from things universally admitted as clear and constant, and is therefore perfectly true, because in consonance with nature. Its function is not to define things universally clear and understood, but to define all others; and not to attempt to prove things intuitively known to men, but to attempt to prove all others. Against this, the true order of knowledge, those alike err who attempt to define and to prove everything, and those who neglect definition and demonstration where things are not self-evident. This is what geometry teaches perfectly. It attempts no definition of such things as _space_, _time_, _motion_, _number_, _equality_, and the like, because these terms designate so naturally the things which they signify, that any attempt at making them more clear ends in making them more obscure. For there is nothing more futile than the talk of those who would define primitive words. {166} . . . . . . . . “In geometry the principles are palpable, but removed from common use. . . . In the sphere of natural wit or acuteness, the principles are in common use and before all eyes—it is only a question of having a good view of them; for they are so subtle and numerous, that some are almost sure to escape observation. . . . All geometers would be men of acuteness if they had sufficient insight, for they never reason falsely on the principles recognised by them. All fine or acute spirits would be geometers if they could fix their thoughts on the unwonted principles of geometry. The reason why some finer spirits are not geometers is, that they cannot turn their attention at all to the principles of geometry; but geometers fail in finer perception, because they do not see all that is before them, and being accustomed to the plain and palpable principles of geometry, and never reasoning until they have well ascertained and handled their principles, they lose themselves in matters of intellectual subtlety, where the principles are not so easily laid hold of. Such things are seen with difficulty; they are felt rather than seen. They are so delicate and multitudinous that it requires a very delicate and neat sense to appreciate them. . . . So it is as rare for geometers to be men of subtle wit as it is for the latter to be geometers, because geometers like to treat these nicer matters geometrically, and so make themselves ridiculous; they like to commence with definition, and then go on to principles—a mode which does not at all suit this sort of reasoning. It is not that the mind does not take this method, but it does so silently, naturally, and without conscious art. The perception of the process belongs only to a few minds, and those of the highest order. . . . Geometers, who are only geometers, are sure to be right, provided the subject come