Oct 27, 2009 ... Over the years, many purported proofs of the parallel postulate were published. However, none were correct, including the 28 "proofs" G. S. ...
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mathworld.wolfram.com/ParallelPostulate.html
mathworld.wolfram.com/ParallelPostulate.html
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The postulate (also known as the Parallel Postulate) attracted immediate attention. The commentator Proclus (c. 410-485) tells us that the postulate was attacked from the very start. He wrote, "This postulate ought even to be struck out of Postulates altogether;
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www.cut-the-knot.org/triangle/pythpar/Fifth.shtml
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Many of the consequences of the Parallel Postulate, taken together with the remainder of the axioms for plane geometry, can be shown in turn to imply the Parallel Postulate. In this sense, these statements can be regarded as equivalent to the Parallel Postulate.
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www.cut-the-knot.org/triangle/pythpar/PTimpliesPP.shtml
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The fifth postulate, also known as the Parallel Postulate, attracted immediate attention. Many substitutes were suggested and many felt it is a consequence of the other postulates. Now, we know that the fifth postulate is independent of the other postulates and it cannot be derived from the other postulates.
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pegasus.cc.ucf.edu/~xli/non-euclid.htm
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parallel postulate One of the five postulates, or axiom s, of Euclid underpinning Euclidean geometry ... Britannica Concise Encyclopedia: parallel postulate...
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www.answers.com/topic/parallel-postulate
www.answers.com/topic/parallel-postulate
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Since the time Euclid included his parallel postulate as a ``self-evident truth'', it has been the subject of controversy, and for two thousand years geometers attempted to prove it.
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www.math.nmsu.edu/~history/monthly/node5.html
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This postulate is usually called the "parallel postulate" since it can be used to prove properties of parallel lines. Euclid develops the theory of parallel lines in propositions through I.31.
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aleph0.clarku.edu/~djoyce/java/elements/bookI/post5.htm...
aleph0.clarku.edu/~djoyce/java/elements/bookI/post5.html
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Corresponding Angles Postulate: If two coplanar lines are cut by a transversal so that two corresponding angles have the same measure, then those lines are parallel. Parallel Lines Postulate: If two lines are parallel and are cut by a transversal, corresponding angles have the same measure.
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library.thinkquest.org/2647/geometry/angle/parallel.htm
library.thinkquest.org/2647/geometry/angle/parallel.htm
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Why did people want to prove the parallel postulate? ... Why did mathematicians feel the need to deduce the parallel postulate from the other axioms of geometry? After all, if you are going to start from some axioms, it doesn't much matter how many there are. Nobody seemed to mind that the other axioms were independent of...
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www.dpmms.cam.ac.uk/~wtg10/parallel.html
www.dpmms.cam.ac.uk/~wtg10/parallel.html
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