Ancient Babylonians Used Geometry That Anticipated Calculus

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Ancient Babylonians Used Geometry That Anticipated Calculus

By Erik Gregersen
In an article published in the January 29, 2016, issue of Science, Mathieu Ossendrijver, a historian of science at Humboldt University in Berlin, describes how Babylonian astronomers between 350 and 50 BCE used geometric methods thought to have been invented 1,400 years later to calculate the motion of Jupiter.

The Babylonians in effect constructed a graph with velocity across the sky as the vertical axis and time as the horizontal axis. By calculating the area under a curve on such a graph, one can obtain the total distance an object has traveled across the sky. In the case of Jupiter, the Babylonians described its motion as what looks like a trapezoid on the graph. They then calculated the trapezoid’s area. Their geometric methods were very similar to the Merton theorem, which was discovered by mathematicians at Oxford’s Merton College in the early 14th century and proved graphically by French bishop Nicholas Oresme around 1361. Such methods are a precursor to calculus.
Ancient Babylonians Used Geometry That Anticipated Calculus

the paper

http://science.sciencemag.org/content/sci/351/6272/482.full.pdf

Wow, really cool!
 
yeah---ok every DELTA-----anticipates calculus--------sir issac newton and I are INCENSED
 
One wonders how many times there were people that were on the verge of major discoveries, and others failed to follow up, and it took many centuries for the development to happen once again.
 
One wonders how many times there were people that were on the verge of major discoveries, and others failed to follow up, and it took many centuries for the development to happen once again.

Rocks-----I was a slightly bored kid in school------tried to sit in the BACK of the room so that I could keep a book on my lap-------long ago----I was about 11----in the
fifth grade-----I grabbed a book---from an available shelf------The book was about
a person upon whose head an apple fell------Sir Isaac Newton. On the flyleaf there
was a quotation-------"IF I HAVE SEEN FURTHER THAN OTHERS IT IS BECAUSE I HAVE STOOD ON THE SHOULDERS OF GIANTS"--------I was no genius but somehow the quotation GRABBED me and I copied it into my notebook---------I refuse
to tell you HOW LONG AGO ----I was 11---------virtually prehistoric and I had no idea
what "CALCULUS" was----------When that horror hit me-------I remembered that
miserable guy who INVENTED IT and those DAMNED GIANTS
 
The ancients were no slouches; that's one of the reasons we're still around.

As I have aged I marvel that the "latest" is not necessarily the "greatest". Logic is not the play ground of the modern human only. Dough nuts maybe, but not logic.
 
The ancients were no slouches; that's one of the reasons we're still around.

As I have aged I marvel that the "latest" is not necessarily the "greatest". Logic is not the play ground of the modern human only. Dough nuts maybe, but not logic.

doughnuts-----fried dough-----seems to show up as various forms of
flat bread----POORI (indian) is fried in oil or ghee----sometimes it is
sweetened----I think-----but no yeast
 
The ancients were no slouches; that's one of the reasons we're still around.

As I have aged I marvel that the "latest" is not necessarily the "greatest". Logic is not the play ground of the modern human only. Dough nuts maybe, but not logic.

doughnuts-----fried dough-----seems to show up as various forms of
flat bread----POORI (indian) is fried in oil or ghee----sometimes it is
sweetened----I think-----but no yeast


Yes Rosie, but cops don't like it. That is our, the modern touch, sugar, which is the rage. Dentists love it also.:dance:
 
The ancients were no slouches; that's one of the reasons we're still around.

As I have aged I marvel that the "latest" is not necessarily the "greatest". Logic is not the play ground of the modern human only. Dough nuts maybe, but not logic.

doughnuts-----fried dough-----seems to show up as various forms of
flat bread----POORI (indian) is fried in oil or ghee----sometimes it is
sweetened----I think-----but no yeast


Yes Rosie, but cops don't like it. That is our, the modern touch, sugar, which is the rage. Dentists love it also.:dance:

Indians love sweets too. Please keep this quiet-------I love indian cuisine--
but not their version of "SWEETS"-----too much cardamom.----I do like AMERICAN
DOUGHNUTS (too damned much)
 
The ancients were no slouches; that's one of the reasons we're still around.

As I have aged I marvel that the "latest" is not necessarily the "greatest". Logic is not the play ground of the modern human only. Dough nuts maybe, but not logic.

doughnuts-----fried dough-----seems to show up as various forms of
flat bread----POORI (indian) is fried in oil or ghee----sometimes it is
sweetened----I think-----but no yeast


Yes Rosie, but cops don't like it. That is our, the modern touch, sugar, which is the rage. Dentists love it also.:dance:

I am not sure when and how refined white sugar was invented-----but it may
have been a Mediterranean or African thing
 

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