By Christopher Cullen
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Additional info for The Suan Shu Shu: A Translation and Study of the Earliest Chinese Mathematical Text
Example text
Cullen 2004 Answer: 163 liǎng 4 ½ zhū. Method: Take 1 jīn unfolded into 16 liǎng to be the divisor; multiply the number of liǎng in the present amount of undressed silk by 7 liǎng to make the dividend; by accommodating the dividend to the divisor obtain the number of the wastage.
Ten mounting on a thousand is a myriad’ In all cases chéng appears, as here , to be equivalent to ‘multiply’, and I have so rendered it. The use of this word may come from the way that two rod numbers are arranged one above the other when multiplication takes place. Faced with phrases such as sān zhī 三之, literally ‘3 it’, I have had to decide whether to be as literal as that, or whether to say ‘triple it’ instead. The former involves using a number as a transitive verb, which is not at all natural in English, while the latter would imply we had on occasion to go all the way up to ‘nonuple’ and ‘decuple’, which would be distinctly odd.
Method: Set out one, and thrice double it to make the divisor. Again set out one dǒu of hulled grain and 3-fold it Again three-fold it and [multiply by] the number of passes to make the dividend for it. Content: This problem falls under one of the types discussed in the 均輸 Jūn shū ‘equitable transport’ section of the Nine Chapters where some of the problems show how to 47 The Suàn shù shū ⟉ᩕ᭡: Translation. Copyright © C. Cullen 2004 work back to an original amount that has been reduced by some proportional deduction.