Eudoxus of Cnidus
c. 408-c. 355 B.C.
Greek Astronomer and Mathematician
First to apply mathematics properly in the study of astronomy, Eudoxus also contributed directly to mathematical study with his theory of proportion and his method of exhaustion. In addition, he worked as a medical doctor, and gained renown as a philosopher and political writer. He also wrote a seven-volume description of his travels entitled Circuit of the Earth.
Born in the Greek colony of Cnidus in Asia Minor, Eudoxus came from a long line of physicians, and trained as doctor. By the age of 23, he had moved to Athens to work as a physicians' assistant, and while in the great city attended lectures by Plato (427-347 B.C.) at the latter's Academy. He then returned to Cnidus, where he completed his studies before going to Egypt with another physician.
It was there, at the observatory in Heliopolis along the Nile, that Cnidus discovered his second calling. As a physician, Eudoxus was accustomed to making detailed observations, one of the few areas in which ancient medicine excelled, and the record of data he compiled at Heliopolis was quite thorough. This he presented in the Phaenomena, a rather straightforward astronomical study containing lists of stars that rise or fall below the horizon at the beginning of each month, as well as locations for all constellations relative to one another.
Returning to Asia Minor with the new course of his career set, Eudoxus founded a school in the town of Cyzicus. There he wrote On Speeds, a much more important work than Phaenomena in which he presented a new theory of the motion made by the Sun, Moon, and planets. Given the spherical shape of Earth, Eudoxus imagined a series of concentric spheres around it, and eventually developed a description of 27 spheres necessary for picturing the movement of all known bodies.
The idea of the concentric spheres seems obvious today: hence people think of a planet's orbit around the Sun—though it is actually elliptical rather than circular—as taking place along the equator of an imaginary sphere. But in Eudoxus's time, this idea, which would eventually be represented physically in a variety of astronomical instruments, was far from obvious.
His theory of proportions and his method of exhaustion would later find their way into the Elements of Euclid (c. 325-c. 250 B.C.). According to Eudoxus, if a given object is larger than a second one, then its ratio to a third object will also be larger than the ratio of the second to the third—which again is a seemingly self-evident point from the perspective of the twenty-first century A.D., but was not so in the fourth century B.C. As for Eudoxus's method of exhaustion, Archimedes (c. 287-212 B.C.) wrote that he gave the first proofs of two propositions already known at the time: that the volume of a pyramid is one-third that of a prism with the same base and height, and that the same relationship is the case for a cone and cylinder.
Eudoxus moved to Athens, but when the people of Cnidus overthrew the oligarchy there and established a democracy, they asked him to come back and write a constitution for the new state. He then made his way home, where after completing his work for the government he founded an observatory and school. According to Aristotle (384-322 B.C.), Eudoxus also made a reputation for himself as a philosopher.
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