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    Re: Finding longitude in the 12th century
    From: Alexandre Eremenko
    Date: 2012 Sep 1, 18:31 -0400

    Dear Lu,
    
    > proves my thesis that it would have been almost impossible to produce a
    > sight reduction method such as HO214 in the 12th century even if the
    > basics of trig were available.
    
    I did not say anything of the sight reduction method.
    "Sight reduction" is solving a spherical triangle.
    This was well known to Ptolemy in II AD.
    
    I was addressing the longitude question.
    
    > looked up "decimal numbers" in Wikipedia and it contains an almost useless
    > history of them, citing obscure civilizations that might have used them
    > three millenia ago, but not giving a whit of history on exactly how and
    > why they displaced Roman numerals in Europe.
    
    The article clearly and correctly says that decimal system was introduced
    in Europe by Simon Stevin in XVI century. The article on "Simon Stevin"
    says in 1585. So it is quite possible that Barentsz did not use it:-)
    
    > Come to think of it, I remember decimals sometimes being
    > called "Arabic numerals"
    
    Because the idea (which apparently originated in India) came to Europe
    through the Arabs .
    
    > So back to the original question -- could someone have determined their
    > latitude in the 12th century?
    
    You probably mean longitude.
    Latitude they could and did find. The cross-stuff was invented in
    the beginning of XIV
    century by Levi ben Gershon, but they had other tools like
    astrolabias.
    
    > The answer seems to be a strong "no" -- at
    > least with respect to any subsequent technique such as lunar distances or
    > the equivalent for star/planet
    
    The answer is the "strong no" unqualified. There were no techniques
    that could be used in 12 century and give sufficient precision.
    On the land, the methods based on the moon could be used IN PRINCIPLE,
    but I am not aware of any actual longitude determination by these methods
    until XVI century. (See my message on Barentsz).
    
    > trigonometry -- the theory may have been known, but practical use of that
    > theory was impossible.
    
    The principle was known, not the theory. The theory of the Moon motion
    reached the needed degree of perfection only in XVIII century, almost
    simultaneously with the invention of chronometer.
    
    This has nothing to do with trigonometry. Trigonometry was well established
    (for calculation of things like HMO) in the Ancient Rome.
    
    Alex.
    
    
    
    
    

       
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