New-York daily tribune. [volume] (New-York [N.Y.]) 1842-1866, 1850-12-26
For The Tribune.
New Elements of Geometry-Again
Last Time.

the - rev EISHSUbb VI -
end, on our part, what seems hkely 70 prove
long and perhaps idle discussion. The remarks
that appeared il The Tribune Of the 18th inst.
were not made in the belief that they would not
be answered that they would be noticed and
contradicted we knew iull well, for who does not
know human nature well enough for that But
10 the subject, Progress says, 1.-The remarks OF
your correspondent are mostly assumptions OF
what he considers as essential facts Who can
read the article Of Progress without having the
home spun moral
1.-The faults ofour neighbors with freedom we blame,
But tax not ourselves though we practice the same
forced on his mind Why the whole article OF
Progress is tissue Of words, and words, too that
do not carry single argument or proof with
them, nor do they reute anything IN the article OF
the 18th inst, No, Progress, must let the artl-
Gle to be bisected stand--he has not got around it
economically yet. although one might think he
had with words. He Pj says that we have made
the bieectipg line part the figure" Why to be
sure-what else can it be We are to divide geo
rneticaly the original trang into two equal parts,
which are to be equal to each other and each equal
to onehal of the whole triangle, and of course
the bisectpg line forms the common boundary OF
the two newly formed trianges. Nor must it eat
up part of the surface by its own breadth-he Hat
tiers himself that by bringing up the carpenters
rule and etlecting linear measurement with 1t,
tnat ne mas SlllllhT CuSC 10 tDc HUONt VI
ing a triangle economically, but who does not see
the nonsense in doing We did not propose
in this notice TO be any more "explicit' than We
were in the last, but will for our further edfca-
ton ia this matter mention more OF these
curious things viz the circumference OF circle
and it's diameter. We do not know whether the
author recognizes the existance of such figure
aemi circle, but if he does, should like to
know what relation the diameter has to it, a..
cording to his ideas He says the diameter OF
circle is strait line passing through its center -
but recolect the line has breadth Of one liinite
therefore as half Of the line lies each side OF
the center which is "a point, and according TO his
own ideas, noticed on the twentyiitth page, 1t
tshe point agrees with Euclids idea of the same.
We say that rs the line lies on each side OF the
center, 1t lies w,tttn the semi circle, and conse-
Quently eats up part oil the surface Now does
he consider this line as no part OF the figure /
Progress saws BY turning TO the 9th proposition
we will see it proved by the breadth Of line,
,hat in the equilaterai triangle whose diameter
is two, the area equals half the circumference,
but on turning to said proposition we only lind
shat he has made use of his thpropostlon prove
the truth of the 9Th, capital geometrcal and
logical mistake, as all Geometers know that
n proposition is not to be used In proof OF another
proposition, until itself is clearly and talrly de-
duced step 10y step from the definitions, particu
lara and axioms laid down and on which the whole
struoture must rest Aud as this attempt to re
sufficient we call for the proofs OF the 1th propo
sition and we mean Geometrcal proof, not an
Arthmetica or Agcbraic one, by hne0Wy halt
an inch in breadth" One form IS all that is
"desirablc; p we will leave the others to yourself
as monuments of your Geometrcal sklll-aud we
roiterate what has been before said, notwithstand
ing eur assumed IGNORANCE that Geometrcal
nr00f is not To be produced except by lnei Doth
curved and straight, which has no breadth-and
since premises must be clearly and lary establish
ed before conclusions are drawn. The whole mum
her of propositions which depend on the 7th mast
stand in fix, improved, until the 1th Is fairly
deduced from our own definitions. Our reason
for italicising the word "ouly Is entirely MS.
faken-we said it in an ironical seuse-not for
8 rnonent supoosina that FACTIONS OF units have
an existence. Again, let us conceive series OF
these unit cubes Grrayed around PLAIN surface,
which the world over understands by a circular
surface or circle Now, according to our author,
the circumference forms no part OF the circle,
therefore it must simply be n certain figure OF
itself whose form and direction is determined
BY the so called circle; but rs our cubes SAY
for instance the unit is one lnchl touch 0hlY
en- the inside edge, VIC can form III orr minds
what sort of figure the circumference OF q circle
is according to the ideas OF Progress" W bat
be Up means when he says, in regard 10 the b
section OF triangle Ge0mctrlcGlig We VIII
suppose that he has made an Algebyalc solution
OF its whole quantity, and reduced It's figure
we leave Tor those VINO are mouea VIII, tae new
what SHAH we say oen"'so'S OF
OF Mr. ta5her 10 aeoae as we 40 not W. t,
DC p4s'eI w N snese "S re ,n h;sSion Of
a' t,'e j ~ he ola .no,i an,3ad more
sle oy e a. o@ w. it antbor wb
anaase.uan' "''u t",, vii mott i; ;,str,
putting "n P@e' ',',s' rSi. bs no ~ ao,,
ton to those VINO re"a Ii tai' 10 " su'
personal remarks IN the article, %n,ea eau eisiy
De disposed o. ne shyS nu' snr4S Sot 49,
were so easy mater tu9t nc "o -. n0t - .'s>
done it hlmseh Now we al kno" Una, =
way. to discuss or consrovert the propositions OF
principles OF Geome'Fya saoeps 'u@t n
cure eomPiete seq Oh y ;'@AI LAM, - ~
telhglble to readers 1t was not, ana is not no"