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    Re: napier and logarithms
    From: J Cora
    Date: 2009 May 28, 21:33 -0700

    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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