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MATHEMATICAL EXERCISES.

By the same Author.

ELEMENTARY GEOMETRICAL DRAWING PART I. including Practical Plane Geometry, the Construction of Scales, the use of the Sector, the Marquois Scales, and the Protractor. Second Edition, in post 8vo. with Plates, price 3s. 6d.

ELEMENTARY GEOMETRICAL DRAWING PART II. the Elements of Descriptive Geometry, with its Application to Horizontal and Isometric Projection, and the Projection of Solids and Shadows. Price 6s. 6d.

'THE Council of Military Education in their official reports denounce the knowledge of geometrical drawing exhibited by the candidates for admission to Woolwich as being vague and unsatisfactory in its na ture and extent, as desultory, and ill-calculated to enable them, after joining the academy, to proceed at once with their Artillery and Engineer studies; and, say they, this state of affairs must arise from the absence of any English work treating of the subject of geometrical drawing in anything like a practical manner. This want Mr. WINTER has now supplied. The first part of his treatise dealt with the plane geometry; the second completes his work by embracing the practical geometry of planes and solids, and its application to horizontal and isometric projection, and the projection of solids and shadows. The system adopted

by the Author avoids the error of considering that sufficient instruction is afforded in such matters, provided the pupil learns how to do a thing, however ignorant he may be of the principles of the theory on which his methods are based, and of the properties and reasoning which prove those methods to be right. In publishing a work which exhibits clearly the leading principles of both plane and solid geometry, and the manner in which those principles are applied to the solution of practical questions, and especially those involved in the prescribed form of military education as at present laid down, Mr. WINTER has conferred a boon on the scholastic profession in general, and on military students in particular; and has, moreover, contributed a valuable ad dition to English educational literature.' CRITIC.

London: LONGMAN and CO.

MATHEMATICAL EXERCISES:

COMPRISING 3,500 EXAMPLES IN THE VARIOUS

BRANCHES OF PURE MATHEMATICS, STATICS, DYNAMICS, AND
HYDROSTATICS, TAKEN FROM MILITARY, CIVIL SERVICE, AND OTHER
EXAMINATION PAPERS; COLLECTED AND ARRANGED IN SETS, FOR

THE USE OF STUDENTS PREPARING FOR EXAMINATION.

WITH TABLES, FORMULE, ANSWERS, AND REFERENCES.

BY

SAMUEL H. WINTER, F.R.A.S.

MILITARY TUTOR.

LONDON:

LONGMAN, GREEN, LONGMAN, ROBERTS, & GREEN.

1864.

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PREFACE.

THE sources from which the following Exercises have been taken are sufficiently indicated by the Table of Contents. This collection differs, in two respects, from any with which the author is acquainted; first, in the arrangement of the questions in such a manner, that each paper, after the first twenty-one, generally contains examples in various subjects; secondly, in the introduction of 'book-work.' It is hoped that both of these changes will increase the usefulness of the work to students about to undergo examinations in which they will encounter similar questions arranged in the same way.

WOOLWICH COMMON: August 1864.

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