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remarkable perseverance and success by his contemporaries Kepler 
and Galileo. The achievements of these two philosophers, which 
were essential contributions towards the advancement ol natuial 
philosophy, were widely different in character, lhe laws ot the 
planetary motions, as discovered by Kepler, were formal relations 
of space and time, determined by observation alone, without refer- 
ence to the action of force whereas Galileos experiments ueie 
expressly directed towards ascertaining laws of force. He proved 
by experiment that a projectile acted upon by gravity at the 
earth’s surface moves in a parabolic path. By this means 
he established (in combination with the law of vis inertias , 
according to which a body persists in a state of rest, or of uniform 
motion m a straight line, unless it be disturbed by extraneous 
force), the fundamental law of the acceleration of a body acted 
upon by a constant force ; viz., that the acceleration, as estimated in 
the direction in which the force acts, takes place in the same degree, 
whatever be the actual motion, and direction of the motion, of the 
body acted upon. 
4. With prospective reference to an argument that is to follow, 
I now assert — what perhaps is not generally understood— that no 
mathematical reasoning, such as that employed by Newton . or 
Laplace, was capable of demonstrating the parabolic motion which 
Galileo ascertained by experiment, and that the whole of the 
mathematical reasoning in physical astronomy depends on. esta- 
blishing by experiment that law of parabolic motion. This was 
perfectfy understood by Newton, who frequently, in his Principia , 
refers to the results of Galileo’s experiments as being of a funda- 
mental character, and in particular calls the parabolic motion 
“ Galileo’s Theorem.” If it be urged that there are well-known 
methods of calculating the parabolic motion of a projectile, without 
reference to Galileo’s experiments, the answer is that these calcula- 
tions take for granted the fundamental law of accelerative action 
above mentioned, which law is incapable of establishment on any 
other basis than that of experiments such as those made by Galileo. 
5. Armed with Galileo’s theorem, and with the powerful method 
of calculation (equivalent to the differential and integral calculus) 
which he had himself discovered, Newton was able to give, an 
a, priori demonstration of Kepler’s Laws. But here it is particu- 
larly to be noticed that this demonstration rests on the hypothesis 
that the force of gravity varies inversely as the square of the dis- 
tance from the particles from which it emanates. Besides this 
hypothesis, it is also assumed, in physical astronomy, that each 
particle of a given body attracts all the particles of the same body , 
as well as all the particles of surrounding bodies, according to the 
law of the inverse square. But physical astronomy furnishes no 
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