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Is there a good survey article listing all the theorems of Euclidean geometry that are equivalent to the parallel postulate?

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Do you mean all the theorems in Euclid equivalent to that postulate? "Euclidean geometry" encompasses many theorems not in the surviving manuscripts (and of course infinitely many others...) so a complete list in this wider sense seems well out of reach. –  Noam D. Elkies Mar 5 '12 at 2:43
A fairly decent list is in the book "Higher geometry" by Efimov (Mir eds.) –  Andres Caicedo Mar 5 '12 at 2:56
found this: en.wikipedia.org/wiki/… –  Will Jagy Mar 5 '12 at 3:09
It has been a while since I last looked, but I remember that M. J. Greenberg has a very long list of theorems equivalent to the parallel postulate in his book "Euclidean and non-Euclidean Geometries: Development and History". –  Robert Bryant Mar 7 '12 at 13:29
Here's a list of 26 with a reference to the source of the list: ics.uci.edu/~eppstein/junkyard/parallel-postulate.html –  Doug Chatham Mar 9 '12 at 11:33
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1 Answer

Doug Chatham's answer is the best I received; see Theorem 23.7 of George E. Martin's "The Foundations of Geometry and the Non-Euclidean Plane".

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@James Propp: Greenberg's list is considerably longer, but now I remember that the list is not actually in the textbook itself; it's in the teacher's supplement to the textbook. One of the projects given in Greenberg's textbook is exactly to compile the longest list one can of theorems equivalent to the parallel postulate. The list in the teacher's supplement is intended to help the teacher cope with the lists that the students' projects will generate. –  Robert Bryant Apr 19 '12 at 11:37
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