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
- ADDITIONS BY M. DE LA GRANGE
- Advertisement
- Chap. I Of Continued Fractions
- Chap. II Solution of some New and Curious Arithmetical Problems
- Chap. III Of the Resolution in Integer Numbers of Equations of the First Degree containing two Unknown Quantities
- Chap. IV General Method for resolving in, Integer Equations of two Unknown Quantities, one of which does not exceed the First Degree
- Chap. V A direct and general Method for finding the values of x, that will render Rational Quantities of the form √(a + bx + cx2), 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
- Chap. VI Of Double and Triple Equalities
- Chap. 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, A and B being given Integer Numbers; and also for finding all the possible Solutions, in Integer Numbers, of indeterminate Quadratic Equations of two unknown Quantities
- Chap. VIII Remarks on Equations of the Form p2=Aq2 + 1, and on the common Method of resolving them in whole Numbers
Chap. VI - Of Double and Triple Equalities
Published online by Cambridge University Press: 05 July 2011
Translated by
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
- ADDITIONS BY M. DE LA GRANGE
- Advertisement
- Chap. I Of Continued Fractions
- Chap. II Solution of some New and Curious Arithmetical Problems
- Chap. III Of the Resolution in Integer Numbers of Equations of the First Degree containing two Unknown Quantities
- Chap. IV General Method for resolving in, Integer Equations of two Unknown Quantities, one of which does not exceed the First Degree
- Chap. V A direct and general Method for finding the values of x, that will render Rational Quantities of the form √(a + bx + cx2), 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
- Chap. VI Of Double and Triple Equalities
- Chap. 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, A and B being given Integer Numbers; and also for finding all the possible Solutions, in Integer Numbers, of indeterminate Quadratic Equations of two unknown Quantities
- Chap. VIII Remarks on Equations of the Form p2=Aq2 + 1, and on the common Method of resolving them in whole Numbers
Summary
A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
- Type
- Chapter
- Information
- Elements of Algebra , pp. 547 - 549Publisher: Cambridge University PressPrint publication year: 2009First published in: 1822