A History of Greek Mathematics and Astronomy

Page 26

In astronomy Apollonius is said to have made special researches regarding the moon, and to have been called ε {e} (Epsilon) because the form of that letter is associated with the moon. He was also a master of the theory of epicycles and eccentrics.

With Archimedes and Apollonius Greek geometry reached its culminating point; indeed, without some more elastic notation and machinery such as algebra provides, geometry was practically at the end of its resources. For some time, however, there were capable geometers who kept up the tradition, filling in details, devising alternative solutions of problems, or discovering new curves for use or investigation.

Nicomedes, probably intermediate in date between Eratosthenes and Apollonius, was the inventor of the conchoid or cochloid, of which, according to Pappus, there were three varieties. Diocles (about the end of the second century B. C.) is known as the discoverer of the cissoid which was used for duplicating the cube. He also wrote a book περι πυρειων {peri pyreiôn}, On burning-mirrors, which probably discussed, among other forms of mirror, surfaces of parabolic or elliptic section, and used the focal properties of the two conics; it was in this work that Diocles gave an independent and clever solution (by means of an ellipse and a rectangular hyperbola) of Archimedes's problem of cutting a sphere into two segments in a given ratio. Dionysodorus gave a solution by means of conics of the auxiliary cubic equation to which Archimedes reduced this problem; he also found the solid content of a tore or anchor-ring.

Perseus is known as the discoverer and investigator of the spiric sections, i. e. certain sections of the σπειρα {speira}, one variety of which is the tore. The spire is generated by the revolution of a circle about a straight line in its plane, which straight line may either be external to the circle (in which case the figure produced is the tore), or may cut or touch the circle.

Zenodorus was the author of a treatise on Isometric figures, the problem in which was to compare the content of different figures, plane or solid, having equal contours or surfaces respectively.

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T. L. Heath
A History of Greek Mathematics and Astronomy

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T. L. Heath A History of Greek Mathematics and Astronomy

Learned Freeware

T. L. Heath
A History of Greek Mathematics and Astronomy