tt*-*00.J BVRPAC** 



ilit* special equations of flmt and second 

 degree will be taken up m th. t\vo succeeding chapters. 

 m desired to show that an algebrmie equation in three 

 iblee represents a surface, and to consider briefly ' 



lasses of surfaces : (1 > cylinders, rfaees which 



are generated by a straight hm- moving parallel to a i 



line, ami always intersecting a fixed curve; and (2) 

 of revolution, i.e., .surfaces generated by revolving 

 plane curve about a fixed straight hue King in it* plane. 



209. Equations in one variable. Planes parallel to coordi- 

 nate planes. I mm the definition ,,t i, , t angular coordinates, 



that the r.|ii.iiionS 



XaO, y.O, I-O, 



represent the coordinate planes, respectively, and that any 

 algebraic equation in one variable and of the first degree 

 represents a plane parallel to one of them. Similarly, an 

 equation in <>n \.uiable and of degree n will represent n 

 such parallel planes. < ith. i real or imaginary. For, the first 

 .Ijer of any such equation, as 



pj* +/V-' 1 +/V*- f -I- +/.,' +p m - i'. 

 can be factored into n linear factors, real or imaginary, 



-*--~--O 



the reasoning of Part I. An. I",..; ( J) \\ill repre 

 sent the loci "f tli" n 



T-r,-0, x-j-,-0, ..., r-r. -0, 



each <>f u Inch is a plane, parallel to the yi- plane, and real if 

 corres|>on<ling root is real. In the same way, an equa- 



