Descriptive geometry for students in engineering science and architecture; a carefully graded course of instruction . vertically on the , conse- 82 TANGENT PLANES TO CONES AND CYLINDERS 83 quently, the circle, which is the circumference of its base, is the of its cur\^edsurface. A plane, tangent to this cone, will therefore have its H T. tangent tothis circular and this is shown at ST. As the apex aa is in the tangentplane, a horizontal line may be drawn through it, lying in the tangent will have its plan parallel to ST, and its elevation will give its at , t
Descriptive geometry for students in engineering science and architecture; a carefully graded course of instruction . vertically on the , conse- 82 TANGENT PLANES TO CONES AND CYLINDERS 83 quently, the circle, which is the circumference of its base, is the of its cur\^edsurface. A plane, tangent to this cone, will therefore have its H T. tangent tothis circular and this is shown at ST. As the apex aa is in the tangentplane, a horizontal line may be drawn through it, lying in the tangent will have its plan parallel to ST, and its elevation will give its at , the of the plane, may then be drawn. It will be realized next, that, as all the generators of the vertical cone meetthe at the same incUnation, therefore the generator whose plan is ab. is atthe same inclination as the generator whose elevation is ac, and whose inclinationis indicated by an arrow-headed arc in the figure; and, since the plane is at thesame inclination as a line in it perpendicular to its trace, and AB is perpendicularto the trace ST. the tangent plane RST is at the angle indicated at Fig. 86. The converse of this problem is specially useful. For instance, if it berequired to fmd the traces of a plane of given inclination to the having in a given direction, it is only necessary to set up a right circular cone whosegenerators are at the given inclination for the required plane, and then make of the plane tangent to the circular trace, the base of the cone is the proceed as before to find the of the plane. In Fig. 86 the of a plane is given at RS. Suppose the plane, whose RS, to be inclined at 6o° to the ,, and let it be required to find its , because any point in this is in the plane and may be taken as theapex of a right circular vertical cone to which the plane is tangent, from any suchpoint A draw the line ac in the at 6o° to the The circumferenceof the circle drawn, with
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Keywords: ., bookcentury1900, bookdecade1910, bookpublisheretcetc, bookyear191
