Cylindrical surface. Directrix and generatrices of a cylindrical surface.
Cylinder. Right cylinder. Oblique cylinder. Circular cylinder. Round
cylinder. Prism as a particular case of a cylinder. Cylindrical sections.
Cylindrical surface is a surface, formed by a motion of a straight line (AB, Fig.82 ), which saves the same direction and intersects with
the given line MN ( or a curve ). A line MN is called a directrix. Straight lines, corresponding to different positions of the straight line AB at its
motion ( A’B’, A”B” etc. ), are called generatrices of cylindrical surface.
Cylinder. A body, limited by cylindrical surface (with a closed directrix) and two parallel planes, is called a cylinder ( Fig.83 ).
Parts of these planes ( ABCDEFG and abcdefg ) are called bases of a cylinder. A distance between the bases ( KM, Fig.83 ) is a height
of a cylinder. A cylinder is right, if its generatrices are perpendicular to its base; otherwise, a cylinder is oblique. A cylinder is circular, if its base is a circle. If a cylinder is simultaneously both right
and circular, it is called a round cylinder. A prism is a particular shape of a cylinder ( why ? ).
Cylindrical sections of a circular cylinder lateral surface ( Fig.84 ). The sections, parallel to a base, are circles
of the same radius. The sections, parallel to a generatrix of cylinder, are pairs of parallel straight lines (AB || CD). The sections, which
are not parallel both to bases and to generatrix, are ellipses.