dullest apprehension that this was not created by man, but was
CHAP. XXXVIII.] OF THE SCIENCE OF NUMBERS. 73 hinges of the joints and knees. Tor what he says is true, and one cannot walk in any other way ; but men find it easier to walk by executing these movements than to attend to them while they are going through them, or to understand when they are told about them. Those, on the other hand, who cannot walk, care still less about such directions, as they cannot prove them by making trial of them. And in the same way a clever man often sees that an inference is unsound more quicldy than he apprehends the rules for it. A dull man, on the other hand, does not see the unsoundness, but much less does he grasp the rules. And in regard to all these laws, we derive more pleasure from them as exhibitions of truth, than assistance in arguing or forming opinions, except perhaps that they put the intellect in better training. We must take care, however, that they do not at the same time make it more inclined to mischief or vanity,—that is to say, that they do not give those who have learnt them an inclination to lead people astray by plausible speech and catching questions, or make them think that they have attained some great thing that gives them an advantage over the good and innocent.
Chap, xxxviii. The science ofnumbers not created, hut only discovered, by man.
56. Coming now to the science of number, it is clear to the dullest apprehension that this was not created by man, but was discovered by investigation. For, though Virgil could at his own pleasure make the first syllable of Italia long, while the ancients pronounced it short, it is not in any man's powder to determine at his pleasure that three times three are not nine, or do not make a square, or are not the triple of three, nor one and a half times the number six, or that it is not true that they are not the double of any number because odd numbers^ have no half. Whether, then, numbers are considered in themselves, or as applied to the laws of figures, or of sounds, or of other motions, they have fixed laws which were not made by man, but which the
• acuteness of ingenious men brought to
light.
57. The man, however, who puts so high a value on these things as to be inclined to boast himself one of the learned,
' Intelligibiles numeri.