AN

EASY INTRODUCTION

TO THE

M A T H E M AT ICS;

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

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,

OXFORD:

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

LONDON ; PARKER, OXFORD ; AND DEIGHTON, CAMBRIDGE,

1814.

kita
Perfeson

William H. Burton
10-14-1930

CONTENT S.

ALGEBRA.

PAGE

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58

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O 11-13-35. mEw

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GENERAL PROBLEMS. Their Nature and Properties explained i

Method of registering the Steps of an Operation. . 17

ARITHMETICAL PROGRESSION.

Its Rules Algebraically investigated .

36

and applied

39

Problems exercising Arithmetical Progression 40

PERMUTATIONS

42

COMBINATIONS

43

SIMPLE INTEREST, its Rules investigated and applied 45

Discount, its Rules investigated and applied .

48

The DOCTRINE OF RATIOS .

49

Continued Fractions ,

PROPORTION, Direct

62

Inverse, or Reciprocal Proportion

69

Harmonical Proportion

70

Contra-harmonical Proportion

73

COMPARISON OF VARIABLE AND DEPENDENT QUANTITIES 74

GEOMETRICAL PROGRESSION.

Its Rules investigated

82

and applied

Problems in Geometrical Progression

89

COMPOUND INTEREST, its Rules investigated and applied. 91

PROPERTIES OF NUMBERS, an Investigation of those which

are most generally useful

93

EQUATIONS OF SEVERAL DIMENSIONS.

A general View of the Nature, Formation, Roots, &c.

of Equations

111

Generation of the higher Equations

113

Depression of Equations

· 117

Transformation of Equations

118

To find the Limits of the Roots

. 126