Thus extension in length, breadth, and depth constitutes the nature of corporeal substance.

All of Descartes' physics rests on this one claim. The entire physical world, he is asserting here, can be explained as a function of extension. Every physical phenomenon, every observable event, can be accounted for just by logically reasoning about the principles of geometry—that is, the study of extended bodies. In this way, we can import the certainty of mathematics into the investigation of the natural world.

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