As thefe Qualities made you eminent in your Profeffion, fo your Integrity gain'd you fuch an Univerfal Efteem, that, with the general Approbation of the People, you were foon called into feveral great Stations, and, at length, defervedly advanced to the highest Dignities in this Kingdom, the Publick Welfare whereof you have conftantly promoted in all the Employments and Offices, which you have fo honourably filled: And, that you may long live the great Ornament thereof, is the hearty Wifh of,

1 THE

CONTENTS.

I

Ntroduction

BOOK I.

Part I. Of whole Quantities.

Chap. IN Otation, &c.

III. Subtraction

IV. Multiplication

V. Divifion

Part II. Of Fractional Quantities.

Chap. I. Notation

II. Reduction

Page

i

2

7

9

II

14

20

20

III and IV. Addition and Subtraction 28

V. Multiplication

VI. Divifion

Part III. Involution.

Chap. I. Of whole Quantities

II. Of Numbers

III. Of Fractions

Part IV. Evolution.

Chap. I. Of whole Quantities

44

II and III. Evolution and mixt Evolution

Part VII. Of the Nature of Equations, &c. 84

Chap. I. The Reduction of Single Equations 86

II. How to reduce Equations containing two

or more unknown Quantities into Single ones

Part VIII. Of Proportionals.

Chap. I. Arithmetical

91

II. Geometrical

III. Mufical

94

99

105

107

Part IX. The Derivation and Compofition of

Equations.

Chap. I. The Origine of Quadratick Equations 108

II. The Origine of Cubick, &c. Equations III

Part X. The Solution of Adfected Quadratick

Equations

115

Part

Part XI. Of Numerical Questions.

Chap. I. Quefiions producing Simple Equations 123

II. Queftions producing Adfected Quadratick,

&c. Equations

147

Part XII. Of feveral Methods of Solving high

Adfected Equations.

Chap. I. Preparations

177

II. The Solution of Cubick Equations by

Cardan's Method

180

187

III. A Rule of Des Cartes's for diffolving a

Biquadratick into two Quadraticks

IV. The Solution of Equations by Stephinus's

Method

190

V. The Solution of fome Equations by Ker-

fey's Method

VI. The Solution of Equations by Sir Ifaac

Newton's Method.

193

Part XIII. How to raise Canons for finding the

Sums of the Powers of an Arithmetical Pro-

greffion continu'd

Part XIV. Of Polygonal Numbers

197

205

Part XV. Of the Nature of Series, or Of Ap-

proximations

Chap. I. The Demonftration of Sir Ifaac New-

ton's Theorem

II. Of the Converging Series

III. Of Logarithms

215

220

236

Part

Part XVI. Of Interest.

Chap. I. Of Simple Intereft

II. Of Compound Intereft

257

264

Part XVII. Some of Diophantus's Questions 278

Part XVIII. Of the Alternations and Combinati-

ons of Quantities.

Chap. I. Of the Alternations of Quantities 285

II. Of the Combinations of Quantities 289

Part XIX. Of Magick Squares.

BOOK II.

292

Chap. I. How to draw Tangents to Carves 400

II. De Maximis & Minimis

III. Of Quadratures

406

411