New-York daily tribune. [volume] (New-York [N.Y.]) 1842-1866, 1851-06-14
REPLY TO PROFESSOR LOOMS.

REPLY TO PROFESSOR LOOMS.
A few months since, a volume of two
hundred pages was published for me in this City, by
Putnam, and in London by Bentley, entitled New
Elements Of Geometry" IN which the science is pre-
scented in a form more simple and more fundamental
than had been given to il before, and in which two
years o. intense mental labor had been OK
pended to carry out the thought and the new fun
damental principle into perfect and harmonious Sys-
TEN. Several very competent Judges who have taken
the trouble to examine the work sufficiently TO I'M
derstand it, have pronounced The new theory per
feCtly demonstrated, and expressed high opinion OF
its great value and importance TO Science. Onc OF
these gentlemen, to use his own deliberate words,
written and published regards the volume of more
value than any one on any subject published IN tins
century"
One other learned gentleman, however-ProfeSSor
Looms, Of the Newly Ork Unlversty-laS looked AT
the work and from some cause or other he can DIS
cover no form or comchneSS about II, but promptly
pfonounces 1t STUFF lie IS determined that the ram
parts of Science shall be in no danger OF being
Slapped or undermined by SmattcrCTS,' while he
stands as sentinel upon the watch tower lie there
fore hits up his voice and CrcS aloud, warning the
scientific world that the volume of New Elements
OF Geometry abOunds N crudluCs." inconsistent
clcs" abSurdlueS," and nonsense" In short, that
It Is a book " nom which the pure mathematics have
been most carefully e8punccd.' THIS crusade against
the "New Elements" was preached few weeks
since by Professor Looms. IA "a lecture before The
KeW-NOrk Academy Of Education, and has now
been published under MS supervision. tie Is there
fore fairly accountable to the world for the language,
and the ideas, and the re.Sunings Which i presents.
I VIII not stop To inquire here Why gentleman OF
so much learning and scientific reputation should
soOp from his high position 70 wage such formidable
battle against "cruditleS" " abSuritleS." and "uOn-
sense" or Why he did not let them die quietly IN
their harmeSSneSS and mSlgnlhCance There IS,
however, tradition abroad IN the world that the APP
proach of new truth always tughienS error, and
makes 1t fight and cry out, They that turn the
world upside down come hlthcr also" Among
all the worShlpperS of false goddess the most zeal
Gus and pugnacOuS ever found 10 DE those whose
vocation II is % make her S8riHeS But Professor
LoOmis Is unnecessarily frightened. The beautiful
truths demonstrated by Euclid and all succeeding
geomeieIS IN no danger ln the language Of the
prntng-ofice of beng knocked into pl -, or, IN
the language OF the street of being knocked into
cooked hat" They VIII still be allowed TO remain
truths, and Professor LOOMS viii undoubtedly be
allowed to teach them even out Of ms own books
for long time To come. And II new and important
truths TO Be addsG 70 those already demonstrated
by gcometerS making the elements of the science
more simple, bringing II down 10 the comprehension
Of children and rendering II one OF the most useful
and important studies for the common school, what
harm Is dOne' And here, u quiet a. soon posi-
bic the fears Of the learned Professor, | Will assure
hun that nothing is required but simple modlacs
uOn Of two or three definitions, 90 make evtrytbag
the Neto EiemoatS" kGr0onise most perfectly ritt
eVerttAiRg ~ IKE old.
The old elements make Geometry deal with three
different kinds of quantities. requiring three different
kinds Of UNITS which are not homogeneous and can
not DC measures OF edCn other. 1RcSc tllec xmas
OF Quantities are solids surfaces anu lines. The unit
OF a solid Is ou6C, a square block, being one m
length one IN breadth, and one IN thu kneSS The
unit OF surface i,a square, being length and
one IN breadth, but having no thickness. And the
unit Ot line Is the abstract idea of length OF dis
lance, having no breadth or thickness Il IS mani
fest that these UNITS from their description,
Ike IN their nature, and cannot be measures Of each
other.
THE New Elements" make but one kY1S Of q,lr-
t'fy IN geometry requiring ou; one unit. Lines, sur
al lot hsn atm all
cube quantities, and are ali measured hy the cubic
unit A geometrlcal line, therefore. M the " New
Elements Is a positive magnitude, having the
breadth and thickness OF the cubic unit And a geo
metrcal >uriace Is positive magnitude, having he
thickness OF the cube unit THIS IS the only clrc--
ence between the New Elements" and the OLD
Now While by The old elements aud definitions Of
geometry lines and >urisceS and solids can never Re
compared with each other N quantity, hy the de6ni.
tons Of the New Elements" they can Gll0agS be
compared With each other IN quantity, and Will al
WAYS be found 10 asrec with each other II cubic
measure precSey as :sCy agree "a GTItkRStca cacN-
IG.'oE. have an apparatus for demonstrating these
principles mechanically 10y measuring water m dlt
terent geOmetrcal f,r-ps such aS the teirahedron,
cube. ociahedron, sphere, cylinder, and cone. BY
this apparatus pour solids into surfaces and INTO
mes. and pour surfaces INTO lines and INTO SohtS
and IN every Instance that can possibly be presented
they agree perfectly In cubs quantity. precisely as
they agree N aIithmetca calculation
Professor Looms diSlkes the pkoscoRv OF the
"New Elements" am Sorry ,,cannot De favored with
the Weigh OF as authority, but Il mus. Try 20 keep
itself IN countenSnce IS Wen a. Il can With such
humble coadlutOr> as Sir Isaac Newton. Dr Barrow
and especially Augusta Comte. SIT Isaac Newton
makes geometry mechanical science. He saws s Il
IL founded IN mechanical practice" DR. Barrow
saws Those which are called mixed or concrete ma
thema;cal sciences are but 50 many examples OF &c
ometr" And many passages might De quoted from
this very learned philosophical Mathematician IN
support Of the new philosophy which 50 troubles
Prot LOOMS Blu, AuguSte Comte, the cleareSi and
most profound philosophical writer OF The present
day IS more explicit IN support OF the peculiar phil
oSOphy of geometry contained in The 3" New BE
menis" AuguSte Comte of Paris, Is yet but little
known In this country. He has been styled the
Bacon OF the Nineieeath Century" and his work,
comprised in ssx large volumes, on the philosophy OF
the sciences, has been called the greatest WORK OF
The present age" One volume Of this authors