Chap. IV. Of Involution and Evolution

???

Page 79

I. Of Involution

81

II. Of Evolution

83

III. Of Surds

91

Chap. V.

99

1. Solrition of Pure Equations 100

II. Solution of Adfected Qua-

dratic Equations

103

III. Solution of Questions produ-

cing Quadratic Equations 108

Chap. VI. Of Indeterminate Problems 121

127

128

Chap. VII. Demonstration of Tbeorems

by Algebra

I. Of Arithmetical Series

11. Of Geometrical Sèrics

III. of Infinite Series

IV. Properties of Numbers

130

133

138

Appendix to Part I.

147

1. Examples of the Use of Lega-

ritbms in resolving Alge-

fraical Questions

148

II. Application of Algebra to Phy-

fics

Page 150

1. Of the Proportion of Variable

Quantities.

152

-2. Examples of Physical Pro-

blems

162

168

III. OS: And Annuities

1. Of Simple Interest

ib.

2. Of Compound Interest 169

3. Of Annuities

171

Of the General Properties and Resolution

of Equations of all Orders.

Chap. I. Of the Origin and Composition

of Equations, and of the

Signs and Coefficients of

their Terms

179

Chap. II. Of the Transformation of E-

quations

Chap. III. Of the Resolution of Equa-

tions

195

I. Cardan's Rule for Cubic Equa-

tions

195

187

II,

II. Solution of Equations whose

Roots are Commensurate Page 198

III. Examples of Questions producing

the higher Equations

IV. Solution of Equations by Appro-

ximation

205

202

211

Chap. I. General Principles

I. Of the Algebraical Expression of

Geometrical Magnitudes

II. The Demonstration of Tbeorems 217

III. Of the Solution of Problems 218

213

Chap. II. Of the Definition of Lines by

Equations

229

ci I. The Determination of the Figure

of a Curve from its Equation 235

II. General Properties of Curves from

their Equations

241

III. The Subdivision of Curves 244

IV. Of the Place of Curves defined

from other Principles, in the
Algebraical System

Page 245

Chap. III.

I. Construction of the Loci of Equa-
tions

249 II. Solution of Problems

252 III. Construction of Equations 258

No. III. Extermination of Unknown

Quantities, and of Radi-
cals

17

25

No, IV. Approximations
No. V. Of Logarithms
No. VI. Arithmetic of Șines, &6.

35

43

Aberdeen, April 1. 1778.

ADVERTISE M E N T.

The following Syllabus was drawn up for

the Use of Students who were to attend the Lectures of the Author; and is not intended to supersede the perusal of a more complete System of Algebra.