The purpose of this thesis is to examine the arithmetical portion of Theon of Smyrna's work entitled: [Greek title omitted] and to determine its significance in the study of the theory of numbers. The thesis comprises three main parts. The first is a brief introductory discussion of the biography of Theon with an attempt to establish his identity and works. Very little scholarly work has been devoted to Theon; what little could be found was dated for the most part in the second half of the nineteenth century, and in Greek mathematical works his activities have attracted little more than a passing mention. In my introductory chapter I have drawn exclusively from this secondary material. The second part of the study is a literal translation of the appropriate arithmetical section of the work. The third part consists of a commentary amounting to a simple exposition of the mathematical content. In a concluding chapter I have attempted to assign to Theon his place in the history of arithmetic and have given some indications of the reasons for his relative unimportance. / Arts, Faculty of / Classical, Near Eastern and Religious Studies, Department of / Graduate