( ) 
IV. Afecond Letter from Mr. Colin M' Laurin, 
frofejfor of Mathematkks in the Unherfity of 
Edinburgh andF. % S. to Martin Polices, £/j} 
concerning the <I(oots of Equations, with the De~ 
monjiration of other ^ules in Algebra ^ being the 
Continuation of the Letter publifhed in the 
Philofophical Tranfadtions, N“ 394. 
Edinburgh, April 19th, I7r9, 
SIR, 
I N the Year 1725', I wrote to you that I had a Me- 
thod of deinonflrating Sir IJ^nac Rule con- 
cerning the iinpoffible Roots of Equations, deduced 
from this obvious Principle, that the Squares of the 
.Differences of real Qiiantities muff always be politive ; 
and fome time after, 1 fent you the firfl Principles of 
that Method, which were publifhed in the Phihfophu 
cal f ran/ anions for the Month May ^ 1726. The 
Defign I have for fome Time had ofpublifliing a Trea- 
tife of Algebra, where I propofed to treat this and fe- 
yeral other Subjeds in a new Manner, made me think 
it unneceffary to fend you the remaining Part of that 
Paper. But fome Reafons have now determined me 
to fend you with the Continuation of my former Me- 
thod, a fliort Account .of two other Methods in which 
1 have treated the fame Subjed, and fome Obfervations 
on Equations that I take to be new, and which will, 
perhaps, be more acceptable to you than what relates 
to the imaginary Roots themfelves. Belides Sir Ifaac 
Neixjtons Rule, there arifes from the following gene- 
ral 
V 
