As these Qualities made you eminent in your Profession, so your Integrity gain’d you such an Universal Esteem, that, with the general Approbation of the People, you were foon called into several great Stations, and, at length, deservedly advanced to the highest Dignities in this Kingdom, the Publick Welfare whereof

you

have constantly promoted in all the Employments and Offices, which you have so honourably filled ; And, that you may long live the great Ornament thereof, is the hearty Wish of,

2

Chap.II:N ac

9

II

20

Part I. Of whole Quantities.

Otation, &c.

. Addition

7

III. Subtraction

IV. Multiplication

V, Division

14

Part II. Of Fractional Quantities.

Chap. I. Notation

II. Reduction

III and IV. Addition and Subtraction 28

V. Multiplication

VI. Division

Part III. Involution.

Chap. I. Of whole Quantities

34

II. Of Numbers

40

III. Of Fractions

20

30

32

Part IV. Evolution.

Chap. I. Of whole Quantities

44

II and III. Evolution and mixt Evolution

of Numbers

50

IV. Of Fractions

60

Part V. Of the Indices of Powers

68

Part VI. Of Surd-Roots.

Chap. I. Definitions

II. Reduction

III. Multiplication

IV. Division

V and VI. Addition and Subtraction

72

73

78

80

81

91

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

Chap. I. Te 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

94

II. Geometrical

99

III. Musical

105

Part IX. The Derivation and Composition of

Equations.

107

Chap. I. The Origine of Quadratick Equations 108

II. The Origine of Cubick, &c.Equations 111

Part X. The Solution of Adfected Quadratick

Equations

115

Part

Part XI. Of Numerical Questions.

Chap. I. Questions producing Simple Equations 123

II. Questions producing Adfected Quadratick,

&c. Equations

147

Part XII. Of several Methods of Solving high

Adfected Equations.

Chap. I. Preparations

177

II. The Solution of Cubick Equations by

Cardan's Method

18o

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

Biquadratick into two Quadraticks

187
IV. The Solution of Equations by Stephinus's

Method

V. The Solution of some Equations by Ker-

sey's Method

191

VI. The Solution of Equations by Sir Isaac

Newton's Method.

193

190

Part XIII. How to raise Canons for finding the

Sums of the Powers of an Arithmetical Pro-

gression continu'd

197.

Part XIV. Of Polygonal Numbers

205

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

proximations

Chap. I. The Demonsiration of Sir Isaac New-

ton's Theorem

215

II. Of the Converging Series

III. Of Logarithms

236

220

Part

Part XVI. Of Interest.

Chap. I. Of Simple Interest

257

II. Of Compound Interest

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.

292

BOOK II.

Part 1. Of Plane Trigonomety

322

Part II. The Solution of Geometrical Problems

333

Chap I. Of Problems producing Simple Equations

334

II. Of Probleris producing Adfected Qua-

dratick Equations

339

III. The Solutio.2 of Problems of several forts

343

Part III. Of Exhaustions.

395

Chap. I. How to draw Tangents to Carves 400

II. De Maxinis & Minimis

III. Of Quadratures

4061

411