Title page of MS Uppsala – O Vet 20

The Arabic manuscripts of the Elements

The extant manuscripts were classified into two groups by J. W. Engroff, in his Ph. D. dissertation at Harvard: The Arabic Tradition of Euclid's Elements: Book V, Cambridge 1980. Generally speaking, "Group A" are those MSS that seem to preserve or at least contain elements from the earlier, al-Ḥaǧǧāǧ-tradition, and "Group B" do not present these features. Please note, however, that all extant manuscripts represent the Isḥāq-Thābit tradition, and no manuscript preserves any of the two early translations by al-Ḥaǧǧāǧ. There are a number of minor and not-so-minor differences between the two groups, which will be presented below. The remarks given here are based on various publications mentioned in the bibliography.

We will first list the MSS, and append a more detailed discussion below.

Group A manuscripts

Group A 1

This group has before the definitions 13 and 14 in book VII (= the Greek definitions 12 and 14) the phrase min iṣlāḥ thābit, which suggests that these two definitions were not part of Isḥāq's version, but later added by Thābit.

  • MS Copenhagen LXXXI
  • MS Istanbul, Fātiḥ 3439/1

Group A 2

  • MS Teheran, Majlis Shūra 200
  • MS Rampur, ‘Arshī 200
  • MS Chester Beatty 3035

(Group A 3)

Definitions 13 and 14 in book VII (= Greek 12 and 14) are absent.

  • MS Escurial, arabe 907

Group B manuscripts

Group B 1

  • MS Oxford, Bod. Lib., Thurston 11
  • MS Uppsala Univ., O. Vet. 20

Group B 2

  • MS Oxford, Bod. Lib., Huntington 435
  • MS Cambridge Univ., add. 1035

Other MSS

Manuscripts discovered or described after the publication of Engroff's thesis, for which an assignment to any of the groups is not possible (for us) at this stage.

  • MS Leningrad, Akademia Nauk ms. C 2145
  • MS Teheran, Malik 3586 (the oldest MS, dated AD 945)
  • Another 10 manuscripts are known, making up a total of 22 MSS (not counting MSS of commentaries, etc – see below)

MSS and editions of commentaries containing the text or part of it

  • al-Nayrīzī's commentary, before early 10th century (MS Leiden 399,1 and MS Qom 6526). It has been edited in: Codex Leidensis 399,1. Euclidis Elementa ex interpretatione al-Hadschdschadschii cum commentariis al-Narizii. Arabice et latine editerunt notisque instruxerunt R. O. Besthorn et J. L. Heiberg, 1897-1905. There is also a reprint, Frankfurt am Main : Institute for the History of Arabic-Islamic Science, 1997.
  • An anonymous commentary, possibly not later than the 11th century (MS Hyderabad SLC, riyāḍī 2 and MS Osmania University Library, 375).

Differences between the groups

We should note the remark of De Young that "the membership of Group A and Group B is not constant." At the beginning of book VIII (or somewhere earlier in book VII??), most Group A manuscripts merge with Group B, except the subgroup A 1 listed above. Then, "with proposition 18 of book VIII, all merge to form a single textual tradition for the remainder of the arithmetical books. The simplest explanation for these changing alignments is that, at an early date, the prototype for the second subfamily of manuscripts in Group A was defective and the remainder of the text was supplied from a prototype for Group B." (De Young 1984: 152)

Furthermore, our present knowledge of the transmission history of the Arabic texts is still very incomplete. Worse still is the fact that earlier judgements on the relationship between the various MSS rests on incomplete evidence: "Looking at the opinions about the different versions connected with the Arabic transmission of the Elements developed since the late nineteenth century, one finds that there is hardly an opinion that has not been contradicted. Considering the contaminated character of most preserved texts, however, it is not to be expected that an evaluation which might be correct for one theorem must be valid for the book in which it is found and that what is correct for one book must be the case for the Elements as a whole." (Brentjes 1996: 205)

Terminological differences