Chapter 38.—The Science of Numbers Not Created, But 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 power 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 numbers114    Intelligibiles numeri. 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, and who does not rather inquire after the source from which those things which he perceives to be true derive their truth, and from which those others which he perceives to be unchangeable also derive their truth and unchangeableness, and who, mounting up from bodily appearances to the mind of man, and finding that it too is changeable (for it is sometimes instructed, at other times uninstructed), although it holds a middle place between the unchangeable truth above it and the changeable things beneath it, does not strive to make all things redound to the praise and love of the one God from whom he knows that all things have their being;—the man, I say, who acts in this way may seem to be learned, but wise he cannot in any sense be deemed.

CAPUT XXXVIII. Numerorum scientia non ex hominum instituto, sed ex rerum natura est ab hominibus adinventa.

56. Jam vero numeri disciplina cuilibet tardissimo clarum est quod non sit ab hominibus instituta, sed potius indagata atque inventa. Non enim sicut primam syllabam Italiae, quam brevem pronuntiaverunt veteres, voluit Virgilius, et longa facta est; ita quisquam potest efficere cum voluerit, ut ter terna aut non sint novem, aut non possint efficere quadratam figuram, aut non ad ternarium numerum tripla sint, ad senarium sescupla, ad nullum dupla, quia intelligibiles numeri semissem non habent. Sive ergo in seipsis considerentur, sive ad figurarum aut ad sonorum aliarumve motionum leges numeri adhibeantur, incommutabiles regulas habent, neque ullo modo ab hominibus institutas, sed ingeniosorum sagacitate compertas.

57. Quae tamen omnia quisquis ita dilexerit, ut jactare se inter imperitos velit, et non potius quaerere unde sint vera, quae tantummodo vera esse persenserit; et unde quaedam non solum vera sed etiam incommutabilia, quae incommutabilia esse comprehenderit; ac sic a specie corporum usque ad humanam mentem perveniens, cum et ipsam mutabilem invenerit, quod nunc docta, nunc indocta sit, constituta tamen inter incommutabilem supra se veritatem, et mutabilia infra se caetera, ad unius Dei laudem atque 0062 dilectionem cuncta convertere, a quo cuncta esse cognoscit; doctus videri potest, esse autem sapiens nullo modo.