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Nothing from Eudoxus is extant (unless we count a poem that paraphrases some of his astronomical work).

Since he is often cited as the originator of both the theory of proportions found in book 5 of the Elements, and of the method of exhaustion, my question is

What is the justification for this claim?

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  • $\begingroup$ The first item is probably based on the Eudemian summary (Eudemus ca. 330 B.C. via Proclus 412-485): " Eudoxus of Cnidus, a little later than Leon and a student of the Platonic school, first increased the number of general theorems, added to the three proportions three more, and raised to a considerable quantity the learning, begun by Plato, on the subject of the (golden) section, to which he applied the analytical method. " This translation is from James Gow, A Short History of Greek Mathematics, Cambridge University Press 1884, p. 136. $\endgroup$
    – njuffa
    Commented Apr 24, 2023 at 3:18
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    $\begingroup$ A scholium to Book V (on p. 280 of vol. 5 of Heiberg & Menge's edition of Euclid's Opera Omnia) contains the phrase "τὸ δὲ βιβλίον Εὐδόξου τινὲς εὕρεσιν εἶναι λέγουσι", i.e. "some say that the book is a discovery/invention of Eudoxus". $\endgroup$
    – Alexander Campbell
    Commented Apr 24, 2023 at 6:16
  • $\begingroup$ As for the method of exhaustion, I have found multiple statements in the literature that it was Archimedes who attributed it to Eudoxus, but none of the authors provides a reference to a specific work by Archimedes to back up this assertion. $\endgroup$
    – njuffa
    Commented Apr 24, 2023 at 9:32
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    $\begingroup$ The introduction to Archimedes, On the Sphere and Cylinder, 225 BC, makes reference to Eudoxus in a matter related to the method of exhaustion, without however making explicit mention of the method used: " those theorems of Eudoxus on solids which are held to be most irrefragably established, namely ... that any cone is one third part of the cylinder which has the same base with the cone and equal height. For, though these properties also were naturally inherent in the figures all along, yet they were in fact unknown to all the many able geometers who lived before Eudoxus ... " $\endgroup$
    – njuffa
    Commented Apr 24, 2023 at 10:10

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