Euclid and his Modern Rivals use for eight months, during the course of 2001. Due to the fisheye effect, only part of the text can be read: Euclid and his Modern Rivals Euclid and his Modern Rivals is a mathematical book published in 1879 by the English mathematician Charles Lutwidge Dodgson (1832–1898), better known under his literary pseudnym "Lewis Carroll". It considers the pedagogic merit of thirteen contemporary geometry textbooks, demonstrating how each in turn is either inferior to or functionally identical to Euclid's "Elements". In it Dodgson supports using Euclid's geometry textbook "The Elements" as the geometry textbook in schools against more modern geometry
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