The essentials of descriptive geometry . is parallel. From each corner of the face draw aperpendicular to the plane R and find where these perpendicularspierce the plane. The plan view of the projection on R is abed— these points being the plan view of the piercing points of theperpendiculars — and the elevation is abcd. AhBhChDhshows the face in its true size after it has been revolved into Habout rR as an axis, and set to one side of the actual plane ofrevolution so as to avoid confusion in the drawing. 62. Special Cases. To project a Hne upon any plane: 1. When the line is parallel to the G
The essentials of descriptive geometry . is parallel. From each corner of the face draw aperpendicular to the plane R and find where these perpendicularspierce the plane. The plan view of the projection on R is abed— these points being the plan view of the piercing points of theperpendiculars — and the elevation is abcd. AhBhChDhshows the face in its true size after it has been revolved into Habout rR as an axis, and set to one side of the actual plane ofrevolution so as to avoid confusion in the drawing. 62. Special Cases. To project a Hne upon any plane: 1. When the line is parallel to the G. L. 2. When the plane is parallel to the G. L. 3. When the plan and elevation of the given line are parallel to the corresponding traces of the given plane. 63. Proposition 12. Given the plan and elevation of a lineand of a point, to find the shortest distance between them. 7° ESSENTIALS OF DESCRIPTIVE GEOMETRY Discussion: First Method. If the line and the point berevolved into H or V about the trace of the plane which contains Ch. \ Fig. s6. them they will be shown in this revolved position in their truerelation. If now from the revolved position of the given pointa perpendicular be drawn to the revolved position of the line, PROBLEMS ON POINTS, LINES, AND PLANES 71 this perpendicular will be the measure of the shortest distancefrom the point to the given hne. If a plan and elevation of thisdistance be required the point must be revolved back to the firstposition, and with it the perpendicular. Construction. Let the construction be made in accordancewith the discussion. Discussion: Second Method. It not infrequently happensthat the relation of the given point to the given line is such asto make the construction by the first method awkward. Insuch cases it will be found more convenient to pass a planethrough the point perpendicular to the Hne, and by finding wherethe given fine pierces this plane a point will be found which, whenjoined to the given point, will be the shor
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