35.

A cone is the solid figure generated by the revolution of a right-angled triangle, about either of the sides containing the right angle.

36.

An ellipsis is the plane figure formed by the section of a cone when cut obliquely through its axis by a plane not meeting the base; as DEFG.

D

E F

37.

A parabola is the plane figure formed by the section of a cone when cut by a plane parallel to the side; as ABC.

B

38.

An hyperbola is the plane figure formed by the section of a cone when cut by a plane parallel to the axis; as DEF.

E

39.

Prisms are solid figures having rectangular planes for their sides, and regular, that is, equilateral and equiangular planes for their ends.

40.

A pyramid has for its sides equal and similar triangles similarly situated, and for its base any equilateral and equiangular plane.

41.

A parallelopipedon is a solid figure contained under six parallelograms, the opposite sides being equal, and all its angles right-angles; as ABCDEFG.

C

B

F

42.

A cube is a parallelopipedon with six equal sides.

43.

A parabolic conoid is the solid generated by the revolution of a semi-parabola about its axis; as ABCD.

A hyperbolic conoid is the solid generated by the rotation of a semi-hyperbola about its axis; as EFGH.

A parabolic spindle is the solid generated by the revolution of a semi-parabola about its ordinate or base; as MNOP.

M

N

P

46.

A spheroid is the solid generated by the rotation of a semi-ellipsis, about either diameter. In the following figure the rotation is about the transverse diameter.

Before we treat of the mensuration of surfaces and solids, it will be useful to give a few problems in Practical Geometry; and these we shall divide into Five Sections.

PRACTICAL GEOMETRY.

SECTION 1.

OF DRAWING AND DIVIDING LINES.

PROBLEM I.

To erect a perpendicular from a given point in a given straight line.

Let AB be the given line, and C the given point in

it, from which a perpendicular is to be erected.