Descriptive geometry . Fig. 140. (§ 93), and the required plane Q is passed through the linesA and B. In Fig. 141 the line A is parallel to V\ hence the directionof VQ is known to be parallel to Av (§ 102). But as neitherA nor B has a F-trace, a point on VQ is determined by notingwhere HQ intersects GL. Corollary II. To find the plane which contains three givenpoints not in the same straight line. Analysis. Connect any two points by a straight line, andthrough the third point draw a second line parallel to the first, X, § 107] PARALLEL LINES AND PLANES 83 thus reducing the problem to two paral
Descriptive geometry . Fig. 140. (§ 93), and the required plane Q is passed through the linesA and B. In Fig. 141 the line A is parallel to V\ hence the directionof VQ is known to be parallel to Av (§ 102). But as neitherA nor B has a F-trace, a point on VQ is determined by notingwhere HQ intersects GL. Corollary II. To find the plane which contains three givenpoints not in the same straight line. Analysis. Connect any two points by a straight line, andthrough the third point draw a second line parallel to the first, X, § 107] PARALLEL LINES AND PLANES 83 thus reducing the problem to two parallel lines. Or, drawlines connecting any point with each of the other two, thusreducing the problem to one of two intersecting ^k\ \s>^ Cjf /1Xi / / 4 / 7 V ^> bv; Fig. 141. Fig. 142. No figure for the general case is thought necessary. It isinteresting to note that this device may be used for passing aplane through a profile line and a point. Thus (Fig. 142), letab be the given line and c the given point. Draw the lines ac(aW, avcv), and be (bhch, bvcv), and pass the required plane Qthrough these lines. This avoids the necessity of finding thetraces of the profile line ab, although its traces, if found, shouldlie on HQ and VQ respectively (§ 96). 107. A Plane Parallel to Lines or to Another Plane. A planewhich is parallel to given lines or to another plane is deter-mined by the fact that a plane containing one of two parallellines is parallel to the other line (§ 105). One plane, and one only, may be found which (a) contains a given line and is parallel to a second givenline that is not parallel to the first line; (b) contains a given point and is parallel to each of two givenlines that are not paral
Size: 1493px × 1674px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometrydescriptive
