PRACTICAL

GEOMETRY AND GRAPHICS

Works by the same Authors uniform with this Volume.

Containing 520 pages, with over 320 illustrations. Crown 8vo, cloth, price 35. net.

PRACTICAL

MATHEMATICS.

Comprising a complete course for Technical Students and Practical Men, and particularly adapted to the requirements of the Syllabus of the Board of Education's "Lower Stage " Examination.

PRACTICAL MATHEMATICS AND
GEOMETRY.

A complete and carefully graded course of instruction specially arranged for the use of classes in which Practical Mathematics and Practical Geometry are taken concurrently.

IN THREE PARTS.

Part 1.—Preliminary Course. Containing 230 pages, with 138 illustrations. IS. 6d. net.

PART 2.-ELEMENTARY COURSE. Containing 230 pages, with 130 illustrations. IS. 6d. net.

3s. net.

Parts 1 and 2 may be had bound together in one vol. PART 3.-ADVANCED COUrse. Containing 320 pages, with 300 illustrations. 3s. net.

B. T. BATSFORD, Publisher, 94, High Holborn, London.

GEOMETRY

& GRAPHICS

A TEXT-BOOK FOR STUDENTS IN TECHNICAL
AND TRADE SCHOOLS, EVENING CLASSES, AND
FOR ENGINEERS, ARTISANS, DRAUGHTSMEN,
ARCHITECTS, BUILDERS, SURVEYORS, &c.,

Specially arranged to meet the revised requirements
of the Board of Education and covering the whole
of the work comprised in the Syllabus of the
Board's "Lower Stage" Examination

BY

EDWARD L. BATES

LECTURER ON GEOMETRY AT THE L.C.C. SCHOOL OF BUILDING,
BRIXTON, LONDON

AND

FREDERICK CHARLESWORTH

WHITWORTH

EXHIBITIONER

LECTURER ON PRACTICAL MATHEMATICS AND GEOMETRY AT THE
SOUTH-WESTERN POLYTECHNIC INSTITUTE, LONDON

Containing a Large Number of Practical Exercises,
with Answers, and about 600 Illustrations

LONDON

B. T. BATSFORD 94 HIGH HOLBORN
1912

PREFACE.

THE Authors have endeavoured, in this book, to present in a direct and simple manner the essentials of Practical Geometry and Graphics, and, as far as space has permitted, to apply the principles to the solution of problems constantly met with in practical work.

The ground covered is such as to comprise a two or three years' course of instruction according to the capability of the student.

In designing the book, two objects have been kept in view: (1) to meet the requirements of engineers, architects, surveyors, draughtsmen, and artisans engaged in the constructive arts as a work to guide them in the study of such Geometry and Graphics as they will require in following their profession or craft; and (2) to meet the requirements of those students in technical or other schools who desire to prepare for such examinations as the Board of Education "Lower Stage" examination in Practical Geometry and Graphics.

The course outlined in the syllabus for the "Lower Stage" examination of the Board of Education in Practical Geometry and Graphics comprises nearly all that is necessary for the majority of those engaged in Engineering and Building; hence, in this book, a large number of examples and exercises have been selected from Board of Education examination papers. Many of these examples will be found not only interesting tests of the knowledge possessed by the student, but excellent examples of the practical application of geometrical principles. It will be found that the book covers fully the syllabus above referred to, and in some sections is in excess of the requirements of students preparing for this examination. The note facing p. 1 of the text should therefore be consulted by such students as to which articles they may omit as regards the examination.

The book is divided into three sections: (1) Plane Geometry;