New-York daily tribune. [volume] (New-York [N.Y.]) 1842-1866, 1850-12-11
:. Ner Elcmea,g 81 Go0metrY' OritIelsoa.

J
----------a------
New Flcmcato Of Geometry Criticised
j., g.te 7',46"re q Monday. ID inst appears
notice OF book the Elements OF deomesfx
hy Seba Smith. Of a commeudatOry nature IS
viii not be considered too much newspaper ga
dscitv' we would ike to offer a few remarks on
tie subject, of an opposite nature The wntor
seems to hail with delight the freedom and inter
lectua holiness" displayed by the author IN att
lacking the principles o. pare Geometry--and tue
idea of applying the principles of modern tree
inquiry" to reform this science. Now the dehos'
tons a4d axicuas Of Geometry, as laid down by ia
cid and received by sL Geometegs. are far above
the reach of this modern mode OF inquiry. TIA
trely beyond this age of progress and reform. ono
neht as " ell attempt to change the nature Of the
Being who formed these Geometrcal truths. AZ
these definitions No matter how great change
free inquiry has wrought in other doctrines, sya-
tens and notions, Geometry suffer 10 change
FROM it, Il admits oil extension no doubt, but th@
extension must be based on the definitions aaa
principles laid down by Euclid. ard the chief a
which may be named, that u point IS that "&ttk
has position, but not mdsnHRde,' and " tiHe 70
length ,oitlsu breadth This is the sine qEd
aon one cannot proceed one step in pure Geoxe
try unless this is granted. The writer says. IN
speaking of the established doctrines OF Georas-
try that no one could doubt their correct
ness, without mourning the suspicion OF ohT'
latsnry or superficial investigation. The author
Of this volume, however, is not liable to either
OF these charges. Now, we beg leave 90
deny this latter, and to say that noshin8 oas
the most vague ideas Of Geometry, and thS
loosest and himsiest kind of Investigation perVade
the whole book. We Judge of a tree by its truits:
and how great devotion to study there may
have been or how honestly the pursuit after truts
may also have been, we leave others to decide
This we know, that he the author has not par
sued Geometry with any kind of success. Vita
regard to the principles Of the New ElomentS.
the grand feature is the idea OF extension exist
ing simultaneously in the three directions-that
is that the unit must exist in the form OF CUBE.
This with the definition OF a line, which s (def' "
"a straight line is composed of succession %
single and equal units a line, therefore, always
has breadth of one aud their applications torna
the great innovation on the true Geometry. Now
| how does our author effect linear measurement
| Why, with the edge of his cube But what "a
| this edgel We speak OF On ideal, geomesrioas
cube, not material, mechanical one Why Ger.
tainly line without breadth or thickness, and
! which takes for granted Euclid $ dehnition. w
see that every straight line is parGleloPped. aae
as the unit of length is the unit OF breadth, iine
must be succession of these cnbes. Let as
bisect a triangle with one of these Ines we
should express our result in this manner EacG
part into which the triangle is divided VIII 9e
. equal to one half Of the whole triangle minus the
! mart eaten up by the line. Now these instances
| L. h., Cd with ont
what absurdities we should be led by diecarding
the mathematical line which is that hmy, airy
thread nor are his concluslons less ABSURD III
comparing lines and surfaces. We think 1t az
great waste oil time to contend with one Wn0
holds such notions as to argue with one VINE
| stoutly and boldly afirms that he has discovered
way to make twice two equal to five In look
ing beyond this notice to the book itself we fatty
contradict the author in his Affirmation that he
discovered bis "harmonies,' as he calls them, by
the Greek (2) rule and compasses" alone" They
are true we believe as tar MS we have examined
them, although they are not as as the author
makes opt-nQr did he ever arrive at them BIZ
propositions depending on his own definitions.
He tactly uses the definitions of Euclid, and
then claims that the whole structure rests on his
own. Now it will only be necessary to convince
oneself of the truth of this TO examine the 7ta
proposition. 1.-THE diameter of circle Inscribed
in nm eguiateral triangle equals twothirds of the
| perpendicular Of the triangle which proposition
can never be proved from the definitions laid
down in the book, particularly that line has
breadth of one in this case it the unit is 0HtS
| half of mn inch
We agree with you that the book may ooa.
mend itself to those who are in quest Of intel
lectual novelties andlwho are for progress and re-
| form and who have clear conception of geoae.
tucal investigation; but matbematicinns and 9th
ers who have just conception OF the subject will
| throw it aside with contempt, and place its title
| on the list OF host of other WOrkg which have
appeared mt various times either to offer " Roy.
| al Road TO Geometry, to give - Geometry
without axoms Tor something of the kind, and
which have had their day but are now forgotten
How tar its holiness and freedom are adapted to
plque the professors of the established SCIENCE
we leave others to decide, but we do know it will
only be necessary Tor them to sci the merest tyro
to point out it's lallocies, that they themselves
may go about a work that will be far more profit.
able. We like progress and reform when right.
" directed but we advise all reiormers and pro.
gress men to let the principles OF geometry alone,
as they can make nothing by il. They have
passed muster too often under the eye and scru.
tiny Of such geDuses as Archimedes, Newton,
Euclid, Barrow and hosts Of others to be over.
turned by a modern poet or any one who wish
es reform du
dT
We cheeriully insert the critiqoe Of our cores
pondent pruning it of some personalities which
add nothing to his argumentj and accept it as g.
proof that our notice of Mr. Smiths Geometry
has had the desired effect Of directing attention
toit inquarters where its meritsmay be stringen-
y canyassed Ed. Ii7G.
PROBABLE MCRDEH or b. R HAnDw.-It
viii be recollected that Mr.. b r. Hardin son of
Ben Hardin, OF Ky. disappeared rather suddenly
from Panama shortly after he had received there
the revocation OF his appointment of Secretary of
m