CYLINDER

, a solid having two equal circular ends, and every plane section parallel to the ends a circle equal to them also.

The cylinder may be conceived to be thus generated: Suppose two parallel circles AB and CD, and a right line carried continually round them, always parallel to itself; this line will describe the curve surface of a cylinder, ABDC, of which the two parallel circles AB and CD form the two ends. When the line, or sides is perpendicular to the ends, the cylinder is a right or perpendicular one; otherwise it is oblique.

Or the right cylinder may be conceived to be generated by the rotation of a rectangle about one of its sides. The axis of the cylinder is the line connecting the centres of its two parallel circular ends; and is equal to the altitude of the cylinder when this is a right one, but exceeds the altitude in the oblique cylinder, in the proportion of radius to the sine of the angle of its inclination to the base.

The convex surface of a cylinder is equal to the product of the axis multiplied by the circumference of its base.

The solidity of a cylinder is equal to the area of its base multiplied by its perpendicular altitude.

Cylinders of equal bases and altitudes, are equal.

Cylinders are to each other, as the product of their bases and altitudes. And equal cylinders have their bases reciprocally as their altitudes.

A cylinder is to its inscribed sphere, or spheroid, as 3 to 2 <*> and to its inscribed cone as 3 to 1. |

The oblique plane sections of a cylinder, are ellipses; but all the sections parallel to the ends, are circles.

For the surfaces and solidities of the ungulas, or oblique slices, of a cylinder, see my Mensuration, pa. 218, 2d edition.