Page:The New International Encyclopædia 1st ed. v. 14.djvu/795

* NUMBER. 677 NUMERATION. TiONAX Number; Negative Quantity; Complex Number; Quatekmons. NUMBERS (Lat. ,.V«»neri, Gk. ■ApiBiMl, Arilliiiiui. lleb. BC'iiiidbar, in the wilderness, the I'ouilh word of the book). Book or. The fourth liouk of the IVntateuch. It consists of thirty-six chapters, and receives its common name 'Xunibers' from the repeated references to the 'numbering' of the people which it con- tains. It is not a separate work, but conslitvites a division of the group of six books — Pentateuch and Josliua — now designated by scholars as the Hejralciicli (q.v. ). The sources in the book are precisely the same that are found in the other divisions of the Pentateuch, viz. (a) the his- torical compilation designated as JE (see Elohi.st and V.iiwi.st) ; (b) the Priestly narra- tive, including portions of the Priestly Code (see Leviticus; Hexateucii) ; together vith (e) the usual additions and etlitorial insertions of the group of writers who welded these constituent elements into a consistent whole. The book in its present form falls naturally into three main sec- tions: (a) i.-x. 10; (b) X. U-xix.; (c) xx.-xxxvi. The first section embraces: (1) the census of the people (i.-ii.) ; (2) series of ordinances for the Priests and Levites (iii.-iv. ), including general and specific duties, positions among the tribes, and census of Levites ; ( 3 ) various laws — leper, marital jealousy, nazirite (v.-vi.) ; (4) dedica- tion of altar (vii.); (5) miscellaneous ordi- nances with illustrative cases ( viii.-x.lO). The second section contains: (1) the wanderings (X. 11-28) ; (2) revolts against Moses by the peo- ]ile. Aaron, and Jliriam (xi.-xii.); (.3) spies sent to Canaan (.xiii.-xiv.) ; (4) various ordinances (XV.) ; (5) re!)ellion of Korah with story of Aaron's selection (xvi.-xvii. ) ; (6) ordinances for priests and people (xviii.-xix.) . The third section embraces: (1) continuation of narrative of traditional history in the wilderness (xx.- xxi.); (2) story of Balaam (xxii.-xxiv.) ; (3) story of cult of Baal-peor (xxv. ) ; (4) second census (xxvi.) ; (5) groups of ordinances with his- torical setting and illustrative cases (xxvii.- xxxvi. ) . The Book of Xunibers thus furnishes an admir- able illustration of the method pursued by the Hebrew compilers in combining various historical sources and in using the Priestly Code (from which all the legal portions of the book are taken) as historical material to illustrate and confirm the religious point of view of the later editors and the theory upon which they base their historical narrative, which carries the com- plete religious organization of Israel back to the days of Jloses. See Hexateuch. Bibliography. Besides the commentaries of Dill- mann. Strack. Bennett, and the forthcoming ones of Baentsch and Gray, and the introductions to the Old Testament by Driver. Cornill, Wildc- boer. Kuenen. and Kautzsch. consult Addis. Dncti- nirntx of the Hp.rniruch (London. ISOS): Car- penter and Batterslev, The Hexateuch (London, mnn). NUMB-FISH. A torpedo-ray. See Torpedo. NUMERALS (Lat. ni(meralis. relating to number, from nKinenix. number). A system of figures or symbols to represent numbers; more particularly the Hindu or Arabic system, which employs the characters 0, 1.2 n, of which all, or sometimes the last nine, are called 'digits.' Thus we speak of writing the numeral for 'five* meaning '5.' The word, however, is applied to other .systems, as in speaking ot the Roman nu- merals or the Greek numerals. Our common nu- merals come from old Sanskrit alphabetic forms. They appear in the tenth century in the form: being attributed to Boethius (q.v.), but are prob- ably due to some later writer. In substantially this form, they are found in the time of Gerbert (see Sylvester II.), written upon counters for use upon one kind of the abacus ( q.v. ), and bear- ing the name 'apices.' This form is essentially that of the Gobar or (lubar (dust) numerals, pos- sibly so called because they were written on the sanded board irsed in the Orient. These numerals appear among the Western Arabs of that period in the following form written from right to left: These numerals changed slowly from the time of their introduction into Europe, notably by Gerbeit and Leonardo of Pisa (see FiBO- N,cci), until they had assumed, at the close of the fifteenth century, a form approximately lilce those known to us. Printed arithmetics then began to appear, and they acted as an obstacle to further changes. These numerals, inherited from the Arabs, have commonly been designated as Arabic, although in their origin they might more properly be called Hindu. Since, however, they were not particularly usable until the introduc- tion of the zero made possible a place value, and since the zero was introduced, so far as we know, by Arab writers, the credit may well be given to the latter. The common numerals are well adapted to the decimal system, having exactly ten symbols. The Roman numerals, on the con- trary, while used with a decimal system of coimting. were not well adapted to it, and al- lowed for no simple place value. See Notation; Numeration. NUMERATION (Lat. tmmemtio, a counting, from inimcniir, to count, from numcrus. num- ber). The oral as opposed to the written expres- sion of numbers. Numeration implies the nam- ing of numerals (q.v.) and groups of numerals expressing numbers, the nomenclature thus em- ployed having much to do with the efficiency of the .system. Thus, if to every number there cor- responded an independent name, a lifetime would not 1)e sufficient in which to learn the numbers from one to a million. The common or decimal system proceeds by using independent names for a few of the smaller numbers and certain groups, and then repeats these names to express various numbers of groups. In this system the funda- mental group is ten. independent names are given to the nuniliers represented by 1. 2,. . . .0, 10, 100, 1000, 1,000,000, and all intervening numbers are expressed by combining these names. In the evo- lution of language the names of a few numbers have lost their suggestiveness. but they are prob- ably not exceptions to the regular .system of for- mation ; e.g. the etymologies of eleven and twelve suggest their original meaning to have been one phoi ten and tiro plu.i ten. In reading numbers it is convenient to sepa- rate the digits, beginning at the decimal point, into groups of three each. The groups of in- tegers are then expressed by units, thousands.