-
By then, the young man had been steeped in geometry for four years, first by studying Euclid's Éléments, then by grasping, more fully than his contemporaries, the full novelty and power of the Brouillon project d’une atteinte aux événements des rencontres du cône avec un plan published by Girard Desargues in 1639. Pascal's essay is in fact a research programme in which he mentions a whole series of results obtained in the preceding months. In it, he adopts Desargues's innovative viewpoints, including the identification of concurrent and parallel lines, thereby introducing points at infinity. The text is so impressive for someone his age that some, such as Descartes, would think its author was his father, Étienne Pascal!
Later, Blaise Pascal wrote a major Traité sur les sections coniques. Gottfried Leibniz was enthusiastic about this highly original text, which Pascal's nephew sent him in 1676. He encouraged its publication, but it ultimately never came out and, alas, only the first chapter has reached us.
Two other readily accessible texts deal with the method and principles of classical geometry: De l’esprit géométrique et de l’art de persuader, and a fragment of the Introduction à la Géométrie, arising from a textbook project intended for the Petites Écoles of Port-Royal and later taken up by Antoine Arnauld.
The Mystical Hexagram
---------------------
