Eudemus of Rhodes

Born: about 350 BC in Rhodes, Greece
Died: about 290 BC

We should certainly credit Eudemus of Rhodes for his achievements in this archive since Eudemus seems to have been the first major historian of mathematics. Simplicius informs us that a biography of Eudemus was written by Damas, who is unknown but for this reference, but sadly no trace of this biography has been found. As exciting aspect of the history of mathematics is that the discovery of this text (and other lost texts) in the future, although highly unlikely, always remains a possibility.

Eudemus was born on Rhodes and we know that he had a brother called Boethus. Of his parents and early life we know nothing, but we do know that he studied with Aristotle. Aristotle spent time in Athens, Assos and other places and it would certainly be good to understand when Eudemus studied with him. Unfortunately there is no record either of time or of place which would let us answer these questions with any degree of certainty. W Jaeger, however, in his discussion of Aristotle [4] (see also [5]) has argued strongly that Eudemus studied with Aristotle during his period in Assos.

Aristotle had two followers, Eudemus and Theophrastus of Lesbos, who were known as his "companions". We should make it clear, however, that there was another philosopher called Eudemus associated with Aristotle, namely Eudemus of Cyprus and it was this other Eudemus after whom Aristotle named his famous text Eudemus. When Aristotle realised that he had only a short time left to live he chose his successor between his two companions, Eudemus and Theophrastus. He chose Theophrastus and it appears that Eudemus, although not unhappy with the decision, left Athens and set up his own school, probably back on his native Rhodes.

To say that Eudemus was not an original mathematician may be fair but just a little harsh, for we do know through Proclus that he wrote an original mathematical work called On the Angle. This work is lost so we are unable to judge its importance but it does seem likely to have been considerably less important than his works on the history of mathematics.

We know of three works on the history of mathematics by Eudemus, namely History of Arithmetic (two or more books), History of Geometry (two or more books), and History of Astronomy (two or more books).

The History of Arithmetic is known to us from only one reference to it in the writing of Porphyry. This reference tell us that the first book dealt with the Pythagorean idea of number and its interrelations with music.

The History of Geometry is the most important of the three mathematical histories of Eudemus. Although the work has not survived, it was available to many later writers who made heavy use of it. We are fortunate therefore that much of the knowledge that Eudemus had of the history of Greek mathematics before Euclid (it had to be before Euclid given the dates when Eudemus was writing) has reached us despite the fact that he book has not. In many of the articles in this archive we have quoted from accounts based on Eudemus. To illustrate with one example, the work of Hippocrates on the quadrature of lunes is only known to us through Eudemus's History of Geometry.

It is unclear exactly when the History of Geometry was lost. Paul Tannery (see for example [7]) believed that it was lost before the time of Pappus while others such as J L Heiberg have argued that Pappus and Eutocius both wrote with an open copy of Eudemus's History of Geometry in front of them.

The History of Astronomy again was heavily used by later writers and in exactly the same way as his geometry text, much information has survived in the works of others despite the loss of the original text. In particular Thales' eclipse prediction was described in Eudemus's work and we believe that Eudoxus's system of concentric spheres was first described there and later transmitted to us through the writing of Simplicius in the second century AD. Other topics in this book included [1]:-

... the cycle of the great year after which all the heavenly bodies are found in the same relative positions; the realisation by Anaximander that the earth is a heavenly body moving about the middle of the universe; the discovery by Anaximenes that the moon reflects the light of the sun and the explanation of lunar eclipses; and the inequality of the times between the solstices and the equinoxes.
We have described above the important contributions of Eudemus to mathematics. However he is even better known for his contribution to saving the work of Aristotle for posterity. But for Eudemus we might not have had access to the works of Aristotle for he used his own lecture notes, Aristotle's lecture notes and recollections from memory to produce volumes of Aristotle's work fit for publication.

One further work is definitely due to Eudemus, namely a work on Physics which was a treatise in four books following the work by Aristotle of the same title fairly closely. Simplicius had a copy of this work which he found very helpful in understanding Aristotle's Physics and perhaps this was precisely the role the Eudemus intended for the work. Another work by Eudemus was on logic, in fact he may well have written two logic books and he also wrote On Discourse.

Some works by Eudemus are harder to identify with Eudemus of Rhodes and may have been written by others with the same name. Certainly there are many references to a work on animals written by a certain Eudemus and one of the references certainly does refer to Eudemus of Rhodes. Since the work seems to have been a collection of fables about animals the subject matter seems too far removed from the serious, scientific and scholarly works which he certainly wrote. Perhaps more likely is a work on the poet Lindos. Since Lindos had connections with Rhodes the link makes this a more likely possibility.

Again there is a reference which seems to imply that Eudemus wrote a history of theology and again this seems highly probable. Many authors refer to Eudemus as the 'pious Eudemus' due to his belief in the 'contemplation of God'. This however may be due to editing by a later Christian who would have seen that clearly Eudemus meant 'contemplation of God' rather than what is much more likely what he wrote 'contemplation of Mind' and "corrected" the text accordingly!

Article by: J J O'Connor and E F Robertson

April 1999
MacTutor History of Mathematics