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Elements of Algebra (4th Edition) by Leonhard Euler, John Hewlett

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Elements of Algebra (4th Edition) written by Leonhard Euler, John Hewlett, Francis Horner, Jean Bernoulli, Joseph Louis Lagrange
"This is a facsimile reprint of John Hewlett's 1840 translation of Euler's Algebra and Lagrange's Additions thereto. Most of Euler's contribution is elementary, nothing more advanced than solving quartic equations, but worth having in order to appreciate his leisurely and effective style---would that more great mathematicians wrote so well and to such pedagogic effect. However, one third of the book is his lucid treatment of questions in number theory, and it is this material that drew Lagrange's comments. Here for the first time are the rigorous treatments of continued fractions and "Pell's" equation, and of quadratic forms. The combination of Euler's and Lagrange's tests, of experimental and theoretical research in Weil's description, is justly celebrated by the editors of Euler's Opera omnia, who print the two together, and it is good to see this classic back in print in English. Every library without much Euler should at least have this volume. It is accompanied by an excerpt of Horner's memoir on the life of Euler, and a eulogy by Truesdell, with a useful bibliography."

All Famous Books of this Author :-
Here is list all books/editions avaliable of this author, We recomended you to download all.
1. Elements of Algebra (4E) by Leonhard Euler, John Hewlett
2. Foundations of Differential Calculus by Leonhard Euler, John D. Blanton

Book Detail :-
Title: Elements of Algebra
Edition: 4th
Author(s): Leonard Euler
Publisher: Springer-Verlag New York
Series:
Year: 1984
Pages: 638
Type: PDF
Language: English
ISBN: 978-1-4613-8513-4,978-1-4613-8511-0
Country:
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  • An old book of Math Algebra

  • Book Contents :-
    Elements of Algebra (4th Edition) written by Leonhard Euler, John Hewlett, Francis Horner, Jean Bernoulli, Joseph Louis Lagrange cover the following topics.
    PART I. Containing- the Analysis o/" Determinate Quantities.
    SECTION I. Ofthe Different Methods of calculating Simple Quantities.
    I. Of Mathematics in general
    II. Explanation of the signs + plus and — minus
    III. Of the Multiplication of Simple Quantities
    IV. Of the nature of whole Numbers, or Integers with respect to their Factors
    V. Of the Division of Simple Quantities
    VI. Of the properties ofIntegers, with respect to their Divisors
    VII. Of Fractions in general
    VIII. Of the Properties of Fractions
    IX. Of the Addition and Subtraction of Fractions
    X. Of the Multiplication and Division of Fractions
    XI. Of Square Numbers
    XII. Of Square Roots, and of Irrational Numbers resulting from them
    XIII. Of Impossible, or Imaginary Quantities, which arise from the same source
    XIV. Of Cubic Numbers
    XV. Of Cube Roots, and of Irrational Numbers resulting from them
    XVI. Of Powers in general
    XVII. Of the Calculation of Powers
    XVIII. Of Roots with relation to Powers in general
    XIX. Of the Method of representing Irrational Numbers by Fractional Exponents
    XX. Of the different Methods of Calculation, and of their Mutual Connexion
    XXI. Of Logarithms in general
    XXII. Of the Logarithmic Tables that are now in use
    XXIII. Of the Method of expressing Logarithms
    SECTION II. Of the different Methods of calculating Compound Quantities.
    I, Of the Addition of Compound Quantities
    II. Of the Subtraction of Compound Quantities
    III. Of the MuItipHcation of Compound Quantities
    IV. Of the Division of Compound Quantities
    V. Of the Resolution of Fractions into Infinite Series
    VI. Of the Squares of Compound Quantities
    VII. Of the Extraction of Roots applied to Compound Quantities
    VIII. Of the Calculation of Irrational Quantities
    IX. Of Cubes, and of the Extraction of Cube Roots
    X. Of the higher Powers of Compound Quantities
    XI. Of the Transposition of the Letters, on which the demonstration of the preceding Rule is founded
    XII. Of the Expression of Irrational Powers by Infinite Series
    XIII. Of the Resolution of Negative Powers
    SECTION III. Of Ratios and Proportions.
    I. Of Arithmetical Ratio, or the Difference between two numbers

    II. Of Arithmetical Proportion
    III. Of Arithmetical Progressions
    IV. Of the Summation of Arithmetical Progressions
    V. Of Figurate, or Polygonal Numbers
    VI. Of Geometrical Ratio
    VII. Of the greatest Common Divisor of two given Numbers
    Vlll. Of Geometrical Proportions
    IX. Observations on the Rules of Proportion and their Utility
    X, Of Compound Relations
    XI. Of Geometrical Progressions
    XII. Of Infinite Decimal Fractions
    XIII. Of the Calculation of Interest
    SECTION IV. Of Algebraic Equations, and of the Resolution of those Equations.
    I. Of the Solution of Problems in General
    II. Of the Resolution of Simple Equations, or Equations of the First Degree
    III. Of the Solution of Questions relating to the preceding Chapter
    IV. Of the Resolution of two or more Equations of the First Degree
    V. Of the Resolution of Pure Quadratic Equations
    VI. Of the Resolution of Mixed Equations of the Second Degree
    VJI. Of the Extraction of the Roots of Polygonal Numbers
    VIII. Of the Extraction of Square Roots of Binomials
    IX. Of the Nature of Equations of the Second Degree
    X. Of Pure Equations of the Third Degree
    XI. Of the Resolution of Complete Equations of the Third Degree
    XII. Of the Rule of Cardan, or that o^ Scipio Ferreo
    XIII. Of the Resolution of Equations of the Fourth Degree
    XIV. Of the Rule of Bomhelli, for reducing the Resolution of Equations of the Fourth Degree to that of Equations of the Third Degree
    XV. Of a new Method of resolving Equations of the Fourth Degree
    XVI. Of the Resolution of Equations by Approximation

    PART II. Containing the hna\ys,\% o/" Indeterminate Quantities.
    I. Of the Resolution of Equations of the First Degree, which contain more than one unknown Quantity
    II. Of the Rule which is called Regu/a Cceci, for determining, by means of two Equations, three or more Unknown Quantities
    III. Of Compound Indeterminate Equations, in which one of the Unknown Quantities does not exceed the First Degree
    IV. Of the Method of rendering Surd Quantities, of the form (^/a + ax + c/t^"-). Rational
    V. Of the Cases in which the Formula a -f- b.v -\- c.%^ can never become a Square
    VI. Of the Cases in Integer Numbers, in which the Formula ax~ -\- b becomes a Square
    VII. Of a particular Method, by which the Formula an^ -\- 1 becomes a Square in Integers
    VIII. Of the Method ofrendering the Irrational Formula (v/a + bx -f- cx^ -h dx^) Rational
    IX. Of the Method of rendering rational the incommensurable Formula {\/ x-\- hx \-cx"-\-dji^-\- ex*
    X. Of the Method of rendering rational the irrational Formula (Va -|- bx +cx^ + da,^)
    XI. Of the Resolution of the Formula o^^-f hxy + cyinto its Factors
    XII. Of the Transformation of the Formula ax- -j- c^- into Squares and higher Powers
    Xlll. Of some Expressions of the Form r/a* + by*^ which are not reducible to Squares
    XIV. Solution of some Questions that belong to this Part of Algebra
    XV. Solutions of some Questions in which Cubes are required

    ADDITIONS BY M. DE LA GRANGE. Advertisement
    I. Of Continued Fractions
    II. Solution of some New and Curious Arithmetical Problems
    III. Of the Resolution in Integer Numbers of Equations of the First Degree containing two Unknown Quantities
    IV. General Method for resolving in Integer Equations of two Unknown Quantities, one of which does not exceed the First Degree
    V. A direct and general Method for finding the values of x, that will render Quantities of the form »y{a-\- bx +cx^) Rational, and for resolving, in Rational Numbers, the indeterminate Equations of the second Degree, which have two Unknown Quantities, when they admit of Solutions of this kind Resolution of the Equation Ap^ +
    sq^ — z^ in Integer Numbers
    VI. Of Double and Triple Equalities - - 547
    VII. A direct and general Method for finding all the values of 2/ expressed in Integer Numbers, by which we may rejider Quantities of the form ^/ {A.y^ + b), rational; a and b being given Integer Numbers; and also for finding all the possible Solutions, in Integer Numbers, of indeterminaie Quadratic Equations of two unknown Quantities Resolution of the Equation Cj/^— 2«_y:2 + nz^=. 1 in Integer Numbers. First Method, Second Method. Of the Manner of finding all the possible Solutions of the Equations cy- — 2nyz + Bz^ = 1, when we know only one of them. Of the Manner of finding all the possible Solutions, in whole Numbers, of Indeterminate Quadratic Equations of two Unknov*n Quantities
    VIII. Remarks on Equations of the Form j3*= Aq--{- \, and on the common Method of resolving them in whole Numbers
    IX. Of the Manner of finding Algebraic Functions of all Degrees, which, when multiplied together, may always produce similar Functions

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