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CLASS LESSONS ON EUCLID

PART 1.

CONTAINING THE

FIRST TWO BOOKS OF THE ELEMENTS

BY

MARIANNE NOPS

ASSOCIATE AND LATE SCHOLAR OF QUEEN'S COLLEGE

MEMBER OF THE UNIVERSITY OF LONDON

LONDON
KEGAN PAUL, TRENCH, & CO., 1 PATERNOSTER SQUARE

1882

183. q.141.

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PREFACE.

The aim of this little book is to make the utmost use of geometry as a mental training, by leading the beginner to enter into the spirit of Euclid's methods, often rendered obscure by his formal language, and by affording as much assistance as possible in applying them. The difficulty most frequently felt by learners is the application of knowledge acquired to original work, as in the solution of problems. The failure in this important respect is continually adverted to by examiners in their reports and by writers on the subject. May not one of the chief reasons of this failure be found in the mode in which the science is presented to the beginner? In a treatise on algebra or arithmetic, the reasons for the various operations are carefully explained; the student is not expected to infer them from a collection of algebraical or arithmetical examples. On the contrary, in a treatise on geometry, the analytical processes by which the constructions are arrived at are invariably suppressed; the beginner is naturally unable to supply them ; consequently he has no principles to guide him in attempting riders, fails in them again and again, and, in too many cases, conceives a distaste for a most valuable and what may be made a most interesting study.

In the following lessons an attempt has been made to

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