"A short cut: given the distance, from a fixed star with a known latitude, of a planet with no latitude, to find the planet's longitude."

And at that time Mars, at an altitude of eight or nine degrees, was observed to be 50°34' from Spica Virginis. So, since it [Mars] stood very close to the ecliptic, in the right triangle between Spica, Spica's ecliptic position, and Mars, the base is given as 50°34' and the side between Spica and the ecliptic is 1°59', which is Spica's latitude. Therefore, the remaining side is 50°32'18". Thus, since Spica was at 18°11' Libra, Mars fell at 8°43'18" Sagittarius. (p.509)

Although spherical triangles do not follow the Pythagorean Theorem (which is true only for flat triangles), since the side corresponding to Spica's latitude is so small, it is quite close. My calculations gave me 50°31'40" for the missing side, which is half-a-minute smaller than Kepler's result. Perhaps he did use the correct geometry for a spherical triangle.