One might fill a volume with the effects that are produced by the endless combinations of the principles of beauty. I have room only for a slight specimen, confined to the simplest figures. A circle and a square are each of them perfectly regular, being equally confined to a precise form, and admitting not the slightest variation. A square however is less beautiful than a circle, because it is less simple. A circle has parts as well as a square; but its parts not being distinct like those of a square, it makes one entire impression; whereas the attention is divided among the sides and angles of a square. The effect of simplicity may be illustrated by another example. A square, though not more regular than a hexagon or octagon, is more beautiful than either; for what other reason, than that a square is more simple, and the attention less divided? This reasoning will appear still more solid when we consider any regular polygon of very many sides; for of such figure the mind can never have any distinct perception. Simplicity thus contributes to beauty.
A square is more beautiful than a parallelogram. The former exceeds the latter in regularity and in uniformity of parts. But this holds with respect to intrinsic beauty only; for in many instances, utility comes in to cast the balance on the side of the parallelogram. This figure for the doors and windows of a dwelling-house, is preferred because of utility; and here we find the beauty of utility prevailing over that of regularity and uniformity.
A parallelogram again depends, for its beauty, on the proportion of its sides. The beauty is lost by a great inequality of sides. It is also lost, on the other hand, by the approximation toward equality. Proportion in this circumstance degenerates into imperfect uniformity; and the figure upon the whole appears an unsuccessful attempt toward a square.
An equilateral triangle yields not to a square in regularity nor in uniformity of parts, and it is more simple. But an equilateral triangle is less beautiful than a square, which must be owing to inferiority of order in the position of its parts. The sides of an equilateral triangle incline to each other in the same angle, which is the most perfect order they are susceptible of. But this order is obscure, and far from being so perfect as the parallelism of the sides of a square. Thus order contributes to the beauty of visible objects, not less than simplicity and regularity.