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The high school algebra : part I

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348 pages
RESERVEyf] THE SCHOOL ALGEBRA.HIGH 1.PART BY J.W. ROBERTSON, B.A., LL.B., Mnthematical St.Institute^ Catharines.^Master^ Collegiate AKD I. J. PH.D.,BIRCHARD, M.A., Mathematical Master^ Collegiate Institute^ Brantford. TORONTO: WESLEYWILLIAM BRIGGS, BUILDINGS, Street West.29 TO 33 Richmond to the Act of the Parliament of in the one thousandEntered, according Canada, year andhundred William in the Office of the Minister ofeight eighty-six, by Brioqb, at Ottawa.Agriculture /^.?// X6-li' PEEFACE. mathematics have for some time felt that theTeachers of Insti-now in use in our Schools andHigh CollegiateAlgebras wants and of thetutes are not to theadapted requirements In these works some of the most important depart-present day. ments of such asElementary Algebra, Factoring, Symmetry, are treated soof Divisors and ofTheory Theory Equations, that the has found itor so pupil impossiblebriefly superficially a of these withoutto obtain satisfactory knowledge subjects of the teacher.on the resourcesdrawing heavily an efibrt has been made to treat withIn the following pages fullness the various either deficient orconsiderable departments hasabsent in the text-books. While no branchwholly ordinary has been devoted to thebeen attention TheorysKghted, special and toof Positive ISTumbers, Factoring, Surds, Sym-Negative of Divisors and of ConvincedQuadratics.
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RESERVEyf]THE
SCHOOL ALGEBRA.HIGH
1.PART
BY
J.W. ROBERTSON, B.A., LL.B.,
Mnthematical St.Institute^ Catharines.^Master^ Collegiate
AKD
I. J. PH.D.,BIRCHARD, M.A.,
Mathematical Master^ Collegiate Institute^ Brantford.
TORONTO:
WESLEYWILLIAM BRIGGS, BUILDINGS,
Street West.29 TO 33 Richmondto the Act of the Parliament of in the one thousandEntered, according Canada, year
andhundred William in the Office of the Minister ofeight eighty-six, by Brioqb,
at Ottawa.Agriculture
/^.?//
X6-li'<'?'3
>PEEFACE.
mathematics have for some time felt that theTeachers of
Insti-now in use in our Schools andHigh CollegiateAlgebras
wants and of thetutes are not to theadapted requirements
In these works some of the most important depart-present day.
ments of such asElementary Algebra, Factoring, Symmetry,
are treated soof Divisors and ofTheory Theory Equations,
that the has found itor so pupil impossiblebriefly superficially
a of these withoutto obtain satisfactory knowledge subjects
of the teacher.on the resourcesdrawing heavily
an efibrt has been made to treat withIn the following pages
fullness the various either deficient orconsiderable departments
hasabsent in the text-books. While no branchwholly ordinary
has been devoted to thebeen attention TheorysKghted, special
and toof Positive ISTumbers, Factoring, Surds, Sym-Negative
of Divisors and of ConvincedQuadratics.Theorymetry, Theory
of is a desider-that a and selectionlarge well-graded problems
in manual intended for class we have selectedatum work,any
as will meet theand constructed with care such wegreat hope
teachers and An efibrt has been madewants of both pupils.
but it is that errors haveto secure accuracy, quite possible may
We shall be to have suchin ourcrept despite vigilance. glad
so that be removed from edi-out they may subsequentpointed
tions.
exist as to the ofSome difference of proprietyopinion may
in which the different have been introduced.the order subjectsIV PREFACE.
and the ofThe treatment of Symmetrical Expressions Theory
until the has consider-Divisors has been acquireddelayed pupil
able with and theirfamiliarity algebraic symbols manipulation.
"svill commend itself to theWe trust that this expe-arrangement
teachers of the Surds andrience of the mathematical country.
the of Indices have been introduced before QuadraticTheory
it to dealas we did not think satisfactorilyEquations, possible
with the of without some of Surds.Quadratics knowledgeTheory
to re-An effort has been made in this work to encourage pupils
in Insort to as much asfactoring possible solving equations.
of this at a of anobject early stage equationspursuance very
of solution resolution into factors,easy character, capable by
have been introduced.
This is intended for all classes of whose studiespupilsAlgebra
do not extend the limits for Second Class Cer-beyond prescribed
tificates and Pass Matriculation. in view theJunior Having
fact that of different attainmentspupils very algebraic study
within these limits we have so the that thegraded problems
teacher can select such as are to a juniorjudicious easily adapted
and leave those more difficult until he becomes well ad-pupil,
understood thatvanced in his work. It beshould, however,
of the in and theproblems Symmetry go beyondmany Factoring
for Second Class work. Should this venturerequirements prove
successful it is the intention of the authors to follow it withup
Part which will deal with the for JuniorII., subjects required
""
Matriculation with Honors and for First Class C Certificates.
W. J. ROBERTSON,
I. J. BIRCHARD.
1SS6.July,CONTENTS.
Chapter L
Paos.
Definitions and of 9Explanations Signs
Notation 13Algebraic
and Number 17Quantity
Numbers 18Algebraic
Chapter II.
— —Addition Subtraction Use of Brackets 20
Addition 20 with Literal 24Coefficients
Subtraction 25 of 28Polynomials
Brackets 29
Chapter III,
32Multiplication
of 34 Polynomials
42Powers of a Binomial
IV.Chapter
Division 45
Homer's Method of Division 49
Chapter V.
54Factoring
Monomial Factors 54
Trinomials 55
56Complete Squares
Diflerence of two 58Squares
Sum and Difference of Cubes 59
61Trinomials
Chapter VI.
of One Unkno'wn 65Simple Equations
ofProblems One Unknown 70Simple EquationsproducingVI CONTENTS^
Chapteb VII.
Paoi.
Common Factors and Common 76Multiples
Common Factor 76Highest
Lowest 84Multiple
Chapter VIII.
Fractions 87
Fractions to their Lowest Terms 88Reducing
in the form of Fractions 91Changes
Lowest Common Denominator 93
Addition and Subtraction of Fractions 94
of Fractions 101Multiplication
Division of Fractions 105 107Complex
Theorems in Fractions 112
Chapter IX.
Fractional 120Simple Equations
Problems Fractional 132producing Equations
Chapter X.
of the FirstSimultaneous 140Equations Degree
Simultaneous of Three Unknowns 148Simple Equations
Problems Simultaneous 152producing Simple Equations
Chapter XI.
and Cube Root 162Square
Hoot 162Square
RootCube 170
Chapter XII.
of Indices 174Theory
XIII.Chapter
Surds 184
209Imaginary Expressions
Chapter XIV.
Surds 212Equations InvolvingSimple
Chapter XV.
217Symmetrical Expressions
Chapi'er XVI.
andof Divisors 234Complete SquaresTh«ory

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