rvRT II 



SOL/I) -4.Y.IA) Tic QEOMl .TAT 



CHAl'Tr.K I 

 COORDINATE SYSTEMS. THE POINT 



199. Solid Analytic Geometry treat* by analytic methods 



lems which concern figures in space, and therefor, 

 volves three dimensions. It is evident that new systems of 

 coordinates must be chosen, involving three variables ; and 

 that the analytic work will therefore be somewhat lui 

 than in the piano geometry. On the other luuid, since a 

 plane may be considered as a special case of a solid where 

 dimension lias the particular value zero, it is to bo 

 expected that the analytic work \\ itli three counlin.itc vari- 

 ables should be entirely consistent \\ith tl. vo vari- 

 able*; merely a simple extension of the latter. Tho student 



il<l ma fail to notice this close analogy in all cases. 

 In the present chapter will be considered tome simple and 

 useful systems of coordinates for determining the position of 

 a point in space, some elementary problems concerning points, 

 and the transformations of coordinates from one system to 

 another. Lati-r chapter \\ill trval briefly of surfaces, par- 

 planes and of surfaces of the second order, and 

 of the straight line. 



881 



