The word neat was borrowed into English in the 1540s, after which it alternated with the spellings nete, net, and nette until the current form prevailed. Prior to that, neat derives from Anglo-French neit and Middle French net (this could mean "clean" or "pure"), showing that there was still variation. Eventually, this all comes from Latin nitidus, which held more metaphorical meanings of "elegant" or "trim" but literally meant "shining" or "gleaming". This is still semantically pretty similar to the current definition, but we drift ever so slightly from that as we proceed back to nitere, or "to shine". Finally, as Proto-Indo-European nei, it also meant "shine". Usage of the word "neat" over the last two centuries has remained pretty constant, as it's really ingrained in our culture now.
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