( ^*0 ) 
' peded greater things from his pregnant and fagacious 
Wit. For he was fcarce xo Years of Age when beheld 
thefe Correfpondencies with Mr. Crabtrie And at the 
Age of z3. he was killed at Marflori’H^oor-Eattle, on 
July X. 1644 fighting for King Chnrles]. His Father 
was Henry Gtfeoigne Efq; of Middleton, between Leeds 
and Wakefield. 
IV. An Attempt towards the Improyement of the Me^ 
thod of approximating, in the ExtraStion of the 
^ots of Equations in Numbers. IBy Brook 
lor. Secretary to the %oyal Society. 
I N Phil, Tran No. xro. Dr. Halley, now Secretary of 
the Royal Society, has publifli’d a very compendious 
and ufeful Method of extrading the Roots of afleded 
Equations of the common Form, in Numbers. This 
Method proceeds by affuming the Root defired nearly 
true to one or two Flaces in Decimals f which is done 
by a Geometrical Conftrudion, or by fome other con- 
venient way) and correding the Aflumption by com- 
paring the Difference between the true Root and the 
affumed, by means of a new Equation whofe Root is 
that Difference, and which he (hews how to form from 
the Equation propofed, by Subflitution of the Value 
of the Root fought, partly in known and partly in un- 
known Terms, 
In doing this he makes ufe of a Table of Produds 
(which he calls Speculum Analyticum,) by which he com- 
putes the Coefficients in the new Equation for finding 
the Difference mentioned. This Table, I obferved, 
was formed in the fame Manner from the Equation 
pro- 
