New-York daily tribune. [volume] (New-York [N.Y.]) 1842-1866, 1851-06-18
The New Eicmonts OF Geometry.

IL me Editor Of The Ir'trac:
On calling at The Trijuae Office 10 pro-
cure tie insertion Of a reply 20 Mr Smiths article,
which appeared tins morning, was told ihdt PAR q
column Was tine utmost space which could oe allowed
me. ] am compelled therefore - omit many things
which wished 20 say. and Will not rccaptuatc What
| have already published i'm the Literary world. l
Will merely notice the argument from authority which
Nh smith puts forth IN ms article OF TINS morning.
On page II of the " New Elem, niS' Mr. smith says
Euclid. and believe All Ofbfr GeDmeters w9o hdrf
irrf.q tifaerfo take their stand upon these denni-
TONS. VIZ. a line is length without BREADTH etc
The preceding state ntnt Is certainly very near tle
truth but tmS morning he says. ms "phho>"phN
must try 10 keep itself m counienance rs wen a>
can. with such humble cOadjutors as SIR Isaac New,
ton, DR.. Barrow. and especially Aususte Oonl'e anu
De adds. Several very competent judges nave pro-
nounced the new theory perfectly demonstrated
THIS last remark IS substantially The same ihlt MI
: made aitermy lecture before he Academy al bdu-
cation and ne mentioned the name of distinguished
Professor IN New England College as beng iaYor-
able 10 his peculiar views. remarked ~ that tlnc,
IN answer to several inquiries, that did not DeueNt
this statement I'm order, h oWeYer not Ia SPEAK
without authority addressed letter 10 thc gentle
man IN question and asked hun whether he was VIII
ing 10 have At understood that he favored IN any man
uerthe peculiar views set forth M me " We" Bic
mcuts" In ms answer which is now before me, ne
SavS-"I dOmOst certainly authorize YOU 70 contra
dict Lir Smiths statement, and shall esteem t as a
personal favor # you Will take occasion 10 DO 50.
should be very unwilling to be understood rs cndors-
ing or approving ~ the slightest degree OF MS peculiar
views The idea Of abandoning the terra hrma' of
the old Geometry Is SrperiGutey rtdirwonS' II l.
apprchended that those who were present IN me
chanel OF the University on the ih OF May last Will
read this announcement with some surprise.
Nj Smiths attempt to bolster up ms peculiar
views by claiming the authority OF Newton j. equal
IL preuoStcious. Every one who has read the frSt
Sr,IOn of the pnnClpld knows that Newton was UNI
wiling to allow line to have so mucn as an Wbnlf-
fy small breadth but he strcnuousy contendel 10!
the rlpOr of the ancient Geometry. Ihdt Mr.. Smlth
tN #
and admlrer OF Euclid while he - attempting 10
force out the cornerstone OF the ancient idoric oil
Geometry. Is, II possible, Stl more absurd.
But he authority upon whom Mr Smlh places ms
chlcf reliance X Auguste COmte In order to be
able to appreciate the support witch Mr. Smth de-
rlNts from tins source 1t is important 10 KNOW
l. WHAT'S the value otComte's opinion ana . Nha'
does he really mean TO teach WI. olhltu say,
c omtc is vet but little known IN TINS country. IL
NAV not. therefore, be amiss 10 state that CoHtc
graduated &c the Polytechnic School of Paris about
the year 1890. In 1889 he was appointed Assistant
Tutor AdOHt ReDetifcur IN the same school ana u
was while n this capacity M 1850 mat ne puoilSh.d
the Treatise from which Mr. smith has quoted Al
though considered a very promising young man,
Comics attAumoHts m Mathematics were at that pc
Rod quite moderate. and did not chtlt Wih 10 speak
with any authority upon disputed questions ,omte
was subsequently promoted 10 the degree OF iuu Iu-
tor. Rtpetttur but never 70 that 81 Professor lie
has not since DISTINGUISHED himself a. a mdthemdli-
CIan Ills old a>sOcatcS dnd juniors even az the TO
yiechnlc School, such as LlOuylllc, lie Fcrrer Du-
hamel etc. have received the reward OF mathcmal-
cal emlnencc by election To the Academy of Sci
ences Comte has received no such mark of regard
from the great scientific tribunal OF Paris. TOquote
COmte, therefore, as authority upon any point IN
which he may differ from Lapiace and Newton IS
ust ~ ludlcrOus as would be on question OF Con-
siltuu0na Law 20 quote the authority OF lawyer
ust admitted 10 the BAR IA opposition TO the decision
OF Daniel Webster.
= let us mquire what COmtc really means 70
teach On page lS4 he SAYS It IS impossible 20 rep
reseat to ones self a surface otherwise than as an
trrfatiV Tim plate, and line Otherwl>e than d> an
lrtaiffiV fue ,1rrGd" hayercad Comics work with
care ana have come 20 the conclusion that ne meant
tot1aCh that surface is 10 be regarded having
thlckHosS ipfnifeig sfg0I But AR. Smith contends
that Inc thickness of surface measurable * itS
length The difference then between Mr.. Smith and
COmte is infinite. | do not, therefore, believe that
Comte meant 10 teach anything AKIN to the doctrines
of the New Elements but even II he hadd so,
certainly u would have found no favor with the Pro-
fe,sor. Of the Polytechnic school. among whomh
teen numbered The names of Lagrange, LacrOlX,
Poisson. Aonge, Cauchy Arago, etc
h.Se but few lines more allowed me. Mr..
Smith says he never saw iiuttons Mathematical
Tracts. Now can call fifty witnesses 10 testify that
the nth Of May last, showed Mr.. Smith the Sc
coHd volume Of these tracts. and pointed out To him
the HndOO diagram which looked like exact copy
Of thai III the New Elements. Mr.. Smith put on ms
Spectace s TOOK the book from my hand and regarded
TIE diagram for some time with fixed attention. Ii,
during a that time, he did not the book, perhaps
he IS entitled to sympathy when he complains that he
cannot see the bearing OF the arguments contained
IN my lecture. +. LOOMS.
Mar York University, June "a