Abraham Bar Ḥiyya Ha-Nasi

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Abraham Bar Ḥiyya Ha-Nasi

also known as Savasorda

(fl. in Barcelona before 1136)

mathematics, astronomy.

In Arabic he was known as Ṣāḥib al-Shurṭa, “Elder of the Royal Suite,” denoting some type of official position; this title later gave rise to the commonly used Latin name of Savasorda. He was also known as Abraham Judaeus. Savasorda’s most influential work by far is his Hebrew treatise on practical geomerty, the Ḥibbūr ha-meshīḥah we-ha-tishboret. Translated into Latin as Liber embadorum by Plato of Tivoli, the work holds an unusual position in the history of mathematics. It is the earliest exposition of Arab algebra written in Europe, and it contains the first complete solution in Europe of the quadratic equation, x2ax + b = 0.

The year the Ḥibbūr was translated (1145) also saw the Robert of Chester translation of al-khwārizmī’s algebra and so may well be regarded as the birth year of European algebra. Thus the Ḥibbūr was among the earliest works to introduce Arab trigonometry into Europe, and it was also the earliest to treat of Euclid’s Book of Divisions. Leonardo Fibonacci was influenced by Savasorda and devoted an entire section of his Practica geometriae to division of figures. Savasorda made a novel contribution when he included the division of geometric figures in a practical treatise. thus effecting a synthesis of Greek theory with the pragmatic aspects of mathmatics.

Savasorda himself recommended Euclid, Theodosius of Bithynia, Menelaus, Autolycus, Apollonius of Perga, Eudemus of Rhodes, and Hero of Alexandria for study in geometry. He knew well alkhwārizmī and al-Karajī. Following Hero and not Euclid he did not accept the Pythagorean figurate numbers in his explanation of plane and square numbers. In general, Savasorda preferred those definitions and explanations that may be aligned more easily and closely with reality.

To understand this approach, it is necessary to go back to the earliest known Hebrew geometry, the Mishnat ha-Middot (ca. a.d. 150). This work may be considered as a link in the chain of transmission of mathematics between Palestine and the early medieval Arab civilization. The Arab mathematicians al-khwārizmī and al-Karajī, and later Savasorda, followed the methodological lines of this old Mishna. Savasorda himself provided a new cross-cultural bridge a thousand years after the Mishna. In his Encyclopedia there is the same teaching of both theory and practice, including not only the art of practical reckoning and business arithmetic but also the theory of numbers and geometric definition. This book is probably the earliest algorismic work written in Western Europe, but knowledge of the work is not apparent in the arithmetical works of either Abraham ibn Ezra or Levi ben Gerson, although they may practice, the had a common origin.

In the history of decimal theory and practice, the two mainstreams of development in the Middle Ages came from the Jewish and Christian cultures. Savasorda, however, did not belong definitely to any one mathematical group. He spent most of his life in Barcelona, an area of both Arab and Christian learning, and was active in translating the masterpieces of Arab science,. In an apologetic epistle on astrology to Jchuda ben Barsillae al-Barceloni, he deplored the lack of knowledge of Arab science and language among the people of Provence. He wrote his own works in Hebrew, but he helped translate the following works into Latin; al-ʿImrānī’s De horarum electionibus (1133–1134), al-Khayyāt’s De nativitatibus (1136), and Almansori’s Judicia seu propositiones,...(1136). Savaasorda may have worked on translations of the Quadriparitum of Ptolemy, the Spherics of Theodosius, the De motu stellarum of al-Battānī, and others, with Plato of Tivoli. It is also possible that he worked with Rudolf of Bruges on the De astrolabia


1. Original Works. Savasorda’s Ḥibbūr, Michael Guttman, ed., was published in Berlin (1912–1913); a Catalan translation was done by J. Millás-Vallicrosa (Barcelona, 1931). Three treatises of savasorda constitute a complete astronomical work: Ẓurat ha-ereẓ (“Form of the Earth,” Bodleian MS 2033) is concenrned with astronomical geography and general astronomy; Ḥeshbon mahlakot hakokhabim (“Calculation of the Movement of the Stars,” Leiden MS 37 Heb.) covers astronomical calculations; and Luḥot hanasi (“Tables of the prince,” Berlin MS 649; Bodleian MS 443,437) follows al-Battānī’s work. His work on the calendar, Sefer ha-’ibbur (“Book on intercalation,” H. Filipowski, ed., London, 1851), written 1122–1123, exerted great influence on Maimonides and Isaac Israeli the Younger. Savasorda’s philosophical works include Megillat ha-magalleh (“Scroll of the Revealer,” A. Poznanski and J. Guttmann, eds., Berlin, 1924) and Hegyon ha-nefesh (“Meditation of the Soul,” E. Freimann, ed., Leipzig, 1860). See also J. Millás-Vallicrosa, ed., Llibre de Geometria (Barcelona, 1931), Llibre revelador (Barcelona, 1929), and La obra enciclopédica yěsodé ha-těbuná u-migdal ha ěmuná, (Madrid-Barcelona, 1952); nd A. Poznanski and J. Guttmann, eds., Megillat ha-nefesh (Berlin, 1924).

II. Secondary Literature. For other studies of mathematics and Savasorda’s contributions, see F. Baer, Die Juden im Christlichen Spanien, I (Berlin, 1929), 81, n. 1; M. Curtze. “Der Liber Embadorum des Abraham bar Chijja Savasorda in der Übersetzung des plato von Tivoli,” in Abhandlungen zur Geschichte der mathematischen wissenschaften, 12 (1902), 1–183; 1. Efros, “Studies in Pre-Tibbonian Philosophical Terminology,” in Jewish Quarterly Review, 14 (1926–1927), 129–164,323–368; S. Gandz., “The Invention of Decimal Fractions....” in Isis, 25 (1936), 17, and “Mishnat ha-Middot,” in Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik, Abt. A. 2 (Berlin, 1932). See also B. goldbertg and L. Rosenkranz, eds., Yesod Olam (Berlin, 1846–1848); J. M. Guttmann, Chibbur ha-Meschicha weha-Teschboreth (Berlin, 1913); M. Levey, “Abraham Savasorda and His Algorism: A Study in Early European Logistic,” in Osiris, 11 (1954), 50–63, and “The Encyclopedia of Abraham Savasorda: A Departure in Mathematical Methodology,” in Isis, 43 (1952), 257–264. Additional studies are by P.A. Intellectual Development, 700–1300 a.d., A Study in Method,” in Isis, 22 (1935), 516–524; M. Steinschneider, Gesammelte Schriften (Berlin, 1925), p. 345; H. Suter, “Die Mathematiker und Astronomen der Araber und Ihre Werke,’ in Abhandlungen zur Geschichte der mathematischen Wissenschaften, 10 (1900); J. Tropfke, “Zur Geschichte der quadratischen Gleichungen ueber dreieinhalb Jahrtausend,” in Jahresbericht der deutschen Mathematiker-vereinigung, 43 (1933), 98–107; 44 (1934), 95–119.

Martin Levey

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