NUMERALS. Just as the first attempts at writing came long after the development of speech, so the first efforts at the graphical representation of numbers came long after people had learned to count. Judging by the habits of primitive tribes of the present as well as by the oldest trace that we have of written or sculptured records, the earliest numerals were simple notches in a stick, scratches on a stone, marks on a piece of pottery, or the like. Having no fixed units of measure, no coins, no commerce beyond the rudest barter, no system of taxation, and no needs beyond those of a savage, there was no necessity for written numerals until about the beginning of what we call historical times.
Early Forms.—The earliest numerals of which we have definite record were simply straight marks for the small numbers, with some special form for ten. These symbols appear in Egypt as early as the ist dynasty (c. 3400 B.c.), and in Mesopotamia as early as c. 3000 B.C. These dates long precede the first known inscriptions containing numerals in India (c. 3rd century B.c.), in China (3rd century B.c.), and in Crete (c. 1200 B.C.).
The vertical marks, I, I I, I I I, etc., may possibly be representa tions of the fingers held as used in counting and computing, a linguistic trace of which is found in the word digit. The hori zontal marks may be representations of computing rods as they lie on a table. The vertical symbols were preferred in Meso potamia and the Mediterranean region, and the horizontal ones in the Far East, where —, rz, and = were commonly used for one, two, and three, = and 1-7. being cursively written to give us our present 2 and 3.
It therefore appears that the primitive numerals were I, II, I I I, 1111, and so on, as we find in Egypt and the Grecian lands, or —, F., and probably so on as we usually find in the East,
each going as far as the simple needs of people required. The idea of a group figure would naturally have occurred to mer chants as soon as there developed a need for numbers beyond 10 or 12 (as was the case in Egypt and Babylon). Once the idea was suggested, probably influenced by the ten fingers, symbols were invented for smaller units, as in the case of those used for four and five as stated above. These naturally suggested special symbols for each of the numbers from one to ten or even farther, and the use of the additive principle to build up larger numbers, as in the Roman XXII. The idea of special symbols for larger groups, as for 20, 3o, and so on, was a natural extension.
For our purposes some leading principles will suffice. The sym bol for I served also for 6o, 3,600, and in general for i X 6on; simi larly the symbol for io served for To X 6on, the context telling what particular value was indicated. The symbols could be made either with the pointed or the circular end of the stylus, as follows: There was also a symbol for ioo, but in general the scribe pre ferred to make use of the symbol for 6o, thus: y1—i00rflrey*---60+60+,0+,0+10+10+10+1+4=174, )) =60-1-6o+zo+1= i3c4.
Following the general custom of the race to use small numbers instead of large ones, the Babylonians employed a subtractive principle, as we do in saying "a quarter to three" instead of "three quarters past two," and "three minutes to six" instead of "57 minutes after five." This appears in such numerals as (ort 10 1-10-I= T9, and ©Gm =20-.3=17.