  What are the historical evidence concerning the turning of the spyglass into
an astronomical instrument, the telescope? In Sidereus Nuncius and in his
private correspondence Galileo tells the reader what he did with the telescope,
but he did not disclose the existence of a theory of the instrument. Still, the
instruments which Galileo produced are extant and can be studied. With replicas
of Galileo's telescopes that magnify 14 and 21 times, we have simulated and
analyzed Galileos practices as he reported them in Sidereus Nuncius. On this
ground, we propose a new solution to this old problem. We establish the
knowledge of optics that Galileo had as it can be read off from the telescopes
he constructed and the way he put them to use. Galileo addressed optical
difficulties associated with illumination, resolution, field of view, and
magnification. His optical knowledge was well thought through, originated as it
did in a radically new optical framework.
