Ibn Ezra, Abraham Ben Meir

also known as Ab? Ish?q Ibr?him al-M?jid ibn Ezra, or Avenare (b. Toledo, Spain, ca. 1090; d. Calahorra, Spain, ca. 1090; d. Calahorra, Spain, ca. 1164–1167 [?])

mathematics, astronomy.

A versatile genius with a charming Hebrew style, Ibn Ezra disseminated rationalistic and scientific Arabic learning in France, England, and Italy. From about 1140 to 1160 he traveled continually, and it was in this last period of his life that his life that his works were written. Ibn Ezra was a Hebrew grammarian, exegete, astrologer, translator from Arabic into Hebrew, and poet, as well as a scientist. His work as a Jewish biblical commentator was much admired by Spinoza. Ibn Ezra considered the physical sciences and astrology fundamental for every branch of Jewish learning.

Three of his treatises were devoted to numbers. Sefer ha-e?ad (“Book of the Unit”) describes the theory of numbers from one to nine; Sefer ha-mispar (“Book of the number”) is on the fundamental operations of arithmetic. The latter describes the decimal system for integers with place value of the numerals from left to right, and the zero is given as galgal (“wheel” or “circle”) in the preface. In the body of the treatise, however, Ibn Ezra returns to use of the letters of the Hebrew alphabet as numberals. The Indian influence is, nevertheless, unmistakable. The third book, Yesod mispar (?The Foundation of Numerals”), is concerned with grammatical peculiarities.

In Ibn Ezra’s translation of al-B?r?n?’s Ta’am? l?h?t al-Chow?rezm? (“Commentary on the Tables of al-Khw?rizm?”; the Arabic original is lost) there is interesting information on the introduction of Indian mathematics and astronomyo intoo Arabic Science during the eighth century.

Ibn Ezra was concerned with permutations and combinations, as is shown in his Sefer ha-’olam(“Book of the World”). In addition to treatises on the calendar, Shalosh She’elot (“Three Chronological Questions”) and Sefer ha-’ibbur (“Book on Intercalation”), and the astrolabe, Keli ha-ne?osher (“The Astrolabe”), Ibn Ezra wrote a number of astrological works (Steinschneider lists more than fifty) that were very popular and were translated into many languages. Two were printed in Latin in 1482 and 1485, respectively; and all of them appeared in Latin in 1507. Only two of the Hebrew originals have been printed, both in modern times. They are rich in original ideas and in the history of scientific subjects. The astrological works were translated into French in 1213 by Hagin, a Jew in the employ of Henry Bate at Malines (Mechelen), who in turn translated the French into Latin. Both the French and the Catalan translations are of great philological interest.

BIBLIOGRAPHY

Works dealing with Ibn Ezra and his writings are Henry Bate et al., De luminaribus et diebus criticis (Padua, 1482–1483); H. Edelmann, Keli ne?oshet (Königberg, 1845); J.L. Fleischer, Sefer ha-m?r?t (Bucharest, 1932); Yekuthiel Ginsburg, “Rabbi Ben Ezra on Permutations and Combinations,” in The Mathematics Teacher, 15 (1922); 347–356, text from Sefer ha-’olam; S.J. Halberstam, Seger ha-’ibbur (lyck [Elk], Poland, 1874); D. Kahana, Rabi Abraham ibn Ezra, II (Warsaw, 1894), 107–111; Martin Levey, Principles of Hindu Reckoning (Madison, Wis., 1965), pp. 8, 35; Raphael Levy, The Astrological Works of Abraham ibn Ezea. A Literary and Linguistic Study With Special Reference to the Old French Translation of Hagin (Baltimore, 1927); Alexander Marx, “The Scienctific Work of Some Outstanding Mediaeval Jewish Scholars,” in Essays and Studies in Memory of Linda R. Miller (New York, 1938), pp. 138–140; Ernst Müller, Abraham ibn Esra Buch der Einheit aus dem Hebräischen übersetzt Parallelstellen und Erläuterungenzur Mathematik Ibn Esras (Berlin, 1921); Samuel Ichs, “Ibn Esras Leben und Werke,” in Monatsschrift für Geschichte und Wissenschaft des Judentums, 60 (1916), 41–58, 118–134, 193–221; M. Olitzki, “Die Zahlensymbolik des Abraham ibn Esra,” in Jubelschrift Hildesheimer (Berlin, 1890), pp. 99–120; S. Pinsker, Yesod mispar (Vienna, 1863), and Abrahami Ibn Esra, Sepher ha-echad, liber de novem numeris cardinalibus cum Simchae Pinsker interpretatione primorum quatuor numerorum. Reliquorum numerorum interpretationem et proemium addidit M. A. Goldhart (Odessa, 1867); Geroge Sarton, Introduction to the History of Science, II, pt. I (Baltimore, 1931), 187–189; M. Silberberg, ed., Sefer ha-mispar. Das Buch der Zahl, ein hebräisch-arithmetisches Werk des R. Abraham ibn Esra... (Frannkfurt, 1895); D. E. Smith and Yekuthiel Ginsburg, “Rabbi Ben Ezra and the Hindu-Arabic Problem,” in American Mathematical Monthly, 25 (1918), 99–108; and the following by M. Steinchneider: “Abraham Judaeus Savsorda und Ibn Esra,” in Zeitschrift für Mathematik, 12 (1867), 1–44, and 25 (1880), supp. 57–128; Verzeichniss der hebräische Handschriften der K. Bibliothek zu Berlin (Berlin,1897; 1901); Die hebräischen Übersetzungen... (repr. Graz, 1956), p. 869; Die arbische Literatur der Juden (repr. Hildesheim, 1964), p. 156; and Mathematic bei den Juden (repr. Hildesheim, 1964), pp. 87–91.

Martin Levey