The book titled Roots and Elements, which was composed by the sage Euclid the Pythagorean, [is so titled] because it includes the entire roots of geometry […] Other sages, too, composed many works on this science, each according to his quality. Yet Euclid’s Book of the Roots is the most important and most comprehensive. It is like the mother, and the other [works] are like its daughters.1
Caleb Afendopolo, 1499
By the time Caleb Afendopolo wrote these words, the study of Euclid in Hebrew was more than three hundred years old. From the twelfth through the sixteenth centuries, that endeavor yielded several Hebrew translations of the Elements, as well as Hebrew commentaries and adaptations.2 The scholars who engaged in the study of the Hebrew Elements shared Afendopolo’s appreciation of Euclid’s magnum opus. For them, the Elements was the essential text for anyone who wished to understand geometry, the requisite foundation for studying other works on that discipline.
The present volume looks at the translations of the Elements from Arabic into Hebrew. It relies on and continues previous research on the topic, carried out by Moritz Steinschneider, Tony Lévy, and Gad Ben Ami Sarfatti. Steinschneider laid the foundations for all subsequent scholarship on the Hebrew Elements. In his monumental Die Hebräischen Übersetzungen des Mittelalters und die Juden als Dolmetscher (1893) he identified versions of the Elements in Hebrew manuscripts and traced many of their copies.3 In particular, Steinschneider noted two complete Arabic-to-Hebrew translations executed in Jewish Provence during the thirteenth century: one by Moses Ibn Tibbon and the other by Jacob ben Makhir.4 Steinschneider also discussed the dates of these translations and the motives for their creation.5 Lévy identified two other Hebrew translations from the Arabic. One is ascribed to “Rabbi Jacob”;6 to judge by the extant copies, it ran from at least Book I through Prop. IX.10. The other is anonymous, and covers only Book I and Book II through Prop. 7.7 Lévy also published an updated list of extant manuscripts of all four translations.8 In addition, he was the first to conduct a systematic comparison of the Hebrew translations and to examine them in light of the Arabic and Latin transmissions. These comparisons enabled him to shed significant light on the Hebrew translations’ reliance on the non-Hebrew transmissions, as well as on the content and evolution of the latter. Sarfatti, in his seminal Mathematical Terminology in Hebrew Scientific Literature of the Middle Ages, published the first discussion of the technical terminology employed in translations by the Tibbonids, and especially in Ibn Tibbon’s and Jacob ben Makhir’s translations of the Elements.9
The present book is a study of the translations by Ibn Tibbon and by “Rabbi Jacob.” The choice of Ibn Tibbon is obvious: the translation is complete and was the most influential Hebrew text Jews used to study geometry during the Middle Ages. Rabbi Jacob’s translation was chosen because it covers a significant part of the Elements and because it does not seem to be dependent on Ibn Tibbon’s. This is not the case with Jacob ben Makhir’s translation: the latter is a revision of Ibn Tibbon’s translation, to which it is very close.10 Also, Ibn Tibbon’s and Jacob ben Makhir’s translations are based on an Arabic tradition of the Elements that is different from the Arabic tradition on which Rabbi Jacob’s translation relies.
This book has two parts. The first discusses the circumstances in which each translation was produced, its sources, methods, and terminology and diagrams. The second part presents critical editions of Books I–II in the two translations. In order to place the edited translations in their respective textual contexts, they are presented in parallel to two other texts. Rabbi Jacob’s translation is displayed alongside the first Latin translation of the Elements, ascribed to Adelard of Bath. As shown by Lévy, this Latin translation stemmed from the Arabic tradition followed by Rabbi Jacob. Ibn Tibbon’s translation is accompanied by my attempt to reconstruct the Arabic text that was its source. I provide it in order to assist future studies of Ibn Tibbon’s translation of the Elements and, more generally, of his work as a translator and of medieval Hebrew mathematical terminology. It does not pretend to have the status of a scientific edition.
A final note: my examination of the version of the Elements preserved in the extant Arabic exemplars of this work drew on sixteen of the eighteen copies that include Books I–II (in whole or part). I have not seen Rampur, Riḍā Library, ʿArshī MS 3656, or Mumbai, Mulla Firuz, R.I.6.
הספר הנקרא שרשים ויסודות חברו החכם אקלידיס הפיתגוריי כי בו כלל שרשי התשבורת […] גם חכמים אחרים חברו ספרים רבים בחכמה הזאת, איש איש כפי מעלתו. אך ספר השרשים לאקלידיס הוא היותר נכבד והיותר כולל, והוא כאם, וזולתם כדמות בנות לה.. See Caleb ben Elijah Afendopolo, Commentary, 46a. On this commentary see Steinschneider, “Miscellen.”
See Lévy, “Les Éléments,” 79–94. See also Lévy, “The Establishment,” 433–434; Lévy, “The Hebrew Mathematics Culture,” 161–162.
See Steinschneider, Hebräischen Übersetzungen, 504–509.
Steinschneider suggested that some versions of the Elements in Hebrew manuscripts might be translations of Latin versions (ibid., 507).
Ibid., 504–505.
See Lévy, “Une version.”
See: Lévy, “Les Éléments,” 85 (§ 20); Lévy, “Une version,” 187; Lévy, “Le manuscrit hébreu Munich 36,” 107.
See Lévy, “Les Éléments.”
See Sarfatti, Mathematical Terminology, 188–200.
See Elior, “The Hebrew Translations.”