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AN

* EASY INTRODUCTION

TO THE

MA T H E MATICS;

IN WHICH

THE THEORY AND PRACTICE
ARE LAID DOWN AND FAMILIARLY EXPLAINED.

To each subject are prefixed,
A BRIEF POPULAR HISTORY OF ITS RISE AND PROGRESS, CONCISE MEMOIRS
· OF NOTED MATHEMATICAL AUTHORS ANCIENT AND MODERN,

AND SOME ACCOUNT OF THEIR WORKS.

The whole forming
A COMPLETE AND EASY SYSTEM

OF

ELEMENTARY INSTRUCTION

+ IN THE

LEADING BRANCHES OF THE MATHEMATICS;

DESIGNED TO FURNISH STUDENTS WITH THE MEANS OF ACQUIRING CONSIDERABLE

PROFICIENCY, WITHOUT THE NECESSITY OF VERBAL ASSISTANCE.

Adapted to the use of
SCHOOLS, JUNIOR STUDENTS AT THE UNIVERSITIES, AND PRIVATE

LEARNERS,
ESPECIALLY THOSE WHO STUDY WITHOUT A TUTOR,

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OXFORD:

PRINTED BY BARTLETT AND NEWMAN;
AND SOLD BY LONGMAN, HURST, REES, ORME, AND BROWN, PATERNOSTER ROW,

LONDON ; PARKER, OXFORD; AND DEIGHTON, CAMBRIDGE.

1814.

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To find the possible Roots of an Equation ... 129

By Newton's Method of Divisors 132

Recurring Equations . . . . . . . . . . 134

CUBIC EQUATIONS, Cardan's Rule ........

BIQUADRATIC EQUATIONS, Des Cartes' Rule . . . . . 143

Euler's Rule . . . . . . 146

Simpson's Rule ..... 147

APPROXIMATION.

To revolve Equations by the simplest Method . . 150

By Simpson's Rule ........... 153

By Bernoulli's Rule ........... 155

Exponential Equations . . . . . . . . . . 159

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

bers by Approximation . . . . . . . . . 162

PROBLEMS PRODUCING EQUATIONS OF THREE OR MORE

DIMENSIONS . . . . . . . . . . . . 163

INDETERMINATE ANALYSIS . . . . . . . . . . . 165

Solution of Indeterminate Problems . . . . . 173

DIOPHANTINE PROBLEMS . . . . . . . . . . . 176

INFINITE SERIES, their Nature, &c. . . . . . . . 181

To reduce Fractions to Infinite Series . . . . . 182

To reduce compound quadratic Surds to Infinite

Series . . . . . . . . . . . . . 184

Newton's Binomial Theorem . . . . . . . . 185

To find the Orders of Differences . . . . . . 190

To find any Term of a Series ........ 191

To interpolate a Series .......... 192

To revert a Series . . . . . . . . . . . 195-

To find the Sum of a Series . . . . . . . . 197

THz InvestigATION AND CONSTRUCTION OF LOGARITHMS,

both hyperbolical and common ...... 204

GEOMETRY.

Historical Introduction . .. ......211

On the Usefulness of Geometry ......: 241

Description of Mathematical Instruments ... 242

Of Geonetry 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 . . . . . . . . . . 259

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On Euclid's second Book ......... 291

On Euclid's third Book . . . . . . . . . 297

On Euclid's fourth Book ......... 301

On Euclid's fifth Book . . . . . . . . . . 304

On Euclid's sixth Book . . . . . . . . . . 308

An Appendix to the above six Books of Euclid . . 314

PRACTICAL GEOMETRY, exemplifying and applying Euclid's

Theory; the Use of the Mathematical Instru-

ments, &c. . . . . . . . . . . . . . 327

Methods of constructing Scales of equal Parts . . 343

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

cants, &c. . . . :. . . . . . . . 344

The Mensuration of a great variety of plane and

solid Figures, Land, Planks, Timber, Stone, &c. 346

TRIGONOMETRY.

Historical Introduction .. . . .. 359

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

Definitions and Principles of Plane Trigonometry 371

Variation of the Algebraic Signs ...... 375

Introductory Propositions . . . . . . . . . 380

Investigation of Formulæ . . . . . . . . . 389

Method of constructing Tables of natural Sines,

Tangents, &c. . . . . . . . . . . . . 394

Method of constructing Tables of Logarithmical

Sines, Tangents, &c. . . . . . . . . . 399

The fundamental Theorems of Plane Trigonometry 400

Solution of right angled Triangles . . . . . . 407

Solution of oblique angled Triangles . . . . . 413

MENSURATION OF INACCESSIBLE Heights AND DISTANCES 423

Description of the Quadrant . . . . . . . . ibid.

Theodolite . . . . . . . 426

Mariner's Compass. ... . ibid.

Perambulator . . . . . . 429

Gunter's Chain . . . . . . ibid.

Measuring Tapes, Rod, &c. . . 430

PROBLEMS . . . . . . . . . . . . . . . ibid.

Conic Sections.

Historical Introduction . . . . . . . . . . 441

The Parabola . .......... 417

The Ellipse . . . . . . . . . . . 458

The Hyperbola .......... 478

LIST OF SUBSCRIBERS . . . . . . . . . . . . 501

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