{6o) 
tal Proportions, a great Variety of new Rules, different 
from his, and from any other hitherto publifhed, for dif. 
covering when an Equation has imaginary Roots. I fhall 
particularly explain one that is more ufeful for that 
Purpofe, than any that have been hitherto publifhed. 
Suppofe there is an Equation of (n) Dimehfions of 
this Form, 
— E^”“^ + Fx 
And that the Roots of this Equation are, 
ij k, /, «3Cc. then fhall Az=za~\-b-\-c-\-d-^e 
f dec. and therefore I call ayb^c, d,e,f, 6Cc. Parts 
or ferms of the Coefficient A. For the fame ReafonI 
C 2 \{ abya adyae^bcybd^c dydec. Parts or Terms of 
the Coefficient abcyabd^abe^acdybcd, 6cc. Parts or 
Terms ofC ; ab c d, ab c e,ab cf. Parts or Terms of the • 
Coefficient D, and fo on. By the D men (tons of any Co- 
efficient ; I mean the Number of Roots or Fa dors that 
are multiplied into each other in its Parts, which is al- 
ways equal to the Number of Terms in the Equation 
that proceed that Coefficient. Thus A is a Coefficient of 
one Dimenfion, B of two, C of three, and fo of the red. 
I call a Part or Term of a Coefficient C limilar to a 
Part or Term- of any Coefficient G, when the Part of 
G involves all the Fadors of the Part of C ; Thus 
abcy abedefg are fimilar Parts of C and G, after the 
fame manner abed^abedef fimilar Parts of D and 
F, the Part of F involving all the Fadors of the Part of 
D. Thofe I call dijfm'tlar Parts that involve no com- 
mon Root or Fador: Thus abcy 2 s\^ defgh arediffimi- 
lar Parts of the Coefficients C and F. The Sum of all 
the 
