Here we find a professor lecturing to a select class, in this case of only two lads, and his pupils, as in the class-room of Dionusios, discussing and elaborating among themselves afterwards the subject-matter of the lecture. Theodoros is mentioned as teaching Geometry, Astronomy, and the theory of Music, as well as the Science of Numbers. Geometry by this time included a good number of the easier propositions which were afterwards incorporated in the works of Euclid; the school of Pythagoras, and, later, that of Plato, did much to develop it. The problem of squaring the circle was already occupying attention.[500] Compasses and the rule were the ordinary geometrical implements: diagrams were drawn on the ground, on dust or sand. In Arithmetic surds[501] were a popular subject: but arithmetical problems, being usually expressed in terms of geometry plane or solid, become as a rule a part of the latter science. To Plato these mathematical studies are alone suitable for secondary education: the philosopher Teles,[502] carrying on the same tradition, makes arithmetic and geometry the special plagues of the lad.[503] But then the philosophers despised Rhetoric. Rhetoric, from the time of Gorgias onwards, formed a very large part of secondary education Isokrates was its greatest professor. He provided in his school a course of three or four years for lads, to occupy their time till they were epheboi. But the methods, the aims, and the personality of this interesting professor will be discussed later. * * * * * Besides mathematics and rhetoric, there were literary studies. The _Axiochos_ gives κριτικοί [kritikoi] among the teachers of a lad. These are the lecturers on literary subjects, who concerned themselves with interpretations, often far-fetched, of the poets; a summary of the literary discussion in the _Protagoras_ may give some idea of such a lesson. “PROTAGORAS. I consider that it is a most important part of a man’s education to be skilled in poetry; to understand, that is, what is rightly said, and what is not, by the poets. Simonides says to Skopas, son of Kreon the Thessalian, ‘To become indeed a good man is hard, a man foursquare, wrought without blame in hands and feet and mind.’ You know the poem? Do you know then that farther on in the same poem he says, ‘But the saying of Pittakos, wise though he was, seems to me not said aright: he said, “’Tis hard to be noble.”’ Don’t you see that the poet has contradicted himself?”