AN

ELEMENTARY COURSE

OF

M A T H E M A T I CS

PREPARED FOR THE USE OF THE

ROYAL MILITARY ACADEMY.

BY ORDER OF THE MASTER-GENERAL AND BOARD OF ORDNANCE.

Topie

VOLUME II.

CONTAINING

THE GEOMETRY.

By T. S. DAVIES, Esq., F.R.S., L. & E. ;

But in consequence of the Death of Mr. Davies, the Volume has been Printed under

the direction of, and the Chapter on Conic SECTIONS supplied

BY STEPHEN FENWICK, Esq.

LONDON:

PRINTED FOR HER MAJESTY'S STATIONERY OFFICE:

PUBLISHED BY

JOHN WEALE, 59 HIGH HOLBORN.

1853.

14225

Math 358153

Trans.rred from

The Lawronco Scientific Schoo',

.

GEOMETRY OF PLANES AND SOLIDS.

Preliminary Note .

Definitions

Parallel Lines and Planes

Perpendicularity

Oblique Line and Plane

Trihedral and Polyhedral Angles

Equality and Symmetry of Trihedral Angles

Volumes of Solids

Cone, Cylinder, and Sphere

Spherical Surface .

142

158

174

181

186

193

205

209

PROJECTION.

Definitions and First Principles

Orthographic Projection

Exercises on Orthographic Projection

TOPOGRAPHIC PROJECTION, OR METHOD OF CONTOURS.

General Principles

Graduation of Horizontally Projected Lines

Planes

339

344

349

THE

ELEMENTS OF EUCLID.

BOOK I.

DEFINITIONS. 1. A Point is that which hath no parts, or which hath no magnitude. 2. A line is length without breadth. 3. The extremities of a line are points.

4. A straight line is that which lies evenly between its extreme points.

5. A superficies is that which hath only length and breadth. 6. The extremities of a superficies are lines.

7. A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies.

8. A plane angle is the inclination of two lines to one another in a plane, which meet together, but are not in the same direction.

9. A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.

When several angles are at one point B, any one of them is expressed by three letters, of which the letter chat is at the vertex of the angle, that is, at the point in which the straight lines that contain the angle meet one another, is put between the other

two letters, and one of these two is somewhere upon one of those straight lines, and the other upon the other line: thus the angle which is contained by the straight lines AB, CB, is named the angle ABC, or CBA ; that which is contained by AB, DB, is named the angle ABD, or DBA ; and that which is contained by DB, CB, is called the angle DBC, or CBD; but, if there be only one angle at a point, it may be expressed by a letter placed at that point: as the angle at E.

10. When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.

B

:

B

VOL II.