清代許桂林《算牖》之研究

Abstract

《算牖》是清代儒家許桂林（西元1779－1821年）的數學著作，成書於清嘉慶辛未年(西元1811年)。「牖」的字意指「窗戶」，根據史書記載，《算牖》是取欽定《數理精蘊》，撮其切於日用者而成的，所以也可以稱它是《數理精蘊》之窗。 康熙六十年（1721）御制《數理精蘊》完成，是一部內容豐富的「初等數學百科全書」，包括上編「立綱明體」五卷，下編「分條致用」四十卷，數學用表四種八卷，共計五十三卷，內容涵蓋了算術、代數、幾何、三角等多方面材料。而反觀《算牖》，則將前者節錄成四卷。第一卷為「總綱」，敘述基本的算學知識，第二卷為「筆算、籌算」的使用及簡捷法，第三卷為簡述「九章」，第四卷為「雜綴」，敘述一些雜法，書中計算工具以「筆、籌、珠」為主。其所使用的籌算，並非中國的古籌，而是指梅文鼎改自於「訥皮爾籌」的半圈式「梅籌」。 《鏡花緣》是清代四大才學小說之一，許桂林曾一度被認為是該書作者。 《鏡花緣》中有關於算學的內容，和《算牖》部份內容雷同，關於這部份收錄在後。

Suan-you（1811）was written by Xu Qui-lin（1779-1821）lived in the Ch’ing Dynasty. The meaning of “you” is the window in Chinese. According to the record of the history book, Xu Qui-lin abstracted the most important of living mathematics from Shuli Jingyun. So we can regard it as a window for Shuli Jingyun. The K'ang-hsi emperor, who ruled from 1662 to 1722, was a great admirer of scientific knowledge and he summoned missionaries to court in order to obtain instruction in astronomy and mathematics. Shuli Jingyun, entitled The Essentials of Numerical Principle, was completed in 1721. Its contents are divided into two sections. The first is entitled Establishing the Outline and Illuminating the Substance. The second is called Distinguishing Each Article and Putting it to Use. In addition to recording aspects of Western mathematical theory, such as arithmetic, geometry , algebra and triangle, which had already been transmitted to China, the book also contains 53 volumes. The inclusionof the words “Imperially Crafted” in its title reveals that it was compiled on the order of the emperor, and therefore relatively widely disseminated. Suan-you contains 4 volumes. Volume I is the basic knowledge of mathematics. Volume II is the methods of counting which is deeply influenced by the works of Mei Weng-ding（1633-1721）. The tools of counting were abacus, pens and rods. The rods were not the ancient Chinese calculus rods but Mei’s half-circle rods which Mei improved from Napier’s rods. Volume III is about Jiu- zhang. Volume IV is the mixed methods of solutions. Ching-Hua-Yuan is one of the famous novels of Ch’ing dynasty. Xu was regarded as the author of it once upon a time. Some of the mathematics in Ching-Hua-Yuan is similar to Suan-you. The result of analyzing and comparing both books is made as an appendix.