CHAPTER V 



40. In order to determine the position of a point in space, it is 

 necessary to refer the point to three fixed planes. These three 

 planes intersect at a point which is taken as the origin ; while any 

 pair of these planes intersect in a straight line which passes 

 through the origin. Thus for the three planes of reference there 

 will be three different pairs of planes, and therefore there will 

 be three different lines of intersection, each one passing through 

 the origin. These three lines of intersection are called " the axes 

 of reference " or " the co-ordinate axes." 



Generally the three planes of reference are rectangular that 

 is, one plane is at right angles to each of the other two. The 



FIG. 1 8. 



three co-ordinate axes will therefore be mutually perpendicular 

 that is, one axis will be perpendicular to each of the other two. 

 This can be well illustrated by means of a cube, with its base 

 horizontal. One corner of the cube ran be taken as the origin ; 

 the three edges which radiate from this corner will be the three 

 axes of reference, while these three edges are the lines of inter- 

 section of the three adjacent plane faces of the cube, two of these 

 being vertical and the other horizontal. 



The position of a point with reference to the three rectangular 

 planes of reference is completely defined by the perpendicular 

 distances of the point from these three planes. 



If the co-ordinates of a point P are (x, y, 2), then x is the per- 



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