usbser sys xp download

projectors from the points in the lines 1, 2, 3, 4, in No. 2, to cut the corresponding ones in No. 1, and through the intersections draw the curved lines as shown, which will be the ones required. Should the axis of the cone be inclined to the VP, still remaining parallel to the HP, and the lines of intersection of the two solids be required, when in this position, proceed as in previous cases to transfer the plan No. 1 to such a position in No. 3 as will bring the axis of the cone to make the required angle with the IL, and then from it and the elevation No. 2 obtain by direct projection the view shown in No. 4. From the problems which have been given in this part of the sub- ject, the student will be able to appreciate the endless variety of posi- tions the solids in combination may be made to assume, but as it is not our object to multiply examples, but to give only such combinations as are likely to occur in practice, we pass on now to the last section in the application of the principles of projection viz., the " Development of the Surfaces of Solids," a subject of the highest importance, not only to the draughtsman, but to all who have to shape or fashion any- thing constructed of sheet metal. CHAPTER XX THE DEVELOPMENT OF THE SURFACES OF SOLIDS 80. To determine the exact form of the surface of any solid, whether it be plane or curved, it is necessary to obtain what is known as its " development " ; or, in other words, the particular shape its sur- face will assume when laid out flat, supposing it possible that it can be so treated. For such a surface to be " developable " it must be one, on every part of which a sheet of any flexible but non-elastic material can be