go 6 Mr. Robertson’s new Demonstration 
you think the following demonstration worthy the attention 
of mathematicians, you will much oblige me by presenting it 
to the Royal Society. 
Oxford, 
March 21st, 1806, 
I am, &c. 
- A. ROBERTSON. 
1. The binomial theorem is a general expression for any 
power of the sum or difference of two quantities. Thus if n 
be any positive or negative whole number, or vulgar fraction, 
and a , b, be any two quantities, the binomial theorem expresses 
in a series the value of a-\-b\ n , or a—b\ a . 
The binomial theorem is of very extensive utility. Besides 
the advantages derived from it in raising powers and ex- 
tracting roots, it enables us to conduct, with clearness and 
ease, a variety of investigations in the higher parts of algebra, 
which, without its assistance, would become perplexed and 
laborious, 
2. If n be a whole positive number, we can raise x-{-a to 
the power denoted by n, in the following manner, by multi- 
plication. 
