IX'J 



1 \ I/. )//< 



[Cu. vnr. 





 111. To trace the ellipse s + j I From equation [1 1 ) 



.Inws that : 



(1 ) The ellipse is symmetrical with regard to the a;-axis ; 

 i.e., with regard to tin- line through the focus and perpen- 

 dicular to the directrix; this line is therefore called the 

 principal axis of the curve; 



{2) The ellipse is symmetrical with regard to the y-axia 

 also ; t.*., with regard t> a line parallel to the directrix and 

 passing through the mid-point of the segment AA! (\ : \^. ^ \ 

 which the curve cuts from its principal axis ; 



(3) For every value of x from a to + a, the two cor- 

 responding values of y are real, equal numerically, 1m t, 

 opposite in sign ; and for every value of y from b i. /-, 

 the two values of x are real and equal numerically, lut, 

 opposite in sign ; and that neither x nor y can have real 

 values beyond these limits. 



The ellipse is, therefore, a closed curve, of one branch, 

 which lies wholly on the same side of the directrix a the, 

 focus ; and the curve has the form represented in Fig. 80, 

 which agrees with the foot-note on p. 71. 



The segment AA! (Fig. 81) of the principal axis inter- 

 cepted by the curve is called its major or transverse axis 



