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Elements of algebra...

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312 pages
Presented to TKe Library of CollegeOntario ofTKe Education TorontoTKe University of by James Amoss n,v %1 *. C '/..^//// Errata. x 3x - -Page 58 last line for + 4 read x'^ + 3.r 4. It"18 -0 = 0. It"1 49c123 49c2 (1"153 7 X + 2 x+ 1 tt"+ 2j^165 12 -2x' " It" 3)=170 36 (4x2 (4x2+ It"197 1 X oc Xy oc Vy ti"251 21 3 9 tt" pai251 24 1 with paid with 100 pieces i: ti"68 ninth256 four'h PREFACE. respectfullyfollowing Treatise is submitted by theThe teachers of Canuda, in the confident beliefauthor to the lighten the labor of the instructor,that it will materially thesame time, facilitate pupil's progress andand, at the comprehension of the principles of the sciencehis thorough algebra. It is the earnest hope of the author that itof same flattering reception,may meet with the and very general introduction into the schools of the country, that kindly accordedhis fellow-teachers have so to his previous productions. of the differentThe order of succession chapters depends mainly on their importance and difficulty, andof course one that appearsthat here adopted is the preferable to the but, as every chapter is nearly independent of theauthor ; easily modify theothers, the teacher can arrangement to suit himself. toThe aim of the work is embrace all that can be pro- in the time usually -allottedfitably discussed to a comnic-n grammar school course; and, indeed, this volume willand at least much the as isbe found to contain as of subject, for the ordinary degree of B. A.
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Presented to
TKe Library of
CollegeOntario ofTKe
Education
TorontoTKe University of
by
James Amossn,v %1
*.
C
'/..^////<yAe////r//
/r/-y'//m/y'/x
'?%
\
\v\:
LOVELL'S SERIES OF SCHOOL BOOKS.
ELEMENTS
ALGEBRA;
DESIGNED FOR THE USE OF
CAHADIAH GRAMMAR AND COMMON SCHOOLS,
HERBERT SANGSTER,BY JOHN M.A.,
AND LECTURER INMATHEMATICAL MASTER CHEMISTRY AND NATDRAI,
IN THE NORMAL SCHOOL FOR UPl'ERPmLOSOPHY CANADA.
IHoutvcat
PRINTED AND PUBLISHED BY JOHN LOVELL,
AND SOLD BY K. MILLER.
ADAM MILLER, 62 KING STREET EAST.
1864.according to tlie Act of the Provincial Pjirlianient, iaBntered,
tlie year one thousand eight hundred and sixty-four, by
Lov?:Lr,, in the OfScc of the RegistrarJohn of the Province
of Canada.
____
S4&-2>
Errata.
x 3x - -Page 58 last line for + 4 read x'^ + 3.r 4.
It"18 -0 = 0.
It"1 49c123 49c2
(1"153 7 X + 2 x+ 1
tt"+ 2j^165 12 -2x'
"
It" 3)=170 36 (4x2 (4x2+
It"197 1 X oc Xy oc Vy
ti"251 21 3 9
tt" pai251 24 1 with paid with 100 pieces i:
ti"68 ninth256 four'hPREFACE.
respectfullyfollowing Treatise is submitted by theThe
teachers of Canuda, in the confident beliefauthor to the
lighten the labor of the instructor,that it will materially
thesame time, facilitate pupil's progress andand, at the
comprehension of the principles of the sciencehis thorough
algebra. It is the earnest hope of the author that itof
same flattering reception,may meet with the and very
general introduction into the schools of the country, that
kindly accordedhis fellow-teachers have so to his previous
productions.
of the differentThe order of succession chapters depends
mainly on their importance and difficulty, andof course
one that appearsthat here adopted is the preferable to the
but, as every chapter is nearly independent of theauthor ;
easily modify theothers, the teacher can arrangement to
suit himself.
toThe aim of the work is embrace all that can be pro-
in the time usually -allottedfitably discussed to a comnic-n
grammar school course; and, indeed, this volume willand
at least much the as isbe found to contain as of subject,
for the ordinary degree of B. A. inrequired to be read
British and Canadian Universities. Chapters on con-the
series, probabilities, andtinued fractions, logarithmicIV PREFACE.
the general theory of eciuutions were prepared, but, in
accordance with the advice of some oi' the leadin*^ educators
of the province, they were omitted as unsuited to tlie de.siti;n
of tothe work, and the requii emonts of cduimon or gram-
mar school.*.
The author has approaclied the subject with the cou-
viction, founded on many years' experience as a teacher of
mathematics, that the science of algebra tries, beyond all
others, the powers and patience of the learner. The ])upil
is commonly introduced to it while his mind is yet in an
undeveloped state its
; language is new to him, and he is
unprepared by previous training to comprehend its
abstractions. The difficulties which thus beset his path
are, of course, for the most part, only to be overcome by
his perseverance,own aided by the knowledge and ingen-
uity of his instructor, yet it appears to the author that
alsovery much depends upon the style and thoroughness
and adaptation of the text-book employed. Accordingly
in the preparatiou of this volume no pains have been spared
rendering the statementof principles,in and the demonstra-
tion of theorems as clear and concise as possible, or iu
illustrating each rule numerousfully by examples carefully
worked out and explained, or in selecting and arranging the
examples of an exercise so as to begin with the simple,
and gradually pass on to the more difficult.
The author hopes that while he has insisted upon
great thoroughness by numerous and appropriate problems,
at the same time, rendered pupil'she has, the advancement
easy and certain by the many explanations and illustra-
tions introduced.
The great majority of the problems and exercises are
new,—being now published for the first time, but there arePKEFACE. V
familiar to the teacher. In select-number alreadyalso a
in every case rigidlyauthor has, he believes,those theino;
by Todhunter, Colenso, andthe rule, adoptedadhered to
alreadya problem unless it hadof not insertingothers,
which case itleast two British authors—inappeared in at
property.regarded as commonis to be
of the pupils of ourthe fact that very manyKecognizing
schools study with the view of com-and grammarcommon
of our excellent Cana-education at some onepleting their
author has, at the end of the book,universities, thedian
embracingcollection of problems and theorems,introduced a
the pass and honor workothers all or nearly all ofamong
examination papershas been given on thein algebra which
the last eight or tenuniversity of Toronto duringof the
shew the pupil the style ofyears. These will serve to
universities,expected to answer at ourquestions he is
measure prepare him forwill, at the same time, in aand
his examinations.
I
introducing his pupils toteacher would think ofAs no
some extent at least, first drillingarithmetic without, to
intelligent teachernotation and numeration, so notliem in
drill his pupils in algebraic notation andwill neglect to
before inti'oducing them to the ordinary rules.numeration
referred to exercises ii, iii,The teacher is re.«pectfully
is recommended to extend and continue theseand iv, and
acquainteduntil his pupil is thoroughly and practically
definitions.with the
Well knowing the great inconvenience to both teacher
mistakes in a work onand pupils of inaccuracies and
algebra, the author has subjected this treatise to a searching
markedrevision and he believes that the few corrections
;
on the back of the title page are the only errors in thePREFACE.VI
exercises and anHWors of the workletter-press of the
is respectfully recommended to cause hisThe teaeher
eitjht trifling alterations therepupils to make the six or
in the body of the work with pen and ink.indicated
more difficultA key, containing full solutions to all the
press and will be issued almost immediatelyproblems, is in
1864.Toronto, January,