New-York daily tribune. [volume] (New-York [N.Y.]) 1842-1866, 1850-12-27


They may find some sympathy with few whose
principles are IN the market to be bought up by
Southern trade; but the great body OF the North
do not understand the Constitution as authorizing
any such procedure The provision itself is a
heavy tax on the spirit Of freedom-suihoiently
so not to be made worse by methods that out.
rage all the legal forms to which treemen are ac.
customed HUMAN RIGHrs
The New Goometry-The Authors Inst.
To the Editor of The Tribune
notice, Mr.. Editor that somebody in Tn.
Tribune of the llth inst. has demolished by
single blow lin his own estimaton) my "New
Elements of Geometry the volume recently
published by Mr. Putnam in this city and by Mr..
Bentley in London. The writer conceals his
name under an algebraical signature but from
the tone of authority with which he assumes to
speak for professional mattenaticians, he doubt
less intended to convey the impression that he
belongs to that respectable and intellectual class
OF society and had right to speak as one having
authority. For he says, in reference to my New
Elements that nothing but the most vague
ideas of Geometry and the loosest and aimsiest
kind of investigation peryade the whole book .
and that mathematicans and others who have a
Just conception of the subject will throw it aside
with contempt
What pity it is that person, who had the
courage lin the dark to such language as
this could not in nearly whole volume of re-
marks, present one single fact or one single de-
monstration to show that he had q r}gh TO uss
such Language Nv volume was all before him
where to pick and choose his points of attack
why did he not by reasoning and demonstrations
show up its fallacies and its errors aud thus by
breaking through its s. loose and nimsy" barriers
place himself upon honorable vantage ground9
Why did he not at 9ast convict it OF one single
, cIror Of principle or demonstration He has not
10 81 in the slightest degree. For reasoning
he advances nothing I I;s hH simple assertion, and
for demonstration, nothing but his CONTEMPT;
But even these arguments, urged with so much
t01ce and so much assumed authority may serve
to deceive readers who are unacquainted with
the subject or who have not seen the volume in
question. The great interests Of truth aud gel.
ence, therefore no less than Justice to myself,
seem to require some further remark.
My assailant SAYS The definitions and ak
IONS Of geometry, as laid down by Euclid and
received by all geometers are far above the
reach of this modern mode of inquiry-entirely
beyond this age of progress and reform. One
might as well attempt to change the nature OF
the Being who formed these geometrcal truths
as these definitions And he adds that the chief
Of these definitions are, that A pint a. ha
,ehic4 has pqsitlon, bW not @!agnltndc'" and " a
line is Length 1CithOut 6re0dth.
What Daniel come to judgment The first
of these two definitions is mol Euclid's, bat very
modern definition, given by Professor Playtair--
Enclid,s definition was, "a point is that which
haiti no parts" And it is but the other day, as it
were that Professor Playfair, applying to this an
cient definition the principles OF modern free in
quiry, and finding it not so good or SO conforms
-, rkn. nUnfh he
CHANGED it for one which he thought better. Now
INV wise antagonist Tor Professor, if he will allow
me to call him So in lieu Of his unspeakable elge'
braic signaturel my wise antagonist Professor
should have known that it has been by no means an
uncommon thing for modern writer's on geometry
to change or modify definitions; Many oil EUCLID
definitions have been changed IN many dlherens
ways BIZ different geOmeters. his dehnltlon OF
a "gtraight line of parallel Ines, OF a pans
of ratio" and others, have been changed ana
modified in various ways TO suit the IDEAS oil Eart
GUS geOmeters. Whenever 1t has been iou1' 'naS
definitions did not truly represent the discoYeiea
principles of geometry, the liked etefnaIy JHlss
ing principles of that unchangpg scence, W0.io,e
it baa been the ractfe o. 3odern free monty
~ w6ic6 nv wise Professor is so Prodlgousiy
c;oItarad IN find definitions that would truly rep,
osat hose principles And this is the head ana
l,t Of INV ofense !" in attacking the principles Oh
nnye geometry" My sinners IN t.ls Psl'is'
p piar are such men as Professors Paytslf Young,
Simson, D'Alembert Boscovch, LeSendFei au'
nany others. Ny sins may be larger than Iaelrs
but thew are certainly of the same klnd. hs. I've
discovered principles in geometry whlcn inc s md
fnitops hitherto in use do nottruly represent u;,
have yentnred to change those definitions "
The case, And have presented demons!te!:l pJ,
n show, that the definitions and the pfiIo'p;1a
agree in every possible case and therefore 0'aND
Kat nav definitions are the right ones e.;a,
prof PLAY fair changed the definition o, Ro.@
have changed the definition OF 'tHs ~ ~ ~ tbe
| done SO? Because | have discovered tnss r Tue
laws and operations OF geometry maze eYelS n .,5
in every possible case, to have the breath aaa
The thickness of the unit used in the caicula'lOa
Tberpfore the old definition, that a ine
ienoth without breadth, did not truly rePreson .
the Ines Of geometrical operation, and 9e,s
cbsnead Il for definitions conformable TO shosI
laws. have also discovered that tue ~ in
onerations of geometry make every SURFACE ,bs
erery possibe case, to have the M'csHeS' ~ oiJ
NIT Jnsed in the calculation. Therefore tns 9 wv
,ie6ntion that surface is length ana DEE ~,
,rJboot Ltsckaess did not truly represent .,s w..
laws Of geometrical operation, and have cn@"s'4
ia iq% or deinitops agreeing with those laws
have discovered that the lays anu f ,oppen;tpg
of geometry recognize but one 6tn9 q o1id;tvot
vi5 that which is generally called sonny ~; ,Ss
solid quantity and that lines and surfaces, y .y
iaws and operations Of geometry are I,a -
.ej;J. az those quantities are woIca 2aS7 "'ifE