prositi

1. to beg
   Jedan starac svaki dan prosi ispred crkve. — An old man begs in front of the church every day.
   Deca su prosila na semaforu. — Children were begging at the traffic lights.
2. (of a girl, + acc.) to ask for someone's hand in marriage
   Po starom običaju, momkova porodica dolazi da prosi devojku. — By old custom, the groom's family comes to ask for the girl's hand.

For “to propose (marriage)” the perfective zaprositi is usually used.