Fractions in the Suàn Shù Shū (China, Beginning of the 2nd Century BCE) = 西汉出土文献《算数书》分数表达


The Suàn Shù Shū contains 301 instances of regular expressions for fractions. They can be "mono-dimensional" (formed with one integer name only) for unit fractions, "bidimensional" (with two integer names) for both unit and non-unit fractions, or lexicalized only for 1/3, 1/2 and 2/3. The present paper gives a complete description of the diversity of these forms. Bidimensional expressions are predicative phrases: the name n fēn of a unit fraction 1/n acts as subject and the numerator's name as predicate; according to the syntactic context, the morpheme zhī can be used as an optional marker of this predicative relation.


西汉出土文献《算数书》中表达分数的短语有 301 例。本文全面描述该 书中的那些短语。在文中,我把它们定义为"一维短语(即包括唯一一 个整数名)"和"二维短语(即包括两个整数名)",前者表达单位分 数,后者表达单位和非单位分数,除此之外还有三个词汇化的短语专门 用于表达 1/3、1/2 和 2/3。在二维短语中,单位分数 1/n 作为短语的 主语表达分母,而表达分子的那个数名作为短语的谓语,根据语境, "之"字可作为短语标志放在主谓语之间。