Mijcellanea Curt of a. 1 5 7 



$d 3 xx 



And confequently s~ 3 2 ddxv— ~ — — , 



dx— xx 



z=z\d 3 v — Id 3 y (by The or. 2.) Therefore now 

 j=^ 3 t;— i^ 3 > And confequently the Area 

 fought, is—v 3 X"^-%dv 3 -| J^ 2 j. — iddvx-\-%d 3 

 -v~%d 3 y. 



Since the Solids and Surfaces generated by 

 the Rotations of Curve Lines, as alfb the 

 Lengths of Curves, and the Centers of Gra- 

 vity of all thefe, do depend upon the Qua- 

 dratures of Curves ; 'tis plain, that thefe 

 are eafily obtain'd too, if they depend upon 

 the foremention'd Curves. 



After I had compos'd thefe Theorems, 

 and (hewn them to the Celebrated Mr. New- 

 ton, (as the fupream Judge in all Matters of 

 this Nature) he was pleas'd to give me a 

 fight of fome Papers of his, by which I find 

 that he has a long time been Mailer of a 

 Method, by which any Trinomial Equation 

 (exprefling the Nature of a Curve) being 

 given, that Curve is either fquar'd, or re- 

 duced to a more fimple one. 



And 'twere to be wifh/d, that he thought 

 fit to communicate to the Publick, not only 

 thofe Things which he has relating to thefe 

 Matters, but others alfo of his Noble In- 

 ventions, which are not a fmall Number 

 neither. And I believe this is not my Wilh 

 alone, but that of the whole Learned World 

 befides. 



I make no queftion but thofe Learned Per- 

 rons (whofe Writings in the Aftt Eruditorum 



and 



