New-York tribune. [volume] (New York [N.Y.]) 1866-1924, 1892-07-05
THE CIRCLE CANNOT DE SQUARED.

THE CIRCLE CANNOT DE SQUARED
TO the Editor OF The Trioune'
Sir This is one Of the polcmic problems whoss
solutions constituted sacred knowledge, not 10 %
attained until the human mind haa reacno' "'s~
plano OF Intellectual development
Many attempts have been made IN every age -
solve these problems and with some success. There
Is said 10 be record OF the quadature OF the circle
in Egypt 500 years before the Exodus u ING
Jews. II Is also claimed that the prohion wss
solved by Hippocrates 800 ID. G.
The Oldest mathematical book In the world the
"Papyrus Rhnd" in the British Muscum, w0
written by Ahmes, Egyptian scribe OF King Raaus'
about 1000 p. C. This, as translated by Eisenons'
contains rule for making square equal " SVEN
circle. This rule says that the diameter on the
circle shortened by oncninh Of itself gives side OF
the required square. But this Is not exact ana
therefore OF no vnlue
without doubt this problem and perhaps others
Of the seven polenic problems were solved and the
solutions with much other Egyptian learning, lost
In the destruction of tho Alexandrian Library
Pythagons was probably the first to solve one OF
tho problems. lie doubled the square. and as q
result Of that discovery we have the Attn Prop. OF
Eucd.
ono record states that a pupil Of Aristotle Iamed
sextus was commissioned to convey tho secret OF
souaring the circle to Archimedes, who at that time
the leading mathematician In applied geometry.
This secret consisted in the knowledge OF certain
ps nnd in circle This p1 "a.
Of Arstotles orgnnon: During more than ,wD
Of host Of mstSematiclans The most r.marabIss
fact connected with It's rcdscovery the sxtrem me
wonders sofnr that q it was no. recorined earlier
Draw diameter In any gwen cire ana , radns ~
. nSSs draw chord d'GTs m One I
diameter This chord is the side on a square equA
Making this line a standard measure for all
eeomstns computations; It becomes solving t,ctos
for all the polemlc problems l. H. W.
New-iork June /, 1892.
III 7. r. W. had read much in the literature OF
the subject; if he had the slightest inkling OF
the real conditions Of the question, he would NOT
have written the above letter. As was recently
pointed out by a wcll-known mathematical writer,
it Ia TO the credit Of America that nobody In thc
United States has been foolish enough by writing
book on this subject TO add his
name to the list Of De Morgan's para
boxers The problem turns not on the meas
urement of line, but on the tracing out OF an
irreducible fraction minute that the area o.
tho sharpest point that could be put on pair OF
dividcrs would be an infinite expanse In COMPARE
son. The machine has never been invented that
might measure with approach TO the
requisite accuracy the line which T. r. w. speaks
of with 40 much reverence. As for the Greeks
and Egyptians-their mathematics was wonderful,
not because II was good; put because 10 was 80 "e-
advanced In comparison with their other knowl-
edge The scholars Of those days were, like
T. r. W., totally unaware of the conditions ttsls
actually required to be met In attempting solu-
ton OF the P-cquaton. 1t is Of recent years. says
the Encyclopedias Britannica, that the most inn
porant advances in the theory Of circlequadraturd
have been made. In 1873 Hermite proved that
the base Epsilon Of the Napierean logarthms can
not be q root Of rational agebrac equation Of
any degree. To prove the same proposition re-
garding Pr is to prove that Euclidean cons
struction for circle-quadrature is impossible.
Hermite did not succeed in his attempt
on Pr; but in 1882, Lindemann, following ex-
actly in Hermites steps, accomplished the desired
result" On the OBSERVATION-DISCLOSURES the remark
is made: Such persons have fourished at alt
times in the history Of mathematics, but the in
terest attaching to them is more psychological
than mathematical ED