Chapter I: 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._

[1] Some separate copies of these Appendixes are printed, for those who may desire to add them to the former editions.

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.