To Ptolemy we are also indebted for a work on Geography used in European schools as late as the fifteenth century. The known world to him was from the Canary Islands eastward to China, and from the equator northward to Caledonia. His maps, however, are very erroneous; for, in the attempt to make them correspond to the spherical figure of the earth, the longitudes are too much to the east; the Mediterranean Sea is twenty degrees too long. Ptolemy's determinations are, therefore, inferior in accuracy to those of his illustrious predecessor Eratosthenes, who made the distance from the sacred promontory in Spain to the eastern mouth of the Ganges to be seventy thousand stadia. Ptolemy also wrote on Optics, the Planisphere, and Astrology. It is not often given to an author to endure for so many ages; perhaps, indeed, few deserve it. The mechanism of the heavens, from his point of view, has however, been greatly misunderstood. Neither he nor Hipparchus ever intended that theory as anything more than a geometrical fiction. It is not to be regarded as a representation of the actual celestial motions. And, as might be expected, for such is the destiny of all unreal abstractions, the theory kept advancing in complexity as facts accumulated, and was on the point of becoming altogether unmanageable, when it was supplanted by the theory of universal gravitation, which has ever exhibited the inalienable attribute of a true theory--affording an explanation of every new fact as soon as it was discovered, without requiring to be burdened with new provisions, and prophetically foretelling phenomena which had not as yet been observed. [Sidenote: The later Alexandrian geometers.] [Sidenote: Decline of the Greek age of Reason.]