

[en. I. 



200. Rectangular coordinates. Let three planes be given 

 fixed in space and perpendicular to i-a.-li other, tin- coordi- 

 nate planes XOY, YOZ, and 

 * ZOX. They wiU intersect 



by pairs in three lines, X'X, 

 FT, and Z'Z, also perpm- 

 dicular to each other, called 

 the coordinate axes. And 

 v these three lines will meet 

 in a common point 0, called 

 the origin. Any three other 

 planes, LP, MP, and NP, 

 parallel respectively to these 



coordinate planes, will intersect in three lines, N'P, L'P, 

 M'P, which will be parallel respectively to the axes; and 

 th so three lines will meet in, and completely determine, 

 a point P in space. The directed distances N'P, L'P, and 

 M'P thus determined, i.e., the perpendicular distances >f 

 the point P from the coordinate planes, are the rectangular 

 coordinates of the point P. They are represented respec- 

 tively by x, y, and z. It is clear that 



x = N*P = LU = NM r = OM ; 

 y = L'P = MM' = LN 1 = ON\ 

 z = M'P = NN 1 = MU = OL. 

 It is generally convenient, however, to consider 

 x = OM, y = MM 1 , and z = M'P. 

 The point may be denoted by the symbol P = (x, y, 2). 



The axes may be directed at pleasure ; it is usual to take 

 the positive directions as shown in the figure. Then the 

 eight portions, or octants, into which space is divided by the 

 coordinate planes, will be distinguished completely by the 

 signs of the coordinates of points within them. 



