242 Review of the Principia of Newtoi. 
proposition is made a problem and the other a theorem.* 
Newton, however, has been censured for concealing the 
means he employed in the investigation of his difficult prob- 
lems, which in the opinion of a great mathematician, must 
have embraced all the artifices and refinements of the mod- 
ern analytics. In reply to this, it may be observed, that 
the exquisite workmanship of a great artist, does not neces- 
sarily imply the possession of superior tools, or that his own 
genius could not supply the want of them, or of any prescribed 
rules. This observation has been remarkably verified by 
our author. There is scarcely a page of the work now be- 
fore us, in which his inventive genius has not, while it con- 
ducted his grand philosophical analysis, developed some new 
occult mathematical relations. The principal object of the 
Principia, to use the words of Dr. Pemberton was, “ to 
search out and distinguish the springs of natural operation ; a 
work infinitely more difficult to accomplish than even the 
speculations, but has also there discovered the greatest dis- 
cernment and consummate judgment, since in his philosophi- 
cal writings, he has never on imposed on by an 
hypothesis, nor by any of the various fallacies which my 
rd Bacon in his novum organum, has reckoned up as the 
causes that had hindered the improvement of the true phi- 
losophy.”” To a mere mathematician, however, the great 
mathematical inventions of this work, will appear not 
less valuable, than those in philosophy. Among. these 
we account this doctrine of prime and ultimate ratios, many 
ook, the invention and frequent use of the fluxional calcu- 
iu ‘Taylor’s theorem in substance, the differential method, 
r 
these could be supposed to be wanting in analysis, is uuly 
unaccountable. The truth is, that he is the ener of the 
analysis of infinites, of their development by his Binomial 
Theorem, and of i ble refi Catal colin These 
are the fundamentals of the modern refined analytics, which 
oar author originated as an auxiliary to this great philosophi- 
* Vide Simson’s preface to Eucid’s Data. 
