All 10 Uses of

contrary

in

Pride and Prejudice

Darcy, on the contrary, had seen a collection of people in whom there was little beauty and no fashion, for none of whom he had felt the smallest interest, and from none received either attention or pleasure.†
p. 18.7

on the contrary = an expression used to intensify denial of an idea

For, though elated by his rank, it did not render him supercilious; on the contrary, he was all attention to everybody.†
p. 19.5 *

Against staying longer, however, Elizabeth was positively resolved—nor did she much expect it would be asked; and fearful, on the contrary, as being considered as intruding themselves needlessly long, she urged Jane to borrow Mr. Bingley's carriage immediately, and at length it was settled that their original design of leaving Netherfield that morning should be mentioned, and the request made.†
p. 58.5

Let me recommend you, however, as a friend, not to give implicit confidence to all his assertions; for as to Mr. Darcy's using him ill, it is perfectly false; for, on the contrary, he has always been remarkably kind to him, though George Wickham has treated Mr. Darcy in a most infamous manner.†
p. 93.3

On the contrary, she was as much disposed to complain of it as her husband.†
p. 126.6

Nothing, on the contrary, could be more natural; and while able to suppose that it cost him a few struggles to relinquish her, she was ready to allow it a wise and desirable measure for both, and could very sincerely wish him happy.†
p. 147.5

On the contrary, every particular relative to his sister was meant to be kept as much as possible to myself; and if I endeavor to undeceive people as to the rest of his conduct, who will believe me?†
p. 218.6

On the contrary, there is something pleasing about his mouth when he speaks.†
p. 247.1

It was, on the contrary, exactly calculated to make her understand her own wishes; and never had she so honestly felt that she could have loved him, as now, when all love must be vain.†
p. 264.9

Definitions:

(1) (contrary as in: a contrary idea)
different (perhaps opposite or mutually exclusive)

In formal logic, contrary propositions or contrary arguments describe two things that cannot both be true. They might be described as mutually exclusive. For example, a pet cannot be both a cat and a dog. It doesn't need to be either, but if it is one, it cannot be the other. So the statement that a pet is a cat and the statement that the same pet is a dog, are contrary statements.
(2) (contrary as in: a contrary personality)
disagreeable -- typically in reference to someone's personality
(3) (contrary to as in: contrary to)
in opposition to

You could also think of this as meaning, despite, or in spite of, or in conflict with; but since a common meaning of contrary is opposite, you many find it easiest to think of contrary to as in opposition to.
(4) (on the contrary as in: on the contrary)
an expression used to intensify denial of an idea

More rarely, on the contrary is used to oppose an idea contained in what was just said rather than to oppose what was literally said. Here is an example: "I will not pay you for the work. On the contrary, I may sue you for damages." Suing for damages does not oppose not paying, but it does oppose the idea of paying.
(5) (to the contrary as in: to the contrary)
with an opposite or different effect; or something with an opposite or different effect
(6) (meaning too rare to warrant focus)