Chap. IV. of Involution and Evolution

gyet

I. Of Involution

II. Of Evolution

III. Of Surds

Page 79

81

83

91

Chap. V.

99

I. Solution of Pure Equations 100

II. Solution of Adfečted Qua-

dratic Equations

103

III. Solution of Questions produ-

cing Quadratic Equations 108

Chap. VI. Of Indeterminate Problems 121

tem

Chap. VII. Demonstration of Theorems

by Algebra

127

I. Of Arithmetical Series 128

II. Of Geometrical Series

130

III. Of Infinite Series

133

IV. Properties of Numbers

138

Appendix to Part I.

147

1. Examples of the Use of Loga-

rithms in resolving Alge-

braical Questions

148

Quantities

II. Application of Algebra to Phya

el fics

Page 150

1. Of the Proportion of Variable

152

-2. Examples of Physical Pro-

blems

162

III. Of Interest and Annuities

168

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-

tion's

195

1. Cardan's Rule for Cubic Equa-

tions

195

II,

187

II. Solution of Equations whose ,

Roots are Commenfurate Page 198

III. Examples of Questions producing

the higher Equations

IV. Solution of Equations by Appro-

ximation

205

202

PART

III.

Of the Application of Algebra to Geometry.

211

Chap. I. General Principles

I. Of the Algebraical Expresion of

Geometrical Magnitudes

II. The Demonstration of Theorems 217

III. Of the Solution of Problems

213

218

Chap. II. Of the Definition of Lines by

Equations

229

of 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

1

17

No. III. Extermination of Unknown

Quantities, and of Radi

cals

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

Aberdeen, April 1. 1778.

ADVERTISEMENT.

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,