(6i ) 
the Produds that can be made by multiplying the Parts 
. of any Coefficient C by all the fimilar Parts of G, I ex- 
prefs byX' G' placing a fmall Line over each Coeffici- 
’ll I manner D'F' exprelTes the Sum 
roduds that can be made by multiplying 
the (imilar Parts of D and F by each other; and C'xG 
^preffes the Sum of the Squares of the Parts of the 
Coefficient C, but C'xC, expreffes the Sum of the 
Produds that can be made by multiplying any two 
Parts C by one another. Thefe Exprellions being 
underltood, and the five Propofitions in~Phil. "tra 7 i(\ 
394j being premifed, next follows 
P R O P. VI. 
of the Dtmen/tons of am t^o 
C and G he called ( m ) then Jhall the 
ProduB of thefe Coeffictents multiplied hy one auo. 
ther he equal to C G' -f fnff x B' H' + - ^ X 
I 
-^Al-f. — -x-^x-^-xIxK. 
Where B and H are the Coefficients adjacent to the 
Coefficient C and G, A arid I the Coefficients adjacent 
to B.and H, I and.K the Coefficients adjacent to B andli 
It IS kno wn tliat C = ^ Zi tr -j- ^ 4 . ^ ^ ^ J. ^ I ■ 
^ j ^ defh-\-ahcd eff 
+ he d efgh^ (3cc. and it is manifefl, ' 
I. That in the Produd CG each Term of GO 
will ante once as a^hc^defg. But 
Produa of al>f and abdefgh,. or of abd and 
c ej g h, oi of ab'e mii ahe dfg k, or of ^ bf and 
ahe d egh^ 
