Books IV to VII of Diophantus’ Arithmetica: in the Arabic Translation Attributed to Qustā ibn Lūqā (Sources in the History of Mathematics and Physical Sciences, 3)

This edition of Books IV to VII of Diophantus' Arithmetica, which are extant only in a recently discovered Arabic translation, is the outgrowth of a doctoral dissertation submitted to the Brown University Department of the History of Mathematics in May 1975. Early in 1973, my thesis adviser, Gerald Toomer, learned of the existence of this manuscript in A. Gulchln-i Macanl's just-published catalogue of the mathematical manuscripts in the Mashhad Shrine Library, and secured a photographic copy of it. In Sep­ tember 1973, he proposed that the study of it be the subject of my dissertation. Since limitations of time compelled us to decide on priorities, the first objective was to establish a critical text and to translate it. For this reason, the Arabic text and the English translation appear here virtually as they did in my thesis. Major changes, however, are found in the mathematical com­ mentary and, even more so, in the Arabic index. The discussion of Greek and Arabic interpolations is entirely new, as is the reconstruction of the history of the Arithmetica from Diophantine to Arabic times. It is with the deepest gratitude that I acknowledge my great debt to Gerald Toomer for his constant encouragement and invaluable assistance. Front Matter....Pages i-xii Front Matter....Pages 1-1 The Four Arabic Books and the Arithmetica ....Pages 3-20 The Extant Arabic Text....Pages 21-47 Tentative Reconstruction of the History of the Arithmetica ....Pages 48-84 Front Matter....Pages 85-86 Fourth Book of the Treatise of Diophantus on Squares and Cubes....Pages 87-125 Fifth Book of the Treatise of Diophantus the Alexandrian on Arithmetical Problems....Pages 126-138 Sixth Book of the Treatise of Diophantus....Pages 139-155 Seventh Book of the Treatise of Diophantus....Pages 156-171 Front Matter....Pages 173-173 Book IV....Pages 175-222 Book V....Pages 223-243 Book VI....Pages 244-260 Book VII....Pages 261-279 Front Matter....Pages 281-282 Book IV....Pages 283-351 Book V....Pages 352-373 Book VI....Pages 374-402 Book VII....Pages 403-429 Back Matter....Pages 431-502