# Euclidean Fifth Postulate

When did Euclidean Fifth Postulate comes to be called the Parallel Postulate? It is taken for granted. Did Euclid refer to the fifth postulate as the Parallel Postulate?

The fifth postulate does not specifically talk about parallel lines, it is only a postulate related to parallelism. Euclid gave the definition of parallel lines in Book I, Definition 23 just before the five postulates. However, we see that there is the following equivalence:

Equivalence to the Euclidean Parallel Postulate

About the history of the fifth postulate see the article

History of the Parallel Postulate by Florence P. Lewis.

• But who first thought the fifth postulate addressed the problem of parallel lines? – user56930 Jan 15 '18 at 2:15
• I think it is answered in the article about the history about the fifth postulate. – Dietrich Burde Jan 15 '18 at 9:47
• Thanks I am going to re-read it carefully. I scanned it. It seems to me that Euclid did not call it a parallel postulate. So he shouldn't be accused of begging any questions – user56930 Jan 15 '18 at 13:19
• Doesn't parallel lines get proven later when parallel planes get transacted by a transversal plane? – user56930 Apr 1 '19 at 19:54
• Article ...thanks – user56930 Dec 21 '19 at 0:32