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n:numerals [2018/03/30 02:06] (current)
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 +<< [[contents:​index| Dictionary Index]] << [[contents:​n|Definitions under N]]
  
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 +====== Numerals ======
 +
 +The names of numerals are very different, not only in several parts of Asia, but in both North and South America. ​
 +
 +"Small stones were used amongst uncivilized nations: hence the words //​calculate//​ and //​calculation//​ appear to have been derived from //​calculus//,​ the Latin for a pebble-stone. Alphabetic letters had also a certain numerical value assigned them, and several Greek characters were employed to express particular numbers. ​
 +
 +"The combination of Greek numerical characters was not well known to the Latins before the thirteenth century, although Greek numerical characters were frequently used in France and Germany, in episcopal letters, and continued to the eleventh century. But of all the Greek ciphers the Episema {{:​n:​episema.png?​nolink|Episema}} was most in use with the Latins: it gradually assumed the form of //G// with a tail, for so it appears in a Latin inscription of the year //296//. It is found to have been used in the fifth century in Latin MSS. It was reckoned for //6//, and this value has been evinced by such a number of monumental proofs, that there is no room to give it any other. Some of the learned, with even Mabillon, have been mistaken in estimating it as //5//, but in a posthumous work he acknowledges his error.
 +
 +"Those authors were led into this error by the medals of the Emperor Justinian having the episema for //5//; but it is a certain fact that the coiners had been mistaken and confounded it with the tailed// U//, for the episema was still in use in the fourth century, and among the Latins was estimated as six, but under a form somewhat different. Whenever it appears in other monuments of the western nations of Europe of that very century, and the following, it is rarely used to express any number except //​5//​. ​
 +
 +"The Etruscans also used their letters for indicating numbers by writing them from right to left, and the ancient Danes copied the example in the application of their letters. ​
 +
 +"The Romans, when they borrowed arts and sciences from the Greeks, learned also their method of using alphabetical numeration. This custom however was not very ancient among them. Before writing was yet current with them they made use of nails for reckoning years, and the method of driving those nails became in process of time a ceremony of their religion. The first eight Roman numerals were composed of the **I** and the **V**. The Roman ten was composed of the V proper, and the V inverted (^), which characters served to reckon as far as forty, but when writing became more general, **I**, **V**, **X**, **L**, **C**, **D**, and **M**, were the only characters appropriated to the indication of numbers. The above seven letters, in their most extensive combination,​ produce six hundred and sixty-six thousand ranged thus, **DCLXVIM**. Some however pretend that the Romans were strangers to any higher number than 100,000. The want of ciphers obliged them to double, treble, and multiply their numerical characters four-fold; according as they had occasion to make them express units, tens, hundreds, &c. &c. For the sake of brevity they had recourse to another expedient; by drawing a small line over any of their numeral characters they made them stand for as many thousands as they contained units. Thus a small line over <wrap numborder>​**I**</​wrap>​ made it 1000, and over <wrap numborder>​**X**</​wrap>​ expressed 10,000, &​c. ​
 +
 +"When the Romans wrote several units following, the first and last were longer than the rest **I<wrap smallcaps>​iiii</​wrap>​I**:​ thus //vir// after those six units, signified //​sex-vir//​. **D** stood for 500, and the perpendicular line of this letter was sometimes separated from the body thus (**IƆ**,) without lessening its value. **M**, whether capital or uncial, expressed 1000. In the uncial form it sometimes assumed that of one of those figures, **CIƆ**, **CD**, <wrap fontsize-15em>​∞</​wrap>,​ {{:​n:​thousand.png?​nolink|thousand}} The cumbent **X** was also used to signify a similar number. ​
 +
 +"As often as a figure of less value appears before a higher number, it denotes that so much must be deducted from the greater number: thus, **I** before **V** makes but four, **I** before **X** gives only nine, **X** preceding **C** produces only //90//, and even two **XX** before **C** reckons for no more than //80//. Such was the general practice with the ancient Romans with respect to their numerical letters, which is still continued in recording accounts in our Exchequer. ​
 +
 +"In ancient MSS. 4 is written **IIII** and not **IV**, //9// thus **VIIII**, and not **IX**, &c. Instead of **V** five units **IIIII** were sometimes used in the eighth century. Half was expressed by an **S** at the end of the figures, **CIIS** was put //102// and a half. This **S** sometimes appeared in the form of our //​5//​. ​
 +
 +"In some old MSS. those numerical figures **LXL** are used to express //90//. The Roman numeral letters were generally used both in England, France, Italy, and Germany, from the earliest times to the middle of the fifteenth century. ​
 +
 +"The ancient people of Spain made use of the same Roman ciphers as we do. The **X** with the top of the right hand stroke in form of a semi-circle reckoned for 40; it merits the more particular notice as it has misled many of the learned. The Roman ciphers however were continued in use with the Spaniards until the fifteenth century. The Germans used the Roman ciphers for a long time, nearly in the same manner as the French." ​
 +
 +"The points after the Roman ciphers were exceedingly various, and never rightly fixed. It is not known when the ancient custom was first introduced of placing an O at top immediately after the Roman characters, as **A° M° L° VI°** &​c"​ — //​Astle//​. ​
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 +^  Numeral Letters ​ ^^^ 
 +|     ​| ​ Roman   ​| ​ Arabic ​  |
 +|  Unus, a, um   ​| ​  ​I ​ |   ​1 ​ |
 +|  Duo, ae, o   ​| ​ II   ​| ​ 2   |
 +|  Tres, ia   ​| ​ III   ​| ​  ​3 ​ |
 +|  Quatuor ​  ​| ​ IV   ​| ​  ​4 ​ |
 +|  Quinque ​  ​| ​ V   ​| ​  ​5 ​ |
 +|  Sex   ​| ​ VI   ​| ​ 6   |
 +|  Septem ​  ​| ​ VII   ​| ​ 7   |
 +|  Octo   ​| ​ VIII   ​| ​  ​8 ​ |
 +|  Novem   ​| ​ IX   ​| ​ 9   |
 +|  Decerm ​  ​| ​ X   ​| ​  ​10 ​ |
 +|  Undecim ​  ​| ​  ​XI ​ |  11   |
 +|  Duodecim ​  ​| ​ XII   ​| ​ 12   |
 +|  Tredecim ​  ​| ​  ​XIII ​ |  13   |
 +|  Quatuordecim ​  ​| ​ XIV   ​| ​ 14   |
 +|  Quindecim ​  ​| ​ XV   ​| ​ 15   |
 +|  Se- sex- decim   ​| ​ XVI   ​| ​  ​16 ​ |
 +|  Septemdecim ​  ​| ​ XVII   ​| ​ 17   |
 +|  Octodecim ​  ​| ​ XVIII   ​| ​ 18   |
 +|  Novemdecim, \\ Undeviginti ​  ​| ​ XIX   ​| ​ 19   |
 +|  Viginti ​  ​| ​  ​XX ​ |  20   |
 +|  Triginta ​  ​| ​  ​XXX ​ |   ​30 ​ |
 +|  Quadraginta ​  ​| ​ XL   ​| ​ 40   |
 +|  Quinquaginta ​  ​| ​ L   ​| ​ 50   |
 +|  Sexaginta ​  ​| ​ LX   ​| ​ 60   |
 +|  Septuaginta ​  ​| ​ LXX   ​| ​ 70   |
 +|  Octoginta ​  ​| ​ LXXX   ​| ​ 80   |
 +|  Nonaginta ​  ​| ​ XC   ​| ​ 90   |
 +|  Centum ​  ​| ​  ​C ​ |  100   |
 +|  Ducenti, ae, a   ​| ​  ​CC ​ |  200   |
 +|  Trecenti, ae, a   ​| ​ CCC   ​| ​ 300   |
 +|  Quadringenti,​ ae, a   ​| ​ CCCC   ​| ​ 400   |
 +|  Quingenti, ae, a   ​| ​ IƆ, or D   ​| ​ 500   |
 +|  Sexcenti, ae, a   ​| ​ DC   ​| ​ 600   |
 +|  Septingenti,​ ae, a   ​| ​ DCC   ​| ​ 700   |
 +|  Octingenti, ae, a   ​| ​ DCCC   ​| ​ 800   |
 +|  Nongenti, ae, a   ​| ​ DCCCC or CM   ​| ​ 900   |
 +|  Mille   ​| ​ M   ​| ​ 1,000   |
 +|  Duo millia, \\ Bis mille   ​| ​ MM   ​| ​ 2,000   |
 +|  Tria millia, \\ Ter mille   ​| ​ MMM   ​| ​ 3,000   |
 +|  Quatuor millia, \\ Quater mille   ​| ​ MMMM   ​| ​ 4,000   |
 +|  Quinque millia, \\ Quinquies mille   ​| ​ IƆƆ, or <wrap numborder>​V</​wrap> ​  ​| ​ 5,000   |
 +|  Decem millia, \\ Decies mille   ​| ​ CCIƆƆ, or  <wrap numborder>​X</​wrap> ​ | 10,​000 ​  |
 +|  Quinquaginta millia, \\ Quinquagies mille   ​| ​ IƆƆƆ, or <wrap numborder>​L</​wrap> ​ |  50,​000 ​  |
 +|  Centum millia, \\ Centies mille   ​| ​ CCCIƆƆƆ, or <wrap numborder>​C</​wrap> ​  ​| ​  ​100,​000 ​ |
 +|  Quingenta millia, \\ Quingenties mille   ​| ​ IƆƆƆƆ, or <wrap numborder>​D</​wrap> ​ | 500,​000 ​  |
 +|  Decies centena millia ​  ​| ​ CCCCIƆƆƆƆ,​ or <wrap numborder>​M</​wrap> ​  ​| ​ 1,​000,​000 ​  |
 +
 +
 +If the lesser number is placed before the greater, the lesser is to be deducted from the greater; thus **IV** signifies one less than five, i. e. four; **IX**, nine; **XC**, ninety. ​
 +
 +If the lesser number be placed after the greater, the lesser is to be added to the greater; thus **VI** signifies one more than five, i. e. six; **XI**, eleven; **CX**, one hundred and ten. 
 +
 +An horizontal stroke over a numeral denotes a thousand: thus <wrap numborder>​**V**</​wrap>​ signifies five thousand; <wrap numborder>​**L**</​wrap>,​ fifty thousand: <wrap numborder>​**M**</​wrap>,​ a thousand times a thousand, or a million. ​
 +
 +**I**, signifies one, because it is the smallest letter. ​
 +
 +**V**.five, because it is sometimes used for U, the fifth vowel. ​
 +
 +**X**, ten, because it represents two Vs. 
 +
 +**L**, fifty, from its resemblance to the lower half of **C**. ​
 +
 +**C**, a hundred, centum. ​
 +
 +**IƆ** or **D**, five hundred, the half of **CIƆ**. ​
 +
 +**M** or **CIƆ**, a thousand, from mille. The latter figures joined at the top {{:​n:​thousand.png?​nolink|thousand}},​ formed the ancient M. — Latin Vocabulary, 18mo. Lond. Valpy, 1823. 
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 +[<6>]