罗德岛的欧德摩斯Eudemus of Rhodes

我们当然应该在这个档案中赞扬罗德岛的欧德摩斯的成就，因为罗德岛的欧德摩斯似乎是第一位重要的数学史家。西里西亚的辛普利修斯告诉我们，罗德岛的欧德摩斯的传记是由达马斯撰写的，除了这个引用外，达马斯不为人知，但遗憾的是，没有找到这部传记的任何痕迹。数学史的一个令人兴奋的方面是，未来发现这个文本（以及其他丢失的文本），尽管极不可能，但始终是一种可能性。

罗德岛的欧德摩斯出生于罗德岛的欧德摩斯，我们知道他有一个名叫博伊修斯的兄弟。关于他的父母和早年生活，我们一无所知，但我们确实知道他师从亚里士多德。亚里士多德在雅典、阿索斯和其他地方度过时光，了解罗德岛的欧德摩斯何时师从他当然会很好。不幸的是，没有时间或地点的记录能让我们以任何程度的确定性回答这些问题。然而，W·耶格尔在他对亚里士多德 [4]的讨论中（另见[5]）强烈主张，罗德岛的欧德摩斯在阿索斯期间师从亚里士多德。

亚里士多德有两个追随者，罗德岛的欧德摩斯和Theophrastus of Lesbos，被称为他的“同伴”。然而，我们应该明确，还有另一位与亚里士多德相关的哲学家叫罗德岛的欧德摩斯，即塞浦路斯的罗德岛的欧德摩斯，正是这位另一位罗德岛的欧德摩斯，亚里士多德以其命名了他的著名文本Eudemus。当亚里士多德意识到自己只剩下很短的时间可活时，他在他的两个同伴罗德岛的欧德摩斯和泰奥弗拉斯托斯之间选择了他的继承人。他选择了泰奥弗拉斯托斯，看来罗德岛的欧德摩斯虽然对这个决定并不不满，但离开了雅典并建立了自己的学派，可能回到了他的故乡罗德岛的欧德摩斯。

说罗德岛的欧德摩斯不是一位原创数学家可能公平但有点苛刻，因为我们确实通过普罗克洛知道他写了一部原创数学著作，名为On the Angle。这部著作已丢失，因此我们无法判断其重要性，但它似乎很可能远不如他关于数学史的著作重要。

我们知道罗德岛的欧德摩斯有三部关于数学史的著作，即History of Arithmetic（两部或更多卷）、History of Geometry（两部或更多卷）和History of Astronomy（两部或更多卷）。

我们仅通过波菲利著作中的一处提及才知道History of Arithmetic。这处提及告诉我们，第一卷讨论了毕达哥拉斯的数观念及其与音乐之间的相互关系。

History of Geometry是罗德岛的欧德摩斯三部数学史著作中最重要的一部。尽管该著作未能流传下来，但许多后来的作者都能获得它并大量使用。因此我们很幸运，尽管该书未能留存，但罗德岛的欧德摩斯在欧几里得之前所掌握的关于希腊数学史的大量知识（鉴于罗德岛的欧德摩斯写作的年代，这必然在欧几里得之前）还是传到了我们手中。在本档案的许多文章中，我们引用了基于罗德岛的欧德摩斯的记述。举一个例子，希俄斯的希波克拉底关于lunes的求积的著作，我们仅通过罗德岛的欧德摩斯的History of Geometry才知道。

History of Geometry究竟何时失传尚不清楚。保罗·塔内里（例如参见[7]）认为它在帕普斯时代之前就已失传，而另一些人如J L Heiberg则主张，帕普斯和阿什凯隆的欧托基奥斯写作时面前都摊着一本罗德岛的欧德摩斯的History of Geometry。

History of Astronomy 再次被后来的作者大量使用，而且方式与他的几何学文本完全相同，尽管原始文本丢失，大量信息仍在其他人的著作中保存下来。特别是 泰勒斯 的日食预测在 罗德岛的欧德摩斯 的著作中有描述，我们相信 欧多克索斯 的 同心球 体系首次在那里被描述，后来通过公元二世纪 西里西亚的辛普利修斯 的著作传给我们。这本书中的其他主题包括 [1]：-

……大年周期，即所有天体再次处于相同相对位置的周期；阿那克西曼德认识到地球是一个在宇宙中央附近运动的天体；Anaximenes发现月球反射太阳的光并解释了月食；以及solstices与二分点之间时间的不等。

我们在上文描述了罗德岛的欧德摩斯对数学的重要贡献。然而，他更为人所知的是他为后世保存亚里士多德著作所作的贡献。若不是罗德岛的欧德摩斯，我们可能无法接触到亚里士多德的著作，因为他利用自己的讲课笔记、亚里士多德的讲课笔记以及凭记忆的回忆，整理出了适合出版的亚里士多德著作卷册。

还有一部著作肯定出自罗德岛的欧德摩斯之手，即一部关于Physics的著作，这是一部四卷本的论著，相当紧密地追随亚里士多德的同名著作。西里西亚的辛普利修斯有一本这部著作的抄本，他发现它在理解亚里士多德的Physics时非常有用，也许这正是罗德岛的欧德摩斯为这部著作所设想的用途。罗德岛的欧德摩斯的另一部著作是关于逻辑的，事实上他很可能写了两部逻辑书，他还写了On Discourse。

罗德岛的欧德摩斯的某些著作较难与罗德岛的欧德摩斯对应起来，可能出自同名的其他人之手。当然，有许多文献提到某位罗德岛的欧德摩斯写的一部关于动物的著作，其中一篇文献确实指的是罗德岛的欧德摩斯。由于这部著作似乎是一部关于动物的寓言集，其主题似乎与他确实写过的严肃、科学和学术著作相去甚远。更可能的是关于诗人Lindos的一部著作。由于Lindos与罗德岛的欧德摩斯有联系，这一关联使这种可能性更大。

同样，有一处文献似乎暗示罗德岛的欧德摩斯写了一部神学史，这同样似乎极有可能。许多作者称罗德岛的欧德摩斯为“虔诚的罗德岛的欧德摩斯”，因为他信奉“对神的沉思”。然而，这可能是后来一位基督徒编辑所致，他显然会认为罗德岛的欧德摩斯意指“对神的沉思”，而不是更可能他所写的“对心灵的沉思”，并据此“修正”了文本！

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!