Talk:Pappus's hexagon theorem

Dual version
In both the figure and main body of the text for the dual version I believe X and Z should be switched. this because X is the first of three letters and on the right of its defining equation there should appear only second and third objects c,C,b,B. Similarly, for Y (which is fine) and Z. Note that the lines X,Y,Z are defined using crossing combinations which should be given the number/name of the letter not entering the cross. Actually, the `problem' is present also in the normal (non-dual) form. I don't change it myself since I am not familiar with Wikipedias changes and do not know how to change the figure anyway. — Preceding unsigned comment added by 78.208.255.210 (talk) 12:03, 8 December 2023 (UTC)

Self Duality of Pappus Configuration
I think that this needs a bit more explanation further down in the main article.

TomyDuby (talk) 06:35, 14 February 2009 (UTC)

The Proof of the Theorem
The only proof of Pappus's theorem I've ever seen is the one given here, using homogeneous coordinates. Yet coordinates were not used in geometry till Descartes invented them in the 17th century. I've never seen Pappus's own proof. Does anyone know it? Ericlord (talk) 14:58, 9 October 2009 (UTC)

Yes! I have found Pappus's work and added an account of his proof to the article. It would also be desirable to say how Pappus's work was understood by, say, Michel Chasles (as well as to consult the 1986 translation of Pappus's Collection by Alexander Jones; I have not got access to this). David Pierce (talk) 11:06, 13 May 2013 (UTC)

Error in colinearity statement?
"That is, if ABC, abc, AbZ, BcX, CaY, Xbc, YcA, and ZaB are all lines"

Shouldn't it be XbC? ᛭ LokiClock (talk) 00:27, 19 April 2010 (UTC)

Diagram shows special case when the triads ABC and abc are in perspective $$ABC \doublebarwedge abc$$
The diagram shows the Pappus line XYZ as concurrent with ABC and abc. But this is iff ABC and abc are in perspective. The text ought to make that clear or a new diagram provided. Busy at the moment but I do hope to contribute to Wikipedia's coverage of finite geometries at some point in the future. A Sextet Short of PG(2,57) (talk) 14:18, 27 January 2014 (UTC)
 * ✅, but perhaps a more general diagram is needed, both here and at Pappus configuration. Bill Cherowitzo (talk) 19:19, 27 January 2014 (UTC)
 * ✅ as well. Bill Cherowitzo (talk) 22:39, 27 January 2014 (UTC)
 * Cheers, Bill. Nice diagram. I will add here by and by. A Sextet Short of PG(2,57) (talk) 11:39, 28 January 2014 (UTC)

Pappus's and Pappus'
It seems that Pappus' theorem ismore common, why do we use Pappus's theorem? --Tosha (talk) 00:18, 23 December 2017 (UTC)

A straightforward proof
Pappus theorem is a projective result. Considering that central projections don't alter colinearity, in the first figure of the text we can, without loss of generality, send line g to infinity. A, B and C become directions. Then the colinearity of X, Y and Z becomes a straightforward application of Thales theorem.