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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.

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 mathML formula 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 1mathML formula 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 (b)[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 1mathML formula 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 3mathML formula 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 34mathML formula English Feet, and the breadth 17mathML formula; that is, it was 20 Cubits long, and 10 Cubits broad, the Cubit being supposed to be 1mathML formula of the English Foot. The difference between this measure and the former is mathML formula, 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, 3mathML formula feet, that is, 2 Cubits broad; and on both sides the way were two banks, like benches, of polish'd marble likewise, 1mathML formula feet broad, and 1mathML formula 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 1mathML formula of a Foot, and consequently the Palm mathML formula of a Foot, ten Palms will be 2mathML formula Feet; seven Palms and three Digits will be 2mathML formula Feet; and twenty five Palms and two Digits will be 7mathML formula Feet.

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Now Mr. Greaves found the measure of the height of the monument within to be 2mathML formula Feet, the breadth within to be 2mathML formula Feet, and the length of the exterior superficies to be 7 Feet, 3 Inches and an half; that is, 7mathML formula 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 3mathML formula 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 (c)[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 1mathML formula. 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.

The greater measures therefore of the antient nations consisted of the round numbers of those lesser measures from which they were derived; and consequently the Schæni of the Ægyptians and the other eastern nations, and the Parasangæ of the Persians, consisted of round numbers of Cubits. Now the least Schænus of the Ægyptians, by the testimony of Artemidorus and Strabo, was equal to thirty Greek Stadia; and the Parasanga, by the testimony of Herodotus, Xenophon, Hesychius, Suidas, Agathias, and others cited by Strabo, was likewise equal to thirty Stadia; and the round number of Cubits, to <417> which so many Stadia were equal, are ten thousand. That Schænus therefore consisted of 10000 Cubits of Memphis, and the Parasanga of as many Persian Cubits; and 10000 of the Cubits of both kinds were equal to 30 Stadia.

The Calculation of the Ægyptian Cubit is confirmed by the present Cubit of the Ægyptians used in the city of Grand Cairo, which Mr. Greaves found to be 1mathML formula of the English Foot. This Cubit approaches nearer to the antient Cubit of Memphis, than to the lesser Cubits of the Greeks, Romans, and Arabians who reigned in Ægypt; and therefore it seems to be derived from that of Memphis. But it is greater than that. And what wonder is it, that a measure should be somewhat increased in the space of above 3000 years? The measures of Feet and Cubits now far exceed the proportion of human members; and yet Mr. Greaves shews from the Ægyptian monuments, that the human stature was the same above 3000 years ago, as it is now. The measures therefore are increased, the reasons of which may be assigned. The instruments, which use to be preserved as standards of measures, by contracting rust are increased. Iron beaten by the hammer may insensibly relax in a long space of time. Artificers likewise in making <418> instruments, choose to err in the excess of the materials; and when by filing they attain any measure, which they think sufficient, they stop, knowing that they can soon correct that little excess by filing, if their master should complain of it; but that they cannot remedy a defect. Let us suppose therefore, that all measures have increased by degrees, especially in the first ages, when less care was taken of them; and the Cubit of Memphis, about the time of the Roman Empire, will be a mean between the antient and the modern Cubit, but will approach nearer to the modern. The antient Cubit was 1mathML formula of the English Foot, and the modern is 1mathML formula of the English Foot. The mean therefore between them will be about 1mathML formula, or 1mathML formula of a Foot. Now 10000 of such mean or middle Cubits make, as they ought, about 30 Attic Stadia.

The former calculation of the Persian Cubit is confirmed by the Arish, or modern Persian Cubit, which (being doubled, as I suppose) Mr. Greaves found by measuring to be 3mathML formula of the English foot. If half of this was the simple Cubit, and it increased from the time of the Greek and Roman Empire after the manner of the Cubit of Memphis, it must antiently have been about 1mathML formula of the English Foot. Herodotus stiles this Cubit, <419> compared with the Cubits of the Greeks and neighbouring nations, the middling Cubit; and tells us, that the royal Persian Cubit was larger than it by 3 Digits. If we understand by them, Digits of the middling Cubit, which was more known to the Greeks, the royal Cubit will be to the middling Cubit as 27 to 24; and since the middling Cubit is 1mathML formula of the English Foot, the royal Cubit will be about 1mathML formula. Now 10000 of such Cubits make, as they ought, about 30 Attic Stadia.

The preceding computations are likewise confirm'd by a certain general reason, by comparing the Feet and Cubits used at first in every nation according to the proportion of the members of a man, from which they were taken. For the Foot of a man is to the Cubit or lower part of the Arm of the same man as about 5 to 9, as I my self have measur'd, and any person may easily find by his own body. And the oldest Feet, of which any account has been transmitted to us, are the Roman, the Ptolemaic, and the Drusian Foot at Tongeren in Germany, the last of which is equal to 13mathML formula Unciæ of the Roman Foot. And to these three Feet, according to the proportion of 5 to 9 answer the three Cubits, 1mathML formula of the English Foot, 1mathML formula of the English Foot, and 1mathML formula of the English Foot; and of about <420> these magnitudes are the antient Cubits determined by us above, viz. those of Memphis, Babylon, and Persia; to which add that of Samos, which Herodotus represents as equal to the Cubit of Memphis. The Greek and Roman Cubits, which were secondary measures, adapted to the measures of the Feet before received, ought not to come under consideration here.

The Cubits of the Eastern Nations, with which the Jews were surrounded, being determined in this manner, we may from hence form a conjecture concerning the magnitude of the Jewish Cubit. The vulgar Jewish Cubit ought not to be greater than them all, nor the sacred Cubit less than them all. The opinion of Villalpandus and others therefore is to be rejected, who represent the vulgar Cubit as equal to two Roman Feet and an half; and I think them likewise mistaken, who make the sacred Cubit and Attic Cubit equal. That the sacred Cubit was very large, appears from the Jewish Calamus or Reed, which contained but six of these Cubits; and from the antiquity of this Cubit, since Noah measured the Ark with it. However, it is not to be magnified in such a manner, that the vulgar Cubit (which in the time of Moses was called the Cubit of a man, Deut. iii.II.) <421> should much exceed the Cubit of a tall man. But we shall circumscribe these Cubits in narrower limits in the following manner.

We learn from the Talmudists and Josephus, that the Jews used the measure of four sacred Palms instead of the Greek Cubit. The Greek Cubit therefore approached nearer to 4 Jewish Palms than to 5 or 3; that is, it was less than 4mathML formula Palms, and greater than 3mathML formula. Hence it follows, that the sacred Cubit of 6 Palms was less than 2mathML formula Attic Feet, and greater than 2 Attic Feet.

The stature of the human body, according to the Talmudists (f)[6], contains about 3 Cubits from the feet to the head; and if the feet be raised, and the arms be lifted up, it will add one Cubit more, and contain 4 Cubits. Now the ordinary stature of men, when they are bare-foot, is greater than 5 Roman Feet, and less than 6 Roman Feet, and may be best fix'd at 5 Feet and an half. Take the third part of this, and the vulgar Cubit will be more than 20 Unciæ, and less than 24 Unciæ of the Roman Foot; and consequently the sacred Cubit will be more than 24 Unciæ, and less than 28mathML formula Unciæ of the same Foot.

Josephus writes, that the Pillars of the great court were as large as could be em <422> braced by three men with their arms join'd. The Orgyia or Fathom of a man is commonly supposed equal to the stature of the same man, but in reality exceeds it about one Palm of the Roman Foot. The common people use the nearest round numbers; in this case the true numbers are to be employed; add therefore a Palm to the measures of the stature of a man above express'd, and the sum being tripled, 15mathML formula Roman Feet will be greater, and 18mathML formula less than the circumference of the pillar.

Now that circumference, according to the Talmudists and Josephus, was, as above, 8 Cubits, at least in the inner court. Taking therefore about an eighth part of the preceding numbers, the sacred Cubit will be greater than two Roman Feet, and less than two and a third. We have taken here the pillars of both courts, that is, in thickness, tho' not in height. It is certain, that the pillars of the inner court were not thicker than those of the outer court; and therefore the latter computation must necessarily be admitted.

A Sabbath-day's journey, by the unanimous consent of the Talmudists and all the Jews, was two thousand Cubits. Hence the Chaldee interpreter upon Ruth i.6. says, "We are commanded to observe the Sabbath and good days, so as not to go above <423> two thousand Cubits." The Jews describing this journey, instead of Cubits, sometimes substitute Paces. Erasmus, in his notes upon Acts i.12. writes thus concerning the Sabbath-day's Journey: The Evangelist means the space of two thousand Paces. It was not lawful for the Jews to travel farther on the Sabbath-day. This is asserted by St. Jerome, writing to Algasia, in his tenth question, viz. that the Jews religiously observed not to walk on the Sabbath-day above two thousand Paces, agreeably to the appointment of Akiba, Simeon [the Just] and Hillel, Rabbins, whom they use to call our masters. Thus writes Erasmus, who reads passus in St. Jerome, and not pedes, as it is corruptly in the printed editions of that father. And hence in Numb. xxxv.4. instead of a thousand Cubits, the Latin interpreter substitutes a thousand Paces. But we must take care not to understand by them the Roman or Greek Paces; for in Sebbolch Lecheth, Tract. 22. cap. de Sabbat. those Paces are thus described: Samuel travell'd thro' the valley, and knew not the limit of the Sabbath. A Sabbath-day's journey is two thousand middling Paces. As if he had said, a Sabbath-day's journey is a journey of two thousand paces of a man travelling upon a sabbath, not with speed, as in the Roman Paces, nor too slowly, but <424> moderately, in the manner of those who travel on the sabbath-day. Now men of a middling stature, in walking in this manner, go every step more than two Roman Feet, and less than two and a third. And within these limits was the sacred Cubit circumscribed.

The Talmudists write, that the height of the steps, by which they ascended to the inner court, was half a Cubit, and their retractions half a Cubit. They mean the sacred Cubit; and we see that Josephus's computation, with regard to the height of these steps, corresponds with them. Now Vitruvius determines, that the height of steps ought not to be more than 10 Roman Unciæ, and the retractions not less than 18 Unciæ; when, since the Jews make the height equal to the retractions, we must suppose that they took a middle proportion, and that the height, as well as the retractions, made about 12, or at most 13 Roman Unciæ. The middle proportion between 10 and 18 is about 13mathML formula. And I should be inclined to maintain, that this height was not at all exceeded, lest it might have been difficult to ascend the steps. The sacred Cubit therefore was less than 27 Roman Unciæ, but not less than 24 Unciæ, in order that the retractions of the steps might not be too much lessen'd.

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The Cubit being thus circumscribed within certain limits, and the erroneous opinions of other writers being thus refuted, we may now assign the more exact measure of it with greater assurance; and this we shall do by the following argument.

It is agreeable to reason to suppose, that the Jews, when they passed out of Chaldea, carried with them into Syria the Cubit which they had received from their ancestors. This is confirmed both by the dimensions of Noah's ark preserv'd by tradition in this Cubit, and by the agreement of this Cubit with the two Cubits, which the Talmudists say were engrav'd on the sides of the city Susan during the empire of the Persians, and that one of them exceeded the sacred Cubit half a Digit, the other a whole Digit. Susan was a city of Babylon, and consequently these Cubits were Chaldaic. We may conceive one of them to be the Cubit of the royal city Susan, the other that of the city of Babylon. The sacred Cubit therefore agreed with the Cubits of divers provinces of Babylon as far as they agreed with each other; and the difference was so small, that all of them might be derived in different countries from the same primitive Cubit, the Jewish Cubit being less inlarged after sacred things began to be determined by it. This <426> therefore was the proper and principal Cubit of the Jews. But that people afterwards going down into Ægypt, and living for above two hundred years under the dominion of the Ægyptians, and enduring an hard service under them, especially in building, where the measures came daily under consideration; they must necessarily learn the Ægyptian cubit. Hence came the double Cubit of the Jews, viz. that of their own country, and the adventitious one, which, from its being used upon ordinary occasions only, was esteemed vulgar and profane. This hypothesis is confirmed by the proportion of the Cubits to each other. For the Babylonian Cubit of two English Feet is to the Cubit of Memphis of 1mathML formula of the English Foot, as 6 to 5mathML formula, that is, as the sacred Cubit to the vulgar Cubit very near. The small fraction of mathML formula might arise from either the difference of the Babylonian Cubits, or the greater antiquity of the Babylonian building, than of the pyramid, or the dimension of the brick, expressed not in the exact, but the nearest round numbers.

Suppose the thickness of the brick to be 6mathML formula English inches, the breadth 8mathML formula inches, and the length 12mathML formula inches; and a Cubit double that length will be to the Cubit of Memphis as 6 to 5. I am inclined therefore <427> to think, that the Cubit of Memphis, at the time when the Jews went down into Ægypt, was equal to 5 Palms of the Chaldæo-Hebraic Cubit; and that the Jews thus determining the magnitude of that Cubit by five Palms of the proper Cubit, the Palms of Memphis became at last neglected, and the double Cubit, with only a simple Palm, remained among the Jews. Besides, as it is reasonable to suppose, that the profane and adventitious Cubit agreed with the Cubits of the nations round about, viz. those of Memphis, Samos, and Persia; so it appears from the following argument, that this Cubit was the same with that of Memphis. The different measures of the Cubit of Memphis, taken from different parts of the Pyramid, were 1mathML formula, 1mathML formula, and 1mathML formula of the English Foot. To these measures in the proportion of the sacred Cubit to the vulgar Jewish Cubit are the measures 2mathML formula, 2mathML formula, and 2mathML formula of the English Foot, which in Unciæ of the Roman Foot are 25mathML formula, 25mathML formula, and 25mathML formula, and consequently fall in the middle of those limits, with which we have before circumscribed the sacred Cubit, and which were 24 and 27 Unciæ of the Roman Foot. Thus therefore, by means of these limits, those measures agree with the sacred Cubit, and consequently the measures of the Cubit of <428> Memphis agree with the vulgar Cubit. Supposing therefore that the Jews learned the Cubit of Memphis in Ægypt, and that it was their vulgar Cubit, and consequently that in the time of Moses, and soon after, when, as Mr. Greaves contend, the Pyramids were built, the vulgar Cubit was of the same magnitude with that of Memphis; the sacred Cubit in those times was not less than 25mathML formula, nor greater than 25mathML formula Unciæ of the Roman foot. Those, who shall hereafter examine the Pyramid, by measuring and comparing together with great accuracy more dimensions of the stones in it, will be able to determine with greater exactness the true measure of the Cubit of Memphis, and from thence likewise of the sacred Cubit. In the mean time for the precise determination of the Cubit of Memphis, I should choose to pitch upon the length of the chamber in the middle of the Pyramid, where the king's monument stood, being very large, and built with admirable skill; which length was the twentieth part of the length of the whole Pyramid, and contained 20 Cubits, and which was very carefully measured by Mr. Greaves, as he informs us himself. And from hence I would infer, that the sacred Cubit of Moses was equal to 25 Unciæ of the Roman Foot, and mathML formula of an Uncia; or, <429> what is equivalent that it had the same proportion to two Roman Feet as 16 to 15.

Mersennus in his treatise de Mensuris, Prop. I. Cor. 4. Writes thus: I find that the Cubit, (upon which a learned Jewish writer, which I received by the favour of the illustrious Hugenius, Knight of the order of St. Michael, supposes the dimensions of the temple were formed,) answers to 23mathML formula of our inches, so that it wants mathML formula of an inch of two of our Feet, and contains two Roman Feet, and two Digits and a Grain, which is mathML formula of a Digit. The Paris Foot, with which Mersennus compared this Cubit, is equal to 1mathML formula of the English Foot, according to Mr. Greaves; and consequently is to the Roman Foot as 1068 to 967. In the same proportion reciprocally are 23mathML formula and 25mathML formula. That Cubit therefore is equal to 25mathML formula Unciæ of the Roman Foot, and consequently falls within the middle of the limits 25mathML formula and 25mathML formula, with which we have just circumscribed the sacred Cubit; so that I suspect this Cubit was taken from some authentic model preserved in a secret manner from the knowledge of the Christians. Lest any person should be surprized, that the Cubit, which we have concluded to have been in the time of Moses 25mathML formula inches, should not have increased more in three thousand years; he may observe, that the Palms <430> used in building at Rome, which was antiently 9 Unciæ of the Roman Foot, is now equal to mathML formula parts of the English Foot, that is, 9mathML formula Unciæ, and consequently that in fifteen hundred years it has increased but mathML formula of an Uncia, though it was not preserved in a religious manner.

Some compute the Cubit from Solomon's brazen sea. Lest any objection should be raised from thence, I shall briefly remark, that the bottom of that sea ought not to be represented spherical, as it generally is, but flat, in such a manner that all the water might run out for the use of the priests, and the vessel might stand commodiously upon the backs of the oxen, and the oxen not hinder the priests from coming to the cocks. However I would not represent it under a cylindrical figure. The following one will be more beautiful. Let the line AB, of ten Cubits, be bisected in C; and taking upon it AD, EB, of a Cubit each, erect the perpendiculars DF, CG, EH, each of them of five Cubits, and with the semiaxes AD, DF, and BE, EH, describe the quadrants of the <431> ellipses AF, BH, and drawing the right line FH, the figure AFGHB convolved round the axis CG, will describe the external superficies of the vessel, whose cavity, if it be an hand-breadth thick, will contain about thousand baths, supposing that a bath was equal to twelve Roman Congii (as Agricola and others maintain) and that seven Congii and an half will fill a Cubic Roman Foot, as Mr. Greaves found by the Farnesian Congius. It is said likewise, that this sea contained three thousand baths; whence some affirm, that there were two kinds of baths. Others understand a dry measure, whose Cumulus equaled half the contents; others suspect a various reading; others imagine, that the sea contained two thousand baths for daily use, but, when full, could receive three thousand baths. I shall not attempt to determine the dispute.

This is what I thought proper to lay down at present with regard to the magnitude of this Cubit. Hereafter perhaps those, who shall view the sacred mount, and the monuments of the Chaldeans, by taking accurately the various dimensions of the stones, bricks, foundations, and walls, and comparing them together, will discover something more certain and exact.

<432>

The Roman Cubit therefore consists of 18 Unciæ, and the sacred Cubit of 25mathML formula Unciæ of the Roman Foot; and consequently those Cubits are to each other in round numbers as 2 to 3 very near. And this proportion is used by Josephus, out of regard to the greater expedition in computing the bulk of the buildings. For writing to the Romans (g)[7], he every where puts three Roman Cubits for about two sacred Cubits, except in some of the most eminent dimensions of the temple, properly so called, and set down in scripture, in which case he thought proper to retain the sacred Cubit. This will appear by comparing the Cubits of Josephus with the sacred Cubits of the Talmudists, in the following table.

Josephus's Cubits. Sacred Cubit. Talmud Cubits. Vulgar Cubits.
The height of the wall Chajil without 40 26mathML formula
within 25 16mathML formula
Difference answering to the 19 steps 15 10
Height of those 19 steps 15 10 9mathML formula
Height of the Septum cancellatum 3 2 2
Height of the gates 30 20 20
Breadth 15 10 10
Height of the altar 15 10 10
Breadth of the altar 50 33mathML formula 32
Height of the temple within 60 40 40
Circumference of the pillars 12 8 8
<433>

Thus likewise, where Josephus in a round number makes the Exhedras thirty Cubits, we must write twenty sacred Cubits, or more exactly twenty two; and the like reduction is necessary in all the other numbers of Josephus.

[1] (a) Vitruvius lib. 3. Hero in Isagoge. Hesychius. Suidas in vocibus ωλέθρον & ωους. Columella lib. 5. de Re Rusticâ, qui cubitum nominat semipedem, quasi pedis & semis. Vid. & Frontin. de Limit. Agrorum; & Isidor. Hispalensem, lib. 15. c. 15. Authors are agreed upon these Cubits, amongst whom Agricola and Mr. Greaves are especially to be consulted.

[2] (b) Abulfedæ Geograph. Arab. and Muhammed Ibn Mesoud, quoted by Mr. Greaves.

[3] (c) Pilgrimage, par. I. lib. I. c. II.

[4] (d) Vide Hygin. de Limitib. constituend. & Siculum Flaccum de Condit. Agrorum.

[5] (e) Hygin. de Limit. constit.

[6] (f) This proportion is expressly set down in Mishnaioth, Tract. de Ghaburim, cap. 4. ה in Comment.

[7] Josephus in Prologo Belli Judaici.

© 2013 The Newton Project

Professor Rob Iliffe
Director, AHRC Newton Papers Project

Scott Mandelbrote,
Fellow & Perne librarian, Peterhouse, Cambridge

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