Ptolemy I Soter rivals after Alexander's death. For example, Arrian's account of the fall of Thebes in 335 BC ("Anabasis" , a rare section of narrative explicitly attributed to Ptolemy by Arrian) shows several significant variations from the parallel account preserved in Diodorus Siculus (17.11–12), most notably in attributing a distinctly unheroic role in proceedings to Perdiccas. More recently, J. Roisman has argued that the case for Ptolemy's blackening of Perdiccas and others has been much exaggerated. Ptolemy personally sponsored the great mathematician Euclid. He found Euclid's seminal work, the "Elements", too difficult to study, so he asked if there were an easier
Spherical geometry geometries exist; see elliptic geometry. The earliest mathematical work of antiquity to come down to our time is "On the rotating sphere" (Peri kinoumenes sphairas) by Autolycus of Pitane, who lived at the end of the fourth century BC. Spherical trigonometry was studied by early Greek mathematicians such as Theodosius of Bithynia, a Greek astronomer and mathematician who wrote the Sphaerics, a book on the geometry of the sphere, and Menelaus of Alexandria, who wrote a book on spherical trigonometry called "Sphaerica" and developed Menelaus' theorem. "The book of unknown arcs of a sphere" written by the Islamic mathematician Al-Jayyani