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PRACTICAL GEOMETRY.

SYLLABUS OF GOVERNMENT

SECOND GRADE ART EXAMINATIONS.

FOR SCHOOLS OF ART, NIGHT CLASSES, AND TRAINING COLLEGES.

The instruments required in this stage will be as required for First Grade Art: viz.,-"A plain scale of inches divided into eighths, pair of dividers, pair of pencil compasses, and two set squares, in addition to the usual stationery; a drawing board, and T square," with the addition of an inking pen to the compasses, a drawing pen for lines, a semicircular protractor, and a set of scales on a six-inch rule; or else (instead of the semicircular protractor and separate scales) a rectangular protractor with scales upon it.

The intention is that the instruction for this stage should embrace the rational construction of the ordinary problems of plane geometrical drawing, including a knowledge of the practical geometry of the straight line, circle, and tangent, the direct application of proportion, the inscription and circumscription of rectilinear figures, and some elementary constructions of the ellipse.

The first notions of solidity should be taught at this stage. Some of the simple solid bodies,-cube, pyramid, prism, cylinder, cone, and sphere, should be explained, as well as the simple idea of projection (plan and elevation) and of section.

Problems will be set in the elementary constructions necessary to geometrical pattern-drawing and simple geometrical tracery, the constructions for a circle passing through three points or touching three lines; the construction of tangents to two circles, the simple cases of inscription and circumscription, the reduction and enlargement of figures, the construction of irregular polygons when the angles and sides are given, the use of plain scales and of the scale of chords, the construction of regular polygons. (In this stage a general method for the construction of polygons will be considered sufficient.) In solid geometry, simple problems will be given on the plan, elevation, and section of the common solids, and the projection of plane figures.

FOR

SECOND GRADE ART PUPILS

AND

PRIVATE SCHOOLS.

BY

THOS. NEWTON ANDREWS, F.S.Sc. (LONDON),

First Prizeman and Silver Medalist-

City and Guilds of London Institute, 1880, and

Certificated Science and Art Teacher-

Science and Art Department.

HEAD MASTER CHARLES SCIENCE AND ART SCHOOL, PLYMOUTH.

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PREFACE.

THE following pages contain a Course of Lessons that I have used with great success since the year 1864, not only in my Art Classes, but also in those of Practical Plane and Solid Geometry (Science Subject I.), as an introductory course for that subject.

My aim has been to make this work as practical as possible by the introduction of methods used by workmen, and with that object I have drawn the diagrams larger than is usually the case in similar works on Geometry.

In the second part of the book I have endeavoured to give the pupil a thorough knowledge of the "Projection of Simple Solids," a subject which similar books seem to treat as of secondary importance.

THOMAS NEWTON ANDREWS.

CHARLES SCHOOL, PLYMOUTH.

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