On a problem of geometry resolved by Diophantine analysis
Euler describes this as a problem in "rational trigonometry" and is looking for the angles where the center of gravity is expressed in rational numbers. He asks that the following three expressions all be squares: 2xx+2yy-zz, 2yy+2zz-xx, 2zz+2xx-yy. He repeats some of the results of E451.
Original Source Citation
Mémoires de l'académie des sciences de St.-Petersbourg, Volume 7, pp. 3-9.
Opera Omnia Citation
Series 1, Volume 5, pp.28-34.