Treatise on the Projective Properties of Figures

work by Poncelet

Also known as: “Traité des propriétés projectives des figures”(Show More)

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July 14, 2026

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Jean-Victor Poncelet's Treatise on the Projective Properties of Figures (1822) is a foundational work in projective geometry. This branch of mathematics studies geometric properties that are preserved under projection, meaning they remain unchanged when a figure is mapped onto another surface, much like a shadow.

Poncelet, inspired by Gaspard Monge's work, developed key concepts such as the principle of duality, which allows for the interchange of points and lines to create new theorems, and the principle of continuity, which extends geometric reasoning by considering transformations. His work unified the study of conic sections and significantly advanced the field, influencing later developments in algebraic geometry.1234

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mathematics
Projective geometry
In 1822 Poncelet published the Traité des propriétés projectives des figures (“Treatise on the Projective Properties of Figures”). From his standpoint every conic section is equivalent to a circle, so his treatise contained a unified treatment of the theory of conic sections. It also established several new results. Geometers who…
Read More
In 1822 Poncelet published the Traité des propriétés projectives des figures (“Treatise on the Projective Properties of Figures”). From his standpoint every conic section is equivalent to a circle, so his treatise contained a unified treatment of the theory of conic sections. It also established several new results. Geometers who…
Read More