摘要
天元术是金元时代人们创造的设未知数列方程的方法,是宋元数学高潮的标志性成就之一.元代祖颐在《四元玉鉴后序》中关于天元术发展史的文字谈的实际上是关于天元术的史前史.元裕给刘如谐的《如积释锁》撰细草,才产生天元术.李冶的《测圆海镜》、《益古演段》是现存最早的使用天元术的著作.实际上,在这两部著作中,天元术是作为一种成熟的数学方法被使用的.《测圆海镜》既不是关于天元术的专门著作,《益古演段》也不是为普及天元术而写的.学术界经常将天元式误认为是方程.实际上,天元式是现今的多项式,经过"如积相消"得出的开方式即一元方程,在一次项旁是不标"元"字的.
Tianyuan shu is a method to set unknowns and equation in the periods of Jin and Yuan. The method is a landmark achievement of mathematical climax in Song and Yuan dynasties. In fact, what Zu Yi said in Yuan dynasty for the development of tianyuan shu in Preface of Jade Mirror of Four Unknowns is a prehistory of tianyuan shu. Tianyuan shu emerged when Yuan Yu wrote detailed draft for Liu Ruxie＇s Ru Ji Shi Suo. Li Ye＇s Ce Yuan Hal Jing and Yi Gu Yan Duan are the earliest works for using tianyuan shu. In the two works, tianyuan shu was actually used as a mature mathematical method. Ce Yuan Hal Jing is not a specialized work of tianyuan shu. That Li Ye wrote Yi Gu Yan Duan was also not for popularizing tianyuan shu. The formula of tianyuan was often mistaken as equation. As a matter of fact, the formula of tianyuan is nowadays polynomial. It becomes formula of extraction, namely equation with one unknown quantity, through ＂ru ji xiang xiao＂. The character ＂yuan＂ was not marked beside the item of first degree.
出处
《高等数学研究》
2013年第4期120-126,F0003,共8页
Studies in College Mathematics
关键词
天元术
列方程
李冶
测圆海镜
四元玉鉴
Tianyuan Method（Tianyuan Shu）, Set up higher equation, Li Ye, Sea Mirror of Circle Measureernent （Ce Yuan Hai Jing）, Jade Mirror of Four Unknowns（Si Yuan Yu Jina）
