134* Mtjcellanea Curiofa. 



The Fluxion of the Curve Line is fome- 

 times more eaftly found by comparing the 

 two finiilar Triangles CED, CBO, for this 

 Proportion arifes, CB : CO : : CD, that is 



for the Circle \J 2rx xx : r : : x : rx 



*J2yx *h xx. 



The Curve of the Cycloid may be deter- 

 mined by the fame Method too. Let (Fig. 2.) 

 ALK be a Semicycloid, whofe generating 

 Circle is ADL. Having any point as B in, 

 the Diameter AL, draw BI parallel to the 

 Bafe LK meeting the Peripheus of the Cir- 

 cle in the point D *, compleat the Re&angle 

 AEIB, and draw FH parallel to EI and infi- 

 nitely near to it, as alfo BI cutting FH in 

 G, and the Curve AK in H. Put ALzid. 



AB (t=: EI ) tux. GHtf x. It is known that 

 the right Line BG is every where equal to. 

 the Sum of the Arch AD and the right Sine 

 BD , whence 'tis manifeft, that the Fluxion 

 IG is alfo the Aggregate of the Fluxions of 

 the Arch AD and the right Sine BD. But 

 the Fluxion of the Arch AD, was found 



idx and the Fluxion of the right 



\l dx t=z xx, 



Sine BD will be found to \>z dx+-*2xx 



2\l dx*-*xx\ 



therefore IG « dx m xx and therefore 



