Mr. Robertson's Demonstration 
3 ° 4 « 
of the quantities of a , b, c. See. Thus the coefficient of the 
third term of any equation, is made up of members, each of 
which contains two of the quantities only, as, a b -j- a c -f b c, 
the coefficient of the third term in the cubic equation. Ancf 
indeed, not only from inspection, but also from considering 
the manner in which the equations are generated, it is evi- 
dent, that each member of any coefficient has as many of the 
quantities in it, as there are terms in the equation preceding 
the term to which it belongs. Thus, ab c + a.b d -p a c d -f- 
bed is the coefficient of the fourth term in the biquadratic,, 
each of the members has three quantities in it, and three terms 
precede that to which they belong. 
5. When any equation is multiplied in order to produce the. 
equation next above it, it is evident that the multiplication by 
x produces a part in the equation to be obtained, which has the 
same coefficients as the equation multiplied. Thus, multiplying 
the cubic equation by x we obtain that part of the biquadratic 
which has the same coefficients as the cubic : the only effect 
of this multiplication being the increase of the exponents of x 
by 1. 
6 . But when the same equation is multiplied by the quan- 
tity adjoined to x by the sign- -f, each term of the product, in 
order to rank under the same power of x, must be drawn one- 
term back. Thus when the first term of the cubic is multi- 
plied by d, the product must be placed in the second term of the. 
biquadratic. When the second term of the cubic is multiplied 
by d , the product must be placed in the third term of the bi- 
quadratic : and so of others. 
7. As the equation last produced is the product of all the 
compound quantities x -\ - a, x b, x c, Sec. into one ano- 
