Text-Book of Practical Solid Geometry; Etc., for the Use of the Royal Military Academy, Woolwich (Paperback)

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1899 edition. Excerpt: ...if it is required to draw a line, or find a point, it is the plan of that line or point which is required. Wherever it is considered useful, freehand drawings have been given, showing the methods used in working. It is hoped that by this means the student may get into the way of imagining his work, in such a manner that it may materially assist the quick and clear conception of a problem. The scale for drawings in all problems and exer-, cises in Lines and Planes in this book is ten units to an inch, unless otherwise stated. Problem I. (Figs. 33 and 34, Plate VI.) Through a given line to draw a plane of given inclination. Let a1 0 bw be a given line, through which it is required to draw a plane M inclined at 70 to the HP. First referring to Fig. 33, let the line A B be placed with the point A in an H P of level 10, the point B resting on the apex of a cone, the base of which lies in the H P10. Let the height of the cone be the difference in level between A and B (=10) and let the angle which the generatrix makes with the base be 70. Then, if a plane M is placed so that it rests against or is tangent to the cone, and also touches A, the plane will contain AB. Also, since the plane M is tangential to a cone of 70 inclination, it is itself inclined at 70. It is therefore the required plane. Now the plan of the intersection of the plane M with the H P1 is the 10 contour of the plane M, and a parallel through the centre of the base of the cone (which is the plan of the apex, height 20) is the 20 contour. Moreover there will be two planes fulfilling the conditions. For another tangent plane could be placed against the cone on the opposite side to that which has been taken in the drawing. Refer now to Fig. 34, and see how the operations...