History
The postulate, as given above, appears in (Coxford 1992, pg. 801) as part of the secondary school geometry curriculum revision of the University of Chicago School Mathematics Project (UCSMP).
The axiomatic foundation of Euclidean geometry can be dated back to the books known as Euclid's Elements (circa 300 B.C.E.). These five initial axioms (called postulates by the ancient Greeks) are not sufficient to establish Euclidean geometry. Many mathematicians have produced complete sets of axioms which do establish Euclidean geometry. One of the most notable of these is due to Hilbert who created a system in the same style as Euclid. Unfortunately, Hilbert's system requires 21 axioms. Other systems have used fewer (but different) axioms. The most appealling of these, from the viewpoint of having the fewest number of axioms, is due to Garrett Birkhoff (1932) which has only four axioms. These four are: the Unique line assumption (which was called the Point-Line Postulate by Birkhoff), the Number line assumption, the Protractor postulate (to permit the measurement of angles) and an axiom that is equivalent to Playfair's axiom (or the parallel postulate).
Read more about this topic: Point-line-plane Postulate
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