( ) 
/—I 
the Number of the Parts of B then x B* muff 
2/ 
always exceed AC — D ^ and thefe eafily fuggefted 
this general Propofition. 
PROP. VIII; 
Let r exprefs the Dmenjions of the. Coefictent 
and s the iJtf erence of the Dlmenffons of the Co- 
efficients C and G, then B and H being Coefficient s> 
adjacent to C and G, n — ■ r — s x r G^ffiall aU 
m^ays he greater than s-j- tXs + ^^xB^H/ when' 
the Roots of the Equation are all real ^antities affi 
fe^ed with the fame Sign. 
For taking the Differences of all thofe Parts of the 
Coefficient C that are fimilar in all their Fadors but- 
one, ah Cyah h^ ah i, 5c c. and multiplying the Square 
of each Difference by fuch Parts of the Coefficient D 
(which is of s Dimenfions) as are diffimilar to both 
the Parts of C in that Difference, the Sum of all thofe 
Squares thus multiplied, willconfifl of Terms of C^G^‘ 
taken pofitively, and of Terms of taken negative- 
ly. By multiplying in this manner ahe — ahhY 
ahc-^abi ' -f- ahe — abhfbic. + ahc — ach^ + 
a he — a c if -j- ahe — ^ a c kf 5cc. -|- ah c h c if -f- 
ahe — he e\^ fah C’—b c kf 5cc. by d efg the Term of 
D, that is diffimilar to all thofe Parts of C, you will 
find that a ^b'^c*defg will arife in the Sum of the Pro- 
s times : For thofe Produds may be 
duds r ■>< n 
;*lfo expreffed thus defga^ c — c — fffic — /(| 
^£.-fdefga^c^ X h. — h[' f b 
/r fh — 5cc.-f- 
defgEc^ 
i 
