21. But though beauty and ugliness, in their proper and genuine signification, are confined to objects of sight; yet in a more lax and figurative signification, they are apply’d to objects of the other senses. They are sometimes apply’d even to abstract terms; for it is not unusual to say, _a beautiful theorem, a beautiful constitution of government_. But I am inclined to think, that we are led to use such expression by conceiving the thing as delineated upon paper, and as in some sort an object of sight.
22. A line composed by a precise rule, is perceived and said to be regular. A straight line, a parabola, a hyperbola, the circumference of a circle, and of an ellipse, are all of them regular lines. A figure composed by a precise rule, is perceived and said to be regular. Thus a circle, a square, a hexagon, an equilateral triangle, are regular figures, being composed by a rule that determines the form of each. When the form of a line or of a figure is ascertained by a rule that leaves nothing arbitrary, the line and the figure are said to be perfectly regular: this is the case of the figures now mentioned; and it is the case of a straight line and of the circumference of a circle. A figure and a line are not perfectly regular where any part or circumstance is left arbitrary. A parallelogram and a rhomb are less regular than a square: the parallelogram is subjected to no rule as to the length of sides, other than that the opposite sides be equal: the rhomb is subjected to no rule as to its angles, other than that the opposite angles be equal. For the same reason, the circumference of an ellipse, the form of which is susceptible of much variety, is less regular than that of a circle.
23. Regularity, properly speaking, belongs, like beauty, to objects of sight: like beauty, it is also apply’d figuratively to other objects. Thus we say, _a regular government, a regular composition of music_, and, _regular discipline_.
24. When two figures are composed of similar parts, they are said to be uniform. Perfect uniformity is where the constituent parts of two figures are precisely similar to each other. Thus two cubes of the same dimensions are perfectly uniform in all their parts. An imperfect uniformity is, where the parts mutually correspond, but without being precisely similar. The uniformity is imperfect betwixt two squares or cubes of unequal dimensions; and still more so betwixt a square and a parallelogram.