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INDEX TO PROBLEMS IN SOLID GEOMETRY.

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Angle; to determine between two planes,
Cone; to find its plan, elevation being given, ...
- ; to find its elevation, plan being given,
— ; to project, whose axis is inclined at angle of 45° to the hori-
zontal plane, but parallel to the vertical,

...
--; to draw the section of, when cut by a plane parallel to its

base, ...
- ; to draw the sectional elevation of, when cut by a vertical

plane, ...
- ; to find the projection of, standing on its base, when the section

plane is perpendicular to the vertical plane, and making an
angle with the horizontal plane ; also a projection of the

cone, showing the true form of the section, ... ...
; to find the projection of, standing on its base, when the section

plane is parallel to one side of the cone, and perpendicular to

the vertical plane, also the true form of the section,
Cube; to find its plan, elevation being given, ... ...
— ; to find its plan, elevation being given, one face inclined to

the ground at an angle of 60°, another face at an angle

of 30°,
—; to find its elevation, plan being given,
—; to construct the projections of, having a face and one of its

edges inclined at given angles, ...
- ; to find the projection of, when one of its diagonals is perpen-

dicular to the plane of projection,
- ; to find section of,
Cylinder; to find the plan of, elevation being given,
— ; to find the elevation of, plan being given, ...
- section; to draw, when lying on the ground with its ends

parallel to the vertical plane, and at right angles to the
horizontal plane ; the plane of section being parallel to the

axis of the cylinder, ... ...
— ; to draw the curve of penetration of two, whose axes are at
right angles to each other,

other, ... ... ... ...

200

201

227

228

247

207
208

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Cylinder section; to draw the curve of penetration of two, whose

diameters are equal, and whose axes are at right angles to

each other, ...
— ; to draw the curve of penetration of two, whose diameters are

equal, and whose axes are at right angles to each other, one

of the cylinders being inclined to the vertical plane, ...
Dodecahedron; to draw the plan and elevation of, when one edge

of its base is inclined at an angle of 30° to the ground

line, ...
Equilateral triangle; to draw the plan of, two of its sides inclined

at 60° and 30° to the horizon, and to determine the inclina-

tion of the plane in which it is situated, ... ...
Line; to draw its plan, elevation given at right angles to the vertical

plane,
- ; to find the plan of, its elevation being given parallel to the two

planes of projection, ...
--; to find the play of, its elevation being given parallel to the

horizontal plane, bu't inclined to the vertical plane of pro-
jection,

... ... ...
- ; to find the plan of, inclined to both planes of projection, its

elevation being given, ... ... ... ... ...
--; to find elevation of, its plan being given, ...

; traces of, given, to find its projections, ...

; given, projections, to find its length, ...
-----; given, projections of, to find the angles which it makes with

the planes of projection, ...
- any; to determine the plan and elevation of, inclined at 60° to

the horizontal plane, and 20° to the vertical plane,
Octahedron; to construct the projections of, when its axis is

vertical, ... ...
— ; to construct the projections of, when it lies on its face on the
horizontal plane,

... ... ... ...
- ; to construct the plan and elevation of, when resting on one of

its faces, and when one edge of this face makes an angle of

15° with the vertical plane, ...
Parallel planes ; traces of being given, to find the distance between
them, ... ... ... ...

"
- ; to determine, by traces, and given distan'oe,
Pipe, hollow; to draw section of, ... ... ...
Plane ; to draw, so that it makes a given angle with a given plane,

and passes through a line in the first, ... ...
--; to determine by its traces, containing three given points, ...
Planes, two; traces of, being given, to find the projections of their

common intersection, ... ... ...
Point; to find the plan of, elevation being given, ...
Prism, triangular; to project the section of, when cut by an oblique
plane, ...

... ... ... ...

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Prism, square; to draw the plan of, its elevation being given, ...
- , pentagonal; to draw the plan of, its elevation being given, ...
- , hexagonal; to find the elevation of, its plan being given, ...
; to draw the plan and elevation of, which has its axis inclined

40° to the paper, and one face parallel to the vertical plane,
- ; to find the plan and elevation of, the height of which is 30',

and length of one side 10', on a scale of 20' to the inch; the

front face being parallel to the vertical plane, ... ...
Pyramid, square; to find the elevation of, its plan being given, ...
— ; to find the vertical projection of the section, parallel to the

section plane, the trace of the plane, which is vertical, being
at right angles to the plan of one of the lateral edges of the

pyramid,
- ; to draw the horizontal projection of the section of, when cut

by a plane parallel to its base, the plane of the base of the

pyramid being inclined at 40°, ...
- , pentagonal; to draw the plan of, when one edge of its base is

inclined at an angle of 45°, ...
-- ; to construct the sectional plan and elevation of, when standing

on its base on the borizontal plane,
. — ; to construct the sectional elevation and plan of, when standing

on its base on the horizontal plane,

hexagonal; to find the plan of, its elevation being given, ...
- ; to determine the plan of, when lying on one of its faces on the

horizontal plane,
- ; to project, when its axis is inclined at an angle of 50° to the

horizontal plane, but parallel to the vertical, ... ...
Rectangular surface; to find the plan of the end elevation of, when

given parallel to the horizontal plane, ... ... ...
Solid, any; the projections of, being given, to determine other pro-

jections from them,
Sphere; to find both plan and elevation of,
Square; to draw the plan of, when its surface is inclined 42°, and

one of its sides is horizontal, "
Straight lines, two; to determine the angle contained by, given by

contained by given by
their projections,
Tetrahedron; to construct the projections of, ...
; to construct the sectional elevation of, upon a vertical plane

parallel to the section plane, the trace of which is at right

angles to one of the lateral edges of the solid, ... ...
Traces of plane ; being given, to find the angles which it makes

with the planes of projection, ...

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PRINTED BY G. PHILIP AND SON, LIVERPOOL

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