ὑπόκειμαι used as Pass. of ὑποτίθημι fut. ὑποκείσομαι aor1 ὑπετέθην to lie under or beneath, Il., Thuc.; c. dat., Plat. in various metaph. senses, to be put under the eyes or mind, i. e. to be submitted or proposed to one, Pind.; αἱ ὑποκείμεναι ἐλπίδες oneʼs present hopes, Dem.; ὑπόκειταί μοι ὅτι . . I have laid down the rule, that . . , Hdt. to be laid down or assumed as an hypothesis, Plat., etc.; τούτων ὑποκειμένων Lat. his positis, Plat.; impers., ὑπόκειται a rule is laid down, Dem.; ὑποκείσθω ὅτι . . let it be granted that . . , Arist. to be suggested, Hdt. to be left at bottom, left remaining, Thuc., Dem. to be subject to, submit to, τινι Plat.: absol. to be submissive, Plat. to be left behind in pledge, to be pledged or mortgaged, τινος for a certain sum, Dem., etc.; ὑποκείμενοι, of persons, bound for payment of a sum of money, Dem. to underlie, as a substratum, Plat., etc. to be subordinate, Plat.