MifceUanea Curiofa. 165 



GC a dy, BC ~ \/dx z + ^ a , and let 

 be any conftant Quantity. Then lhall 



dx 1 

 ~ — , whence dx \/a ^ sly % 



/ s/a 



VyVdx ZJ rdy* 



%Jdx z -\-dy*. But now in all Curves, 'tis 



dx : : 2 -\-dy 2 as the Subtangent, to 

 the Tangent. Therefore the Nature of the 

 Curve fought is fuch, that its Subtangent, is 

 to the Tangent, as s/a : sly, which that it is 

 a Property of the Cycloid, is known to all, 

 that know that the Tangent of the Cycloid, 

 is parallel to the Chord of the Conterminal 

 Arch, in the Generating Circle, whofe Dia- 

 meter is a, and whofe Vertex is downwards. 



And with the like eafe, I can find the 

 Curve of the Swiftefi Defcent, in any other 

 Hypothefis of Gravity. 



M 3 The 



