Aristotle on Arts
Ethics Bk VI: Ch. 3
“state of capacity to make, involving a true course of reason. ”
St. Thomas on Beauty
“Obj.1 Its seems that goodness has not the aspect of a final cause, but rather of the other causes. For, as a Dionysius says, Goodness is praised as beauty. But beauty has the aspect of formal cause. Therefore goodness has the aspect of a formal cause.
Reply Obj.1 Beauty and goodness in a thing are identical fundamentally, for they are based upon the same thing, namely, the form; and this is why goodness is praised as beauty. But they differ logically, for goodness properly relates to appetite (goodness being what all things desire), and therefore it has the aspect of an end (the appetite being a kind of movement towards a thing). On the other hand, beauty relates to a cognitive power [intellectual virtue], for those things are said to be beautiful which please when seen [or heard]. Hence beauty consists in due proportion, for the senses delight [pleasure being key to learning here] in things duly proportioned, as in what is like them – because the sense too is a sort of reason, as is every cognitive power. Now since knowledge is by assimilation, and likeness relates to form, beauty properly belongs to the nature of a formal cause.”
Aristotle on Beauty
Metaphysics XIII Ch. 3
"Now since the good is distinct from the beautiful (for the good is always s in action but the beautiful may also be in what is immovable), those who assert that the mathematical sciences say nothing about the beautiful or the good speak falsely. For they do speak about and show these, and in the highest degree. The fact that they do not use the names, while they do exhibit construction and theorems about them, does not mean that they say nothing about them. Now the most important kinds of the beautiful are order, symmetry, and definiteness, and the mathematical sciences exhibit properties of these in the highest degree. And since these (that is, order and definiteness) appear to be causes of many things, it is clear that the mathematical sciences must be dealing in some way with such a cause, that is, the cause in the sense of beauty."
“that which is beautiful, whether an animal or any other thing which is composed of a number of parts, should have not only these parts [properly] ordered but also a magnitude, and not any chance magnitude. Indeed, beauty exists in magnitude as well as in order;”
“for the visual grasp of it and of its parts does not take place simultaneously, so its unity and wholeness are lost for the viewer.”
“The proper limit of [a good tragedy or plot] according to its own nature is this: the greater the length up to the limit of being grasped as a whole.”
Leon Batista Alberti
Ten Books of Architecture Bk VI Ch2
"I shall define Beauty to be a harmony of all the parts, in whatsoever subject it appears, fitted together with such proportion and connection, that nothing could be added, diminished or altered, but for the worse."