2 $o Mr. Wilson’s jEss^y on the 
differences must have both equal roots, and consequently be re- 
ducible by the reasoning in Art. 11, 12, and 13. Again, 
three quantities, however distinct in themselves, give a set of 
differences marked with a peculiar relation, any two of them 
being equal to the third; ( a , b, c,) being three quantities, 
(a — b -{- b — c — a — c). Also, if the three quantities be so cho- 
sen originally as to have their sum equal nothing, one of them 
must necessarily equal in magnitude the sum of the remaining 
two; and therefore, whether taken simply or summed in pairs, 
their relative magnitudes must remain the same. Again, four 
quantities, of any sort whatever, may be pursued to a constant 
relation, though somewhat more remote, and grounded upon 
very different causes; viz. ( a , b, c, d,) being four quantities, 
from their combinations by pairs ( ab , ac, ad, be, bd, cd,) six in 
number, added together two by two, thus, 
( ab cd) 
( ac -j- bd) 
( ad -|- be) 
three quantities are formed, sufficiently distinguished from the 
group of similar combinations to be found separately, as will 
be shewn hereafter. And also, if the four quantities are origi- 
nally so taken as to have their sum equal to nothing, their 
sums in pairs, though six in number, will be reduced to three 
in effect; for, if [a -f- b -j- c -f- d= o), by transposition, 
[a -f b = — c — d) 
(a -{• c=. — b — d ) 
(a d= — b — c) 
i. e. three of the six must be merely the negatives of the other 
three ; which relation, if they are squared, will become equality, 
so that the number of distinct squares will be only three. These 
