The Cube Duplication by Abū Bakr al-Harawī

Abstract

The text of the cube duplication by Abū Bakr al-Harawī (here denoted as A) is taken from the Bibliothèque nationale ms. arabe (Slane) 2457, f. 194r–195r, where it appears as an appendix to the angle trisection by Thàbit ibn Qurra (ibid., no. 45; see chap. C). For purposes of comparison I have set it in parallel with portions of the two versions of the Philonian neusis method given by John Philoponus in his commentary on the Posterior Analytics. One of these (denoted PK) is there attributed to Apollonius, while the other (PJ) is unattributed; I also indicate certain points of resemblance with another of John’s methods (AJ), equivalent to the Heronian neusis, but which he assigns to Apollonius. Detailed surveys of AJ and of PJ and PK, in the context of related texts, have already been given in Part I, chaps. 1 and 3. My subdivision of the present texts, as indicated by letters in square brackets, conforms with that adopted in those chapters. In view of the particularly strong affinity of A with PK, I have chosen to include with the transcription of A a facsimile of the latter (denoted A2), from Heiberg’s edition of Apollonius, II, pp. 105–107. This text is taken by Heiberg from the Aldine (1534) edition of Philoponus, and is also reproduced in the apparatus of M. Wallies’ edition (CAG 13, pt. 3, p. 105n). Line references in A correspond to the Paris manuscript, also reproduced here in facsimile.