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. Hypsicles (second half of second century B. C.) wrote what became known as 'Book XIV' of the _Elements_ containing supplementary propositions on the regular solids (partly drawn from Aristaeus and Apollonius); he seems also to have written on polygonal numbers. A mediocre astronomical work (Αναφορικος {Anaphorikos}) attributed to him is the first Greek book in which we find the division of the zodiac circle into 360 parts or degrees. Posidonius the Stoic (about 135-51 B. C.) wrote on geography and astronomy under the titles _On the Ocean_ and περι μετεωρων {peri meteôrôn}. He made a new but faulty calculation of the circumference of the earth (240,000 stades). _Per contra_, in a separate tract on the size of the sun (in refutation of the Epicurean view that it is as big as it _looks_), he made assumptions (partly guesswork) which give for the diameter of the sun a figure of 3,000,000 stades (39-1/4 times the diameter of the earth), a result much nearer the truth than those obtained by Aristarchus, Hipparchus, and Ptolemy. In elementary geometry Posidonius gave certain definitions (notably of parallels, based on the idea of equidistance).