Σχετικά με αυτό το βιβλίο
Η βιβλιοθήκη μου
Βιβλία στο Google Play
CONTENTS.
INTRODUCTION.
Explanation of the Algebraic method of notation :—
Definitions and Axioms,
CHAPTER I.
On the Addition, Subtraction, Multiplication, and Division
of Algebraic Quantities.
SECT.
I. 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.
PAGE
1
11
18
22
33
50
On Algebraic Fractions.
I. 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
73
V. Addition and subtraction of algebraic fractions
VI. Multiplication and division of algebraic fractions
CHAPTER III.
.85
91
On Simple Equations involving only one unknown Quantity
95
I. Reduction of simple equations -
96
II. Resolution of simple equations, involving only one
unknown quantity -
101
III. Examples in simple equations, involving only one
108
CHAPTER IV.
On the Solution of Problems producing Simple Equa-
tions
I. Solution of problems producing simple equations,
involving only one unknown quantity -
CHAPTER V.
117
On Simple Equations involving two or more unknown
quantities
I. Elimination of unknown quantities from any num-
ber of simple equations
II. Resolution of simple equations, involving two un-
known quantities
Examples in which the preceding rules are applied
in the solution of simple equations, involving two
unknown quantities
134
III. Resolution of simple equations, involving three or
more unknown quantities
140
152
158
IV. Solution of problems producing simple equations,
involving more than one unknown quantity - 164
CHAPTER VI.
On the Involution and Evolution of Numbers, and of
Algebraic Quantities.
II. Evolution of algebraic quantities -
184
III. Investigation of the rules for the extraction of the
is a simple or a binomial surd, to another that
shall have a rational denominator
213
I. Solution of pure equations of the first degree by
involution
ib.
II. Solution of pure equations of the second, and other
higher degrees, by evolution.
230
III. Examples in which the preceding rules are applied
in the solution of pure equations
CHAPTER IX.
231
I. Solution of adfected quadratic equations, involving
only one unknown quantity.
II. Solution of adfected quadratic equations, involving
two unknown quantities
CHAPTER XI.
Equations.
On the Solution of Problems producing Quadratic
I. Solution of problems producing quadratic equa-
tions, involving only one unknown quantity -
II. Solution of problems producing quadratic equations,
involving more than one unknown quantity -
246
254
361
366
CHAPTER XII.
On the Expansion of Series
I. Resolution of algebraic fractions, or quotients, into
infinite series
II. Investigation of the binomial theorem
III. Application of the binomial theorem to the expan-
272
289
296
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.
299
302
307
308
I. Theory of logarithms
II. Application of logarithms to the solution of expo-
nential equations
CHAPTER XV.
311
312
317
On the Resolution of Equations of the third and higher
degrees.
I. Theory and transformation of equations
II. Resolution of cubic equations by the rule of CAR-
DAN, or of SCIPIO FERREO
320
326
III. Resolution of biquadratic equations by the method
of DES CARTES -
331
IV. Resolution of numeral equations by the method of
V. Resolution of numeral equations, by NEWTON'S
method of approximation -
336
APPENDIX.
Algebraic method of demonstrating the propositions
in the fifth book of Euclid's Elements, according
to the text and arrangements in Simson's edition
341