ὑθποκείσθωσαν

ὑθποκείσθωσαν γὰρ νῦν οἱ καταφατικοὶ προσδιορισμοὶ, τὰς γὰρ καταφάσεις μόνον τέως ζητοῦμεν
Now, let us take up affirmative quantifiers for until now we have been studying affirmations only. / for all this time we are studying affirmations only.
Is it ok to use ‘take up’ here?
Which variant is better?

ὑποκείσθωσαν

LSJ has some examples: “ὑποκείσθω τι” let it be taken for granted, Id.EN1103b32, cf. 1129a11, al., Gal.15.175; ὑποκείσθω ὅτι . . let it be taken for granted that . . ,

I am not sure it fits the context.

Maybe let the affirmative quantifiers now be established

i want to take it in the meaning of être placé sous les yeux, être proposé, that’s why I thought of to take up.

Here’s the text (p. 25), Stephanus’s comm. on Arist’s De interp.

“Take up,” “be set out,” “be established” is fine. οἱ καταφατικοὶ προσδιορισμοί refers to the two different quantitative applications of affirmative statements: either “all” or “some”; the former is an affirmative statement with general application (καθόλου καταφατικός), the latter with a partial application (μερικὸς κ.). Note that ζητοῦμεν is present; your second option is closer. τέως “to begin with.” “To begin with, we are only investigating affirmative statements” [apophatic statements come later].