P. HISTORY OF ' AATHEMATICAL - School of Mathematics

OLD NUMERAL SYMBOLS 33
Cappellil "one finds, often in French documents of the Middle Ages,
the multipiication of 20 expressed by two small x's which are placed
as exponents to the numerals 111, VI, VIII, etc., as in IIIIxx=80,
VIxxXI = 131."
52. A Spanish writer2 quotes from a manuscript for the year 1392
the following:
M C
"1111, 1111, LXXIII florins" for 4,473 florins.
M XX
"111 C 1111 111 florins" for 3,183 (?) florins.
In a Dutch arithmetic, printed in 1771, one finds3
C
c m c
i ~giij for 123, i giij iiij Ioj for 123,456.
53. For 1,000 the Romans had not only the symbol M, but also I,
m and C13 According to Priscian, the celebrated Latin grammarian
of about 500. A.D., the m was the ancient Greek sign X for 1,000, but
modified by connecting the sides by curved lines so as to distinguish it
from the Roman X for 10. As late as 1593 the m is used by C. Dasypodius4
the designer of the famous clock in the cathedral at Strasbourg.
The C 13 was a I inclosed in parentheses (or apostrophos). When only
the right-hand parenthesis is written, 13, the value represented is
only half, i.e., 500. According to Priscian15 "quinque milia per I et
duas in dextera parte apostrophos, 133. decem milia per supra dictam
formam additis in sinistra parte contrariis duabus notis quam sunt
apostrophi, CCI 33." Accordingly, 133 stood for 5,000, CC133 for
10,000; also 1333 represented 50,000; and CCC1333, 100,000;
(a,), 1,000,000. If we may trust Priscian, the symbols that look like
the letters C, or those letters facing in the opposite direction, were
not really letters C, but were apostrophes or what- we have called
1 op. cil., p. fix.
2Liciniano Saez, Demostracidn Hisl6riea del verdadero valor de Todm Las
Monedas que cmian en Caslilla durante el repado del Seiior Don Enrique 111
(Madrid, 1796).
a De Vernieuwde Cyfleringe van Mf Willem Bartjens. Herstelt, . . . . door
Mr Jan van Dam, . . . . en van alle voorgaande Fauten gezuyvert door . . . .
Klaas Bosch (Amsterdam, 1771), p. 8.
4 Cunradi Dasypodii Institutionurn Mathematicarum voluminis primi Erotemala
(1593), p. 23.
5 "De figuris numerorum," Henrici Keilii Grammatici Lalini (Lipsiae, 1859),
Vol: 111, 2, p. 407.