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BY JOHN WILEY & SONS.
ELECTROTYPED AND PRINTED
BY RAND, AVERY, AND COMPANY,
J. J. SYLVESTER,
A.M., CAM.; F.R.S., L. AND E.; CORRESPONDING MEMBER INSTITUTE OF FRANCE; MEMBER
ACADEMY OF SCIENCES IN BERLIN, GÖTTINGEN, NAPLES, MILAN, ST. PETERSBURG,
ETC.; LL.D., UNIV. OF DUBLIN, AND U. OF E.; D.C.L., OXFORD; HON.
FELLOW OF ST. JOHN'S COL., ÇAM.; SAVILIAN PROFESSOR
OF GEOMETRY IN THE UNIVERSITY OF OXFORD;
In Grateful Remembrance
OF BENEFITS CONFERRED THROUGHOUT TWO
In America the geometries most in vogue at present are vitiated by the immediate assumption and misuse of that subtile term “ direction;" and teachers who know something of the Non-Euclidian, or even the modern synthetic geometries, are seeing the evils of this superficial “directional ” method.
Moreover the attempt, in these books, to take away by definition from the familiar word “distance" its abstract character and connection with length-units, only confuses the ordinary student. A reference to the article Measurement in the "Encyclopædia Britannica” will show that around the word “distance” centers the most abstruse advance in pure science and philosophy. An elementary geometry has no need of the words direction and distance.
The present work, composed with special reference to use in teaching, yet strives to present the Elements of Geometry in a way so absolutely logical and compact, that they may be ready as rock-foundation for more advanced study.
Besides the acquirement of facts, there properly belongs to Geometry an educational value beyond any other elementary subject
In it the mind first finds logic a practical instrument of real power.
The method published in my Mensuration for the treatment of solid angles, with my words steregon and steradian, having been adopted by such eminent authorities, may I venture to recommend the use of the word sect suggested in the same volume ?
From 1877 I regularly gave my classes the method of Book IX. In 1883 my pupil, H. B. Fine, at my suggestion, wrote out a Syllabus of Spherical Geometry on the lines of my teaching, which I have followed in Book IX.
The figures, which I think give this geometry a special advantage, owe all their beauty to my colleague, Professor A. V. Lane, who has given them the benefit of his artistic skill and mastery of graphics.
The whole work is greatly indebted to my pupil and friend, Dr. F. A. C. Perrine. We have striven after accuracy. Any corrections or suggestions relating to the book will be thankfully received.
GEORGE BRUCE HALSTED.
2004 Matilde Street,