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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