduction_n give_v will_v be_v 6885_o penny_n and_o then_o 6885_o ×_o 283_o =_o 1948455_o as_o by_o the_o work_n in_o the_o margin_n and_o so_o many_o penny_n 08_o be_v require_v to_o pay_v off_o the_o 283_o man_n and_o 1948455_o penny_n be_v reduce_v into_o the_o former_a denomination_n they_o will_v be_v find_v equal_a to_o 8118_o pound_n 11_o shilling_n and_o 3_o penny_n 3._o when_o a_o numbeâ—_n of_o diverse_a denomination_n be_v give_v to_o be_v multiply_v by_o another_o of_o diverse_a denomination_n also_o but_o denomination_n of_o the_o same_o kind_n it_o will_v be_v convenient_a to_o reduce_v both_o the_o number_n into_o number_n of_o the_o least_o denomination_n give_v before_o you_o begin_v your_o multiplication_n and_o after_o your_o multiplication_n be_v finish_v to_o reduce_v the_o product_n into_o the_o former_a denomination_n give_v for_o example_n let_v it_o be_v require_v to_o multiply_v 2_o pound_n 9_o shilling_n and_o 6_o penny_n by_o itself_o reduction_n be_v make_v according_a to_o the_o former_a direction_n the_o number_n of_o penny_n in_o each_o number_n will_v be_v 594_o and_o 594_o penny_n be_v multiply_v by_o 594_o penny_n the_o product_n will_v be_v 352836_o square_a penny_n which_o be_v divide_v by_o 57600_o the_o number_n of_o square_a penny_n in_o a_o pound_n the_o quotient_n will_v be_v 6_o pound_n 2_o shilling_n 6_o penny_n and_o â—_o â—_o of_o a_o farthing_n as_o by_o the_o operation_n it_o do_v appear_v 4._o another_o way_n in_o the_o annex_v diagram_n let_v there_o be_v two_o number_n of_o three_o denomination_n give_v and_o let_v a_o f_o be_v the_o square_a or_o rect_a angle_n make_v of_o the_o great_a denomination_n in_o both_o number_n e_z k_o and_o b_o g_z two_o rect_a angle_n make_v by_o multiply_v the_o first_o denomination_n by_o the_o second_o the_o product_n be_v divide_v by_o a_o integer_fw-la of_o the_o great_a denomination_n reduce_v into_o the_o part_n of_o the_o second_o the_o quotient_n shall_v be_v of_o the_o same_o denomination_n with_o the_o great_a and_o the_o remainder_n of_o the_o same_o denomination_n with_o the_o second_o f_o l_o be_v the_o square_a of_o the_o second_o denomination_n which_o be_v divide_v by_o a_o integer_fw-la of_o the_o first_o or_o great_a reduce_v into_o the_o part_n of_o the_o second_o the_o quotient_n shall_v be_v of_o the_o same_o denomination_n with_o the_o second_o and_o if_o there_o be_v any_o remainder_n it_o must_v be_v multiply_v by_o a_o number_n which_o in_o the_o three_o denomination_n be_v equal_a to_o a_o integer_fw-la in_o the_o second_o the_o quotient_n shall_v be_v of_o the_o three_o denomination_n and_o if_o there_o be_v yet_o a_o remainder_n it_o must_v be_v multiply_v by_o a_o number_n which_o in_o the_o four_o denomination_n be_v equal_a to_o a_o integer_fw-la in_o the_o thid_v and_o divide_v as_o before_o the_o quotient_n shall_v be_v of_o the_o four_o denomination_n and_o so_o forward_o till_o the_o remainder_n can_v be_v reduce_v into_o lesser_a term_n and_o thus_o you_o have_v do_v with_o the_o square_n or_o rect_a angle_n a_o c_o lh_n from_o this_o diagram_n thus_o explain_v the_o multiplication_n of_o pound_n shilling_n and_o penny_n by_o pound_n shilling_n and_o penny_n will_v be_v plain_a and_o easy_a for_o 1._o pound_n multiply_v by_o pound_n produce_v pound_n 2._o pound_n multiply_v by_o shilling_n and_o the_o product_v divide_v by_o 20_o the_o quotient_n will_v be_v pound_n and_o the_o remainder_n shilling_n 3._o shilling_n multiply_v by_o shilling_n the_o product_n will_v be_v the_o numerator_n of_o a_o fraction_n who_o denominator_fw-la be_v 400_o the_o square_a of_o shilling_n in_o a_o pound_n the_o value_n of_o which_o fraction_n may_v be_v find_v by_o multiply_v the_o numerator_n first_o by_o 20_o and_o divide_v the_o product_n by_o 400_o the_o quotient_n shall_v be_v shilling_n and_o the_o remainder_n the_o fraction_n of_o a_o shilling_n which_o be_v multiply_v by_o 12_o and_o the_o product_v divide_v by_o 400_o the_o quotient_n shall_v be_v penny_n and_o the_o remainder_n the_o fraction_n of_o a_o penny_n which_o be_v multiply_v by_o 4_o and_o the_o product_v divide_v by_o 400_o the_o quotient_n shall_v be_v farthing_n &_o the_o remainder_n shall_v be_v the_o fraction_n of_o a_o farthing_n example_n if_o 19_o shilling_n be_v give_v to_o be_v multiply_v by_o 19_o shilling_n the_o product_n will_v be_v 361_o for_o the_o numerator_n of_o a_o fraction_n who_o denominator_fw-la be_v 400_o which_o fraction_n be_v multiply_v and_o divide_v according_a to_o the_o former_a direction_n the_o value_n thereof_o will_v be_v 18_o shilling_n 0_o penny_n 2_o farthing_n 4_o 10._o set_a the_o work_n thus_o or_o thus_o shilling_n multiply_v by_o shilling_n and_o the_o product_v divide_v by_o 20_o the_o quotient_n will_v be_v shilling_n and_o the_o remainder_n the_o fraction_n of_o a_o shilling_n as_o the_o former_a product_n 361_o be_v divide_v by_o 20_o the_o quotient_n be_v 18_o shilling_n as_o before_o and_o the_o remainder_n be_v 1_o 20_o which_o be_v reduce_v be_v 0_o d._n 2_o f._n &_o 4_o 10._o 4._o pound_n multiply_v by_o penny_n the_o product_n be_v the_o numerator_n of_o a_o fraction_n who_o denominator_fw-la be_v 240_o the_o number_n of_o penny_n in_o a_o pound_n thus_o 2_o pound_n be_v multiply_v by_o 11_o penny_n the_o product_n be_v 22_o for_o the_o numerator_n to_o 240_o now_o than_o if_o you_o multiply_v 22_o by_o 20_o and_o divide_v the_o product_n by_o 240_o the_o quotient_n will_v be_v 1200_o â—40_n shilling_n and_o this_o also_o be_v multiply_v by_o 12_o and_o the_o product_v divide_v by_o 240_o the_o quotient_n will_v be_v 10_o penny_n or_o thus_o pound_n multiply_v by_o penny_n and_o the_o product_v divide_v by_o 12_o the_o quotient_n will_v be_v shilling_n and_o the_o remainder_n penny_n thus_o re-divided_n by_o 12_o give_v 1_o shilling_n 10_o penny_n as_o before_o 5._o shilling_n multiply_v by_o penny_n the_o product_n will_v be_v the_o numerator_n of_o a_o fraction_n who_o denominator_fw-la be_v 240_o the_o number_n of_o penny_n in_o a_o pound_n and_o this_o numerator_n be_v multiply_v by_o 12_o and_o the_o product_v divide_v by_o 240_o the_o quotient_n will_v be_v penny_n and_o the_o remainder_n the_o fraction_n of_o a_o penny_n which_o be_v multiply_v by_o 4_o and_o the_o product_v divide_v by_o 240_o the_o quotient_n will_v be_v farthing_n and_o the_o remainder_n the_o fraction_n of_o a_o farthing_n example_n 19_o shilling_n be_v multiply_v by_o 11_o penny_n the_o product_n be_v 209_o which_o be_v multiply_v by_o 12_o the_o product_n be_v 2508_o and_o this_o product_n be_v divide_v by_o 240_o the_o quotient_n be_v 10_o penny_n and_o the_o remainder_n 108_o which_o be_v multiply_v by_o 4_o the_o product_n be_v 432_o and_o this_o product_n be_v also_o divide_v by_o 240_o the_o quotient_n be_v one_o farthing_n and_o 19â—_n 240_o or_o â…˜_n or_o thus_o shilling_n multiply_v by_o penny_n and_o the_o product_v divide_v by_o 20_o the_o quotient_n will_v be_v penny_n and_o the_o remainder_n the_o fraction_n of_o a_o penny_n thus_o 209_o being_n divide_v by_o 20_o the_o quotient_n be_v 10_o penny_n and_o one_o farthing_n and_o 16_o 20_o or_o â…˜_n as_o before_o 6._o penny_n multiply_v by_o penny_n the_o product_n will_v be_v the_o numerator_n of_o a_o fraction_n who_o denominator_fw-la must_v be_v 57600_o the_o number_n of_o square_a penny_n in_o a_o pound_n which_o numerator_n be_v multiply_v by_o 20_o by_o 12_o and_o by_o 4_o continual_o and_o the_o last_o product_n be_v divide_v by_o 57600_o the_o quotient_n will_v be_v farthing_n and_o the_o remainder_n the_o fraction_n of_o a_o farthing_n example_n lâ—t_v 11_o penny_n be_v give_v to_o be_v multiply_v by_o 11_o penny_n the_o product_n be_v 121_o which_o be_v multiply_v by_o 20_o the_o product_n be_v 2420_o and_o 2420_o be_v multiply_v by_o 12_o the_o product_n be_v 29040_o and_o this_o also_o be_v multiply_v by_o 4_o the_o product_n be_v 116160_o and_o this_o last_o product_n be_v divide_v by_o 57600_o the_o quotient_n be_v 2_o farthing_n 57â—60_n 6â—0_n or_o 1_o 60._o or_o thus_o 121_o be_v multiply_v by_o 4_o the_o product_n will_v be_v 484_o which_o be_v divide_v by_o 240_o the_o number_n of_o penny_n in_o a_o pound_n the_o quotient_n will_v be_v two_o farthing_n 4_o 24â—_n or_o 1_o 6â—_n as_o before_o for_o
wish_v that_o the_o same_o be_v also_o do_v in_o all_o other_o astronomical_a canon_n how_o such_o fraction_n therefore_o may_v be_v convert_v into_o decimal_n the_o follow_a example_n will_v sufficient_o declare_v â—â—â—_o as_o much_o as_o 60_o minute_n make_v a_o degree_n 60_o second_n a_o minute_n 60_o three_o a_o second_o and_o so_o forward_o as_o far_o as_o you_o please_v if_o you_o divide_v the_o minute_n give_v with_o cypher_n annex_v by_o 60_o the_o quotient_n shall_v be_v the_o decimal_n seek_v thus_o if_o the_o decimal_n of_o 45_o minute_n be_v require_v i_o divide_v 450000_o etc._n etc._n by_o 60_o and_o the_o quotient_n be_v 75_o for_o the_o decimal_n of_o 45_o minute_n if_o the_o decimal_n of_o second_o be_v require_v your_o divisor_n must_v be_v 3600_o if_o the_o decimal_n of_o three_o be_v require_v your_o divisor_n must_v be_v 216000_o and_o 12960000_o for_o fourth_n but_o if_o there_o be_v diverse_a sexagesimal_n species_n join_v to_o integer_n suppose_v 127_o deg_n 32_o min._n 00_o sec._n 09_o three_o 45_o fourth_n you_o may_v use_v this_o compendium_n under_o the_o integer_v 127_o set_v the_o sexagesimal_a species_n in_o a_o oblique_a descent_n as_o here_o you_o see_v in_o the_o margin_n then_o begin_v at_o the_o low_a divide_v every_o of_o they_o continual_o f._n by_o 6_o and_o set_v the_o quotient_n over_o their_o head_n join_v they_o to_o the_o row_n next_o above_o until_o you_o come_v to_o the_o integer_n so_o shall_v the_o last_o quotient_n be_v the_o decimal_n seek_v oughtred_n clavis_fw-la chap._n 6._o thus_o 45_o fourth_n be_v divide_v by_o 6_o the_o quotient_n be_v 7_o and_o the_o next_o dividend_n 09.75_o which_o be_v also_o divide_v by_o 6_o the_o quotient_n be_v 1625_o and_o the_o next_o dividend_n 00.1625_o f._n which_o be_v also_o divide_v by_o 6_o the_o quotient_n be_v 002708333_o and_o the_o next_o dividend_n 32.002708333_o fourth_n which_o be_v divide_v by_o 6_o the_o quotient_a 5333784722_o be_v the_o decimal_n seek_v 8._o when_o a_o decimal_a fraction_n be_v give_v and_o the_o value_n thereof_o in_o the_o know_a part_n of_o the_o integer_fw-la be_v require_v multiply_v the_o decimal_n propound_v by_o the_o number_n of_o know_a part_n of_o the_o next_o inferior_a denomination_n which_o be_v equal_a to_o the_o integer_n and_o from_o that_o product_n cut_v off_o as_o many_o figure_n towards_o the_o right_n as_o the_o decimal_n give_v do_v consist_v of_o place_n the_o figure_n remain_v be_v the_o value_n of_o that_o fraction_n in_o the_o next_o inferior_a denomination_n and_o the_o value_n of_o the_o remain_a part_n of_o the_o decimal_n give_v in_o the_o next_o inferior_a denomination_n may_v be_v find_v by_o the_o same_o rule_n and_o so_o forward_o till_o you_o come_v to_o the_o last_o know_v part_n example_n let_v the_o value_n of_o this_o decimal_n .98563_o be_v require_v in_o the_o know_a part_n of_o a_o pound_n sterling_a this_o decimal_n 98563_o be_v multiply_v by_o 20_o that_o product_n be_v 19_o 71260_o from_o which_o i_o cut_v off_o five_o figure_n the_o rest_n be_v 19_o shilling_n and_o the_o figure_n cut_v off_o namely_o 71,260_o be_v multiply_v by_o 12_o the_o product_n be_v 8.55120_o that_o be_v 8_o f._n penny_n and_o 55120_o part_n of_o a_o shilling_n which_o be_v multiply_v by_o 4_o the_o product_n be_v 2,220480_o that_o be_v 2_o farthing_n and_o the_o remainder_n 20480_o be_v the_o decimal_a part_n of_o a_o farthing_n and_o so_o the_o value_n of_o the_o decimal_n fraction_n give_v be_v 19_o shilling_n 8_o penny_n ½_o penny_n but_o the_o value_n of_o a_o decimal_n fraction_n in_o the_o know_a part_n of_o a_o pound_n may_v be_v know_v by_o inspection_n for_o the_o first_o figure_n double_v give_v the_o number_n of_o shilling_n the_o two_o next_o figure_n be_v the_o farthing_n thus_o in_o the_o decimal_n give_v 98563_o the_o figure_n 9_o be_v double_v be_v 18_o shilling_n and_o 85_o farthing_n that_o be_v 21_o penny_n and_o a_o farthing_n but_o more_o exact_o thus_o from_o 85_o deduct_v 75_o which_o be_v the_o decimal_n of_o 18_o penny_n the_o remainder_n be_v 10_o farthing_n or_o 2_o penny_n half_a penny_n that_o be_v in_o all_o 19_o −_o 8d_n 2_o farthing_n as_o before_o if_o the_o decimal_n fraction_n give_v who_o value_n be_v inquire_v be_v the_o decimal_n of_o the_o degree_n for_o a_o circle_n you_o must_v divide_v the_o decimal_n give_v by_o six_o continual_o and_o write_v the_o product_n underneath_o in_o every_o row_n cut_v off_o one_o place_n towards_o the_o right_a hand_n so_o shall_v you_o have_v the_o value_n desire_v let_v the_o decimal_n fraction_n give_v be_v 127.5333784723_o and_o let_v the_o value_n thereof_o in_o minute_n and_o second_n be_v desire_v this_o fraction_n be_v multiply_v by_o 6_o the_o product_n be_v 32.002708332_o from_o f._n which_o cut_v off_o one_o place_n of_o the_o fraction_n give_v the_o figure_n remain_v give_v 32_o minute_n and_o so_o multiply_v of_o the_o remainder_n by_o 6_o continual_o the_o product_n give_v 00_o second_n 09_o three_o and_o 45_o fourth_n almost_o as_o by_o the_o operation_n in_o the_o margin_n do_v appear_v a_o table_n for_o the_o speedy_a reduce_n of_o english_a money_n and_o the_o part_n of_o a_o ounce_n in_o troy_n weight_n into_o decimal_n and_o the_o contrary_n t._n w._n penc_n 0_o 1_o 2_o 3_o 46_o 23_o 095833_o 096875_o 097916_o 098958_o 44_o 22_o 091666_o 092708_o 093750_o 094791_o 42_o 21_o 087500_o 088541_o 089583_o 526090_o 40_o 20_o 083333_o 084375_o 085416_o 086458_o 38_o 19_o 079166_o 0â—0208_n 081250_o 082291_o 36_o 18_o 075000_o 076014_o 077083_o 078125_o 34_o 17_o 070833_o 071874_o 072916_o 073958_o 32_o 16_o 066666_o 067708_o 068750_o 069792_o 30_o 15_o 062500_o 063542_o 064583_o 065625_o 28_o 14_o 058333_o 059375_o 060416_o 061458_o 26_o 13_o 054166_o 055208_o 065250_o 057292_o 24_o 12_o 050000_o 05104â—_n 052083_o 053125_o 22_o 11_o 045833_o 046875_o 047016_o 048958_o 20_o 10_o 041666_o 042708_o 043750_o 044791_o 18_o 9_o 037500_o 038541_o 039583_o 040625_o 16_o 8_o 033333_o 034375_o 035416_o 036458_o 14_o 7_o 029166_o 030208_o 031250_o 032291_o 12_o 6_o 025000_o 026014_o 027083_o 028125_o 10_o 5_o 020833_o 021874_o 022916_o 023958_o 8_o â—_o 016666_o 017708_o 018750_o 019791_o 6_o 3_o 012500_o 013541_o 014583_o 015925_o 4_o 2_o â—08333_n 009375_o 010416_o 011458_o 2_o 1_o 004166_o 005208_o 006250_o 007291_o 0_o 0_o 0000â—0_n 001â—42_n 002083_o 003125_o the_o use_n of_o the_o table_n this_o table_n do_v consist_v of_o six_o column_n in_o the_o first_o you_o have_v each_o other_o grain_n in_o two_o penny_n weight_n troy_n in_o the_o second_o every_o penny_n in_o two_o shilling_n in_o the_o other_o four_o column_n you_o have_v the_o decimal_n answer_v to_o the_o grain_n in_o troy_n weight_n and_o to_o the_o penny_n and_o farthing_n not_o exceed_v two_o shilling_n in_o english_a money_n example_n let_v the_o decimal_n 1_o penny_n weight_n and_o 16_o grain_n be_v require_v or_o the_o decimal_n of_o 40_o grain_n i_o look_v for_o 40_o grain_n in_o the_o first_o column_n and_o in_o the_o three_o i_o find_v the_o decimal_n thereof_o to_o be_v 083333._o or_o let_v the_o decimal_n of_o 1_o penny_n weight_n and_o 11_o grain_n be_v require_v that_o be_v the_o decimal_n of_o 35_o grain_n 34_o grain_n i_o find_v in_o the_o table_n and_o therefore_o in_o the_o same_o line_n in_o the_o first_o column_n i_o find_v 072916_o for_o the_o decimal_n thereof_o if_o the_o decimal_n of_o 17_o penny_n weight_n and_o 13_o grain_n be_v require_v the_o decimal_n of_o 16_o penny_n weight_n be_v the_o half_a thereof_o viz._n 8_o and_o that_o decimal_n of_o one_o penny_n weight_n 13_o grain_n be_v 077083_o and_o so_o the_o decimal_n require_v be_v 8.077083_o the_o like_a may_v be_v do_v for_o any_o other_o and_o so_o for_o money_n you_o have_v the_o penny_n in_o the_o second_o column_n and_o the_o farthing_n in_o the_o top_n of_o that_o page_n and_o in_o the_o angle_n of_o meet_v the_o decimal_n answer_v thereunto_o thus_o the_o decimal_n of_o 19_o penny_n 3_o farthing_n be_v 08â—291_n and_o so_o for_o any_o other_o chap._n xvi_o of_o the_o addition_n and_o subtraction_n of_o decimal_n 1._o the_o essential_a numeration_n of_o decimal_a fraction_n in_o all_o the_o four_o specey_n to_o wit_n of_o addition_n subtraction_n multiplication_n and_o division_n be_v the_o same_o as_o in_o whole_a number_n only_o if_o the_o number_n give_v to_o be_v add_v subtract_v multiply_v or_o divide_v be_v any_o of_o they_o mix_v number_n that_o be_v one_o part_n of_o a_o whole_a number_n and_o the_o other_o a_o decimal_n fraction_n or_o that_o in_o the_o several_a operation_n integer_n shall_v arise_v in_o the_o work_n the_o great_a difficulty_n be_v to_o distinguish_v the_o integer_n from_o the_o decimal_a part_n which_o yet_o in_o the_o three_o first_o species_n of_o
7_o shilling_n the_o value_n of_o one_o escus_fw-la d'or_fw-la who_o product_n be_v 896_o shilling_n and_o then_o the_o question_n must_v be_v thus_o state_v if_o 14_o shilling_n be_v worth_a 1_o pistolet_n how_o many_o pistolet_n be_v 896_o worth_n facit_fw-la 64_o pistolet_n 7._o sometime_o a_o question_n belong_v to_o this_o rule_n must_v be_v prepare_v for_o solution_n by_o multiplication_n and_o addition_n sometime_o by_o multiplication_n and_o subtraction_n as_o in_o these_o example_n follow_v the_o first_o of_o which_o require_v multiplication_n and_o addition_n a_o butcher_n send_v his_o man_n with_o 216_o pound_n sterling_a to_o buy_v cattle_n ox_n at_o 11_o pound_n apiece_o cow_n at_o 2_o pound_n a_o piece_n colt_n at_o one_o pound_n 5_o shilling_n hog_n at_o 1_o pound_n 15_o shilling_n a_o piece_n and_o of_o each_o a_o like_a number_n the_o question_n be_v how_o many_o of_o each_o he_o may_v buy_v for_o that_o money_n to_o resolve_v this_o question_n i_o must_v first_o reduce_v the_o pound_n sterling_a into_o shilling_n by_o multiplication_n and_o 216_o pound_n be_v multiply_v by_o 20_o the_o product_n be_v 4320_o shilling_n and_o the_o several_a prize_n of_o the_o cattle_n must_v be_v reduce_v into_o shilling_n also_o and_o thus_o 11_o pound_n for_o a_o ox_n be_v 220_o shilling_n the_o price_n of_o a_o cow_n be_v 40_o shilling_n the_o price_n of_o a_o colt_n 25_o shilling_n and_o the_o price_n of_o a_o hog_n be_v 35_o shilling_n the_o sum_n of_o these_o several_a prize_n be_v 320_o shilling_n this_o do_v the_o question_n may_v be_v thus_o state_v if_o 320_o shilling_n buy_v 1_o of_o each_o sort_n how_o many_o shall_v 4160_o buy_v facit_fw-la 13._o 2._o example_n in_o the_o which_o the_o question_n be_v to_o be_v prepare_v by_o multiplication_n and_o subtraction_n if_o 128_o gallon_n of_o water_n run_v into_o a_o cistern_n in_o a_o hour_n time_n from_o one_o cock_n and_o 174_o gallon_n of_o water_n run_v into_o another_o cistern_n in_o a_o hour_n time_n also_o but_o not_o begin_v to_o run_v till_o 4_o hour_n after_o the_o first_o in_o what_o time_n will_v the_o quantity_n of_o water_n run_v out_o of_o both_o be_v equal_a to_o resolve_v this_o question_n one_o of_o the_o term_n give_v must_v be_v prepare_v by_o multiplication_n and_o another_o by_o subtraction_n first_o there_o must_v be_v compute_v how_o much_o water_n be_v run_v out_o of_o the_o first_o cock_n before_o the_o second_o begin_v and_o that_o be_v 4_o time_n 128_o gallon_n that_o be_v 512_o second_o it_o must_v be_v consider_v how_o many_o gallon_n more_o do_v run_v out_o of_o the_o last_o cock_n than_o do_v out_o of_o the_o first_o in_o a_o hour_n time_n which_o by_o subtract_v 128_o from_o 174_o i_o find_v to_o be_v 46_o and_o hence_o this_o question_n be_v to_o be_v thus_o state_v if_o i_o gain_v 46_o gallon_n in_o one_o hour_n in_o how_o many_o hour_n shall_v i_o gain_v 512_o gallon_n facit_fw-la 11._o 8._o sometime_o a_o question_n belong_v to_o this_o rule_n must_v be_v prepare_v for_o solution_n by_o arithmetical_a or_o geometrical_a proportion_n as_o in_o these_o question_n follow_v a_o man_n go_v a_o journey_n spend_v one_o shilling_n the_o first_o day_n 3_o the_o second_o 5_o the_o three_o 7_o the_o four_o still_o increase_a his_o expense_n by_o this_o proportion_n till_o he_o have_v spend_v 1500_o shilling_n i_o demand_v in_o how_o many_o day_n that_o sum_n be_v spend_v to_o resolve_v this_o question_n the_o sum_n of_o such_o a_o arithmetical_a progression_n for_o some_o certain_a time_n must_v be_v first_o compute_v as_o suppose_v for_o thirty_o day_n which_o will_v be_v find_v to_o be_v 900_o shilling_n and_o hence_o it_o may_v be_v thus_o conclude_v if_o 900_o shilling_n last_v i_o 30_o day_n how_o long_o shall_v 1500_o shilling_n last_v i_o facit_fw-la 50._o another_o question_n may_v be_v this_o if_o a_o piece_n of_o cloth_n contain_v 40_o yard_n do_v cost_v i_o 30_o pound_n at_o what_o rate_n must_v that_o cloth_n be_v sell_v to_o gain_v 12_o pound_n in_o the_o hundred_o before_o this_o question_n can_v be_v resolve_v i_o must_v find_v the_o price_n of_o one_o yard_n by_o a_o proportion_n geometrical_a by_o way_n of_o preparation_n thus_o if_o 4â—_n yard_n cost_v 50_o pound_n what_o shall_v one_o yard_n cost_n facit_fw-la 1¼_n then_o i_o say_v if_o 100_o pound_n be_v increase_v to_o 112_o to_o what_o shall_v 1¼_n be_v increase_v answer_v 1â…–_n chap._n xxii_o the_o rule_n of_o three_o in_o fraction_n 1._o fraction_n as_o i_o have_v already_o show_v be_v of_o 3_o sort_n viz._n such_o as_o be_v many_o time_n express_v like_o integer_n such_o as_o be_v express_v by_o their_o numerator_n and_o denominator_n and_o such_o as_o have_v a_o unite_v with_o cipher_n annex_v for_o their_o denominator_fw-la and_o now_o know_v by_o the_o name_n of_o decimal_a fraction_n in_o each_o of_o these_o i_o will_v exemplify_v this_o rule_n by_o some_o few_o example_n and_o first_o in_o such_o fraction_n as_o be_v express_v like_o integer_n 2._o your_o question_n be_v state_v bring_v your_o number_n propound_v into_o the_o least_o name_n mention_v or_o as_o low_o as_o you_o desire_v the_o question_n to_o be_v answer_v in_o then_o multiply_v the_o second_o and_o three_o and_o divide_v the_o product_n by_o the_o first_o if_o your_o question_n belong_v to_o the_o rule_n of_o three_o direct_v or_o multiply_v the_o first_o and_o second_o and_o divide_v by_o the_o three_o if_o it_o belong_v to_o the_o rule_n of_o three_o inverse_n the_o quotient_a be_v reduce_v shall_v be_v the_o answer_n require_v example_n if_o 7_o lib._n 8_o ounce_n of_o currant_n cost_v 2s_n 7d_o what_o shall_v 100½_n 13_o lib._n cost_n in_o this_o question_n the_o first_o and_o three_o term_n must_v be_v reduce_v into_o ounce_n and_o the_o second_o term_n into_o penny_n and_o then_o the_o question_n will_v stand_v thus_o if_o 112_o ounce_n cost_v 31_o penny_n what_o shall_v 1267_o ounce_n cost_n facit_fw-la 359d_o 1_o 64_o 112_o farthing_n that_o be_v 1l_o 9_n 11d_o 1f_o â…˜_n of_o a_o farthing_n a_o second_o example_n may_v be_v this_o a_o man_n do_v borrow_v of_o his_o friend_n 246_o lib._n 7_o shilling_n and_o 6_o penny_n for_o 27_o week_n for_o how_o long_a time_n must_v he_o lend_v his_o friend_n 329_o lib._n 13_o shilling_n 4d_o to_o require_v his_o kindness_n here_o it_o be_v plain_a that_o the_o four_o term_v require_v must_v be_v less_o than_o the_o second_o term_n give_v and_o therefore_o the_o great_a extreme_a must_v be_v the_o divisor_n and_o the_o number_n be_v reduce_v and_o place_v as_o have_v be_v direct_v they_o will_v stand_v thus_o 59130_o 187_o 79120_o in_o which_o the_o great_a extreme_a being_n in_o the_o three_o place_n do_v plain_o show_v that_o this_o question_n do_v belong_v to_o the_o rule_n of_o three_o inverse_n and_o therefore_o as_o 3_o example_n in_o sexagenary_a number_n if_o 48_o fir_v 28_o second_n give_v 60_o minute_n what_o shall_v 25_o minute_n 12_o second_o give_v according_a to_o the_o former_a rule_n give_v in_o multiplication_n 25_o fir_v 12_o second_o be_v multiply_v by_o 60_o minute_n the_o product_n be_v 25_o degree_n 12_o fir_v 00_o second_n which_o be_v divide_v by_o 48_o fir_v 28_o second_n the_o quotient_n will_v be_v 31_o fir_v 08_o second_n 4._o example_n in_o vulgar_a fraction_n if_o â…”_n of_o a_o yard_n of_o velvet_n be_v sell_v for_o â…˜_n of_o a_o pound_n sterling_a what_o shall_v â…ž_n of_o a_o yard_n cost_n if_o respect_n be_v have_v to_o the_o rule_n of_o the_o multiplication_n and_o division_n of_o fraction_n already_o deliver_v in_o the_o 14_o chapter_n the_o work_n of_o this_o rule_n in_o fraction_n will_v be_v the_o same_o as_o in_o whole_a number_n thus_o â…˜_n and_o â…ž_n be_v multiply_v together_o the_o product_n will_v be_v 28_o 40_o which_o be_v divide_v by_o â…”_n 7_o â…”_n the_o quotient_n be_v 84_o â—0_n or_o 1_o lib._n 4_o â—0_n or_o 1_o 20_o and_o so_o the_o answer_n be_v 1_o pound_n and_o one_o shilling_n otherwise_o thus_o multiply_v the_o denominator_fw-la of_o the_o first_o number_n by_o the_o numerator_n of_o the_o second_o and_o three_o continual_o so_o shall_v the_o last_o product_n be_v a_o new_a numerator_n then_o multiply_v the_o numerator_n of_o the_o first_o number_n by_o the_o denominator_n of_o the_o second_o and_o three_o number_n continual_o so_o shall_v the_o last_o product_n be_v a_o new_a denominator_fw-la and_o this_o fraction_n shall_v be_v the_o quotient_a desire_a thus_o the_o denominator_fw-la 3_o being_n multiply_v first_o by_o 4_o and_o then_o by_o 7_o the_o last_o product_n be_v 84_o and_o the_o numerator_n 2_o be_v multiply_v first_o by_o 5_o and_o then_o by_o 8_o the_o last_o product_n will_v be_v 80_o for_o a_o new_a denominator_fw-la and_o so_o the_o
imprimis_fw-la ready_a money_n of_o the_o 1000l_n 58.0000_o item_n 808_o ell_n of_o taffety_n worth_a 323_o 2000_o item_n 35_o piece_n of_o dowlace_n worth_n 125.1882_o item_n 55_o piece_n of_o holland_n worth_n 493.6092_o that_o be_v 999_o lib._n 19_o shil_fw-la and_o 11½_n penny_n 999.9974_o the_o account_n for_o the_o 64_o piece_n of_o cloth_n which_o cost_v 30.4_o pound_n sterling_a per_fw-la piece_n that_o be_v in_o all_o 1945.6_o lib._n star_z be_v thus_o first_o then_o for_o the_o worth_n of_o the_o 77_o pistolet_n pistolet_n star_z  _fw-fr pist._n star_z 275._o 1945._o 6_o 77_o 544.768_o second_o for_o the_o worth_n of_o the_o 5546_o florin_n the_o term_n of_o the_o question_n will_v stand_v thus_o 1945.6_o lib._n sterling_a =_o 275_o spanish_a pistolet_n 198_o span._n pisto_n =_o 5821_o florin_n 5546_o florin_n =_o lib._n sterling_a here_o the_o number_n in_o the_o first_o column_n to_o be_v multiply_v together_o be_v 1945._o 6._o 198._o 5546_o and_o the_o product_n be_v 21364789248_o for_o the_o dividend_n and_o the_o number_n in_o the_o second_o column_n to_o be_v multiply_v be_v 275.5821_o who_o product_n be_v 1600775_o for_o the_o divisor_n and_o the_o quotient_a arise_v from_o these_o two_o product_n be_v 1334.6528_o which_o be_v the_o value_n of_o 5546_o florin_n in_o pound_n sterling_a last_o for_o the_o worth_n of_o 114._o 158_o flemish_a the_o term_n of_o the_o question_n will_v stand_v thus_o 1945._o 6_o lib._n sterling_a =_o 274_o spanish_a pistolet_n 198_o spanish_a pisto_n =_o 5821_o florin_n 275_o florin_n =_o 114._o 158_o lib._n flemish_n 114._o 158_o lib._n flem_n =_o pound_n sterling_a where_o neglect_v the_o 275_o pistolet_n in_o one_o column_n and_o 275_o florin_n in_o the_o other_o and_o 114._o 158_o lib._n flemish_n in_o both_o the_o number_n in_o the_o first_o column_n to_o be_v multiply_v be_v 1945._o 6_o and_o 198_o who_o product_n be_v 3852288_o for_o the_o dividend_n and_o 5821_o in_o the_o other_o column_n be_v the_o divisor_n and_o the_o quotient_a arise_v from_o two_o number_n be_v 66._o 1791_o lib._n sterling_a for_o the_o value_n of_o 114._o 158_o lib._n flem._n so_o that_o for_o the_o 64_o piece_n of_o cloth_n the_o factor_n have_v in_o his_o hand_n  _fw-fr sterling_n imprimis_fw-la 77_o pistolet_n worth_a 544._o 7680_o item_n 5546_o florin_n worth_a 1334._o 6528_o item_n 114._o 158_o lib._n flemish_n worth_a 66._o 1791_o and_o the_o balance_n be_v 1945._o 5999_o chap._n xxvii_o the_o rule_n of_o aligation_n 1._o alligation_n be_v a_o art_n by_o which_o we_o resolve_v question_n that_o concern_v the_o mix_n of_o divers_a simple_n together_o 2._o alligation_n be_v twofold_a medial_n and_o alternate_a 3._o alligation_n medial_a be_v when_o the_o several_a quantity_n and_o rate_n of_o divers_a simple_n be_v we_o find_v out_o a_o mean_a rate_n for_o which_o a_o mixture_n make_v of_o these_o simple_n may_v be_v afford_v to_o effect_v this_o the_o sum_n of_o the_o quantity_n be_v give_v with_o the_o value_n of_o all_o the_o simple_n the_o proportion_n be_v as_o the_o sum_n of_o the_o quantity_n be_v to_o the_o value_n of_o all_o the_o simple_n so_o be_v any_o part_n of_o the_o mixture_n propound_v to_o the_o mean_a rate_n that_o be_v require_v example_n let_v 12_o gallon_n of_o canary_n at_o 4_o shil_fw-la the_o gallon_n 36_o gallon_n of_o sherry_n at_o 3_o shilling_n the_o gallon_n and_o 52_o gallon_n of_o white-wine_n at_o 2_o shilling_n 8_o penny_n the_o gallon_n be_v mix_v together_o and_o let_v the_o price_n of_o one_o gallon_n of_o that_o mixture_n be_v require_v the_o sum_n of_o 12_o 36_o and_o 52_o gallon_n be_v 100_o gallon_n and_o the_o value_n of_o 12_o gallon_n of_o canary_n at_o 4_o shilling_n or_o 48_o penny_n by_o the_o gallon_n be_v 576d_o the_o value_n of_o 36_o gallon_n of_o sherry_n at_o 3_o shil_fw-la or_o 36_o penny_n be_v 1296d_o and_o the_o value_n of_o 52_o gallon_n of_o white-wine_n at_o 2_o shilling_n 8_o penny_n the_o gallon_n or_o 32_o penny_n be_v 1664_o penny_n and_o all_o these_o value_v add_v together_o do_v make_v in_o the_o whole_a 3536d_o now_o then_o by_o the_o rule_n of_o three_o 100_o 3536_o 1_o 35_o 36_o 104_o that_o be_v 35_o penny_n and_o 36_o hundred_o of_o a_o penny_n for_o proof_n of_o the_o work_n compare_v the_o total_a value_n of_o the_o several_a simple_n with_o the_o value_n of_o the_o whole_a mixture_n if_o their_o sum_n agree_v the_o work_n be_v true_a as_o in_o this_o example_n  _fw-fr l_o s_o d_o the_o value_n of_o 12_o gallon_n of_o canary_n at_o 4_o shilling_n per_fw-la gallon_n be_v 2_o 08_o 00_o the_o value_n of_o 36_o gallon_n of_o sherry_n at_o 3_o shilling_n the_o gallon_n be_v 5_o 08_o 00_o and_o the_o value_n of_o 52_o gallon_n of_o white_a wine_n at_o 2_o shil_fw-la 8_o penny_n the_o gallon_n be_v 6_o 18_o 08_o all_o which_o amount_v to_o 14_o 14_o 08_o and_o the_o value_n of_o 100_o gallon_n at_o 35d_o and_o 36_o hundred_o of_o a_o penny_n by_o the_o gallon_n be_v 14_o 14_o 08_o as_o before_o 5._o alligation_n alternate_a be_v when_o several_a rate_n of_o divers_a simple_n be_v give_v such_o a_o mixture_n be_v require_v as_o may_v be_v sell_v at_o a_o certain_a mean_a rate_n propound_v 6._o alligation_n alternate_a be_v either_o partial_a or_o total_a 7._o alternation_n partial_a be_v when_o the_o several_a rate_n of_o divers_a simple_n with_o the_o quantity_n of_o one_o of_o they_o be_v give_v and_o the_o several_a quantity_n of_o the_o rest_n be_v require_v in_o such_o sort_n that_o a_o mixture_n be_v make_v according_a to_o the_o give_v quantity_n and_o the_o quantity_n so_o find_v that_o mixture_n may_v bear_v a_o certain_a rate_n propound_v 8._o alternation_n total_a be_v when_o the_o total_a quantity_n of_o all_o the_o simple_n with_o their_o several_a rate_n be_v give_v we_o find_v out_o their_o several_a quantity_n in_o such_o sort_n as_o that_o a_o mixture_n of_o they_o be_v make_v according_a to_o the_o quantity_n so_o find_v that_o mixture_n may_v bear_v a_o certain_a mean_a rate_n propound_v 9_o in_o both_o these_o kind_n of_o alternation_n there_o be_v some_o preparation_n to_o be_v make_v before_o the_o rule_n by_o which_o such_o question_n may_v be_v resolve_v can_v be_v well_o deliver_v 10._o the_o preparation_n to_o be_v make_v do_v partly_o consist_v in_o place_v the_o give_v rate_n of_o the_o thing_n propound_v and_o take_v the_o difference_n between_o those_o rate_n and_o the_o mean_a price_n you_o will_v have_v they_o bear_v 11._o the_o give_v rate_n of_o the_o thing_n propound_v must_v be_v place_v one_o under_o another_o so_o as_o that_o they_o may_v orderly_o increase_v or_o decrease_v and_o the_o mean_a price_n that_o you_o will_v have_v they_o bear_v may_v stand_v on_o the_o right_a hand_n of_o the_o rank_n about_o the_o middle_n for_o example_n let_v the_o give_v rate_n be_v 12._o 24._o 36._o 48._o and_o the_o mean_a price_n 28d_o which_o be_v place_v one_o under_o another_o descend_v i_o 0_o draw_v a_o line_n of_o connexion_n and_o on_o the_o left_a hand_n thereof_o i_o set_v 28_o by_o the_o mean_a price_n by_o itself_o as_o here_o you_o see_v the_o term_n be_v thus_o rank_v in_o their_o due_a order_n link_v they_o together_o by_o certain_a arch_n in_o such_o sort_n as_o that_o one_o that_o be_v great_a than_o the_o mean_a price_n may_v be_v still_o couple_v with_o another_o that_o be_v less_o so_o in_o the_o premise_a example_n 12_o may_v be_v link_v with_o 36_o or_o 48_o and_o 24_o may_v be_v link_v with_o 48_o or_o 36_o and_o the_o work_n will_v stand_v thus_o or_o thus_o the_o term_n be_v thus_o rank_v and_o link_v together_o proceed_v to_o find_v the_o difference_n between_o the_o give_v rate_n and_o the_o mean_a price_n and_o write_v that_o difference_n just_a against_o his_o respective_a yoke-fellow_n thus_o the_o difference_n between_o 12_o and_o 28_o be_v 16_o i_o place_v 16_o against_o 48_o its_o respective_a yoke-fellow_n and_o the_o difference_n between_o 24_o and_o 28_o be_v 4_o i_o place_v 4_o against_o 36_o the_o difference_n between_o 28_o and_o 36_o be_v 8_o i_o place_v 8_o against_o 24_o last_o 20_o be_v the_o difference_n between_o 28_o and_o 48_o i_o place_v 20_o against_o 12_o and_o the_o work_n will_v stand_v according_a to_o the_o first_o way_n of_o link_a the_o rate_n propound_v as_o here_o you_o see_v they_o but_o the_o branch_n be_v link_v after_o the_o other_o manner_n the_o difference_n must_v be_v otherwise_o place_v for_o here_o 24_o have_v 48_o for_o his_o yoke-fellow_n and_o 12_o have_v 36_o for_o he_o 0_o 12._o and_o many_o time_n it_o so_o fall_v out_o that_o one_o of_o the_o give_v rate_n may_v be_v link_v with_o two_o or_o more_o of_o the_o other_o rate_v give_v in_o which_o case_n