4 INTRODUCTORY. [CHAP. L 



lengths is represented by a number (in the general sense) viz. by 

 the number of centimetres contained in it. It is clear that OP 



Fig. 1. 



is a diagonal of a parallelepiped and that OM, MN, NP are three 

 edges no two of which are parallel. The position of a point is 

 therefore determined by means of a parallelepiped whose edges 

 are parallel to the lines of reference, and one of whose diagonals 

 is the line joining the origin to the point. 



It is generally preferable to take the set of lines of reference 

 to be three lines mutually at right angles, then the faces of the 

 trihedral angle are also at right angles; sets of lines so chosen 

 are called systems of rectangular axes, and the planes that contain 

 two of them are coordinate planes*. It is clear from the figure 



Fig. 2. 



* We shall, in the course of this book, make use of rectangular coordinates 

 only. 



