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The book mentions that Napier discarded this method of calculating
logarithms.  Raising 2 to the power 10000 by hand absolutely boggles
my mind.   I appreciate your explanation which was clear and
demonstrates the genius and perseverance of Napier in knowing when to
change his methodology.

I worked the sqrt of 100000 in about 2 hours.  Of course I knew the
values ahead of time which saved a lot of time checking the work.
I was dismayed with the number of errors I made squaring the terms.
Squaring 7 digit numbers by hand does require rather intense
concentration.  I wonder why Napier settled on 7 decimal places for
his table of logarithms?
Also this leads to the question as to whether Napier or Briggs were
able to find the value of log(2) or log(3) to 7 decimal places or did
that have to wait for Euler.
After receiving my slide rule in the mail and trying a few
calculations, I have decided that weak eyesight precludes this method.
 So tables are once again the practical solution.


On Thu, May 28, 2009 at 10:40 AM,   wrote:
>
> A number with 3011 places must be between 1*10**3010 and 10*10**3010.  Or 
equivalently, between 10**3010 and 10**3011.  Since this is 2**10,000, let's 
take the 10,000th root of both sides.
>
> If lower end of range:
>
>  2**10,000 = 10**3010
>
> take the root by dividing the exponents by 10,000:
>
>  2**(10,000/10,000)=10**(3010/10,000)
>
>  2**1=10**.3010
>
>  2=10**.3010
>
>  log 2 =.3010
>
> If upper end of range, same method;
>
>  log 2 =.3011
>
> So it's somewhere in between.  Why not guess .30105?  In fact, 10**.30105=2.000092126 or so.
>
>
> >
>

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