Note, forms of most grace have least of the straight line in them.
It is to be observed, that straight lines vary only in length, and therefore are least ornamental.
That curved lines as they can be varied in their degrees of curvature as well as in their lengths, begin on that account to be ornamental.
That straight and curv'd lines join'd, being a compound line, vary more than curves alone, and so become somewhat more ornamental.
That the waving line, or line of beauty, varying still more, being composed of two curves contrasted, becomes still more ornamental and pleasing, insomuch that the hand takes a lively movement in making it with pen or pencil.
And that the serpentine line, by its waving and winding at the same time different ways, leads the eye in a pleasing manner along the continuity of its variety, if I may be allowed the expression; and which by its twisting so many different ways, may be said to inclose (tho' but a single line) varied contents; and therefore all its variety cannot be express'd on paper by one continued line, without the assistance of the imagination, or the help of a figure; see * where that sort of proportion'd, winding line, which will hereafter be call'd the precise serpentine line, or line of grace, is represented by a fine wire, properly twisted round the elegant and varied figure of a carol.
The Analysis of Beauty, by William Hogarth