Perhaps the ancient Greeks have taken the first step towards today´s ventilation, with its warming so-called hypocaust system (Greek: heat from below). The air was heated by wood burning ovens in the ground from where the hot smoke found its way out through the chimneys on the roof through channels in the floor and flues in walls. When the fire was out, one opened small floor shutters to release the hot air in the room.
It is doubtful that hypocaust system can be regarded as a ventilation system. Certainly brought the warm air to the rooms, but the air was both smoky, hot and probably quite unpleasant to inhale. This principle utilized that the warm air rises, however, it came in handy much later in more clear ventilation purposes.