men for those principles of the mathematicians, which, if they be not granted, they cannot advance a single step; such as that a point is a thing which has no magnitude,—that an extremity or levelness, as it were, is a space which has no thickness,—that a line is length without breadth. Though I should grant that all these axioms are true, if I were to add an oath, do you think a wise man would swear that the sun is many degrees greater than the earth, before Archimedes had, before his eyes, made out all those calculations by which it is proved? If he does, then he will be despising the sun which he considers a god. But if he will not believe the mathematical calculations which employ a sort of constraint in teaching,—as you yourselves say,—surely he will be very far from believing the arguments of philosophers; or, if he does believe any such, which school will he believe? One may explain all the principles of natural philosophers, but it would take a long time: I ask, however, whom he will follow? Suppose for a moment that some one is now being made a wise man, but is not one yet,—what system and what school shall he select above all others? For, whatever one he selects, he will select while he is still unwise. But grant that he is a man of godlike genius, which of all the natural philosophers will he approve of above all others? For he cannot approve of more than one. I will not pursue an infinite number of questions; only let us see whom he will approve of with respect to the elements of things of which all things are composed; for there is a great disagreement among the greatest men on this subject.
XXXVII. First of all, Thales, one of the seven, to whom they say that the other six yielded the preeminence, said that everything originated out of water; but he failed to convince Anaximander, his countryman and companion, of this theory; for his idea was that there was an infinity of nature from which all things were produced. After him, his pupil, Anaximenes, said that the air was infinite, but that the things which were generated from it were finite; and that the earth, and water, and fire, were generated, and that from them was produced everything else. Anaxagoras said that matter was infinite; but that from it were produced minute particles resembling one another; that at first they were confused, but afterwards brought into order by divine intellect. Xenophanes, who was a little more ancient still, asserted that
