Page:A History Of Mathematical Notations Vol I (1928).djvu/51

Rh the initial of centum; and ↀ assimilated to ordinary letters CIↃ. The half of ↀ, viz., D, was taken to be ½ 1,000, i.e., 500; X probably from the ancient form of ϴ, viz., ⊗, being adopted for 10, the half of it V was taken for 5.”

47. Our lack of positive information on the origin and early history of the Roman numerals is not due to a failure to advance working hypotheses. In fact, the imagination of historians has been unusually active in this field. The dominating feature in the Roman notation is the principle of addition, as seen in II, XII, CC, MDC, etc.

48. Conspicuous also is the frequent use of the principle of subtraction. If a letter is placed before another of greater value, its value is to be subtracted from that of the greater. One sees this in IV, IX, XL. Occasionally one encounters this principle in the Babylonian notations. Remarks on the use of it are made by Adriano Cappelli in the following passage:

“The well-known rule that a smaller number, placed to the left of a larger, shall be subtracted from the latter, as ↀIↃↃ=4,000, etc., was seldom applied by the old Romans and during the entire Middle Ages one finds only a few instances of it. The cases that I have found belong to the middle of the fifteenth century and are all cases of IX, never of IV, and occurring more especially in French and Piedmontese documents. Walther, in his Lexicon diplomaticum, Gettingen, 1745–47, finds the notation LXL=90 in use in the eighth century. On the other hand one finds, conversely, the numbers IIIX, VIX with the meaning of 13 and 10, in order to conserve, as Lupi remarks, the Latin terms tertio decimo and sexto decimo.” L. C. Karpinski points out that the subtractive principle is found on some early tombstones and on a signboard of 130 B.C., where at the crowded end of a line 83 is written XXCIII, instead of LXXXIII.