Where can I find a reference to a complete proof of the Braikenridge–Maclaurin theorem, which is stated as:
If the three pairs of opposite sides of (an irregular) hexagon meet at three collinear points, then the six vertices lie on a conic, which may degenerate into a pair of lines.
Most sources online refer to one of two books by Coxeter (Projective Geometry, Geometry Revisited), but I took a look at them and they don't have complete proofs.
Any help in locating a complete proof would be much appreciated, thanks.
The first time I came across this theorem, it was in Undergraduate Algebraic Geometry by Miles Reid. Printed by Cambridge University Press in 1988, originally in the series ' London Mathematical Society Student Texts'. Section 2.11 in this book is called 'Pascal's theorem', but contains and proves the statement in both directions. It thus proves both Pascal's theorem and the Braikenridge–Maclaurin theorem.
I must warn that, even though this book gives a rather detailed proof, I wouldn't generally recommend reading anything in this book, since the material isn't very well presented.
The book also mentions another reference for the proof, which is chapter 16 of the Springer edition(s?) Geometry I and II by M. Berger.