The subject matter of this chapter should be placed normally among the issues treated in the previous chapter, dealing with Greek Algebra (and Logistic). Its separate treatment is due to the fact that the history of fractions has recently become a topic of independent study among historians of ancient mathematics, though a comprehensive book on the topic does not yet exist, as Jim Ritter points out in his introduction of the collective work Histoire des fractions, ">fraction d'histoire.¹ This bibliographic lacuna is particularly notable for the period from the end of the Middle Ages until the utilization and popularization of techniques involving decimal fractions in Western Europe at the end of the sixteenth century. With respect to Antiquity the gap is less significant, though the disagreement among historians as to the appropriate criteria of what constitutes a fraction leaves room for simplistic views, which, in particular, occurred frequently in the works of the older historiography.