As I was about to commit this book to the press, I learned that a certain man of acute genius, well learned in the sacred letters, had found out that there were of old two kinds of cubit in use among the Hebrews, and that they are not obscurely signified in sacred Scripture: the one common, of which we discoursed a little above; the other, which he calls ‘sacred,’ much greater than the common cubit. For the common cubit contains twenty-four fingers, this sacred one forty-two; that, six palms, this ten palms and a half-palm; that, a foot and a half, this two feet and a half and besides an eighth part of a foot; that, finally, two Roman palms, this three Roman palms and over half a palm besides. The sacred cubit, then, contained the common one, and besides the half of it and the half of the half. And the author of this opinion judges that divine Scripture used a sacred cubit of this kind in describing the construction of the Ark of Noah, the Tabernacle of Moses, and the Temple of Solomon.²

And that the sacred cubit consisted of the measure we have stated, he proves from what is written about the Bronze Sea which was in the Temple of Solomon. For it is recorded, in the second book of Paralipomenon (Chronicles), ch. 4, that Solomon made a bronze sea of ten cubits from brim to brim, round in compass, five cubits in height, whose circumference was thirty cubits; and it held three thousand baths, or metretes. From this passage he argues, by a mathematical reasoning, that the cubits of the circumference of that bronze sea were not common but sacred — namely, of that measure which we set forth a little before. I have here subjoined the whole argumentation of that man, comprised in the greatest possible brevity.³

The Roman amphora, or Quadrantal, is a cubic vessel whose length, breadth, and height is a Roman foot; and the Roman foot is a measure containing four palms, or sixteen fingers, or twelve inches — or (what is the same) a Roman palm and a third part of it besides, so that the proportion of the foot to the palm is one-and-a-third (sesquitertia, 4:3). Now this amphora holds two urns, or three modii, or 48 sextarii. The metretes (also called the Attic amphora) contains one amphora and a half, that is three urns or 72 sextarii; wherefore the proportion of the metretes to the Roman amphora is one-and-a-half (sesquialtera, 3:2). But if a third measure be set up containing one and a half metretes, this will have to the metretes the proportion one-and-a-half, but to the amphora the proportion two-and-a-quarter (dupla sesquiquarta), namely 9 to 4, as appears in these three terms 9, 6, 4…⁴

…in which are continued two proportions of one-and-a-half: the one, of that third measure containing a metretes and a half, which is 9 to 6; the other, of the metretes to the amphora, namely 6 to 4. These being laid down, since the Bronze Sea, round in compass and having the form of a hemisphere, had a diameter of 10 cubits, a height of 5 cubits, and finally a circuit of 30 cubits, hence it comes that, if we multiply the half-circumference, 15 cubits, by the half-diameter, 5 cubits, we make the area of the greatest circle (that is, the mouth of the sea) 75 square cubits; and again, if we multiply this greatest circle of 75 square cubits by a third part of the diameter — that is, by 3⅓ cubits — we shall find that the solidity of the hemisphere contains 250 cubic, or solid, cubits; which 250 solid cubits are equal to 4,500 amphorae, or 3,000 metretes (for so much did the Bronze Sea hold), or 2,000 measures, each of which we said contains a metretes and a half. Wherefore, if 2,000 such measures (which are equal to 3,000 metretes) be divided by 250 solid cubits, we shall find that one solid cubit contains 8 such cubic measures, which are equal to 12 metretes. Wherefore, if each of the sides of the solid cubit be cut in two, and through the opposite sections planes be drawn, the solid cube will be cut into eight equal cubes, each of which will be equal to the cubic measure that holds a metretes and a half. And thus we have, if this measure containing one and a half metretes be cubed, that the side of this cube is half of the cubit mentioned in the description of the Bronze Sea. If, then, we shall know the magnitude of the side of this cube (which is the eighth part of the solid cubit) with respect to the Roman foot known to us, and that magnitude be doubled, the sacred cubit will become known with respect to the same Roman foot. And this must be investigated in this manner. It was said above that the cubic measure which contains a metretes and a half (and is the eighth part of the solid cubit) has to the Quadrantal, or to the Amphora, the same proportion as 9 to 4; and consequently the amphora has to such a cube the proportion of 4 to 9. Therefore, if between the Roman foot and a straight line which has to the Roman foot the proportion of 9 to 4 (such as is that which contains the foot twice and a fourth part of it besides), two mean proportionals be found, the line found which is nearest to the Roman foot will be the side of the cube which is the eighth part of the solid cubit. And since (as was said above) the side of such a cube is half of the sacred cubit, it is plain that, if that side be doubled, the whole length of the cubit comes forth, which will contain two feet and ten seventeenths — that is, three Roman palms and a half, a little less. It is established, therefore, that if a cubic vessel be set up containing two amphorae and a fourth part of an amphora besides (or a metretes and a half), its side doubled is equal to the sacred cubit which we were seek-…⁵

…ing. And since the length of the Ark was 300 cubits, the breadth 50, the height 30, if by geometrical reckoning you multiply the 300 cubits of length into the 50 of breadth, there will result fifteen thousand square cubits; multiplying these again into the 30 cubits of height, there will result four hundred and fifty thousand solid cubits, and this was the capacity of the Ark. But if the sacred cubit was greater than the common one by one Roman palm and nearly a half, and the dimensions of the Ark consisted of such cubits, its length of 300 such cubits would contain 525 common cubits; the breadth of 50 cubits would have, of common ones, 87½; and finally the height of 30 cubits would be of common cubits 52½. And if the 525 cubits of length be multiplied by the 87½ of breadth, there will result 45,937½ square common cubits; which if you again multiply by the 52½ of height, you will have, of solid common cubits in all, 2,411,718¾ — that is, two million, four hundred and eleven thousand, seven hundred and eighteen, and three quarters. And this was the capacity of the Ark according to the vulgar and common cubits.⁶

But why both the novelty and the trustworthiness of this opinion seem suspect to me, I will say as briefly as I can. Altogether, the foundation on which this view chiefly rests seems quite weak and fragile. For it lays down as most certain that that Bronze Sea — which sacred Scripture calls ‘round’ and Josephus names ‘hemispherical’ — was most perfectly round, that is, according to the exact reckoning of mathematical roundness; which, however, is neither proved by these men, nor (as I think) can be easily proved. Nay, rather, it is more credible that divine Scripture — both elsewhere, when it speaks of the figures of things, and in that very place where it treats of the roundness of that Sea — speaks of such things not according to that most refined and most absolute reckoning of mathematical subtlety, but according to the common use and sense and the common custom of men in speaking. For what approaches a round figure more nearly than any other, and falls little short of roundness — and such a falling-short is not easily detected by the judgment of the senses — that, in popular estimation, is reckoned and called ‘round.’ It is uncertain, therefore, whether that Sea was called round mathematically, or rather popularly; and if it was not mathematically round, since it is not clear how much it fell short of mathematical roundness, the reasoning which is built by these men upon its mathematical and perfect roundness can neither have firm force nor make sure conviction.⁷

Next, the approvers of this opinion say (for now, as I hear, it has begun to have followers) that this kind of sacred cubit is signified in the sacred books neither once nor obscure-…⁸

…ly. But I, to confess frankly (if it be so, my ignorance), have been able as yet to see no traces in the divine letters by which such a cubit could be tracked out, much less found. These men adduce something or other from the second book of Paralipomenon, ch. 3, where it is written that the length of the temple was sixty cubits ‘in the first measure.’ They think that by those words ‘in the first measure’ this sacred cubit of theirs is signified. But this is refuted in two ways. For that ‘in the first measure’ is not referred to the cubit, but signifies that, in the first laying-out and description of the foundations of the temple, the oracle or sanctuary was not separately designated, and the temple itself apart, but that the foundations of both were measured undivided, of a length of sixty cubits; and afterward, separately and properly, out of those sixty cubits twenty were destined and assigned to the sanctuary, but forty to that which is called the temple. And this interpretation, which — since it inheres in the sense of the words — is quite probable, plainly does not at all help the opinion of these men. But be it so: let the sacred cubit be signified by those words ‘in the first measure.’ Yet whence do these men prove that the cubit of ‘the first measure’ was as great as they make it? Nay, rather, ‘the cubit of the first measure’ signifies nothing else than a cubit of a just, exact, and unvarying measure — such as were the measures and weights of the sanctuary, by whose standard the common measures were tested and examined, so that, if any fraud lay beneath them, it could be detected by comparison with these. And of these measures and weights of the sanctuary frequent mention is made in the Mosaic books, as in Exodus 30 and 38, Leviticus (last chapter), and Numbers 18.⁹

But this, in my judgment, seems to convince that that opinion is false: that Ezekiel, in chapter 43, defining the measure of the sacred cubit (whose use, namely, was in the temple, and which there the blessed Jerome named the ‘truest cubit,’ and the Septuagint translators the ‘perfect cubit’), makes it greater than the common and vulgar by one palm only, that is, four fingers; for he speaks of the lesser, or mathematical, palm, not of the greater, or (as they call it) Roman, which is four times greater. Wherefore in that place it is called by the Septuagint translators palaistē, by which name the lesser palm is signified; and Jerome, in the commentary on that passage, interpreting the name ‘palm,’ says it is the sixth part of a cubit. Therefore, according to Ezekiel, the sacred cubit was greater than the common by one palm only, or four fingers; but according to these men it was greater by four palms and a half, or eighteen fingers: their opinion, therefore, does not agree with the doctrine of Ezekiel. These things I wished for the present to dispute briefly concerning the aforesaid opinion; which if, nevertheless, it shall seem to anyone firm and probable enough, and our refutation of it ineffectual, he may follow it, with no resistance from me. I have judged it the part of my office not to pass over in silence, nor without some examination, a new opinion, contrary or at least diverse from the view received by all up to this day, and (as it seems to me) by no means agreeing with the doctrine of the sacred letters…¹⁰

…[an opinion] by no means agreeing [with Scripture]. For the rest, I leave the decision and judgment of this whole dispute to the learned reader.¹¹