Alexander Gottlieb Baumgarten is in many ways the founder of modern aesthetics; it was he who first used the word 'aesthetica' to describe matters concerned with beauty (the word actually means 'matters concerned with the senses'). Baumgarten took aesthetics to be the art of thinking beautifully. The curate, however, is ahead of his time; he is actually closely paraphrasing Tolstoy writing some ninety years later in What is Art?. Tolstoy arguably doesn't get Baumgarten quite right; the idea that beauty is sensible apprehension of perfection is Wolffian, and Baumgarten, it can be argued, actually switches this up a bit, holding that beauty is the perfection of the apprehension itself (which may, of course, partly depend on perfection in the object). But Tolstoy also has an axe to grind; in great measure What is Art? is an attack on any high-flying metaphysics of beauty (he thinks that people talk a lot about beauty but give the terms they use no serious content). It is in this context that Tolstoy specifically talks about the "Trinity" of Baumgarten:
If a theory justifies the false position in which a certain part of a society is living, then, however unfounded or even obviously false the theory may be, it is accepted, and becomes an article of faith to that section of society....However unfounded such theories are, however contrary to all that is known and confessed by humanity, and however obviously immoral they may be, they are accepted with credulity, pass uncriticized, and are preached, perchance for centuries, until the conditions are destroyed which they served to justify, or until their absurdity has become too evident. To this class belongs this astonishing theory of the Baumgartenian Trinity, — Goodness, Beauty, and Truth, — according to which it appears that the very best that can be done by the art of nations after 1900 years of Christian teaching, is to choose as the ideal of their life the ideal that was held by a small, semi-savage, slave-holding people who lived 2000 years ago, who imitated the nude human body extremely well, and erected buildings pleasant to look at.
Tolstoy is not an admirer of the Classical and, unlike the curate, not an admirer of Baumgarten.