Pascal's Theory of Indivisibles and Jansenistic World View

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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.