8 o i Mif cellanea Curio f t . 



the'firft Column where eis not found) which 

 they call the Homogeneum Comparationis, and 

 let the difference be "Vb, In the next place, 

 take the fumof all the Co-efficients of e in the 

 fecond Column, to which put m s. Laftly, in 

 the third Column let there be put down the 

 fum of all the Co-efficients of ee, which fum 

 call r. Then will the Root z. ftand thus in 



the Rational Formula viz.. z, a 4r — r ; 



s s ^ tb 



and thus in the Irrational Formula^ viz.. 

 z,zzaLp~s^ \/| ss^ bt y which perhaps it 



< — i 



may^be^worth while to Iiluftrate by fome 

 Examples. And inftead of an Inftrument, let 

 this Table ferve, which fhews the Genefis of 

 the feveral Powers of a-Ve^ and if need be, 

 may eafily be continued farther*, which for 

 its ufe I may rightly call a General Analytical 

 Speculum. The forementioned Powers arifing" 

 from a continual Multiplication by a\*e ( zzz) 

 come out thus with their adjoyned Co-effici- 

 ents. See the Table. But HOW, if it be a—c^z, 

 the Table is compos'd of rhe fame Members, 

 only the odd Powers of e 7 as e % <? 5 , e 7 are 

 Negative, and the even Powers, ase%e4, e", 

 Affirmative. Alfo let the fum of the Co-effi- 

 cients of the fide e, be 'th s ; the fum of the 

 Co-efficients of the Square eezz /, the fum of 

 the Co-efficint of e 1 r=i u ; of e *zz w *, of e 5 bs x , 

 of e 6 zzy, &c. But now, fince e is ftippofed 

 only a fmall part of the Root that is to be en- 

 quir'd, all the Powers of <?, will be much lefs 

 than the correfpondent Powers of a^ and fo far - 



