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Re: Finding longitude in the 12th century
From: Alexandre Eremenko
Date: 2012 Sep 2, 09:48 -0400
From: Alexandre Eremenko
Date: 2012 Sep 2, 09:48 -0400
> 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?? Alex. > On Sat, Sep 1, 2012 at 8:22 PM, Lu Abelwrote: > >> 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" >> *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. >> >> >> >> >> >> >> > > > > > : http://fer3.com/arc/m2.aspx?i=120527 > > >
