Burlington free press. [volume] (Burlington, Vt.) 1827-1865, 1847-12-10

dsoined the historical part of his article from his i'm
provement and moral reilcctons,tha is has disloned
the component parts of his review OF the author, by
the gulf reserved for review OF the work. This.
however, the better enables the reviewer to attempt
by one fell sno2p, by one general nnathcma, to de-
moish and annhilatc him and his works, who shall
provoke the ire of those who claim to have the charge
OF public opinion, by an attempt to detect and expose
popular errors conceiving, no doubt. that timely
and rebuke bestowed upon the author will ope
rate as an admonton to mankind not to disturb the
things that established nor to rely upon their
own powers in the investigation OF important matters
and by way of consolatory nduccmcnt to adopt such
course the reviewer presumcs the very probable fact
or consequence, that if my course had been SUCH in
lieu OF "rclying on my powers" should have sat
isiicd myself that the quadratue of the circle is i'm
abc,-that the Newtonan law OF gravity is the
law, and that the alteration OF the fixed stars at
'ords satisfactory proof of the progressive motion Of
light
And now having gone the reviewers article,
will return TO consideration Of his strange exposition
OF the quadraure OF the circle, and OF the law OF gray
ity,-and also TO his exposition OF the alteration OF the
fixed stars and the progressive motion OF light, il the
designed limits Of this article will admit.
The reviewer in treating of that branch my work
which relates to the quadiature has, in general been
candid, save little vomit in his concluding remarks
and in his unwarranted allegation that he has pro-
c 'eded in his exposition by process which Idcknow-
ledge to be- legitimate; which acknowledgment here
deny: And ! wish the reviewer had been manly
enough TO have proceeded in discussion of the vari
subjects, without frequently alleging that he has
proceeded in his exposition in accordance with prin
ciples which have avowcd; when in fact, they are
often the very Perhaps however, in the fore
going instance, lin accordance with his mode of
soning he inferred that ii must be So in sequence
of the deserved compliment; which he says had paid
| to the 18th proposition of Euclid. And will here
remark that my process for obtaining the qualraturc
is in strict conformity with the principle that the sum
OF the squares of the two equal sides of right anglel
ioscees triangle is the square Of the hypohenuse
longest side.
| lagrce with the reviewer, that if a circle hive n
| regular poygon inscribed and another crcumscrbed
the circumference OF the circle lying between the two
will be longer than the permctcr OF the inscribed and
shorter than the pernetcr of the circumscribed poly
gon but his allegation that the difference between
the periphery OF the circle and the permctcrs OF the
poygons will decrease with the increase OF the num-
Der OF sides OF the poygons, though true in certain
sense, requires explanation, lest msapprchcnsion
should occur (Which explanation he should have Civ
/
riphery of the circle is proportional between
the permctcr of an inscribed, and like circunscrbcd
polyg0n.
so also his allegation that the process by him de-
scrbed may be carried Oh until the pcrimccrs and the
periphery OF the circle shall coince any assignable
extent, requires explanation for it is preposterous
suppose that the periphery OF the circle concide in
nearly but not quite its whole le,gth, wh either an
inscribed or circumscribed permctcr IT, however, the
reviewer intended to refer such coincidence to nu-
mcrical expression only, [and charity would pre-
sumo, or at least would make the correcton) the ale
CATION would be substantially tne in all where
the periphery cannot be expressed by definite nu
merical quantity.
But will pass from criticisms upon the reviewers
enunciaous and allegations, to a consideration of
what the reviewer is pleased to send forth to the world
as review OF my treatise upon the quadaturc, which
review may be detailed follows, viz. the number Of
pages occupedby my rcatlsc,-my ratio Of the diam
etcr of the circle TO its circumference, viz. as ! to
3l7iSG!0, &c-the popular approximate ratio viz as
to 81 1896, &c,together with the difference by
the above ratios between two pepheIies it the dame
ter of the circle be 100 inches and thinks that the
world could not have been aborng under great an
error from the days of Archimcdes to the present
Aud lac considers this grare question, in order
tat it may be fairly settled he his diagram and
again presents the public like similar exposition
of the quadaturc those which have been presented
thousands OF times and until the world has become
tired OF tue monotony Tor the reviewer himself says
that the basis upon which he proceeds is the same
basis upon which the quadrature has been sought ever
since the days OF Archinedes " and then proceeds to
aIcgc the important fact, that as long ago as l'l5
the Academy OF Sciences at Paris announced that
Snl,.
jcct and shortly after the Royal Society OF England
lupted the same resolution"
Aud to me it is somewhat surprising that their pa
thence held SO long in hearing one and the same
story thousand and times told, which, however
ingenious would probably not have paciiicd the Grand
Sultan OF Bagdad would its repetition have con-
ver,cd fiction into truth And perhaps the reviewer
knows why he preferred TO send forth his EXPOSE
ton rather than refer lie Genders Geometry where
t may be found an exposition quite similar somewhat
more extended however,-and perhaps quite as clearly
presented and expressed which work OF lie Gender
in of its various TRANSACTIONS is to be iount
i'll almost every students and scholars hands i'll tn,
; land.
r Such, however, followed by a few general remarks
OF the reviewer, in which he conicsses that he ha
not the acuteness to discover that have advance,
d even one plausible argument, but in which he ha
> not even named commented upon, or attempted Il
: confue a single position which have assumcd or pu
> forth in support of my ratio OF the diameter OF the cir
u Gle its circumference what he would impose up
r on the public a rereD OF the II pages which h
Il says have devoted to the quadraure.
Now if the reviewer had not the acuteness to dis
a cover any thing plausible in my arguments, he Nigh
e have given to the public OF the evidence upol
r which | rely for peradyenture there are some VIII