Review of the Principia 6f Newtou. ‘31 
shecessful, but has left to his successors the details of his 
work, and all the minor advantages of his immense fabric. 
But even that grand object could not be accomplished with- 
out great skill, and address in the mathematics. This sci- 
ence, at his time embraced little more than what had been 
handed down from the Grecian and Alexandrine schools, and 
the.improvements of Des-Cartes, Vieta, Wallis, and a few 
moderns. Those regarded principally the elements of the 
science. eometry in the time of our author, was insuffi- 
cient for the determination of the Drajediceisa, | in which the 
celestial bodies move, not even by observations. neir me- 
thods of obtaining this object were tentative, indirect, and hy- 
pothetical. ry application, therefore, of the laws of force, 
as investigated in the 2d and 3d sections, aps constitu- 
ting a new era in philosophy, could only ap y to some po 
tential movements, which were not known = ee before the 
a posteriori process from observation had proved their reali- 
ty. This problem of finding the trajectories by observation, 
and mathematics only, is indeterminate ; still, however, it was 
necessary for that approximation, which has been resorted to 
which are purely mathematical. The principal physical ap-. 
plication of them will be found in determining the orbits of 
the comets, or any new planet which may a pear. he difs 
ficulty in this grand problem consists Principally i in pariae . the 
the radius vector at any time, which can only be do 
rrec 
by an assumption of those very principles, which i it was the ob-- 
ject of Newton to verify. This verification, Aan rg 
torily obtained by the numerous successive observations, which 
have been made on the edlecitsl bodies b adanainipan, 
ages, whereby their periodical times have been ascertained 
with great accuracy. ‘Their radii vectores in respect to the 
sun, may also be inferred, from those observations made from 
the earth, and the laws of Kepler deduced as he actually has 
deduced them wholly from phenomena. The accordance of 
Newton’s physical principles with those long and numerous: 
tions, would alone have been sufficient for the verifi- 
new planets. 
more comprehensive, and went to the extension and i improv: 
ment of astronomy, and physics _ teigich ae the aid of his 
discoveries. This work too, has been accomplished by hira 
ce 
