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Use "at" when the physical closeness between the object of the preposition and the word that the prepositional phrase modifies is the most important idea to be conveyed by the sentence concerned. "On" also usually implies physical closeness, but it has an additional and usually more important implication of literal or metaphorical support of the word modified by the prepositional phrase by the object of the preposition. There are also numerous idiomatic phrases that require a choice not easily inferred from these two principles: "on time", "on sale", and "on call" probably being the most common. Also note the two phrases, "at hand" and "on hand", where only "at hand" implies physical closeness, while "on hand" means readily available, but not necessarily nearby.

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14y ago

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