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106, note †. for Leirinde alle Reckeningen read
leerende alle rekeninghen.
111, line 11, for testime read testerne..
137, note ‡, for Spix and Martin read Spix and
THE DECIMAL SYSTEM,
NUMBERS, COINS, AND ACCOUNTS.
ANCIENT HISTORY OF ARITHMETICAL NUMERALS.
EVERY human being-man, woman, and child—has been provided with a set of decimal machines, in the shape of fingers and toes, which, even from early childhood, and among the rudest nations, have been used for the purposes of account. Ovid speaks of the fingers with which we are accustomed to enumerate *—the word digits, in its Latin signification, meaning equally fingers and arithmetical figures. So, in German, Zehen is used alike for tens and toes. John Quincy Adams says, "The division of numbers by decimal arithmetic is distinctly proved to have been established before the general deluge," which proof may, indeed, be deduced from the fact that as ten fingers were given to man, they would naturally be employed for intellectual as well as physical purposes, to calculate with, and to perform the common handicraft functions of existence. Certain it is, that the years of the antediluvian patriarchs are spoken of, in the Book of Genesis, in hundreds, and tens, and units; and that three tens, and five tens, and three hundreds of cubits are reported as the height, and the breadth, and the length of the ark. So four times ten days, and four times ten nights, are stated as the time during which the rain fell upon the earth, where it rested a hundred and half a hundred days. The first time that the word "thousand" occurs in the Bible is where Abimelech tells Sarah he has given her brother a thousand pieces of silver(Gen. xx. 16). The word "thousands" first is found where
* See p. 48.
millions are also mentioned, and benedictions are brought to Rebekah (Gen. xxiv. 60) as the mother of future "thousands of millions;" and it is somewhat remarkable that this is the only instance where the word "million" occurs from one end of the Bible to the other. The greatest numbers mentioned anterior to the flood are the years of Methuselah, which amounted to nine hundred (i. e. hundreds) and sixty (i. e. six tens) and nine years.
It is curious to trace the various exhibitions of the decimal notation through all the tongues and tribes of the world. In all early histories, the Bible not excepted, men are grouped together in tens, and hundreds, and thousands, and tens of thousands. The common title given to the Emperor of China, in the temples of that empire,
Wan Sui, wan sui, wan wan sui-ten thousand, ten thousand, ten thousand times ten thousand years; which, indeed, implies immortality. Viva usted mil años-" May you live a thousand years"—is the ordinary phrase in Spain for wishing longevity to a friend. So in Chinese, for a man of unchangeable purpose, they say, "One mind ten thousand years;" and to teach prudence in conversation, they have a proverb, "A whispered word may be heard a thousand miles away." We, to express a strong conviction, say "Ten to one," "A hundred to one," "A thousand to one."One of the commonest forms of asseveration in Chinese is, Wan yih, which means, "Ten thousand to one it is so and so." Again, instead of saying, "Wine assists the settlement of disputes," the Chinese proverb runs, One cup thousand affairs."
will arrange ten
The opposite Table, exhibiting the comparative number of times in which arithmetical figures occur in the Bible, has been calculated from the passages referred to in Cruden's concordance.*
In the Book of I. Genesis (xviii. 24-32), Abraham implores the Lord to spare the city of Sodom if there be fifty righteous found within the city he lowers the number by five to forty-five, and then to forty, and then to thirty, and then to twenty, and then to ten, and proceeds no farther in his intercessions.
The groupings in scores (i.e., two tens) is a common mode of representing numbers, and the phrase "forty less one” is found an apter and more popular way of speaking than simply to use "thirtynine." Threescore, threescore and ten, and fourscore, are commonly employed for sixty, seventy, and eighty. In various parts of the
* London 4to edition, 1828.
Bible decimal progression is employed. In the Book of Genesis, in Jethro's counsel to Moses, he is recommended to nominate “rulers of thousands, and rulers of hundreds, rulers of fifties, and rulers of tens" (Exodus xviii. 21); and in the assembly of the people spoken of in the Book of Judges (xx. 10), they decided to take "ten men of a hundred throughout all the tribes of Israel, and a hundred of a thousand, and a thousand of ten thousand, to fetch victuals for the people." So in Amos, Jehovah decrees, “The city that went out by a thousand shall have a hundred, and that which went forth by a hundred shall have ten." In Leviticus (xxvi. 6) it is foretold to the Hebrews that "Five shall chase a hundred, and a hundred put ten thousand to flight." "A thousand shall fall at thy side, and ten thousand at thy right hand." (Psalm xci. 7.) Again in the Apocrypha, "There is no inquisition in the years, whether thou have lived ten, or an hundred, or a thousand years." (Ecclesiasticus xli. 4.) "Judas ordained captains over the people, even captains over thousands, and over hundreds, and over fifties, and over tens." (1 Maccabees iii. 55.)
Fix on what portion we may of ancient history, we shall find the decimal notation prevailing. When Herodotus (Book II.) gives an account of the building of the pyramids, he says, they were the work of bodies of 100,000 men, who were occupied 10 years in making the road over which the stones were dragged for erecting the pyramids, and that 20 years were employed in the construction; that each stone was 30 feet in length; that the cost of radishes, onions, and garlic, for the consumption of the workmen, was 160,000 silver talents; and that the pyramids stood on a hill, which is 100 feet high. Herodotus reports that the Egyptians accurately number the years, and states that between Hercules and Amases 17,000 years elapsed, and between Pan and Abasis 15,000 years; but, as he comes nearer to his own time, he uses the word "about," and says he lived about 800 years after the siege of Troy. (Book II.)
The employment of numerals representing large amounts is an evidence of considerable intellectual development, and may be accepted as an undoubted proof that the civilisation of the earliest periods recorded in the Bible was greatly superior to that of the more barbarous tribes who now occupy large portions of the earth's surface. The associations of vast numbers with the sands of the sea, or the stars of heaven, which are found in the earliest biblical records, would be alike discovered in the traditions and in the