His great works have to do with geography and astronomy. In the former field he makes an advance upon Strabo, citing the latitude of no fewer than five thousand places. In the field of astronomy, his great service was to have made known to the world the labors of Hipparchus. Ptolemy has been accused of taking the star-chart of his great predecessor without due credit, and indeed it seems difficult to clear him of this charge. Yet it is at least open to doubt whether be intended any impropriety, inasmuch as be all along is sedulous in his references to his predecessor. Indeed, his work might almost be called an exposition of the astronomical doctrines of Hipparchus. No one pretends that Ptolemy is to be compared with the Rhodesian observer as an original investigator, but as a popular expounder his superiority is evidenced in the fact that the writings of Ptolemy became practically the sole astronomical text-book of the Middle Ages both in the East and in the West, while the writings of Hipparchus were allowed to perish.

The most noted of all the writings of Ptolemy is the work which became famous under the Arabic name of Almagest. This word is curiously derived from the Greek title , "the greatest construction," a name given the book to distinguish it from a work on astrology in four books by the same author. For convenience of reference it came to be spoken of merely as , from which the Arabs form the title Tabair al Magisthi, under which title the book was published in the year 827. From this it derived the word Almagest, by which Ptolemy's work continued to be known among the Arabs, and subsequently among Europeans when the book again became known in the West. Ptolemy's book, as has been said, is virtually an elaboration of the doctrines of Hipparchus. It assumes that the earth is the fixed centre of the solar system, and that the stars and planets revolve about it in twenty-four hours, the earth being, of course, spherical. It was not to be expected that Ptolemy should have adopted the heliocentric idea of Aristarchus. Yet it is much to be regretted that he failed to do so, since the deference which was accorded his authority throughout the Middle Ages would doubtless have been extended in some measure at least to this theory as well, had he championed it. Contrariwise, his unqualified acceptance of the geocentric doctrine sufficed to place that doctrine beyond the range of challenge.

The Almagest treats of all manner of astronomical problems, but the feature of it which gained it widest celebrity was perhaps that which has to do with eccentrics and epicycles. This theory was, of course, but an elaboration of the ideas of Hipparchus; but, owing to the celebrity of the expositor, it has come to be spoken of as the theory of Ptolemy. We have sufficiently detailed the theory in speaking of Hipparchus. It should be explained, however, that, with both Hipparchus and Ptolemy, the theory of epicycles would appear to have been held rather as a working hypothesis than as a certainty, so far as the actuality of the minor spheres or epicycles is concerned. That is to say, these astronomers probably did not conceive either the epicycles or the greater spheres as constituting actual solid substances. Subsequent generations, however, put this interpretation upon the theory, conceiving the various spheres as actual crystalline bodies. It is difficult to imagine just how the various epicycles were supposed to revolve without interfering with the major spheres, but perhaps this is no greater difficulty than is presented by the alleged properties of the ether, which physicists of to-day accept as at least a working hypothesis. We shall see later on how firmly the conception of concentric crystalline spheres was held to, and that no real challenge was ever given that theory until the discovery was made that comets have an orbit that must necessarily intersect the spheres of the various planets.

Ptolemy's system of geography in eight books, founded on that of Marinus of Tyre, was scarcely less celebrated throughout the Middle Ages than the Almagest. It contained little, however, that need concern us here, being rather an elaboration of the doctrines to which we have already sufficiently referred. None of Ptolemy's original manuscripts has come down to us, but there is an alleged fifth-century manuscript attributed to Agathadamon of Alexandria which has peculiar interest because it contains a series of twenty-seven elaborately colored maps that are supposed to be derived from maps drawn up by Ptolemy himself. In these maps the sea is colored green, the mountains red or dark yellow, and the land white. Ptolemy assumed that a degree at the equator was 500 stadia instead of 604 stadia in length. We are not informed as to the grounds on which this assumption was made, but it has been suggested that the error was at least partially instrumental in leading to one very curious result. "Taking the parallel of Rhodes," says Donaldson,[5] "he calculated the longitudes from the Fortunate Islands to Cattigara or the west coast of Borneo at 180 degrees, conceiving this to be one-half the circumference of the globe. The real distance is only 125 degrees or 127 degrees, so that his measurement is wrong by one third of the whole, one-sixth for the error in the measurement of a degree and one-sixth for the errors in measuring the distance geometrically. These errors, owing to the authority attributed to the geography of Ptolemy in the Middle Ages, produced a consequence of the greatest importance. They really led to the discovery of America. For the design of Columbus to sail from the west of Europe to the east of Asia was founded on the supposition that the distance was less by one third than it really was." This view is perhaps a trifle fanciful, since there is nothing to suggest that the courage of Columbus would have balked at the greater distance, and since the protests of the sailors, which nearly thwarted his efforts, were made long before the distance as estimated by Ptolemy had been covered; nevertheless it is interesting to recall that the great geographical doctrines, upon which Columbus must chiefly have based his arguments, had been before the world in an authoritative form practically unheeded for more than twelve hundred years, awaiting a champion with courage enough to put them to the test.