Leviathan and the Air-Pump (Shapiin, 1985)
One of the various cover designs of Steven Shapin and Simon Schaffer's 1985 Leviathan and the Air Pump, showing a fish inside of the receiver "vacuum bulb" (top part), the part below the turn valve, at the bottom of the bulb, being the "air pump". [2]
In science, air pump (TR:5) is combination vacuum pump, i.e. able to suck air out of a vacuum bulb or "receiver", and able pump air into the vacuum bulb or receiver.
-
Overview
The original 1647 pump designs of Otto Guericke were "vacuum pumps", a product of him trying to suck the air out of beer keg (see: beer keg experiment). The 1659 re-design of the former by Robert Boyle was a combination vacuum pump and air pump, which Boyle referred to as a "pneumatical engine", but which latter came to be called or classified, particularly by historians, as a "air pump". The following is a timeline map of the spread of the construction of air pumps, starting with Guericke's vacuum pump, which was followed by Boyle's air pump, then Christiaan Huygens pump, possibly Henry Power's pump, and Denis Papin's pump, being the main versions: [2]
Guericke map 2

Note
The term “air pump”, as used in engineer and science discussion, is not to be confused with a typical air pump, such as used to fill a bicycle tire, as these types of devices simply push air into deflated tire tubes, but aren't able to make vacuums.

Quotes
The following are related quotes:

Papin's project of 1687, for using gunpowder, is of no real utility: indeed, he was sensible that he had not succeeded, and said he published it only to excite the learned of other countries to perfect it. (See the Acta Eruditorem for 1688, p. 497.) He proposed to employ a cylinder with a piston fitted into it, and to the rod of this piston the weights which were to be raised were applied by a rope conducted over pulleys, and they were to be lifted by the pressure of the atmospheric air upon the piston, when the air was exhausted from the cylinder. Thus far, he followed Otto Guericke; but instead of exhausting the cylinder by an air pump, Papin proposed to drive out the air by firing off a small quantity of gunpowder in the inside of the cylinder. The piston had a large aperture in it, covered by a valve opening upwards; and he thought that the sudden blast of flame produced by the explosion of the gunpowder would lift up the valve, and drive out the air at the aperture; but when the flame ceased, the valve would fall, and prevent the return of the air into the cylinder, so as to leave it exhausted, and then the pressure of the atmosphere on the upper surface of the piston not being balanced by any air beneath, would press the piston down with great force. Papin speaks of two models of this machine which he tried; one of them five inches diameter and 16, inches high; but he says he could never succeed in expelling the whole of the air from the inside of the cylinder: about one-fifth always remained, and that fifth, as he says, reduced the force to one-half of what it would have been if he could have expelled the whole of the air.”
John Farey (1827), A Treatise on the Steam Engine [1]

Boyle’s original [pneumatic] machine [1658/1659] was presented to the Royal Society of London; he had one or two redesigned machines built for him by 1662, operating mainly in Oxford; Christiaan Huygens had one made in The Hague in 1661; thee was one at the Montmor Academy (ΡΊ) in Paris; there was one at Christ’s College, Cambridge, by the mid-1660s; and Henry Power may have possessed on in Halifax from 1661. So far as can be found out, these were all the pumps that existed in the decade after their invention.”
Steven Shapin (1985), Leviathan and the Air Pump (co-author: Simon Schaffer) (pg. 38-39) [2]

References
1. Farey, John. (1827). A Treatise on the Steam Engine: Historical, Practical, and Descriptive (pgs. 94-98). Longman.
2. Shapin, Steven; Schaffer, Simon. (1985). Leviathan and the Air Pump: Hobbes, Boyle, and the Experimental Life (quote, pgs. 38-39; map, pg. 228). Princeton, 2011.

TDics icon ns