The following problem, originally proposed by Fermat to Torricelli, To find the point the sum of whose distances from three given points is the least possible, seems to have given considerable trouble to the older mathematicians, and even in modern times (see Gregory's Examples, p. 126) to have been solved in a very tedious manner. Simpler solutions have since been given (e.g., Cambridge and Dublin Mathematical Journal, viii. p. 92), but none, to my knowledge, so direct as that indicated by Quaternions. The object of this note is to show the simplicity of the quaternion method.