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ERRATA.
P. 16, Note, for" at the end of Art. 39," read “ in Art. 66.”
P. 73, dele the first five lines.
P. 144, 1. 3 from bottom, dele comma after
a
1-2
P. 208, The Answer to Ex. 11. has been omitted; viz.
CONTENTS.
SECT.
I.
II.
INTRODUCTION.
Explanation of the Algebraic method of notation
Exemplification of the Algebraic signs and symbols -
CHAP. I.
PAGE
1
4
On the Addition, Subtraction, Multiplication,
and Division of Algebraic Quantities.
VII.
VIII.
Multiplication
Division
On the application of the foregoing rules to quan-
tities with literal coefficients -
Some general theorems, deduced by means of the
foregoing rules -
СНАР. ІІ.
On Algebraic Fractions.
On the reduction of fractions
On the addition, subtraction, multiplication, and
division of fractions
IX.
X.
31
XI.
On the method of finding the greatest common mea-
sure of two or more quantities
On the Involution and Evolution of Numbers and
of Algebraic Quantities.
On the involution of numbers and simple algebraic
XII.
quantities
41
XIII.
On the involution of compound algebraic quantities, 42
XIV.
XV.
XVI.
XVII.
XVIII.
XIX.
XX.
XXI.
XXII.
XXIII.
On the evolution of algebraic quantities
48
On the investigation of the rules for the extraction
of the square and cube roots of numbers
On the general mode of expressing the powers and
roots of quantities by means of indices
CHAP. IV.
On Simple Equations.
On the solution of simple equations containing
only one unknown quantity -
On the solution of simple equations containing two
or more unknown quantities
. The solution of questions producing simple equations, 75
CHAP. V.
On Quadratic Equations.
On the solution of pure quadratic equations
On the solution of adfected quadratic equations
On the solution of questions producing quadratic
equations -
On quadratic equations having impossible roots
XXIV. On the solution of quadratic equations of the form
On the solution of quadratic equations containing
two unknown quantities
XXVI.
-
On the solution of certain equations, in which the
two unknown quantities (x and y) are similarly
involved
108
CHAP. VI.
On Ratios, Proportion, and Variation.
XXVII. Definitions
XXVIII. On the comparison and composition of ratios
XXXII. On arithmetical progression
XXXIII. On geometrical progression
XXXIV. On the method of finding any number of arithmetic
or geometric means between two numbers
- 130
XXXV. On the solution of equations relating to numbers in
arithmetical or geometrical progression -
- 131
XXXVI. On the summation of an infinite series of fractions
in geometric progression; and on the method of
finding the value of circulating decimals
CHAP. VIII.
On Surds.
XXXVII. On the reduction of surds
136
138
140
144
XXXVIII. On the application of the fundamental rules of
arithmetic to surd quantities
XXXIX. On the method of finding multipliers which shall
render binomial surd quantities rational
On the method of extracting the square root of
binomial surds
XL.
151
154
157
160
- 163
- 166
- 168
171
- 173
CHAP. X.
On the Binomial Theorem, and subjects connected
XLVII.
XLVIII.
XLIX.
L.
with it.
- 176
The general demonstration of this Theorem
Some observations arising out of the foregoing
theorem
On the expansion of series
On the method of finding the approximate ratio
of the powers and roots of numbers whose dif-
ference is small
179
- 181
187
- 188
- 194
On the method of extracting the nth root of a bi-
nomial quadratic surd
LI.
LII.
On the method of reverting a series
CHAP. XI.
On Logarithms, and subjects connected with them.
Definition and properties of logarithms
LIII.
LIV.
LV.
LVI.
LVII.
On the method of finding the logarithm of any
given number
198
On the method of constructing logarithmic tables, 200
On the application of logarithms to complex arith-
metical operations, and to the solution of expo-
nential equations
On the summation of geometric series
LVIII. On compound interest
On the method of finding the increase of popula-
tion in any country, under given circumstances
of births and mortality -
A Table, exhibiting the period in which the po-
pulation of a country has a tendency to DOUBLE
itself, from an estimate of its increase per cent.
at the end of every ten years
206