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    Re: Finding longitude in the 12th century
    From: John Huth
    Date: 2012 Sep 2, 08:04 -0400
    I'm trying to recall from memory JK Wright's article "Latitude and Longitude in the Middle Ages".   He made some quotations about using eclipses to find longitude, but I don't think there were any concrete examples.   The concept had been around prior to the middle ages for sure.    

    Longitudes in that era were largely. if not exclusively, figured from dead reckoning. The trick was understanding which prime meridian was used in any given table.  

    BTW, trig functions were mostly done with geometric constructions that could be found on the backs of quadrants and astrolabes.   

    The earliest use that I'm aware of of using eclipses for longitude was the attempt by Columbus on his last voyage when marooned in St. Annes' Bay in what is now Jamaica.   He used an ephemeris publish by Regiomontanus. 

    On Sat, Sep 1, 2012 at 8:22 PM, Lu Abel <luabel@ymail.com> wrote:
    You're right, Alex, I did substitute "latitude" for "longitude" in my note.   Bad typo....

    But the question remains.   Could someone in the 12th century, burdened by Roman numerals and pen-and-paper calculations, have determined his longitude, even on land much less at sea? 

    Yes, Barentz did do an excellent job of determining his longitude, as you noted.   But what post 12th century knowledge was required to do that?

    Sent: Saturday, September 1, 2012 3:31 PM

    Subject: [NavList] Re: Finding longitude in the 12th century

    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

    > 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.


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