ἁμιλλᾶσθαι
From LSJ
προγράψαντες οὖν τά τε θεωρήματα καὶ τὰ ἐπιτάγματα τὰ χρεῖαν ἔχοντα εἰς τὰς ἀποδείξιας αὐτῶν μετὰ ταῦτα γραψοῦμές τοι τὰ προκείμενα → having therefore written at the beginning the theorems and the postulates that are necessary for their proofs, we will then write out for you the propositions
Greek > English (Woodhouse Verbs Reversed)
(see also ἁμιλλάομαι): contend, hasten, argue with, compete with, contend with, discuss with, dispute with, emulate a person
Lexicon Thucydideum
certare inter se, aemulari, struggle with each other, to compete, 6.31.3.