Another important fact to be noted at the outset is the absence of the arch from Greek architecture.  It is reported by the Roman philosopher, Seneca, that the principle of the arch was “discovered” by the Greek philosopher, Democritus, who lived in the latter half of the fifth century B. C. That he independently discovered the arch as a practical possibility is most unlikely, seeing that it had been used for ages in Egypt and Mesopotamia; but it may be that he discussed, however imperfectly, the mathematical theory of the subject.  If so, it would seem likely that he had practical illustrations about him; and this view receives some support from the existence of a few subterranean vaults which perhaps go back to the good Greek period.  Be that as it may, the arch plays absolutely no part in the columnar architecture of Greece.  In a Greek temple or similar building only the flat ceiling was known.  Above the exterior portico and the vestibules of a temple the ceiling was sometimes of stone or marble, sometimes of wood; in the interior it was always of wood.  It follows that no very wide space could be ceiled over without extra supports.  At Priene in Asia Minor we find a temple (Fig. 49) whose cella, slightly over thirty feet in breadth, has no interior columns.  The architect of the Temple of Athena on the island of AEgina (Fig. 52) was less venturesome.  Although the cella there is only 21 1/4 feet in breadth, we find, as in large temples, a double row of columns to help support the ceiling.  And when a really large room was built, like the Hall of Initiation at Eleusis or the Assembly Hall of the Arcadians at Megalopolis, such a forest of pillars was required as must have seriously interfered with the convenience of congregations.  We are now ready to study the plan of a Greek temple.  The essential feature is an enclosed chamber, commonly called by the Latin name cella, in which stood, as a rule, the image of the god or goddess to whom the temple was dedicated.  Fig. 47 shows a very simple plan.  Here the side walls of the cella are prolonged in front and terminate in antae (see below, page 88).  Between the antae are two columns.  This type of temple is called a templum in antis.  Were the vestibule (pronaos) repeated at the other end of the building, it would be called an opisthodomos, and the whole building would be a double templum in antis.  In Fig. 48 the vestibules are formed by rows of columns extending across the whole width of the cella, whose side walls are not prolonged.  Did a vestibule exist at the front only, the temple would be called prostyle; as it is, it is amphiprostyle.  Only small Greek temples have as simple a plan as those just described.  Larger temples are peripteral, i.e., are surrounded by a colonnade or peristyle (Figs. 49. 50).  In Fig. 49 the cella with its vestibules has the form of a double templum in antis, in Fig 50 it is amphiprostyle.  A further difference should be noted.  In Fig. 49, which is the plan of an Ionic temple, the antae and columns of the vestibules are in line with columns of the outer row, at both the ends and the sides; in Fig. 50, which is the plan of a Doric temple, the exterior columns are set without regard to the cella wall, and the columns of the vestibules.  This is a regular difference between Doric and Ionic temples, though the rule is subject to a few exceptions in the case of the former.