Descriptive geometry . race with the hori- LINES LYING IN PLANES 19 zontal projection of the vertical trace to obtainthe horizontal projection of the line. Connectthe vertical trace with the vertical projectionof the horizontal trace to obtain the verticalprojection of the line. 27. Conditions governing lines lying in aplane. Since the traces of a plane are lines ofthe plane, they must intersect all other lines ofthe plane, and conversely, all lines of a planemust have their traces in the traces of theplane. See lines A and B, Figs. 5b and 56. 28. If a line is parallel to IT, it intersectsH at
Descriptive geometry . race with the hori- LINES LYING IN PLANES 19 zontal projection of the vertical trace to obtainthe horizontal projection of the line. Connectthe vertical trace with the vertical projectionof the horizontal trace to obtain the verticalprojection of the line. 27. Conditions governing lines lying in aplane. Since the traces of a plane are lines ofthe plane, they must intersect all other lines ofthe plane, and conversely, all lines of a planemust have their traces in the traces of theplane. See lines A and B, Figs. 5b and 56. 28. If a line is parallel to IT, it intersectsH at infinity; therefore, its horizontal trace isat infinity and its horizontal projection isparallel to the horizontal trace of the plane inwhich it lies, its vertical projection beingparallel to the ground line. See line (7, and 58. Likewise if a line is parallel to V^its vertical projection is parallel to the verticaltrace of the plane in which it lies, and itshorizontal projection is parallel to the Fig\55 Fig. 58. 20 DESCRIPTIVE GEOMETRY 29. If the traces of any plane be drawnthrough the traces of a Ime, the plane mustcontain the line ; therefore, an infinite numberof planes may be passed through any line. InFig. 59, planes iV, R, T, and S all contain lineE. 30. To pass a plane through two intersect-ing or parallel lines. PtiiNCiPLE. The traces of the plane mustcontain the traces of the lines (Art. 27,page 19). Case 1. Method. 1. Determine the tracesof the given lines. 2. Connect the two hori-zontal traces of the lines to obtain the horizon-tal trace of the plane, and connect the twovertical traces of the lines to obtain thevertical trace of the plane. Construction. Fig. 60. A and B are thegiven intersecting lines. Determine theirhorizontal traces c^ and d}^ and their verticaltraces e and /^ (Art. 21, page 16). Con-nect the horizontal traces to determine HTand the vertical traces to determine the traces of the plane must meet in GL^ only three tra
Size: 3089px × 809px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1900, booksubjectgeometrydescriptive
