English translation (word)
English translation (etymon)
Ἡρωδιανὸς δὲ λέγει ὅτι Χρύσιππος φησὶ παρὰ τὸ ἀσκεῖν τὸ σημαῖνον τὸ διδάσκειν τι· ἀσκῶ, διάσκω· καὶ ἐπενθέσει τοῦ δ διδάσκω
Herodian (Lentz III/2, p. 178) says that according to Chrysippus it comes from askeîn "to exercise", which means "to teach" something: askô, *di-askō, and through insertion of [d], didaskō
The quotation is given here with the punctuation of Lentz. In that case, διδάσκω is supposedly derived from ἀσκέω "to exercise", which every teacher knows is consubstantial to teaching. The derivational path implies then that the verb receives the preverb δια- (διασκέω is attested) and there is then one formal manipulation, the insertion of a consonant at the boundary between the preverb and the verb. However, Arnim punctuates differently: παρὰ τὸ ἀσκεῖν τὸ σημαῖνον τὸ διδάσκειν· τι ἀσκῶ, διάσκω etc. "from askeîn meaning "to teach": "I exercise in something" (ti askô), diaskō etc. In that case, the etymology relies on the transformation of a verb phrase into a verbal compound. The first element is identified as the indefinite pronoun τι "something". This segmentation requires two formal manipulations, the transformation of the voiceless dental into a voiced one, and the insertion of a consonant at the junction between the two members of the compound. In either case, this explanation relies on the transitive use of ἀσκέω "to train someone", matching the transitive meaning of διδάσκω "to teach someone".
Greek grammarians all analysed the verb correctly as reduplicated, not as a compound, but this etymology by Chrysippus is in the cratylean tradition
Ps.-Zonaras, Lexicon, delta, p. 543 (ὁ δὲ Ἡρωδιανὸς καὶ Χρύσιππος παρὰ τὸ ἀσκεῖν τὸ σημαῖνον τὸ διδάσκω, καὶ πλεονασμῷ τοῦ δ διδάσκω)