从《杨辉算法》看南宋区域农业经济史的两个侧面

Viewing Two Aspects of Regional Agricultural Economic History in the Southern Song Dynasty from Yang Hui Suanfa

《杨辉算法》是南宋后期杨辉所编撰的一部算学著作集,该著以算题形式为我们保存了当时台州地籍的一些原始资料。因此,我们可以通过这些算题对南宋后期整个江浙丘陵地区的农业生产状况作一粗略估计,尤其是根据民间粮食交易的客观需要,杨辉还对“方斛”或“方积”与“圆斛”或“圆积”之间的数量关系进行了换算,从而为不同形制的量斛制造提供了科学依据。杨辉作为南宋晚期一名应用数学家,以数理科学为工具,对南宋市井民量进行大胆改造,从而使当时民间商品交易更趋于公平合理,这种力行实践的科学精神值得肯定。

Yang Hui Suanfais a collection of arithmetic works compiled by Yang Hui in the late Southern Song Dynasty, which preserves some original materials of Taizhou cadastre at that time in form of arithmetical question.Therefore, we can make a rough estimate of the agricultural production status in the entire Jiangsu and Zhejiang hilly areas in the late Southern Song Dynasty through these arithmetical questions. Especially, according to the objective needs of private grain transactions, Yang Hui converted the quantity relationship between “Fanghu” or “Fangji” and“Yuanhu”or “Yuanji”, thus providing a scientific(practical) basis for the manufacture of different shape of Lianghu.Using mathematical and physical sciences as tool, Yang Hui, as an applied mathematician in the late Southern Song Dynasty, boldly transformed the measurement way, thereby making the private commodity trades at that time tended to fair and reasonable. This scientific spirit of practice is worthy of affirmation.