Abstract

If one wishes to understand medieval philosophical descriptions of the nature of the various sciences, a familiarity with the scientific knowledge possessed at that time is necessary. An excellent example of the basic characteristics of medieval mathematics can be found in this critical edition of De numeris datis. The work itself is the first advanced algebra text produced in Western Europe. It is a study of the general methods of solving problems for unknown numbers if one knows, is given, other numbers and the relationships between them. Although the mathematical ideas Jordanus presents will be familiar to readers of this book, their development differs from that of contemporary algebra. The differences illuminate the medieval approach to mathematics. Medieval mathematicians approached this sort of problem by starting with the known numbers and working through to the unknown rather than concentrating on manipulation of the unknown variables as is done in modern approaches to mathematics. Medieval mathematics also viewed numbers as semi-geometric things. Solutions to algebraic problems were often seen in terms of geometric approaches to the areas and sides of rectangles. In this work Jordanus follows a more "algebraic" approach, but this approach did not replace the dominant medieval geometric approach to mathematics. In fact, as Hughes notes, the marginal notations in later copies of the work are usually geometric diagrams of the concepts. One can read such statements about medieval mathematics easily enough, but if one reads medieval mathematical thought in its original form the sort of thinking involved in medieval mathematics is much clearer. Such a background is useful in interpreting the descriptions writers like Aquinas offer of the nature of mathematics.