Mr. Robertson's new Demonstration 
310 
X 
x + b =q 
1 ^ 
T^jj; -\-abr=zpq; a quadratic equation, or an equation of 
* two dimensions. 
x 4 -c=r 
+b\ a;* 4 -ac lx -\-abc=pqr; a cubic, or an equation of three 
+^J +bci dimensions. 
x 4 —d^z s 
x*-^-a^\ — j - ab 
+Hx’+f 
•j —C I —J ~DC 
~f -d) \-ad 
+bd 
•| -cd. 
x 4 — 
-\-abc ~ 1 
> x* -\-abcd=:pqrs ; a biquadratic, 
( »/'•*' -fuvLLi—jJifij , a uiijuttuidiR/, OR an 
T equation of four di- 
mensions. 
4 -& 4 ’^ 
-j-r Kr 4 -j-fc 
"\~d j — | ~ad 
+ e J "i-bd 
-j -cd 
+ ae 
-j- be 
+ ce 
•j- de~ 
>x 
~J” abc~ 
4~ abd 
4 ~acd 
-J -bed 
3 4“ abe 
4- ace 
4- bee 
4 -ade 
4“ bde 
4“ ede- 
&c. 
4 -abccT\ 
- \-abce j 
>x* -\-abde >x 4 “ abede = pqrst ; a sur- 
4 -aede solid, or an equation of 
•\-bcdej five dimensions. 
6 . From the above it appears, that the coefficient of the 
highest power of x in any equation is 1 ; but the coefficient of 
any other power of x in the same equation consists of a cer- 
tain number of members, each of which contains one, two, 
three, &c. of the quantities a , b, c , &c. Thus the coefficient of 
