Descriptive geometry . ly, may be found which contains (a) two intersecting lines ;(6) two parallel lines ; (c) a line and a point not on the line; (d) three points not in the same straight line. Problem 6. To find the plane which contains two given intersectingor parallel lines. / y\\ \^4 ^^P^ 11 1 V^ Fig. 134. Analysis. The trace of the required plane on any coordinateplane must contain the trace of each of the given lines (§ 96).The plane is found when its II and V traces are found. Construction (Fig. 134). Let A and B, intersecting at pointc, be the given lines. Find the traces of A and B
Descriptive geometry . ly, may be found which contains (a) two intersecting lines ;(6) two parallel lines ; (c) a line and a point not on the line; (d) three points not in the same straight line. Problem 6. To find the plane which contains two given intersectingor parallel lines. / y\\ \^4 ^^P^ 11 1 V^ Fig. 134. Analysis. The trace of the required plane on any coordinateplane must contain the trace of each of the given lines (§ 96).The plane is found when its II and V traces are found. Construction (Fig. 134). Let A and B, intersecting at pointc, be the given lines. Find the traces of A and B (Prob. 1,§ 37). The required trace HQ is determined by the twoiZ-traces sx and s2; the trace VQ by the two P-traces tx and L. Check. The H- and F-traces of a plane must intersect onthe ground line (§ 46). Hence IIQ and VQ, when produced,must intersect on GL. 80 DESCRIPTIVE GEOMETRY [X, § 106 A plane which contains two given parallel lines is shown inEig. 135. The construction is entirely similar to that just Fig. 135. In Fig. 136 the IZ-trace of the given line B is too far removedto be used in the construction. The plane Q, containing A and
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometrydescriptive
