Eudoxus of Cnidus (**Eudoxos ho Knidios; 408-355 BC**) was a Greek astronomer, mathematician, scholar and student of Plato. All of his works are lost, though some fragments are preserved in Hipparchus' commentary on Aratus's poem on astronomy. Theodosius of Bithynia's important work, Sphaerics, may be based on a work of Eudoxus.

Eudoxus is considered by some to be the greatest of classical Greek mathematicians, and in all antiquity second only to Archimedes. He rigorously developed Antiphon's method of exhaustion, a precursor to the integral calculus which was also used in a masterly way by Archimedes in the following century. In applying the method, Eudoxus proved such mathematical statements as: areas of circles are to one another as the squares of their radii, volumes of spheres are to one another as the cubes of their radii, the volume of a pyramid is one-third the volume of a prism with the same base and altitude, and the volume of a cone is one-third that of the corresponding cylinder.

Identifying the astronomical work of Eudoxus as a separate category is therefore a modern convenience. Some of Eudoxus' astronomical texts whose names have survived include:

- Disappearances of the Sun, possibly on eclipses

- Oktaeteris, on an eight-year lunisolar cycle of the calendar

- Phaenomena and Entropon, on spherical astronomy, probably based on observations made by Eudoxus in Egypt and Cnidus

- On Speeds, on planetary motions

Aristotle, in The Nicomachean Ethics attributes to Eudoxus an argument in favor of hedonism, that is, that pleasure is the ultimate good that activity strives for. According to Aristotle, Eudoxus put forward the following arguments for this position:

- All things, rational and irrational, aim at pleasure; things aim at what they believe to be good; a good indication of what the chief good is would be the thing that most things aim at.

- Similarly, pleasure's opposite ? pain ? is universally avoided, which provides additional support for the idea that pleasure is universally considered good.

- People don't seek pleasure as a means to something else, but as an end in its own right.

- Any other good that you can think of would be better if pleasure were added to it, and it is only by good that good can be increased.

Of all of the things that are good, happiness is peculiar for not being praised, which may show that it is the crowning good.

Many of the early commentators believed that Plato was the inspiration for Eudoxus's representation of planetary motion by his system of homocentric spheres. These view are still quite widely held but the article argues convincingly that this is not so and that the ideas which influenced Eudoxus to come up with his masterpiece of 3-dimensional geometry were Pythagorean and not from Plato.

As a final comment we should note that Eudoxus also wrote a book on geography called Tour of the Earth which, although lost, is fairly well known through around 100 quotes in various sources. The work consisted of seven books and studied the peoples of the Earth known to Eudoxus, in particular examining their political systems, their history and background. Eudoxus wrote about Egypt and the religion of that country with particular authority and it is clear that he learnt much about that country in the year he spent there. In the seventh book Eudoxus wrote at length on the Pythagorean Society in Italy again about which he was clearly extremely knowledgeable.

### Source: wikipedia

Eudoxus is considered by some to be the greatest of classical Greek mathematicians, and in all antiquity second only to Archimedes. He rigorously developed Antiphon's method of exhaustion, a precursor to the integral calculus which was also used in a masterly way by Archimedes in the following century. In applying the method, Eudoxus proved such mathematical statements as: areas of circles are to one another as the squares of their radii, volumes of spheres are to one another as the cubes of their radii, the volume of a pyramid is one-third the volume of a prism with the same base and altitude, and the volume of a cone is one-third that of the corresponding cylinder.

Identifying the astronomical work of Eudoxus as a separate category is therefore a modern convenience. Some of Eudoxus' astronomical texts whose names have survived include:

- Disappearances of the Sun, possibly on eclipses

- Oktaeteris, on an eight-year lunisolar cycle of the calendar

- Phaenomena and Entropon, on spherical astronomy, probably based on observations made by Eudoxus in Egypt and Cnidus

- On Speeds, on planetary motions

Aristotle, in The Nicomachean Ethics attributes to Eudoxus an argument in favor of hedonism, that is, that pleasure is the ultimate good that activity strives for. According to Aristotle, Eudoxus put forward the following arguments for this position:

- All things, rational and irrational, aim at pleasure; things aim at what they believe to be good; a good indication of what the chief good is would be the thing that most things aim at.

- Similarly, pleasure's opposite ? pain ? is universally avoided, which provides additional support for the idea that pleasure is universally considered good.

- People don't seek pleasure as a means to something else, but as an end in its own right.

- Any other good that you can think of would be better if pleasure were added to it, and it is only by good that good can be increased.

Of all of the things that are good, happiness is peculiar for not being praised, which may show that it is the crowning good.

Many of the early commentators believed that Plato was the inspiration for Eudoxus's representation of planetary motion by his system of homocentric spheres. These view are still quite widely held but the article argues convincingly that this is not so and that the ideas which influenced Eudoxus to come up with his masterpiece of 3-dimensional geometry were Pythagorean and not from Plato.

As a final comment we should note that Eudoxus also wrote a book on geography called Tour of the Earth which, although lost, is fairly well known through around 100 quotes in various sources. The work consisted of seven books and studied the peoples of the Earth known to Eudoxus, in particular examining their political systems, their history and background. Eudoxus wrote about Egypt and the religion of that country with particular authority and it is clear that he learnt much about that country in the year he spent there. In the seventh book Eudoxus wrote at length on the Pythagorean Society in Italy again about which he was clearly extremely knowledgeable.