Hebrew and Latin Versions of an Unknown Mathematical Text by Abraham Ibn Ezra

Tony Levy Hebrew and Latin Versions of an Unknown Mathematical Text by Abraham Ibn Ezra Two Texts and Their Relationship to Abraham Ibn Ezra The Hebrew manuscript Monte Cassino, Biblioteca dell'Abbazia, Caravita 5IO1 contains three important mathematical texts in Hebrew. Two are well-known translations from the Arabic by Moses Ibn Tibbon: Euclid's Elements (fols. Ia-132b) and Theodosius' Sphaeries (fols. 142a-171a). In between these two is a text whose beginning is clearly missing. E. Renan describes it as the Sefer ha-Mispar, i.e., The Book of the Number, by Abraham Ibn Ezra. In fact, the colophon reads: "k.m.l. Sefer ha-Middot we-hu Sefer ha-Mispar le-rabbi Avraham ben Ezrah [sic] ben rabbi MeDir ha-sefaradi z"l Tehillah Ia0El " (fol. 141b, 11.7-8), i.e., "The Book of Geometry is complete, this is Microfilm number 34894 at the Institute for Microfilmed Hebrew Manuscripts, The Jewish National and University Library, Jerusalem. A. Caravita, / Codici de le arti a Monte Cassino I (Monte Cassino, 1869), p. 140-42. Renan is the author of the Hebrew part of the catalogue. The manuscript is not dated; it has been suggested, on the basis of the handwriting, that it dates from the fourteenth or fifteenth century. Aleph 1 (2001) 295 the Book of Number by Rabbi Abraham Ibn Ezra son of Rabbi Meir the Spaniard, of blessed memory. Praise be to God." The first word is doubtless a transcription in Hebrew characters of the Arabic word kamala, meaning "is complete," or "has been completed." In fact, the "Arabic connection" of our text, and of the manuscript itself, is reinforced by a word written twice, in Arabic characters, once above and once below the colophon: n.q.L, i.e. naql, meaning recension or copy.3 A cursory reading of the text suffices to show that it is not Abraham Ibn Ezra's well-known Sefer ha-Mispar, the Book of Arithmetic, as we know if from M. Silberberg's edition; nor does it consist of excerpts from this work. Although the text opens with a series of disparate notes on arithmetical subjects (fols. 133a-134b), the greater part (fols. 134b-141b) is an exposition of elementary practical geometry, a subject not treated in Sefer ha-Mispar (except for a short passage on the circle). This text is thus intriguing enough on its own terms, if only to establish its authorship. The text became even more intriguing after I attended a conference at which my friend Charles Burnett (The Warburg Institute) gave a paper on "Hindu-Arabic Numerals and the Transmission of Symbolic Notations."5 One of the texts cited and commented on by Burnett is catalogued under the title De proportione numerorum et figurarum geometricarum.6 It uses the so-called "oriental" or "eastern" forms for the Hindu-Arabic numerals; these forms are found in only a small number of twelfth-century Latin manuscripts, the majority of which contain works attributed to Ibn Ezra. Although Burnett cautiously entitled his paper "An Anonymous Latin Text in Search of an Author," he was inclined to conjecture that it was another work by Abraham Ibn Ezra. Burnett was kind enough to put at my disposal a preliminary transcription of the text (L); a comparison with the Hebrew text in the Monte Cassino manuscript (H) quickly revealed that certain phrases in H have a precise equivalent in L, including omissions and errors. The 296 Tony Levy subsequent methodical comparison of H and L allows me to corroborate Burnett's intuition and conclude as follows: L is mostly a literal translation (but at times an adaptation) ofthe source from which H derived, small differences between the two texts notwithstanding. In view of the importance of the text and of its supposed author, Charles Burnett and I have decided to publish conjointly critical editions of both texts, accompanied by commentaries that will highlight their significance, both for the history of mathematics in medieval Europe and for what we know of the literary activity of Abraham Ibn Ezra. In the present brief note, I will indicate what conclusions can be drawn at this stage and advance some hypotheses that future research will...