not, is the negative of thought, as οὐ of statement, i. e. μή says that one thinks a thing is not, οὐ that it is not. The same differences hold for all compds. of μή and οὐ.
A.μή in INDEPENDENT sentences,
3.with Opt. to express a wish that a thing may not happen, ἃ μὴ κραίνοι τύχη which may fortune not bring to pass, Aesch.:—also in wishes that refer to past time and therefore cannot be fulfilled, μή ποτ᾽ ὤφελον λιπεῖν Soph.
4.in vows and oaths, where οὐ might be expected, ἴστω Ζεὺς μὴ μὲν τοῖς ἵπποισιν ἀνὴρ ἐποχήσεται ἄλλος Zeus be my witness, not another man shall ride on these horses, Il.; μὰ τὴν Ἀφροδίτην, μὴ ἐγώ σ᾽ ἀφήσω Ar.
B.In DEPENDENT clauses:
1.with Final Conjunctions, ἵνα μή, ὅπως μή, ὥς μή, ὄφρα, that not, Lat. ne, Il., attic:— μή often stands alone = ἵνα μή, Hom., attic
2.in the protasis of conditional sentences, after εἰ (epic αἰ), εἴ κε (αἴ κε), εἰ ἄν, ἤν, ἐάν, ἄ_ν, Lat. nisi, Hom., etc.;—so, ὅτε μή ῀ εἰ μή; etc.
3.in relat. clauses, when they imply a condition or supposition, λέγονθ᾽ ἃ μὴ δεῖ such things as one ought not, Soph.; λόγοις τοιούτοις οἷς σὺ μὴ τέρψει κλύων id=Soph.
4.with Inf., always except when the Inf. represents Ind. or Opt., as in oratio obliqua.
5.with Participle, when it can be resolved into a conditional clause, μὴ ἀπενείκας ῀ εἰ μὴ ἀπήνεικε Hdt.; μὴ θέλων ῀ εἰ μὴ θέλεις, Aesch.; so in a general sense, δίδασκέ μ᾽ ὡς μὴ εἰδότα = ut qui nihil sciam, Soph.
6.with abstract Nouns as with Partic., τὰ μὴ δίκαια ῀ ἃ ἂν μὴ ᾖ δίκαια, Aesch.; τὸ μὴ καλόν Soph.; ἡ μὴ 'μπειρία ῀ τὸ μὴ ἔχειν ἐμπειρίαν, want of experience, Ar.
a.when the thing feared is fut., with pres. Subj., I fear he may persuade thee, Il.
b.with Opt. for Subj., according to the sequence of moods and tenses, Hom., etc.
c.when the action is present or past, the Ind. is used, φοβούμεθα μὴ ἡμαρτήκαμεν we fear we have made a mistake, Thuc.
C.In QUESTIONS:
I.Direct questions,
a.with Ind., implying a negat. answer, surely not, you don't mean to say that, Lat. num? whereas with οὐ an affirm. answer is expected, Lat. nonne? ἆρ᾽ οὐ τέθνηκε; surely he is dead, is he not? ἆρα μὴ τέθνηκε; surely he is not dead, is he?:—when οὐ and μή appear in consecutive clauses, each negat. retains its proper force, οὐ σῖγ᾽ ἀνέξει μηδὲ δειλίαν ἀρεῖς; will you not be silent, and will you be cowardly? i. e. be silent and be not cowardly, Soph.