Aorist Tense:

 Remember  that only the aorist indicative relates happenings in the past, the infinitive does not.
The infinitive only expresses aspect of the action:
Simple fact.
Once and for all.
Specific.
 
ὁ Φίλιππος ἐβούλετο παῦσαι τὴν τῶν νεανιῶν μάχην.
Philip wanted to stop the young men's fight. (once and for all, stop that one specific fight)
versus
ὁ Φίλιππος ἀεὶ βούλεται μάχας παύειν, παύειν τῶν ἄλλων μαχομένων.
Philip always wanted to stop fights (in general), stop others from fighting. (as he is such a peace-loving child)

ὁ φύλαξ ἀναβάλλει τὴν χεῖρα. δεῖ ἡμᾶς παύσασθαι.
The guard lifts [=throws up] his hand. We must stop.

  Aorist Infinitive Forms  
 
  active  
to hear (sth. specific)
      NO past tense marker 
 ἀκοῦσ      1st aorist stem 
    αι     active infinitive marker  
         
  middle  
to set out
      NO past tense marker 
 πορεύσ      1st aorist stem 
    ασθαι     middle infinitive marker  
 
 Note 
1. The 1st aorist infinitive ending -αι is short but
2. The accent is not recessive and stays on the stem end syllable.
2. In the active voice the accent is
acute if the stem-vowel is short
circumflex if the stem-vowel is long or if there is a diphthong.
 
2. Examples:   κόπτω ἔκοψα κόψαι  to knock
 αἰτέω ᾔτησα αἰτῆσαι  to ask for
 δακρύω     ἐδάκρῡσα   δακρῦσαι    to weep
 διώκω ἐδίωξα διῶξαι  to chase
 ἐγείρω ἤγειρα ἐγεῖραι  to wake sb. up  
 πείθω ἔπεισα πεῖσαι  to persuade