The spirit of democracy. [volume] (Woodsfield, Ohio) 1844-1994, 1857-06-03

Of one denomination from a number of a
different denomination though we can add
numbers of different kinds together strict.
ly speaking. 90 sso.et ''H2 8
Compound numbers are analogous in
every respect to simple ones, the princi-i
Piles in each case are identical! The sew
eral processes. made use of in the addi-
ton, subtraction, multiplication and divi-
sion of simple numbers are strictly appli-
cable to the same computations of com-
pound numbers. The only difference OBJ
servable is the irregularity in the forma-
tion of orders in the latter.
Fractions are Justly regarded as q diff
cult feature in common arithmetic, and it
requires much skill and accumen on the
part of the teacher to dispose of them
successfully. To explain all the princi-
pies involved in the discussion of fractions,
would merely be travelling over the same
road that was passed in treating numera-
tion, and reconciling them to the analysis
of fractions, together with some new truths
that are dedueed from admitted facts.
Finding the greatest common divisor and
least common multiple, for instance, can
not be explained intelligibly without an
accompanying demonstration. .-4F
The division of fractions into two clas-
ses is suggested by the peculiar character
of common and decimal fractions, each, of
which have particular properties not COM
mon to both. The most Obvious distinc-
ton that occurs is the denominators, while
the .denominator of common fraction may
be any number, that of decimal is ten
or some multiple Of ten by itself. Some
parts of a unit, too, cannot be exactly ex-
pressed decimally, as seven-ninths for in
stance; though its approximate value may
be so nearly written that the difference is
inconceivable No difference in the prin-
cipies of the several operations required
to be performed exists, the most general
properties of the one. are properties o!
tie other, generally the value of vulgar
fraction may be expressed decima!ly. The
name of vulgar fraction is derived from a
latin word signifying common, formerly
everything common was called vulgar. as
the people, yulgate, &c. Decimal is q
name derived from decimus tenth In
practice, especially percentage, decimal
| fractions are the most convenient, and, in
many cases almost indispensable to the
man of business. t -.
- Proportion is the most useful, interest
/ ing and important division of arithme.
tie, ~the most useful because the, mos
applicable to the various pursuits Of bust
ness; the most interesting, because. it
principles embody the most natural rela
ton that exists in the elementary scienc,
Of. numbers; and the most important be
cause il is indispensable in the computa
tions of ordinary mercantile transactions
/, The laws of all created matter are mad
4 conformable to this principle, of whicl
The rules of proportion as treated in arith
Emetic, are "a modification. Upon all tn
:, works of nature infinite wisdom has stamp
led this peculiar property; everything in tn
materia! world that owes its origin to God
8 possesses in an eminent degree, the al
) tribltesof eract proportion. The sturd
oak of century's growth, towering hig
& in the ethereal vault. " is held in its plac,
J in an upright position by the proportio
|. iof it's several parts. The tender herb
/, !, not the less distinguished by its conform
vlty to the same unerring law. The elt
: phant, the lion and the little mouse al
: each furnished with a physical structul
: suggested by the same necessity, bestowe
a by the same author and designed to al
; swer the some purpose. The shape {
, the birds that cleaye the air, the insect
! whose home is the same element, and til
!. diminutive ant are each formed with res
!, = ularity and symmetry. A vast system ,
: planets, fixed stars and other heavenl
). bodies; are the most sublime and beautifl
v examples of the necessity Of this law,
o the theory of creation. These reflection
! Head us at once to the conviction that tt
: author OF, the universe, when he create
!. matter impressed this principle upon
: and from which it can never depart.
. Descending from the consideration
f the subject in this view, We must note Il
n correspondence III OIL dpotidC1 SOuSC,
applied in. arithmetic. This is most
. accordance with the present theme. If {
. analogy can be traced between the laws
Il proportion as applied to animate beini
= and the abstraction of science, basis
n established for imputing increased il
rs portance to the study of proportion, ho'
$ ever it may be treated of.
,e Could Impressions. akin to these
# made upon the Students mind, it is b
10 lieved that more interest would be mai
. tested in its study. The relation of nul
iee bers with each other SO connected as
s. form an endless chain, of principles, t
!. bcognate properties of things so sassimil
ted Herewith as to show correspo
: fdence, is what should be sought for
rv every intelligent instructor of the you
=. mind. sfs
AZ The value Of correct knowledge
I'd proportion in commercial transaction
Mt long since made it an important branch
IS, study in schools established for the ed
he cation of business men. The whole routi