ἐγκαταδύομαι

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

Source

Russian (Dvoretsky)

ἐγκαταδύομαι: (aor. 2 ἐγκατέδυν) погружаться, нырять (ὕδασι Anth.).