Long-lost text shows Archimedes had begun to discover the principles of calculus | Hacker News Reader

Long-lost text shows Archimedes had begun to discover the principles of calculus

sciencenews.org

66 pointsrobg10 comments

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).

I agree with you.

To italicize, use * * around the word.

I think you meant Ramanujan.

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.

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.

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.

There is some good detail in the Wikipedia article.

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

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

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

>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.

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