NOTATION (Lat. notatio, designation, from notare, to mark, from nob', mark). In arith metic% a term applied to a system of designating numbers by figures, or notm, as they were often called in the Middle Ages. The chief number notations of the early races, before the perfecting of the position system, conform to one of three systems, the repeating, the alphabetic, and the initial-letter systems. although these are not mutually exelusive. By the repeating system is nie:Int the plan of repeating a chosen symbol, especially for 1, 10, 100—on the additive prin ciple, so as to represent other numbers twice, or three or more times as great. Thus. in the Egyptian system, the symbol stands for 10, and the eombination nnn stands for 30. By the alphabetic system is meant the plan of rep resenting numbers by letters in alphabetic order. And by the initial-letter system is meant the plan of representing numbers by the initial letters of the corresponding language forms. These ten deneies are exhibited in the following tables: The llebrew system was used by Hebrew writers as late as the twelfth century, in eonnec that with zero, after contaet with the Arabic system.
the Egyptians numbers were written running front right to in the hieratie writ ing, with varying direction in the hieroglyphics. In the latter the numbers were either written out in words or represented by symbols for eaelf unit, repeated as often as neeessary. In the hieratic symbols the figure for the unit of higher order stands to the right of the one of lower order. The Pluenivian system contained twenty two characters, derived front the symbols of the Egyptians.
The Babylonian cuneiform inscriptions proceed front left to right, which imist be looked upon as exceptional in a Semitic language. The units of higher order stand on the left of those of lower order. The symbols used in writing are chiefly a horizontal wedge, a vertical wedge, and a combination of the two at an angle. The symbols were written beside one another, or, for ease of reading and to save space, over one another. The symbols for 1, 4, 10, 100, 14, 400, respectively, are as follows: Y.V'Y • a, ?• 400 For numbers exceeding 100 there was also used, besides the mere juxtaposition, a multiplicative principle; 1110 symbol representing the number of hundreds was placed at the left of the symbol for hundreds, as in the of 400, already shown.
The Itabylonians probably had no symbol for zero.
The oldest Greek numerals (aside from the written words) were, in general, the initial let ters of the fundamental numbers, 1 for 1, II for 5 (rivre), A for 10 (S1 Ka) , and these were repeated as often as neeessary. These numerals are described by the Byzantine grammarian Herodianus (e.200 A.D.). and hence are spoken of as Herodianie numbers. Shortly after B.C. 500 new systems appeared. (Ole used the 24 letters of the _Ionic alphabet in their natural order for the numbers from 1 to 24. The other arranged these letters apparently at random, hut actually in an order fixed arbitrarily; thus, a = 1, # = o a =10, K 20, p = 100, 0- = 200, etc. For 6, 90, and 900 ex ception was made, and the symbols s 9 ') were used respectively. Here, too, there is no special symbol for the zero.
The Roman numerals were probably inherited from the Etruscans. The noteworthy peculiari ties are the lack of the zero; the subtractive principle whereby the value of a symbol was diminished by placing before it one of a lower order IX = 9, XL = 40, 1C=90), even in cases where the language itself did not signify a subtraction; and finally the multipli cative effect of a bar over the numerals (XXX = 30,000, 100,000). Also for certain fractions there were special symbols and names. According to Monimsen, the Roman number-sym bols I, N", X represent the finger, the hand, and the double hand. but they are more probably from old Etruscan letter forms. The use of the bar (vincu/unt or titit/us) was very uncertain. Thus in the tenth century we find it used over the I and X (as among later Romans) to in crease the value 1000-fold, but over the M it had no significance. The symbols, too, were carelessly used. Thus, .N1 meant 10. 1000' and C M meant 100. 1000. The subtractive prin ciple, although known to the later Romans, little used until very recently, as witness MI for IV, continued from the early clock faces to those of to-day.