As Hortensio watches Lucentio woo Bianca (with some biased reinforcement from Tranio)—in Act Four, scene two, of Shakespeare's The Taming of the Shrew—the man pretending to be a music teacher to gain Bianca's love finally swears that he has had enough.
First, Hortensio admits that he is not the music teacher that he pretends to be. Hortensio agrees with Tranio that Bianca lacks loyalty. It bothers him that Bianca would prefer a man of lower social standing (Cambio, who is really Lucentio) over him. When Tranio (pretending to be Lucentio, another suitor—in support of Lucentio's pursuit of Bianca) swears he will no longer pursue Bianca if Hortensio will do the same, Hortensio joins him, swearing the he will stop his attempts to woo Bianca, finding her not the woman he believed her to be.
Signior Hortensio, I have often heard
Of your entire affection to Bianca;
And since mine eyes are witness of her lightness,
I will with you, if you be so contented, (25)
Forswear Bianca and her love for ever.
See, how they kiss and court! Signior Lucentio,
Here is my hand, and here I firmly vow
Never to woo her no more, but do forswear her,
As one unworthy all the former favours (30)
That I have fondly flatter'd her withal.
Once so sworn, Hortensio announces that he will marry a wealthy widow whom he has only known a short time, who has loved him as much as he has loved Bianca. He promises that from now on, when searching for love, he will look for kindness in women, rather than their beauty. I.e., he will look for the beauty within, rather than outward beauty.
For me, that I may surely keep mine oath,
I will be married to a wealthy widow,
Ere three days pass, which hath as long loved me
As I have loved this proud disdainful haggard.
And so farewell, Signior Lucentio. (40)
Kindness in women, not their beauteous looks,
Shall win my love: and so I take my leave,
In resolution as I swore before.
It would seem with Hortensio's departure that the competition Lucentio has faced has been reduced to make his pursuit of the lovely Bianca that much easier.