Descriptive Geometry a Treatise From a Mathematical Standpoint Together With a
Descriptive Geometry a Treatise From a Mathematical Standpoint Together With a
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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.
What to read after Descriptive Geometry a Treatise From a Mathematical Standpoint Together With a?
You can find similar books in the "Read Also" column, or choose other free books by Victor T Victor Tyson Wilson to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
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.
What to read after Descriptive Geometry a Treatise From a Mathematical Standpoint Together With a?
You can find similar books in the "Read Also" column, or choose other free books by Victor T Victor Tyson Wilson to read onlineMoreLess
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