mental motion that man can establish is unrestrained. But a
perception of the uniformity and perpetuity of motion lies at the very
basis of physical astronomy. With difficulty the true idea was attained.
The same may be said as respects rectilinear direction, for many
supposed that uniform motion can only take place in a circle.

[Sidenote: Establishment of the first law of motion,] The establishment
of the first law of motion was essential to the discovery of the laws of
falling bodies, in which the descent is made under the influence of a
continually acting force, the velocity increasing in consequence
thereof. Galileo saw clearly that, whether a body is moving slowly or
swiftly, it will be equally affected by gravity. This principle was with
difficulty admitted by some, who were disposed to believe that a swiftly
moving body would not be as much affected by a constant force like
gravity as one the motion of which is slower. With difficulty, also, was
the old Aristotelian error eradicated that a heavy body falls more
swiftly than a light one.

[Sidenote: and of the second,] The second law of motion was also
established and illustrated by Galileo. In his "Dialogues" he shows that
a body projected horizontally must have, from what has been said, a
uniform horizontal motion, but that it will also have compounded
therewith an accelerated motion downward. Here again we perceive it is
necessary to retain a steady conception of this intermingling of forces
without deterioration, and, though it may seem simple enough to us,
there were some eminent men of those times who did not receive it as
true. The special case offered by Galileo is theoretically connected
with the paths of military projectiles, though in practice, since they
move in a resisting medium, the air, their path is essentially different
from the parabola. Curvilinear motions, which necessarily arise from the
constant action of a central force, making a body depart from the
rectilinear path it must otherwise take, are chiefly of interest, as we
shall presently find, in the movements of the celestial bodies.

[Sidenote: and of the third.] A thorough exposition of the third law of
motion was left by Galileo to his successors, who had directed their
attention especially to the determination of the laws of impact. Indeed,
the whole subject was illustrated and the truth of the three laws
verified in many different cases by an examination of the phenomena of
freely f