

Long-lost text shows Archimedes had begun to discover the principles of calculus - robg
http://www.sciencenews.org/view/generic/id/8974/title/A_Prayer_for_Archimedes

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likpok
This is intriguing, but not necessarily surprising. People have been
rediscovering calculus for ages.

It does bring to mind the question of what /else/ has been lost to the ages,
and how far ahead we would be right now without it. Like Ramujan, brilliance
is not limited to the wealthy; just that the application of it often is (the
wealthy can afford the time/energy to become educated, etc).

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tomjen
The most interesting thing that has been lost to history, would properly be
some of the works of Aristotle, as the western worlds understanding of science
was bootstrapped from his works during the reformation.

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dice
I thought this had been known for a while?

I recall discussing in a class that Archimedes was known to have approximated
integrals and may have even known enough about limits to have derived integral
calculus.

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ewiethoff
Article subtitle is "A long-lost text by the ancient Greek mathematician shows
that he had begun to discover the principles of calculus." This has been known
for several decades, ever since Heiberg transcribed some of the text (I don't
know how much), per the article.

I refer you to _The History of the Calculus and Its Conceptual Development,_ a
1949 book by Carl B. Boyer, reprinted by Dover Publications [ISBN 0486605094].
Boyer writes several pages about Archimedes' method of exhaustion, notions of
the infinitesimal, and so on. The main footnote reads:

For the works of Archimedes in general, see Heiberg, _Archimedes opera omnia_
and T. L. Heath, _The Works of Archimedes._ For Archimedes' Method, see T. L.
Heath, _The Method of Archimedes, Recently Discovered by Heiberg_ ; Heiberg
and Zeuthen, "Eine neue Schrift des Archimedes"; and Smith, "A Newly
Discovered Treatise of Archimedes."

Boyer is clearly using Heiberg's work on the Archimedes Palimpsest.

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tokenadult
There is some good detail in the Wikipedia article.

<http://en.wikipedia.org/wiki/Archimedes_Palimpsest>

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pixcavator
The bottom line is you can’t do calculus without algebra.

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tokenadult
Have you looked at how Newton presented the results of calculus in the
Principia?

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pixcavator
>Have you looked at how Newton presented the results of calculus in the
Principia?

No. But I did now and in the light of the new information I would like to
rephrase myself: you shouldn’t do calculus without algebra.

