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
- Chap. I Of Arithmetical Ratio, or the Difference between two Numbers
- Chap. II Of Arithmetical Proportion
- Chap. III Of Arithmetical Progressions
- Chap. IV Of the Summation of Arithmetical Progressions
- Chap. V Of Figurate, or Polygonal Numbers
- Chap. VI Of Geometrial Ratio
- Chap. VII Of the greatest Common Divisor of two given Numbers
- Chap. VIII Of Geometrical Proportions
- Chap. IX Observations on the Rules of Proportion and their Utility
- Chap. X Of Compound Relations
- Chap. XI Of Geometrical Progressions
- Chap. XII Of Infinite Decimal Fractions
- Chap. XIII Of the Calculation of Interest
- 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
Chap. I - Of Arithmetical Ratio, or the Difference between two Numbers
Published online by Cambridge University Press: 05 July 2011
- 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
- Chap. I Of Arithmetical Ratio, or the Difference between two Numbers
- Chap. II Of Arithmetical Proportion
- Chap. III Of Arithmetical Progressions
- Chap. IV Of the Summation of Arithmetical Progressions
- Chap. V Of Figurate, or Polygonal Numbers
- Chap. VI Of Geometrial Ratio
- Chap. VII Of the greatest Common Divisor of two given Numbers
- Chap. VIII Of Geometrical Proportions
- Chap. IX Observations on the Rules of Proportion and their Utility
- Chap. X Of Compound Relations
- Chap. XI Of Geometrical Progressions
- Chap. XII Of Infinite Decimal Fractions
- Chap. XIII Of the Calculation of Interest
- 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
Summary
378. Two quantities are either equal to one another, or they are not. In the latter case, where one is greater than the other, we may consider their inequality under two different points of view: we may ask, how much one of the quantities is greater than the other? Or we may ask, how many times the one is greater than the other? The results which constitute the answers to these two questions are both called relations or ratios. We usually call the former an arithmetical ratio and the latter a geometrical ratio, without however these denominations having any connexion with the subject itself. The adoption of these expressions has been entirely arbitrary.
379. It is evident, that the quantities of which we speak must be of one and the same kind; otherwise we could not determine any thing with regard to their equality, or inequality: for it would be absurd to ask if two pounds and three ells are equal quantities. So that in what follows, quantities of the same kind only are to be considered; and as they may always be expressed by numbers, it is of numbers only that we shall treat, as was mentioned at the beginning.
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- Elements of Algebra , pp. 126 - 128Publisher: Cambridge University PressPrint publication year: 2009First published in: 1822