Spherical law of cosines
Ley de los cosenos esféricos
- Date
- c. 900 · confidence low
- Place
- Raqqa, Syria
- Credited to
- al-Battani (developed progressively within medieval Islamic spherical trigonometry)
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What was discovered
A trigonometric relation linking the three sides and one angle of a spherical triangle, analogous to the planar law of cosines; developed progressively by medieval Islamic astronomers and mathematicians to solve spherical trigonometry problems applied to astronomy.
Attribution and date uncertain: the spherical law of cosines developed progressively within medieval Islamic spherical trigonometry, with no single well-documented author or date.
What it led to
- Fundamental tool of spherical astronomy and navigation
- Solved astronomical-triangle problems (positions of celestial bodies)
- Precursor to modern spherical trigonometry used in geodesy and GPS