Mifcellanea Curio fa. 233 



therefore the Cylindrick Superficies fhall 

 there alfo be greateft. Laftly, Becaufe the 

 fame is to be faid of Cylindrick Superficies 

 cut off by a Plane that make any Angle with 

 the Plane of the Balis, as is wheu the faid 

 Angle is half a right one \ the Truth of 

 what was afferted is evident univerfally. 



LEMMA. 



(Fig. 37.) Any Curve as AFQ^, defcriPA 

 by the Evolution of another Curve KU, 

 if upon any Ordinate^ as FB (at right 

 Angles to the Axis AB) be let fall per- 

 pendicularly UR, from the correspondent 

 Point U in the Curve KU ; then (the 

 Fluxion of the Axis AB continuing 

 the fame) fjja/l the Fluxion of the 

 Fluxion of the Ordinate BF, the 

 Fluxion of the Curve AF, and the right 

 Line FR be continual Proportionals. 



Let the Lineola Ff be produc'd 'till it meets 

 the next Ordinate w<p in 0, And becaufe by 

 the Hypothefis Fs = fw, alfo mail of = Ff, 

 and confequently op fhall be the Fluxion of 

 fs, that is the Fluxion of the Fluxion of the 

 Ordinate. Farther, the Triangles o <p f, f FR, 

 are Equiangular, becaufe opf=its Alter- 

 nate f FR,. and fo<p = (F f r=) FfR, be- 

 caufe their difference R f r is as nothing in 

 refpecl: of either of them, lince R r is no- 

 thing in refped of fr. And therefore o <?: 

 ? f : : f F : FR 5 but 9 f = f F, fince they dif-, 



fer 



