Pascal's Theory of Indivisibles and Jansenistic World View

这项研究的目的是阐明帕斯卡在其不可分割的几何学中数学运算的独创性，并从他的简森主义世界观来判断是什么使他提出了这一点。我们想指出以下四点。卡瓦列里的不可分割理论作为一种计算工具非常有用，但不一定准确。关于这个不可分割的概念，许多数学家提出了各种各样的问题。我们看到了帕斯卡如何解决这个模棱两可的问题，并授权了这个几何图形。注意到帕斯卡与其他数学家的区别，提出了帕斯卡具体数学运算的独到之处。数学运算与数学家的世界观有着天然的联系。从这个角度出发，我们认为帕斯卡的整合是其具体操作的理想基础。我们指出，这个基础就是简森主义的宿命论。

The aim of this research is to make clear the originality of Pascal's mathematical operations in his indivisible geometry, and to judge what make him bring forth that, from his Jansenistic world view. We should like to point out next four points.1. Cavalieri's theory of indivisibles is very useful as a calculating tool, but is not necessarily exact. With regard to this concept of indivisible various problems was brought forth by many mathematicians. We saw in what way Pascal resolved this ambiguity and authorize this geometry.2. Paying attention to the difference between pascal and other mathematicians, we brought out the originality of Pascal's concrete mathematical operations.3. Mathematical operations is naturally related to the world view of mathematician. From this point of view, we considered the ideal foundation of Pascal's concrete operations of integration.4. We indicated that this foundation was the theory of Jansenistic predestination.