Page images
PDF
EPUB

A

THE

ELEMENTS OF GEOMETRY.

REVISED EDITION.

BY

WEBSTER WELLS, S.B.,

PROFESSOR OF MATHEMATICS IN THE MASSACHUSETTS
INSTITUTE OF TECHNOLOGY.

BOSTON, U.S.A.

D. C. HEATH & CO., PUBLISHERS
1899

QA
453

1899

COPYRIGHT, 1894,

BY WEBSTER WELLS.

TYPOGRAPHY BY C. J. PETERS & SON.
BERWICK & SMITHI, PRINTERS,
BOSTON, U.S.A.

6-24180

1111591-210

PREFACE.

IN the revision of the author's work on PLANE AND SOLID GEOMETRY, many important improvements have been effected.

With a class just commencing the study of Geometry, too much emphasis cannot be laid on the form in which an oral or written demonstration should be presented.

The beginner requires a certain amount of practice before he can acquire the art of putting a proof in a clear and logical form.

To give this drill, the author has, through the whole of Book I., placed directly after each step in the proof the full statement of the reason, in smaller type, enclosed in brackets.

But too much assistance of this nature is open to serious objections, as it has a tendency to make the pupil a mere automaton, and confirm him in indolent habits of study. It has seemed advisable, therefore, in Books II. to V., inclusive, to give only the number of the section where the required authority is to be found.

The above plan has been submitted to a large number of representative teachers, and in nearly every case has met with the most unqualified approval.

In the Solid Geometry, references are given in full in the first sixteen propositions of Book VI., and by section numbers only through the remainder of the work. On pages ix, x, and xi of the Introduction will be found a few propositions put in a form which is recommended for blackboard work.

Particular attention has been given to the arrangement of the propositions and corollaries in a form for convenient reference. The statement of the corollary has in every case been printed in italics; and in nearly every proposition in which more than one truth is stated, the various parts are distinguished by numerals. Thus, when reference is made to a preceding section, the pupil will readily find the precise statement which is to be quoted.

The exercises are upwards of eight hundred in number, and have been selected with great care. In certain exercises which might otherwise present difficulties to the pupil, reference is made to a previous section or exercise which may be used in the solution. The exercises in each Book are numbered consecutively.

In the Plane Geometry, the new exercises are largely numerical; but in the Solid Geometry, there is a considerable increase in the number of both numerical exercises and original theorems. A number of the exercises are in the nature of alternative methods of proof for preceding propositions.

In the Appendix to the Plane Geometry will be found an additional set of exercises of somewhat greater difficulty than those previously given.

The pages have been arranged in such a way as to avoid the necessity, while reading a proof, of turning the page for reference to the figure.

The attention of teachers is specially invited to the explanations given in the Introduction, commencing on page vii.

The author desires to express his thanks to the many teachers, in all parts of the country, who have furnished him with valuable suggestions and criticisms.

WEBSTER WELLS.

MASSACHUSETTS INSTITUTE OF TECHNOLOGY,

1894.

« PreviousContinue »