New-York daily tribune. [volume] (New-York [N.Y.]) 1842-1866, 1851-05-28
GEOMETRY.
Smiths New Geometry.

The n. \. Academy OF Education met
at the n. Y University on the evening OF the l4th
inst, the President, JOEL BLAcKMER, in the Chair
A Criticism was then read 10y Prof E. LOOMS, of
the University, on the " New Elements Of GeOme-
try by Seba Smith, Prof L. proceeded to state
l. Some of the fundamental principles Of Geome
try as they have been received by all mathematclans
from Euclid to the present time The object of Ge-
ometry is the measure OF extension or space. Exten-
SION in its largest has three dimensions, length
breadth and thickness. Pure Geometry does not
treat of the properties of material bodies but OF space
not supposed TO contain matter. Having the idea OF
extension IN three directions, 1t Is easy to form AN
idea of 1t in two, length and breadth, which is sur
face with no reference to thickness. From the idea
OF a surface we derive that of a Inc, apart from
breadth, and mathematiclans say line has length
without breadth or thickness As me mas nei n
either but position only. which Is point. maihe-
NAUTICAL line has no material existence but is con-
ceDtion of the mind Without this ideal standard
Geometry would cease 10 he exact. The Importance
of this is found IN the application OF Geometry 70
Natural Philosophy, Astronomy, Navigation ana
Surveying Has the parallel OF ioHynme degrees
between the British possessions ana the Onlted
States anv breadth-an intermediate strip OF land be-
longing TO neither party The same IrnciplS Is IL
Illustrated by reference TO the generally received
standard Of weights and measures. The pendulum
which forms the standard OF all our measures Is
defined to be- a single particle OF matter SUSPENDED
by a line without weight, and making one VIBRATION
Der second an ideal standard 10 which al the mea-
SureS of Great Britain ana thc united states are IT,
ferred
H. Some particulars IN which Mr.. smith differs
from the mathematlclanS Mr.. ) asserts IN his New
Elements of Geometry" that lines surfaces ana sol
ids are all of the same nature. That 1t Is nnpossl-
bic a line can exist unless II occupies portion OF
Space"-p 90. An inch, therefore, Is always cubic
inch" material line must have breadth and thick
ness But such not the lines oil Euclid ana II Is
because they are ideal that the Propositions OF Geom-
etry are absolutely true. Prop VII. IN the new Iii
CmeniS reads thus The diameter oil circle IN
lafar frI4n ta
the perpendicular of the Triangle ms IS true by
the definitions OF Euclid bui not BY those OF MI ),
as II is obvious the diameter of the circle has not the
same length IN the two definitions IN tie iaer me
diameter has breadth and must meet the clTcunier-
Cnce OF the circle III two points, and the cnd OF the
rectsngle Is a chord OF the circle The length of
such a diameter cannot be the same rs that OF one
with no breadth. Most Of the propositions OF the
New Elements arc selected to illustrate one pTn-
cipe-that an inch always means 1t cubic men. Al Is
not strange therefore, that the book should ABOUND
IN crudtes inconsistencies and abSurdltleS. For
ample ON page IS. MIR. :. SAYS; II we OiSoct line,
the place of biSection where the two halves of tue
lines must meet each other We call point On
page - he saws. mathematical line IS made up OF
a succession OF single and equal units Ana these
units he SAYS, are cubes To bsect dhne, therefore,
Is 10 blsect a cube, and the place OF dissection, he
saws is point IL follows from these premises that
a point has breadth and thickness. But on page p,
he says, 1.-The nature of point i nightly gwen mlhe
books" and the books agree that point has neither
breadth nor thickness,
Prof L. proceeded to give numerous other exam
pies OF similar nature, from the New Elements OF
Geometry." 10 illustrate the character OF the oooA
He SAID that no one could be surprised, after such
examples, TO learn that Alr ). pronounced the disl-
sion OF the mathematics INTO pure and mixed TO De
only an imaginary one, and that he proposed 70 eX-
puHgC SO useless an abSuTdlty from the books. THIS
advice has been literally followed IN the " New Ele
menis," from which the pure mathematics have been
most carefully cxpUnged In conclusion, SAID Prof.
l., the substance of the preceding review may be
summed up IN two propositions !. The new prin-
cipeS which Mr >mith processes 10 nave discovered.
50 Ear as they are true, have been known 20 mathe
maticianS from time immemOrSl , TINS neW PHI
loSophy IS calculated to spread a veil OF darkness
over subject which before was clear rs MONDAY.
4 very interesting and somewhat exciting discus
sion then followed between Mr. Smith and Professor
Looms which the limits OF tins article prevent our
reporting On motion OF Geo w. Clarke, Esq,
vote Of thanks was returned 10 Prof l.. FOR The ln-
structye Lecture he hal given. Prof Jas Thorn
son, kSQ., then moved that Prot L. DC requested 10
give TO the public. IN such way as should be most
agreeable To- HIM. The views contained IN hl> Lecture
before The Academy Of EDUCATION