The Use of Analogy in Book VII of Apollonius’ Conica

Abstract

ArgumentApollonius of Perga’s Conica, like almost all Greek mathematical works, relies heavily on the use of proportion, of analogia. Analogy as the assertion of a resemblance, however, also plays a role in the Conica. The homologue, which Apollonius introduces in Book VII, is a striking example of analogia in both senses. On the one hand, the homologue is defined by means of a precise proportion relating the diameter and latus rectum of a conic section to fixed segments along the diameter. On the other hand, Apollonius’ use of the homologue in Book VII makes it clear that he meant it truly to evoke the latus rectum in the reader’s mind; in this way, Apollonius treats the homologue as an image of the latus rectum. The example of the homologue thus suggests the possibility that, in Greek mathematics, proportion was not only a vital manipulatory tool but also a means of making images.