Ptolemy's range extended well beyond the heavens. His Geography attempted to map the entire known world by coordinates of latitude and longitude, laying out methods of projecting the sphere onto a plane and listing the positions of thousands of places. Its coordinates were often inaccurate, and its underestimate of the size of the Earth would, much later, encourage Columbus to think Asia within reach across the Atlantic, but the idea of a mathematical, coordinate-based cartography was enormously influential when the work was recovered in the Renaissance. He also wrote on optics, on the mathematics of musical harmony, and on astronomical instruments.
His legacy is double-edged in a revealing way. The astronomical system of the Almagest, for all its long dominance, was in the end overthrown: the geocentric universe gave way to the heliocentric, and Ptolemy became the great example of an authoritative science later proved wrong in its foundations.
Yet the Tetrabiblos was never refuted in the same way, because astrology does not rest on the geocentric error alone, and it continued as a living practice long after the cosmos it assumed had been abandoned. Ptolemy thus stands at the head of two traditions with opposite fates, a discarded astronomy and an enduring astrology, both flowing from the same Alexandrian pen.