Menelaus's theorem
Teorema de Menelao
- Date
- c. 100 · confidence low
- Place
- Alexandria, Egypt
- Credited to
- Menelaus of Alexandria
- Field
- Knowledge & symbols
What was discovered
In his work 'Sphaerica', Menelaus established that the product of three segment ratios determined by a transversal cutting the sides of a triangle equals -1 in signed lengths. Ptolemy later applied it to spherical astronomy in the Almagest, and medieval Islamic mathematicians developed it extensively as 'the proposition of the secants', influencing the sine rule.
The original Greek work has not survived; Menelaus is placed in Alexandria based on his epithet, though he made documented astronomical observations in Rome in the year 98.
What it led to
- Ptolemy's application to spherical astronomy (Almagest)
- Development in medieval Islamic mathematics
- Influence on the sine rule
Built on
- Classical Greek triangle geometry