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From Middle Englishturnpyke(“spiked barrier across a road”), originally used to block access to such a road until toll was paid. Equivalent to modern turn + pike(“shaft”).
A frame consisting of two bars crossing each other at right angles and turning on a post or pin, to hinder the passage of animals, but admitting a person to pass between the arms; a turnstile.
1626, Ben Jonson, The Staple of News, Act III, Scene 1, Yale Studies in English Vol. 28, New York: Henry Holt, 1905, p. 58,
I moue vpon my axell, like a turne-pike, / Fit my face to the parties, and become / Straight one of them.
A gate or bar set across a road to stop carriages, animals, and sometimes people, until a toll is paid,
it was rumour’d that an order of the Government was to be issued out, to place Turn-pikes and Barriers on the Road, to prevent Peoples travelling;
1728, Daniel Defoe, The Political History of the Devil, Part II, ch. 1:
[…] Pope Pelagius, then Bishop of Rome[…] thereupon assum'd the Power of opening and shutting Heaven's Gates; and he afterwards setting a Price or Toll upon the Entrance, as we do here at passing a Turn-pike[…]
1830, Sir Walter Scott, History of Scotland in two volumes Vol II, A AND W GALIGNANI, pages 463-464:
Ramsay stabbed Ruthven accordingly and James lending his assistance they thrust the wounded man down the turnpike by which Ramsay had ascended Voices and steps were now heard advancing upwards and Ramsay knowing the accents called out to sir Thomas Erskine to come up the turnpike stair even to the head Sir Thomas Erskine was accompanied by sir Hugh Harris the king's physician a lame man and unfit for fighting Near the bottom of the turnpike sir Thomas Erskine in his ascent met Ruthven bleeding in the face and neck and called out Fie strike I this is the traitor l on which Alexander Ruthven was run through the body having only breath remaining to say Alas I had no blame of it
1769, Daniel Defoe, A Tour Through the Whole Island of Great Britain, 7th edition, volume II, page 184:
Eleven Pair of Mills ſtand within Four Miles of the Place, which bring a great Trade to it: But the Road is by this means ſo continually torn, that it is one of the worſt Turnpikes about London.
2006, Alexander J. Zaslavski, Turnpike Properties in the Calculus of Variations and Optimal Control, →ISBN:
In the monograph we discuss a number of results concerning turnpike properties in the calculus of variations and optimal control which were obtained by the author in the last ten years.
Turnpike theory on Wikipedia.Wikipedia 