All 13 Uses of

contrary
in
Gulliver's Travels

Yet, so far have you been from answering my expectation in any of your letters; that on the contrary you are loading our carrier every week with libels, and keys, and reflections, and memoirs, and second parts; wherein I see myself accused of reflecting upon great state folk; of degrading human nature (for so they have still the confidence to style it), and of abusing the female sex.†
Chpt Intr. *

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

There are some laws and customs in this empire very peculiar; and if they were not so directly contrary to those of my own dear country, I should be tempted to say a little in their justification.†
Chpt 1 *

contrary to = in opposition to

'That the said Quinbus Flestrin, contrary to the duty of a faithful subject, is now preparing to make a voyage to the court and empire of Blefuscu, for which he has received only verbal license from his imperial majesty; and, under colour of the said license, does falsely and traitorously intend to take the said voyage, and thereby to aid, comfort, and abet the emperor of Blefuscu, so lately an enemy, and in open war with his imperial majesty aforesaid.'†
Chpt 1

The rest of my cattle I got safe ashore, and set them a-grazing in a bowling-green at Greenwich, where the fineness of the grass made them feed very heartily, though I had always feared the contrary: neither could I possibly have preserved them in so long a voyage, if the captain had not allowed me some of his best biscuit, which, rubbed to powder, and mingled with water, was their constant food.†
Chpt 1 *

I one day took the freedom to tell his majesty, "that the contempt he discovered towards Europe, and the rest of the world, did not seem answerable to those excellent qualities of mind that he was master of; that reason did not extend itself with the bulk of the body; on the contrary, we observed in our country, that the tallest persons were usually the least provided with it; that among other animals, bees and ants had the reputation of more industry, art, and sagacity, than many of the larger kinds; and that, as inconsiderable as he took me to be, I hoped I might live to do his majesty some signal service."†
Chpt 2

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

For, I remember very well, in a discourse one day with the king, when I happened to say, "there were several thousand books among us written upon the art of government," it gave him (directly contrary to my intention) a very mean opinion of our understandings.†
Chpt 2

contrary to = in opposition to

I could not forbear admiring at these odd appearances, both in town and country; and I made bold to desire my conductor, that he would be pleased to explain to me, what could be meant by so many busy heads, hands, and faces, both in the streets and the fields, because I did not discover any good effects they produced; but, on the contrary, I never knew a soil so unhappily cultivated, houses so ill contrived and so ruinous, or a people whose countenances and habit expressed so much misery and want.†
Chpt 3

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

I told him "we fed on a thousand things which operated contrary to each other;†
Chpt 4

contrary to = in opposition to

Whether they had ever, at different times, pleaded for and against the same cause, and cited precedents to prove contrary opinions?†
Chpt 2 *

I was complaining of a small fit of the colic, upon which my conductor led me into a room where a great physician resided, who was famous for curing that disease, by contrary operations from the same instrument.†
Chpt 3

He likewise directed, "that every senator in the great council of a nation, after he had delivered his opinion, and argued in the defence of it, should be obliged to give his vote directly contrary; because if that were done, the result would infallibly terminate in the good of the public."†
Chpt 3

The second was of an opinion directly contrary; "to tax those qualities of body and mind, for which men chiefly value themselves; the rate to be more or less, according to the degrees of excelling; the decision whereof should be left entirely to their own breast."†
Chpt 3

For nature (as the physicians allege) having intended the superior anterior orifice only for the intromission of solids and liquids, and the inferior posterior for ejection, these artists ingeniously considering that in all diseases nature is forced out of her seat, therefore, to replace her in it, the body must be treated in a manner directly contrary, by interchanging the use of each orifice; forcing solids and liquids in at the anus, and making evacuations at the mouth.†
Chpt 4

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