Zu Archimedes kam ein wissbegieriger Jüngling, Weihe mich, sprach er zu ihm, ein in die göttliche Kunst, Die so herrliche Dienste der Sternenkunde geleistet, Hinter dem Uranos noch einen Planeten entdeckt. Göttlich nennst Du die Kunst, sie ist’s, versetzte der Weise, Aber sie war es, bevor noch sie den Kosmos erforscht, Ehe sie herrliche Dienste der Sternenkunde geleistet, Hinter dem Uranos noch einen Planeten entdeckt. Was Du im Kosmos erblickst, ist nur der Göttlichen Abglanz, In der Olympier Schaar thronet die ewige Zahl. --JACOBI, C. G. J. _Journal für Mathematik, Bd. 101 (1887), p. 338._ To Archimedes came a youth intent upon knowledge, Quoth he, “Initiate me into the science divine Which to astronomy, lo! such excellent service has rendered, And beyond Uranus’ orb a hidden planet revealed.” “Call’st thou the science divine? So it is,” the wise man responded, “But so it was long before its light on the Cosmos it shed, Ere in astronomy’s realm such excellent service it rendered, And beyond Uranus’ orb a hidden planet revealed. Only reflection divine is that which Cosmos discloses, Number herself sits enthroned among Olympia’s hosts.” =1644.= The higher arithmetic presents us with an inexhaustible store of interesting truths,--of truths too, which are not isolated, but stand in a close internal connexion, and between which, as our knowledge increases, we are continually discovering new and sometimes wholly unexpected ties. A great part of its theories derives an additional charm from the peculiarity that important propositions, with the impress of simplicity upon them, are often easily discoverable by induction, and yet are of so profound a character that we cannot find their demonstration till after many vain attempts; and even then, when we do succeed, it is often by some tedious and artificial process, while the simpler methods may long remain concealed.--GAUSS, C. F. _Preface to Eisenstein’s Mathematische Abhandlungen (Berlin, 1847), [H. J. S. Smith]._ =1645.= The Theory of Numbers has acquired a great and increasing claim to the attention of mathematicians. It is equally remarkable for the number and importance of its results, for the precision and rigorousness of its demonstrations, for the variety of its methods, for the intimate relations between truths apparently isolated which it sometimes discloses, and for the numerous applications of which it is susceptible in other parts of analysis.--SMITH, H. J. S.