Greek Mathematics

XI. Theaetetus

(a) General

Suidas, s.v. Θεαίτητος

Θεαίτητος, Ἀθηναῖος, ἀστρολόγος, φιλόσοφος, μαθητὴς Σωκράτους, ἐδίδαξεν ἐν Ἡρακλείᾳ. πρῶτος δὲ τὰ πέντε καλούμενα στερεὰ ἔγραψε. γέγονε δὲ μετὰ τὰ Πελοποννησιακά.

(b) The Five RegularSolids

Schol. i. in Ecul. Elem. xiii., Eucl.ed. Heiberg v. 654

Ἐν τούτῳ τῷ βιβλίῳ, τουτέστι τῷ ιγ΄, γράφεται τὰ λεγόμενα Πλάτωνος  σχήματα, ἃ αὐτοῦ μὲν οὐκ ἔστιν, τρία δὲ τῶν προειρημένων  σχημάτων τῶν Πυθαγορείων ἐστίν, ὅ τε κύβος καὶ ἡ πυραμὶς καὶ τὸ δωδεκάεδρον, Θεαιτήτου δὲ τό τε ὀκτάεδρον καὶ τὸ εἰκοσάεδρον. τὴν δὲ προσωνυμίαν ἔλαβεν Πλάτωνος διὰ τὸ μεμνῆσθαι αὐτὸν ἐν τῷ Τιμαίῳ περὶ αὐτῶν.



XL Theaetetusa

(a) General

Suidas, s.v. Theaetetus

Theaetetus, an Athenian, astronomer, philosopher, a pupil of Socrates, taught in Heraclea. He was the first to describeb the five solids so-called. He lived after the Peloponnesian wars.

(b)The Five Regular Solids

Euclid, Elements xiii., Scholium i., Eucl. ed. Heiberg v. 654

In this book, that is, the thirteenth, are described the five Platonic figures, which are however not his, three of the aforesaid five figures being due to the Pythagoreans,c namely, the cube, the pyramid and the dodecahedron, while the octahedron and icosahedrons are due to Theaetetus. They received the name Platonic because he discourses in the Timaeus about them.

  • aTheaetetus lived about 415–369 b.c. He is the subject of a dissertation De Theaeteto Atheniensi by Eva Sachs (Berlin, 1914).
  • b Possibly “construct.”
  • c For the relation of the Pythagoreans to the five regular solids, see supra, pp. 216-225. Theaetetus was probably the first to construct all five theoretically; the Pythagoreans could not have done that. For a full discussion, see Eva Sachs, Die fünf Platonischen Körper,
DOI: 10.4159/DLCL.theaetetus-mathematical_works.1939