[21]. Isthm. 1, 2.

[22]. So C. F. Hermann (ap. Ed. Teub.) for δυσί τῶν ἱερῶν.

[23]. Here several words of the text have been lost.

[24]. Many words have been lost (three separate lacunae).

[25]. Reading διεκώλυεν for διακούων.

[26]. Supplying προσδοκῶν, as Ed. Teub.

[27]. Many words are here lost, to the general effect of those in the brackets.

[28]. i. e. each of the four sides of each of the six faces. The Greek word for ‘side’ and ‘face’ is the same.

[29]. This problem (mentioned by Plutarch also in the E at Delphi, see p. [63]) was in fact solved by Menaechmus, a pupil of Eudoxus, through Conic Sections, and also by Archytas, whose method is much more elaborate. See Preface, p. [xiv].

[30]. Il. 10, 279; Od. 13, 300-1.