Review of the Principia of Newton. 35 | 
aldus and others, to be erroneous, and not applicable to As- 
tronomy, except in orbits of little excentricity. 
ur author’s fertile genius has produced a third solution 
of this great astronomical problem, which, though by the 
‘commentators of his work esteemed as most ingenious, is not 
so direct as the preceding, and, in our opinion, not better 
calculated for practice. 
hese, and many other varied solutions of the most diffi- 
enlt problems in the Principia, are generally delivered with- 
out any analysis, by which term I would be understood to 
mean, the principles by which the auth ived at the solution, 
whether geometrical or algebraical, and not that dexterity of 
symbolical operations, or refined artifices of managing them, 
to which the use of the word has been almost exclusively ap- 
plied by John Bernouilli, and others since his time. To this 
mathematician, who was perpetually boasting of his superior 
skill in analysis, which, in effect, was merely an expedite cal- 
culus, Dr. Brooke Taylor very aptly replied, “ Analysin 
constituunt precepta, juxta que deinde instituitur calculus ; 
qui non est Analysis, sed instrumentum Analyseos.” _Analy- 
sis indeed, as it is called by Bernouilli, furnishes excellent tools ; 
but these are of no use, except they be employed on pronci- 
ples, which, for their invention and development, require 
aculties of the mind much superior to the mechanical opera- 
tions of symbols. 
he succeeding 7th, 8th and 9th Sections of the Principia 
relate to the inverse problem of centripetal forces, which, if 
that of the three bodies be considered as a compo} 
part, may be pronounced the most sublime and diffict 
of any on which the human mind has ever been exerted 
with success. The inventions of our author have be 
most fertile in consequences on every subject, but on none 
more than in those which have resulted from this part of his 
work. The author himself has pursued them as far as was 
necessary for his object, and has laid down the leading prin 
ciples of what has been done since, by Maclaurin, Simpson, 
lairant, Euler, Le Place, &c. The review of this im- 
portant part of our author’s work will be given in some fe-~ 
ture number. : 
