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Linguistic Note on Minute
The word minute, in the context of the measurement both of time and of angle, derives from its initial definition as a minute part of an hour or of a degree of arc.
In this context the word minute (meaning: the aggregation of $60$ seconds) is pronounced min-it.
The word minute (as used in the phrase minute part) is pronounced my-nyoot and means small.
So the fact that the two words are spelt identically is not a coincidence.