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STANDARD EDUCATIONAL WORKS.

A MANUAL OF MODERN GEOGRAPHY, MATHEMATICAL,

PHYSICAL, AND POLITICAL. By the Rev. ALEX. MACKAY, LL.D. F.R.G.S. A New Edition, showing the result of the Census of the British Empire for 1871. 78. 6d.

ELEMENTS OF MODERN GEOGRAPHY. By the SAME.

Thirty-fourth Thousand, revised to the present time. 38.

THE INTERMEDIATE GEOGRAPHY, PHYSICAL, INDUS

TRIAL, AND COMMERCIAL. Intended as an Intermediate book between the Author's ' Outlines of Geography' and ' Elements of Geography.' By the Same. Second Edition, revised. Crown 8vo, pp. 224, 2s.

OUTLINES OF MODERN GEOGRAPHY.

Seventy-sixth Thousand, revised to the present time. ls.

By the SAME.

INTRODUCTORY TEXT-BOOK OF PHYSICAL GEOGRA

PHY. By DAVID PAGE, LL.D., F.G.S., &c., Professor of Geology in the Durham University College of Physical Science, Newcastle. Seventh Edition, revised and extended. 28. 6d.

ADVANCED TEXT-BOOK OF PHYSICAL GEOGRAPHY.

By the Same. Second Edition, enlarged. 58.

A NEW CONCISE ENGLISH DICTIONARY, ETYMOLOGI

CAL AND PRONOUNCING, including a very copious selection of Scientific, Technical, and other Terms and Phrases. Designed for use in Schools and Colleges, and as a Handy-book for General Reference. By the Revs. JAMES STORMONTH and P. H. PHELP. Second Edition, revised and enlarged. Crown 8vo, pp. 785, 78. 6d.

SCHOOLROOM EDITION OF THE ABOVE. Combining

the advantages of an ordinary Pronouncing School Dictionary and an Etymclogical Spelling-book. Fcap. 8vo, pp. 254, 28.

THE HANDY SCHOOL DICTIONARY, PRONOUNCING AND

EXPLANATORY. Containing Lists of Prefixes and Postfixes; Rules for Spelling correctly; Words same in Sound but different in Spelling and Meaning; Common Abbreviations; Common Quotations from the Latin, French, &c. For use in Elementary Schools. By the SAME. 16mo, pp. 260, 9d.

ENGLISH PROSE COMPOSITION: A PRACTICAL MANUAL

FOR USE IN SCHOOLS. By JAMES CURRIE, M.A. Eleventh Edition, Is. 6d. 2

A MANUAL OF ENGLISH PROSE LITERATURE, Bio

GRAPHICAL AND CRITICAL: designed mainly to show characteristics of Style. By W. MINTO, M.A. Crown 8vo, 10s. 6d.

CHARACTERISTICS OF ENGLISH POETS, FROM CHAUCER

TO SAIRLEY. By the SAME. Crown 8vo, 9s.

ANCIENT CLASSICS FOR ENGLISH READERS. By

VARIOUS AUTHORS. Edited by the Rev. W. LUCAS COLLINS, M.A. 20 vols. fcap. 8vo, 2s. 6d. each.

ADITUS FACILIORES : An Easy Latin Construing Book, with

Complete Vocabulary. By A. W. POTTS, LL.D., Head-Master of Fettes College, Edinburgh, and sometime Fellow of St John's College, Cambridge; and the Rev. C. DARN ELL, M.A., Head-Master of Cargilfield Preparatory School, Edinburgh, and late Scholar of Pembroke and Downing Colleges, Cambridge. Second Edition. 38. 6d.

A

MANUAL OF ZOOLOGY, FOR THE USE OF STUDENTS. With a General Introduction on the Principles of Zoology. By HENRY ALLEYNE NICHOLSON, M.D., F.R.S. E., F.G.S., &c., Professor of Natural History in the University of St Andrews. Fourth Edition, revised and enlarged. Crown 8vo, pp. 732, with 300 Engravings on Wood. 128. 6d.

TEXT-BOOK OF ZOOLOGY, FOR THE USE OF SCHOOLS. By

the SAME. Second Edition, enlarged. Crown 8vo, with 188 Engravings on Wood. 6s.

INTRODUCTORY TEXT-BOOK OF ZOOLOGY, FOR THE

Use of JUNIOR CLASSES. By the SAME. A New Edition, revised and enlarged. With 156 Engravings. 3s.

OUTLINES OF NATURAL HISTORY, FOR BEGINNERS ;

being Descriptions of a Progressive Series of Zoological Types. By the SAME. Fcap. 8vo, with Engravings. ls. 6d.

ADVANCED TEXT-BOOK OF GEOLOGY, DESCRIPTIVE AND

INDUSTRIAL. By DAVID PAGE, LL.D., F.G.S., &c., Professor of Geology in the Durham University College of Physical Science, Newcastle. With Engravings and Glossary of Scientific Terms. Fifth Edition, revised and enlarged. 7s. 6d.

INTRODUCTORY TEXT-BOOK OF GEOLOGY.

SAME. Tenth and Enlarged Edition. 28. 6d.

By the

A MANUAL OF BOTANY, ANATOMICAL AND PHYSIOLOGICAL,

for the Use of Students. By ROBERT BROWN, M.A., Ph.D., F.R.G.S., Lecturer on Botany under the Science and Art Department of the Committee of the Privy Council on Education. Crown 8vo, with numerous Illustrations. 12s. 60.

WILLIAM BLACKWOOD & SONS, EDINBURGH AND LONDON.

PRIMER OF GEOMETRY

AN EASY INTRODUCTION

TO

THE PROPOSITIONS OF EUCLID

BY

FRANCIS CUTHBERTSON, M.A., LL.D.

LATE FELLOW OF CORPUS CHRISTI COLL., CAMBRIDGE

HEAD MATHEMATICAL MASTER OF THE

CITY OF LONDON SCHOOL

WILLIAM BLACKWOOD AND SONS

EDINBURGH AND LONDON

MDCCCLXXVI

183 g. 90.

PRE FACE.

WHILST many of the Propositions of Euclid are very easy, there are others equally hard for the student to understand; moreover, they are not graduated according to their difficulty. Thus the Fifth Proposition of his First Book is invariably found to be a greater stumbling-block than most of those which follow. Now the earliest time at which the study of the Elements can be commenced is necessarily fixed by the difficult parts. Accordingly, inasmuch as those whose capacity is considerably below the limit thus indicated could master the easy portions, it follows that, by means of a course of Geometry embracing these, the subject might be introduced much sooner than it usually is.

As the beginner is always more interested in Problems than Theorems, one half of this work will be found to consist of Problems. The solu

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