ON

Positioned at the upper surface of, touching from above.

Example: "A vase of flowers stood on the table."

Positioned at or resting against the outer surface of; attached to.

Example: "He had a scar on the side of his face."

Expressing figurative placement or attachment.

Example: "All of the responsibility is on him."

Denoting performance or action by contact with the surface, upper part, or outside of anything; hence, by means of; with.

Example: "To play on a violin or piano"

At or in (a certain region or location).

Example: "The lighthouse that you can see is on the mainland."

Near; adjacent to; alongside.

Example: "Croton-on-hudson, rostov-on-don, southend-on-sea"

Supported by (the specified part of itself).

Example: "A table can't stand on two legs."

So as to impart force to.

Example: "Tug on the rope; push hard on the door"

So as to impact; against.

Example: "I stubbed my toe on an old tree stump."

Covering.

Example: "He wore old shoes on his feet."

(with certain modes of transport, especially public transport) inside (a vehicle) for the purpose of travelling.

Example: "On a bus, on a train, on a plane"

At the date of.

Example: "Born on the 4th of july."

Some time during the day of.

Example: "Can i see you on a different day?"

At a given time after the start of something; at.

Example: "Smith scored again on twelve minutes, doubling mudchester rovers' lead."

Dealing with the subject of; about; concerning.

Example: "I have no opinion on this subject."

In the possession of.

Example: "I haven't got any money on me."

Because of, or due to.

Example: "To arrest someone on suspicion of bribery"

Upon; at the time of (and often because of).

Example: "On jack's entry, william got up to leave."

Paid for by.

Example: "I paid for the airfare and meals for my family, but the hotel room was on the company."

Indicating a means or medium.

Example: "Can't you see i'm on the phone?"

Indicating the target of, or thing affected by, an event or action.

Example: "Her words made a lasting impression on my mind."

Toward; for; indicating the object of an emotion.

Example: "Have pity or compassion on him."

Indicating a means of subsistence.

Example: "The dog survived three weeks on rainwater."

Away or occupied with (e.g. a scheduled activity).

Example: "He's on his lunch break."

Regularly taking (a drug).

Example: "He's acting so strangely, i think he must be on something."

Under the influence of (a drug).

Example: "He's acting crazy because he's on crack right now."

Having identical domain and codomain.

Example: "A function on"

Having v^n as domain and v as codomain, for some set v and integer n.

Example: "An operator on"

Generated by.

Example: "The free group on four letters"

In addition to; besides; indicating multiplication or succession in a series.

Example: "Heaps on heaps of food"

Of

Indicating dependence or reliance; with confidence in.

Example: "He will promise on certain conditions."

At the peril of, or for the safety of.

In the service of; connected with; of the number of.

Example: "He is on a newspaper; i am on the committee."

By virtue of; with the pledge of.

Example: "He affirmed or promised on his word, or on his honour."

To the account or detriment of; denoting imprecation or invocation, or coming to, falling, or resting upon.

Example: "A curse on him!"

(especially when numbers of combatants or competitors are specified) against; in opposition to.

Example: "The fight was three on one, and he never stood a chance."

Without.