Euclid, Elements
Thomas L. Heath, Sir Thomas Little Heath, Ed.

must have known Greek as well as his father, made his translation direct from the Greek. The revision must apparently have been the subject of an arrangement between Is[hnull ]āq and Thābit as the latter died in 901 or nine years before Is[hnull ]āq. Thābit undoubtedly consulted Greek MSS. for the purposes of his revision. This is expressly stated in a marginal note to a Hebrew version of the Elements, made from Ishāq's, attributed to one of two scholars belonging to the same family, viz. either to Moses b. Tibbon (about 1244-1274) or to Jakob b. Machir (who died soon after 1306)¹. Moreover Thābit observes, on the proposition which he gives as IX. 31, that he had not found this proposition and the one before it in the Greek but only in the Arabic; from which statement Klamroth draws two conclusions, (1) that the Arabs had already begun to interest themselves in the authenticity of the text and (2) that Thābit did not alter the numbers of the propositions in Ishāq's translation². The Fihrist also says that Yu[hnull ]annā al-Qass (i.e. “the Priest” ) had seen in the Greek copy in his possession the proposition in Book I. which Thābit took credit for, and that this was confirmed by Na[znull ]īf, the physician, to whom Yuhannā had shown it. This proposition may have been wanting in Ishāq, and Thābit may have added it, but without claiming it as his own discovery³. As a fact, I. 45 is missing in the translation by al-[Hnull ]ajjāj.

The original version of Is[hnull ]āq without the improvements by Thābit has probably not survived any more than the first of the two versions by al-Hajjāj; the divergences between the MSS. are apparently due to the voluntary or involuntary changes of copyists, the former class varying according to the degree of mathematical knowledge possessed by the copyists and the extent to which they were influenced by considerations of practical utility for teaching purposes⁴. Two MSS. of the Ishāq-Thābit version exist in the Bodleian Library (No. 279 belonging to the year 1238, and No. 280 written in 1260-1)⁵; Books I.—XIII. are in the Is[hnull ]āq-Thābit version, the non-Euclidean Books XIV., XV. in the translation of Qustā b. L'ūqā al-Ba`labakkī (d. about 912). The first of these MSS. (No. 279) is that (O) used by Klamroth for the purpose of his paper on the Arabian Euclid. The other MS. used by Klamroth is (K) Kjobenhavn LXXXI, undated but probably of the 13th c., containing Books V.—XV., Books V.—X. being in the Is[hnull ]āq-Thābit version, Books XI.—XIII. purporting to be in al-Hajjāj's translation, and Books XIV., XV. in the version of Qus[tnull ]ā b. Lūqā. In not a few propositions K and O show not the slightest difference, and, even where the proofs show considerable differences, they are generally such that, by a careful comparison, it is possible to reconstruct the common archetype, so that it is fairly clear that we have in these cases, not two recensions of one translation, but arbitrarily altered and