Sec. 7. An infinite number of different lines, more or less violent in curvature according to the measurements we adopt in designing them, are included, or defined, by each of the laws just explained. But the number of these laws themselves is also infinite. There is no limit to the multitude of conditions which may be invented, each producing a group of curves of a certain common nature. Some of these laws, indeed, produce single curves, which, like the circle, can vary only in size; but, for the most part, they vary also, like the lines we have just traced, in the rapidity of their curvature. Among these innumerable lines, however, there is one source of difference in character which divides them, infinite as they are in number, into two great classes. The first class consists of those which are limited in their course, either ending abruptly, or returning to some point from which they set out; the second class, of those lines whose nature is to proceed for ever into space. Any portion of a circle, for instance, is, by the law of its being, compelled, if it continue its course, to return to the point from which it set out; so also any portion of the oval curve (called an ellipse), produced by cutting a cylinder obliquely across. And if a single point be marked on the rim of a carriage wheel, this point, as the wheel rolls along the road, will trace a curve in the air from one part of the road to another, which is called a cycloid, and to which the law of its existence appoints that it shall always follow a similar course, and be terminated by the level line on which the wheel rolls. All such curves are of inferior beauty: and the curves which are incapable of being completely drawn, because, as in the two cases above given, the law of their being supposes them to proceed for ever into space, are of a higher beauty. Sec. 8. Thus, in the very first elements of form, a lesson is given us as to the true source of the nobleness and chooseableness of all things. The two classes of curves thus sternly separated from each other, may most properly be distinguished as the "Mortal and Immortal Curves;" the one having an appointed term of existence, the other absolutely incomprehensible and endless, only to be seen or grasped during a certain moment of their course. And it is found universally that the class to which the human mind is attached for its chief enjoyment are the Endless or Immortal lines. Sec. 9. "Nay," but the reader answers, "what right have you to say that one class is more beautiful than the other? Suppose I like the finite curves best, who shall say which of us is right?"