卷三
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并者，各自为实。实如法而一。〕
今有甲持粟三升，乙持粝米三升，丙持粝饭三升。欲令合而分之，问各几何？
答曰：甲二升一十分升之七；乙四升一十分升之五；丙一升一十分升之八。
术曰：以粟率五十、粝米率三十、粝饭率七十五为衰，而反衰之。副并为法。
以九升乘未并者，各自为实。实如法得一升。
〔按：此术，三人所持升数虽等，论其本率，精粗不同。米率虽少，令最得
多；饭率虽多，反使得少。故令反之，使精得多而粗得少。于今有术，副并为所
有率，未并者各为所求率，九升为所有数，而今有之，即得。〕
今有丝一斤，价直二百四十。今有钱一千三百二十八，问得丝几何？答曰：
五斤八两一十二铢五分铢之四。
术曰：以一斤价数为法，以一斤乘今有钱数为实。实如法得丝数。
〔按：此术今有之义，以一斤价为所有率，一斤为所求率，今有钱为所有数，
而今有之，即得。〕
今有丝一斤，价直三百四十五。今有丝七两一十二铢，问得钱几何？答曰：
一百六十一钱三十二分钱之二十三。
术曰：以一斤铢数为法，以一斤价数乘七两一十二铢为实。实如法得钱数。
〔淳风等按：此术亦今有之义。以丝一斤铢数为所有率，价钱为所求率，今
有丝为所有数，而今有之，即得。〕
今有缣一丈，价直一百二十八。今有缣一匹九尺五寸，问得钱几何？答曰：
六百三十三钱五分钱之三。
术曰：以一丈寸数为法，以价钱数乘今有缣寸数为实。实如法得钱数。
〔淳风等按：此术亦今有之义。以缣一丈寸数为所有率，价钱为所求率，今
有缣寸数为所有数，而今有之，即得。〕
今有布一匹，价直一百二十五。今有布二丈七尺，问得钱几何？答曰：八十
四钱八分钱之三。
术曰：以一匹尺数为法，今有布尺数乘价钱为实。实如法得钱数。
〔淳风等按：此术亦今有之义。以一匹尺数为所有率，价钱为所求率，今有
布为所有数，今有之，即得。〕
今有素一匹一丈，价直六百二十五。今有钱五百，问得素几何？答曰：得素
一匹。
术曰：以价直为法，以一匹一丈尺数乘今有钱数为实。实如法得素数。
〔淳风等按：此术亦今有之义。以价钱为所有率，五丈尺数为所求率，今有
钱为所有数，今有之，即得。〕
今有与人丝一十四斤，约得缣一十斤。今与人丝四十五斤八两，问得缣几何？
答曰：三十二斤八两。
术曰：以一十四斤两数为法，以一十斤乘今有丝两数为实。实如法得缣数。
〔淳风等按：此术亦今有之义。以一十四斤两数为所有率，一十斤为所求率，
今有丝为所有数，而今有之，即得。〕
今有丝一斤，耗七两。今有丝二十三斤五两，问耗几何？答曰：一百六十三
两四铢半。
术曰：以一斤展十六两为法。以七两乘今有丝两数为实。实如法得耗数。
〔淳风等按：此术亦今有之义。以一斤为十六两为所有率，七两为所求率，
今有丝为所有数，而今有之，即得。〕
今有生丝三十斤，干之，耗三斤十二两。今有干丝一十二斤，问生丝几何？
答曰：一十三斤一十一两十铢七分铢之二。
术曰：置生丝两数，除耗数，余，以为法。
〔馀四百二十两，即干丝率。〕
三十斤乘干丝两数为实。实如法得生丝数。
〔凡所得率，如细则俱细，粗则俱粗，两数相抱而已。故品物不同，如上缣、
丝之比，相与率焉。三十斤凡四百八十两，今生丝率四百八十两，今干丝率四百
二十两，则其数相通。可俱为铢，可俱为两，可俱为斤，，无所归滞也。若然，
宜以所有干丝斤数乘生丝两数为实。今以斤、两错互而亦同归者，使干丝以两数
为率，生丝以斤数为率，譬之异类，亦各有一定之势。
淳风等按：此术，置生丝两数，除耗数，余即干丝之率，于今有术为所有率；
三十斤为所求率，干丝两数为所有数。凡所为率者，细则俱细，粗则俱粗。今有
一斤乘两知，干丝即以两数为率，生丝即以斤数为率，譬之异物，各有一定之率
也。〕
今有田一亩，收粟六升太半升。今有田一顷二十六亩一百五十九步，问收粟
几何？答曰：八斛四斗四升一十二分升之五。
术曰：以亩二百四十步为法。以六升太半升乘今有田积步为实。实如法得粟
数。
〔淳风等按：此术亦今有之义。以一亩步数为所有率，六升太半升为所求率，
今有田积步为所有数，而今有之，即得。〕
今有取保，一岁价钱二千五百。今先取一千二百，问当作日几何？答曰：一
百六十九日二十五分日之二十三。
术曰：以价钱为法，以一岁三百五十四日乘先取钱数为实。实如法得日数。
〔淳风等按：此术亦今有之义。以价为所有率，一岁日数为所求率，取钱为
所有数，而今有之，即得。〕
今有贷人千钱，月息三十。今有贷人七百五十钱，九日归之，问息几何？答
曰：六钱四分钱之三。
术曰：以月三十日乘千钱为法。
〔以三十日乘千钱为法者，得三万，是为贷人钱三万，一日息三十也。〕
以息三十乘今所贷钱数，又以九日乘之，为实。实如法得一钱。
〔以九日乘今所贷钱为今一日所有钱，于今有术为所有数，息三十为所求率；
三万钱为所有率。此又可以一月三十日约息三十钱，为十分一日，以乘今一日所
有钱为实；千钱为法。为率者，当等之于一也。故三十日或可乘本，或可约息，
皆所以等之也。〕
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