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

Authors

Leonhard Euler

Enestrom Number

713

Fuss Index

322

Original Language

Latin

Published as

Journal article

Published Date

1801

Written Date

1778

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."

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

2018-09-25

Included in

Mathematics Commons

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