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Re: Finding longitude in the 12th century
From: John Huth
Date: 2012 Sep 2, 09:57 -0400
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:
I read somewhere that the error was 18 degrees.
> 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.
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??
Alex.
>> ------------------------------
> 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
> : http://fer3.com/arc/m2.aspx?i=120527>>
>>
>> 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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