數：筭與術－－以九數之方程為例

Chinese Mathematics: Counting Sticks and Techniques — Using Fangcheng as an Example

方程是中國古代九數之一。本文從籌筭的角度重新考察方程，展現籌筭的技藝化特徵，並證明從筭籌到文字數字再到筭圖的變化與數學內容之互動。本文利用出土筭籌和傳世文獻重新考察方程正負術，表明古今算法之同歸殊途，展現對應觀念對於數學內容之滲透。本文又對秦九韶《數書九章》補草用圖的成書過程分析表明：算器和物質基礎─筭籌和紙張、對應觀念和曆算、社會因素─朝廷改曆，這些都是影響中國古代數學內容的因素。

Fangcheng 方程 was one of the nine mathematical calculation methods in ancient China. Through a reinvestigation of fangcheng, this paper reveals characteristics of the mathematical techniques of ancient China, and proves that the fangcheng technique itself was changed by the process of evolution from the use of real counting sticks to pictorial representations. This article also re-examines the techniques for handling positive and negative numbers using unearthed counting sticks and extant historical literature. This clearly shows the differences in the way positive and negative numbers are handled nowadays compared to ancient times and the permeation of ancient mathematics with traditional ways of thinking. By analyzing the process by which Qin Jiushao 秦九韶 wrote his Shu shu jiu zhang 數書九章, external factors that influenced mathematics in ancient China are identified that include the use of counting sticks and paper, corresponding traditional ideas, calendrical calculations, and social factors such as government moves to reform the calendar.