1 9 o Mijcellanea Curio [a. 



three Series only, that is, of fb many as their 

 Indices, excepting the firft. But if it hap- 

 pens withal, that n be equal to h-Vp ;H r as 

 it always happens in our Theorem^ then the 

 Numerator beginning by m~n \ \, and be- 

 ing continued to fo many Terms as there are 

 Units in h + p F r or », the laft Term will be 

 m neceflarily, fo if you invert the Series and 

 make that the firftTerm which was the lafl:, 

 the Numerator will be m x m *- i * m 2 

 * m >— 3, &o continued to fo many Terms 

 as there are Units in the Sum of the Indices 

 of each Product, exceping the firft Index. 

 There remains but one thing to demonftrate, 

 which is, that, what I have faid of Powers 

 whofe Index is an Integer, may be adapted 

 to Roots, or Powers whofe Index is a Fra- 

 ction ^ but it appears at firft fight why it 

 fhould be fo : For, the fime Reafon which 

 makes me confider Roots under the Notion 

 of Powers, will make me conclude, that what- 

 ever is faid of one may be faid of t'other } 

 however, I think fometime to give a more 

 formal Demonfi ration of it. . 



A 



