Elements of Geometry

work by Legendre

Also known as: “Éléments de géométrie”

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June 26, 2026

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Adrien-Marie Legendre, a French mathematician, significantly influenced geometry with his work, particularly his reorganization and simplification of Euclid's Elements in his 1794 publication, Éléments de géométrie. This textbook, which made geometry more accessible, was widely adopted in Europe and the United States. Legendre's approach involved using trigonometry, omitting proofs of obvious statements, and removing Euclid's complex treatment of incommensurables.12

While Euclid's Elements served as the ultimate geometry textbook for centuries, Legendre's version aimed to streamline the subject for a broader audience. His work contributed to the ongoing discussion and evolution of geometric principles, even as mathematicians continued to explore foundational questions, particularly concerning Euclid's parallel postulate.213

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mathematics
Foundations of geometry
was Adrien-Marie Legendre’s textbook Éléments de géométrie (Elements of Geometry and Trigonometry), the first edition of which appeared in 1794. Legendre presented an elegant demonstration that purported to show that the sum of the angles of a triangle is equal to two right angles. He believed that he had…
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was Adrien-Marie Legendre’s textbook Éléments de géométrie (Elements of Geometry and Trigonometry), the first edition of which appeared in 1794. Legendre presented an elegant demonstration that purported to show that the sum of the angles of a triangle is equal to two right angles. He believed that he had…
Read More

Adrien-Marie Legendre
…published Éléments de géométrie (Elements of Geometry), a reorganization and simplification of the propositions from Euclid’s Elements that was widely adopted in Europe, even though it is full of fallacious attempts to defend the parallel postulate. Legendre also gave a simple proof that π is irrational, as well as…
Read More
…published Éléments de géométrie (Elements of Geometry), a reorganization and simplification of the propositions from Euclid’s Elements that was widely adopted in Europe, even though it is full of fallacious attempts to defend the parallel postulate. Legendre also gave a simple proof that π is irrational, as well as…
Read More