All 8 Uses of

contrary
in
Incidents in the Life of a Slave Girl

I asked him if he didn't know it was contrary to law; and that slaves were whipped and imprisoned for teaching each other to read.
Chpt 13 *

contrary to = in opposition to

On the contrary, I had always been kindly treated, and tenderly cared for, until I came into the hands of Dr. Flint.†
Chpt 21 *

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

Meantime, we would take it for granted that all were friends, till they proved to the contrary.†
Chpt 31 *

On the contrary, you were taken into the house, and treated as one of us, and almost as free; and we, at least, felt that you were above disgracing yourself by running away.†
Chpt 34

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

I wished he had kept at a distance, but as he was here, and knew where I was, I concluded there was nothing to be gained by trying to avoid him; on the contrary, it might be the means of exciting his ill will.†
Chpt 36

He said it was contrary to their custom, but he would see that we had berths below; he would also try to obtain comfortable seats for us in the cars; of that he was not certain, but he would speak to the conductor about it, when the boat arrived.
Chpt 36

contrary to = in opposition to

This honorable gentleman would not have voted for the Fugitive Slave Law, as did the senator in "Uncle Tom's Cabin;" on the contrary, he was strongly opposed to it; but he was enough under its influence to be afraid of having me remain in his house many hours.†
Chpt 40

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

I was doing harm to no one; on the contrary, I was doing all the good I could in my small way; yet I could never go out to breathe God's free air without trepidation at my heart.†
Chpt 41

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