To this he with a certain youthful rashness adds, that in a pyramid consisting of triangles, the sides inclining to the juncture are unequal, and yet do not exceed one another in that they are greater. Thus does he keep the common notions. For if there is any thing greater and not exceeding, there will be also something less and not deficient, and so also something unequal which neither exceeds nor is deficient; that is, there will be an unequal thing equal, a greater not greater, and a less not less. See it yet farther, in what manner he answered Democritus, enquiring philosophically and properly, if a cone is divided by a plane parallel with its base, what is to be thought of the superficies of its segments, whether they are equal or unequal; for if they are unequal, they will render the cone uneven, receiving many step-like incisions and roughnesses; but if they are equal, the sections will be equal, and the cone will seem to have the same qualities as the cylinder, to wit, to be composed not of unequal but of equal circles; which is most absurd. Here, that he may convince Democritus of ignorance, he says, that the superficies are neither equal or unequal, but that the bodies are unequal, because the superficies are neither equal nor unequal. Indeed to assert this for a law, that bodies are unequal while the superficies are not unequal, is the part of a man who takes to himself a wonderful liberty of writing whatever comes into his head. For reason and manifest evidence, on the contrary, give us to understand, that the superficies of unequal bodies are unequal, and that the bigger the body is, the greater also is the superficies, unless the excess, by which it is the greater, is void of a superficies. For if the superficies of the greater bodies do not exceed those of the less, but sooner fail, a part of that body which has an end will be without an end and infinite. For if he says that he is compelled to this, . . . For those rabbeted incisions, which he suspects in a cone, are made by the inequality of the body, and not of the superficies. It is ridiculous therefore to take the superficies out of the account, and after all to leave the inequality in the bodies themselves. But to persist still in this matter, what is more repugnant to sense than the imagining of such things? For if we admit that one superficies is neither equal nor unequal to another, we may say also of magnitude and of number, that one is neither equal nor unequal to another; and this, not having any thing that we can call or think to be a neuter or medium between equal and unequal. Besides, if there are superficies neither equal nor unequal, what hinders but there may be also circles neither equal nor unequal? For indeed these superficies of conic sections are circles. And if circles, why may not also their diameters be neither equal nor unequal? And if so, why not also angles, triangles, parallelograms, parallelepipeds, and bodies? For if the longitudes are neither equal nor unequal to one another, so will the weight, percussion, and bodies be neither equal nor unequal. How then dare these men inveigh against those who introduce vacuities, and suppose that there are some indivisible atoms, and who say that motion and rest are not inconsistent with each other, when themselves affirm such axioms as these to be false: If any things are not equal to one another, they are unequal to one another; and the same things are not equal and unequal to one another? But when he says that there is something greater and yet not exceeding, it were worth the while to ask, whether these things quadrate with one another. For if they quadrate, how is either the greater? And if they do not quadrate, how can it be but the one must exceed and the other fall short? For if neither of these be, the other both will and will not quadrate with the greater. For those who keep not the common conceptions must of necessity fall into such perplexities.