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Mikhail Katz
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Desargues certainly pioneered original mathematics. The notion of a point at infinity in projective geometry is usually attributed to him. Kepler apparently did not work in projective geometry but rather in astronomy and pioneered a number of mathematical techniques such as infinitesimals. I am not aware of any interactions between Desargues and Kepler, but Desargues did play an interesting role of attempting to resolve a dispute between his junior colleagues Fermat and Descartes.

I now see that wiki attributes the notion of the point at infinity to Kepler, citing Coxeter. This seems like a novelty to me. Kepler did talk about points at infinity, but not in the context of projective geometry as we understand it, but rather as a way of developing a unified technique for treating conic sections through a kind of a continuity principle. This is closer to calculus than projective geometry.

Mikhail Katz
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