# Talk:The Method of Mechanical Theorems

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## The Method

Some pages of the Method remained unused by the author of the Palimpsest and then they are still -surely forever- lost. Between them, an annonced result was about the volume of the intersection of two cylinders, a figure that Apostol and Mnatsakian have renamed n=4 Archimedian Globe (and the half of it, n=4 Archimedian Dome), whose volume relates to the n polygonal pyramid. This is amusing because the collaboration on indivisibles between Galileo and Cavalieri -ranging between years 1626 to around 1635- has as a main argument the hull and pyramid of the n=infinity dome. So in some sense it is true that the Method is only a theorem back from the modern infinitesimal theory.

See Apostol-Mnatsakanian in American Mathematical Monthly 111, June-July 2004 aditya kalra

## Use of infinitesimals

A citation for "Archimedes disbelieved in the use of infinitesimals" is http://science-student.com/science-news/a-long-lost-text-by-achimedes-found-contains-some-work-on-calculus I can't work out how to put this in the article, but there it is for someone else to do so. 210.55.146.99 08:39, 23 October 2007 (UTC)

- Your link wasn't working but I found the page, while I am loathe to edit someones talk comment, I've fixed it for convenience. Unfortunately it's a rather poor article, with spelling errors in the title and calling him Aristotle near the end. The article does state that he argued against the actual infinite, but then goes on to describe how he used it firsthand. It is clear that he argued against it though, we describe modern use of the infinite excluding the actual as Archimedean. I'll try to dig up the source of this. Nazlfrag (talk) 04:51, 27 June 2008 (UTC)