Ceva's theorem
Teorema de Ceva
- Date
- 1678 · confidence high
- Place
- Milan, Lombardy, Italy
- Credited to
- Giovanni Ceva; proved centuries earlier by Yusuf al-Mu'taman ibn Hud
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What was discovered
Ceva published in 'De lineis rectis' (1678) the theorem giving the condition for three cevians of a triangle, drawn from each vertex, to meet at a single point, via a product of segment ratios. The result had already been proved in the 11th century by the mathematician-king Yusuf al-Mu'taman ibn Hud of Zaragoza, whose work fell into obscurity and was not rediscovered until 1985.
The exact city where Ceva worked out the result is not confirmed; he was a professor in Mantua/Milan around that time. The Andalusian mathematician Yusuf al-Mu'taman ibn Hud had already proved it in the 11th century, but his work was not rediscovered until 1985.
What it led to
- Generalizations to higher-dimensional simplexes
- Extensions to spherical and hyperbolic geometry
- Link to Menelaus's theorem
Built on
- Classical Euclidean affine geometry