GALILEI, GALILEO (b. Pisa, Italy, 15 February 1564; d. Arcetri, Italy, 8 January 1642), physics, astronomy.

    an idea previously published by Giovanni Battista Benedetti in 1553-1554 and again in 1585. In the same treatise, Galileo derived the law governing equilibrium of weights on inclined planes and attempted to relate this law to speeds of descent. The result did not accord with experience—as Galileo noted—which may be the principal reason for his having withheld the treatise from publication. The discrepancy arose from his neglect of acceleration, a phenomenon that he then considered to be evanescent in free fall and that he accounted for by a Hipparchian theory of residual impressed force. In order to reconcile that theory with fall from rest, Galileo introduced a conception of static forces closely allied to Newton's third law of motion. Equality of action and reaction, together with the idea of virtual velocities, pervades much of Galileo's physics. From his earliest demonstrations of equilibrium on inclined planes, Galileo limited the action of tendencies to motion to infinitesimal distances, unlike his ancient and medieval predecessors. In so doing, he was able to relate vertical fall to descent along circular arcs and tangential inclined planes, an achievement that was to provide him with the key to many phenomena after he recognized the essential role of acceleration.

In his De motu, Galileo undertook to destroy the Aristotelian dichotomy of all motions into natural and forced motions. He did this by introducing imaginary rotations of massive spheres. Rotations of homogeneous spheres, or of any sphere having its geometric center or its center of gravity at the center of the universe, he declared to be “neutral” motions, neither natural nor forced. Motions on the horizontal plane, or on imaginary spheres concentric with the earth's center, were likewise neutral—a conception that led Galileo to his restricted concept of inertia in terrestrial physics. His discussion of spheres in De motu shows further that in 1590 Galileo had not yet abandoned the geocentric astronomy, but suggests that he saw no difficulty in the earth's rotation as assumed in the semi-Tychonic astronomy.

Vincenzio Galilei died in 1591, leaving Galileo, as eldest son, with heavy domestic and financial responsibilities. Galileo's position at Pisa was poorly paid; he was out of favor with the faculty of philosophy and he had offended Giovanni de' Medici by criticizing a scheme for the dredging of the harbor of Leghorn. His disrespectful attitude toward the university administration is reflected in a jocular poem he composed against the wearing of academic robes. Thus, at the end of his three-year contract, Galileo had no hope of strengthening his position at Pisa and little promise even of reappointment. Once more with the aid of Guidobaldo, he moved to the chair of mathematics at Padua. The rival candidate was again Magini, whose hostility toward Galileo after this defeat became extreme.

Professorship at Padua.

The atmosphere at Padua was propitious in every way to Galileo's development. He quickly made the acquaintance of free and erudite spirits, in such men as G. V. Pinelli and Paolo Sarpi. Among his students were Gianfrancesco Sagredo and Benedetto Castelli. A conservative professor, Cesare Cremonini, became his personal friend while staunchly opposing his anti-Aristotelian views. Padua was a gathering point of the best scholars in Italy and drew students from all over Europe. Under the Venetian government, the university enjoyed virtually complete freedom from outside interference.

Galileo lectured publicly on the prescribed topics: Euclid, Sacrobosco, Ptolemy, and the pseudo-Aristotelian Questions of Mechanics. Privately he gave instruction also on fortification, military engineering, mechanics, and possibly also on astronomy, although we lack concrete evidence of his having become deeply interested in that subject much before 1604. He composed several treatises for the use of his students. One, usually known as Le meccaniche, survives in three successive forms, dating probably from 1593, 1594, and about 1600. In this treatise, besides developing further his treatment of inclined planes, he utilized as a bridge between statics and dynamics the remark that an infinitesimal force would serve to disturb equilibrium. This move, although itself not unobjectionable, removed serious existing obstacles (which had been raised on logical grounds by Guidobaldo and Simon Stevin) from the mathematical analysis of dynamic problems. Galileo's treatise, before it was first published in a French translation by Marin Mersenne in 1634, circulated widely in manuscript, and an English manuscript translation was made in 1626. Its authorship was not always known to readers even in Italy, because Galileo's treatises composed for his students were invariably supplied in copies bearing no title or signature.

In May 1597 Galileo wrote to his former colleague at Pisa, Jacopo Mazzoni, defending the Copernican system against a mistaken criticism. In August of the same year he received copies of the Mysterium cosmographicum, the first book by Johannes Kepler, to whom he wrote expressing his sympathies with Copernicanism. Kepler replied, urging him to support Copernicus openly, but Galileo allowed this correspondence to languish. His preference for Copernicus at this time seems to have had a mechanical rather than an astronomical basis; he wrote to Kepler that it afforded an explanation of physical effects not given by its rivals. This referred to a tidal theory of Galileo's