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Identifier: descriptivegeome00anth Title: Descriptive geometry Year: 1909 (1900s) Authors: Anthony, Gardner Chace, 1856- [from old catalog] Ashley, George Francis, [from old catalog] joint author Subjects: Geometry, Descriptive Publisher: Boston, D. C. Heath & co. Contributing Library: The Library of Congress Digitizing Sponsor: The Library of Congress 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: and the surface generated will be aright helicoid. This type is illustrated by thesquare-threaded screw (Fig. 146, page 69). 154. If the generatrix does not intersectthe axis, as in the preceding cases, a moregeneral type will be generated, as shown inFig. 193. In this case the generatrix is gov-erned by two helical directrices and a conedirector, the generatrix being tangent to thecylinder on which the inner helix is described. 155. Hyperboloid of Revolution of one Nappe.This is a surface of revolution which may begenerated by the revolution of an hyperbolaabout its conjugate axis, as illustrated in Fig.194. It is also a warped surface in that itmay be generated by the revolution of a rightline about an axis which it does not intersect,and to which it is not parallel. Furthermore,it will be shown that the rectilinear generatrixmay be governed by three rectilinear direc-trices, by three curvilinear directrices, or bytwo curvilinear directrices and a cone director. WARPED HELICOIDS 119 Text Appearing After Image: Fig. 191 Fig. 192. Fig. 193, 120 DESCRIPTIVE GEOMETRY In Fig. 194 conceive the generatrix cd asmaking the constant angle c^cth with a hori-zontal plane, and revolving about a verticalaxis through o. Point e will describe the circleof the upper base cgl, point d will describe thecircle of the lower base dmf^ and the point e,the nearest to the axis, will describe the circleelan, which is called the circle of the gorge.All other points of the generatrix will simi-larly describe circles, and by drawing theseparallels of the surface, the meridian line willbe determined, and is an hyperbola. Thuspoint s, in the generatrix cd^ will be in theposition t when it lies in the principal me-ridian plane, and f will be a point in the ver-tical contour, which is an hyperbola. 156. Through any point of the surface todraw an element. If one projection of thepoint be given, draw a parallel of the surfacethrough this point to determine the other pro-jection. Through the horizontal projectionof this point 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.