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CONTENTS.
INTRODUCTION.
Explanation of the Algebraic method of notation :---
Definitions and Axioms,
CHAPTER I.
Page
1
On the Addition, Subtraction, Multiplication, and Division of
Algebraic Quantities.
SECT.
J. Addition of algebraic quantities
II. Subtraction of algebraic quantities
III. Multiplication of algebraic quantities
IV. Division of algebraic quantities
V. Some general theorems, observations, &c.
CHAPTER II.
11
18
22
33
50
On Algebraic Fractions.
1. Theory of algebraic fractions
55
II. Method of finding the greatest common divisor of
two or more quantities
60
III. Method of finding the least common multiple of two
or more quantities -
72
IV. Reduction of algebraic fractions
V. Addition and subtraction of algebraic fractions
VI. Multiplication and division of algebraic fractions
VII. Resolution of algebraic fractions or quotients into
infinite series
II. Resolution of simple equations, involving only one
unknown quantity
117
III. Examples in simple equations, involving only one
125
CHAPTER IV.
On Simple Equations involving two or more un-
known quantities
I. Elimination of unknown quantities from any num-
ber of simple equations
135
136
II. Resolution of simple equations, involving two un-
160
Examples in which the preceding rules are applied
in the solution of simple equations, involving
two unknown quantities
172
III. Resolution of simple equations, involving three or
more unknown quantities
178
CHAPTER V.
On the Solution of Problems, producing Simple Equa-
tions
184
I. Solution of problems producing simple equations,
involving only one unknown quantity
II. Solution of problems producing simple equations,
involving more than one unknown quantity -
185
203
CHAPTER VI.
On the Involution and Evolution of Numbers,
and of Algebraic Quantities.
I. Involution of algebraic quantities
214
II. Evolution of algebraic quantities
III. Investigation of the rules for the extraction of
the square and cube roots of numbers
223
230
CHAPTER VII.
On Irrational and Imaginary Quantities.
I. Theory of irrational quantities -
237
II. Reduction of radical quantities or surds
243
III. Application of the fundamental rules of arithme-
tic to surd quantities
246
IV. Method of reducing a fraction whose denomina-
tor is a simple or a binomial surd, to another
that shall have a rational denominator
252
V. Method of extracting the square root of binomial
surds
I. Solution of pure equations of the first degree by
II. Solution of pure equations of the second, and
III. Examples in which the preceding rules are ap-
plied in the solution of pure equations
I. Solution of adfected quadratic equations, involving
only one unknown quantity
285
II. Solution of adfected quadratic equations, involv-
ing two unknown quantities
293
CHAPTER XI.
On the Solution of Problems producing Quadratic
Equations.
1. Solution of problems producing quadratic equa-
tions, involving only one unknown quantity
II. Solution of problems producing quadratic equa-
tions involving more than one unknown quanti-
ty
On the Binomial Theorem
I. Investigation of the binomial theorem
II. Application of the binomial theorem to the ex-
pansion of series
300
305
311
ib.
318
CHAPTER XIII.
On Proportion and Progression.
I. Arithmetical proportion and progression
II. Geometrical proportion and progression
III. Harmonical proportion and progression
IV. Problems in proportion and progression
On Logarithms
CHAPTER XIV.
321
324
329
330
I. Theory of logarithms
II. Application of logarithms to the solution of expo-
nential equations
CHAPTER XV.
ECT.
On the Resolution of Equations of the third and
higher degrees.
333
334
339
I. Theory and transformation of equations
II. Resolution of cubic equations by the rule of CAr-
DAN, or of SCIPIO FERREO
II. Resolution of biquadratic equations by the me-
thod of DES CARTES
353
V. Resolution of numeral equations by the method
of Divisors
355
V. Resolution of numeral equations, by NEWTON'S
method of approximation -
358
APPENDIX.
Algebraic method of demonstrating the propositions
in the fifth book of Euclid's Elements, according
to the text and arrangement in Simson's edition 363