Elements of Algebra
Leonard Euler
in Springer Books from Springer
Date: 1972
Edition: Fifth Edition
ISBN: 978-1-4613-8511-0
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Chapters in this book:
- Ch Chapter I Of Mathematics in general
- Leonard Euler
- Ch Chapter I Of Arithmetical Ratio, or of the Difference between two Numbers
- Leonard Euler
- Ch Chapter I Of the Addition of Compound Quantities
- Leonard Euler
- Ch Chapter I Of the Solution of Problems in general
- Leonard Euler
- Ch Chapter I On Continued Fractions
- Leonard Euler
- Ch Chapter I Of the Resolution of Equations of the First Degree which contain more than one unknown Quantity
- Leonard Euler
- Ch Chapter II Of the Resolution of Simple Equations, or Equations of the First Degree
- Leonard Euler
- Ch Chapter II Of Arithmetical Proportion
- Leonard Euler
- Ch Chapter II Solution of some curious and new Arithmetical Problems
- Leonard Euler
- Ch Chapter II Explanation of the Signs + Plus and — Minus
- Leonard Euler
- Ch Chapter II Of the Subtraction of Compound Quantities
- Leonard Euler
- Ch Chapter II Of the Rule which is called Regula Cæci, for determining by means of two Equations, three or more Unknown Quantities
- Leonard Euler
- Ch Chapter III Of the Multiplication of Compound Quantities
- Leonard Euler
- Ch Chapter III Of the Multiplication of Simple Quantities
- Leonard Euler
- Ch Chapter III Of the Resolution, in Integer Numbers, of Equations of the first Degree, containing two unknown Quantities
- Leonard Euler
- Ch Chapter III Of the Solution of Questions relating to the preceding Chapter
- Leonard Euler
- Ch Chapter III Of Compound Indeterminate Equations, in which one of the Unknown Quantities does not exceed the First Degree
- Leonard Euler
- Ch Chapter III Of Arithmetical Progressions
- Leonard Euler
- Ch Chapter IV Of the Division of Compound Quantities
- Leonard Euler
- Ch Chapter IV Of the Nature of whole Numbers, or Integers, with respect to their Factors
- Leonard Euler
- Ch Chapter IV Of the Resolution of two or more Equations of the First Degree
- Leonard Euler
- Ch Chapter IV Of the Summation of Arithmetical Progressions
- Leonard Euler
- Ch Chapter IV On the Method of rendering Surd Quantities of the form √ (a+bx+cx2) Rational
- Leonard Euler
- Ch Chapter IV General Method for resolving, in Integer Numbers, Equations with two unknown Quantities, of which one does not exceed the first Degree
- Leonard Euler
- Ch Chapter IX Of Cubes, and of the Extraction of Cube Roots
- Leonard Euler
- Ch Chapter IX Of the Method of rendering Rational the incommensurable Formula, √ (a + bx + cx2 + dx3 + ex4)
- Leonard Euler
- Ch Chapter IX Observations on the Rules of Proportion and their Utility
- Leonard Euler
- Ch Chapter IX Of the Addition and Subtraction of Fractions
- Leonard Euler
- Ch Chapter IX Of the Nature of Equations of the Second Degree
- Leonard Euler
- Ch Chapter IX Of the Manner of finding Algebraic Functions of all Degrees, which, when multiplied together, may always produce Similar Functions
- Leonard Euler
- Ch Chapter V Of the Cases in which the Formula a+bx+cx2can never become a Square
- Leonard Euler
- Ch Chapter V Of the Resolution of Pure Quadratic Equations
- Leonard Euler
- Ch Chapter V A direct and general Method for finding the values of x, that will render Quantities of the form √(a+bx+cx2) 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
- Leonard Euler
- Ch Chapter V Of Figurate, or Polygonal Numbers
- Leonard Euler
- Ch Chapter V Of the Division of Simple Quantities
- Leonard Euler
- Ch Chapter V Of the Resolution of Fractions into Infinite Series
- Leonard Euler
- Ch Chapter VI Of the Resolution of Mixed Equations of the Second Degree
- Leonard Euler
- Ch Chapter VI Of the Squares of Compound Quantities
- Leonard Euler
- Ch Chapter VI Of Geometrical Ratio
- Leonard Euler
- Ch Chapter VI Of the Properties of Integers, with respect to their Divisors
- Leonard Euler
- Ch Chapter VI Of the Cases in Integer Numbers, in which the Formula ax2 + b becomes a Square
- Leonard Euler
- Ch Chapter VI Of Double and Triple Equalities
- Leonard Euler
- Ch Chapter VII Of the Extraction of the Roots of Polygonal Numbers
- Leonard Euler
- Ch Chapter VII A direct and general Method for finding all the values of y expressed in Integer Numbers, by which we may render Quantities of the form √ (ay2+b), rational;aandbbeing given Integer Numbers; and also for finding all the possible Solutions, in Integer Numbers, of indeterminate Quadratic Equations of two unknown Quantities
- Leonard Euler
- Ch Chapter VII Of the Extraction of Roots applied to Compound Quantities
- Leonard Euler
- Ch Chapter VII Of Fractions in general
- Leonard Euler
- Ch Chapter VII Of a particular Method, by which the Formula, an2 + 1, becomes a Square in Integers
- Leonard Euler
- Ch Chapter VII Of the Greatest Common Divisor of two given Numbers
- Leonard Euler
- Ch Chapter VIII Of the Properties of Fractions
- Leonard Euler
- Ch Chapter VIII Of the Extraction of the Square Roots of Binomials
- Leonard Euler
- Ch Chapter VIII Remarks on Equations of the form p2=aq2+1, and on the common method of resolving them in Whole Numbers
- Leonard Euler
- Ch Chapter VIII Of the Method of rendering the Irrational Formula, √(a + bx + cx2 + dx3), Rational
- Leonard Euler
- Ch Chapter VIII Of the Calculation of Irrational Quantities
- Leonard Euler
- Ch Chapter VIII Of Geometrical Proportions
- Leonard Euler
- Ch Chapter X Of the Multiplication and Division of Fractions
- Leonard Euler
- Ch Chapter X Of the higher Powers of Compound Quantities
- Leonard Euler
- Ch Chapter X Of the Method of rendering rational the irrational Formula, $$ \mathop{\surd }\limits^{3} \left( {a + bx + c{x^{2}} + d{x^{3}}} \right) $$
- Leonard Euler
- Ch Chapter X Of Compound Relations
- Leonard Euler
- Ch Chapter X Of Pure Equations of the Third Degree
- Leonard Euler
- Ch Chapter XI Of the Resolution of the Formula, ax2+bxy+cy2into its Factors
- Leonard Euler
- Ch Chapter XI Of the Transposition of the Letters, on which the demonstration of the preceding Rule is founded
- Leonard Euler
- Ch Chapter XI Of Square Numbers
- Leonard Euler
- Ch Chapter XI Of Geometrical Progressions
- Leonard Euler
- Ch Chapter XI Of the Resolution of Complete Equations of the Third Degree
- Leonard Euler
- Ch Chapter XII Of Square roots, and of Irrational Numbers resulting from them
- Leonard Euler
- Ch Chapter XII Of the Transformation of the Formula ax2+cy2into Squares, and higher Powers
- Leonard Euler
- Ch Chapter XII Of the Expression of Irrational Powers by Infinite Series
- Leonard Euler
- Ch Chapter XII Of Infinite Decimal Fractions
- Leonard Euler
- Ch Chapter XII Of the Rule of Cardan, or of Scipio Ferreo
- Leonard Euler
- Ch Chapter XIII Of the Resolution of Equations of the Fourth Degree
- Leonard Euler
- Ch Chapter XIII Of some Expressions of the Form ax4+by4, which are not reducible to Squares
- Leonard Euler
- Ch Chapter XIII Of the Resolution of Negative Powers
- Leonard Euler
- Ch Chapter XIII Of the Calculation of Interest
- Leonard Euler
- Ch Chapter XIII Of Impossible, or Imaginary Quantities, which arise from the same source
- Leonard Euler
- Ch Chapter XIV Solution of some Questions that belong to this part of Algebra
- Leonard Euler
- Ch Chapter XIV Of Cubic Numbers
- Leonard Euler
- Ch Chapter XIV Of the Rule of Bombelli for reducing the Resolution of Equations of the Fourth Degree to that of Equations of the Third Degree
- Leonard Euler
- Ch Chapter XIX Of the Method of representing Irrational Numbers by Fractional Exponents
- Leonard Euler
- Ch Chapter XV Of Cube Roots, and of Irrational Numbers resulting from them
- Leonard Euler
- Ch Chapter XV Solutions of some Questions in which Cubes are required
- Leonard Euler
- Ch Chapter XV Of a new Method of resolving Equations of the Fourth Degree
- Leonard Euler
- Ch Chapter XVI Of the Resolution of Equations by Approximation
- Leonard Euler
- Ch Chapter XVI Of Powers in general
- Leonard Euler
- Ch Chapter XVII Of the Calculation of Powers
- Leonard Euler
- Ch Chapter XVIII Of Roots, with relation to Powers in general
- Leonard Euler
- Ch Chapter XX Of the different Methods of Calculation, and of their mutual Connexion
- Leonard Euler
- Ch Chapter XXI Of Logarithms in general
- Leonard Euler
- Ch Chapter XXII Of the Logarithmic Tables now in use
- Leonard Euler
- Ch Chapter XXIII Of the Method of expressing Logarithms
- Leonard Euler
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DOI: 10.1007/978-1-4613-8511-0
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