ANAl.Y in QBOMBTBT 



[Cn. Mil. 



diameter, AT .\ tangent ; draw an\ line as OQ8 through 0, 

 meeting tlu- circle in Q and the tangent in *V. and on this 

 line layoff the distance OP = QS : the locus ..I the poim 

 P, as the line OS revolves about 0, is the cissoid.* 



in this definition, the equation of the cissoid, refer n-d 

 to the rectangular axes OX and OF, is readily d ii\< .1. 



Let the coordinates of J* 1 > ./ 

 and y, and let Cln th. oentei 

 of the circle so that 



OC=CA= CK=a. 



Since trial ' ' I//' and 



ONQ are similar, 



.-.MPiOMnNQi ON,.(\) 



and since OP = 

 NA 



^, therefore 



x moreover 



Substituting these values in 

 equation (1) gives 



whence 



y : x : : V(2a-z)a: : (2a - x), 



f- 



(-0 



(3) 



which is the required rectangular equation of the ( i->>id. 



The definition of the cissoid, as well as the equation just 

 derived, shows that the curve is symmetric with regard to 



Diocles named his curve "cinsoid" (from a Greek word meaning 



auae of its resemblance to a vine climbing upwards. The i 

 " cissoid " is sometimes, though rarely, applied to other curves which are 

 generated as stated in the definition given above, except that some oilx r 

 basic curve is employed instead of a circle. For other, but equivalent, d< iini- 

 tions of the cissoid see Note 3, b; low. 



