to enable the astronomer to bring the anomalies of the planetary bodies, as they increased under observation, within the axioms of a metaphysical physics. The genius exhibited in the development of the mathematical technique places the names of Apollonius of Perga, Hipparchus of Nicaea, and Ptolemy among the great mathematicians of the world, but they never felt themselves free to attack by their hypotheses the fundamental assumptions of the ancient metaphysical doctrine of the universe. Thus it was said of Hipparchus by Adrastus, a philosopher of the first century A. D., in explaining his preference for the epicycle to the eccentric as a means of analyzing the motions of the planetary bodies: "He preferred and adopted the principle of the epicycle as more probable to his mind, because it ordered the system of the heavens with more symmetry and with a more intimate dependence with reference to the center of the universe. Although he guarded himself from assuming the role of the physicist in devoting himself to the investigations of the real movements of the stars, and in undertaking to distinguish between the motions which nature has adopted from those which the appearances present to our eyes, he assumed that every planet revolved along an epicycle, the center of which describes a circumference concentric with the earth." Even mathematical astronomy does not offer an exception to the scientific method of the ancient world, that of bringing to consciousness the concepts involved in their world of experience, organizing these concepts with reference to each, analyzing and restating them within the limits of their essential accidents, and assimilating the concrete objects of experience to these typical forms as more or less complete realizations.