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Carlo Beenakker
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I guess you'll find what you need in the monograph by J.V. Field and J.J. Gray, The Geometrical Work of Girard Desargues.

They give substantial critical and exegetical commentaries as well as valuable introductory essays placing Desargues and his various works in historical context. Particularly attractive is the authors' demonstration of how Desargues' highly original ideas developed from the contemporary technical mathematical context, and their elegant exposition of the importance of the 'practical tradition of applied geometry' in stimulating his work.

Desargues had a limited range of interactions, which apparently did not include Kepler. Quoting from Gale's Science and Its Times:

Desargues spent many years in Paris with a group of mathematicians that included Descartes and Pascal as well as the Jesuit scientist Marin Mersenne (1588-1648) and Etienne Pascal (1588-1651). Desargues's work on projective geometry was printed principally for this limited readership of friends. Unfortunately, however, his views were very unorthodox and unpopular during his life — Blaise Pascal (1623-1662) was one of his few admirers. Only 50 copies of his book on projective geometry were printed, many of them later destroyed by the publisher. Desargues's work slipped into obscurity for nearly 200 years after the publication of his defining text on the subject.

Carlo Beenakker
  • 188.3k
  • 18
  • 448
  • 651