In theorem1 of his celebrated Principia, Newton showed that if one assumes a central force, Kepler’s area law follows. In this work, we report a study where two different ways of deriving this relationship, one geometrical ( la Newton) and the other analytical (using vector calculus), were presented to pre-service physics teachers. The participants were asked to formulate the essential arguments and to discuss issues that they did not understand. The findings consist of the participants’ main difficulties to understand the arguments, as well as indications of their preference for more geometrical or analytical derivations.

中文翻译：

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从中心力量到开普勒地区法：学生的困难和偏好有两个推导

牛顿在他著名的《原理》中的定理1中表明，如果有人担负中心力量，开普勒的面积定律就会遵循。在这项工作中，我们报告了一项研究，其中将两种不同的推导这种关系的方法，一种是几何的（la Newton），另一种是分析的（使用矢量演算），介绍给了职前物理教师。要求参与者提出基本论点并讨论他们不理解的问题。研究结果包括参与者难以理解这些论点的主要困难，以及他们倾向于采用更多几何或分析推导的迹象。