E325 -- Solutio facilis problematum quorundam geometricorum difficillimorum

(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 (center of gravity, center of inscribed circle, center of circumscribed circle) given in terms of the lengths of the sides of the triangle. He also poses the 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 talks about the case when these three points are collinear and then does an example.

According to the records, it was presented to the Petersburg Academy on December 12, 1763.

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