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La Géométrie

René Descartes · 1637

Descartes's 1637 mathematical appendix that united algebra and geometry, founding analytic geometry and modern algebraic notation.

Descartes's own mathematical appendix, source of analytic geometry and the coordinate system named after him.

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Title page of the 1637 first edition of Descartes' Discours de la Methode, in French. The text lists it with La Dioptrique, Les Meteores, and La Geometrie as essays of this method, printed at Leyde by Ian Maire. A small engraved vignette of a figure with a tree and landscape appears in the center.
René Descartes, La Géométrie, title page, 1637. Leiden.

About this source

What it is

A mathematical appendix written by René Descartes, published in 1637 alongside the Discourse on Method. It introduced the idea of translating geometric shapes into algebraic equations and the notation for variables and powers still used today.

Why it matters

This short text had an outsized influence: it founded analytic geometry and shaped the mathematical ideas later used by Leibniz and Newton in developing calculus. It shows Descartes's ambition to apply his new method of reasoning not just to philosophy but to mathematics, transforming how problems could be solved.

Look closer

  • Why might Descartes have deliberately left out many details, saying he wanted to give readers 'the pleasure of discovering it for themselves'?
  • How does joining algebra and geometry change the way a mathematical problem can be approached?
  • What does the notation he introduced (like x, y, z) still look like in today's mathematics?

This document is part of the curated material that grounds the AI version of Rene Descartes on Humy.ai — when students ask about related events, the AI can quote it and cite it.

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Title page of the 1637 first edition of Discours de la Methode, in old French printed type. Text reads Discours de la Methode, Pour bien conduire sa raison, & chercher la verite dans les sciences, plus La Dioptrique, Les Meteores, et La Geometrie, with a small woodcut emblem of a figure with a lantern in a laurel wreath, and imprint A Leyde, De l'Imprimerie de Ian Maire, 1637.Book

Primary source

Discourse on the Method

René Descartes · 1637

Title page of the 1641 Latin edition of Descartes' Meditationes de prima philosophia, printed in Paris by Michael Soly. Red and black type, with an engraved emblem of a phoenix rising from flames within a circle, and the date M.DC.XLI at the bottom.Book

Primary source

Meditations on First Philosophy

René Descartes · 1641

Oil painting of a man with shoulder-length dark wavy hair, a thin mustache, and a white collar over a dark jacket, turning his head toward the viewer against a brown background, with one hand visible at the lower right.Painting

Primary source

Portrait of René Descartes

Frans Hals · 1649

Title page of a book reading 'Renati Des-Cartes Principia Philosophiae', with a Latin subtitle, an engraving of a winged figure and a robed figure beside a armillary sphere with banner 'Indefessus Agendo', an oval library stamp, and imprint 'Amstelodami, Ex Typographia Blaviana, MDCLXXXV'.Book

Primary source

Principles of Philosophy

René Descartes · 1644

Title page of the 1649 French edition of Les Passions de l'Ame by René Descartes. Large serif title 'LES PASSIONS DE L'AME', 'PAR RENE DES CARTES' below, a crowned fleur-de-lis coat of arms in an oval wreath, and a Paris publication imprint at the bottom.Book

Primary source

Passions of the Soul

René Descartes · 1649

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