62 



PRACTICAL MATHEMATICS 



pendicular distance of the point from the plane YOZ, and the 

 point must therefore lie on a plane parallel to YOZ, the distance 

 between these planes being x. y is the perpendicular distance 

 of the point from the plane ZOX, and the point must therefore 

 lie on a plane parallel to ZOX, the distance between these planes 

 being y. z is the perpendicular distance of the point from the 

 plane XOY, and the point must therefore lie on a plane parallel 

 to XOY, the distance between these planes being z. 



The intersection of these three new planes will give the position 

 of the point P, and these three planes combined with the three 

 planes of reference produce a right rectangular prism one corner 



of which is the origin and the opposite corner the point P, while 

 OP is a solid diagonal of the prism. The lengths of the three 

 edges, PL, PM, and PN, meeting at the point P, are the co-ordi- 

 nates of that point; while the lengths of the three edges OA, 

 OB, and OC, meeting at the origin, are also the co-ordinates of 

 the point P. Hence, to find the position of the point whose 

 co-ordinates are (x, y, z), we have to measure OA = x, along OX, 

 OB = y, along OY, and OC = x, along OZ. Take OA, OB, and 

 OC to be the three adjacent edges of a right rectangular prism, 

 and complete the prism. The required point will be the corner 

 opposite to the origin. 



41. The plane ZOY (Fig. 19) is taken as a front vertical plane, 

 and any line drawn parallel to the axis OX will be perpendicular 

 to that plane. The x co-ordinate of a point P may be positive 

 or negative. It is positive when P lies in front of the plane ZOY, 



