30 Review of the Principia of Newtou. 
most difficult questions, those which arose out of our author’s 
inventions, and which he had neglected to pursue, were the 
most prominent. Among these were the problems of finding 
equal times in a vertical line ; another to find the curve along 
which, the body descending would describe equal distances 
om the point of its departure in the same time. But 
_ sian philosopher. This was to find a curve along which a 
body would descend by the force of gravity from one given 
point to another not in the same vertical line, in the shortest 
time possible. On account of the supposed difficulty of the 
problem, Bernouilli allowed to mathematicians one whole 
year for its solution. In a short time after its promulgation 
through Europe, he was presented with an anonymous solu- 
i this great problem, on which he observed, “ that 
though the author had not given his name, he saw clearly on 
his work the stamp of the lion.” This first solution was pro- 
duced by Newton ; afterwards others were given by Taylor, 
De la Hospital, Leibuitz, &c. The part of our author’s solu- 
tion which shows the relation between the time of descending 
down a plane or right line compared with that of the Bra- 
one of the most beautiful synthetic demonstrations in the 
whole compass of the mathematics. These remarks may ap- 
ar digressive, but they are not irrelevant to our object, in- 
asmuch as all these and other analogous problems, have ema- 
nated from the general principles of motion under the influ- 
ence of certain forces developed in the 2d and 3d sections of 
the Principia, and may be properly considered as supplemen- 
to them. : 
pe ee not the object of Newton to pursue a subject, which 
he had originated, even though most fertile in consequences, 
through all its ramifications, and which. when three or more 
forces are acting on a body, and in different directions, would 
require volumes and all the refinements of his own analysis, 
to develope, to the full extent of which it might be suscepti- 
ble. The principal if not the only end in view in the Prin- 
Cipla appears to be, the substantiation of the author’s system 
of philosophy by mathematical demonstrations. In_ this 
» be has been completely — 
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