'Do you imagine,' says Socrates to Aristippus, 'that what is good is not beautiful? Have you not observed that these appearances always coincide? Virtue, for instance, in the same respect as to which we call it good, is ever acknowledged to be beautiful also. In the characters of men we always [1] join the two denominations together. The beauty of human bodies corresponds, in like manner, with that economy of parts which constitutes them good; and in every circumstance of life, the same object is constantly accounted both beautiful and good, inasmuch as it answers the purposes for which it was designed.' --_Xenophont. Memorab. Socrat_. 1.iii.c.8. This excellent observation has been illustrated and extended by the noble restorer of ancient philosophy. (See the _Characteristics_, vol. ii., pp. 339 and 422, and vol. iii., p. 181.) And another ingenious author has particularly shewn, that it holds in the general laws of nature, in the works of art, and the conduct of the sciences (_Inquiry into the Original of our Ideas of Beauty and Virtue_, treat, i. Section 8). As to the connexion between beauty and truth, there are two opinions concerning it. Some philosophers assert an independent and invariable law in nature, in consequence of which all rational beings must alike perceive beauty in some certain proportions, and deformity in the contrary. And this necessity being supposed the same with that which commands the assent or dissent of the understanding, it follows, of course, that beauty is founded on the universal and unchangeable law of truth. But others there are who believe beauty to be merely a relative and arbitrary thing; that, indeed, it was a benevolent provision in nature to annex so delightful a sensation to those objects which are best and most perfect in themselves, that so we might be engaged to the choice of them at once, and without staying to infer their usefulness from their structure and effects; but that it is not impossible, in a physical sense, that two beings, of equal capacities for truth, should perceive, one of them beauty, and the other deformity, in the same proportions. And upon this supposition, by that truth which is always connected with beauty, nothing more can be meant than the conformity of any object to those proportions upon which, after careful examination, the beauty of that species is found to depend. Polycletus, for instance, a famous ancient sculptor, from an accurate mensuration of the several parts of the most perfect human bodies, deduced a canon or system of proportions, which was the rule of all succeeding artists. Suppose a statue modelled according to this: a man of mere natural taste, upon looking at it, without entering into its proportions, confesses and admires its beauty; whereas a professor of the art applies his measures to the head, the neck, or the hand, and, without attending to its beauty, pronounces the workmanship to be just and true.