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;

to project, whose axis is inclined at angle of 45° to the hori-
zontal plane, but parallel to the vertical,

237

...

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

245

...

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; 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,

...

255

256

258

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200

; 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°,

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; to find its elevation, plan being given,

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; to construct the projections of, having a face and one of its
edges inclined at given angles,

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; to find the projection of, when one of its diagonals is perpen-
dicular to the plane of projection,

; to find section of,

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Cylinder; to find the plan of, elevation being given,

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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,

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

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PAGE

Cylinder section; to draw the curve of penetration of two, whose
diameters are equal, and whose axes are at right angles to
each other,

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261

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; 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,

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262

243

222

194

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; to find the plan of, its elevation being given parallel to the two
planes of projection,

195

; to find the plan of, its elevation being given parallel to the
horizontal plane, but inclined to the vertical plane of pro-
jection,

196

...

to find the plan of, inclined to both planes of projection, its
elevation being given,

196

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; given, projections of, to find the angles which it makes with
the planes of projection,

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-, 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

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

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; 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,

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Parallel planes; traces of being given, to find the distance between

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Plane; to draw, so that it makes a given angle with a given plane,

and passes through a line in the first,

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; 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,

plane,

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Prism, triangular; to project the section of, when cut by an oblique

PAGE

,

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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°,

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202

203

204

230

232

206

252

...

; to construct the sectional plan and elevation of, when standing
on its base on the horizontal 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,

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216

239

; 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
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.

PHILIPS'

EDUCATIONAL CATALOGUE.

ATLASES.

Philips' Comprehensive School Atlas

Of Ancient and Modern Geography, comprising Thirty-seven
Modern and Seven Ancient Maps, constructed from the latest
and best authorities. The Maps carefully printed in colors.
Edited by W. Hughes, F.R.G.S. Accompanied by a Con-
sulting Index, carefully compiled. New and improved edition.
Imperial 8vo., strongly half-bound, 10s. 6d.

Philips' Student's Atlas,

Comprising Thirty-eight authentic Maps of the Principal Countries
of the World. The Maps carefully printed in colors. Edited
by William Hughes, F.R.G.S. With a copious Consulting
Index. Imperial 8vo., strongly bound in cloth, 7s. 6d.

Philips Select School Atlas,

Comprising Twenty-four authentic Maps of the Principal Countries
of the World. The Maps carefully printed in colors. Edited
by William Hughes, F.R. G. S. With a copious Consulting
Index. Imperial 8vo., new and cheaper edition, strongly
bound in cloth, 5s.

Philips' Introductory School Atlas,

Comprising Eighteen Maps of the Principal Countries of the World,
clearly engraved, and carefully printed in colors. Edited by
W. Hughes, F.R.G.S. Accompanied by a Consulting Index.
New and cheaper edition. Imperial 8vo., bound in cloth,
3s. 6d.

Philips' Young Student's Atlas,

Comprising Thirty-six Maps of the Principal Countries of the
World, printed in colors. Edited by W. Hughes, F.R. G.S.
Imperial 4to., bound in cloth, 3s. 6d.

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