Items related to Textbook on Practical Solid or Descriptive Geometry...
Synopsis
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. 1891 edition. Excerpt: ...X Y at B2, the angle A B2 a will be the inclination of the line A B, and also of the plane LMNto the horizontal plane. The inclination of the plane to the vertical plane is found by a similar construction, which is shown in fig. 68. The construction just given will apply whatever be the position of the traces. But when the traces are parallel, it is not necessary to make a construction for finding the inclination to the vertical plane after the inclination to the horizontal plane has been found, as the one angle is the complement of the other. PROBLEM 33. To draw the traces of a plane, having given its inclinations to the co-ordinate planes. Let the plane be inclined at 0 degrees to the horizontal plane and (j degrees to the vertical plane. Note. The sum of the angles 0 and j must lie between 90 and 180. First method. At any point, A, in X Y make the angle L'AO equal to 6, the inclination of the plane to the horizontal 69 plane. Draw L'ON perpen dicular to X Y and 0 B perpendicular to L'A. With O as centre and 0 B as radius, describe an arc, and draw NC to touch this arc and meet X Y at an angle equal to f, the inclination of the plane to the vertical plaDe. With O as centre and O C as radius, describe another arc; the line L' M drawn through L' to touch this second arc will be the required vertical trace, and MN the horizontal trace. The theory of this construction is that if two cones be drawn enveloping the same sphere, having their bases in the planes of projection, and their slant sides inclined, at the given angles, the plane which touches these two cones will be inclined to the co-ordinate planes at the same angles as the slant sides of the cones, and therefore at the given angles. In fig. 69, 0 is the centre of the sphere, and O B...
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