Al-Kashi's law of cosines
Teorema del coseno de al-Kashi
- Date
- 1427 · confidence high
- Place
- Samarkand, Uzbekistan
- Credited to
- Jamshid al-Kashi
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What was discovered
In The Key to Arithmetic he gives the law of cosines in trigonometric form suited to solving triangles, along with a method for extracting nth roots equivalent to the Ruffini-Horner method. In France it is still called théorème d'Al-Kashi.
Euclid (II.12-13) gives the geometric version, and al-Battani uses equivalent relations in spherical trigonometry; al-Kashi gives the first explicit formulation for plane triangles.
What it led to
- triangulation and surveying
- numerical calculation of roots
- trigonometry in European manuals