This section is from the book "The Engineer's And Mechanic's Encyclopaedia", by Luke Hebert. Also available from Amazon: Engineer's And Mechanic's Encyclopaedia.

**Plane** in Geometry and Mechanics, a perfectly flat surface in whatever position, as horizontal plane, vertical plane, inclined plane. If a sphere be cut by a plane, the section will be a circle. If a prism or cylinder be cut by a plane, either through or parallel to its axis, the section will be a parallelogram; and if either of these be cut by a plane parallel to its base, the section will be similar to that base. Also, if a cylinder be cut obliquely by a plane passing through its opposite sides, the section will be an oval or ellipse. If a pyramid or cone be cut by a plane passing through the axis, the section will be a triangle; but if they be cut parallel to the base, the section will be similar to the base. If a cone be cut by a plane parallel to its side, the section will be a parabola; if it be cut obliquely, so that the plane does not pass through either the base or the opposite cone, the section is an ellipse; if it be cut by a plane which passes through the base and the opposite cone, but does not pass through the vertex, the section is a hyperbola; and, lastly, if it be cut by a plane, either parallel to the base, or in sub-contrary position to it, the section is a circle.

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