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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