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**About this book .- **
**Elements of Algebra (4E) ** written by
** Leonhard Euler, John Hewlett**.

The background assumed is that usually obtained in the freshman-sophomore calculus sequence. Linear algebra is not assumed to be known but is developed in the first chapter. Subjects discussed include all the topics usually found in texts on advanced calculus. However. there is more than the usual emphasis on applications and on physical motivation. Vectors are introduced at the outset and serve at many points to indicate geometrical and physical significance of mathematical relations. Numerical methods are touched upon at various points, both because of their practical value and because of the insights they give into the theory. A sound level of rigor is maintained throughout. Definitions are clearly labeled as such and all important results are formulated as theorems. A few of the finer points of real variable theory are treated at the ends of Chapters 2, 4, and 6. A large number of problems (with answers) are distributed throughout the text. These include simple exercises as well as complex ones planned to stimulate critical reading. Some -points of the theory are relegated to the problems. with hints given where appropriate. Generous references to the literature are given, and each chapter concludes with a list of books for supplementary reading. Starred sections are less essential in a first course.

**Book Detail .- **
** Title. ** Elements of Algebra
** Edition. ** 4th
** Author(s). ** Leonhard Euler, John Hewlett
** Publisher. ** Printed for Logman, Rees Orme and Co. Paternoster-Row
** Series. **
** Year. ** 1984
** Pages. ** 638
** Type. ** PDF
** Language. ** English
** ISBN. ** 978-1-4613-8513-4,978-1-4613-8511-0
** Country. ** Russia
** Get this book from Amazon**

**About Author :- **

** Leonhard Euler ** traslated from Latin Institutiones Calculi Differentialis, Chapter 1 to 9.
Leonhard Euler (1707–1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function.[3] He is also known for his work in mechanics, fluid dynamics, optics, astronomy and music theory. Euler was one of the most eminent mathematicians of the 18th century and is held to be one of the greatest in history. He is also widely considered to be the most prolific mathematician of all time.

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** • Download PDF Elements of Algebra (4E) by Leonhard Euler, John Hewlett **

** • Download PDF Foundations of Differential Calculus by Leonhard Euler, John Blanton **

** • Download PDF Leonhard Euler by Emil Fellmann, Gautschi **

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**Book Contents .- **
**Elements of Algebra (4E) ** written by
** Leonhard Euler, John Hewlett**
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

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

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

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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