English Title

An investigation of a triangle in which the distances of the angles from the center of gravity of it may be expressed rationally


Leonhard Euler

Enestrom Number


Fuss Index


Original Language


Content Summary

"This memoir was made to please a small number of amateurs of Indeterminate Analysis, and contains a very beautiful solution to the problem announced in the title. Here it is in a few words: Let the sides of the desired triangle be 2a, 2b, 2c, and the lengths drawn from their midpoints to the opposite angles be f, g and h, respectively. Take two numbers q and r, and find M = (5qqrr)/(4qq) and N = (5rr–9qq)/(4rr). Reduce the fraction ((MN)2–4)/(4(M+N)) to its lowest terms and name the numerator x and the denominator y, and you will have the side 2a = 2qx + (MN)qy, and the line f = rx–(1/2)(MN)ry. Make p=x+y and x=xy, and you will have the sides 2b = prqs and 2c = pr+qs, and the lengths g = (3pq+rs)/2 and h = (3pqrs)/2."

Published as

Journal article

Published Date


Written Date


Original Source Citation

Nova Acta Academiae Scientiarum Imperialis Petropolitanae, Volume 12, pp. 101-113.

Opera Omnia Citation

Series 1, Volume 4, pp.290-302.

Record Created


Included in

Mathematics Commons