《数学汇编》中的数学问题在中国——兼与古希腊数学思想比较

帕普斯的《数学汇编》是世界数学史中一部承前启后的重要数学著作,它对希腊经典数学问题的研究为后来的数学指出了方向,拓展和预见了许多数学新领域。本文分析了明末至清末近300年间传入的《数学汇编》中的典型问题,探讨了中算家对古希腊传统问题的理解、接受情况。通过比较发现其在中国和在希腊发展的差异,西方由此导致了数学的进化,而中国延续了中算以算为主和重视实用的传统,发展了不严谨的证明方法,在西学的引导下触及到了数学发展的一些理论问题,所有这些为中国进一步接受近代数学奠定了基础。

The Mathematical Problems in Mathematical Collections in China

Pappus’s Mathematical Collection has much value for the study of the ancient Greek mathematics and its successions.Its study of the classical problems of ancient Greek mathematics has guided later research,enlarged and foreseen several new mathfields.This paper tries to analyze some typical problems with Mathematical Collection during the late Ming and the late Qingdynasties,and discuss the knowledge and the comprehension of the Chinese mathematicians of them.It concludes that theseproblems led to the evolution of the Western math,while the Chinese mathematicians attached importance to arithmetic andcontinued its tradition of practicality,while the Chinese mathematicians attached importance to its arithmetic method and continuedits tradition of practicality,and developed some semi-proof-methods which were not very strict in the Ming and Qing dynasties.Meanwhile,under the guide of Western math,Chinese math reached a few theories.All of these laid the foundation for the Chineseto accept modern math.