=843.= There is something sublime in the secrecy in which the really great deeds of the mathematician are done. No popular applause follows the act; neither contemporary nor succeeding generations of the people understand it. The geometer must be tried by his peers, and those who truly deserve the title of geometer or analyst have usually been unable to find so many as twelve living peers to form a jury. Archimedes so far outstripped his competitors in the race, that more than a thousand years elapsed before any man appeared, able to sit in judgment on his work, and to say how far he had really gone. And in judging of those men whose names are worthy of being mentioned in connection with his,--Galileo, Descartes, Leibnitz, Newton, and the mathematicians created by Leibnitz and Newton’s calculus,--we are forced to depend upon their testimony of one another. They are too far above our reach for us to judge of them.--HILL, THOMAS. _Imagination in Mathematics; North American Review, Vol. 85, p. 223._ =844.= To think the thinkable--that is the mathematician’s aim. --KEYSER, C. J. _The Universe and Beyond; Hibbert Journal, Vol. 3 (1904-1905), p. 312._ =845.= Every common mechanic has something to say in his craft about good and evil, useful and useless, but these practical considerations never enter into the purview of the mathematician. --ARISTIPPUS THE CYRENAIC. _Quoted in Hicks, R. D., Stoic and Epicurean, (New York, 1910) p. 210._ CHAPTER IX PERSONS AND ANECDOTES (A-M) =901.= Alexander is said to have asked Menæchmus to teach him geometry concisely, but Menæchmus replied: “O king, through the country there are royal roads and roads for common citizens, but in geometry there is one road for all.” _Stobœus (Edition Wachsmuth, Berlin, 1884), Ecl. 2, p. 30._ =902.= Alexander the king of the Macedonians, began like a wretch to learn geometry, that he might know how little the earth was, whereof he had possessed very little. Thus, I say, like a wretch for this, because he was to understand that he did bear a false surname. For who can be great in so small a thing? Those things that were delivered were subtile, and to be learned by diligent attention: not which that mad man could perceive, who sent his thoughts beyond the ocean sea. Teach me, saith he, easy things. To whom his master said: These things be the same, and alike difficult unto all. Think thou that the nature of things saith this. These things whereof thou complainest, they are the same unto all: more easy things can be given unto none; but whosoever will, shall make those things more easy unto himself. How? With uprightness of mind.--SENECA.