The constant use made of lines by mathematicians, as well as painters, in describing things upon paper, hath establish'd a conception of them, as if actually existing on the real forms themselves. This likewise we suppose, and shall set out with saying in general--That _the straight line_, and _the circular line_, together with their different combinations, and variations, &c. bound, and circumscribe all visible objects whatsoever, thereby producing such endless variety of forms, as lays us under the necessity of dividing, and distinguishing them into general classes; leaving the intervening mixtures of appearances to the reader's own farther observation. First, [Fig. 23 T p. I] objects composed of straight lines only, as the cube, or of circular lines, as the sphere, or of both together, as cylinders and cones, &c. [Illustration: Fig. 23] Secondly, [Fig. 24 T p. I] those composed of straight lines, circular lines, and of lines partly straight, and partly circular, as the capitals of columns, and vases, &c. [Illustration: Fig. 24] Thirdly, [Fig. 25 T p. I] those composed of all the former together with an addition of the waving line, which is a line more productive of beauty than any of the former, as in flowers, and other forms of the ornamental kind: for which reason we shall call it the line of beauty. [Illustration: Fig. 25] Fourthly, [Fig. 26 T p. I] those composed of all the former together with the serpentine line, as the human form, which line hath the power of super-adding grace to beauty. Note, forms of most grace have least of the straight line in them. [Illustration: Fig. 26] 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 [Fig. 26 T p. I] 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 cone. CHAPTER VIII.