Carroll free press. [volume] (Carrollton [Ohio]) 1834-1861, 1843-01-06
FkKE'S L[(1II[S
ON THE
Philosophy Of Numbers
AND THE
ADAPTATION OF ARITHMETIC
To the business purposes Of life.

90
THE above book is not designed to
interfere with any publication used 10
our Schools, but rather 10 give teachers
and others, disposed to investigate, means
Of understanding The subject so far as il
can lie done without resOrting 10 the
higher branches Of mathematics science.
Too many content themselves with a
knowledge OF arbitrary rules, and think
they understand The science Of numbers.
because they can solve questions as a ma.
chine performs lis work, but if they
would educate the mind, and proceed
nnderstapdlngly. they must investigate
the reasons IN which their operations
are based. To enable every Que to do
this pleasantly anG eifecluaIIy the "Phi
losophy of Numbers" has been prepat-
ed. la 1t principles are advanced, ard
the rationale OF rules shown, while solu-
tons are performed in various WAYS
and their relative advantages pointed out
Especially are the Analytic and Synthet
&c modes explained and applied. A.
monest the problems solved are many OF
the catch questions of The dav.
The plan Of lectures would not be adj
mIssable in an elementary work, but
seems well adapted 10 one of an advan-
ced character. 1t enables The author TO
point out clearly the different views Of
which Tie subject admits, and 10 sketch
lis history, applications 10 business. &c.
ThIs mode is new and has met with gen.
eral approval. Ia ii teachers will find
modes OF iliuslratIuHs hat will he useful
10 them 10 their class room; and advan-
ccd classes my probably study The Lee,
lures a. a ttxt took, alter completing
their usual course OF Arithmetic.
The following very brief summary OF
the contents may give some idea of the
matter contaIued ~ The book.
Lecture LIST. The study Of Arithmetic
lis History, advantages &c. Modes Of
teaching Deaf aud Dumb, B lind &c.
2. Comparative view of The rules oil
Arithmetic; showing wherein they are
similar or dissimilar.
3. Principles of NUMBERING. WHY
ten is adopted as a basis by nearly all
nations. Other bases. Hebrew, Greek
and Roman Notation. Arabian system.
a, 6, &, Z, 8 aud 8, are devoted 10 the
Natural and Accidental Properties Of
Numbers. In these are embraced The
various relations and properties of mum
bers, going very fully into detail on The
doctrine Of Fractions, Ratio, Evolution
lnVoIuiiou &c, and showing The ordi.
nary rules of Arithmetic are built upon
these relations.
10. Modes of solving problems, with
the "Why and Wherefore" What uues
lions can and what cannot be solved BY
Position.
II. Interest DiscoUnt-Equation.-
NOTWITHSTANDING, &c.
IL. Proportion, amongst lines, Surfa-
ces aud Solids, with the origin of such
constant multlpliers as 1854, 3.I4I6,
1923, &c.
ID. Proofs. Coniraclions Mental Cal.
culaIions &c Zerah Colburn.
IA and Is, Solution of Problems, re.
sumed, with explanations.
l6. Theory Of Wheel Carriages; con
thinning, 1t is believed, a fuller lnvestiga
llon OF The subject than can readily be
found elsewhere.
II Tie uses to which a know edge o
Arithmetic is applied, in The several oc
equations of life.
IS. One Hundred Select Problems.
Ia A collection of Rules.
gu. Pursuit of knowledge under diff
c%uItles, with anecdotes Of eminent lndI
viduals.
Throughout the whole, solutions ar,
given Tor Illustration, and every opporlu
NIFTY embraced 10 point out The principle
and applications of the Science.
GrWe deem it unnecessary to publisI
the testimonials of appreciation will
which the work has been favored.
G-Ihe attention Of teachers is espe
ciaIiy inpited.
The above work is printed on the hes
OF paper, and contains 1856 pages duod
ecImo' Price, ia full binding, one dol
: lar at %retsiI.
For sale wholesale and retail By III
Publisher, ZGneSpiHe, Ohio. U. 2
!, James, Cincinnati; l. " Whiting 1
Huntington. Columbus; and Charles Rus
sell. Lebanon h may be had al rar,ou
other PLACES in Ohio, and the OdjOtninI
States.
U. P. BENNETT,