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    Re: Finding longitude in the 12th century
    From: John Huth
    Date: 2012 Sep 2, 09:57 -0400
    Yes, he was way off on longitude.   I forget the exact amount, but 18 degrees is certainly the right order of magnitude.

    I agree that someone else probably attempted using the eclipse method prior to Columbus, I'm just not aware of it.   I've done a bit of toying around with water clocks to understand their likely accuracy.    If you're trying for an interval of, say, 6 hours, which would be necessary for the eclipse method, I reckon that with some care, you might be able to get within about one and a half degrees (6 minutes).   

    On Sun, Sep 2, 2012 at 9:48 AM, <eremenko@math.purdue.edu> wrote:

    > 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.

    I read somewhere that the error was  18 degrees.
    But it would be very interesting to know whether this was indeed
    the earliest attempt in history.

    I do not mean only seamen, but also geographers/astronomers.
    The principle which was known for 1400 years at least was tested
    by Columbus for the first time??


    > On Sat, Sep 1, 2012 at 8:22 PM, Lu Abel <luabel---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?
    >>   ------------------------------
    >> *From:* "eremenko---purdue.edu" <eremenko---purdue.edu>
    >> *To:* NavList@fer3.com
    >> *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
    >> 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.
    > View and reply to this message: http://fer3.com/arc/m2.aspx?i=120527

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