Principles of spherical trigonometry drawn from the method of the maxima and minima
Euler uses a simple result from his earlier work on the "method of maxima and minima" (renamed, a few years later, the "calculus of variations") to re-derive, without classical geometry, all the formulae to resolve a spherical triangle; that is, knowing any three measures from the set of three angles and three sides, to compute the other three. He begins with the case of a right spherical triangle, and then considers general triangles. Special attention is called to those formulae which are suited to the use of logarithms.
Original Source Citation
Mémoires de l'académie des sciences de Berlin, Volume 9, pp. 223-257.
Opera Omnia Citation
Series 1, Volume 27, pp.277-308.