Sidebilder
PDF
ePub
[ocr errors]

PREFACE TO SECOND EDITION ...

FROM PREFACE TO FIRST EDITION

INTRODUCTION

DEFINITIONS

POSTULATES ...

AXIOMS ... ... ...

THEOREMS AND PROBLEMS

SECTION I., PROPOSITIONS 1–6.–First Case of Equality of Two

Triangles, with Accessory Problems ... ... ... ...

SECTION II., Props. 7—12.—Second Case of Equality of Two

Triangles, with Applications

... ... ...

SECTION III., PROPs. 13—17.-Angles which Two Intersecting

Straight Lines make with one another and with a Third ...

SECTION IV., ProPs. 18—25.-Inequalities of Parts of Triangles,

and Accessory Problems ... ... ... ... ... ...

SECTION V., PROP. 26.—Third and Fourth Cases of Equality of Two

Triangles ... ... ... ... ...

SECTION VI., PROPS. 27–31.–Parallelism ... ... ... ...

SECTION VII., PROP. 32, AND COROLLARIES.- Interior and Exterior

Angles of Rectilineal Figures ... ...

Section VIII., PROPs. 33, 34.-Parts of a Parallelogram... ...

SECTION IX., PROPS. 35—42.- Parallelism in relation to Equivalent

Parallelograms and Triangles ... ... ... ... ... 98

SECTION X., PROP8. 43_-45.-Complementary Parallelograms and

the Reduction of Rectilineal Figures to Parallelograms of

Equal Area ... ... ... .. ... ... ... ... 109

SECTION XI., PROPS. 46–48.—Squares and the Sides of the Right-

angled Triangle ... ... ... ... ... ... ... 116

EXAMINATION PAPERS FOR REVISION ... ... ... ... ... 122

THE GEOMETRY OF TEN RECENT GOVERNMENT SCIENCE PAPERS ... 135

APPENDIX-ALTERNATIVE DEMONSTRATIONS ... ... ... ... 141

DIAGRAMS I.-IV. ... ... ... ... ... ... ... ... 149

Note.-The Diagrams at the end are upon tough paper, and each of
them opens out for ready use with any other page of the book.

PREFACE TO SECOND EDITION.

The principles of this little work have met with much approbation from teachers and authorities of high standing. In the preparation of a new edition, therefore, a great effort has been made to carry out those principles fully, while providing for as small an expenditure of time and labour on the part of both pupil and teacher as will be effective. The book is now stereotyped, and hence teachers may use it with the assurance that it will meet with little or no alteration in future.

In reference to the changes which have been made, it may be noted that the extracts from the London University Matriculation papers have apparently disappeared. All the problems in them, however, which were new or otherwise important, have been absorbed into the “Papers for Revision.” Room was made for them by omitting some less useful questions, and by adding one new paper. In place of the portions of Matriculation papers referred to, those of the Science and Art Department have been brought up to date, and now form a most useful series of ten. In the body of the work, questions formerly occurred here and there which were found to be more or less vague, and therefore to invite guessing answers. Some of these have been amended, and others removed. Other questions, again, involved repetition carried somewhat to excess, and for that reason have been considered unnecessary.

[graphic]

PUBLIS

FRANCIS

89 FARRINGDO

A SHORT

GU

In Twelve Numbers, interleaved

first Lessons in

1

“The A translation, ... In fine make better will be need useful men choly and re in the presei “ The Han

"The Bax instruction to the Aut translation

OR, PENCILLED COPIES For the use of Schools and Fami

for the Dra

BY GEORGE
Principal Drawing Master in the St

CON
No. 1. Straight Lines and their

Combinations, &c.
No. 2. Rectilineal Figures.
No. 3. Curves.
No. 4. Outlines of Familiar Objects.
No. 5. Shaded Figures.

No. 6. Introduction to Perspective. The Series embraces a complete course priate and carefully graduated Copies, ad difficult outline, printed in pencil-colour tated. The Exercises have been so simpl of attainment as that of Writing. As so

sis, and it learner."

[merged small][ocr errors][ocr errors][merged small][ocr errors]
[ocr errors]
[ocr errors]
[ocr errors]

Epitome
Aurelius
Latin Verz
Medical Sa
Gregory's

Or sepa

[graphic]
« ForrigeFortsett »