it i'. in: i: /-/..IN/. < t uvxa 



NOTE 1. It U usually implrloigwlqaaUoM(l)ftiia (2) 





as representing the cycloid; b then the independent variable, while * 

 an. I y at- l,ih rOOCtkMM : U 



The cycloid belongs to the kind of curves call* 

 These curves are generated by a point which b invariably 

 i A curve which roll*, without sliding, upon a given Axed 



both the rolling and the Axed corves are ctofas, then the 

 generated b designated by the general name of twcfciii. If the 

 crating i*.i..t b on the cirrum/mnci of the rolling circle, and tab < 

 rolb on the ouitide of a Axed circle, then the curve described b called an 

 epicycloid ; Uu if it roll* on tin- intidt of the Axed circle, the generated 

 b called a hypocycloid. The cycloid may be regarded either as 

 AH - picycloid or a h> [ >r which the Axed circle has iu center 



At infinity and an intimU) radius. 



The hypocycloid. Lot tin* Iiypocycloid APR81 

 ! traced by tin- j.,,;m /' .,n the cirm inference of the circle 

 /ij whoee radios is 6, and \\ liich rulls uu liie iiwide of the 



MM 



circle AQB* whose radius is a. Also let P a (x, y) 

 any position of the generating point. I* line 



the onl u.l Ml\ tlu radius (PP, and the 



