Galileo's father, Vincenzio, was an impoverished descendant of a noble
Florentine house, which had exchanged the surname of Bonajuti
for that of Galilei, on the election, in 5343, of one of its
members, Tommaso de’ Bonajuti, to the college of the twelve
Buonuomini.
The
invention of the microscope, attributed to Galileo by his
first biographer, Vincenzio Viviani, does not in truth belong
to him. Such an instrument was made’ as early as 1590 by
Zacharias Jansen of Middleburg; and although Galileo
discovered, in 1616, a means of adapting his telescope to the
examination of minute objects, he did not become acquainted
with the compound microscope until 1624 when he saw one of
Drebbel’s instruments in Rome, and, with characteristic
ingenuity, immediately introduced some material improvements
into its construction. 
The most
substantial, if not the most brilliant part of his work
consisted undoubtedly in his contributions towards the
establishment of mechanics as a science. Some valuable but
isolated facts and theorems had been previously discovered and
proved, but it was he who first clearly grasped the idea of
force as a mechanical agent, and extended to the external
world the conception of the invariability of the relation
between cause and effect. From the time of Archimedes there
had existed a science of equilibrium, but the science of
motion began with Galileo. It is not too much to say that the
final triumph of the Copernican system was due in larger
measure to his labors in this department than to his direct
arguments in its favor. The problem of the heavens is
essentially a mechanical one; and without the mechanical
conceptions of the dependence of motion upon force which
Galileo familiarized to men’s minds, that problem might have
remained a sealed book even to the intelligence of
Newton.
The
interdependence of motion and force was not indeed formulated
into definite laws by Galileo, but his writings on dynamics
are everywhere suggestive of those laws, and his solutions of
dynamical problems involve their recognition. The
extraordinary advances made by him in this branch of knowledge
were owing to his happy method of applying mathematical
analysis to physical problems. As a pure mathematician he was,
it is true, surpassed in profundity by more than one among his
pupils and contemporaries; and in the wider imaginative grasp
of abstract geometrical principles he cannot be compared with
Fermat, Descartes or Pascal, to say nothing of Newton or
Leibnitz.
The first
law of motion, that which expresses the principle of inertia,
is virtually contained in the idea of uniformly accelerated
velocity. The recognition of the second, that of the
independence of different motions, must be added to form the
true theory of projectiles. This was due to Galileo. Up to his
time it was universally held in the schools that the motion of
a body should cease with the impulse communicated to it, but
for the “ reaction of the medium “ helping it forward.
Galileo showed, on the contrary, that the nature of motion
once impressed is to continue indefinitely in a uniform
direction, and that the effect of the medium is a retarding,
not an impelling one. Another commonly received axiom was that
no body could be affected by more than one movement at one
time, and it was thus supposed that a cannon ball, or other
projectile, moves forward in a right line until its first
impulse is exhausted, when it falls vertically to the
ground.
In the
fourth of Galileo’s dialogues on mechanics, he demonstrated
that the path described by a projectile, being the result of
the. combination of a uniform transverse motion with a
uniformly accelerated vertical motion, must, apart from the
resistance of the air, be a parabola. The establishment of the
principle of the composition of motions formed a conclusive
answer to the most formidable of the arguments used against
the rotation of the earth, and we find it accordingly
triumphantly brought forward by Galileo in the second of his
dialogues on the systems of the world. It was urged by
anti-Copernicans that a body flung upward or cast downward
would, if the earth were in motion, be left behind by the
rapid translation of the point from which it started; Galileo
proved on the contrary that the reception of a fresh impulse
in no way interfered with the movement already impressed, and
that the rotation of the earth was insensible, because shared
equally by all bodies at its surface.
His theory
of the inclined plane, combined with his satisfactory
definition of “momentum,” led him towards the third law of
motion. We find Newton’s theorem, that “action and
reaction are equal and opposite,” stated with approximate
precision in his treatise Della scienza meccanica,
which contains the substance of lectures delivered during his
professorship at Padua; and the same principle is involved in
the axiom enunciated in the third of his mechanical dialogues,
that “the propensity of a body to fall is equal to the least
resistance which suffices to support it.” The problems of
percussion, however, received no definitive solution until
after his death.
His
services were as conspicuous in the static as in the kinetic
division of mechanics. He gave the first satisfactory
demonstration of equilibrium on an inclined plane, reducing it
to the level by a sound and ingenious train of reasoning;
while, by establishing the theory of “ virtual
velocities,” he laid down the fundamental principle which,
in the opinion of Lagrange, contains the general expression of
the laws of equilibrium.