27 1 



Hist* 



One of the fir.-t problems involving a locus upon a sphere to be Bolved by 



use of spherical r-oordii.; - - 'he following: Find tht 



of a spherical triangle having a constant area and a fixed base. With the base 



AB fixed. Fie. 1. and the area of the spherical triangle APB constant, the 



Fi s- i 



locus of P was shown to be a small circle. This result was derived by Johann 

 Lexell 1 1740-1784), an astronomer at St. Petersburg, in 1781. The problem 

 was found to have been solved earlier. 1778, by Euler. 1 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 



r.t's s 



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 Xicholaus Fuss (1755-1826), a native of Basel, 

 and an assistant to Euler at St. Petersburg from 1773 until Filler's death 

 in 1783. 



Frederick Theodore Schubert, a Russian astronomer, a conternporary 

 of Fuss, published solutions to a number of spherical loci, types of which 

 ; Cantor, Vol. IV, p. 3S4, p. 416. 



