New-York daily tribune. [volume] (New-York [N.Y.]) 1842-1866, 1850-12-16
New Elements of Geometry--A Grille Grill.
riscI.

- ,, - 1-,'.'' y 10 4''g4.s.
o. LINEN IN your paper OF " ednesdag
lIth instant, you publish aa article purportins to
be critiaue on Mr. Ssba Smiths .Navv Ela,,o,,,
of Geometry. e,3 d., ~
'' ''' O. ''e'9 "''~u AP
pcaieu ~ your paper .! Tue ii instant noticing
that work
/ have nothing to Do with Mr. Smiths book. noy
/ with vop- sr+;cf. bnt &, ,F, ,.s,,.;,l .,.,;i,.
o.. IL, - 49, sS''-''' p A'~i.''es
~ - 'ca h4s reasoning IS BASED, hare an latege1
ol somewhat older date :haa his publication anl
therefore may ,v;,l, ,,-,;,,,. ,ss,,,, D., },e,,l
T.. =, wa i'o''.s'S assure - ''e's1 ~
'Heil' ne remarks Of Your correspondent >
are mostly assumptions Of what he coDsiJs-s
as essential facts In o,,l, 80.
nicit i, sta,in, cass '',e ''-09 > "0 Ca
-. e''a a 'ine with ofeadth
N"lou . 'lo suoJee' o. 'ae arsament conflicts Ia
] practice with bis views OF the PRINCIPLES Of ia
ometry r says let US bisect a tr;a,,l., ,,,;s
ZONE. Of these lines We sbo1i5 ,bar g.
/ ...,,,,lt;r So ,,.,,,,or - uu'
ies1'' - ms ~" part mo winch the
triangle IS divided VIII be equal to ouehalf Of
the whole triangle, minus the par. eaten an By
.ttba line He thus. as IL viii bs $40, r,aLn.
-. -. - ,-,o34l, ., L.,
80 ''''N ~ nc "o"'V'
Let US now see 10" iaF ne mas understood the
subject, or If he has really understood it, how fsF
his eutatioDs and the resrllt as he yyo,ldav
-. I -.
PIess I pms '''' ~ 'N'' @'ii ''e Se'
leSStsi u t.o Naoe 81. H.,
41l : "1''u ''aliNS lio ~ CNt' ~ nc 0'S0' shs.
Ill ~, I'VE uiust , ua'e o'o"U'1; l'oI ."a' '1e
oic@4tL ~ S'e ~ - oHc a. soLe
point III li'e y. ususes' =. az some ue'i,ite sc,
non OF magnitude IA 'uis tespeSg ne faS SIN.
Ply taken the denloosIrs''oh o. another with en-
ilFe .'oetty 70 Yo So 1uG ~ tH"' ueHlo5 sFatoa
ne u"s 80 ~ So +" '.a' i oo"u'u " taN
IN -. ~ aau t1s
- $3.50; 80 - - ~ 'ue il5''s e.s'
on5 tsoIiis '''OH u Pa" ns
u 80 - - &c., >, Nj; ,,,,, NJ, g,
,n+ :. Nv po(or j.; H. S,,1.ts 80 ssatss
onodroura hos shown Hat tb, ", 3e
- ~ Ia sule u
- - :; 80 - -; ~ u IOuse
S''. a. oi. oI &c ''a w
'.He nm 'l'9 80, y
ot.et WITS, ti@' LUZ ".,,OI - tue ueased
'HiAe, i0i 4i's nv F''s w. w 49,, aaf
| more thah CafPe"tef rue, win "hch ne
measures a surface OF uuoe; 'ofins t any part Of
! the surface or Cuoo measured Il thih6 cannet
measure tsell, nor can 1t De the measure OF Itself
! Things are measured only BY comparison WITH
other things. foot rule, tor example, IL certain
Hynontitv onIv es we mentally refer the rule IN
tbe foof II we Insect or MEASURE a triangle ky
geomstry yye simnIv determine the Quantity If
Re- r,boiss or its narfs in tbeir relation to soma
otbor cnent;tv already deterrnined 1t is evident
thsrsfora from Mr. Parker's demonstration, and
fro,, The nncess;tv Of the case that line which
l. n,eda tho measure Of eny figure. forms no psr
of the feure measured. but is of itself mani.
tude entirely distinct from the figure With
these premises. Mr. Smith sets out In his reason.
ing but your correspondent makes him 10 mesn
that line with breadth is part of the figure
/ bisectcd or measured BY it, Need | say anything
more to prove that the case and it's resultsM
stated by your correspondent, is wholly inappl
cable, utterly devoid OF truth and of mathematical
accuracy?
our correspondent goes on 90 remark on Nj,
circle inscribed in an eouiletera triangle eausls
two thirds the perpendicular which proDos.
ton he saws, "can never be proved from the de.
Gnitjons laid down in the book particularly thaEa
line has breadth OF one in this case it the unit
is Oa2v half en- inch" He itacises the word
"onlyf' evidently with the intention Of giving 10
the demonstration the appearance of contradie
ton, as ii one magnitude, which is equal to 9ae /
| half inch were not as much unit as one whole
inch
1t is true, Mr.. Smith has not demonstrated US I
18th proposition by the breadth OF line aud yo1 4
correspondent hence assumes mat II can never Os
proved by 1t Ry turning to the oh pTop9stt@1 i
however nc III thcie sec ~ plofTu W snI oleSua
OF llne mat II the e4ulatleIai triangle "hose /
diameter is TWO, the area equaS nan inc cicuM I
| ference and with Mr.. smith tue diameter oil any
plain figure is always the diameter oil an inscribed
circle The calculation Is tnen reduced 20 hSa'ss
and by very simple law OF numbers II the area
be divided by one;thIrd OF itseil, IT WIN glyesle
perpendicular, which is three, and because 1as
! diameter OF the inscribed circle IS Known 10 10 4
two, 1t therefore equals TWO thlras the pefPeluEa
lar this should not be Sufficiently tthe IN
propostion may be proved BY, the breadth Of lIns
in as many forms as is desirable 5i. Bat wnat aa
been said will be sufficient tnlnA, 10 SATISFY sns
one that the assertion ol your correspondent VA
it can never be proved is maze N lsn ~
thstit is mere caYli and not iopnuea III 'iu'u4
reason. .,.-......Ia (. i,
For our further edltication IN t9s mater ss
require Of your sortepondsn ,son to % bsasas
and biseGt triangle oy NE % s%a an Ofs As
we VIII suppose tnqt ne m msS and rodpea
oraic solution Oh s InU. lii 1q done this by Ia,
| Its il9ures. Dut HkS ne ttdtI uolV st' - - IN