Analytic geometry
Geometría analítica
- Date
- 1637 · confidence high
- Place
- Leiden, Netherlands
- Credited to
- René Descartes (La Géométrie); Pierre de Fermat (Ad locos planos, independent)
- People
- 👤 Pierre de Fermat1601–1665👤 René Descartes1596–1650
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What was discovered
The translation of geometric problems into equations with coordinates and vice versa, unifying algebra and geometry. With it, a curve becomes an equation, a prerequisite for infinitesimal calculus.
Fermat developed the method around 1629 but did not publish it in his lifetime; the modern Cartesian system with perpendicular axes is a later systematisation. Merged with 'Analytic geometry (coordinates)' (duplicate, 23-09-2026).
What it led to
- infinitesimal calculus
- algebraic geometry
- graphs and functions
- differential geometry
- Newton and Leibniz's infinitesimal calculus
- mathematical mechanics and planetary orbits
- graphing of data and functions in science
- cartography and ballistics by equations
Built on
- Symbolic algebra1591
- Marin Getaldić's application of algebra to geometry1630 (póstumo)
- Apollonius's conics
- Viete's algebra
- Oresme's graphs
- Oresme's latitude of forms
Made possible
- Infinitesimal calculus1665-1684
- Sketchpad, computer-aided design and interactive graphics1963
- computer graphics
- modern cartography
- Statistical graphics (Playfair, 18th century)
- Design of lenses and optical curves