Ipsius autem theatri conformatio sic est facienda, uti, quam magna futura est perimetros imi, centro medio collocato circumagatur linea rutundationis, in eaque quattuor scribantur trigona paribus lateribus; intervallis extremam lineam circinationis tangant, quibus etiam in duodecim signorum caelestium astrologia ex musica convenientia astrorum ratiocinantur. ex his trigonis cuius latus fuerit proximum scaenae, ea regione, qua praecidit curvaturam circinationis, ibi finiatur scaenae frons, et ab eo loco per centrum parallelos linea ducatur, quae disiungat proscaenii pulpitum et orchestrae regionem. ita latius factum fuerit pulpitum quam Graecorum, quod omnes artifices in scaena dant operam, in orchestra autem senatorum sunt sedibus loca designata. et eius pulpiti altitudo sit ne plus pedum quinque, uti, qui in orchestra sederint, spectare possint omnium agentium gestus. cunei spectaculorum in theatro ita dividantur, uti anguli trigonorum, qui currunt circum curvaturam circinationis, dirigant ascensus scalasque inter cuneos ad primam praecinctionem; supra autem alternis itineribus superiores cunei medii dirigantur.
(Vitruvius, Arch. 5.6.1-2)
The plan of the theatre is to be thus arranged: that the centre is to be taken, of the dimension allotted to the orchestra at the ground level. The circumference is to be drawn; and in it four equilateral triangles are to be described touching the circumference at intervals (just as in the case of the twelve celestial signs, astronomers calculate from the musical division of the constellations). Of these triangles the side of that which is nearest the scene, will determine the front of the scene, in the part where it cuts the curve of the circle. Through the centre of the circle a parallel line is drawn which is to divide the platform of the proscenium from the orchestra. Thus the stage will be made wider than that of the Greeks because all the actors play their parts on the stage, whereas the orchestra is allotted to the seats of the senators. The height of the stage is not to be more than 5 feet, so that those who are seated in the orchestra can see the gestures of all the actors. The blocks of seats in the theatre are so to be divided that the angles of the triangles which run round the curve of the circle indicate the ascents and the steps between the blocks to the first circular passage. Above, the upper blocks of seats are arranged with alternate staircases facing the middle of the lower blocks. (tr. Frank Granger)