According to Galileo by John L. Heilbron (Galileo’s extrusion argument):
p. 272 “Ptolemy had agrued that objects not fastened to the Earth would be thrown off if the glove spun. Galileo countered that irrespective of the speed of rotation, no such extrusion can occur.”
p. 273 “He [Galileo] could not think himself away from the Earth anymore, than Simplicio could imagine himself on the planet.”
I have searched about this issue in Internet and have found a good historical overview of the problem.
P Palmieri – Journal for the History of Astronomy, Nov 2008, Vol. 39 Issue 4, p425
Galileus Deceptus, Non Minime Decepit: A Re-appraisal of a Counter-argument in Dialogo to the Extrusion Effect of a Rotating Earth
‘As we shall see, Galileo basically wishes to prove that no matter how fast the Earth rotates daily on its polar axis, objects on its surface would never be extruded, i.e., they would never fly off toward the sky. That this should be the case was a rather common objection raised by anti-Copernicans at that time. Thus, in the late 1930s, Alexandre Koyré pointed out that “Galileo’s argument … is extremely subtle and seductive. Unfortunately it is incorrect; and what is worse, it is manifestly incorrect”. Others followed Huygens and Koyré in their negative assessment of Galileo’s argument.’