224

HISTORICAL VIEW OF THE

wide field open before him, and in this new region ofresearch he perceived that many geometrical truths ofgreat value and utility were to be discovered ; thequadrature of the circle, and of many other curves,together with an incalculable variety of applications ofsuch results hearing upon a number of points of physicalenquiry, were all inviting research, promising a richharvest of further discoveries, and stimulating the at-tempts of the enquirer with the prospect of an immor-tality of fame.

ft occurred to him, that if the equations of the curveswhich he had squared were ranged in a regular series,from the simpler to the more complex, their areaswould constitute another corresppnding series, the termsof which were all known. He further remarked, thatin the first of these series, the equation to the circlemight he introduced, and would occupy the middleplace between the first and second terms of the series,or between the equation of a straight line, and that ofthe parabola. He concluded, therefore, that if in thesecond series he could interpolate a term in the middle,between its first and second terms, this term mustnecessarily he no other than the area of the circle. Butwhen he proceeded to pursue this very refined andphilosophical idea, .he was not so fortunate; and hisattempt towards the requisite interpolation, though itdid not entirely fail, and made known a curious pro-perty of the area of the circle, did not lead to an inde-finite quadrature of that curve.

In these researches Wallis was closely associatedwith sir C. Wren, who in his early youth had evincedhigh mathemetical talents; he gave a rectification ofthe cycloid and several other mathemetical investigations,which Wallis published in his treatise on the cycloid.He devoted himself much to astronomy, and becameprofessor of that science at Oxford in 16'70, as well asin Gresham college; he also entered largely into thedynamical questions then discussed by the English philosophers and Huyghens . But ultimately his mag-