Review of the Principia of Newton. 333 
relation, a of any other space fallen through, to any 
other time, must be determined by measuring an area corres- 
ponding to ae time by a line drawn from the extremity of 
the diameter of the circle, or infinitely diminished ellipse to 
the extremity of the circular, parabolic, or hyperbolic ordinate. 
The area will express the times, and the intercepted part of 
the diameter, or the abscissa will represent the space passed 
over. Our author has solved this by similar and analogous 
principles of motion, which had been developed in the prece- 
ding sections of his work. The velocity of a falling body 
under the influence of a force varying as had been before in- 
vestigated, has been determined with great ingenuity on the 
same principles, so as to form a well compacted system of 
rectilinear and curvilimear Stee Bg the parts of which are mu- 
tually dependent on one another, and all founded, as is the 
mathematics generally, on the most simple elementary 
eiples. ‘The Principia has derived its celebrity fe from the dig- 
nity of its subjects, the almost miraculous profundity of its 
investigations, and its complete development of the great 
operative powers of nature. These great points have eclips- 
inor excellencies of the work, viz. its concise a 
nt demonstrations, the logical, systematic and 
pd of the principal topics, so as naturally to grow 
out ef each other by an admirably connected chain of argu- 
ments, all tending to one object---the establishment of a new, 
and before the author’s time, wholly unknown system of phi- 
losophy. Newton, in all these particulars, may justly be con- 
sidered as the Euclid of philosophy, differing from him, who 
has had the highest reputation for more than 2000 years, in 
what is very remarkable, that he was the sole inventor of — 
all the great truths he delivered, whereas the other was a 
piler, and ingenious systematic manager, of materials far- 
nished at his hand. 
But to return now to the subjects under review ; the recti- 
linear motion of bodies, acted on by a force, such as obtains 
in the natural world, is fully investigated in the 32d and suc- 
ceeding propositions, and some curious results are from them 
obtained. One, in ee is worthy of notice in this 
place, viz. that a body revolving ina circle, if the velocity 
with which it revolves, be turned directly contrary to the 
direction of the centripetal force, it will rise to double the 
height it first had from the center of force. 
