All 6 Uses

nonetheless
in
The Turn of the Screw
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Nonetheless, the rest of the day I watched for further occasion to approach my colleague, especially as, toward evening, I began to fancy she rather sought to avoid me.†
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nonetheless = in spite of that (used to connect contrasting ideas)
I knew, nonetheless, exactly what dreadful face she had to show; and I wondered whether, if instead of being above I had been below, I should have had, for going up, the same nerve I had lately shown Quint.†
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She didn't know—no one knew—how proud I had been to serve him and to stick to our terms; yet she nonetheless took the measure, I think, of the warning I now gave her.†
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But nonetheless, between Miles and me, it's now all out.†
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On the point of taking leave of her, nonetheless, I was to some extent embarrassed.†
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No attempt, nonetheless, could well require more tact than just this attempt to supply, one's self, ALL the nature.†
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Definitions:

(1) (nonetheless)
in spite of that (Used to connect contrasting ideas. Other synonyms could include words and phrases such as nevertheless, all the same, still, and however.)
(2) (meaning too rare to warrant focus)