PREFACE.
The preceding editions of this work were published in 1830, 1832, 1835, and 1840. This fifth edition differs from the three preceding, as to the body of the work, in nothing which need prevent the four, or any two of them, from being used together in a class. But it is considerably augmented by the addition of eleven new Appendixes,[1] relating to matters on which it is most desirable that the advanced student should possess information. The [first Appendix, on Computation], and the [sixth, on Decimal Money], should be read and practised by every student with as much attention as any part of the work. The mastery of the rules for instantaneous conversion of the usual fractions of a pound sterling into decimal fractions, gives the possessor the greater part of the advantage which he would derive from the introduction of a decimal coinage.
At the time when this work was first published, the importance of establishing arithmetic in the young mind upon reason and demonstration, was not admitted by many. The case is now altered: schools exist in which rational arithmetic is taught, and mere rules are made to do no more than their proper duty. There is no necessity to advocate a change which is actually in progress, as the works which are published every day sufficiently shew. And my principal reason for alluding to the subject here, is merely to warn those who want nothing but routine, that this is not the book for their purpose.
A. De Morgan.
London, May 1, 1846.
TABLE OF CONTENTS.
| BOOK I. | ||
| SECTION | PAGE | |
| I. | Numeration | [ 1] |
| II. | Addition and Subtraction | [14] |
| III. | Multiplication | [24] |
| IV. | Division | [34] |
| V. | Fractions | [51] |
| VI. | Decimal Fractions | [65] |
| VII. | Square Root | [89] |
| VIII. | Proportion | [100] |
| IX. | Permutations and Combinations | [118] |
| BOOK II. | ||
| I. | Weights and Measures, &c. | [124] |
| II. | Rule of Three | [144] |
| III. | Interest, &c. | [150] |
| APPENDIX. | ||
| I. | On the mode of computing | [161] |
| II. | On verification by casting out nines and elevens | [166] |
| III. | On scales of notation | [168] |
| IV. | On the definition of fractions | [171] |
| V. | On characteristics | [174] |
| VI. | On decimal money | [176] |
| VII. | On the main principle of book-keeping | [180] |
| VIII. | On the reduction of fractions to others of nearly equal value | [190] |
| IX. | On some general properties of numbers | [193] |
| X. | On combinations | [201] |
| XI. | On Horner’s method of solving equations | [210] |
| XII. | Rules for the application of arithmetic to geometry | [217] |
ELEMENTS OF ARITHMETIC.
BOOK I.
PRINCIPLES OF ARITHMETIC.