File:A manual of elementary geometrical drawing, involving three dimensions. Designed for use in high schools, academies, engineering schools, etc. - and for the self-instruction of inventors,artizans, (14579179169).jpg

Identifier: manualofelementa01warr (find matches)
Title: A manual of elementary geometrical drawing, involving three dimensions. Designed for use in high schools, academies, engineering schools, etc. : and for the self-instruction of inventors,artizans, etc. ... In five divisions ..
Year: 1867 (1860s)
Authors: Warren, S. Edward (Samuel Edward), 1831-1909
Subjects: Geometrical drawing Mechanical drawing
Publisher: New York : J. Wiley and son
Contributing Library: The Library of Congress
Digitizing Sponsor: The Library of Congress

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III. A., Fig. 1. Let the cylinder, ADBG—AB, be vertical, and the cuttingplane, PQP, be perpendicular only to the vertical plane. Allpoints in such a plane must have their vertical projections (that is,must be vertically projected) in the vertical trace, QP, of theplane, but the required curve must also be embraced by the visiblelimits, AA and BB, of the cylinder. Hence, ah is the verti-cal projection of this curve. Again, as the cylinder is vertical, allpoints on its convex siirface must be horizontally projected inADBG. Hence, this circle is the horizontal projection of therequired curve. 64 (2). When a plane revolves about any line in it as an axis,every point of it, not in the axis, moves in a circular arc, whoseradii are all perpendicular to the axis. The representation of therevolution is much simplified by taking the axis in, parallel to, orperpendicular to, a plane of projection. Prob. 25.—To revolve the curve found in the last problem, so asto show its true size. I on. I.
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ELEME)^JTAEY INTERSECTIOlSrS, 25 Let AB—ah\ the longer axis of the cnive, and which is parallelto the vertical plane of projection, be taken as the axis of revolu-tion. The curve may then be revolved till parallel to that plane,when its real size and form will appear. Then, at c, (?, &c., thevertical projections of C and H, D and G, &c., draw perpendicu-lars, as ch\ to ab, and make cc—ch~nC. Proceed likewiseat d\ &c., since the lines, as nC, being parallel to the horizontalplane, are seen in their true size in horizontal projection ; and jointhe points a, h\g\ &c., which will give the required true form andsize of the curve of intersection before found. Memark.—This curve is an oval, called an ellipse. Its true sizecould have been shown by revolving its original position aboutDG as an axis, till parallel to the horizontal plane. The studentmay add this construction to the plate. 64 (3). The convex surface of a cylinder is wholly composed ofstraight lines, calledmanualofelementa01warr

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