312 



J.v.l L \ lie (,l.nMi-;utY 



[Cu. Mil. 



For Newton's metim<l . i drawing the cissoid by continuous mot 

 see Salmon's Higher I'lune Curves, p. 183, or Lardner's Algol H.H.; 

 Geoinrtiy. j.. 196. 



186. The conchoid of Nicomedes.* The conchoid may be 

 (iHined as follows: LetPRP'Q be a given circle of radius 

 a whose center S moves along a fixed straight lim- OX: 1 i 

 LK be a straight line drawn through a fixed point A and 

 the center *S T of this moving circle, and let P and P 1 bu tin- 

 intersections of this line and the circle; thru the locus 

 traced by P (and by P') as S moves along OX is a conchoid. 



y 



Fio 125 



This definition may also be stated thus : If A is a fi\( 

 point, OX a fixed line, and S the point in which OX 

 intersected by a line LK revolving about A, then the locus 

 of a point P on LK, so taken that SP is always equal to a 

 given constant a, is a conchoid. 



Tli ti\< -d point -d. is called the pole, the constant panimet 

 a the modulus, and tin- lixcd line OX the directrix of 

 conchoid. 



* Th .-I was invented by a Greek mathematician named Niconu 



probably in the second century B.C. Like the cissoid, it was invented for 

 purpose of solving the famous problem of tin: " duplication of the cube"; 

 is, however, easily applied to the solution of the related, and no less 

 problem of the trisection of a given angle (see Note 3, below). 



