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

has been and will still continue for time
question of politics. The value of money
has become almost universal from pole to
pole, and it is reasonably suggested that,
its value should be established by the
same Authority.
This essay has been extended farther
than was anticipated at the commence
ment, and / shall leave arithmetic With
you and pass on to a briefsynopsis of the
other departments of mathematics referred
to above
Algebra follows arithmetic in aconnect-
ed view, forming a ink in an extended
chain of analysis, which pervaae every de-
partment ofmathematica science. The va
rious principles here treated of are similar
to those of arithmetic, treated ina more alb
sract manner, Algebra is defined by one
author on the subject "to be system of
short handed writing" Numbers rela-
tions. &C., are expressed in symbols,
which for the most part are letters and
figures.
These signs are entirely arbitrary, and
in general have the same meaning as in
Arithmetic. Letters are substantiated
for the known and unknown quantities of
a given equation and the several requi-.
red operatios are performed in the same
manner as if the quantities were known
and it was required to prove the solution.
The greatest difficulty experienced by
young beginners in this branch of science
is the appreciation of the distractions that
are here treated of this. however, is obvia-
ted by starting scholar in the right way,
and requiring him or her to learn every
thing as it occurs in the text, non -atten-
tion to this important object is what blights
success, and stamps encouragement upon
the minds many intelligent students.
When a correct system of study is enfer-
ced Algebra becomes the most interesting
one in elementary mathematics, and is
prosecuted with zeal and interest seldom
witnessed in any.other branch of primary
education, delightful scene is constantly
opening out before the mind, seldom real
| lied in other studies, this at least has been
the authors humble experience, which is
supported by the evidence of others with
whom have conversed upon this subject.
Previous to entering upon the study OF
higher mathematics knowledge of high
er Algebra is indispensable, 1t is, more.
over, very useful to the teacher in Illus
tratipg the principle of arithmetic.
] II is only within the last twenty year;
that, Algebra has been pursued as a study
except in the highest institutions of learn.
ling, and these only to a limited extent, =,
At that time there were but tfew. American
/. authors who wrote upon the subject ant
textbooks were generally supplied by
European authors. DAY, + believe. was
/ about the first American who published
a work on this, subject. Since then ;
multiplicity of text books by as many diff
ferent authors, wincing the growing interes
that's taken in the pursuit ofthis subjec
as a study in the lower grade Of schools.
n No branch ofscience is more useful thai
Elementary Geometry In fact its neces
!, sity suggested the science in the. yariou
|, applications of domestic life.
!, The history of Geometry furnishes
, striking illustration of the maxim .sneces
sity is the parent of invention Il
Egypt, as early as the time of the Phara
! obs and probably at an earlier date, tn
, lands bordering on the Nile became thron
: ged with dense population; subsistenc
required unremitting attention to agrieul
] tural pursuits; difficulties between adjoin
! ing landholders became common, and n
3 certain means were at hand to determi1
the boundaries with accuracy independen
E of temporary marks, subject to that deca
4 which time stamps upon all ltempora
$ things. At this. interesting epoch. Geom
e Ietry, in rude state was introduced by me
of science and patronized by Kingly sup
S port, serving to quell the existing jelous
: les and contentious that had become quit
: common Silence then it has served i
not few instances, to quell disturbance
f of similar character. # =
: A striking illustration of this truth
e fevinced in difficulty that has recentl
: been settled between the governments {
e Great Britain and the United States,
q reference to portion of the boundary b'
e tween the possessions of the former an
}, latter in North America. BY a treat
e made some years since the St Croix rive
e was declared the boundary line betwee
e two parties The commissioners WI
It made the treaty perhaps are since dea
y and it became necessary some twenl
= year since to determine what was tue S
Croix river mentioned in the treaty, owiI
e to the vague indeterminate manner
'e which it was referred to it was impossible
u determine with certainty whether the riv
r now called by that name was the one, al
y another negotiation was necessary to Sc
Is tie the disputed point.
N Thus twenty years was spent in usele
le contention about question that cou
re have been settled in week or less, b;
n the point been established by Astronol
IN icaI observation, founded upon princlpl
w or rules derived Immediately from Geol
be etry Such unfortunate dilemmas a
h. now happily avoided, owing to the adva