Al-Jayyānī wrote
The book of unknown arcs of a sphere, which is considered "the first treatise on
spherical trigonometry", although spherical trigonometry in its ancient Hellenistic form was dealt with by earlier mathematicians such as
Menelaus of Alexandria, whose treatise the
Spherics included
Menelaus' theorem, still a basic tool for solving spherical geometry problems in Al-Jayyānī's time. However,
E. S. Kennedy points out that while it was possible in pre-Islamic mathematics to compute the magnitudes of a spherical figure, in principle, by use of the table of chords and Menelaus' theorem, the application of the theorem to spherical problems was very difficult in practice. Al-Jayyānī's work on spherical trigonometry "contains formulae for
right-handed triangles, the general
law of sines, and the solution of a
spherical triangle by means of the
polar triangle." This treatise later had a "strong influence on European mathematics", and his "definition of
ratios as numbers" and "method of solving a spherical triangle when all sides are unknown" are likely to have influenced
Regiomontanus. The short treatise
On twilight was incorrectly attributed to
Ibn al-Haytham for several centuries, due to a reference made by
Gerard of Cremona, who translated it into Latin. The first printed edition of Cremona's translation (
Allacen arabis uetustissimi liber de crepusculis, Gerardo Cremonensi interprete) was made in 1542, by the Portuguese mathematician and cosmographer
Pedro Nunes. == See also ==