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Preposition ἐπί with the dative: condition
καὶ ἐπὶ τούτοις ὠμόσθησαν οἱ ὅρκοι
‘And on those conditions the oaths were sworn.’ (Xen. Hell. 7.4.11)
The preposition ἐπί with the dative signals a condition.
ἐφ᾽ οἷς τὴν εἰρήνην ἐποιησάμεθα
on what terms we made the peace [provisional translation]
αὐτοί τε τοῖς περὶ τὸν Ἀννίβαν ἔδοσαν πίστεις καὶ παρ’ ἐκείνων ἔλαβον ἐπὶ τούτοις [...]
They gave pledges of loyalty to Hannibal and his entourage and vice versa on the following conditions: […]
ἐπὶ τούτοις γὰρ οἱ ἄνδρες παρέδοσαν τὴν πόλιν καὶ ταῦτα συνέθεντο.
NO DUTCH TRANSLATION [provisional translation]
ἐπὶ τούτοις ἐγγυησάμενοι παρέξειν εἰς αὔριον ᾤχοντο ἀπιόντες.
They pledged to hand him over the following day on these conditions, and then they left.