All 14 Uses of

contrary
in
Utopia, by Thomas More

On the contrary, they would look on the mitigation of the punishment as an invitation to commit more crimes.'†
*

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

But such discourses as mine, which only call past evils to mind and give warning of what may follow, leave nothing in them that is so absurd that they may not be used at any time, for they can only be unpleasant to those who are resolved to run headlong the contrary way; and if we must let alone everything as absurd or extravagant—which, by reason of the wicked lives of many, may seem uncouth—we must, even among Christians, give over pressing the greatest part of those things that Christ hath taught us, though He has commanded us not to conceal them, but to proclaim on the housetops that which He taught in secret.†

"On the contrary," answered I, "it seems to me that men cannot live conveniently where all things are common.†

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

From hence the old men take occasion to entertain those about them with some useful and pleasant enlargements; but they do not engross the whole discourse so to themselves during their meals that the younger may not put in for a share; on the contrary, they engage them to talk, that so they may, in that free way of conversation, find out the force of every one's spirit and observe his temper.†

The folly of men has enhanced the value of gold and silver because of their scarcity; whereas, on the contrary, it is their opinion that Nature, as an indulgent parent, has freely given us all the best things in great abundance, such as water and earth, but has laid up and hid from us the things that are vain and useless.†

A life of pleasure is either a real evil, and in that case we ought not to assist others in their pursuit of it, but, on the contrary, to keep them from it all we can, as from that which is most hurtful and deadly; or if it is a good thing, so that we not only may but ought to help others to it, why, then, ought not a man to begin with himself?†

They also observe that in order to our supporting the pleasures of life, Nature inclines us to enter into society; for there is no man so much raised above the rest of mankind as to be the only favourite of Nature, who, on the contrary, seems to have placed on a level all those that belong to the same species.†

and, on the contrary, they think it a sign of a gentle and good soul for a man to dispense with his own advantage for the good of others, and that by this means a good man finds as much pleasure one way as he parts with another;†

There are many things that in themselves have nothing that is truly delightful; on the contrary, they have a good deal of bitterness in them; and yet, from our perverse appetites after forbidden objects, are not only ranked among the pleasures, but are made even the greatest designs, of life.†

Thus though the rabble of mankind look upon these, and on innumerable other things of the same nature, as pleasures, the Utopians, on the contrary, observing that there is nothing in them truly pleasant, conclude that they are not to be reckoned among pleasures;†

These are, indeed, the lowest of pleasures, and the least pure, for we can never relish them but when they are mixed with the contrary pains.†
*

on the contrary, they are on this account the sooner broken, some slight pretence being found in the words of the treaties, which are purposely couched in such ambiguous terms that they can never be so strictly bound but they will always find some loophole to escape at, and thus they break both their leagues and their faith;†

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

But as they force no man to go into any foreign war against his will, so they do not hinder those women who are willing to go along with their husbands; on the contrary, they encourage and praise them, and they stand often next their husbands in the front of the army.†

He being newly baptised did, notwithstanding all that we could say to the contrary, dispute publicly concerning the Christian religion, with more zeal than discretion, and with so much heat, that he not only preferred our worship to theirs, but condemned all their rites as profane, and cried out against all that adhered to them as impious and sacrilegious persons, that were to be damned to everlasting burnings.†

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