Islamicate societies were of different sizes and different demographic compositions. The large territorial states like the caliphates from the eighth to the thirteenth centuries or the main empires from the fifteenth to the twentieth centuries consisted of many different population groups speaking different languages in different registers for different purposes. They were in a double sense plurilingual: horizontally by encompassing at different times and in different regions people who spoke as their daily-life languages various dialectal forms of Arabic, Aramaic, Greek, Coptic, Berber, Turkic, Persian, Slavonic, Romance, Indic, and other members of diverse linguistic families; vertically by using more literary or so-called classical registers of some of those languages in prayer, preaching, court procedures, petitions, diplomatic protocols, poetry, literary prose, or scientific, religious, medical, philosophical, and other intellectual writings, teachings, or public debates. Translating occurred side by side with communicating in more than just one language, depending on specific socio-cultural settings like dynastic courts or scholarly circles and schools. While plurilingual scholarly, literary, mercantile, or commercial communication happened in many urban centers crossed by major trade or pilgrimage routes or sea routes between ports in at least four seas (Indian Ocean, Arabian, Red and Mediterranean seas), translations as a formal act of rendering a text in one language as a spoken or written composition in another language on a daily basis are often less well documented. Nonetheless, there were several major phases in which interlingual translation was a widespread cultural activity. One such phase occurred between the seventh and the twelfth centuries in the Umayyad and Abbasid caliphates. Religious, historical, diplomatic, mathematical, medical, philosophical, alchemical, and other types of texts were transferred from one, two, and in rare cases also three source languages into one or two target languages: Greek, Syriac, Middle Persian, Sanskrit, Arabic. Many translations were made from Greek into Syriac and from Greek into Arabic, followed by translations from Syriac into Arabic. Translations from Syriac or Greek into Middle Persian and from there into Arabic or from Middle Persian or Sanskrit into Arabic took place less often or are less well documented. This plurilingual environment of translating was enabled by the presence of people speaking, writing, and thinking concomitantly in two or three of those languages. Traces of this plurilingualism permeate even translations where only two languages were involved. An example of this situation can be found in the extant Arabic copies of Euclidâs (third century BCE) Elements, called translations or corrections of translations. The people involved as translators and correctors were three members of three different faith communities (Islam, Christianity, Sabian astral religion)âal-ḤajjÄj ibn YÅ«suf ibn Maá¹ar (d. after 827), IsḥÄq ibn Ḥunayn (d. 911), and ThÄbit ibn Qurra (d. 901). The first knew Arabic and Greek, perhaps also Syriac, but may not have been fluent in the second and third languages, while IsḥÄq and ThÄbit were equally well versed in all three languages. In addition to some twenty copies of an Arabic text attributed in about half of the copies as a translation to IsḥÄq but corrected by ThÄbit, reports in narrative sources, mostly of a bio-bibliographical nature, and in editions of the Elements by scholars skilled in the mathematical sciences about the translation history and some of the properties of the work of the three men were compiled from the late ninth to the late thirteenth century and are available in modern editions or in manuscript form. According to these reports, al-ḤajjÄj translated the Elements first in the late eighth century, either for Caliph al-HÄrÅ«n al-RashÄ«d (r. 786â809) or for his Barmakid vizier YaḥyÄ ibn KhÄlid (d. 803). He is said to have retranslated the Greek book a second time for Caliph al-MaʾmÅ«n (r. 813â833), probably in the 820s.1 Another report claims that this second version was not a new translation but an edition in which the translator adapted the language and the content of his first translation to suit the taste and interests of the intended, probably courtly audience, deleted superfluities and filled in gaps.2 IsḥÄq is said to have translated the Elements anew at some time in the 870s, possibly for the vizier Ibn Bulbul (in office between 885 and 892; d. 892). But due to some unspecified reason, ThÄbit was charged with the task of correcting or editing this translation.3 Modern historians or Arabists have assumed that this division of labor reflected IsḥÄqâs inferior mathematical competence in comparison with ThÄbit who was indeed a leading, if not the leading scholar of the mathematical sciences during the entire century.
The scholarly reports are occasionally contradictory. But they agree that the two textual traditions derived from those translations differed substantially. Al-ḤajjÄj was described as having reordered the sequence of propositions in several books, having presented various propositions either as a sequence of separate special cases, for instance a right-, obtuse- and acute-angled triangle instead of an arbitrary triangle, or as a simpler, less general case, for instance a triangle or a square instead of a parallelogram, and included a lesser number of propositions, for instance in Books I, III, VIII, or X. IsḥÄqâs and ThÄbitâs work was described in the opposite mannerâas treating the general instead of particular cases, having substantially more propositions, and having ordered several books differently. Some versions attribute numerical examples and simplified diagrams to al-ḤajjÄj.
These scholarly comments on specific manuscript instantiations of the different translations contradict the claim of the tenth-century book trader and erudite Ibn al-NadÄ«m (d. 990) that al-ḤajjÄjâs work had receded into the background and IsḥÄqâs and ThÄbitâs collaborative work dominated scholarly engagement with the Elements. During the thirteenth century, several new editions of the Elements in Arabic were produced by scholars in Syria, Iraq, and Iran. The one compiled by Naṣīr al-DÄ«n al-ṬūsÄ« outshone all others and also pushed to the back of scholarly as well as educational lives the versions representing in some manner the translations. Nonetheless, modern researchers have concluded that Ibn al-NadÄ«mâs evaluation and the descriptions by other scholars until the early fourteenth century meant that al-ḤajjÄjâs work has been lost to us, except for very limited extracts included in some copies of the edited translation attributed to IsḥÄq and ThÄbit, some fragments in the texts or margins of some editions, and certain translations into Latin during the twelfth century and into Syriac done at an unspecified time.
But various other Arabic editions as well as translations into Persian survived in this highly competitive space of mathematical literature. One of those singular versions, produced by an anonymous scholar in all likelihood in the ninth century, in communication with the then-dominant translations and some of the editorial versions already under way since the early ninth century, surprisingly turned out to be the ultimate challenge for understanding the surviving copies of the translations, the practices adhered to by translators and editors of Euclidâs Elements in the late eighth and throughout the ninth centuries, and the various historical accounts produced by different actors (book traders, philosophers, scholars of the mathematical sciences, administrators, physicians, literati) between the ninth and the fourteenth century. This incomplete edition, bought in the late nineteenth century by a Zoroastrian mobed âpriestâ from Mumbai as a potential tool for reorganizing the ritual calendar of the Parsee community in that town, indicates that everything the surviving sourcesâwhether mathematical, bio-bibliographical, or historicalâpresent as reliable information and source-based evaluation is actually profoundly erroneous. It offers strong evidence that all surviving forms of the translations either represent or derive from al-ḤajjÄjâs work. Hence, the efforts to understand the process of translating Euclidâs Elements into Arabic stand once again at the very beginning.
The things that we do know, however, independently of such issues as who produced them why, where, when, and for what purpose, concern linguistic features of the extant textual variants, among them a small number of items that testify to the plurilingual environment in which the translations took place and the multiple levels of skills and qualifications that stimulated different textual choices. In the following, cases that exemplify such translational practices are presented.
Translations of Euclidâs Elements
The extant Arabic texts acknowledged as translations and various fragments show that al-ḤajjÄj had translated a Greek text. Traditionally, it was argued that he used a very literal style of translation. This has recently been shown to be wrong. In contrast, IsḥÄq was believed to have rendered the mathematical content according to the grammatical rules of Classical Arabic. But if indeed any of the extant texts includes a part of his translation in the edition of Thabit, this too seems to be wrong, and IsḥÄq seems to have followed much more closely Greek syntax. If, however, none of the extant specimens does contain a part of IsḥÄqâs translation, then al-ḤajjÄj used two different styles when translating and/or editing the Elements. One of the two is much Arabicized, is translated not ad verbum but ad sensum, and includes terms from other parts of the mathematical sciences, Syriacisms, and at least one word that might be an allusion to the vivid debates among different Muslim factions in the early ninth century about whether God has a body and, if so, whether it is of blood and flesh like the human body. The second mode of translation documented in the extant Arabic versions is noticeably closer to Greek style and grammar, translates Greek technical terms often literally, has no Syriacisms, nor alien or practical terms, and no allusions to religious and political debates.
In the twelfth century, Euclidâs Elements were translated by three different translators from Arabic into Latin and by a fourth translator from Greek. Here, only the translators of an Arabic version are representedâAdelard of Bath (d. ca. 1149â1150), Hermann of Carinthia (active 1138â1143), and Gerard of Cremona (d. 1187). It is widely believed that Adelard of Bath translated one of al-ḤajjÄjâs texts, that Gerard of Cremona translated Thabitâs edition of IsḥÄqâs translation with additions from some alternative version, and that Hermann of Carinthia translated one of al-ḤajjÄjâs versions and heavily abbreviated it. In contrast, it seems more likely that Adelard translated a later Arabic edition of one of al-ḤajjÄjâs texts, that Gerard translated one of al-ḤajjÄjâs versions adding extracts from a later edition of one of them and that Hermann translated a later Arabic edition, possibly again of one of al-ḤajjÄjâs versions, which might already have been heavily abbreviated, and abbreviated it further.
Explanation English translations are used if they exist and a further translation, as literal as possible, is added. If none exists, only the latter is provided. At times it was very difficult to achieve such a literal translation. The purpose is to allow the reader to recognize the differences between the variants in the three languages and hence some of the difficulties the translators may have faced.
Examples
Excerpt I
a. Greek (VII, def.1):
Î¼Î¿Î½á½±Ï á¼ÏÏιν ,καθ᾽ ἣν á¼ÎºÎ±ÏÏον Ïῶν á½Î½ÏÏν á¼Î½ λέγεÏαι .4A unit is that by virtue of which each of the things that exist is called one. [literally: the unit is (that) according to which each of the existing (things) is called one.]
b. Arabic 1 (VII, def. 1):
â®â®
اÙÙØدة Ù٠اÙØ´ÙØ¡ اÙØ°Ù ÙÙا٠ÙÙÙ ÙاØد ٠٠اÙÙ ÙجÙدات ÙاØد .â5â¬â¬ââ¬âThe unit is the thing by which every one of the things in existence is called one.6
[literally: the unit is the thing (according to) which one says for each one of the existing (things) one.]
c. Arabic 2 (VII, def. 1):
â®â®
اÙÙØدة Ù٠اÙت٠ÙÙا٠بÙا ÙÙÙ Ù ÙجÙد ÙاØد .â7â¬â¬ââ¬âThe unit is that by which every existing [thing] is called one.8 [literally: the unit, she is that (according to) which one says for each existing (thing) one.]
d. Adelard of Bath (VII, def. 1):Unitas est qua dicitur omnis res una.9The unit is [that] by which each thing is called one.
e. Gerard of Cremona (VII, def 1):Unitas est qua dicitur omnis res una.10The unit is [that] by which each thing is called one.
f. Hermann of Carinthia (VII, def. 1):Unitas est qua dicitur omnis res una.11The unit is [that] by which each thing is called one.
Excerpt II
a. Greek (VII, def. 12):
ÏÏῶÏοι ÏÏá½¸Ï á¼Î»Î»á½µÎ»Î¿Ï Ï á¼Ïιθμοί εἰÏιν οἱ μονάδι μόνῠμεÏÏούμενοι κοινῷ μέÏÏῳ .12Numbers prime to one another are those which are measured by a unit alone as a common measure. [literally: ⦠those being measured by the unit alone as a common measure.]
b. Arabic 1 (VII, def. 16):
â®â®
اÙاعداد اÙ٠تباÙÙØ© Ù٠اÙت٠اÙضا ÙعدÙا عدا ٠شترÙا اÙÙاØد ÙÙØ· .â13â¬â¬ââ¬âMutually incommensurable numbers are those which only a unit measures as a common measure.14 [literally: the numbers that are mutually different are those that also only the one measures as a common measure.]
c. Arabic 2 (VII, def 13):
â®â®
اÙاعداد اÙت٠ÙÙا٠ÙبعضÙا اÙ٠عÙد بعض Ù٠اÙت٠ÙÙس ÙÙا Ø´ÙØ¡ ٠شتر٠Ùعدا٠اÙا اÙÙاØد .â15â¬â¬ââ¬âNumbers, some of which are called prime to others, are those which do not have anything common which measures them except the unit.16 [literally: the numbers, of which one calls one prime to another one, are those to which there is not a common thing by which the two are measured except the one.]
d. Adelard of Bath (VII, def. 10):
Numeri incommunicantes quorum uterque ad alterum primus sunt illi qui nullum habent communem numerum se numerantem preter solam unitatem.17
Numbers not in communication, of which one of the two is prime to the other, are those which have no common number measuring them except the unit alone.
e. Gerard of Cremona (VII, def. 13):
Numeri ad invicem primi sunt quibus non est numerus communis numerans eos communiter nisi unitas tantum.18
Numbers mutually prime are those for which there is no common number measuring them together, but only the unit.
f. Hermann of Carinthia (VII, def. 10):
Numeri contra se primi dicuntur qui nullo numero excepta sola unitate communiter numerantur.19
Numbers are called prime against themselves, which are measured jointly by no number except by the unit alone.
Excerpt III
a. Greek (VII, theorem 27):
á¼á½°Î½ δύο á¼Ïιθμοὶ ÏÏῶÏοι ÏÏá½¸Ï á¼Î»Î»á½µÎ»Î¿Ï Ï á½¦Ïιν ,καὶ ÏολλαÏλαÏιάÏÎ±Ï á¼Îºá½±ÏεÏÎ¿Ï á¼Î±Ï Ïὸν ÏοιῠÏινα ,οἱ γενόμενοι á¼Î¾ αá½Ïῶν ÏÏῶÏοι ÏÏá½¸Ï á¼Î»Î»á½µÎ»Î¿Ï Ï á¼ÏονÏαι ,κá¼Î½ οἱ á¼Î¾ á¼ÏÏá¿Ï ÏÎ¿á½ºÏ Î³ÎµÎ½Î¿Î¼á½³Î½Î¿Ï Ï ÏολλαÏλαÏιάÏανÏÎµÏ ÏοιῶÏá½·ÏÎ¹Î½Î±Ï ,κá¼ÎºÎµá¿Î½Î¿Î¹ ÏÏῶÏοι ÏÏá½¸Ï á¼Î»Î»á½µÎ»Î¿Ï Ï á¼ÏονÏαι {καὶ á¼Îµá½¶ ÏεÏὶ ÏÎ¿á½ºÏ á¼ÎºÏÎ¿Ï Ï ÏοῦÏο ÏÏ Î¼Î²Î±á½·Î½ÎµÎ¹ }.20If two numbers be prime to one another, and each by multiplying itself make a certain number, the products will be prime to one another; and, if the original numbers by multiplying the products make certain numbers, the latter will also be prime to one another {and this is always the case with the extremes}. [literally: if two numbers are prime to each other, and each one, having made itself multiple, makes some (number), the ones, having come into being from that, are prime to each other; and when the ones that have been made multiple from the ones that came into being at the beginning make some (numbers), the (numbers) also are prime to each other {and this always happens around the farthest points}.]
b. Arabic 1 (VII, theorem 27):
â®â®
Ù٠عددÙ٠٠تباÙÙÙÙ Ùضرب ÙÙ ÙاØد Ù ÙÙ٠ا ÙÙ Ù Ø«ÙÙ Ùإ٠٠ربعÙÙ٠ا ٠تباÙÙا٠.ÙÙØ°Ù٠إ٠ضرب اÙ٠ربعا٠Ù٠جذرÙÙ٠ا ÙÙ٠ا اÙعددا٠اÙاÙÙا٠Ù٠٠ربع Ù٠جذر٠Ùإ٠اÙÙ ÙعبÙ٠اÙضا ٠تباÙÙا٠.ÙÙØ°ÙÙ Ùا Ùزا٠Ù٠اÙاطرا٠ÙاÙاعداد اÙاÙاخر .â21â¬â¬ââ¬âWhen any two mutually incommensurable numbers are multiplied, each one of the two into its equal, the squares of the two of them are mutually incommensurable, and, likewise, if the two squares are multiplied into their roots, namely the original numbers, each square into its root, the cubes also are mutually incommensurable, and likewise [this] does not change in the case of the extremes and the last numbers.22 [literally: Each two mutually different numbers, each one of them of the two is beaten (= multiplied) with itself, then their two squares are indeed mutually different. Likewise, if the two squares are beaten with their two roots, which are the two first numbers, each square with its root, then the two cubes are indeed also mutually different. Likewise, this does not stop at the extremes, which are the last numbers.]
c. Arabic 2 (VII, theorem 27):
â®â®
إذا Ùا٠عددا٠ÙÙا٠ÙÙ ÙاØد Ù ÙÙ٠ا اÙÙا عÙد اÙآخر Ùضرب ÙÙ ÙاØد Ù ÙÙ٠ا ÙÙ Ù Ø«ÙÙ ÙØ¥Ù ÙÙ ÙاØد ٠٠٠ربعÙÙ٠ا اÙ٠عÙد اÙآخر .ÙÙØ°Ù٠إ٠ضرب اÙ٠ربعا٠Ù٠اÙعددÙ٠اÙاÙÙÙÙ ÙÙ ÙاØد Ù ÙÙ٠ا Ù٠جذر٠ÙØ¥Ù ÙÙ ÙاØد ٠٠اÙعددÙ٠اÙ٠جس٠Ù٠اÙضا اÙ٠عÙد اÙآخر .ÙÙØ°ÙÙ Ùا Ùذا٠Ù٠اÙاطرا٠اÙاÙاخر .â23â¬â¬ââ¬âIf there are two numbers, and one of the two of them is prime to the other, and each of the two of them is multiplied into its equal, then each one of the squares of the two of them is prime to the other; likewise, if the two squares are multiplied into the two original numbers, each one of them into its root, then each one of the two resulting numbers is also prime to the other; likewise, this does not cease in [the case of] the furthest limits.24 [literally: If there are two numbers, where each one of the two is prime to the other, and if each one of the two is beaten with itself, then each one of their two squares is indeed prime to the other. Likewise, if the two squares are beaten with the two first numbers, each one of the two with its root, then each one of the two solid numbers indeed is also prime to the other. Likewise, this does not stop at the last extremes.]
d. Adelard of Bath (VII, theorem 27):
Cum propositi fuerint duo numeri uterque ad alterum primi ducaturque uterque eorum in seipsum, erunt qui ex eis producentur uterque ad alterum primi. Itaque si in hos principia ipsa ducantur, erunt quoque ex eis producti ad invicem primi, eodemque modo infinite omnium in se ductorum extremitates.25
When two numbers have been proposed, each one being prime to the other, and each one of them is prolonged into (= multiplied with) itself, the ones that will be produced from them will be prime each one to the other. And so, if the beginnings (= first numbers) themselves are prolonged into these, the products from them will also be mutually prime, and in the same way the extreme limits of all that were prolonged into themselves forever.
e. Gerard of Cremona (VII, theorem 27):
Si fuerint duo numeri quorum unusquisque sit ad alterum primus et multiplicetur unusquisque eorum in se ipsum, quisque duorum quadratorum ipsorum est ad alterum primus. Et similiter si duo quadrati multiplicentur in numeros primos scilicet quisque eorum in radicem suam, quisque duorum cubicorum etiam erit ad alterum primus. Et similiter incessanter in extremitatibus postremorum erunt incommunicantes sicut qui multiplicantur in numeros primos.26
If there have been two numbers, of which each one is prime to the other and if each of them is multiplied into itself, each of the two squares of themselves is prime to the other. And similarly, if two squares are multiplied into the first numbers, that is each of them into its root, each of the two cubes also will be prime to the other. And similarly, incessantly, (those that are multiplied) in the extreme limits of the last (ones) will be not in communication, like the ones that are multiplied into the first numbers.
Figure 4.8.1
Euclides, Geometria, Definition VII, 1; MS Paris, Latin 7374, fol. 77r; 13th century, a version related to Abelard of Bathâs translation
Bibliothèque nationale de France. Département des manuscrits
f. Hermann of Carinthia (VII, theorem 27):
Si duo numeri ad invicem sunt primi, quos uterque in se ipsum ductus producunt similiter ad invicem erunt primi. Itemque si in utrumque productorum suus utriusque submultiplex ducatur, ad invicem primos producent. Eoque pacto infinite eorum extremitates constabunt.27
If two numbers are mutually prime, those that they produce when each one of the two has been prolonged into itself will similarly be mutually prime. And equally, if each submultiple is prolonged into both of their products, they will produce mutually primes. If this is done infinitely, the extreme limits of them will be stable.
Symbols
| { } |
found in the extant manuscript tradition but rejected by the editor as spurious, that is, as not belonging to the genuine text |
Dodge, Fihrist of al-Nadīm, 2: 634.
Codex Leidensis 399,1, Pars I, 2, 4â5.
Dodge, Fihrist of al-Nadīm, 2: 634.
Euclides Elementa II, 103.
De Young, Arithmetic Books of Euclid, I.1, 2.
De Young, Arithmetic Books of Euclid, II.1, 4.
De Young, Arithmetic Books of Euclid, I.2, 318.
De Young, Arithmetic Books of Euclid, II.2, 285.
Adelard of Bath, First Latin Translation of Euclidâs Elements, 196.
Gerard of Cremona, The Latin Translation, c. 165.
Hermann of Carinthia, Translation of the Elements, 21.
Euclides Elementa II, 104.
De Young, Arithmetic Books of Euclid, I.1, 4.
De Young, Arithmetic Books of Euclid, II.1, 6.
De Young, Arithmetic Books of Euclid, I.2, 320.
De Young, Arithmetic Books of Euclid, II.2, 286.
Adelard of Bath, First Latin Translation of Euclidâs Elements, 196.
Gerard of Cremona, The Latin Translation, c. 165.
Hermann of Carinthia, Translation of the Elements, 21.
Euclides Elementa II, 133â134.
De Young, Arithmetic Books of Euclid, I.1, 80.
De Young, Arithmetic Books of Euclid, II.1, 71.
De Young, Arithmetic Books of Euclid, I.2, 392.
De Young, Arithmetic Books of Euclid, II.2, 355.
Adelard of Bath, First Latin Translation of Euclidâs Elements, 215.
Gerard of Cremona, The Latin Translation, c. 180.
Hermann of Carinthia, Translation of the Elements, 36.
Bibliography
Primary Texts
Adelard of Bath. The First Latin Translation of Euclidâs Elements Commonly Ascribed to Adelard of Bath. Edited by Hubertus L.L. Busard. Toronto: Pontifical Institute of Mediaeval Studies, 1983.
De Young, Gregg. The Arithmetic Books of Euclidâs Elements in the Arabic Tradition: An Edition, Translation, and Commentary. 4 vols. Unpublished PhD diss., Harvard University, 1981.
Euclid. Euclides Elementa II. Edited by Johannes Ludevig Heiberg and Evangelos S. Stamatis. Leipzig: Teubner, 1970.
Gerard of Cremona. The Latin Translation of the Arabic Version of Euclidâs Elements Commonly Ascribed to Gerard of Cremona. Introduction, Edition, and Critical apparatus. Edited by Hubertus L.L. Busard. Leiden: New Rhine Publishers, 1983.
Hermann of Carinthia (?). The Translation of the Elements of Euclid from the Arabic into Latin by Hermann of Carinthia (?) Books VIIâXII. Edited by Hubertus L.L. Busard. Amsterdam: Mathematisch Centrum, 1967.
Further Primary Sources
Codex Leidensis 399,1. Euclidis Elementa ex interpretatione al-Hadschdschadschii cum commentariis al-Narizii. Edited by R.O. Besthorn and J.L. Heiberg, Pars I, 2. Copenhagen: Libraria Gyldeniana, 1892.
Dodge, Bayard, ed., trans. The Fihrist of al-Nadīm: A Tenth-Century Survey of Muslim Culture. 2 vols. New York: Columbia University Press, 1970.