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τῷ with infinitive: instrument, cause or manner
τῷ with the infinitive signals a satellite with semantic roles such as instrument, cause, manner or limitation.
ἔστι δὲ τοῦθ’ ὡς ἁπλῶς εἰπεῖν αἱρετὴ τυραννίς, διαφέρουσα δὲ τῆς βαρβαρικῆς οὐ τῷ μὴ κατὰ νόμον ἀλλὰ τῷ μὴ πάτριος εἶναι μόνον.
That - to put it bluntly - is a voluntary tyranny, which does not differ from that of barbarians in terms of lawfulness, but only in terms of heredity.
ἐγὼ δὲ οἶμαι τὸν ἄρχοντα οὐ τῷ ῥᾳδιουργεῖν χρῆναι διαφέρειν τῶν ἀρχομένων, ἀλλὰ τῷ προνοεῖν καὶ φιλοπονεῖν .
NO DUTCH TRANSLATION [provisional translation]
τὸ μὲν γὰρ τῶν Ῥωμαίων στρατόπεδον ἐξιέναι μὲν πρὸς μάχην οὐκ ἐθάρρει τῷ δεδιέναι τοὺς τῶν πολεμίων ἱππεῖς.
The Roman army lacked the courage to go to battle for fear of the enemy's cavalry.