Easy solutions to some difficult geometric problems
Euler focuses on the centers of triangles, giving formulas for deterimining the locations of the bases of the altitudes of a triangle, as well as for the intersection of the altitudes, along with other formulas (for center of gravity, center of inscribed circle, and center of circumscribed circle) given in terms of the lengths of the sides of the triangle. He also poses the inverse problem: given the location of the intersection of the altitudes, center of gravity, and center of inscribed circle, determine what triangle these come from. He explores the case when these three points are collinear, and then does an example.
Original Source Citation
Novi Commentarii academiae scientiarum Petropolitanae, Volume 11, pp. 103-123.
Opera Omnia Citation
Series 1, Volume 26, pp.139-157.