Descriptive geometry . arises if Av is taken perpendicular to theground line, while Ah is not. (b) (Fig. 49). The projections, Bh and Bv, are both perpen-dicular to the ground line, but at different points. Let ch beany point on Bh; the projector from ch is parallel to Bv, andthere is no point on B to correspond with c\ Similarly, if dvis any point on Bv, the projector from d is parallel to Bh, andthere is no point dh. Therefore there is in space no line Bcorresponding to these two projections. (c) (Fig. 50). The projections O1 and Ovare both perpendicu-lar to the ground line, and at the same
Descriptive geometry . arises if Av is taken perpendicular to theground line, while Ah is not. (b) (Fig. 49). The projections, Bh and Bv, are both perpen-dicular to the ground line, but at different points. Let ch beany point on Bh; the projector from ch is parallel to Bv, andthere is no point on B to correspond with c\ Similarly, if dvis any point on Bv, the projector from d is parallel to Bh, andthere is no point dh. Therefore there is in space no line Bcorresponding to these two projections. (c) (Fig. 50). The projections O1 and Ovare both perpendicu-lar to the ground line, and at the same point. Let a/ be anypoint on Ch. The projector from ah coincides with O, and theparticular point, a, on C, which corresponds with ah cannotbe determined. The line C is therefore indeterminate. Buiif the line be projected by means of two of its points (§ 29), itat once becomes determined. Thus the line de, Fig. 50, is adefinite line, lying in a plane perpendicular to the ground line. 24 DESCRIPTIVE GEOMETRY [III, § 35. 35. The Profile Line. A plane which is perpendicular tothe ground line is known as a profile plane, and any line lyingin a profile plane is termed a profile line. We have just seenthat such a line cannot be projected in the same way as thegeneral straight line. Hence problems in which such linesoccur will usually — but not always — call for particular solu-tions. The simplest method of dealing with a profile line isusually by means of an additional plane or projection. Thesolution of cases involving such lineswill be deferred, in general,until Chap-ter VI, where this topic is A Point Lying in a Line (). It follows at once from thesecond proposition of § 28, that if apoint lies in a line, the projectionsof the point lie in the projectionsFlG- 51- of the line. This condition is suffi- cient if the line does not lie in a profile plane. (See § 35.) 37. Traces of a Line. Of all the pointsin a straight line, the two in which itpierces the pl
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