The extension of the Fregier circle area proposition to all longer orbits

Let $n$ be an integer with $n>3$, and consider the proposition immediately preceding this statement, which asserts that the sum of the areas of the Frégier circles associated with an $n$-orbit has a constant value. Fregier-circle area conjecture. The proposition is valid for every integer $n$ greater than $3$. This extends the preceding result beyond the explicitly treated case $n=3$; the supplied text gives no proof or resolution for the general case.