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

new Oh anu
Last Time.
MEssRs. EDITORS: We beg your indulgence
for this me only, in publishing a few remarks ca
the New Elements of Geometry" and will then
end, on our part, what seems likely to prove
long and perhaps idle discussion. The remarks
that appeared in The Tribune of the llth inst
were not made in the belief that they would not
be answered that they would be noticed and
contradicted we knew full well, for who does not
know human nature well enough for that? But
TO the subject, Progress says, 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
"The faults of our neighbors with freedom we blame
But TAX Ourselves though we practice the same
forced on bis mind2 Why the whole article of
Progress is tissue of words, and words, too, that
do not carry one single argument or proof with
them do they retute anything IN the article OF
the 18th inst No 4" Progress must let the arti-
Gle to be bisected stand-he has not got around 1t
economically yet, although one might think he
bad with words He (Pl says that we have made
the bsecting line part OF the figure. VIII to be
sure-what else CAN'T be Z w are TO divide geo.
metriCaly the original triangle into two equal parts,
which are to be equal to each other and each equal
TO one half Of the whole triangle, and OF course
the bisecting line forms the common boundary OF
the two newly formed triangles. Nor must 1t eat
up pant Of the surface by its own breadth-he flat
tiers himself that by bringing up the carpenters
rule and etlectug linear measurement with 1t,
that he has similar case to the above OF bIsect-
ing a triangle COMMERCIALLY but who does not see
the nonsense in so doing We did not propose
in this n9 t a to be s any 9F further edioa
ton in this matter mention one more OF these
curious things, viz the circumference OF circle
ooJ dianeter w do not know whether the
author recognizes the eXistance of such hgure as
q semi circle, but if he does, we should like to
know what relation the diameter has to 1t, ac-
cording to his ideas he says the diameter OF
circle is strait line passing through It's center =
but recoect the line has breadth OF one ttiniteJ
therefore as half of the line lies on each side OF
the center, which is q point, and according to his
own ideas, noticed on the twenty-tith page 1t
ltbe point agrees with Euclids idea OF the same.
We say that as the line lies on each side OF the
center it lies ptth3n the semicrcle, and conse-
ouently eats up part OF the surface, Now does
he considerths 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,
that in the equilateral triangle whose diameter
is two, the area equals bali the circumference,
Int on turning to said proposition we only lind
that he has made use Of his proposition to prove
the truth of the 9TH capital geometrlcal and
logical mistake, as all GeOmeters know that
Dronosilion is not to be used in proof Of another
proposition, until itself is clearly and larry de
duced, step by step, from the definitions particQ-
lars and aXioms l9ld down and on Whlch the Whoe
structure must rest And as this attempt to re
fnte the charge made in our last article rs not
sufficient" we call for the proofs OF the 9TH propo'
sition and we mean GeOmetrlcal proof, not an
Arithmetical or Agebrelc one by line 0iRY hall
nm inch III breadth. One form is all that IS
desirable we will leave the others to yourself
as monuments OF your Geometrica skill-and we
reiterate what has been before said, notwithstand
! ing our assumed ignorance that Geometrca
proof is not to be produced except by llae, both
curved and straight, which has no byeadth-and
since PREMISES mus. he cear y and fairly estabhsh
ed before conclusions are drawn The whole mum
Der OF propositions which depend on the tn must
stand in R /" fix approved, until the 9TH Is fairly
deduced from our own definitions Our reason
for italicising the word "only is entirely mis-
taken-we said it in an irouical sense-not tor
moment supposing that fractions OF UNITS nave
an existence. Again, let rs conceive series oil
these unit cubes arrayed around plain surface,
| which the world over understands by circular
surface or circle Now, according 10 our author,
the circumference forms no part OF the circle,
therefore it must simply DC a certain inquire OF
itself whose form and direction IS determined
by the so called circle; bat as our cubes tsay
for instance the unit is one inch touch only
on the inside edge, we can form IN our minds
what sort Of figure the circumference OF circle
is according TO the Ideas OF Progress. W nat
/ he tP means when he says in regard to the bl.
section OF triangle Gtometricailg We will
suppose that he has made Algebraic solution
of its whole quantity, and reduced It's figure,
we leave for those who are imbUed with the ne
what shall we say }-defnitions or principles
of Mr. Parker to decide, as we do not profess to
be posted up in these new methods We think
that the fsncied scene of the dissection Of tran.
gle by pupil Of the old school afforded more
amusement and satisfaction II It's author while
putting il on paper than it viii profit IN instruc-
lion TO those who read r This brings Us to some
personal remarks in the article, which can easily
be disposed of he SAWS But think you ii II
were SO easy matter that lie would not have
done il himself Now we al know that 8
newspaper is not the place, except N general
way, TO discuss or controvert the propositions OF
principles OF Geometry-a subject that would re
ouire e complete set OF diagrams to make 1t IN
telligible TO readers. II was not, and Is not now
considered necessary in this place but in gener-
81 wav, to call the attention Of the author and
those Interested to what We call grave errors IN
the book But clear, full, and explicit demon
stration Of every proposition in s work on Ieon e
try is looked for by the mathematical pnbiic IN
.hs, book itself Whether Mr Snith clalms the
merit of being the discoyereg OF the breadth Of
lines we know not and care not but We do Know
that he has made an attempt TO use TINS klnd OF
line in GeQmetrical way, and tins was the only
r,ont brought in question, and IN thus simply
taking the demonstration OF another he has
shown how far be has examined the subject tof
himself.
We will, with ali due Difference to the parties
concerned, venture guess on the whole mat