I have just finished reading an English translation of Espingarda Perfeyta (The Perfect Gun) first published in Portugal in 1718. Even in English this book takes some interpretation, but I think that a form of "jug" or "relief" choke boring is clearly discussed. Bird shot is called "hail-shot" and the section I quote is preceded by a wood cut of a hunter shooting flying birds with a flint-lock.
The translator and editor say the book was in process in the "17th century" (late 1600s) and the authors quote another book, Arte de Ballesteria by Spinar (possibly Spanish or Italian), which would date the information back to the late 1600s. Here's what they were saying about improving pattern by modifying the barrel at the muzzle, two centuries before Fred Kimble, in his senility post-1910, decided he had retroactively "invented" choke boring in 1868:
At p.361: "...Good adjustment of the barrel consists of firing far with the hail-shot close together and this length, that gives it esteem, until now the ultimate point to which art can cause a shot to go with undispersed ammunition, is fifty paces..."
The authors then discuss the proper boring of a ball musket and return to a "hail-shot" scatter-gun at P.371, quoting Spinar:
"'...The most proven remedy for correcting this ill [1], is to widen it at the muzzle two or three fingers within [2], in such a manner that this widening becomes an adarme [3], or an adarme and a half more hollow [4], than the remainder of the gun.'"
I other words: [1] The "ill" is blowing a pattern and not keeping the shot charge together to a killing distance;
[2] The gunmakers would go in the muzzle "two or three fingers" (being about 1 1/2- to 2 1/2-inches) and open up the bore size, making it [4] "more hollow," by about [3] "an adarme or adarme and a half," an adarme being a unit of weight of lead, or, in effect saying that a 12-balls-to-the-pound "12-bore" should be relief-choked a couple inches from the muzzle to ten-bore.
And Spinar, being quoted by the authors, explains: "'...This widening serves for two things, which are that the pressure, and force which the powder makes in the narrow part of the gun may be less with that widening, in order to give ease to the hail shot that it may leave well, and keep together, for in this I have great experience, and never err, and have therewith corrected many guns...'"
Then the authors of The Perfect Gun conclude their discourse on choke boring: "We could add other authorities, but reasons are unnecessary, where there is experience to teach the best manner..."
There it is: Choke Boring is described by method (bore-size relief behind the muzzle), effect (that the hail-shot should leave the barrel well and stay together), and by in-practice experience sufficiently well-known in the trade so the authors don't bother quoting additional authorities. This in a Portuguese book published in 1718 referring to another book published in the 1600s. EDM
