Descriptive geometry . vedsurface when it contains one, and only oneelement of that surface. The two lines com-monly determining a tangent plane are the tan-gent element and a tangent to the surface atsome point in this element. If this secondline lies in one of the coordinate planes it willbe a trace of the tangent plane. In Fig. 152 point d is on the surface of acone to which a tangent plane is to be line drawn through point d and the apexof the cone will be the element at which the plane is to be tangent and, therefore, one lineof the tangent plane. If a second line, ck^ bedrawn t
Descriptive geometry . vedsurface when it contains one, and only oneelement of that surface. The two lines com-monly determining a tangent plane are the tan-gent element and a tangent to the surface atsome point in this element. If this secondline lies in one of the coordinate planes it willbe a trace of the tangent plane. In Fig. 152 point d is on the surface of acone to which a tangent plane is to be line drawn through point d and the apexof the cone will be the element at which the plane is to be tangent and, therefore, one lineof the tangent plane. If a second line, ck^ bedrawn through point d, and tangent to anysection of the cone containing this point, itwill be a second line of the tangent traces of these lines will determine ^aSand VS^ the traces of the required tangentplane. If the base of the single-curved sur-face coincides with one of the coordinateplanes, as in Fig. 152, hk can be used forthe tangent line, thus determining the hori-zontal trace directly. 72 TANGENT PLANES 73. 105. One projection of a point on a single-curved surface being given, it is required topass a plane tangent to the surface at the ele-ment containing the given point. Principle. The tangent plane will be de-termined by two intersecting lines, one ofwhich is the element of the surface on whichthe given point lies, and the second is a lineintersecting this element and tangent to thesingle-curved surface, preferably in the planeof the base. Method. 1. Draw the projections of theelement containing the given point. 2. Inthe plane of the base draw a second linetangent to the base at the tangent Determine the plane of these lines. If the plane of the base coincides with oneof the coordinate planes, the tangent line willbe one of the traces of the required tangentplane. Note. In this and the following problemsthe base of the single-curved surface is consid-ered as lying on one of the coordinate planes. 74 DESCRIPTIVE GEOMETRY Construction. Fig. 153. Let the
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