订正与会通:勾股定理在晚明《几何原本》(1607)中的呈现

Correction and Integration:The Representation of the Pythagorean Theorem in the Chinese Translation of Euclid’s Elements in Late Ming(1607)

在利玛窦、徐光启译介的晚明西学经典《几何原本》中,述论勾股定理的第一卷第四十七题的呈现颇富意趣。从明刊本中留存的文字阙空可知,该题在版印之初曾经订正,利玛窦和徐光启作为翻译、校阅者剜其衍字而存其图示的处理,饱含着他们对定理证明方式一般性的深入理解。定理之后所附直角三角形任知两边而求其余边的问题及其解法,虽基本依照拉丁底本转译而与内涵近同的中算知识“句股术”在表述方式上有所区别,却相较底本文句表现出更为鲜明的算法特征,并借用“自乘”“幂”“开方尽实”等古代算学用语。这显示出本土知识背景对于徐光启译笔的隐微影响,亦由此揭示中西会通已自然地蕴藏在数学知识的翻译过程之中。

This article investigates two passages in the early modern Chinese translation of Euclid’s Elements(Jihe Yuanben,1607),which Matteo Ricci and Xu Guangqi carried out on the basis of Christoph Clavius’s Latin version(1574).The first passage is the 47th proposition of the first chapter,the so-called Pythagorean theorem.We focus on a blank in the Chinese copies printed in the Ming dynasty,suggesting that this clue indicates that the translators revised their previous translation.This change shows their deep understanding of the generality of the proof of the Pythagorean theorem in the Elements.The second passage,which is stated as a scholion in Clavius’s Latin text,was translated as an addition to the 47th proposition.Aiming at finding out a side of a right-angled triangle when knowing its two other sides,this problem is similar in some sense to the procedure known as“The Right-angled Triangle(Gou⁃Gu)Procedure”in ancient China.The addition was basically translated in accordance with the scholion by Clavius.However,the translation presented more arithmetical features than the original text and borrowed some traditional Chinese mathematical terms.This shows the implicit and subtle influence of the local knowledge on Xu Guangqi’s treatment of the translation,and further reveals that the so-called“integration of Western and Chinese knowledge”(Zhong Xi Hui Tong)was already naturally embedded in the translation process.