# Moses ibn Tibbon’s Hebrew Translation of al-Hassar's Kitab al Bayan - The Hindu (Indian) Numerals

Author(s):
Jeremy I. Pfeffer (Hebrew University of Jerusalem)

In their passage from east to west, the original Hindu (Indian) numerals evolved into a number of different forms. Our present European numerals are descended from the set of 11th century glyphs known as the Western Arabic or “Gobar” numerals (digits) that developed in the Maghreb and Andalusia (see Figure 4). The term “Gobar” derives from the Arabic ghubār, meaning a sand or dust board, the device on which the numerals that the Arabs developed from the original Hindu forms were first written. In his Hebrew translation of al-Hassar’s Kitāb al-Bayān, Moses ibn Tibbon translates the term as אבק = dust. The zero digit – ṣifr in Arabic and צפר in Hebrew – was a small circle.

Figure 4. Top row: The Gobar (Western Arabic) numerals (digits) from one to nine in the Gotha manuscript (in ascending order from right to left), as reproduced in Suter’s translation (1901, p. 15). Bottom row: The corresponding Eastern Arabic numerals on fol. 4r of the Schoenberg manuscript.

Whereas the 15th century Italian copyist of the Vatican manuscript chose to employ a contemporary European form of the Gobar-based digits for the numbers in his text (Figure 5), the unnamed copyist of the Christ Church manuscript chose the first nine letters of the Hebrew alphabet, Aleph to Tet; not as gematria but as the digits of a positional decimal notation (Figure 6). Thus, writing the numbers from left to right in a Provencal/Sefardic Hebrew cursive script, he denotes the integer 543 by

 גדה

(the expression on the right is in modern Hebrew block letters), and he denotes the integer 583696 by

 וטוגחה

as perhaps Moses ibn Tibbon did before him in his original translation (see Note). By contrast, in the decimal multiplication table on fol. 3v of the Christ Church manuscript, the copyist inscribed the numbers in the traditional Hebrew format from right to left (Figure 7).

Figure 5. The 15th century European numerals used by the Italian copyist of the Vatican manuscript (fol. 2v). (Image used by permission of Vatican Library)

 א     ב     ג     ד     ה     ו     ז     ח     ט

Figure 6. The schema in the margin of fol. 1v of the Christ Church manuscript showing the contemporary 15th century European numerals and the Hebrew letters in cursive Provencal/Sefardic script used exclusively by the copyist for the digits from one to nine; the corresponding modern Hebrew block letters are shown below for reference. (Image used by permission of Christ Church College Library)

 10          9          8          7          6          5         4         3         2         1 1 2 3 4 5 6 7 8 9 10

Figure 7. The decimal multiplication table on fol. 3v of the Christ Church manuscript in which the numbers are written in the traditional Hebrew format from right to left. The same table, though not as neatly drawn, appears in the Vatican manuscript (fol. 7v). (Image used by permission of Christ Church College Library)

Note. For a 15th century use of the letters of the Greek alphabet as symbolic numerals, see Karl Menninger’s Number Words and Number Symbols, p. 274.

Jeremy I. Pfeffer (Hebrew University of Jerusalem), "Moses ibn Tibbon’s Hebrew Translation of al-Hassar's Kitab al Bayan - The Hindu (Indian) Numerals," Convergence (May 2017)