The essentials of descriptive geometry . 2. To find the length of a Hne which Has in the profile plane. 40. Proposition 2. Given two views of a Hne to find where itpierces the planes of projection. Discussion. The point where the line pierces H must He onthe line itself and in the H plane. Therefore, the projections ofthe required piercing point will He on the projections of the given PROBLEMS ON THE LINE 49 Kne, and the elevation will lie on the G. L. If the elevation ofthe line be extended to meet the G. L. this point will be the ele-vation of the required piercing point; its plan view will
The essentials of descriptive geometry . 2. To find the length of a Hne which Has in the profile plane. 40. Proposition 2. Given two views of a Hne to find where itpierces the planes of projection. Discussion. The point where the line pierces H must He onthe line itself and in the H plane. Therefore, the projections ofthe required piercing point will He on the projections of the given PROBLEMS ON THE LINE 49 Kne, and the elevation will lie on the G. L. If the elevation ofthe line be extended to meet the G. L. this point will be the ele-vation of the required piercing point; its plan view will lie on the. Fig. 45. plan view of the Kne and in a perpendicular from the a similar manner the V piercing point may be found. Construction. In Fig. 45 let the problem be to find the planand elevation of the point where the center Hne OP of the timberpierces H and V. By extending op to the G. L. the point m 50 ESSENTIALS OF DESCRIPTIVE GEOMETRY is found; m is the elevation of the point where the line OPpierces the H plane. The plan view of this H piercing point wiUbe on op where the perpendicular from m intersects op at m;since M is in H (as shown by the elevation m) and on OP (as mand m show) it will be the point where OP pierces H. To find where OP pierces V, op is extended to the G. L. at n,and n is located on op as shown. The point N, being in V andon the hne OP, will be the point where OP pierces V and n is theplan and n the elevation of this point. In a similar manner the P piercing point, if it be required, maybe found. 41. Special Cases, i. Given the location of the H and Vpie
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