What is a good reference for the following result which I believe is proved by Tchebotarev.
There are exactly 5 types of Lunes that are squarable. (Hippocrates produced three and then two more were given by Euler).
"The Problem of Squarable Lunes." M. M. Postnikov, translated from the Russian by Abe Shenitzer. The American Mathematical Monthly. Vol. 107, No. 7 (Aug.-Sep., 2000), pp. 645-651. JSTOR link.
See also the MathPages web page entitled "The Five Squarable Lunes,"
and the Wikipedia page "Lune of Hippocrates," from which this image
of the "lunes of Alhazen" is taken: