Examples of “procure abortion” from The BYU-Corpus of Early Modern English

1712: “an approved Medicine to procure Abortion”  The lucubrations of Isaac Bickerstaff, The Tatler, No. 245 (Oct 31 - Nov 2, 1710), "Advertisement"
“Isaac Bickerstaff” was a pseudonym invented by the famous satirist Jonathan Swift, who suggested in the essay, A Modest Proposal, that overpopulation in Ireland be alleviated by selling Irish children as edible delicacies. Jonathan Swift, Britannica, https://www.britannica.com/biography/Jonathan-Swift.  This text from COEME appeared in The Tatler, a publication produced by Swift and other satirists. The context of the quote is an "Advertisement" to recover stolen goods; “approved Medicine to procure Abortion” appears along with such improbable items as “Lockets with the Hair of dead and living Lovers” and “Frog Spawn Water.”

1757: “the habit unmarried women have of procuring abortion, in which they rarely fail” William Burke, An account of the European settlements in America: In six parts (London 1757), Eighteenth Century Collections Online, available at  http://name.umdl.umich.edu/004909745.0001.002
This quote comes from the chapter on “The Manners and Customs of the original inhabitants,” and the larger context is “Probably, that severe life which both sexes lead, is not favourable to procreation. And the habit unmarried women have of procuring abortions, in which they rarely fail, makes them the more unfit for bearing children afterwards.”

1769: “have an abortion procured by order of the magistrate
Adam Ferguson, An Essay on the history of civil society 208 (Dublin 1767) Eighteenth Century Collections Online, available at http://name.umdl.umich.edu/004846977.0001.000   
“IN warmer latitudes …the numbers of mankind increase … and the commerce of the sexes, without any concern for population, is made a subject of mere debauch. In some places, we are told, it is even made the object of a barbarous policy, to defeat or to restrain the intentions of nature. In the island of Formosa, the males are prohibited to marry before the age of forty; and females, if pregnant before the age of thirty-six, have an abortion procured by order of the magistrate, who employs a violence that endangers the life of the mother, together with that of the child.”

1773:   “use every mean to avoid conception, and even to procure abortions”
Henry Horne, Sketches of the history of man (Dublin), Eighteenth Century Collections Online, available at http://name.umdl.umich.edu/004843629.0001.001
“the slaves continually decrease so as to need frequent recruits from Africa. "This decrease," says the author of a late account of Guiana, "is commonly attributed to oppression and hard labour; tho ' with little reason, as the slaves are much more robust, healthy, and vigorous, than their masters. The true cause is, the commerce of white men with young negro wenches, who, to support that commerce, use every mean to avoid conception , and even to procure abortion. By such practices they are incapacitated to bear children when they settle in marriage with their own countrymen.”