The relations between different areas of knowledge have been a subject of interest to philosophers as well as to scientists and mathematicians from antiquity. While recent work in this direction has been largely concerned with the question whether one branch of knowledge (such as arithmetic) can be reduced to another (such as logic), the questions which exercised the Greek philosophers on these matters have a different starting point. Taking for granted that there are a number of distinct areas of knowledge, they proceeded to consider a variety of relations which they observed to hold among the sciences as they knew them; the question of the priority of one science to another is a recurrent theme. In fact, three sorts of orderings were noticed, and the associated conceptions of priority are interesting. Only one of them is the concern of the present paper, though, and I shall briefly describe the remaining two only for purposes of contrast.