The Austin weekly statesman. (Austin, Tex.) 1883-1898, 1883-11-29

position, the line of all dimensions but
length, and the surface of any idea
but thickness. Thus he would have
through himself those cautions which
in the test books stand as the only
definitions. Let geometry be COM
pared with grammar. Is not the
mathematical science palmer, more
straight forward, less changing and
complex? Is it not free from anoma-
lies, and are not its conclusions with
out exception? The distinction be-
tween transitiVe and an intransitive
verb is one of the most elementary
requirements III grammar; but l ap-
peal to the experienced teacher to
know If a pupil is not more easily
taught to make the distinction be-
tween an obtuse angle and an acute.
do not mean to say that geometry
should be studied rather than gram
mar, for under the second Of my three
principal propositions the utility of
grammar should give it a prominent
| place; but do claim that the popular
| fancy which pronounces geometry so
| much more difficult is altogether
without foundation.
1t is hard to see why teachers will
introduce their pupils to algebra be-
fore geometry. The best results in
modern science have been achieved by
combining the two, and perhaps they
should be studied in connection from
the beginning, but if either is to be
taken up first 1t should be the latter.
1t is less abstract, and therefore closer
to nature. All that we know is pri-
marily deduced from physical facts,
observed through the medium of the
senses. It is the observed fact OF
which we have the strongest conVic-
ltion, and the further we
iget from nature by intellectual
process, the more liable to error we
become, and the more uncertain OF
our conclusions we feel. This truth
is now seen all along the line of edu-
cational work with its appliances
from the kindergarten to the scientific
labratory. The propositions of geom.
etry mostly depend upon the congru'
ency Of the parts which may by super
position be made to coincide. Thus
they become apparent to the eye, anC
hence the pupil is most stongly con-
WINGED of their truth. They are more
clearly comprehended than their alge-
braic, OF even their arithmetical ana
logues, when they have them. Tit
beginner will recognize the constitu
ent parts IF the square on the sum o.
: two lines more readily than he will
, perceive the parts of the algebrait
: square of plus b, oreven the parts Of
| the arithmetical square of number
, consisting of tens and units. Else
, why the use cube root blocks2
That geometry Is such mystery te
so many students that have tried tt
, learn it in this country, is partly thu
fault Of teachers, and partly due tt
authors. In arithmetic one method il
given and dozen examples to illus
, trate; in most textbooks on geometry
under most teachers the student pro
: ceeds from theorem to theorem with
J out single exercise requiring the usC
, of the demonstrated truth. Is not TIT
| error plain? I speak of things a
they have been. They are getting
: better now, thanks to enlighGenin&
influences.
, 1t was my intention to put thu
! whole of my argument in single
communication, but it would be tot
: long. IT you see fit to publish this,
shall extend it to one more article, o.
possibly two; and / hope that teach
: ers and superintendent will %eigii
} my reasons. GEO. P.G1nRfsoN.
Dripping Springs, Z ov. ID, 1888.