|WikiProject Mathematics||(Rated Start-class, Low-priority)|
Not only are sections of this article poorly written, but there is also a knotty problem with the section on the relationship to Euclid's 5th postulate. The article repeats the near-nonsense that can be found in Henderson's text - and that's the rub, this is sourced material. The argument goes – they are not equivalent since one holds in spherical geometry and the other doesn't. Leaving aside Henderson's deliberate confounding of spherical and elliptic geometry (there is a viewpoint from which this makes sense, but that is a very abstract advanced topic which does not belong at this level of treatment), the only thing that this argument shows is that the two concepts are not tautologically related. This is a straw-man argument, no one to my knowledge has ever claimed that the statements were logically equivalent. The equivalence must be established within the context of the geometry in which the statements make sense. Without that context (that is, the axioms which define the geometry) one can not provide a proof that either statement implies the other. What can be said in this situation is that the two statements are equivalent in the context of Euclidean geometry, while they are not equivalent when interpreted in the spherical model. Henderson's fixation on the spherical model distorts the way he emphasizes his statements and it is this distortion which is being repeated in this article. Conclusions about which statement is "stronger" just don't make any sense. It is not clear to me how I should fix this without just wiping it all away. Bill Cherowitzo (talk) 18:03, 9 October 2013 (UTC)
It appears that Henderson has come out with a new edition and has picked up a co-author. Circumstantial evidence indicates that the language has been toned down and is now in line with what I have written above (but I haven't seen a copy of this edition). I think I can now rewrite the offending section appropriately. Bill Cherowitzo (talk) 22:44, 9 October 2013 (UTC)
It is stated policy WP:Secondary source that the ideal references are secondary sources such as the survey by Morris Kline that has just been re-instated. There are not many articles that have extended comments on Playfair’s axiom but Kline’s survey of geometry in 1964 is one. The article first describes the consequences of Playfair’s axiom in the plane before venturing into conditions denied by Playfair: multiple parallels or no parallels. The article has recently become generally available and gives a reader a sense of the utility of this particular phrasing of a geometric condition. The reference is:
- This is one of your more ridiculous inclusions. You have placed a totally non-notable statement in the history section for no reason that I can discern. Kline does not say anything more about Playfair's axiom than anyone else who has written about the subject, in a nutshell, it is equivalent to Euclid's parallel postulate and is easier to understand. In what sense do you see this as an extended comment? What is the historical import of this survey article? And, to be perfectly clear, a secondary source uses and details primary sources, Kline is not doing this in this survey, this is not a secondary source! Bill Cherowitzo (talk) 04:37, 11 January 2015 (UTC)
uniformising citations to Dr Playfair's 'Elements of Geometry'
i noticed that different versions of Dr Playfair's 'Elements of Geometry' are being used as citations. given that google books now requires flash & signing, i was hoping we could use the 1846 version that's freely available on the archives. no wikipedia source should require users to log in to google in order to inspect the supplied citation.
the edition i'm proposing we use for uniformising citations is given here: https://archive.org/details/elementsgeometr05playgoog
this page could really benefit from consolidation of sources and clean up. some cites seem a bit excessive but i think we need to have a healthy discussion as to how to tackle this.