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
Enestrom Number
713
Fuss Index
322
Original Language
Latin
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 = (5qq–rr)/(4qq) and N = (5rr–9qq)/(4rr). Reduce the fraction ((M–N)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 + (M–N)qy, and the line f = rx–(1/2)(M–N)ry. Make p=x+y and x=x–y, and you will have the sides 2b = pr–qs and 2c = pr+qs, and the lengths g = (3pq+rs)/2 and h = (3pq–rs)/2."
Published as
Journal article
Published Date
1801
Written Date
1778
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
