Aristaeus the Elder

c. 370-c. 399 b.c.

Greek Mathematician

The details of Aristaeus the Elder's life are scanty, and the list of his writings—all of them lost—is in question. Some of this may be accounted for by a confusion with a figure of whom even less is known, if indeed he actually existed: Aristaeus the Younger. Of the elder Aristaeus, however, historians do know that he was among the originators of conics and conic section theory, a man judged a "worthy mathematician" by no less a figure than his contemporary Euclid (c. 325-c. 250 b.c.).

The few known facts about Aristaeus the Elder come from the writings of Pappus (fl. c. a.d. 320), who lived six centuries later. In his Treasury of Analysis, Pappus referred to Aristaeus as "the Elder," leading to the inference that there must have been another Aristaeus born later; but this is the only indication that the other Aristaeus ever lived.

In Pappus's time, copies of Five Books Concerning Solid Loci still existed, and the later author used this work as a resource when discussing Aristaeus's ideas. The curves, lines, and points of cones were the subject matter of the book, which Euclid later credited as the source for much of his own writing on conics in Book XIII of his Elements. (Indeed, the latter may represent a version of at least part of Aristaeus's Five Books, edited and greatly amended by Euclid.)

According to Hypsicles (c. 190-c. 120 b.c.), Aristaeus also wrote another book called Comparison of the Five Regular Solids, in which he supposedly developed a theorem later applied by Apollonius (c. 262-c. 190 b.c.) in introducing his own comprehensive theory of conic sections. Some historians, however, believe that Comparison was written by the hypothesized younger Aristaeus.

Adding to the confusion surrounding Aristaeus the Elder is the fact that the "five" in the title of that second work calls to mind the name of the Five Books. Even more reminiscent of the title of Aristaeus's one confirmed work, however, is the name Five Books of the Elements of Conic Sections. The latter is allegedly yet another book by Aristaeus, and if it existed, it may have been written to further elucidate concepts explored in Five Books Concerning Solid Loci.

Whatever the details of Aristaeus's life, career, and writings, it is certain that he held a high place in the history of Greek geometry prior to Euclid. With the latter and Apollonius, he is regarded as one of the leading figures in the development of methods for analyzing conic sections.

JUDSON KNIGHT