The following insight appears in the text you referenced (Acheson, Elementary Fluid Dynamics, OUP, 1990). It is basically a quote from Principa.
"In Book II of the Principia (1687) Newton writes:
The circular motion of fluids
The resistance arising from the want of lubricity in the parts of a fluid is, other things being equal, proportional to the velocity with which the parts of the fluid are separated from one another.
PROPOSITION LI. THEOREM XXXIX
If a solid cylinder infinitely long, in an uniform and infinite fluid, revolves with an uniform motion about an axis given in position, and the fluid be forced round by only this impulse of the cylinder, and every part of the fluid continues uniformly in its motion: I say, that the periodic times of the parts of the fluid are as their distances from the axis of the cylinder. This is the essence of what Newton has to say about viscous flow.
The hypothesis, of course, gets the subject off to a good start, but it is contained and applied wholly within a section on the circular motion of fluids, and it is immediately followed by a proposition which is false"
The unabridged version of Oxford English Dictionary also quotes Robert Boyle from 1669:
R. Boyle Contin. New Exper. Physico-mech. (1682) ii. 140 That liquor is very thin, and hath no viscosity to resist the pervading body.