1811.] 
€71 Isoperhmtncal Prohlems. 
X 
yHC 
which 
f ioned above ; but, had he only been 
able to have read the elements of the 
fluxional calculus, and to have learned 
the dilferent systems of notation made 
use of by the French and German philo¬ 
sophers, the terrific form under which 
those frightful formulag appear, would 
have vanished. In short, from reading 
this review', an unfavourable opinion 
would be entertained of the worh,, and 
hence another reason why mathematics 
do not flourish in this country, since, how'- 
ever eminent a man may become, his practised by John Bernomlli to liis 
wor.ts are almost certain to be depiecmu i,rQtlier James, in order to conceal his 
€0 by some anonymous blockheod. But own plagiarisms, are here very justly ex- 
fate. s posed. In the third section we have 
Mr, Woodhouse justly observes, “ there 
GT , MG EG 
= In vTTc ^ = 
GT , . EG GT 
Tn'" 
is the same result as was found in page 
5. In the next section we have the so¬ 
lution of a far more dillicult problem, 
proposed by James Bernouiilij and solved 
by ins brother John. In this section also 
we have Brook Taylor s solution, and the 
imperfections of his and the Bei-nuidllis* 
solutions are pointed out. The mean 
needs no other apology for the present 
work, than the mere statement of the 
fact; that there is, on the same subject, 
no English, and only one foreign, treatise, 
of which the celebrated I^uler is the au¬ 
thor.” It is evident, then, that Pvlr. W, 
has rendered very essential service to 
English students, by presenting them 
with a small work, the subject matter of 
which had engaged men of the sublimest 
genius in almost every country in Europe, 
Suring the last century ; hut wl}ich was 
written in various languages, and scat¬ 
tered through a number of large tomes 
not easily procured. The history of iso- 
perinietrical problems may he met with 
in Bonnycasrie's translation of Bossaut's 
History of Mathematics; Mr. W. h:is, 
liowever, given sufficient historical infor¬ 
mation to enable the student to trace the 
gradual improvements made by every 
author on the subject. Mr. Woodhouse 
begins his first ciiapterby giving usjain-cs 
Bernouilli’s solution of the following prob¬ 
lem, proposed by his brother John, viz. 
To determine the curve of quickest de¬ 
scent between two given points.” To 
those who are fond of geometrical dis¬ 
cussions, and who love to trace out the 
tract by which science proceeds from its 
birth to maturity, the present solution 
will be particularly gratifying. 
The solution, by James Bernouiilij is 
extremely plain, but Mr. W. has render¬ 
ed it much more so, by converting Ber- 
nouiUBs geometrical forrnuiaj into the 
analytical formulre of the dilFerential cal¬ 
culus. At page the 9ih, Mr. W. has 
abridged Benioidlli's, solution, but his 
conclusion would have been rather neat¬ 
er, and something shorter, if he had 
used the folio 
Lne 1: “ 
5 EG ;; LN ; GT, therefore 
Enler'^s first inemoir on his isoperimetrical 
problems, table of fornuilse, and the so¬ 
lutions of problems hy it, together with 
the solutions of our countrymen SwipsoUf 
Erney'sony Maclaurm. In the next sec¬ 
tion we have EulerT second memoir of 
the general formultE of solution, the cha¬ 
racters of distinction which problems ad¬ 
mit of, and exceptions to the geneial for¬ 
mulas. The fifth section brings us to 
Euler’s tract, entitled Methodus inve- 
niendi liiieas curvas proprietate maxiuu 
minimive gaudentes.” Here we ha^ e the 
distribution of cases into relative and ab¬ 
solute maximaand minima, rules for find¬ 
ing the increment of quantities depend¬ 
ent on their varied state, with formulieof 
solution. The Sixth chapter contains 
the Calculus hy VariationSj invented by 
La Grange, and we believe chat this is 
the only work, in Etiglislt, where that 
calculus is to be met with : after explain¬ 
ing the calculus, it is applied to the in¬ 
vention of new forniukc. We are next 
presented with La Grange’s general me¬ 
thod of treating isoperimetrical prob¬ 
lems, the equation of limits, and casco 
of relative maxima atid minima reduced 
to those of absolute. In the eighth 
cliapter, particular formulae ore deduced 
from the general one, for the purpose of 
facilitating the solution of problems ; and 
this chapter concludes with the solutions 
of twenty-nine .problems, the solution to 
many of wl>rch might in vain be sought 
for in any oilier English author, Tims i 
have given a brief analysis of Mr. Wood- 
house’s work, tiiid, to students who arc 
properly prepared for perusing it, I may 
atfirni, that no difficulties can occur, ex¬ 
cept such as are naturally attendant on 
difiiculc subjects. Those persons who 
isiii me- 
to con- 
Principles of Analytical Calcula- 
by the same author; a profound 
lowing process; see page 10 onacpuiintcd •will, the forei 
or Iroin similar triangles/ ,iiod of notation, woul.l do well 
___ . EG ciilr Pri (1 f'l rtiinc itf AnitivMGal ( 
suit 
MG tions 
