Sum of angles of a triangle to zero. For a spherical triangle, the sum of the angles is greater than 180° and can be up to 540°. Specifically, the sum of the angles is where "f" is the fraction of the sphere's area which is enclosed by the triangle. Note that spherical geometry does not satisfy several of Euclid's axioms (including the parallel postulate.) Angles between adjacent sides of a triangle are referred to as "interior" angles in Euclidean and other geometries. "Exterior" angles can be also defined, and the Euclidean triangle postulate can be formulated as the exterior angle theorem. One can also consider the
Divergence of the sum of the reciprocals of the primes logarithm of each side, then he used the Taylor series expansion for as well as the sum of a converging series: for a fixed constant . Then he invoked the relation which he explained, for instance in a later 1748 work, by setting in the Taylor series expansion This allowed him to conclude that It is almost certain that Euler meant that the sum of the reciprocals of the primes less than is asymptotic to as approaches infinity. It turns out this is indeed the case, and a more precise version of this fact was rigorously proved by Franz Mertens