THE ACCUSATIVE

Basic function: that at which the action is directed.

In everyday practice:

I. Attracted (i.e expected to be present because of certain introductory words):

a) as complement to the prepositions ἀμφι/ἀμφ΄, ἀνὰ/ἀν’, διὰ/δι’,
     εἰς/ἐς, ἐπὶ/ἐπ’/ἐφ’, κατὰ/κατ’/καθ’, μετὰ/μετ’/μεθ’, παρὰ/παρ’,
     περὶ, πρὸς, ὑπὲρ, ὑπὸ/ὑπ’/ὑφ’,
     ὡς[1] (underlined are those that have no other case than the Ac)

b) By far the most verbs have their direct object in the Ac, so much so
     that this is not even mentioned in the lexicon. There are even verbs
     with two objects in the Ac, e.g. “to teach someone something”, “to   
     rob someone of something” and a few more.

II. Unattracted (i.e. popping up unexpectedly):

a) Ac of limitation: the presence of a quality or action of a verb is
     limited to a certain         
     part. Οὖτος ὁ ἵππος μέλάς ἐστι τοὺς πόδας. Ἀλγῶ τοὺς πόδας.
      The horse is black at the feet > has black feet. I am in pain in my feet>have pain in my feet.

 [1] This is no more than a relatively rare value of the word ὡς

b) Ac of extent in time and space: time passed or to be passed, distance
     covered or to be covered. Τρεῖς σταδίους βάντες τρεῖς ὦρας    
     μενοῦμεν. Having travelled three stadia  we shall stay for three hours

c) Adverbial Ac: >Ne sg Ac  or >Ne pl Ac of an adjective instead of an adverb:   
    Μαχόμενοι μέγα βοῶσιν οἱ Ἕλληνες. When fighting the Hellenes yell
      loudly.
    [This type of  Ac is regular for the comparative (>Ne sg Ac) and the
      superlative (>Ne pl Ac ].
     
d) Ac of direction (mainly poetical): Οὐρανὸν ἤιξεν. He flew
       heavenwards.

e) Ac of the subject of an infinitive: see infinitive.

 III. Agreeing Accusatives, amongst which the predicate Ac
       accompanying the direct object of such words as νομίζω,
       ἀποδείκνυμι: Αὖθις τὸν Περικλέα ἀποδείξωμεν στρατηγόν.
         Let us again appoint Pericles as commander.