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CHAPTER VIII.

EQUATIONS OF THE FIRST DEGREE.

Definitions-Axioms employed..

Transformation of Equations.....

Solution of Equations.......

Solution of Problems

CHAPTER IX.

EQUATIONS WITII MORE THAN ONE UNKNOWN QUANTITY.

Different Methods of Elimination

Equations containing three or more Unknown Quantities...

Problems involving several Unknown Quantities........

CHAPTER X.

DISCUSSION OF PROBLEMS.

Positive Values of x-Negative Values........

Zero and Infinity........

Indeterminate Solutions.

Inequalities........

CHAPTER XI.

INVOLUTION.

Powers of Monomials....

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Multiplication and Division of Radical Quantities....

Powers and Roots of Radical Quantities

Operations on Imaginary Quantities....

To find Multipliers which shall render Surds rational.....

Square Root of a Binomial Surd.........

Equations containing Radical Quantities......

CHAPTER XIV.

EQUATIONS OF THE SECOND DEGREE.

Incomplete Equations of the Second Degree.........

Complete Equations of the Second Degree........

Equations which may be solved like Quadratics.......

Problems producing Equations of the Second Degree......

Equations containing two unknown Quantities........

General Properties of Equations of the Second Degree.......

Discussion of the general Equation of the Second Degree......

Discussion of particular Problems

Geometrical Construction of Equations.......

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GENERAL THEORY OF EQUATIONS.

Definitions and general Properties.........

An Equation of the nth Degree has n Roots...

Law of the Coefficients of every Equation.......

Number of imaginary Roots..

Transformation of Equations

Descartes's Rule of Signs.....

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