δεῖ + present participle

Greek Learning Greek
1

I’m currently working through Beetham’s “Greek with Plato.” While working through the beginning of Plato’s Meno, I have encountered a construction that I am unable to understand grammatically (I understand the semantics of the sentence).

εἰ δὲ βούλει γυναικὸς ἀρετήν, οὐ χαλεπὸν διελθεῖν, ὅτι δεῖ αὐτὴν τὴν οἰκίαν εὖ οἰκεῖν, σῴζουσάν τε τὰ ἔνδον καὶ κατήκοον οὖσαν τοῦ ἀνδρός. [Meno 71e]

Why are σῴζουσάν and οὖσαν present participles? I would have expected them to be infinitives, like οἰκεῖν.

Thanks in advance for any help!

2

The participles specify the two broad duties that, according to the speaker, managing a home well consists in:
…"she needs to manage the home well, taking care of matters indoors, and being obedient to her husband.
The construction is not δεῖ + present participle, but participles in agreement with the accusative subject of an acc. + infin.