FRACTIONS IN THE SUÀN SHÙ SHŪ (CHINA, BEGINNING OF THE 2 ND CENTURY BCE)

西漢出土文獻《算數書》分數表達

Rémi Anicotte (1)

1 CRLAO - Centre de Recherches Linguistiques sur l'Asie Orientale

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.

西漢出土文獻《算數書》中表達分數的短語有301例。本文全面描述該書中的那些短語。在文中，我把它們定義為“一維短語（即包括唯一一個整數名）”和“二維短語（即包括兩個整數名）”，前者表達單位分數，後者表達單位和非單位分數，除此之外還有三個詞彙化的短語專門用於表達1/3、1/2和2/3。在二維短語中，單位分數1/n作為短語的主語表達分母，而表達分子的那個數名作為短語的謂語，根據語境，“之”字可作為短語標誌放在主謂語之間。

Mots clés: Chinese historical syntax; Suàn Shù Shū; Measure words; Separable semantic units; Numerical expressions; Fractions History Ratio and proportion History

Mots clés: 中文語法歷史; 分數; 《算數書》; 表数短語; 離合詞組; 量詞

Domaines: Linguistique; Histoire et perspectives sur les mathématiques [math.HO]; Histoire, Philosophie et Sociologie des sciences

Rémi Anicotte. FRACTIONS IN THE SUÀN SHÙ SHŪ (CHINA, BEGINNING OF THE 2 ND CENTURY BCE). 2016. ⟨hal-01393062v1⟩