Winternitz Theorem

From: andreas wagener (108076_at_gmx.net)
Date: 09/24/04 

Date: Fri, 24 Sep 2004 01:00:06 +0000 (UTC)

The following nice theorem (phrased as an exercise) appears in
Yaglom/Boltyanskii's book "Convex Figures" (p. 36):

"A convex figure is divided into two parts by a line L that passes
through its center of gravity. Prove that the ratio of the areas of
the two parts always lies between the bounds 4/5 and 5/4."

Yaglom and Boltyanskii called this "Winternitz' Theorem". However,
they do not provide an original reference, and I was not able to trace
back the original source for this theorem either.

Can anybody help me? Is there more literature on Winternitz' Theorem?