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LONDON: RELFE BROTHERS,
6, CHARTERHOUSE BUILDINGS, ALDERSGATE.

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BY THE SAME AUTHOR.

FIRST PRINCIPLES OF ENGLISH HISTORY.

Fcap. 8vo., 1s. cloth. “What does it matter to nine-tenths of mankind whether William mar. ied Planche or Matilda- whether this king had three wives or six-whether that one was crowned at Westminster or Winchester ? But it does concern each and all of us to know why a devastating war raged between the king and his parliament: what principles were involved ; and how it might have been avoided : to trace the growth of trial by jury through successive generations; to learn how one man's character influenced the whole realm for good or evil; to know that our deeds outlive us and bear fruit of which we little dream."-Author's Preface.

FIRST PRINCIPLES OF FRENCH HISTORY.

Fcap. 8vo., Ls. cloth. “Mr. Taylor's experience has given him an insight into the tastes and powers of children, and has enabled him to write quite the best Elementary History of France which has yet come under our notice.'

SATURDAY REVIEW.

FIRST PRINCIPLES OF ROMAN HISTORY.

Fcap. 8vo., 1s. cloth. "Intended to give clear ideas as to the leading facts of Roman History and to show the successive steps in the growth and decline of the Roman Empire and people.”

FIRST PRINCIPLES OF ENGLISH GRAMMAR.

Fcap. 8vo., 1s. cloth. “The First Principles of English Grammar is also an admirable little book."-SATURDAY REVIEW.

FIRST PRINCIPLES OF MODERN HISTORY.

Fcap. 8vo., Is. cloth. “We wish this little book all possible success; it should be read by all."

METROPOLITAN.

Relfe, Brothers, School Booksellers and Publishers,

CHARTERHOUSE BUILDINGS ALDERSGATA LONDON, E.C.

INDEX TO EUCLID'S PROPOSITIONS.

PAGE

PAGE

82

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83
102
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108

I. 30

Euclid I. 1

I. 2
I. 3
I. 4
I. 5
I. 6
I. 7.
I. 8
1. 9
I. IO
I. II
I. 12

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92
94
75
29
32
35

I. 31
I. 32
I. 33

II2

115
118

1. 34

I. 35

I21

I. 36

38
48

I. 13

I. 37

124
126
126

99

I. 14

I. 38

I. 15

I. 39

I. 16

>

I. 40 .....

I. 17

I. 41

I. 18

I. 42

I. 19

51
54
56
59
61
63
65
66
23
41
79

1. 43

127
128
128
129
131
133
135
137
139
142

I. 20

I. 21
I. 22

I. 44
I. 45
I. 46

I. 47

I. 23
I. 24

I. 48

INTRODUCTION.

" THE interest of a class of children in Euclid is generally languid in the extreme. It requires an excellent teacher to make Euclid palatable to the majority of a class. The first few children take an intelligent interest in the subject. . . . But the rest of the class know the proposition by frequent repetition only, and thus unconsciously they come to say it and to write it by heart.

“The percentage of boys who are capable of correctly proving a simple geometrical deduction is lamentably small.” 1

A lengthened scholastic experience has proved to me incontestibly the truth of these words. Some time ago I set myself the task of finding out the reason why. After careful observation of many pupils, and patient inquiry into the difficulties they met with, I came to the conclusion (a conclusion I

arrived at by many thoughtful teachers) that the reason is threefold.

In the first place, when Euclid wrote his Elements, more than two thousand years ago, he little thought they would form a text-book for English boys of the present day. And so he constructed his work on a plan which is logically consistent, but altogether wanting in that gradation which is so essential to beginners.

1 Extract from a paper on the Teaching of Geometry, by Mr. P. Magnus, B.Sc. ; read before the College of Preceptors, February 18th, 188

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