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Levi Ben Gerson

Levi Ben Gerson

(b. Bagnols, Gard, France, 1288; d. 20 April 1344),

mathematics, astronomy, physics, philosophy, commentary on the Bible and the Talmud.

Levi was also called RaLBaG (a monogram of Rabbi Levi ben Gerson) by the Jewish writers and Gersoni, Gersonides, Leo de Bannolis or Balneolis, Leo Judaeus, and Leo Hebraeus (not to be confused with Leone Ebreo [d. 1521/1535], author of the Dialoghi d’Amore) by Latin writers. He lived in Orange and Avignon, which were not affected by the expulsion of the Jews from France in 1306 by the order of King Philip the Fair. He seems to have maintained good relations with the papal court—the Latin translations of De sinibus, chordis et arcubus and Tractatus instrumenti astronomie were dedicated to Clement VI in 1342—and with eminent French and Provencal personalities: his Luhot and De harmonicis numeris were written at the request of a group of Jews and Christian noblemen and at the request of Philip of Vitry, bishop of Meaux, respectively. It has been insinuated, without foundation, that he embraced Christianity. It is possible that he practiced medicine, although the evidence is scant. He probably knew neither Arabic nor Latin and thus had to base his work on available Hebrew translations.

In 1321 or 1322 Levi finished the Sefer ha mispar (“Book of Number”), also called Ma‘aseh hosheb (“Work of the Computer”; see Exodus 26:1). It deals with general principles of arithmetic and algebra and their applications to calculation: summations of series and combinatorial analysis (permutations and combinations). He used mathematical induction in his demonstrations earlier than Francesco Maurolico (1575) and Pascal (ca. 1654). He explained place value notation, but instead of figures, he uses Hebrew letters according to their numerical value, as well as sexagesimal fractions.

In 1342 Levi wrote De harmonicis numeris, of which only the Latin translation survives. Its purpose was to demonstrate that, except for the pairs 1-2, 2-3, 3-4, and 8-9, it is impossible for two numbers that follow each other to be composed of the factors 2 and 3.

Levi’s trigonometrical work is in De sinibus, chordis et arcubus (dated 1343) based on the Hebrew text of his Sefer Tekunah. He uses chords, sines, versed sines, and cosines but no tangents (known in Europe since 1126). Following Ptolemaic methods, he calculated sine tables with great precision. He also formulated the sine theorem for plane triangles; this theorem had been known in the Orient since the end of the tenth century, but it is not clear whether Levi rediscovered it independently or knew it through Jābir ibn Aflah (twelfth century).

Levi wrote two geometrical works: a commentary on book I–V of Euclid’s Elements that used the Hebrew translation by Moses ibn Tibbon (Montpellier, 1270)—an attempt to construct a geometry without axioms—and the treatise Hibbur hokmat ha–tishboret (“Science of Geometry”), of which only a fragment has been preserved.

The greatest work by Levi ben Gerson is philosophical in character. It is entitled Milhamot Adonai (“The Wars of the Lord”) and is divided into six books. The fifth book deals with astronomy and is composed of three treatises, the first of which is known as Sefer Tekunah (“Book of Astronomy”). Completed in 1328 and revised in 1340, it was translated into Latin in the fourteenth century. It is divided

into 136 chapters and includes two works that are frequently found separately in the manuscripts: the Luhot (chapter 99), astronomical tables calculated for the meridian of Ezob (Izop; Orange) in 1320, and his description of the construction and use of the instrument called the Jacob’s staff (chapters 4-11). Levi treated this instrument not only in the chapters mentioned (which were translated into Latin by Peter of Alexandria in 1342) but also in two Hebrew poems. In these versions it is called keli (“instrument”) and megalleh ‘amūqqōt (“secretum revelator”; see Job 12:22); on the other hand, one of these two poems bears the subtitle “‘al ha–maqel” (“Concerning the Staff”) and in it he refers to Jacob’s staff (Genesis 32:10). This is the origin of the expression baculus Jacobi, used in some Latin manuscripts, and of the misunderstanding that he wanted to attribute his invention to someone called Jacob. The instrument is also called baculus geometricus, baculus astronomicus, or balestilha. It consists of a graduated rod and a plate that moves along the rod perpendicular to it. In order to measure an angle, the observer must look at both ends of the plate. The angle α is determined solving triangle ABC. This instrument helped Levi in his attempts to determine the center of vision in the eye; unfortunately the experiment was not sufficiently precise and Levi concluded that the center of vision is in the crystalline lens, thus agreeing with Galen and Ibn al–Haytham.

Levi’s astronomical system began with a critique of the Almagest and of al–Bitrūji’s Kitāb al–hay’a (translated into Hebrew in the thirteenth century). His principal sources were al–Battānī (whom he could have known through Abraham bar Hiyya), the Islāh al–Majistī of Jābir ibn Aflah (translated by Moses ibn Tibbon in 1274), Ibn Rushd, and Abraham ibn ‘Ezra. He followed the doctrine of al–Farghānī (Hebrew translation by Jacob Anatoli, ca. 1231-1235) concerning the motion of the solar apogee. He rejected the planetary systems of Ptolemy and al–Bitrūjī because he did not feel that they conformed with the data obtained by observation, as in the variations in the apparent sizes of the planets. Thus Levi observed that, according to Ptolemy, the apparent size of Mars must vary sixfold while, according to his own observations, it varies twice. The Ptolemaic epicycles also did not agree with observations (accepting the one of the moon would imply that we see both sides alternately). In the same way Levi rejected the theory of the trepidation of the equinoxes. This theoretical work was accompanied by many years of well–defined observation (1321-1339) in which Levi used his staff and the camera obscura. The use of the camera obscura in astronomy dates back to Ibn al–Haytham and was known in Europe in the second half of the thirteenth century; Levi is distinguished for his careful instructions on how the observations should be performed and for his explanation of the theoretical basis of the camera obscura.

The planetary system conceived by Levi contains a mixture of technical considerations with others of a metaphysical character. He postulates the existence of forty–eight spheres, some concentric with the earth and others not. The movement is transmitted from the innermost sphere to the outermost by means of an intermediate nonresistant fluid. The stars are affixed to the last sphere of their own system, and each sphere or system of spheres is moved by an immaterial intelligence. The number of spirits that move the heavens is, then, forty–eight or eight. Within this general framework, Levi investigated particularly the sun and the moon. His lunar model eliminated the use of epicycles; its results were practically equivalent to those of Ptolemy’s model at syzygy and quadrature (where Levi believed them to be adequate enough) but an entirely new correction was introduced by him at the octants (where Ptolemaic theory could not be accepted because of systematic discrepancies with observation): there is no evidence to suggest a relationship between Levi and Tycho Brahe concerning the latter’s discovery of variation (an inequality that reaches its maximum at octant). It is also clear that Levi’s model represented the two first lunar inequalities better than Ptolemy’s model did. Finally he eliminated practically all the variations in lunar distance from the earth, for which he rightly criticized Ptolemy’s model.

The movements of the planets were less extensively dealt with (chapters 103-135). Levi carefully studied the controversial question concerning the places of Venus and Mercury with respect to the sun (chapters 129-135) without arriving at any definitive conclusion. Finally, one of his greatest contributions to medieval astronomy was his extraordinary enlargement of the Ptolemaic universe—for example, the maximum distance of Venus (Ptolemy, 1,079 earth radii; Levi, 8,971,112 earth radii); the distance of the fixed stars from the center of the earth (Ptolemy, 20,000 earth radii; Levi, 159 × 1012 + 6,515 × 108 + 1,338 × 104 + 944 earth radii); and the diameter of first–magnitude stars (Ptolemy, 4.5 + 1/20 earth radii; Levi, more than 328 × 108 earth radii).

A few astrological treatises of Levi have been preserved, including a prediction addressed to Pope Benedict XII in 1339 and his Prognosticon de conjunctione Saturni et Jovis (et Martis) a.D. 1345, left unfinished at his death (the Latin translation by Peter of Alexandria and Solomon ben Gerson, Levi’s brother, is extant). This conjunction of the three superior planets was also the subject of predictions by John of Murs and Firminus de Bellavalle (Firmin de Beauval). At the outbreak of the black plague of 1348 the conjunction was believed, retrospectively, to be the celestial cause that had corrupted the air.

Levi’s work was influential in Europe until the eighteenth century. In the fourteenth century his astronomical tables were used by Jacob ben David Yomtob in constucting his own tables (Perpignan, 1361). It influenced the astrological work of Symon de Covino (d. 1367), as well as the astronomical work of Immanuel ben Jacob of Tarascon (fl. ca. 1340-1377). In the fifteenth century the Sefer Tekunah was praised by Abraham Zacuto (ca. 1450-1510); and the treatise De sinibus was the model for the De triangulis of Regiomontanus (1464; published 1533). The latter, as well as his disciples Bernhard Walther (1430-1504) and Martin Behaim (d. 1507), used the Jacob’s staff, and it continued to be widely used in navigation, with various improvements, until the middle of the eighteenth century. In the seventeenth century Kepler wrote to his friend Johannes Ramus, asking him to send a copy of the Sefer Tekunah to him. There is also a curious cosmographical treatise written in Hebrew by an unknown Roman Jew who cites Levi as being among the greatest authors of the past.

BIBLIOGRAPHY

I. Original Works. Gerson Lange, Die Praxis des Rechners (Frankfurt, 1909), contains an edited German trans. of the Ma‘aseh Hosheb; Joseph Carlebach, Lewi als Mathematiker (Berlin, 1910), has an ed. of the De numeris harmonicis on pp. 125-144. Maximilian Curtze, “Die Abhandlungen des Levi ben Gerson über Trigonometrie und den Jacobstab,” in Bibliotheca mathematica, 2nd ser., 12 (1898), 97-112, is a Latin trans. of theDe sinibus and the Tractatus instrumenti astronomie. The eds. of the Milhamot Adonai do not include the Sefer Tekunah, which traditionally is considered as a separate work. On the latter see Ernest Renan, “Les écrivains juifs français du XIVe siècle,” in Histoire littéraire de la France, XXXI (Paris, 1893), 586-644—see esp. pp. 624-641, the Hebrew and Latin texts of the intro. and table of contents of the Sefer Tekunah; see also Baldassarre Boncompagni, “Intorno ad un trattato d’aritmetica stampato nel 1478,” in Atti dell’ Accademia Pontificia dei Nuovi Lincei (1863), 741-753, a textual study of three Latin MSS from the above–mentioned work plus some short. fragments. Goldstein (“Levi ben Gerson’s Lunar Model” quoted below) gives an English translation of the significant passages concerning Levi’s lunar theory. On the MSS of the Sefer Tekunah, as well as the remaining unpublished works by Levi, see Moritz Steinschneider, Mathematik bei denJuden (Leipzig, 1893-1899; Frankfurt, 1901; Hildesheim, 1964).

II. Secondary Literature. See F. Cantera Burgos, El judio salamantino Abraham Zacut. Notas para la historia de la astronomia en la España medieval (Madrid, n.d.), pp. 53, 55, 153, 189-190; Pamela H. Espenshade, “A Text on Trigonometry by Levi ben Gerson,” in Mathematics Teacher,60 (1967), 628-637; Bernard R. Goldstein, “The Town of Ezob/Aurayca,” in Revue des études juives,126 (1967), 269-271; “Preliminary Remarks on Leiv ben Gerson’s Contributions to Astronomy,” in Proceedings of the Israel Academy of Sciences and Humanities,3, no. 9 (1969), 239-254; Al–Bitrūjī: On the Principles of Astronomy, I (New Haven–London, 1971), 40-43; “Levi ben Gerson’s Lunar Model,” in Centaurus,16 (1972), 257-283; and “Theory and Observation in Medieval Astronomy,” in Isis,63 (1972), 39-47; Isidore Loeb, “La ville d’Hysope,” in Revue des études juives, 1 (1880), 72-82; D. C. Lindberg, “The Theory of Pinhole Images in the Fourteenth Century,” in Archives for History of Exact Sciences,6 (1970), 299-325, esp.pp.303 ff.; José M. Millás Vallicrosa and David Romano, Cosmografía de un judio romano del siglo XVII (Madrid–Barcelona, 1954), pp. 20, 33, 65, 70, 76-77, 85, 87; B. A. Rosenfeld, “Dokazatelstva piatogo postulata Evklida srednevekovykh matematikov Khasana Ibn alKhaisana i Lva Gersonida” (“The Proofs of Euclid’s Fifth Postulate by the Medieval Mathematicians Ibn al–Haytham and Levi ben Gerson”), in Istoriko–matematicheskie issledovaniya,11 (1958), 733-782; George Sarton, Introduction to the History of Science, III (Baltimore, 1947-1948), 594-607, and the bibliography given there—see also pp. 129, 886, 1116, 1516, 1518; and Lynn Thorndike, A History of Magic and Experimental Science, III (New York–London, 1934), 38, 303-305, 309-311.

Julio SamsÓ

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Levi ben Gershon

Levi ben Gershon

The medieval Jewish scientist, philosopher, and theologian Levi ben Gershon (1288-ca. 1344), also called Gersonides and Leo Hebraeus, is known for his continuation of the Jewish Aristotelian tradition in philosophy and for his advanced scientific studies.

Levi ben Gershon was born at Bagnols in the Languedoc region of France. He derived from a scholarly family and probably supported himself by practicing medicine. He lived most of his life in the cities of Avignon, Orange, and Perpignan, where the Jews were protected by the papacy. The exact date of his death is unknown.

Modern historians admire Levi ben Gershon for the breadth of his knowledge and writings. He also reflects the close coincidence between Jewish and Christian philosophy in the later Middle Ages. Philosophers of both faiths reacted excitedly to the rediscovery of Aristotle's writings. In the 13th and 14th centuries, both Judaism and Christianity tried to reconcile faith and reason. Theologians of each religion tried to reconcile their faith to the pagan philosophy of Aristotle, although in each case reason lost out to faith in the 14th and 15th centuries.

Levi ben Gershon ranks as the most radical of Jewish Aristotelians, or, more properly, Averroists, the name applied to medieval philosophers who derived their knowledge of Aristotle from the Arab philosopher Averroës. Asan Averroist, Levi ben Gershon insisted that Judaism was compatible with Aristotle's teachings. When the two conflicted, he reinterpreted Jewish Scripture to its detriment, at least in the opinion of his opponents. They called his major work, Milhamot Adonai (Wars of the Lord), by a derogatory title: "Wars against the Lord."

More radical in his thinking than the outstanding Jewish Aristotelian, Maimonides, Levi ben Gershon marked the end of his school of thought. Both philosophers were attacked and rejected by such later writers as Hasdai Crescas. Levi ben Gershon wrote on many other subjects, in Hebrew, and admiring Christian scholars translated much of his work into Latin. His book on trigonometry was very advanced, and Pope Clement VI had it translated as De sinibus, chordis et arcubus. Levi ben Gershon improved the camera obscura, and he may have invented the cross-staff, which he called Jacob's staff, for measuring the altitude of stars. He also accomplished valuable astronomical work, although he rejected the heliocentric theory.

A distinguished Talmudist, Levi ben Gershon was a remarkably learned and intelligent man who materially advanced the science and philosophy of his period. Much of his scientific and philosophical thought is contained in his magnum opus, Milhamot Adonai.

Further Reading

The most informative book on Levi ben Gershon and his philosophical tradition is Isaac Husik, A History of Medieval JewishPhilosophy (1916). For the milieu in which Levi ben Gershon lived see S. W. Baron, A Social and Religious History of the Jews, vol. 8 (1969). □

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Gershon, Levi ben

Levi ben Gershon: see Gersonides.

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Levi ben Gershon

Levi ben Gershon: see Gersonides.

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Ralbag

Ralbag (acronym): see LEVI BEN GERSHOM.

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