NUMERALS 



NUMISMATICS 



549 



phi, ehi, and theta as phonetic signs, retained them 

 as numerals, with arbitrary values. In this case the 

 C would be originally 0, assimilated to C, because 

 C was the initial of centum. The old 0, used for 

 1000, came to be written CIO, afterwards con- 

 founded with fl or M . the initial of mi/le. The 

 L would be a derivative from an old Chalcidian 

 form of chi, inscribed for lapidary purposes JL, and 

 then simplified. Those who do not accept the 

 theory of the dropped Greek letters suppose that 

 M is from a circle with a vertical stroke, the C a 

 circle with a horizontal stroke or a cross, . The 

 X, V, and L might all come from this letter. In 

 any case, X is twice V ( whether or not the latter 

 originated in the hand held with the thumb to one 

 side and the other fingers together); and D (for 

 500) or 10 is half CIO. See the articles in this 

 work on the letters C, D, L, and M. 



It is doubtful how far the Abacus (q.v.) has to 

 do with the development of the system of numerals, 

 in which the value of the cipher depends on its 

 position. There were abacus boards so arranged 

 that the first column meant units, the second tens, 

 the third hundreds, the fourth thousands ; or, 

 conversely, a method of writing numbers derived 

 from this was actually used in 

 Europe in the middle ages ; we 

 show the columnar arrangement 

 simplifving the reading in the 

 several' cases, 654, 030, 604, 54. 



In the decimal scheme of 

 figures as now used by us, the 

 nine numerals with the zero, which enables the 

 value of the position to be secured without abacus 

 or columnar arrangement, are known as the Arabic 

 numerals, but are unquestionably of Indian origin. 

 From India they were apparently brought to Bag- 

 dad after the middle of the 8th century, and their 

 value and use was set forth early next century by 

 the Arab mathematician Abu ja'far Mohammed 

 Ben Mu^i, or Al-Kharizmi ('native of Khwarizm' 

 Khiva); whence the system came to be known 

 in Europe, where it became familiar in the 12th 

 century as Algorism (erroneously Algorithm). 

 The earliest European forms of these characters are 

 found in MSS. of the 12th century ; by the 14th 

 they were practically of the same shape as now. 

 The 12th century numerals are evidently forms of 

 the Gobar or western Arabic numerals used in 



* K S? < 

 9 



ft 



a, Indian, 10th century ; 6, Gobar, 10th century ; 

 c, European, 12th century. 



Persia in the 10th century. These can be traced 

 to the contemporary Indian Devanagari numerals, 

 which again are as certainly based on an old series 

 of characters used in cave-inscriptions in the 1st 

 and 2d centuries. These Canon Taylor contends 

 are (mainly, at least) degraded forms of the Indo- 

 liactrian alphabet. See ALPHABET, Vol. I. p. 188. 

 The modern arithmetic was not practised in Eng- 

 land till about the middle of tne 16th century, 

 and for a long time after its introduction was 

 taught only in the universities. 



The decimal system, possessing only nine sym- 

 bolsviz, 1, 2, 3, 4, 5, 6, 7, 8, 9 (called the nine 

 digits) adopts the principle of giving to each 

 HVIII Uil or ' figure ' two values, one the absolute 

 value, and the other a value depending upon its 



position, a figure moved one place to the left being 

 held to be increased in value ten times. When 

 such a number as 6473 is analysed, it is seen to 

 mean (6 times 1000) + (4 x 100) + (7 x 10) + (3 x 

 1); and 6004 becomes (6 x 1000) + (4xl). In 

 this latter instance the peculiar importance of the 

 figure is seen (see DECIMAL SYSTEM). 



It should be mentioned that European nations 

 do not all read the numerals in the same way, as 

 regards larger numbers. Let us take the figures 

 56,084,763,204,504 ; these, read after the fashion of 

 the French and other continental arithmeticians, 

 are liftv-six trillions, eighty-four billions, seven- 

 hundred-and-sixty-three millions, two-hundred-and- 

 four thousands, five-hundred-and-four units ; and 

 so also in America. In Britain, instead of billions, 

 we have, according to the current usage, thousands 

 of millions ; after this, tens of thousands of millions 

 and hundreds of thousands of millions, and then 

 billions, which are the same as the French trillions. 

 The above number, according to the British mode, 

 would be read fifty-six billions, eiglity-fonr-thou- 

 sand-seven-hundred-and-sixty-three millions, two- 

 hundred-and-four thousands, five-hundred-and-four 

 units. The British trillion has nineteen figures, the 

 continental has thirteen. 



As to the Indian origin of oar numerals, see Canon 

 Taylor, The Alphabet (1883; vol. ii. p. 263-268); 

 Woepke, Memoire $ur la Propagation de> Chiffrtt Indient 

 (1863); Huniell, South Indian Palatograpky (1874); 

 Treutlein, Oftchichte untrer ZaMzeichen (1875). 



Vlllllidia (Gr. Nomadia, 'land of Nomads'), 

 the name given by the Romans to a part of the 

 north coast of Africa, corresponding to some extent 

 with the modern Algiers, anil lying between 

 Mauritania and the Roman province of Africa ; on 

 the south it reached to the chains of Mount Atlas. 

 The inhabitants of Numidia, as of Mauritania, 

 belonged to the race from which the modern 

 Berbers are descended. They were a warlike race, 

 and excelled as horsemen, out were proverbially 

 faithless and unscrupulous. Of their tribes the 

 Mttssyli in the east and the Alasscesyli in the 

 west were the most powerful. In the grand 

 strnggle between Hie Carthaginians and the 

 Romans they at first fought on the side of the 

 former, but subsequently the king of the Eastern 

 Numidians, Massinissa, joined the Romans, and 

 rendered them effectual service in the war with 

 Hannibal. Favoured by the conquerors, he united 

 all Numidia under his sway. Of his successors in 

 this kingdom Jugurtha and Juba are the most 

 famous. After the victory of Csesar over Juba I. 

 in the African war Numidia became a Roman 

 province (46 B.C.) ; but Augustus afterwards gave 

 the western part, with Mauritania, to Juba II., 

 and the name Numidia became limited to the 

 eastern part. Among important places were Hippo 

 Regius, Zama, and Cirta (the residence of the 

 Numidian kings), afterwards called Constantina, a 

 name still preserved in Constantine. For the 

 modern history of Numidia, see ALGIERS. 



Numismatics ( Gr. nomiana, from nomos, 'law,' 

 'a legally current coin') is the science which 

 embraces the study of the current coins of all 

 nations. In the wider, though less accurate, accepta- 

 tion of the term it includes also that of medals, 

 both artistic and historical. The various branches 

 of numismatics are (1) Greek, Phoenician, &c. ; 

 (2) Roman and Byzantine; (3) Mediaeval and 

 Modern; and (4) Oriental. The chief value of 

 numismatics consists in the light which coins 

 throw upon history. The secondary importance 

 of the science is purely artistic. The study of 

 coins is also of great use in elucidating the mytho- 

 logy of the ancients, in fixing the chronology 

 of the different systems of alphabetical writing 



