Weekly national intelligencer. [volume] (Washington [D.C.]) 1841-1869, 1846-09-26
QUADRATURE OF THE CIRCLE.

history Of the innumeIable instances in which the
squaring of The circle" has been discovered would be
valuable manual This most simple and important ge
ometca figure has exercised the ingenuity of geomecians
in every age since geometry became science The mother
of gonomey, the child has been less mysterious than the
parent but the acute mathematician suggest per-
haps why the circle has refused be squared
is that the operation is impossible difficulty which am not
much inclined attempt the removal Of short walk along
the ngodden path Of science may be agreeable and
instructive than the task of either climbing the skies de-
scending the centre Of the earth.
The earliest record possess of attempt give the
portions between the diameter and circumference of the circle
by Archimede to 30 The great author, perhaps
correctly recorder of this proportion killed ante u
2l2 the siege of Syracuse Nearly eighteen hundred
passed Europe after the age OF Archimdes, before
approach made the real relations of the circle
Francis Viea, Frenchman, who lived between 1910 and
l603 with Metus the first in modern Europe, who in
the advance towards the quadaure of the circle surpassed in
accuracy the ratio Of Archimedes These latter gave ID to
1885, and made real progress in science The numbers be
ing formed by repetition of the three first odd cphers is
readily impressed on the memory.
But let here notice circumstance of great interest in
the history of the investigations the CIRCLE and which has
been strangely overlooked In the very age of Metus and
Vieta published in India, the Ayn Akbery or INsTI
TurEs THE EaPERoR AKBER, in which the proportions
of the diameter and circumference of the circle given at
1850 1927 The suboned table shows the comparison Of
the three ratios I that of Archimedes I'd, Metus and
Vieta and 3d. that of India all reduced decimal
pressions respectively
tt % TO 8 l42s555t
ll3 : 355 to | 3.l4l5936+
1850 1927 to 3.l4l5l
Any person acquainted with common arithmetic test
these proportions and whoever makes the experiment will find
a tLa
therefore evidently approximate forever and yet reach
ing the goal.
The second that of Veta recorded in Brandes Die
tonary, under the article Circle carried by its author
to :" 10 places in decimas and Van Cuean to SO. Mr.
Abraham Sharp computed the ratio to 72 places of figures
and, finally De Lagny, in the Menairs Of the Academy Of
Sciences Of Paris, xended 1913 example of pa
tient industry without use."
"Supposng the diameter H., adds Brande, the first SO
figures by which the circumference expressed Cor the ratio
found by Van Cuean) are
"3l4l59, 26535, s9793 23s46, 26433 s3379, 5O2ss."
Though received in general science by European
tons, the Indian proportion out in the fifth decimal
figure without remainder and thus far differs only 000Os
from that of Vieta-a fraction for all useful purposes utterly
valueess The Indian ratio, must repeat, having the great
superiority of coming without remainder the fifth
decimal
ANY person Win geometry py
brief portion Of time in elegant amusement render evident
the eye the most important properties of the circle, by taking
any diameter will and project circle Then, within the
Gle, project after another from the sympe poygon
the equatera iange then the square, pentagon hexagon
&C. Such process will demonstrate that with the increased
sides Of the poygons the aggregate left between their
sides and the circle will dmnish and will suggest
with all the force OF mathematical evidence, that all
practical uses, the circle may be regarded infinite
poygon and composed Of infinite series of isosceles
triangle their apex acute angles uniting the
tire, and their sides equal to the radius of the circle This
being understood and admitted follows tna the area
sesceles ianges similar to all other anges the product
of the perpendicular multiplied by half the base and hence
Of circle must be the product of half the radius by
the whole circumference, equal paaeogam in length
equal to the circumference and breadth equal the fourth
Of the diameter Of given circle.
From all these data find the circle dependant on one
element il either the diameter circumference or area gven
all the others deducible Since the invention of the
nnesms calculus the discovery Of series for the REcTI-
FrcATIoS and QUADRATunK of the Circle is matter OF
comparative facility Albert Euler, quoted BIZ Brunde.
That person who decides what Newton, Haley Albert
Euler, La Grange Lapace Legendre &c. recoled from
gave up in despair, will fame which Time itself will
/ respect. WILLIAM DARBY.
Il