Über die überlieferung der elemente Euklids über die länder des nahen ostens nach West-Europa

AbstractIn this paper I show how the Elements of Euclid was transmitted to Western Europe via the countries of the Middle East. Since Campanus had used not only an Adelard II text for his edition, but also works of his contemporaries and a Greek edition, we shall first turn our attention to the Latin translations from the Arabic of Adelard I and II, Hermann of Carinthia and Gerard of Cremona. The most important Arabic editions are those of al-Ḣaǧǧāǧ I and II and IsḢq-Tābit. In sections 1.1 and 1.2 I point out the differences between these Arabic editions and in section 1.3 I pose that Adelard I and Hermann of Carinthia go back to an al-Ḣaǧǧāǧ I text, Adelard II however to an al-Ḣaǧǧāǧ II text. In section 1.4 I show that there is a great resemblance between a Syriac fragment, al-Ḣaǧǧāg I and Adelard I. I cannot answer however the question whether al-Ḣaǧǧāǧ borrowed his version from a Syriac one or conversely. In section 1.5 I investigated the Gerard edition. On the whole Gerard follows the Isḣāq-Ṫābit edition, but he or his Arabic ancestor inserted proofs of al-Ḣǧǧāǧ I. According to an-Nayrīzī the propositions VIII.25 and 26, which are missing in the Greek Euclid and in the al-Ḣaǧǧāǧ versions, are from Heron. In chapter 2 I pose the question: What can the Arabic-Latin tradition teach us about the Greek edition of Heiberg. Heiberg III.12 has to be removed since an-Nayrīzī said it was of Heron. Health has said that all porisms are omitted in the Arabic except the porisms to VI.8, VIII.2 and X.3. This is not true since in the explicit of some Adelard II MSS 11 porisms have been mentioned, which are all in the text. Moreover, the Syriac fragment, Adelard I, Hermann and Gerard contain the porism I.15 which is missing in the Heiberg edition. In section 2.3 I show that of the Heiberg lemmas to X.32, 41 and XIII.18 the first is ascribed to Iohanicius Babiloniensis by Gerard and the second to Iezidi; Gerard inserted the third in the scholia, which he has added to his edition. So all these lemmas have to be cancelled. In the last section I state that the proofs of X.68–70 diverge totally from Heiberg and al-Haǧǧāǧ I. I cannot solve however the question which proofs are euclidean. In appendix I I give the text of the lemma to X.32 and in appendix II those of the lemma to X.41