Arabic traces of lost works of Apollonius (Q1078545)

This article is an involved attempt to reconstruct some fragments of the minor Apollonian mathematical works, now lost in the original Greek, but which seem to have been translated into Arabic. The tenth-century Arabic works in which these fragments have survived are attributed to Ibrahim b. Sinan and to al-Sijzi, both reknowned geometricians of their time. In this article, the author supplies a detailed analysis of the relevant passages elucidating the Greek works and concludes by appending editions of the Arabic fragments in which the Greek texts have survived. The author then goes on to supply English translations of the fragments that he himself had edited, as well as the ones which were edited by others, notably by Dr. Saidan. The author concludes from this analysis that six minor works of Apollonius, namely the Cutting off of a ratio, Cutting off of an area, Tangencies, Determinate Section, Neusis and the Plane Loci, were either completely or partially translated into Arabic sometime during or before the tenth century. This reviewer has a great respect for the author's erudition in reconstructing the Greek texts, his ability to bring desparate material from both the Greek and the Arabic sources to bear on his reconstruction and for his success in making much more sense than what would first appear of passages that are embedded in other texts and which could have been very easily missed by more innocent readers. But this reviewer questions the author's approach to the Arabic texts when he attempts to edit them, for then the question of the real intent of the edition is not clear. One would assume that a critical edition of a text would normally supply the reader with a coherent text, well punctuated to determine the original contents of the text, and grammatically resolved to indicate the intended syntax. The author does not do any of that; instead he leaves the text without any punctuation, he leaves incorrect grammatical forms that occur in the text, and he even inserts some incorrect grammatical forms of his own. This reviewer fails to see the wisdom behind avoiding punctuating the Arabic text, when the English translation is itself punctuated. Once one punctuates the English, one has already determined the punctuation of the Arabic. To refuse to insert those punctuations that have determined the understanding of the text for which the English translation is supplied is to signal the reader that the Arabic text is still in a state of flux, and thus one should take the English translation as a tentative translation until the original Arabic text is critically edited. This reviewer does not think that the author wants to send this signal, for then he would have given a translation of the text only, without an attempt at the critical edition of the Arabic. Although this reviewer disagrees with the author's readings at certain points, and with his translations at various other points, he feels that he has essentially captured the original intention of the texts. For students of Greek and Arabic geometry in general, and for students of Apollonius in particular, this article offers many gems that should not be missed by any serious scholar. But the most important conclusion of this article, which is not so articulated by the author, is the light it sheds on the problems of the transmission of Greek Science into Arabic, as revealed in the attitude of the Muslim mathematicians who used these translations of Greek texts; in every case cited by him, the Greek texts seem to be embedded in other Arabic texts dealing with their own set of geometrical problems. The Arabic writers therefore seem to have been interested in the Greek texts for their own utilitarian purposes, and were obviously not possessed by any antiquarian interests. They seem to have thought of geometry as a global structure, and they would use whatever theorem or lemma that would help to complete the structure irrespective of the original context of the theorem or the lemma. In that sense they were using the Greek texts, and not simply transmitting them.