作　　者： ;

机构地区： 中山大学

出　　处： 《自然科学史研究》 2011年第2期 193-206,共14页

摘　　要： 《数书九章》所载之大衍总数术,是一项世界级的数学成就。然而在此之前,大衍总数术的发展情形并不清楚。秦九韶《数书九章》自序云：＂独大衍法不载《九章》,未有能推之者。历家演法颇用之,以为方程者,误也。＂因此学术界粗略地认为,大衍术来自历家之方程,但又一致认为此方程并不是中国传统数学之方程。本文认为历家之方程即传统之方程,只是运算目的不同。并据此给出一种推测性解释：如果把此方程三横行布筭的最上面一横行删去,用辗转相除替代直除（两者相通）,把左下角和右上角两数位置调换,并把运算之负数全改为正数（这不影响结果）,那么它就是《数书九章》所载之＂大衍求等术＂。如果再把两数做约化处理,那么它的形式与算法就和＂大衍求一术＂完全一样。同时,本文认为＂约奇弗约偶＂之奇偶即指元数的单双。提出元数约化法则,利用筭图优化历家之方程,是秦九韶之贡献。这样我们亦可了解大衍术在历算中的发展情况。另外,历家之方程在运算过程中可自然地得到一系列的渐近分数。由于这种算法既符合中国古代筹筭之过程,又无需用到比《九章筭术》更高深的数学知识,因此可以自然地解释祖冲之圆周率,以及中国历史上出现的其他大量渐近分数。 The Dayan method in Mathematical Treatise in Nine Sections, which is also called Chinese remainder theorem, is a great accomplishment. Its origin and development, however, are not known clearly. According to Qin Jiushao＇s preface, scholars have argued that Dayan comes from the Fangcheng of astronomers, which is not a real Fangcheng in Nine Chapters on the Mathematical Art. This article holds that astronomers＇ Fangcheng is a real Facngcheng while its purpose is different. The article also presents the original meaning of Yuejifuyueou, which refers to odd number and even number. The fact is that Dayanqiuyi rule can be easily viewed by deducing astronomers＇ Fangcheng, which not only tells us what is Qin＇s contribution to the Dayan method, but also offers a new idea about its origin and development. Using the Fangcheng of astronomers, a series of convergent fractions can be naturally obtained. And Zu Chongzhi＇s Circular Constant and other convergent fractions in history of China can be explained anew.

关 键 词： 秦九韶 祖冲之 方程 大衍 约奇弗约偶

分 类 号： [N092 O112]

领　　域： [] []