B14 



ANALYTIC OXOMSTBT 



|('u. Mil. 



draw OHX perpendicular to the other side of the angle (/>' ) ; thru lay 



Off OK - '-' />'//. -u..l OOMtnid tin- r.mrlmi.l A'/-;/-' \\ilh /; a> i.l- an.l 



2BH = OK as modulus, and OX as di Draw / j. a rail. 1 to BC 



and counect Ji with /, thru the angle BC. = iXC; for, join 7>, the 



middle point of ML, to //, then ML = OK = 2 BH = 2 HD, and the 

 three angles marked a are all equal, as are also the two marked (3; more- 

 over, ft = 2 a, being the exterior angle of the triangle HLD, which proves 

 that angle LBC = \ABC. 



187. The witch of Agnesi.* The witch may be defined 



follows : Let OKAQ be a given ii\-d 

 circle of radius a, OA a diameter, und Q 

 any point on the circle ; if now the ordi- 

 nate MQ be produced to P, so that 



MQiMPiiMAiOA, . . (1) 



then the locus of P, as Q moves around 

 the circle, is the witch. To derive 1 1n- 

 rectangular equation nf the witrli. 1ft 

 P == (#, y) be any point on the cur 

 then, since 



MQ = 



The witch was invented by Donna Maria Gaetana Agnesi (1718-17 

 an Italian lady who was appointed professor of mathematics at the University 

 of Bologna, in 1760. 





