Page:A History Of Mathematical Notations Vol I (1928).djvu/53

Cappelli^[1] “one finds, often in French documents of the Middle Ages, the multiplication of 20 expressed by two small x’s which are placed as exponents to the numerals III, VI, VIII, etc., as in IIIIˣˣ=80, VIˣˣXI=131.”

52. A Spanish writer^[2] quotes from a manuscript for the year 1392 the following:

“M
IIII, C
IIII, LXXIII florins” for 4,473 florins.

“III C IIII III florins" for 3,183 (?) florins.

In a Dutch arithmetic, printed in 1771, one finds^[3]

c
𝔦 𝔵𝔵𝔦𝔦𝔧 for 123, c
𝔦 m
𝔵𝔵𝔦𝔦𝔧 c
𝔦𝔦𝔦𝔧 𝔩𝔳𝔧 for 123,456.

53. For 1,000 the Romans had not only the symbol M, but also I, ∞ and CIↃ. According to Priscian, the celebrated Latin grammarian of about 500 A.D., the ∞ was the ancient Greek sign Χ 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 ∞ is used by C. Dasypodius^[4] the designer of the famous clock in the cathedral at Strasbourg. The CIↃ was a I inclosed in parentheses (or apostrophos). When only the right-hand parenthesis is written, IↃ, the value represented is only half, i.e., 500. According to Priscian,^[5] “quinque milia per I et duas in dextera parte apostrophos, IↃↃ. decem milia per supra dictam formam additis in sinistra parte contrariis duabus notis quam sunt apostrophi, CCIↃↃ.” Accordingly, IↃↃ stood for 5,000, CCIↃↃ for 10,000; also IↃↃↃ represented 50,000; and CCCIↃↃↃ, 100,000; (∞), 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. cit., p. xlix.
2. Liciniano Saez, Demostración Histórica del verdadero valor de Todas Las Monedas que corrían en Castilla durante el reynado del Señor Don Enrique III (Madrid, 1796).
3. De Vernieuwde Cyfferinge van M^r. Willem Bartjens. Herstelt, . . . . door M^r Jan van Dam, . . . . en van alle voorgaande Fauten gezuyyert door . . . . Klaas Bosch (Amsterdam, 1771), p. 8.
4. Cunradi Dasypodii Institutionum Mathematicarum voluminis primi Erotemata (1593), p. 23.
5. “De figuris numerorum,” Henrici Keilii Grammatici Latini (Lipsiae, 1859), Vol. III, 2, p. 407.