The Massachusetts spy, and Worcester County advertiser. [volume] ([Worcester, Mass.]) 1825-1831, 1829-04-01

for 3475 pounds"-so he multiples the two
numbers together, and is sure that he has
obtained the true answer.
might take every question in the Rule
OF Three, and make it equally manifest res
pecting each, that the analytical rule is
worse than useless-but these examples
are sufficient for the purpose.
The objection to synthetical arithmetic,
which 1T was incumbent on "Philom" to
obVlate, IS not against rules, but against tg-
norance OF ruteS, or against such rules so
introduced that their principle cannot be
easily understood.
This critic seems to be ignorant that Col
burn has published any other arithmetic
than the little manual styled Intellectual
Arithmetic" or that those who learn arith-
metic analytically have any knowledge of
the use of figures, for he asks, Shall our
children spend weeks, months, and years,
In counting their fingers; in proving two
and two make four or, at most in gaining
knowledge of the first principles of arith-
metlc Z" and then urges the frivolous and
! wholly impairment objection, that the eX-
perience of all ages goes to prove that men
tai calculation Is not to be depended on"
AS if there could be any other but mental
calculation. For Philom's information, |
will state that there is larger work, by the
same author, in use, designed to succeed
the intellectual arithmetic, and entitled
"Colburn's Sequel" In this book he may
find rules similar to those contained in syn
thetical arithmetics, but so introduced and
explained that they may be easily under
stood-he may find the design and use of
figures explained as clearly and definitely
as in any other book, and as difficult and
useful arithmetical questions, with as good
directions for solving them.
do not say that superficial knowledge
Of subject is not better than no knowl-
edge; but | do say, that thorough knowl-
edge, when it can be as easily obtained, is
better than superficial knowledge,-and
this, 1t appears to me, is the difference be-
tween these two systems of arithmetic.
The one teaches to do a thing ignorantly,
not knowing the nature or reason of the
operation-the Other, so far as it goes,
teaches to do the same thing understand
ingly, having this best Of rules for the op-
Grafton, viz, thorough knowledge of its
nature and effect.
am not prepared, however, to maintain
that Colburn's arithmetic is perfect. On
DEFICIENCIES which the same author, or 9TH
ers, may be able to supply. But this am
prepared to affirm, that when a scholar has
learned Colburn's arithmetic as it ought to
be learned, and as it may be by almost any
scholar, who is not absolutely a Ounce, in
time spent :" in purchase of its WORTH" he is
prepared, not only to learn any thing of
arithmetic which is not contained in Col
burn, and which may be useful to him in
business but to pursue the higher branches
of mathematics, with a degree of facility
and pleasure, and to degree of under
standing knowledge which many, who can
write the names, and talk auently of the
works and discoveries of Thales, Pythago-
ras, Briggs, Napier, Newton, and such men,
however early and easily they may have
learned to count their fingers, never did,
and never will, possess. Never, certainly,
till they go back to Colburn's lessons in
arithmetic, and learn better to appreciate
their merits than the writer of the article
signed Pbilom can do. w.