A DISSERTATION upon the Sacred Cubit of the Jews and the Cubits of the several Nations; in which, from the Dimensions of the greatest Egyptian Pyramid, as taken by Mr. John Greaves, the antient Cubit of Memphis is determined.
Translated from the Latin of Sir Isaac Newton, not yet published.
source: http://www.newtonpro...lized/THEM00276
TO the description of the Temple belongs the knowledge of the Sacred Cubit; to the understanding of which, the knowledge of the Cubits of the different nations will be conducive.
The Roman and Greek Cubits (a)[1] were a Foot and a half, and, like the Sacred Cubit, consisted of six Palms, and twenty four Digits. For the Roman and Greek Feet contain'd four Palms, and sixteen Digits. The Roman Foot was likewise divided into <406> twelve Unciæ or Pollices, and was equal to 9671000 of the English Foot, as Mr. Greaves, who examined diligently the antient monuments in Italy, and consider'd the arguments of former writers, as Philander, Agricola, Pætus, Villalpandus, Snellius and others, has determined with the greatest accuracy of all other authors. The Roman Cubit is therefore 1450510000 of the English Foot.
Of the Greek Feet, the Attic was most eminent. Modern writers represent it as equal to a Roman Foot and a Semuncia of that Foot; because the Greek Stadium consisted of six hundred Greek Feet; and a Roman Milliare, or Mile, of a thousand of the greater Roman Passus, or five thousand Feet; and antiently eight Greek Stadia were equal to a Roman Milliare. But it is probable, that the nearest round numbers were used here; and if we say, that the antients sometimes made the Stadium equal to an hundred and twenty-five Passus, that proportion might be deduced, not from a comparison of the Feet with one another, but from the foregoing proportion of the Stadium to the Milliare, express'd very near the truth in round numbers. This conjecture is confirm'd by reflecting, that Polybius, cited by Strabo, receded from this vulgar computation, and represented the Milliare as equal to 8 Sta <407> dia, and one third part; by which means the Attic Foot will be equal to the Roman. The former computation is favour'd by the Ptolemaic Foot, which is equal to a Roman Foot and a Semuncia, if the latter Foot was deriv'd from the Attic. The latter computation is countenanc'd by the Porphyry pillar dug up at Rome, with this inscription, ΠΟΔ. Θ that is, nine Feet; for the Foot of this pillar, as measured by Philander, exceeded the Roman foot only a ninth part of an Uncia. This difference shews the Foot not to be Roman, and the inscription proves it to be the Greek Foot. But whether it was the Attic Foot, let others determine. Till something more certain shall appear, we shall assume nothing, but that the Attic Foot was neither less than the Roman, nor greater than the Roman above a Semuncia. This being granted, we shall have the magnitude of the Attic Cubit to pretty great exactness.
The Derah, or Arabian Cubit (
[2] consisted in like manner of six Palms, and 24 digits; and, in my opinion, was very near equal to the Roman or Attic Cubit. For it was a fifth part of the Royal Cubit of Ægypt; that is, as will immediately be <408> shewn, four simple Cubits of Ægypt, which are now equal to five Roman ones.
Three Arabian Miles were likewise equal to the Persian Parasanga, that is, to thirty Attic Stadia, and consisted of 1000 Orgyiæ, or Arabian Paces, that is, 4000 Cubits; by which means the Arabian Cubit will be equal to the Attic. For the wandering Arabians at first serving in war under the Romans, and afterwards founding an empire in Syria, learned from the conquered people the money, weights, and measures of the Romans and Greeks. We shall pass over this Cubit therefore, and proceed to those which are more antient.
From the Pyramids of Ægypt accurately measured by Mr. John Greaves, I collect the length of the antient Cubit of Memphis in this manner. The side of the first Pyramid was 693 English feet. It is very probable, that at first the measure of it was determined by some round number of Ægyptian Cubits. Ibn Abd Alhokm, quoted by Mr. Greaves, tells us, that the measure of each side was an 100 Royal Cubits of the antient times. But it is probable, that the Ægyptians learn'd, from the Orgyiæ of the Greeks, their measure of four Cubits of Memphis, and gave it the name of the Royal Cubit. Thus the side of the Pyramid will be 400 <409> simple Cubits, or four Arouræ; and the Cubit of Memphis will be equal to 17321000 of the English Foot.
That the Pyramid was built by the Cubit of this magnitude, appears from several dimensions of it. The square passage leading into it of polished marble was in breadth and height 34631000 of the English Foot, that is, two of the above-mentioned Cubits of Memphis. And of the same breadth and height were the four other galleries. In the middle of the Pyramid was a chamber most exquisitely form'd of polish'd marble, containing the monument of the king. The length of this chamber was 3438100 English Feet, and the breadth 1719100; that is, it was 20 Cubits long, and 10 Cubits broad, the Cubit being supposed to be 17191000 of the English Foot. The difference between this measure and the former is 12510000, or one thirtieth of a Foot, that is, about one seventh of an Inch; an error of no importance, if we consider the much greater irregularities observ'd by Mr. Greaves in the best buildings of the Romans. The roof of this chamber consisted of nine oblong and parallel stones; the seven middle ones of which were of the same breadth, but the two outermost were less by half in breadth than the rest; and the breadth of them all <410> together was equal to the length of the chamber, or to 20 Cubits; so that the length of the middle stones was two Cubits and an half. The marble gallery, which led into this chamber, was 6 feet and 87 of 100 parts of a foot, that is, 4 Cubits of the chamber, in breadth. In the middle of this gallery was a way of polished marble, 34351000 feet, that is, 2 Cubits broad; and on both sides the way were two banks, like benches, of polish'd marble likewise, 17171000 feet broad, and 17171000 feet deep; that is, in breadth and depth one Cubit. Who will therefore imagine, that so many dimensions not at all depending upon each other, should correspond by mere chance with the length of the Cubit assigned by us?
Besides, the division of this Cubit into 6 Palms is evident from the dimensions of the Pyramid. For the height of the gallery, according to Mr. Greaves, was about 26 Feet, that is, 15 Cubits. Subtract the height of the benches, and the remaining height will be 14 Cubits. This was divided into seven parts, according to the 7 ranges of the stones in the walls of the gallery; and every upper range projected over the lower about three inches, as is represented in the annexed figure; <411> where AB expresses the breadth of the way, ACD the bank or bench, DE the height of the first range of stone, EF the projection of the second range, and FG the height of it; GH the projection of the third range, and HI the height of it; and so on to the roof KL, which answers to the way AB. The height therefore of every range of stone was two Cubits; and the 6 projections EF, GH, &c. answering to one Cubit, were Palmares.
There are likewise, in the king's monument above-mentioned, specimens of the division of the Cubit. For since the Cubit DC is 17171000 of a Foot, and consequently the Palm 2861000 of a Foot, ten Palms will be 286100 Feet; seven Palms and three Digits will be 27171000 Feet; and twenty five Palms and two Digits will be 72931000 Feet.
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Now Mr. Greaves found the measure of the height of the monument within to be 28601000 Feet, the breadth within to be 22181000 Feet, and the length of the exterior superficies to be 7 Feet, 3 Inches and an half; that is, 72921000 Feet. The height of the monument within was therefore 10 Palms, the breadth within 7 Palms and 3 Digits, and the length of the exterior superficies 25 Palms and 2 Digits, without any sensible error. The height and breadth of the exterior superficies was 3 Feet, 3 Inches and 3 quarters; that is, 11 Palms and 2 Digits and a quarter, if Mr. Greaves has been sufficiently exact in setting down the dimensions of it.
There are also other specimens of this Cubit; as particularly that the whole length of that gallery, with the hypothenuse of a rectangular triangle, whose base was 15 Feet, and height about 5 or 6, or perhaps 7 Feet, being measured by a cord, was 154 Feet. Subtract the hypothenuse, and there will remain the length of the gallery, 138 Feet; that is, 20 times the breadth, or 20 Royal Cubits. Two other galleries were likewise measured, and found to be in length 110 Feet, that is, sixteen Royal Cubits; and another Chamber was in breadth about 17 Feet, that is, 10 Cubits; and an Anticameretta, or Anticloset, was in length 7 Feet, in breadth about 312 Feet; that is, 4 Cubits long, and <413> about 2 Cubits broad. And it is my opinion, that the Pyramid was built throughout after the measure of this Cubit.
If any person shall hereafter exhibit in this manner the dimensions of the remains of the old buildings of the Babylonians and other nations, it will not be difficult to determine from thence the antient Cubits of those countries. In the mean time I shall produce one instance, which occurs, as a specimen of this calculation. Mr. Purchas ©[3] informs us, that there is still extant between the antient Babylon and Bagdad, a vast rude structure of brick; the bricks of which his friend Mr. Allen found to be one Foot long, eight Inches broad, and six Inches thick; he means Inches of the English Foot. These proportions shew, that the bricks were regularly formed, and consequently, that in the making of them regard was had to some particular measure used by the Babylonians, which was of great use, to enable the workmen from the number of bricks to determine immediately the dimensions of the walls with respect to the length, breadth, and thickness, and vice versa to compute the number of the bricks necessary to the building of the wall agreed upon. As the Babylonians therefore measur'd their buildings by Cubits, it follows, that the bricks according to their length, breadth, and <414> thickness conjunctly must compose the measure of the Cubit. Now two bricks according to their length, three according to their breadth, and four according to their thickness, form the same measure; and consequently the measure is that of a Cubit. A Babylonian Cubit is therefore equal to two English Feet; and the component parts intimate the division of this Cubit into six Palms, so that the dimensions of the bricks may be express'd in round numbers of Palms; the length by 3 Palms, the breadth by 2, and the thickness by 112. This Cubit may perhaps be determined hereafter with more exactness by a greater variety of observations.
The magnitude of the Persian Cubit, I think, may be determin'd from their Parasanga. For it is to be considered, that the greater measures, which exceeded the human members, us'd to be deduced from the lesser by multiplication, in which multiplication the denary and sometimes the binary numbers were employ'd. Thus the Roman (d)[4] Calamus or Pertica consisted of ten Feet; the Scrupulum of ten Feet in length, and ten in breadth; the Versus of an hundred Feet in length, and an hundred in breadth; the Clima (a measure deriv'd from the Greeks, as the name shews) of ten Orgyiæ in length, and <415> ten in breadth; the Actus of two Climata in length, and two in breadth; the Jugerum of two square Actus in length, and ten in breadth; the Centuria of ten Decumani in length, and ten in breadth, within Italy; but without, of twice that number; the Saltus of an hundred Decumani in length, and an hundred in breadth; the Milliare, or Mile, of a thousand Passus in length; and the Iter Diei, or Day's Journey, of twice ten Milliaria. The Greek Reed, call'd Ἀκαινα, consisted of ten Feet; the Clima of ten Feet in length, and ten in breadth; the Plethrum of an hundred Feet in length and breadth; the Stadium of an hundred Orgyiæ in length; and the Iter Diei, according to Herodotus, of two hundred Stadia. And in the province of Cyrene, in the lands which Ptolemy a Greek king of Ægypt left to the Roman people, the (e)[5] Plinthides consisted of fifty Limites in length, and fifty in breadth; and each side of those square Limites were ten Stadia.
It appears also from several instances, that as the western nations proceeded from the Foot multiplied by ten, so the eastern did from the Cubit multiplied in the same manner. Thus among the Jews, a nation us'd to the feeding of cattle, the Kibrath Terræ, <416> or pasture-land, sufficient, I think, for a flock under one shepherd, was determined by the space of a thousand Cubits, and a Sabbath-day's Journey by that of two thousand Cubits. And thus among the Ægyptians, the Aroura consisted of an hundred Cubits in length, and an hundred in breadth. And because the Ægyptians every year after the inundation of the Nile divided their lands into Arouræ, the Reed ought, for the greater expedition in measuring, to consist of ten Cubits, that by the repetition of ten they might make an Aroura. And for the like reason the greater measures, into which those lands were divided, ought to consist of tens and hundreds of Arouræ.