I*-, m : Hi'. 



in equal 



v; ) : 2o, . . . (2) 



which is the equation sought. 



The definition of the witch, a* well as the equation just 



ved, shows th.it the curve is symmetrical with regard to 



that it lies wholly between the y-axis and the 



lin : and that it has two infinite branches to each of 



ue x 2 a is an asymptote. 



iaa The lemniscate of Bernoulli!. The lemniscate may 

 defined as follows: let LTARNA'K be a rectangular 

 <> its center, OX and OY it* axes, and TE a tan- 



\Uo let OG be a perpen- 



i the center upon this tangent, and let /' lie the 

 of their intersection : then the locus of P as T moves 



hyperbola in called the lemniscate. 

 I'-rive the rectangular equation of this curve, let 

 )A = <i, ami let the on in! mates of T le Xj and y v ; then the 

 [nation of the tangent 



, v - ,,# = a, . . 

 theiMji perjH-ndictilar upon this tan- 



.... 



1. .nniHcmie WM inventnl by Jacqne* Bernouilli (1064-1705). a 

 mathematician and profeMor in the Unireimity of Baflle. It it, how- 

 only a special CMC of the Caatinian orate ; vis. . of iha locos of the TW 

 a triangle whose base is given In length and position, and the product 

 whose other two sides is a constant See Salmon's Higher Plane Cunres, 

 Gregory's Examples, or Cramer's Introduction to the Analysis of 



