  The Appendix of the article arXiv:1212.5056 [math.CO] "On growth in an
abstract plane" by Nick Gill, H. A. Helfgott, Misha Rudnev, contains a general
"geometric Ruzsa triangle inequality" in a Desarguesian projective plane. The
purpose of this note is to give a similar inequality for metric spaces with
dilations, that is in the absence of an algebraic or incidence structure.
