Sec. 5. These three curves being all governed by the same general law, with a difference only in dimensions of lines, together with all the other curves so constructible, varied as they may be infinitely, either by changing the lengths of line, or the inclination of the lines to each other, are considered by mathematicians only as one curve, having this peculiar character about it, different from that of most other infinite lines, that any portion of it is a magnified repetition of the preceding portion; that is to say, the portion between _e_ and _g_ is precisely what that between _c_ and _e_ would look, if seen through a lens which magnified somewhat more than twice. There is therefore a peculiar equanimity and harmony about the look of lines of this kind, differing, I think, from the expression of any others except the circle. Beyond the point _a_ the curve may be imagined to continue to an infinite degree of smallness, always circling nearer and nearer to a point, which, however, it can never reach. [Illustration: FIG. 94.] Sec. 6. Again: if, along the horizontal line, A B, Fig. 94, we measure any number of equal distances, A _b_, _b c_, &c., and raise perpendiculars from the points _b_, _c_, _d_, &c., of which each perpendicular shall be longer, by some given proportion (in this figure it is one third), than the preceding one, the curve _x y_, traced through their extremities, will continually change its direction, but will advance into space in the direction of _y_ as long as we continue to measure distances along the line A B, always inclining more and more to the nature of a straight line, yet never becoming one, even if continued to infinity. It would, in like manner, continue to infinity in the direction of _x_, always approaching the line A B, yet never touching it.