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HISTORICAL VIEW OF THE

From the university of Cambridge , Wallis was trans-planted to Oxford, by an appointment to the Savilianprofessorship of geometry, in 16 -i<). In one of his let-ters referring to that period, we are presented with aninteresting illustration of the state of mathematical know-ledge in the former university which has since so amplyredeemed its credit in this respect.—“ Mathematicswere not at that time (with us) looked upon as acade-mical learning.and of more than two hun-

dred students at that time in our college, I do not knowof any two who had more mathematics than myself,which was but very little, having never made it myserious study (otherwise than as a pleasant diversion)till some little time before I was designed for a professorof it.”

Thus unfurnished at the outset, the powers of Wallis’sgenius will appear the more conspicuous when we con-sider the rapid progress he made in mathematical pur-suits, whilst at the same time he was scarcely lessdistinguished for his attainments in various branches ofliterature, philosophy, and theology. Besides a numberof controversial works, the “ Commercium Epistolicum ”contains the best evidence of the zeal and ability withwhich he entered upon the important and then difficultenquiries relative to the rectification and quadrature ofcurves, and other topics connected with these. Hisedition of “ Archimedes de Arenario,” &c. bespeaks hiscritical acuteness; while his “ Essay on the Tides,” andhis “Mechanics,’’ exhibit those dynamical enquiries inthe highest state of developement which they had asyet attained. The “Mathesis Universalis” comprises hiselaborate treatises on algebra and the arithmetic ofinfinites; and the early volumes of the PhilosophicalTransactions are enriched by many communications fromhim. He died in 1703.

It is in his “Arithmetic of Infinites” that Wallis hasdisplayed to the greatest advantage his powers of originalinvention. He here avails himself of the principle,already admitted to a partial extent by Kepler and