=1754.= [Function] theory was, in effect, founded by Cauchy; but, outside his own investigations, it at first made slow and hesitating progress. At the present day, its fundamental ideas may be said almost to govern most departments of the analysis of continuous quantity. On many of them, it has shed a completely new light; it has educed relations between them before unknown. It may be doubted whether any subject is at the present day so richly endowed with variety of method and fertility of resource; its activity is prodigious, and no less remarkable than its activity is its freshness.--FORSYTH, A. R. _Presidential Address British Association for the Advancement of Science (1897); Nature, Vol. 56, p. 378._ =1755.= Let me mention one other contribution which this theory [Theory of functions of a complex variable] has made to knowledge lying somewhat outside our track. During the rigorous revision to which the foundations of the theory have been subjected in its re-establishment by Weierstrass, new ideas as regards number and continuity have been introduced. With him and with others influenced by him, there has thence sprung a new theory of higher arithmetic; and with its growth, much has concurrently been effected in the elucidation of the general notions of number and quantity.... It thus appears to be the fact that, as with Plato, or Descartes, or Leibnitz, or Kant, the activity of pure mathematics is again lending some assistance to the better comprehension of those notions of time, space, number, quantity, which underlie a philosophical conception of the universe. --FORSYTH, A. R. _Presidential Address British Association for the Advancement of Science (1897); Nature, Vol. 56, p. 378._ CHAPTER XVIII GEOMETRY =1801.= The science of figures is most glorious and beautiful. But how inaptly it has received the name geometry!--FRISCHLINUS, N. _Dialog 1._ =1802.= Plato said that God geometrizes continually.--PLUTARCH. _Convivialium disputationum, liber 8, 2._ =1803.= μηδεὶς ἐγεωμέτρητος εἰσίτω μοῦ τὴν στέγην. [Let no one ignorant of geometry enter my door.]--PLATO. _Tzetzes, Chiliad, 8, 972._ =1804.= All the authorities agree that he [Plato] made a study of geometry or some exact science an indispensable preliminary to that of philosophy. The inscription over the entrance to his school ran “Let none ignorant of geometry enter my door,” and on one occasion an applicant who knew no geometry is said to have been refused admission as a student.--BALL, W. W. R. _History of Mathematics (London, 1901), p. 45._