nab.t:post-Nmathematical termCHEMLA 2003: differenceThis word occurs only in the commentaries, and not in JZ. One might think of 差 as the result the operation of substraction. In the formulation xy 差 "difference between x and y" the reference is to the result of subtracting the smaller one of x and y from the larger.JZ 9.5, Liu Hui's comm: 是其冪以股弦差為廣股弦并為袤 "As for this its quantified extension one takes the difference between the height and the hypotenuse as width, and one takes the sum of the height and the hypotenuse as length." Note that while bìng 并 is used both before and after the two terms added, and can even intervene between the two, chà 差 only occurs in "inverse Polish notation" word order, after the two terms between which the difference is calculated.JZ 9.15: 句弦差減股為圓徑 "Subtracting the difference between the base and the hypotenuse from the height makes the diameter of a circle."JZ 9.15, Liu Hui's comm: 以句弦差乘股弦差而倍之，開方除之... "Multiplying the difference between the base and the hypotenuse by the difference between the height and the hypotenuse, doubling this and dividing the result (note that 之 regularly refers to the result of the operation immediately preceding, thus not being strictly anaphoric) by extraction of the square root..."When the difference between x and y itself becomes a term in further calculation, it can be referred to only by chà 差, never by 減. The operation itself, also, must then always be designated with chà 差.
nabactdistinction made; differentiation in practice
nabmathematical termCHEMLA 2003: differenceJZ 9.6, Liu Hui's comm: 減此差冪於矩冪 "One subtracts the square of this difference from the quantified extension of the gnomon."
vt(oN)be different; be an exception
vi2deviate from each other, be inconsistent with each other