

1W-1W.J 



x = \ac<*0 + 

 and* = fain*- 



, by trigonoov 

 800*0+ ooeSla 





hence equation* (4) beoooM 



nd 



. . (.'-) 



which is the oomm 

 equation of the four-ciuped b 

 laid. 



SPIRALS 



193. \ spiral is a t ranscendental raced by a |. 



:u \\liil. it revolves about a fixed point called the center, 

 also continually recedes from this center, according to some 

 definite law. 



The portion <>f the spiral generated during one revolution 

 he tracing point is called a spire ; and the circle whose 

 radius is the radius vector of the generating point at the 

 end of the first revolution is called the measuring circle of 

 the spiral. Thus, in Fig. 185, ABClH measuring 



circle, OQSUWA i> tin- iir>t .spin-, and .I/7//..VU the sec- 



194. The spiral of Archimedes. t Thi* . ur\. is tnic-ed by 



in \\ln.-li moves about a tixed point in a pl.ui.- i 



If Ihfe equation be nllnitallzr.1. It 



Although the hypocycloid U, in general, a 





particular value* of the rmtio of the radii of the cirdat, 

 t This curve to anally fappoeed to have been discovered by 

 its principal properties wen> investigated by the 



