JMtfcettanea Curiofa. 1 3 5 

 T H? ( - IGf-h GH2 ) pa *W - ; from 



aV dd*-* dx . i i • 



-whence IH ^ * — : — ■ — -r 5=3 ^ a? a-, 



A/dx~XX 



22 



and confequently M^idx zziy/dxzzi&D* 

 This Conclufion may alio very eafily be de- 

 idd from the known Property of the Tan- 

 r,t. For fince the little part of it, as IH, 

 s always parallel to the Chord AD, the 

 I 'mgles IGH, ABD are fimilar, whence 



AB : AD : : GH : IH, that is, a? : Vdx : : x : 



2 ^ a • 



xy'dx. therefore IR^xw'dx d x x. By 



the help of the Fluxion IH alfo, we may 

 inveftigate the Area of the Cycloid. The 

 Fluxion of the Area AEI, is the Re&angle 



EIG ^ dxx x 2 x - xS/dx'^ xx. But the 

 \J dx «-h xx 



Fluxion of the Portion ABD is the fame; 

 therefore the Area AEI and the correfponr- 

 dent Portion (of the Circle) ABD, are al- 

 ways equal. 



k 4 Lct 



