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Image from page 159 of "Descriptive geometry" (1918)

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Identifier: descriptivegeome00keni Title: Descriptive geometry Year: 1918 (1910s) Authors: Kenison, Ervin Bradley, Harry Cyrus, 1871-1936 Subjects: Geometry, Descriptive Publisher: New York : The Macmillan Company Contributing Library: University of California Libraries Digitizing Sponsor: MSN View Book Page: Book Viewer About This Book: Catalog Entry View All Images: All Images From Book Click here to view book online to see this illustration in context in a browseable online version of this book. Text Appearing Before Image: left; (4) downward, backward, to the left.(See § 49.) The slope of a plane is the same as the slope ofits lines of maximum inclination to H. These lines, if desired,may be found by Problem 16, Cor. 3, § 133. Special Case. The sum of a and ft is 90°. The plane isthen parallel to the ground line, and its profile trace is its edgeview. Hence (Eig. 216), assume any profile plane of projec-tion. Draw two non-par-allel profile traces makingthe given angles with Hand V, and find the corre-sponding H- and F-traces.Only two results are possi-ble, corresponding to thetwo possible slopes : down-ward and forward, anddownward and backward(or upward and backward,upward and forward). Other special cases,which may be solved byinspection, result when(1) either a or ft is 0°, in which case the other angle must be90° (one result) ; (2) either « or ft is 90°, the other angle beinggreater than 0° and less than 90° (two results) ; (3) a = ft = 90°(one result). These cases are left to the student. Text Appearing After Image: Fig. 216. CHAPTER XV OTHER PROBLEMS INVOLVING THE REVOLUTION OFPLANES 138. The Revolution of a Plane about One of Its Traces. Avery useful revolution of a plane is that in which the plane isrevolved about one of its own traces as an axis. For example,the plane Q may be revolved about HQ as an axis until Qcoincides with H. The figure is left for the student to draw.Any points, lines, or figures contained in Q Avill be carried bythis revolution into the coordinate plane., where they willappear in their true sizes and relations. Problem 21. To find the position of a point lying in a plane,when the plane is revolved into H or V about the corresponding trace. Note. Since only one projection of a point lying in a plane can, ingeneral, be assumed, it may be necessary to find the second projection bytbe use of Problem 10 (§133), before attempting to solve the presentX>roblem. Analysis. Suppose point a lying in plane Q, to be revolvedabout IIQ until it lies in //. The figure is left to the Note About Images Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original work.



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