274 
HISTORICAL. 
One of the first problems involving a locus upon a sphere to be solved by 
use of spherical coédrdinates was the following: Find the locus of the vertex 
of a spherical triangle having a constant area and a fixed base. With the base 
AB fixed, Fig. 1, and the area of the spherical triangle APB constant, the 
P 
Fagal 
locus of P was shown to be a small circle. This result was derived by Johann 
Lexell (1740-1784), an astronomer at St. Petersburg, in 1781. The problem 
was found to have been solved earlier, 1778, by Euler.!. The result is:some- 
times known as Lexell’s theorem. 
A second spherical locus appeared as the solution of the problem: To 
find the locus of the vertex of a spherical triangle upon a fixed base, such that 
the sum of the two variable sides is a constant. This problem defines a locus 
P 
Fig. 2) 
upon the sphere analogous to the ordinary definition of an ellipse in the 
plane. The locus of P is called the Spherical Ellipse. The solution of this 
problem was found in 1785 by Nicholaus Fuss (1755-1826), a native of Basel, 
and an assistant to Euler at St. Petersburg from 1773 until Euler’s death 
in 1783. 
Frederick Theodore Schubert, a Russian astronomer, a contemporary 
of Fuss, published solutions to a number of spherical loci, types of which 
1 Cantor, Vol. IV, p. 384, p. 416. 
