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Hero of Alexandria and Mordekhai Komtino

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Hero of Alexandria and Mordekhai Komtino Hero of Alexandria and Mordekhai Komtino: The Encounter between Mathematics in Hebrew and the Greek Metrological Corpus in Fifteenth-Century Constantinople Tony Lévy, Bernard Vitrac To cite this version: Tony Lévy, Bernard Vitrac. Hero of Alexandria and Mordekhai Komtino: The Encounter between Mathematics in Hebrew and the Greek Metrological Corpus in Fifteenth-Century Constantinople. Aleph, Indiana University Press, 2018. hal-03328208 HAL Id: hal-03328208 https://hal.archives-ouvertes.fr/hal-03328208 Submitted on 29 Aug 2021 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Tony Lévy and Bernard Vitrac Hero of Alexandria and Mordekhai Komtino: The Encounter between Mathematics in Hebrew and the Greek Metrological Corpus in Fifteenth- Century Constantinople ABSTRACT Mordekhai ben Eliezer Komtino (1402–1482) was a well-known scholar in the Judeo-Byzantine world—philosopher, exegete, mathematician, and astronomer. Among his works was Sefer ha-Ḥeshbon we-ha-middot. This paper deals with the geometrical part of that work. Although Euclid is sometimes quoted by the author, Komtino’s geometry is not Euclidean. It comes from the field of metrological geometry (“practical geometry”). In addition to the famous Hebrew geometry composed by Abraham bar Ḥiyya in the twelfth century, Ḥibbur ha-meshiḥah we-ha-tishboret, Komtino also had before him a Greek manuscript containing the unique extant copy of Hero of Alexandria’s Metrica (first or second century) and other metrological writings attributed to him. Mordekhai Komtino’s Place in the History of the Hebrew Scientific Culture: The State of the Question Scientific literature in Hebrew, and notably its mathematical branch, originated Tony Lévy is at the CNRS, UMR 7219 (SPHERE), email: [email protected]. Bernard Vitrac is at the CNRS UMR 8210 (AnHiMA), email: [email protected]. © Aleph 18.1 (2018) pp. 181-262 181 Hero of Alexandria and Mordekhai Komtino at the start of the twelfth century1 and continued through the sixteenth century, in very different places, eras, and cultural contexts.2 In this paper we will present a rather late and highly interesting link in this tradition: Rabbi Mordekhai Komtino in fifteenth-century Constantinople. Komtino in his Milieu Mordekhai ben Eliezer Komtino, also spelled Komtiano or Komatiano3 (1402– 1482), is one link in the line of Jewish polymaths who, in addition to their commentaries on canonical texts, also wrote on the sciences;4 in his case, astronomy and mathematics. We should also underscore the frequent references 1 Tony Lévy, “The Establishment of the Mathematical Bookshelf of the Medieval Hebrew Scholar,” Science in Context 10(3) (1997): 431–451. 2 Tony Lévy, “The Hebrew Mathematics Culture (Twelfth-Sixteenth Centuries),” in Gad Freudenthal, ed., Science in Medieval Jewish Cultures (Cambridge: Cambridge University Press, 2011), pp. 155–171, on p. 160: “Mathematics in the Judeo-Byzantine Scholarly World (Fifteenth-Sixteenth Centuries).” 3 As summarized by Jean-Christophe Attias, Le commentaire biblique. Mordekhai Komtino ou l’herméneutique du dialogue (Paris: Le Cerf, 1991), “The exact pronunciation of seems to have divided researchers. Its Hebrew orthography is (כומטינו) Komtino’s name certainly fluctuating and seems to authorize several readings” (p. 20); see also nn. 3–12. see Steven ;(כומאטייאנו) Langermann, following Bowman, opts for the reading Komatiano Bowman, The Jews of Byzantium 1204–1453 (Tuscaloosa: University of Alabama Press, 1985) p. 149, n.68; Y. Tzvi Langermann, “Science in the Jewish Communities of the Byzantine Cultural Orbit. New Perspectives,” in Freudenthal, ed., Science in Medieval Jewish Cultures, pp. 438–453, on p. 438, n.1. Other Hebrew representations are attested We note, however, that the oldest manuscript of the .(כומיטינו/חומטייאנו/כומטייאנו) mathematical text analyzed here (see below, the colophon of the New York manuscript JTS 2639) was copied in the author’s lifetime, in 1478; there the copyist presents the author may God protect and give him life, the ,(כומטיינו) by the scribe as “Mordechai Komtiano son of Eliezer Komtiano.” We do not feel adequate to decide the question, which depends on more than paleography. We have chosen to go here with Komtino. 4 For a first overview of the scientific activity of the Judeo-Byzantine communities between the eight and sixteenth centuries, see Langermann, “Science in the Jewish Communities of the Byzantine Cultural Orbit.” With regard to Komtino, Langermann writes (p. 439): “For the most part, his writings remain unstudied; if they ever are closely studied, surely our picture of Byzantine Jewish culture will benefit.” 182 Tony Lévy and Bernard Vitrac to the sciences in his exegetical works, including his commentary on the Pentateuch,5 his commentary on works by Abraham Ibn Ezra,6 his glosses on Maimonides’ Treatise on Logic, known in Hebrew as Millot ha-higgayon,7 and his commentary on the Guide of the Perplexed (completed in 1480).8 The biographical data about Komtino are sparse and fragmentary.9 He lived in a century that was marked by a crucial event: the Ottoman expansion and conquest of Constantinople in 1453, which had a powerful effect on the Judeo- Byzantine communities.10 On the cultural and thus on the scientific plane, these communities’ encounter with the stream of exiles from the Iberian Peninsula (from the end of the fourteenth and continuing into the sixteenth century), with their influential traditions, was a major turning point. Finally, we should underscore Komtino’s special relationship with the Karaites of Constantinople (Jewish sectarians who deny the authority of the rabbinic Oral Law); several of its members were among his students. This circumstance no doubt encouraged Komtino’s scholarly work, as evidenced by the fact that several of his works are dedicated to his Karaite students.11 5 Attias, Le commentaire biblique, pp. 72–73. 6 Sefer Yesod mora’ (Book of the Foundation of Piety), Sefer ha-Shem (The Book of the Name), and Sefer ha-Eḥad (The Book of the One). For the first of these commentaries by Komtino, see Dov Schwartz, Perush qadmon le-sefer Yesod moraʾ (An Early Commentary on Yesod mora) (Ramat Gan: Bar-Ilan University, 2010). 7 This text, the only work by Komtino published before the twenty-first century, is a pendant to Maimonides’ text, along with the commentary by Moses Mendelssohn: Millot ha-higgayon, ed. David Slucki (Warsaw: Baumritter, 1865). See Charles H. Manekin, “Logic in Jewish Medieval Culture,” in Freudenthal, ed., Science in Medieval Jewish Cultures, p. 129. 8 Dov Schwartz “Understanding in Context: Rabbi Mordechai Komtino’s Commentary on the Guide of the Perplexed,” Pe‘amim 133–134 (2013): 127–183 (Heb). 9 Attias, Le commentaire biblique, pp. 19–22. 10 Joseph Hacker, “Ottoman Policy toward the Jews and Jewish Attitudes toward the Ottomans during the Fifteenth Century,” in Benjamin Braude and Bernard Lewis, eds., Christians and Jews in the Ottoman Empire, vol. 1 (New York: Holmes & Meier, 1982), pp. 117–126; idem, “The Sürgün System and Jewish Society in the Ottoman Empire during the Fifteenth to the Seventeenth Centuries,” in Aron Rodrigue, ed., Ottoman and Turkish Jewry (Bloomington: Indiana University Press, 1992), pp. 1–66. 11 Attias, Le commentaire biblique, pp. 15–16, 30–31, 41–44. 183 Hero of Alexandria and Mordekhai Komtino הקושטנדיני—”Komtino represents himself as “a Greek of Constantinople His command of Greek is attested in his commentaries on the Pentateuch .היוני and on Maimonides and in his celestial catalogue, which provides the names of stars in both Greek and Hebrew.12 Our study of his geometrical treatise confirms his fluency in Greek and his concern to convey its nuances. What scientific heritage could Komtino have had in his day? Many older manuscripts were being copied in Constantinople/Istanbul; translations into Hebrew were being executed from Arabic, Greek, and even directly from Persian.13 Alongside a number of scientific encyclopedias compiled in Hebrew there were also original writings, with a three-fold heritage: the works of Abraham Bar Ḥiyya and Abraham Ibn Ezra; the translations of Arabic works that issued from Provence; and treatises such as those by Gersonides and Immanuel Bonfils. To this we must add works in Arabic and Greek that were not available in Hebrew. Mordekhai Komtino’s Scientific Writings The pioneering labors of Ḥayyim Jonah Gurland (1843–1890), a Russian rabbi and orientalist, produced the first overview of Komtino’s writings, which he accessed in the manuscript collection of the Imperial Library in St. Petersburg.14 12 Ibid., pp. 31–33. According to Attias, the glosses in Arabic do not necessarily reflect a real knowledge of the language. Such knowledge does seem to be attested for one of his most lauded pupils, Eli Mizrachi (1435–1526), the author, among other works, of a substantial commentary on the Almagest. In the latter Langermann has identified many exact and accurate references to both the Greek and Arabic versions of the Almagest; see Langermann, “Science in the Jewish Communities,” p. 447. 13 This is the case, for now unique, of a medical formulary by Zayn al-Dīn al-Jurjānī (d. 1136/7); see ibid, p. 443. 14 Gurland published the results of his studies in a monograph in Russian: Novye Matierialy dlia istorii Ievrieïskoï Literatury XV Stolietia. M. Koumatiano (New materials on the history of Hebrew literature in the 15th century by M. Koumatiano) (St Petersburg: Imperial Academy of Sciences, 1866). It was accompanied by a substantial appendix of excerpts from the Hebrew manuscripts consulted by Gurland.
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