4] 



POSITION. 



that a set of rectangular coordinate planes divide the space about 

 a point into eight compartments, the particular trihedral angle 

 OABC being one compartment. The lengths OM, MN, NP of 

 Fig. 1, taken with certain signs, are called the coordinates of the 

 point P, and are denoted by the letters x, y, z. The rule of signs 

 is that x is equal to the number of units of length in the length 

 OM when P and A are on the same side of the plane BOG, and 

 is equal to this number with a minus sign when P and A are on 

 opposite sides of the plane BOG, and similarly for y and z. We 

 can express the conventions as regards sign by means of the 

 following table, in which A' t B', G' denote points in AO, BO, CO 

 produced : 



It is clear that the coordinates x, y, z determine the position 

 of the point P with reference to the lines OA, OB, OG. 



A set of lines of reference such as OA, OB, OG with respect 

 to which the position of a point P can be determined will be 

 called a frame of reference. 



