What distinctions are admitted by continuous quantity? There is the line, the surface, and the solid; for extension may exist in one, two or three dimensions (and thus count the numerical elements of continuous size) instead of establishing species.[389] In numbers thus considered as anterior or posterior to each other, there is nothing in common, which would constitute a genus. Likewise in the first, second and third increases (of a line, surface, and solid) there is nothing in common; but as far as quantity is found, there is also equality (and inequality), although there be no extension which is quantitative more than any other.[390] However, one may have dimensions greater than another. It is therefore only in so far as they are all numbers, that numbers can have anything in common. Perhaps, indeed, it is not the monad that begets the pair, nor the pair that begets the triad, but it may be the same principle which begets all the numbers. If numbers be not derivative, but exist by themselves, we may, at least within our own thought, consider them as begotten (or, derivative). We conceive of the smaller number as the anterior, the greater as posterior. But numbers, as such, may all be reduced to unity. STUDY OF GEOMETRICAL FIGURES. The method of classification adopted for numbers may be applied to sizes, and thus distinguish the line, the surface, and the solid or body, because those are sizes which form different species. If besides each of these species were to be divided, lines might be subdivided into straight, curved and spiral; surfaces into straight and curved; solids into round or polyhedral bodies. Further, as geometers do, may come the triangle, the quadrilateral, and others. STUDY OF THE STRAIGHT LINE. 14. But what about the straight line? Is it not a magnitude? Possibly; but if it be a magnitude, it is a qualified one.[391] It is even possible that straightness constitutes a difference of the (very nature of the) line, as line, for straightness refers solely to a line; and besides, we often deduce the differences of "Essence" from its qualities. That a straight line is a quantity added to a difference does not cause its being composed of the line, and of the property of straightness; for, were it thus composed, straightness would be its chief difference. STUDY OF THE TRIANGLE.