The terms antipodes and antichthones, along with others such as antoikoi and perioikoi, referred to hypothetical peoples dwelling beyond the extent of the known world. These terms were the product of a mathematically based astronomy in which the spherical nature of the Earth was a fundamental element. Calculations of the size of the Earth resulted in the conjecture that inhabited land existed beyond the known world of Asia, Europe, and Africa/Libya. Such land was usually thought to be inaccessible owing to the expanse of Ocean, or because of the extremes of heat and cold found, respectively, at the Equator and the poles.The concept of the antipodes appears to have emerged from Pythagorean thought. Pythagoras was credited with the doctrine that inhabitation was not restricted to the known world, and specifically that there were inhabitants on the opposite side of the Earth, whose “down” was “up” for those in the known world; certain Pythagoreans conceived of an antichthon, or counter-Earth, in relation to the known world (Diog. Laert., Vitae Philosophorum 8.
Apollonius (3) (3rd cent. bce) served *Ptolemy (1) II as chief minister (dioikētēs) in Egypt and is best known as holder of a 10,000-aroura (2,750-ha: 6,800-acre) crown-gift estate near Philadelphia (1) in the *Fayūm. This estate formed the centre of a series of agricultural experiments (in *arboriculture, viticulture, crops, and livestock) and was managed by Zenon, a Carian immigrant from *Caunus, who came to the Fayūm in 256 and stayed on in the area after leaving Apollonius' service in 248/7. The collection of Zenon's papyri is the largest from the period and is now scattered throughout European and North American collections. It illustrates these and Apollonius' other interests: *textile-manufacturing at *Memphis, his contacts in *Alexandria (1), and commercial dealings, including slave-trading, in the Levant (see slavery).
Evidence for Greek and Roman artillery comes from the surviving technical treatises, incidental historical and subliterary references, and, most importantly, finds of both machine-fittings and projectiles. The latter at present date from the 2nd cent. bce to the 4th cent. ce.In 399 bce artificers of *Dionysius (1) I apparently invented the first artillery piece (Diod. Sic. 14. 42. 1). The gastraphetēs shot arrows only, and somewhat resembled an early medieval crossbow. Propulsion force was supplied by a composite bow, which, being too powerful for a man to draw by hand, was bent by means of a slide and stock. Later gastraphetai, some of which were stone-throwers, used a winch and had a stand. Torsion catapults appeared around 340 bce, possibly invented by *Philip (1) II's engineers. Stock, winch, and base remained much the same, but two springs, bundles of rope made from animal sinew and held at high tension in a metal-plated wooden frame, now provided propulsive power. Torsion machines improved continuously in efficiency through the Roman period. From c.