Green’s Dictionary of Slang

(orig. milit.) sexual intercourse.

[1732-1820		Order of the Beggar's Benison and Merryland (1892) 19: Dinner Sentiments [...] Navel Battles! Midnight Campaigns! Success doubtful! Engagement perpetual!].
1904		Lustful Memoirs of a Young and Passionated Girl 25: it was not many minutes before he was preparing for another engagement. [Ibid.] 41–2: He had fought too many such engagements not to know how best to cause his partner to enjoy the most of the sweetest pleasures.
1966		Trimble 5000 Adult Sex Words and Phrases.