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Цитата: //dictionary.compay through the nose

Pay an excessive amount for something, as in We paid through the nose for that vacation. The origin of this term has been lost. Possibly it alludes to the Danish nose tax, imposed in Ireland in the 9th century, whereby delinquent taxpayers were punished by having their noses slit. [Second half of 1600s]

The idiom in question has obviously lost its motivation. The history of the expression given in the above quotation is quite vague. The thing which I can't get why there is this preposition through. If people were punished for not paying the tax by a slit nose what is the reason to use preposition "through"? The whole phrase denotes to pay excessively and taking into the consideration the origin of the phrase, it should imply to pay the tax in order to save one's nose from slitting. Then it should be something like to pay for the nose  .