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HISTORICAL VIEW OP THE

the ancient geometers will retain their pre-eminence asmodels to succeeding ages.

The invention of mechanical modes of construction,by which certain curves could be traced out and someproblems solved, and which began to prevail withEudoxus, Archytas , and their followers, was muchcensured by Plato , who considered such methods dero-gatory to the abstract philosophic dignity of geometry,and destructive to its purely intellectual character. Thissentiment, to a certain degree perfectly just, was ex-tensively adopted by the philosophers of the Platonicschool, and produced the effect of alienating mechanicalinvention from mathematical speculation: a result highlyinjurious to the former science, and repressive of muchof the spirit of invention and improvement in the latter.Indeed, it was, probably, to the wide distinction main-tained in the ideas of many of the ancient philosophers,between the respective characters of geometrical and ofphysical investigation, that we may attribute much ofthe neglect of the latter, and the slowness of its progress,from the want not only of the powerful aid it mighthave derived from the former, but even of recognitionas a legitimate branch of philosophy. Nothing, indeed,can be more striking, than the contrast afforded by themanner in which these two classes of enquiry wererespectively carried on: and we can hardly help feelingastonished, that the same philosophical genius whichwas so rigorously precise in its demands for the perfectdemonstration of the most primary notions on whichmathematical truth was to rest, should have been readyto satisfy itself with the most flimsy conjectures orunsubstantial analogies, in matters of physical specu-lation.