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By then, the young man had been immersed in geometry for four years, first studying Euclid's Éléments (The Elements), then grasping, more fully than his contemporaries, how forward-looking and powerful Girard Desargues's Brouillon project d’une atteinte aux événements des rencontres du cône avec un plan, published in 1639, was. Pascal's essay was in fact a research program in which he mentioned a whole series of results obtained over the previous months. He adopted Desargues's innovative ideas, such as putting concurrent and parallel lines on the same footing, thereby introducing points at infinity. The text was so impressive for someone his age that some, including Descartes, came to believe that its author was his father, Étienne Pascal!
Later, Blaise Pascal wrote an extensive Traité sur les sections coniques (Treatise on Conic Sections). Gottfried Leibniz was thrilled by this highly original text, which Pascal's nephew sent him in 1676. He encouraged its publication, but it never appeared and, sadly, only the first chapter has survived.
Two other texts that remain readily available explore the method and principles of classical geometry: De l’esprit géométrique et de l’art de persuader (On the Geometrical Spirit and the Art of Persuasion), and a fragment of the Introduction à la Géométrie (Introduction to Geometry). Both grew out of a textbook project for the Petites Écoles de Port-Royal, later taken up by Antoine Arnauld.
The mystic hexagram
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