PAGE

To find the possible Roots of an Equation . . 129

By Newton's Method of Divisors 132

Recurring Equations

CUBIC EQUATIONS, Cardan's Rule

BIQUADRATIC EQUATIONS, Des Cartes' Rule

To revolve Equations by the simplest Method

By Simpson's Rule

By Bernoulli's Rule

Exponential Equations

Dr. Hutton's Rule for extracting the Roots of Num-

bers by Approximation

PROBLEMS PRODUCING EQUATIONS OF THREE OR MORE

DIMENSIONS

INDETERMINATE ANALYSIS

Solution of Indeterminate Problems

DIOPHANTINE PROBLEMS

INFINITE SERIES, their Nature, &c.

To reduce Fractions to Infinite Series

To reduce compound quadratic Surds to Infinite

Series

Newton's Binomial Theorem

. 165

173

176

€ 181

To find the Orders of Differences

To find any Term of a Series

THE INVESTIGATION AND CONSTRUCTION OF LOGARITHMS,

both hyperbolical and common

GEOMETRY.

Historical Introduction

On the Usefulness of Geometry

Description of Mathematical Instruments

Of Geometry considered as the Science of Demon-
stration, with some Account of the Principles of
Reasoning, as introductory to the Study of Euclid 250

Observations on some Parts of the first Book of

Euclid's Elements

314

An Appendix to the above six Books of Euclid
PRACTICAL GEOMETRY, exemplifying and applying Euclid's
Theory; the Use of the Mathematical Instru-
ments, &c.

Methods of constructing Scales of equal Parts

To construct Scales of Chords, Sines, Tangents, Se-

cants, &c.

327

343

344

346

The Mensuration of a great variety of plane and
solid Figures, Land, Planks, Timber, Stone, &c.

TRIGONOMETRY.

Historical Introduction

On the new (French) Division of the Quadrant (note) 367

Definitions and Principles of Plane Trigonometry 371

Variation of the Algebraic Signs

. 375

ERRAT A.

PAGE

7 To the note at the bottom of the page add, "The sign denotes therefore."

18 Last line, for the difference, read d=the difference. -1 read n-1.

44 Line 8, for n

Line 20, for n.n—1.n—2.n—3.n—4, read

n.n-1.n-2.n-3.n-4.

64 Line 3, for Fo since, read For since ad.

66 Art. 68, after the word CONVERTENDO, add, Euclid pr. E. Book 5.

71 The note at the bottom is useless here, as it occurs in the latter part of The Properties of Numbers, pp. 108, 109.

97 Last line, for b=1.q, read b+1.q.

123 Dele the third and five following lines.

252 Art. 15. line 2, dele “or simple."

320 The three lines AG, BD, and EC in the figure, should intersect in the point Fon the circumference. Two or three of the figures in Part X. are very indifferently cut, but it is hoped that there is nothing which can possibly mislead, or affect the demonstrations.