We mentioned above that the place where the ephebi received their gymnastic instruction, or practised on their own account, was the gymnasium. The gymnasia, of which every town possessed one or more, were not, like the wrestling schools, private undertakings on the part of gymnastic teachers, but State institutions. At Athens the two oldest institutions of the kind were the _Academy_ and the _Cynosarges_, at the foot of the _Lycabettos_, and in the time of Pericles the _Lyceum_ was added as a third; the gymnasium of Ptolemy was not built till the Hellenistic period. The originally simple structure and arrangement of these institutions became in the course of centuries more complicated and extensive; and, though the first gymnasia were probably not more than simple halls supported by columns, with a racecourse attached, in course of time other rooms were added, and also baths, since the gymnastic exercises rendered bathing immediately afterwards absolutely necessary. At the time of Plato a number of different rooms belonging to the gymnasia are mentioned, which show that even at that time these must have been very extensive. We cannot clearly tell, from the accounts of the Greek writers, how these rooms were arranged and connected, and the description given by Vitruvius of a gymnasium is but unsatisfactory, because in many points he is not clear in his expressions. Moreover, it does not give a general scheme, but only a particular description, and this may not refer to his own period, as has been generally assumed, since the Roman gymnasia were on a far more complicated plan than the one described by Vitruvius, but rather to an earlier period, though not the best.