The Galileian telescope furnishes erect images, but has an extremely narrow field of view, which rapidly diminishes with increasing magnification. If, in fact, the field of view of a Galileian telescope with twenty magnifications is indicatively 15 minutes, that is, about half the apparent diameter of the Moon, it decreases to the order of only 5 minutes in a telescope with fifty magnifications. Such limited fields not only made the Galilean telescope unfeasible for civil and military purposes, but above all prevented, in the astronomical field, increments in performance over a few tenths of a magnification.

Johann Kepler (1571-1630) (fig.1) the German astronomer famous for his three laws on planetary motion (fig.2), had however demonstrated, since 1611, the possibility of replaced the diverging eyepiece of the Galileian telescope with a converging lens, with the ensuing advantage of a much vaster and more highly contrasted field of view. But this optical combination, known today as the Keplerian (or astronomical) telescope, furnished upside-down images that made it unsuitable for terrestrial use. Galileo (1564-1642)(fig.3) was to remain always faithful to the optical combination that bears his name. However, in the 1630s, the Keplerian telescope began to be widely used, mainly due to the work of the Neapolitan optician Francesco Fontana (c. 1580-1656)(fig.4), to the point of entirely superceding the Galileian one toward the middle of the century. The last great astronomical achievement (fig.5) made with a telescope of this type, published by Hevelius (1611-1687) in 1647, was the representation of the lunar surface (fig.6). Moreover, the Keplerian telescope soon predominated for terrestrial purposes as well, thanks to the introduction of the so-called erector (fig.7), an optical device, usually consisting of two convex lenses with the same focal length, which turned the image (fig.8) produced by the objective upright.