A similar custom is seen in Hebrew number names, in the occasional use of IV. for four and IX. for nine in the Roman inscriptions. The Romans also used units de viginti for 19, and duo de viginti for i8, occasionally writing these numbers as XIX. (or IXX.) and IIXX., respec tively. On the whole, however, the subtractive principle was lit tle used in the numerals of the classical period.
Egyptian Hieroglyphics.— The Egyptian numerals in hiero glyphic writing differed somewhat from those in the hieratic and demotic, but the last two were degenerate forms of the first, with certain additions. It will suffice to call attention to the principles of the first and second. In doing so, however, it should be observed that the Egyptians generally wrote from right to left, as in the Semitic script, but the hieroglyphics were occasion ally written from left to right or (as also the Hieratic) from top to bottom. The numerals from i to io were as follows: It will therefore be seen that the general plan of the hiero glyphic notation was to have special symbols for powers of io, and to repeat these as necessary. The Hieratic had special symbols for 5, 7, 8, and 9—a step towards the later Hindu sys tem. The Hieroglyphic was similar in principle to the Etrusco Roman, except that the latter introduced special numerals for 5, 5o, and Soo.
Greek Numerals.—The Greeks had two important systems of numerals, besides the primitive plan of repeating single strokes, as in III III for six. Their prede cessors in culture—the Babylo nians, Egyptians, and Phoenicians —had generally repeated the units up to nine, with a special symbol for ten, and so on. The early Greeks also repeated the units to nine, and probably had various symbols for ten. In Crete, whose early civilization was so much influenced by that of Phoenicia and Egypt, the symbol for ten was —, a circle was used for ioo, and a rhombus for i,000.
Cyprus also used the horizontal bar for ten, but the precise forms are not of so much significance as that the grouping by tens, with special symbols for certain powers of ten, was characteristic of the early systems of the Near East.
The Greeks, entering the field much later, and influenced as to their alphabet by the Phoenicians, based their first elaborate system chiefly on the initial letters of the numeral names. This
was a natural thing for all early civilizations, since the custom of writing out the names for large numbers was at first quite general, and the use of an initial by way of abbreviation of a word is universal. These initial numerals, in modern characters, were H, pi, for IIENTE (pence), five; A, delta, for AEKA (deka), ten; often written like 0; H, an old Attic breathing, like our h, later represented by a special symbol like `, for HEKATON (hekaton), hundred; X, chi, for XIAIOI (chil'ioi), thousand; M, mu, for MTPIOI (myr' ioi, nur'ioi), ten thousand.
This system appears in records of the 3rd century B.C. but was probably used much earlier. In the 2nd century of our era it was described by the grammarian Herodianus, and hence characters are often spoken of as Herodianic numerals. They are more properly called Attic numerals, being the ones always found in the Attic inscriptions.
As early as the 3rd century B.C. another system came into use, running parallel to the initial-letter one, being better adapted to the theory of numbers, and being more difficult of compre hension by the trading class. It consisted in assigning nine letters of the alphabet to the numbers 1-9, nine letters to the numbers 1o, 20, 3o, , go, and nine letters to the numbers ioo, 200, 300, • • • 900. Since, however, there were only 24 letters in the Greek alphabet, three were added, namely the Phoenician vau (shaped like our letter F), koph or qoph (shaped somewhat like our letter Q, which indeed is derived from the same source, and represented below as Q), and a character known in modern times as sampi (and then shaped somewhat like the Greek 7r, but tipped about to the right and represented below as &). An earlier form of this last symbol was i. The numerical values of the letters were therefore as follows: Such numeral forms were not particularly difficult for com puting purposes, once the operator was able automatically to recall the meaning of each. To be able to express 10,407 by MTZ would have seemed to a Greek considerably simpler than by our system. The capital letters were used by the Greeks, the small letters being a relatively modern invention.