nab.t:post-Nmathematical termCHEMLA 2003: half ofJIUZHANG 8.10: 乙半 "half of the (amount of money possessed by) X"LIUHUI 9.11: 差半 "half of the difference". Sometimes (with binomial modifiers) with 之 as in LIUHUI 9.11 加相多之半 "one adds half of the excess (quantity)".
nabmathematical termCHEMLA 2003: a half (of an identified kind of items) (This must be carefully distinguished from the notion of a half of an amount 二分之一.) In this meaning, 半 is almost enclitic, and always follows after designations of units or numbers, rather than after designations of concrete items. Moreover, the measure is never repeated after 半. Reference to the fraction as such is always in terms of 二分之一. JIUZHANG 1.9 又有二分之一 "Again, suppose we have one half (of something)" JIUZHANG 4.1 and 4.2 has counterexamples that are only apparent, because they involve resumption of post-nominal 半.Note incidentally that the fraction 2/3 is expressed in JIUZHANG as 太半 as well as 三分之二, there being no clear distinction in meaning between these two. Shào bàn 少半 as well as 三分之一 are used - indifferently - to refer to the fraction 1/3. Possibly, the choice among these alternatives might be a basis for dating various parts of the text in which these terms occur.
nadNN=period of timein the middle of the N-period; halfway through N
nadVhalf, half-way; to the tune of one half, half of the number
vadNmathematical termCHEMLA 2003: half ofLIU HUI 1.32 故以半周乘半徑而為圓冪 "Therefore with the half of the circumference one multiplies half of the diameter and thus arrives at the area of the circle."
vibe one half
vtoNmathematical termCHEMLA 2003: take one half of; occasionally with preposed object resumed by 之 in 半之. Thus X 半之 comes to mean "take half of X". Note that 半, whether as adjective or as transitive verb, never has a scope that extends across multiplication chéng 乘.JIUZHANG 1.6 可半者半之 "(the numerators and the denominators) that can be halved, one halves" JIUZHANG 1.21: 半廣以乘正從 "One reduces by half the width and with (the result of this operation) you multiply this with the height (lit: "straight vertical")." Note that 半廣 might conceivably be construed as a adjective-noun construction here, although this would lead to considerable analytic contortions in the interpretation of the text.
vtoNmathematical termCHEMLA 2003: be halvedJIUZHANG 1.6 可半者半之 "(the numerators and the denominators) that can be halved, one halves". Note that not all mathematical operations are necessarily referred to in the passive mode.
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