Within the last few years the reputation of Archimedes in pure mathematics has been greatly enhanced by the discovery by Professor Heiberg of a lost work of the great Alexandrian professor in Constantinople. Archimedes himself stated in a dedication of the work to Eratosthenes the method employed in this. He says: "I have thought it well to analyze and lay down for you {78} in this same book a peculiar method by means of which it will be possible for you to derive instruction as to how certain mathematical questions may be investigated by means of mechanics. And I am convinced that this is equally profitable in demonstrating a proposition itself, for much that was made evident to me through the medium of mechanics was later proved by means of geometry, because the treatment by the former method had not yet been established by way of a demonstration. For of course it is easier to establish a proof, if one has in this way previously obtained a conception of the questions, than for him to seek it without such a preliminary notion. . . . Indeed, I assume that some one among the investigators of to-day or in the future, will discover by the method here set forth still other propositions which have not yet occurred to me." On this Professor Smith comments: "Perhaps in all the history of mathematics no such prophetic truth was ever put into words. It would almost seem as if Archimedes must have seen as in a vision the methods of Galileo, Cavalieri, Pascal, Newton, and many other great makers of the mathematics of the Renaissance and the present time." Many other distinguished professors of mathematics have, since this declaration of Archimedes came under their notice, declared that he must have had almost a prophetic vision of certain developments of mathematics and especially applied {79} mathematics and mechanics and their relation to one another, that were only to come in much later and indeed comparatively modern times. Undoubtedly Archimedes' works proved the germ of magnificent development not only immediately after his own time but in the long-after time of the Renaissance, when their translation awakened minds to mathematical problems and their solutions that would not otherwise have come.