=643.= A student who wishes now-a-days to study geometry by dividing it sharply from analysis, without taking account of the progress which the latter has made and is making, that student no matter how great his genius, will never be a whole geometer. He will not possess those powerful instruments of research which modern analysis puts into the hands of modern geometry. He will remain ignorant of many geometrical results which are to be found, perhaps implicitly, in the writings of the analyst. And not only will he be unable to use them in his own researches, but he will probably toil to discover them himself, and, as happens very often, he will publish them as new, when really he has only rediscovered them.--SEGRE, CORRADI. _On some recent Tendencies in Geometrical Investigations; Rivista di Matematica, 1891, p. 43. Bulletin American Mathematical Society, 1904, p. 443 [Young, J. W.]._ =644.= Research may start from definite problems whose importance it recognizes and whose solution is sought more or less directly by all forces. But equally legitimate is the other method of research which only selects the field of its activity and, contrary to the first method, freely reconnoitres in the search for problems which are capable of solution. Different individuals will hold different views as to the relative value of these two methods. If the first method leads to greater penetration it is also easily exposed to the danger of unproductivity. To the second method we owe the acquisition of large and new fields, in which the details of many things remain to be determined and explored by the first method.--CLEBSCH, A. _Zum Gedächtniss an Julius Plücker; Göttinger Abhandlungen, 16, 1871, Mathematische Classe, p. 6._ =645.= During a conversation with the writer in the last weeks of his life, _Sylvester_ remarked as curious that notwithstanding he had always considered the bent of his mind to be rather analytical than geometrical, he found in nearly every case that the solution of an analytical problem turned upon some quite simple geometrical notion, and that he was never satisfied until he could present the argument in geometrical language. --MACMAHON, P. A. _Proceedings London Royal Society, Vol. 63, p. 17._