Non-Euclidean geometry that are both perpendicular to a third line: Euclidean geometry, named after the Greek mathematician Euclid, includes some of the oldest known mathematics, and geometries that deviated from this were not widely accepted as legitimate until the 19th century. The debate that eventually led to the discovery of the non-Euclidean geometries began almost as soon as Euclid's work "Elements" was written. In the "Elements", Euclid began with a limited number of assumptions (23 definitions, five common notions, and five postulates) and sought to prove all the other results (propositions) in the work. The most notorious of the postulates is often
Lighthouse of Alexandria this mole, and the Ras el-Tin promontory represents all that is left of the island of Pharos, the site of the lighthouse at its eastern point having been weathered away by the sea. The lighthouse was constructed in the 3rd century BC. After Alexander the Great died, the first Ptolemy (Ptolemy I Soter) announced himself king in 305 BC, and commissioned its construction shortly thereafter. The building was finished during the reign of his son, the second Ptolemy (Ptolemy II Philadelphus). It took twelve years to complete, at a total cost of 800 talents, and served as a prototype for