All 7 Uses

nevertheless
in
Medea, by Euripides - (translated by: T.A. Buckley)
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I will do it, but I fear that I shall not persuade my mistress; nevertheless I will give you this favor of my labor.†
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nevertheless = despite that (used to connect contrasting ideas)
And now I see that I am doing wrong, O lady, but nevertheless thou shalt obtain thy request; but this I warn thee, if to-morrow's light of the God of day shall behold thee and thy children within the confines of these realms, thou shalt die: this word is spoken in truth.†
But nevertheless even after this am I come, not wearied with my friends, providing for thee, O woman, that thou mightest not be banished with thy children, either without money, or in want of any thing.†
Come (for I will converse with thee as with a friend, not expecting to receive any benefit from thee at least, but nevertheless I will; for when questioned thou wilt appear more base), now whither shall I turn?†
Jason, thou hast well adorned these arguments of thine, but nevertheless to me, although I speak reluctantly, thou appearest, in betraying thy wife, to act unjustly.†
For although thou slayest them, nevertheless they at least were dear, but I a wretched woman.†
Nevertheless my hand slew them not.†

Definitions:

(1) (nevertheless)
despite that

Based on idea 1 we might not expect idea 2, but this is a way of saying that even though idea 1 was just stated, we still have idea 2. Synonyms include in spite of that, despite that, nevertheless, nonetheless, on the other hand, in contrast and but.
(2) (meaning too rare to warrant focus)