$02 Mr. Robertson's Demonstration 
of squares in the rectangle K F is equal to the number of 
units qyp\ and consequently pq = qp. 
Hence it follows that pqrs = spqr; for by the above, 
p q r x s = s yp qr. Also sp qr is equal to psqr ; for sp q r 
= spyqyr = (by the above) p s x q x r. Again, p s q r = 
pqsr ; for psqr=pysqr=pyqsr=pqsr, by the 
above. And if x a =p, x-\-b = q,x + c = r, x-\-d = s t 
x-\ -e — t, &c. then x a y x b y x c yx d xx~+ 7 = 
p qr s t = x -}- a y x -f- b x x -f- c x x e x x -|- d = p q r t s = 
any other arrangement which can take place in the quan- 
tities. 
2. It is evident that each of the quantities a, b> c, &c. will 
be found the same number of times in the compound product 
arising from x-\-axx-{-bxx-\-cxx-{-dxx-\-e, &c. For 
this product is equal to p qr st —p q r s x x -(- e =p qrty 
x + d = pqstyX-{-c=prstyX-\-b = qrstyx-\-a y 
by substituting for the compound quantities, x -j- ■ a, x-j-b, & c. 
their equals p, q, &c. Wherefore, in the compound product, 
each of the quantities a, 6, c, &c. will be found multiplied into 
the products of all the others. 
3. These things being premised, we may proceed to the 
multiplication of the compound quantities a: -{• a, x b, x c, 
&c. into one another ; and in order to be as clear as possible in 
what follows, let us consider the sum of the quantities, a , b , c, &c. 
or the sum of any number of them multiplied into one another, 
as coefficients to the several powers of x, which arise in the 
multiplication. By considering products which contain the 
same number of the quantities a, b, c, &c. as homologous, the 
