Historical reference:
Euclid (300 BC) was a Greek mathematician known as the "Father of Geometry". His works, some originating with earlier mathematicians, were published as the Elements (13 volumes devoted to Geometry) which is known as one of the most influential works in the history of mathematics.

In the Elements, Euclid created the foundation of Geometry using definitions, common notions, and his five famous postulates. (Postulates are statements made without proofs.) The fifth postulate established a basis for working with parallel lines.
Read more about Euclid's Fifth Postulate at Euclidean Geometry Introduction.
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Euclid


The Parallel Postulate
In a plane, at most one line can be drawn through a point not on a given line parallel to the given line.
This statement is equivalent to Euclid's Fifth Postulate, and as stated, describes the type of geometry known as Euclidean Geometry.

parallelpostulate

From the time the fifth postulate was first stated, mathematicians believed that the statement was not a true postulate, but was rather a theorem which could be proven using the other four postulates. It wasn't until the nineteenth century that mathematicians finally realized that it was not possible to "prove" the fifth postulate. While they could prove that the lines were parallel, they could not prove, using only existing postulates and theorems, that there was only ONE line through the point that was parallel to the given line. To this day, the Parallel Postulate is assumed true without proof.

The assumption that there possibly "could" be two lines through a point both parallel to a third line led to the discovery of non-Euclidean Geometries. For more information on non-Euclidean Geometries, see Euclidean Geometry Introduction.

Note: There are several postulates that are considered "equivalent" to Euclid's fifth postulate.
The one stated above is the equivalent form known as Playfairs;s axiom, and is the the basis of connecting Euclidean Geometry with non-Euclidean Geometries through parallel lines. As such, this version carries the title of Parallel Postulate.

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