Book contents
- Frontmatter
- ADVERTISEMENT
- MEMOIR OF THE LIFE AND CHARACTER OF EULER, BY THE LATE FRANCIS HORNER, ESQ., M. P.
- ADVERTISEMENT BY THE EDITORS OF THE ORIGINAL, IN GERMAN
- ADVERTISEMENT BY M. BERNOULLI, THE FRENCH TRANSLATOR
- Contents
- PART I Containing the Analysis of Determinate Quantities
- SECTION I Of the Different Methods of calculating Simple Quantities
- SECTION II Of the different Methods of calculating Compound Quantities
- SECTION III Of Ratios and Proportions
- SECTION IV Of Algebraic Equations, and of the Resolution of those Equations
- PART II Containing the Analysis of Indeterminate Quantities
- Chap. I Of the Resolution of Equations of the First Degree, which contain more than one unknown Quantity
- Chap. II Of the Rule which is called Regula Cæci, for determining, by means of two Equations, three or more Unknown Quantities
- Chap. III Of Compound Indeterminate Equations, in which one of the Unknown Quantities does not exceed the First Degree
- Chap. IV Of the Method of rendering Surd Quantities, of the form (√a + ax + cx2), Rational
- Chap. V Of the Cases in which the Formula a + bx + cx2 can never become a Square
- Chap. VI Of the Cases in Integer Numbers, in which the Formula ax2 + b becomes a Square
- Chap. VII Of a particular Method, by which the Formula an2 + 1 becomes a Square in Integers
- Chap. VIII Of the Method of rendering the Irrational Formula (√a + bx + cx2 + dx3) Rational
- Chap. IX Of the Method of rendering rational the incommensurable Formula (√x + bx + cx2 + dx3 + ex4)
- Chap. X Of the Method of rendering rational the irrational Formula (3 √a + bx + cx2 + dx3)
- Chap. XI Of the Resolution of the Formula ax2 + bxy + cy2 into its Factors
- Chap. XII Of the Transformation of the Formula ax2 + cy2 into Squares and higher Powers
- Chap. XIII Of some Expressions of the Form ax4 + by4, which are not reducible to Squares
- Chap. XIV Solution of some Questions that belong to this Part of Algebra
- Chap. XV Solutions of some Questions in which Cubes are required
- ADDITIONS BY M. DE LA GRANGE
Chap. IV - Of the Method of rendering Surd Quantities, of the form (√a + ax + cx2), Rational
Published online by Cambridge University Press: 05 July 2011
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Book contents
- Frontmatter
- ADVERTISEMENT
- MEMOIR OF THE LIFE AND CHARACTER OF EULER, BY THE LATE FRANCIS HORNER, ESQ., M. P.
- ADVERTISEMENT BY THE EDITORS OF THE ORIGINAL, IN GERMAN
- ADVERTISEMENT BY M. BERNOULLI, THE FRENCH TRANSLATOR
- Contents
- PART I Containing the Analysis of Determinate Quantities
- SECTION I Of the Different Methods of calculating Simple Quantities
- SECTION II Of the different Methods of calculating Compound Quantities
- SECTION III Of Ratios and Proportions
- SECTION IV Of Algebraic Equations, and of the Resolution of those Equations
- PART II Containing the Analysis of Indeterminate Quantities
- Chap. I Of the Resolution of Equations of the First Degree, which contain more than one unknown Quantity
- Chap. II Of the Rule which is called Regula Cæci, for determining, by means of two Equations, three or more Unknown Quantities
- Chap. III Of Compound Indeterminate Equations, in which one of the Unknown Quantities does not exceed the First Degree
- Chap. IV Of the Method of rendering Surd Quantities, of the form (√a + ax + cx2), Rational
- Chap. V Of the Cases in which the Formula a + bx + cx2 can never become a Square
- Chap. VI Of the Cases in Integer Numbers, in which the Formula ax2 + b becomes a Square
- Chap. VII Of a particular Method, by which the Formula an2 + 1 becomes a Square in Integers
- Chap. VIII Of the Method of rendering the Irrational Formula (√a + bx + cx2 + dx3) Rational
- Chap. IX Of the Method of rendering rational the incommensurable Formula (√x + bx + cx2 + dx3 + ex4)
- Chap. X Of the Method of rendering rational the irrational Formula (3 √a + bx + cx2 + dx3)
- Chap. XI Of the Resolution of the Formula ax2 + bxy + cy2 into its Factors
- Chap. XII Of the Transformation of the Formula ax2 + cy2 into Squares and higher Powers
- Chap. XIII Of some Expressions of the Form ax4 + by4, which are not reducible to Squares
- Chap. XIV Solution of some Questions that belong to this Part of Algebra
- Chap. XV Solutions of some Questions in which Cubes are required
- ADDITIONS BY M. DE LA GRANGE
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- Elements of Algebra , pp. 322 - 335Publisher: Cambridge University PressPrint publication year: 2009First published in: 1822