File:Descriptive geometry (1909) (14595758850).jpg

Identifier: descriptivegeome00anth (find matches)
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