[ 2 4 8 ] 
alfo even, it mail have two real roots at leaft : becaufe 
the number of dimenfions being even, and the num- 
ber of impofiible roots always even , the number of 
real ones mud be even alfo. 
6. If any equation be divided by the unknown 
quantity minus one of its roots, it will be reduced one 
dimenfion lower. And as every equation contains as 
many roots as it has dimenfions, it follows, 
7. That if you deduCt the number of impofiible 
roots from the whole number of its roots, that is, 
from the number of its dimenfions, the remainder 
will give the number of its real roots. 
8. When you have found by the rulers, what 
thofe real roots are, put the unknown quantity („v) 
equal to each of them, tranfpofe the terms in each 
equation to one fide, multiply all the equations toge- 
ther, and divide the equation propofed by their pro- 
duct ; then make the quotient equal to nothing, and 
you have an equation containing all your impofiible 
roots, without any real ones intermixed. Then 
thofe impofiible roots may be found by the method 
for that purpofe laid down by Monf. de Bougainville 
in his T raite du Calcul integral , in the fifth and fixth 
chapters of his introduction j ahd which is the bed 
method I know of. 
His method confifls in parting the equation into 
two others, of the fame number of dimenfions in- 
deed, but fuch as fhall involve no other than real 
roots ; which real roots you may then find by thefe 
rulers, orotherwife; and from thence you will obtain 
all the impofiible roots of your equation. But becaufe 
few Engliih mathematicians, I fufpeCt, are acquainted 
with 
