( ^^I ) 
To find the Vmm which ought to be prefixt to eve- 
ry Produdt, I confider the Sum of Units contained in 
the Indices of the Letters which compofe it (the [ndex 
of a excepted) I write as raany Terms of the Series 
tny^m — ixw— zxw — j^^c. as there ^x^Vnits in the Sum 
of thefe Indices, this Series is to be the Numerator of a 
Fra£l:ion, whole Denominator is the Prodad of the fe- 
veral Series ixix3X4X5',CS'c. iX2X3X4X5'-, 
1 X X4 X 5* X 6, ^c. the i^^^ of which contains as 
m^oy Terms as there are Vnits in the Index of the 
many as there are Vnits in the Index of c, the 3^ as 
mmy as there are Vnits in the Index of the 4^^ as 
many as there are Vnits in the Index of 
Demonflratien, 
To raife the Series az'\'lzz'\'cz^ + ^2^» to a- 
ny Power whatfoever, write fo many Series equal to it 
as thefe are Vnits in the Index of the Power demanded. 
Now it is evident that when thefe Series are fo Multi- 
plied, there are feveral Produfts in which there is the 
iarae Power of z, thus if the Series az-^-hzz^cz^ -\-dz^ 
&c. is rais'd to its Cube, you have the Produds 
l^z^, alcz^^ Wz^, in which ^you find the fame Powers ^ 
Therefore let us confider what is the Condition that can 
make fome Produdts to contain the fame Power of 2:, 
the firft thing that wiJl appear in relation to it, is that 
in any Produft whatfoever, the Index of z is ths Sum 
of the particular Indices of z in the Multiplying Terms 
(this follows from the the nature of Indices) ihwsl^z^ 
is the Produd of izS ^ zS and the Sum of the In- 
dices in the Multiplying Terms, is 2+2+2.== 6 ; 
alcz^ in the Produd of az^ Izz^ cz^^ and the Sumof them 
Indices of z in the Multiplying Terms is 1+2+3—6 
aadz^ is the Produd of az.az.dz"^^ and the Sum of the 
Z 2 2 2 Indices 
