Euthanase

This morning I offered to euthanase a sickly and diseased young lady whom I discovered floccillating on my way to breakfast. The brave girl's only objection, uttered in a quavering voice, was that she wasn't sure that euthanase was really a verb.

So I fled to a dictionary and found that indeed euthanase is not the right word, nor does it even pop up on google. The Americans say euthanize, but according to the word of The Almighty OED we English make do with euthanatize. However, the only citation is from a Spectator of  1873:

I saw a crab euthanatising a sickly fish, doubtless from the highest motives

I also didn't realise that euthanasia meant a peaceful or happy death long before it meant deliberately bringing about such an expiration, an idea that didn't pop up until 1869. Moreover it was originally anglicized to euthanasy. The root, since you ask, is simply eu for good as in eugenics or The Eurhythmics, and thanatos meaning death, as in Aimée Thanatogenos (the heroine of Evelyn Waugh's The Loved One) whose name means death-born beloved — or as in thanatologist which is a euphemism for undertaker — or as in thanatorium which is a place people go to be killed.

Darkling I listen; and, for many a time
I have been half in love with easeful Death,
Call’d him soft names in many a mused rhyme,
To take into the air my quiet breath;
Now more than ever seems it rich to die,
To cease upon the midnight with no pain,
While thou art pouring forth thy soul abroad
In such an ecstasy!
Still wouldst thou sing, and I have ears in vain—
To thy high requiem become a sod.