Once upon a time in America, particularly during the 1970s, if you asked an American whether they ‘fancied a shag’, they might well have thought of this:

And therefore declined the offer for fear of rug-burn.
Meanwhile their kids, being still innocent, would have likely assented to the request, hoping that Scooby might be part of the offer:

But then the British Invasion poisoned all such bucolic memories once Austin Powers: The Spy Who Shagged Me hit the American cinema:

Lest any doubt remain about what is being discussed here, the following scintillating dialogue should wipe all those away:
Vanessa Kensington: Look, I know I'm being neurotic, but I can't shake off this suspicious feeling about that Italian secretary. You know, Miss Fagina. I don't want to sound paranoid, but I've had some bad relationships in the past, and I have been known to be jealous. I'm sorry.
Austin Powers: No, don't be sorry, baby. You're right to be suspicious. I shagged her.
Vanessa Kensington: What?
Austin Powers: I shagged her rotten, baby, yeah!
Vanessa Kensington: I don't believe you, Austin! I mean, she was repellant.
Austin Powers: Saucer of milk, table 2. Meow.
Vanessa Kensington: Well, did you use protection?
Austin Powers: Of course. I had my 9mm automatic.
Vanessa Kensington: You know I meant 'did you use a condom'?
Austin Powers: No. Only sailors use condoms, baby.
Vanessa Kensington: Not in the 90's, Austin.
Austin Powers: Well they should, those filthy buggers. They go from port to port.
My question is, where did this sense of shag come from? The OED calls this copulatory sense “of obscure origin” and provides a first citation dating from Grose’s Dictionary of the Vulgar Tongue of 1788, in which the modern sense is first given.
But where does it really come from? Surely if it made a vulgar dictionary in 1788, there must be possible antedatings of the written not merely oral form.
