中国科技史杂志

三杆问题是17世纪一个重要科学挑战问题，也是解析几何理论发展初期的一个试金石，牛顿和笛卡尔对该问题的不同解法体现了该学科在最初半个世纪的长足进展。牛顿解法中有两处比较关键的断言，可依托当时的语境和背景分别建立天文模型进行阐释。牛顿在求解中创造了一种特殊符号；在分析牛顿证明圆锥曲线是椭圆的过程以及他用待定符号设点坐标的方式后，认为他创造这种符号的动机是为了改进笛卡尔的解法，且该符号的本质含义在于表达正号或负号的待定，并非学者通常认为的正负号。此外，通过对二者求解思路的比较，可从坐标系和解法两方面分析牛顿解法的进步之处，这有助于更深入地理解牛顿对解析几何的独特贡献。

The three-stave problem was an important scientific challenge in the 17th century and a touchstone in the early development of analytic geometry. The different solutions of Newton and Descartes to the problem reflect the great progress of the discipline in the beginning half century. For the two key assertions in Newton's solution, we established respectively astronomical models based on the context and background of the time to clarify them. Newton created a special symbol in his solution. By analyzing Newton's proof that the conic in question is ellipse and his way of using undetermined symbols to set point coordinates, we believe that his purpose of creating this symbol was to improve Descartes' solution. The essential meaning of this symbol was to express the undetermined positive or negative sign, rather than the composite positive and negative sign that scholars have commonly assumed. In addition, by comparing Newton's and Descartes' s approaches, this paper analyses the advances represented by Newton's solution in terms of the coordinate system and the method of solution, thereby deepening our understanding of Newton's unique contribution to analytic geometry.