II
NUMERAL SYMBOLS AND COMBINATIONS OF SYMBOLS
BABYLONIANS
1. In the Babylonian notation of numbers a vertical wedge 𒁹 stood for 1, while the characters 𒌋 and 𒈨 signified 10 and 100, respectively. Grotefend[1] believes the character for 10 originally to have been the picture of two hands, as held in prayer, the palms being pressed together, the fingers close to each other, but the thumbs thrust out. Ordinarily, two principles were employed in the Babylonial notation—the additive and multiplicative. We shall see that limited use was made of a third principle, that of subtraction.
2. Numbers below 200 were expressed ordinarily by symbols whose respective values were to be added. Thus, 𒈨𒎙𒐈 stands for 123. The principle of multiplication reveals itself in 𒌋𒈨 where the smaller symbol 10, placed before the 100, is to be multiplied by 100, so that this symbolism designates 1,000.
3. These cuneiform symbols were probably invented by the early Sumerians. Their inscriptions disclose the use of a decimal scale of numbers and also of a sexagesimal scale.[2]
Early Sumerian clay tablets contain also numerals expressed by circles and curved signs, made with the blunt circular end of a stylus, the ordinary wedge-shaped characters being made with the pointed end. A circle ● stood for 10, a semicircular or lunar sign stood for 1. Thus, a "round-up" of cattle shows ● ●
● ᗞᗞᗞ
ᗞᗞᗞ, or 36, cows.[3]
4. The sexagesimal scale was first discovered on a tablet by E. Hincks[4] in 1854. It records the magnitude of the illuminated portion
- ↑ His first papers appeared in Göttingische Gelehrte Anzeigen (1802), Stück 149 und 178; ibid. (1803), Stück 60 und 17.
- ↑ In the division of the year and of the day, the Babylonians used also the duodecimal plan.
- ↑ G. A. Barton, Haverford Library Collection of Tablets, Part I (Philadelphia, 1905), Plate 3, HCL 17, obverse; see also Plates 20, 26, 34, 35. Allotte de la Fuye, "En-e-tar-zi patési de Lagaš," H. V. Hilprecht Anniversary Volume (Chicago, 1909), p. 128, 133.
- ↑ "On the Assyrian Mythology," Transactions of the Royal Irish Academy. "Polite Literature," Vol. XXII, Part 6 (Dublin, 1855), p. 406, 407.
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