“τὰ μὲν καθ᾽ ἡμᾶς ἔμοιγε δοκεῖ καλῶς ἔχειν: ἀλλὰ τὰ πλάγια λυπεὶ με” the part where we are seems to me to be well disposed, but the wings cause me uneasiness”
I checked both CGCG and Smyth on this preposition, but neither of them had an explanation of this substantivization. Can someone explain how “τὰ καθ᾽ ἡμᾶς” means “the part where we are”? (My guess is, “the things(spacial place) according to us”=“The part where we are is the logic here”, but neither Smyth nor CGCG explains this usage so I wanted to get more info.)
What should be immediately clear is that τὰ μὲν καθ᾽ἡμᾶς is being contrasted with τὰ πλάγια, and without needing to look at a translation or to read any further into the context it’s obvious that τὰ μὲν καθ᾽ ἡμᾶς here will be meaning something like “the parts where we are” (the center, presumably). In certain contexts καθ’ἡμᾶς would mean “according to us” but κατά has a variety of applications (not always “according to”), and meaning is not independent of context.
So there’s no real difficulty here. As to the substantivization, well, any prepositional phrase can be substantivized by putting τό or τά in front of it, so it’s hardly worthwhile looking up particular collocations.