Moses ibn Tibbon’s Hebrew Translation of al-Hassar's Kitab al Bayan - Surviving Manuscripts

The earliest known external reference to a mathematical opus by Abu Bakr Muhammad ibn Abdallah ibn Ayyash al-Hassar appears in ibn Khaldun’s 14th century work Muqaddimah (see Note 1), where he refers to it as “the little al-Hassar.” Five centuries were to pass, however, before an actual copy of al-Hassar’s Kitāb al-Bayān wa-l-tadhkār was discovered and then only in the guise of a Hebrew translation. It was Moritz Steinschneider who, in 1874, first made the connection between “the little al-Hassar” cited by ibn Khaldun and a Hebrew manuscript of a mathematical treatise by Abu Bakr al-Hassar in the Vatican Library (Steinschneider, pp. 557-558). Six years later, Adolf Neubauer, a librarian at the Bodleian Library, Oxford, identified a second copy of the same Hebrew translation at the Christ Church Library, Oxford. A third Hebrew version of al-Hassar’s treatise has surfaced more recently as one of the works in a composite codex at the Russian State Library, Moscow.

Only in 1893 was an Arabic manuscript of al-Hassar’s Kitāb al-Bayān first found and identified by W. Pertsch among the Arabic manuscripts in the Gotha Library, University of Erfuth (Ms. 1489, noted in Pertsch, p. 114). In 1901, the mathematician Heinrich Suter translated extracts from this manuscript into German in the course of his extensive study of medieval Arabic mathematical texts (Suter 1901, pp. 12-40). There is no copyist’s colophon as such but the last line in the manuscript reads [in translation]:

The blessed book is finished, praise be to Allah, for his help and favour … on Tuesday, 13^th Muḥarram 836 [September 9, 1432].

The existence of a further six Arabic manuscripts containing all or parts of the Kitāb al-Bayān has since been reported, making a total of seven copies in all. The oldest of these is in the Lawrence J. Schoenberg Collection at the University of Pennsylvania. Written in Baghdad and dated Safar 590 [January/February 1194], it lacks the last quarter of the text of the Gotha manuscript (see Note 2). The most recently uncovered copy is a 16th century manuscript sold at auction in London in 2016. The remaining five Arabic manuscripts are cited in two articles by Paul Kunitzsch (2002-03 and undated).

The Vatican Library, Rome, manuscript

The colophon in the Vatican manuscript (folio 76v) gives the name of the copyist as Baruch b. Solomon b. Joab, or, in Hebrew, ברוך הבי"א [הצעיר בבית אבי] ב"ר שלמה אבי ישר"ו ב"ר יואב ישר"ו, and the date and place of its completion as Thursday, 25th Shevat 5211 [February 6, 1451] and Montalcino, Italy; it does not, however, name the translator from the original Arabic. The best match to the partial watermarks clearly visible in the paper is Briquet 6645, which, if correct, would indicate that the paper was also used for documents created or found in Lucca, Italy, in 1445, according to Charles Briquet’s Les Filigranes. The manuscript is bound in a codex measuring 21 x 15 cm. which has the insignias of Pope Urbanus VIII (who held the office of Pope from 1623 to 1644) and of his nephew and librarian Francisco Barberini (1626-1633) embossed in gold onto its green front and back covers, respectively. Thus, the binding evidently dates from some time around 1630. There are, however, clear indications that the folios were severely cropped, both top and bottom, at the time. The original length of the pages, at least 22 cm., can be gauged from fol. 16v which has a long marginal note starting down the right hand side and continuing across the page below the main text. Cropping the bottom of the folio to the same length as the other folios would have meant losing all or part of the last three lines of the marginal note. To avoid this, the conscientious binders folded over the bottom centimetre of the folio instead of cutting it off! The outer spine of the codex was replaced in the 19th century and bears the insignias of Pope Pius IX (1846-1878) and his librarian Angelus Mai (1853-1854).

Notwithstanding, the codex is unfortunately not in the best of condition. The binding has broken open in a number of places and folios have come loose. Furthermore, in two instances the foliation does not correspond to the flow of the text: the folios numbered 17 and 19 should actually follow folio 9 leaving just folio 18 between folios 16 and 20 (see Note 3). It would appear that the foliation predates the binding in 1630, for in numerous instances the cropping cuts straight through the folio numbers in the top left-hand corner of the recto pages. The said folios were apparently already out of place even before the manuscript was bound, or more likely rebound, into the present codex around 1630.

The Christ Church Library, Oxford, manuscript

By contrast, the Christ Church manuscript (to which we will often refer as codex 189) is in almost mint condition. Measuring 30 x 23 cm., it comprises a total of 77 folios: 43 blank sheets of coarse paper (no watermark) – six at the front and 37 at the back – and 34 folios of watermarked paper sandwiched between them on which the Hebrew text is written (see Figure 1). The script is Provencal/Sefardic cursive and the text is configured in a single column on fols. 1r to 4v and double columns from fol. 5r to fol. 33r. The purpose of the 43 blank sheets is unclear.

The watermark in the Christ Church codex 189	Briquet 8941	Zonghi 938 (Italy 1456)

Figure 1. The watermark in the 34 folios in the Christ Church codex on which Moses ibn Tibbon’s Hebrew translation is written (left) is compared with two possible watermarks of the era. Paper with the watermark labeled "Briquet 8941" (middle) was used for documents created or found in Palermo in 1467, Bavière 1470, Naples 1470, Amalfi 1471, and Catania 1472, according to Charles Briquet’s Les Filigranes (p. 478). Alternatively, documents on paper with the watermark "Zonghi 938" (right) were created or found in Italy in 1456, according to Zonghi’s Watermarks. All of these dates are consistent with those in the copyist’s colophon.

Figure 2. Fol. 31v of codex 189, Christ Church College Library. Note the two colophons at the foot of the right-hand column, that of the translator, Moses bar Shmuel Tibbon, and, below it, that of the unnamed copyist. Hebrew is read right to left, top to bottom. The lefthand column contains the start of an appendix to al-Hassar's Kitāb al-Bayān consisting of nine additional worked examples that do not appear in any of the extant Arabic manuscripts. The Hebrew translation was evidently quite widely dispersed amongst the Jews of Provence and Italy and these additional examples, which will be discussed in the final webpage of this article, are indicative of the move from the sandboard to paper-and-ink as the knowledge of arithmetic spread into Europe, a transition without which mathematics as a whole could not have developed as it did. (Image used by permission of Christ Church College Library)

As shown in Figure 2, above, there are two colophons in the righthand column of fol. 31v. The first is that of Moses ibn Tibbon, the translator into Hebrew of the Arabic original:

The work is done; and it is the Book of Arithmetic by Abu Bakr Mohammad, son of Abdullah, son of Abbas al-Hassar; and R. Moses ben R. Shmuel [ibn Tibbon], ben R. Yehudah, ben R. Shaul of blessed memory from Ramon Sefarad (Spain), translated it; and its translation was completed on the 18th day of the month of Iyar in the year 31 [May 12, 1271] in the city of Montpelier.

The second colophon is that of the manuscript’s copyist:

And here Bari[?] (והנה בארי), its transcription was completed on the 12^th day of the month of Adar Bet in the year 236 of the sixth millennium [March 17, 1476], one thousand four hundred and eight years since the destruction of the Temple, may it be speedily rebuilt, Amen Selah.

The copyist is not named. In order to discuss possible alternatives for "Bari," we magnify the copyist's colophon (see Figure 3).

Figure 3. The copyist’s colophon in the Christ Church College manuscript reads: “… its transcription was completed ... one thousand four hundred and eight years after the destruction of the Temple.” A note below in a darker ink reads: “The Temple was destroyed 68 years after the incarnation (נחרב הבית ס"ח שנים אחר ההגשמה).” Adding these 68 years from the birth of Jesus also gives 1476 AD for the year the manuscript was written. (Image used by permission of Christ Church College Library)

There is a copyist’s mark, ד', above the word בארי in the top line of the colophon (see Figure 3). Its purpose appears to be to indicate that the word is unusual or exceptional, i.e., not a regular Hebrew word or an abbreviation (see Note 4). The word בארי as such appears just twice in the Hebrew Bible, each time as a person’s name (Genesis 26:34; Hosea 1:1). In the present instance it may refer to a location and should be understood as “in Ari (ארי)” or as an actual place-name, i.e., “Bari.” Alternatively, it could be the singular possessive form of the word באר, i.e., “my elucidation” or “my clear rendering” (Deuteronomy 1:5; 27:8; Habakkuk 2:2).

In the absence of any known place of Jewish habitation in the 15^th century called Ari, the city of Bari in southern Italy, which had a flourishing Jewish community until the expulsion of the Jews from the kingdom of Naples in 1510-1511, would appear to be the better alternative (see Note 5). Assuming the other possibility, namely, that it is the singular possessive form of the word באר, the colophon would read “Behold my clear rendition, its transcription was completed …” It may even be that the copyist intended the word בארי to have a double meaning and to indicate both where the text was written and to point to the fine quality of his script.

The Russian State Library, Moscow, manuscript

The Hebrew version of al-Hassar’s treatise at the Russian State Library, Moscow, is titled “Abu Bakr’s Book of Fractions.” It is the fourth of six medieval Hebrew works on mathematics and related subjects collected in a codex (see Note 6). Its text is, however, somewhat different from that in the Vatican and Christ Church manuscripts: a number of the worked examples in those manuscripts have been omitted and others amended or added, the last third of the text is arranged differently, the mathematical notation is in places at variance with that in those two texts, and there are also numerous copyist errors throughout. The colophon (fol. 38r) gives the name of the copyist as Gad Ashtruck ben Yaacov (גד אשתרוק בן יעקב) and the year of its composition 5263 [1502/3]; there is no reference to the translator. This colophon is worded as a receipt for payments the copyist had received for lessons given to a person called Baruch and for the sale of a manuscript to him; the work is described as “… the book that I and al-Hassar, who is called Abu Bakr, wrote on Arithmetic …” At best, it appears to be an abridged redaction of Moses ibn Tibbon’s translation.

Note 1. Walī al-Dīn Abd al-Raḥmān ibn Muḥammad ibn Muḥammad ibn Abī Bakr Muḥammad ibn al-Ḥasan Ibn Khaldūn (1332-1406) was an Arab historian and historiographer who developed one of the earliest nonreligious philosophies of history in his Muqaddimah (Introduction). He is regarded as one of the founders of sociology, demography and economics.

Note 2. The missing text is that from fols. 98 to 127 in the Gotha manuscript, which corresponds in the Christ Church manuscript to the Hebrew text from the fourteenth line of the right-hand column of fol. 24v to the twenty first line of the right-hand column of fol. 31v and in the Vatican manuscript to that from the thirteenth line of fol. 56v to the second word in the fourth line from the bottom of fol. 76r.

Note 3. The correct order of the folios according to the flow of the text is: 1 to 9, 17, 19, 10 to 16, 18, 20 to 77.

Note 4. The same mark appears above anomalous words elsewhere in the manuscript – for example, in the phrase

(בחסרון הוו)

(the expression on the right is in Hebrew block letters), meaning “without the [Hebrew letter/conjunction] vav" – in the sub-sections numbered 61 to 69 in Part Two of the Christ Church Manuscript (fols. 16r to 17v). (Image used by permission of Christ Church College Library)

Note 5. The word בארי appears as the name of a location in the colophon of four other extant 15^th century Hebrew manuscripts: IMHM Film Nos. 14563 (1451), 13819 (1473), 14619 (1480 and 6405 (1487).

Note 6. The other five works are Abraham ibn Ezra’s Sefer ha-Mispar, Gersonides’ Maaseh Hoshev and three works composed by the copyist himself: a Treatise on Jewish Monetary Law and two short treatises on Arithmetic.