Books IV to VII of Diophantus’ Arithmetica : in the Arabic Translation Attributed to Qustā ibn Lūqā One: Introduction I. The Four Arabic Books and the Arithmetica II. The Extant Arabic Text III. Tentative Reconstruction of the History of the Arithmetica Two: Translation Book IV Book V Book VI Book VII Three: Mathematical Commentary Book IV Book V Book VI Book VII Four: Text Book IV Book V Book VI Book VII Five: Arabic Index General Index. 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 Macanls 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.