Second Cafe of the Cubick Equation x z -qx~r, 939 
to fhew the truth of the foregoing reafonings. Their 
difference is only — — parts of an unit, which is only 
the 13426 th part of 8.055,810, See. or the true value 
of x. 
40. N. B. This equation x 3 - 50^=1 20 expreffes the 
f elation between the diameter of a circle and three chords 
in it that lie contiguous to each other, and together take 
up a femicircle, and form a trapezium of which the dia- 
meter of the circle is the fourth fide. For if the three 
' 
chords are called b, k and /, and the diameter of the cir- 
cle is called x, the relation between them will be ex- 
-bb' 
prefled by the cubick equation ~kk 
-tt 
x X- zbkt , which. 
if the numbers 3, 4 and 5 are fubftituted inftead of the 
J ' 
letters b , k, and t, will become x z ~ ^ox=i20. See Sir 
Isaac newton’s Arithmetica Univerfalis r Edit. ad. 
J722, page 10 1. 
EXAMPLE II. 
41. Let it be required to find by means of the fame f cries 
. the root of the equation x % - x-\> 
Now in this equation q is = i ? -*■ is -f, ~ k». : p j* 
-or ee, is = and — is « ~, which is greater than 
6 A 2 
or 
