Descriptive Geometry a Treatise From a Mathematical Standpoint Together With a

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Descriptive Geometry a Treatise From a Mathematical Standpoint Together With a
Victor T Victor Tyson Wilson
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99. THEOREM XL A plane which contains two consecutive rectilinear elements of a single curved surface will be tangent to the surface throughout these elements, * and conversely, if a plane is tangent to a single curved surface, it will contain at least two consecutive rectilinear elements of the surface.
Proof: For, if through any point of one element, a secant plane is passed, it will cut a curve from the surface having consecutive points common to both ele- ments. A line connecting these poin
...ts will (by Sec. 93) lie in the plane of the curve of the section and (by Sec. 98) in the tangent plane. Hence the given plane will be tangent at the assumed point or all along the element which is the locus of the assumed points.
100. A cylinder is defined as a single curved surface generated by a line which moves so that its successive positions are parallel, and touch a curve. In the most common interpretation, the curve is a plane curve.
* While the words, 'these elements' are used, it is understood that the common conception of ' an element of tangency ' prevails.


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