What did Blaise Pascal write about conic sections in 1640?

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French philosopher Blaise Pascal — Blaise Pascal Blaise Pascal, oil painting by an anonymous artist, c. 1650; in the Musée Carnavalet–Histoire de Paris, Paris. Pascal laid the foundation for probability theory.

In 1640, Blaise Pascal wrote an essay titled Essai pour les coniques (Essay on Conic Sections). This work was based on his study of the synthetic projective geometry developed by Girard Desargues.1

In this essay, Pascal presented a significant discovery now known as Pascal’s theorem. He demonstrated that for a hexagon inscribed in a conic section, the three intersection points of the three pairs of opposite sides are collinear. While he initially established this property for a circle, he used the projective point of view to show that the theorem holds for any conic section, effectively unifying the study of ellipses, parabolas, and hyperbolas. This youthful work was highly successful in the mathematical community of the time.231