be the Numerator of a Fradlion whofe Denbminator 
j[i;all be the Produd: of the Series, ixxx3X4Xj, &c. 
I X 2 X 5. X 4x 5, 1x2x3x4x5x6,(5^^ 1x1x3x4x5, 
&c. whereoi the I'^isto contain as many Terms, as 
thiere Units in the 1^^ Index m — h ; the 2^ as many as 
there are Units in the index h ; the 3^ as matiy 
there are Units in the 3^ Index p; the 4^^ as many as 
there are Units in the 4'^ Irtdexs r. Bat the Numera- 
tor and Denominator of th^s Fraftion have a common 
Divifbr, viz the Series 1x1x3x4x5, &c, continued to 
fo many Terms as there are Units in the 1^^ Index m — n; 
therefore let both this Numerator and Denominator be 
Divided by this common Diyifior, then this new Nume- 
rator will begin with tn — , whereas t'other began 
with and will contain fo many Terms as there arc 
Units in h-^p-^-r , that is fo many as there are Units in 
the Sum of all the Indices, excepting the i'"^ ; as for the 
new Denominator, it will be the Produft of 3 Ssries 
only, that is of fo many as there Indices, excepting the 
i^^^ But if it happens withal, that n be equal to 
i;^pj^r as it always happens in our Theorem^ then the 
Numerator beg-inning by w — »+i , and being continu- 
ed to (6 many Terms as there are Units in h-^-p-^-r or 
», the kft Term will be tn neceffarily, fo if you in- 
vert the Series and make that the firft TeriQ which was 
the LaftjtheNumerator will be w x i x i x m — 3, 
&c. conntinued to fo many Terms as there are 
Units in the Sum of the Indices of each Produd, ex- 
cepting the i*^ Index. There remains but one thing 
to demonflrate which is, that, what I have (aid of 
Powers whofe Index is an Integer, may be adapted to 
Hoots, or Powers whofe Index is a Frad:ion ; but it 
appears at firft fight why it fliould be fo : ^br , the 
lame Reafbn which makes me confider Roots un- 
der the Notion of Powers „ will make me conclude, 
that 
