The Angle Trisection by Thābit ibn Qurra

Abstract

The text of the angle trisection by Thābit ibn Qurra (here denoted as C) is taken from Bibl. nat. ms. arab. (Slane) 2457, no. 45 (f. 192v-4r). Its first part is in verbatim agreement with the text on the hyperbola construction in Apollonius, Conies II, 4, as given in the 9th century Arabic recension of the work by Hilāl ibn Abī Hilāl al-Himsī and Thābit (cf. Sezgin, V, p. 139). The latter text is preserved in the Bodleian ms. Marsh 667; I denote it by C2 and indicate in the notes its differences from C. As for the remaining two sections of Thābit’s trisection, they stand in close agreement with the treatments by Pappus and Ahmad ibn Mūsā (see chap. B) as far as the geometric method is concerned, but differ considerably from the viewpoint of text. As indicated below, there are subtle signs that Thābit, like Ahmad, produced his version as a translation, rather than as an independent composition or paraphrase in Arabic.