infinite Series x+ ~ + A- + + y + Sec. 899 
the remainder thereby obtained will be nearly equal to 
the propofed infinite fenes x+— + + z- + -- + 
4 
&C. Qj E. I. 
example of the foregoing method of fumming the faid 
infinite feries. 
3. As an example of this method of finding the value 
of the feries x + ^ + — + — + -- + 4 - + See. let us fup- 
23456 r 
pofe x to be equal to 7 9 -. 
Then we fhall have 1 -x — 1 - T 9 - = T '-, and — - =10, 
Now, fince the logarithm of 1 o in bkiggs’s Syftem of loga- 
rithms is 1, the logarithm of the 1,000, 000, 000, oooth 
root of 10 mull be the 1,000, 000, 000, oooth part of 1, 
or muft be = .000,000,000,001. This logarithm is 
too fmall to be found in the common tables of loga- 
rithms, which go only to feven places of figures; and 
therefore the number correfponding to it, that is, the 
1, 000, 000, 000, oooth root of 10, cannot be found by 
the help of thofe tables; but it may be found in the 
manner following. The 1,000, 000, 000, oooth root of 
1 o is a number that is fornewhat, and but a very little, 
greater than 1. That number, therefore, and 1 will repre- 
fent two ordinates to the axis, or afymptote, of a logarith- 
mick curve that are very nearly contiguous to each other : 
whence it follows, that the fub-tangent of the curve will 
5 T 1 bear 
