The essentials of descriptive geometry . are usually givenwhich determine which point is intended, otherwise two solutionsto such problems are possible. In Fig. 93 a similar problem is shown. In this case the planview of the point is assumed and its elevation located at one ofthe points x or y, depending on which side of the cone the pointis to be taken. loi. Proposition 26. Given the axis of a cone, the size andlocation of its right section to find the plan and elevation of thecone. • Discussion. If the cone be revolved parallel to a plane ofprojection, the given right section may be drawn in
The essentials of descriptive geometry . are usually givenwhich determine which point is intended, otherwise two solutionsto such problems are possible. In Fig. 93 a similar problem is shown. In this case the planview of the point is assumed and its elevation located at one ofthe points x or y, depending on which side of the cone the pointis to be taken. loi. Proposition 26. Given the axis of a cone, the size andlocation of its right section to find the plan and elevation of thecone. • Discussion. If the cone be revolved parallel to a plane ofprojection, the given right section may be drawn in its givenlocation. If, then, elements be drawn through this section from CONICAL SURFACES 117 the apex the base of the cone in H or V may be found by findingwhere the elements pierce H or V. Construction. In Fig. 94, OQ is the given axis, and P thegiven point on this axis where it pierces the given right right section in this construction is taken as a circle whosediameter is equal to xy- Revolve OQ parallel to V; in this. Fig. 94. 9 9 position it is projected at oq^ and oq and P falls at p^ and xy equal to the given diameter of the right section per-pendicular to oq; this Hne will be the elevation of the right sec-tion, since OQ is parallel to V, and the ellipse x^y^ will be the planview. Now through x and y draw the elements projectedon V at qd and qa, and on H at q^d^ and q^a^. Theseelements pierce H at a^ and d^, which points will be the ends ofthe major axis of the base in H. To find the minor axis of the Il8 ESSENTIALS OF DESCRIPTIVE GEOMETRY base bisect a^d/ by the line whose direction is b^c^. The lengthof the line is as yet unknown but whatever this may be, since itis perpendicular to V, the line will be projected on V at the pointbc. Join bc with q; this will be the elevation of the twoelements which pierce H at the ends of the minor axis. Nowthese elements cut the curve of right section in its revolvedposition at M and N, and if through these po
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Keywords: ., bookcentury1900, bookdecade1910, bookidcu3192400462, bookyear1915
