Petruchio brings Katherina to his country house. He has been in a shrewish rage all the way, according to his servant, Grumio, who arrives there first. When Petruchio comes onstage, he continues to seem mad with passion. Kate can't rest, eat, or sleep for his yelling and discontent with everything.
This, however, merely continues the role he has been playing since the day of his wooing. The servants who know him aren't fooled. One says:
—Act IV, scene i, line 174
And Petruchio himself, in a soliloquy, tells the audience:
—Act IV, scene i, lines 182-83
Of course, Petruchio has the money for which he married Katherina. But he wants, we may suppose, a quiet, loving wife too, and it is for this he plans his course of action.
Meanwhile Lucentio's wooing progresses wonderfully well. In his guise as a schoolmaster teaching Latin, he says:
—Act IV, scene ii, line 8
This is Ovid's book which had been indirectly hinted at by Tranio at the very start of the play. The disguised Lucentio says he not only reads The Art to Love, he practices it, and Bianca demurely says she hopes he's good at it.
Hortensio, in his guise as Litio the music teacher, is outraged at Bianca's open preference for someone who seems a lowborn rascal, and abandons her, saying he will go marry a widow who has long been after him.
But while Bianca is accepting the real Lucentio, Tranio (the false Lucentio) must find a false Vincentio to win over Bianca's father. At last an old Pedant who looks the part comes onstage and Tranio stops him and asks if he is traveling on. The Pedant says:
—Act IV, scene ii, lines 75-76
It is a longish journey he plans. It is 250 miles overland due south from Padua to Rome, and then 600 miles across the sea to Tripoli, which is on the north African coast.
When asked where he is from, he answers:
—Act IV, scene ii, line 77
Mantua is sixty miles west of Padua, so that if he has come to Padua from Mantua on his way to Rome, he has gone at right angles to his proper course. But then, he may not have come directly from Mantua.
In any case, Tranio at once invents a proclamation in Padua, announcing death to all Mantuans in the city because of some high political quarrel, and offers to save the Pedant's life by allowing him to pose as a Pisan; that is, as Vincentio. The Pedant gratefully accepts.
Katherina is slowly wearing down from lack of food and sleep. She is trying to beg food from Petruchio's servant, Grumio, saying that she is
—Act IV, scene iii, lines 9-12
Surely, this is a key passage. He is wearing her down and forcing her to accept whatever she is offered, not out of cruelty, but in order to force her eventually to accept the one important thing-love.
It is precisely this which is hardest for her to accept, for, as she says, she is more annoyed at being offered love than at being denied food and sleep. And it is precisely love which she must accept.
For all her begging, though, Katherina continues to get no food. What's more, Petruchio promises her clothes but when the haberdasher and tailor arrive, he is utterly discontented with what they offer. Although Katherina cries out that she likes them, he will have none of them, and when Katherina protests, he calmly pretends she is agreeing with him.
They make ready to go to Padua and visit Katherina's father without new clothes, but in exactly what they are wearing. Petruchio casually says it is seven o'clock and Kate tells him, politely enough, that it is two. Whereupon Petruchio falls into a passion:
—Act IV, scene iii, lines 192-93
That is what Petruchio is after. He must train Katherina to accept as true whatever he says, however ridiculous it must seem to her.
The Pedant in the guise of old Vincentio goes through the matter of the dowry with old Baptista in very satisfactory fashion, and while the fathers are thus engaged, the real Lucentio makes ready to elope with Bianca.
Meanwhile Petruchio and Katherina (along with Hortensio) are on the road to Padua. Petruchio comments on the brightness of the moon. Katherina points out it is the sun. Whereupon Petruchio falls into a rage again, and says:
—Act IV, scene v, lines 6-8
Finally Katherina breaks down and says, wearily:
—Act IV, scene v, lines 12-15
Petruchio puts her through her paces, making her say first that the object in the sky is the moon, then the sun. When they meet an old man, he has Katherina greet him first as a young maiden and then apologize and greet him as an old man. Katherina follows the flicking of Petruchio's whip perfectly, accepting whatever he says as true.
And that prepares her to accept the one thing he has constantly been saying from the moment he met her-that he loves her.