Parallel (geometry) as a pair of straight lines in a plane which do not meet appears as Definition 23 in Book I of Euclid's Elements. Alternative definitions were discussed by other Greeks, often as part of an attempt to prove the parallel postulate. Proclus attributes a definition of parallel lines as equidistant lines to Posidonius and quotes Geminus in a similar vein. Simplicius also mentions Posidonius' definition as well as its modification by the philosopher Aganis. At the end of the nineteenth century, in England, Euclid's Elements was still the standard textbook in secondary schools. The traditional treatment of geometry was being
Ptolemy (name) Ptolemy (name) The name Ptolemy or Ptolemaeus may refer to: Ptolemy, or Ptolemaeus, or Tolomeo (Italian spelling) may also refer to: According to Georg Autenrieth, the English name Ptolemy comes from the Ancient Greek name Πτολεμαῖος ("Ptolemaios"), "warlike" or "son of war". Autienrieth renders the meaning of the name to be an adjective from πτόλεμος ("ptólemos"), explained as a Homeric Greek form of πόλεμος ("pólemos"), "war". A nephew of Antigonus I Monophthalmus was called "Polemaeus", the normal form of the adjective. "Ptolemaios" is first attested in Homer's Iliad and is the name of an Achaean warrior, son of Piraeus, father