On the most rapid (descending) motion of weights along curves of a specified type
One problem Euler treats in this paper, as described by Homer White: Given two points A (higher) and B (lower), to find, among all semi-ellipses whose axes lie along the line AB, that semi-ellipse which permits the most rapid descent of a weight from A to B.
Original Source Citation
Novi Commentarii academiae scientiarum Petropolitanae, Volume 17, pp. 488-504.
Opera Omnia Citation
Series 1, Volume 25, pp.236-249.