LUCENTIO [Kneeling] Pardon, sweet father. VINCENTIO Lives my sweet son? (5.1.2)
In order for the play to set the world in its rightful place and restore the proper social order, children must reconcile with their parents. We're not sure why Vincentio forgives Lucentio so quickly and easily (aside from the obvious fact that he's happy to see his kid is alive and the play can't drag on forever). It does seem, however, that gesture must be made publicly in order for things to work out. Bianca follows suit in the next lines. Later, of course, Kate makes the exact same gesture toward Petruchio in Act 5, Scene 2, kneeling at his feet before a very public audience.