The native American. [volume] (Washington City [i.e. Washington, D.C.]) 1837-1840, 1837-10-07

~ss Thu SoS0nhy OkE oV tkSb0 6t&SGEG~
we have undertaken This article, because We have
reason 70 know, that there still persons, who
Ignorance Of the real question, are turning their
aienhon 10 this useful and exploded problem, and de-
themselves and their neghbors into the belief
sasy nave sacceeded In doing that which has been
repeatedly shown y bs impossible. BY the rectifca
non OF circle 70 meant the finding of straight line
which shall De equal in length to the circumference Of
given circle, or the two ends OF which when bent
sGuns snoud exactly meet by the rature Of
In snrace to given circle, that is to the whole sna
contained inside its circumference. There i No d;as
|culty in doing these problems in a manner mors IN.
sufficiently correct for all useful purposes. IT, for ex
ample, we take circle as large the earths orbt
and an atom as small as the smallest insect which !.
microscope ever showed In drop Of water. notbiny
would be more easy than find the circumference q
this circle so nearly that the error committed should
be less than the length of that atom. The problem
which has puzzled many generations is the finding
what's called geometrca quad nature of the Circle
What this Is proceed to explain. u is the object
OF geometry to find out, by reasoning all truths which
relate TO the various figures which draughtsman can
construct. Not that these figures are precisely the
objects Of geometical reasoning; for Inns
has no breadth thickness but only length while tho
line we draw with penci has small degree both Of
breadth and thickness. 1t is agreed by geoeters to
take te for granted possible and 70 make their
propositions arise out Of the smallest number Of simple
truths 1t s also agreed imagine the existence Of
as few figures possible II therefore the prac-
tice of the ancient geometres to no problems
except the following: l. straight line can be dawn
from one point to another. Q. straight line, when
finished can afterwards be made longer. g. Aacjrcle
can be drawn with any point CENTRE and any line
as radius. All lines, except the straight line and civ
cie and afterwards the co, c secons called me-
chanica, as distinguished from geonetrcal lines; and
and il any problem arose, the fret attempt was always
to solve it economically, and only when that failed
were mechanical means Tesorted to, or where other
curves constructed, the construction Of which once
ooIuo tho nPOhIo
and nechanca applied to distinguish one sort of
solution from another, may be improper; but that s not
the question. When man asserts that he has found
ge0metrical quadratuIe of the CIRCLE he either does
in the word in the Of the ancient geome
ters II he does, and his solution is correct he has
certainly solved the problem; but that no one has vet
done this is universally avmtied. If he does not use
the word eeomerical in the ancient Specification his
solution has nothing to do with the problem, which
has hitherto remained unsoved. Many ways have
been discovered of finding the Of circle, which
take something more tor granted than the use Of he
ruler and compasses only, and any person, with rea-
sonable knowledge Of mathematics, might add dozen
to the number in couple of hours So much for the
geomeuical solution Of the problem.
was proved long before the Christian era, that the
lcircumere Of two different cces are TO one an.
other as the radi, that is whatever number Of times
circumference contains its radius the other crcum-
ference contains its radius many times or whatever
fraction radius Ia of s circumfe:en the same
fraction is the other radius of circumference From
this it follows that if any number Of circles were taken
having for radii foot yard mile, &C., whatever
number Of feet and parts would On round tho first
The number Of miles and similar parts Of miles
would 60 round the third and on. Hence it became
question Of importance to discover what was the
number Of units and parts of units contained in the
circumference of circle whose radius was the unit
Again. it was proved that the number Of square feet
parts of square feet in circle Of foot radius
was the the number Of square miles and SINH
parts Of square miles contained in the circle Of
mile radius. Archimedes showed tho, circle Of ono
foot in radius contained nearly square feet and of
a square foot, which does not differ from the III
so much as l-5 Of square inch, and gives the clc
too great BY about its three housand,h part. An an
cient measure Of the Hndoos makes it square fee:
and III parts out Ct 1850 Of square foot This j,
much nearer to the TRUTH differing from it about one
thousandth part Of square inch but still little too
much Metius, who foarished in the beginning Of the
seventeenth century found that if square foot be d.
vded into parts the circle Of one foot radius con-
contains about 355 Of these pars result Of surprising
accuracy when the simplicity Of the number is consid-
cred il is too great by about the fifty thousandth part
Of square inch. These numbers may be very easily
recoected, since, when put together thew Give the
first three old numbers, each repeated twice: tins
1885.
The following simple rules will enable every one Of
readers to find the circumference Of circle IF anv
one OF them would 60 direct round the world he would
by means Of them, if the earth perfect sphere;
be able 70 tell the length Of his journey within less
than four yards. From til I'm the word inch NAV be-
taken out, and any other unit substituted.
To find the length Of the circumference of circle,
multiply the number Of inches in the diameter Cor twice
the radus) by 255, and divide the product by l33-
The result is the number Of inches in the eli cumfer-
ence.
10 find the area, surface Of circle, multiply the
number OF inches IN the radius by ITSELF and that pro-
duct by 1885, divide the result by 49, the quoiien Of
which is the number of square inches in the area.
We might 60 on to describe still more accurate me-
thods; it will be sufficient say thathe latest Of them
gives the area Of circle true to 100 decimal places,
it is called; that il, il the radius be 1000 &c. feet
the cphers being 1877 in number the area ofthe circle
Will be obtained without error Of square foot.
Still this is only an approximation, and however
yearly the circumference of circle has been obtained
It has never been obtained exactly. Numberless at
tempts have been made find the exact ratio Of tho
circumference to the diameter, but without success
the reason being, afterwards proved, that he
thing is impossible.
EXHIBITION or PAINTINGS.
Now exhibiting in the brick blu ding, the o. ~
street. ennsy vana Avenue, door Mrs KennciFs
Roang house, he celebrated paint ing, Of the interior ST.
Peters, church tomc also view of the Bay aud City, OF
Naples painted from nature, by G. Cooke.
Open from O'Clock A. M. to 6 y. NJ
Abundance, Is cents, Children i21 cents.