Talk:The Method of Mechanical Theorems

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)

Suggest moving this page
to "The Method", so it can be listed with the rest of his works.Likebox (talk) 16:48, 9 January 2009 (UTC)


 * The Method is a disambiguation page. One of the items listed is "The Method of Mechanical Theorems]], which directs to Archimedes Palimpsest. Michael Hardy (talk) 17:45, 10 January 2009 (UTC)


 * Yes, that's the problem--- the work is being conflated with the most notable surviving copy. The palimpset is about the object, not the work itself. This page talks about the content of the work. Perhaps this could be "The Method of Mechanical Theorems" or "Archimedes' Mechanical Method"?Likebox (talk) 19:38, 10 January 2009 (UTC)
 * From the style guide WikiProject Mathematics/Proofs, here are two lengthy passages which I think have not been followed here:
 * "Unlike textbooks, Wikipedia does not strive to provide an axiomatic introduction to mathematics. Thus it is not necessary for a Wikipedia article to prove every fact that is mentioned. Our best articles include references to good textbooks that the interested reader can consult for an axiomatic presentation of the field."
 * "In particular, WP:NOTTEXTBOOK applies. If the proof can be found verbatim in any standard textbook on a subject, then it is better off transwikied to a project such as Wikibooks, Wikiversity, or ProofWiki. There is also no point in presenting a novel proof not appearing before in print, because it falls afoul of WP:OR.These necessary conditions have not been very controversial"
 * Mr Serjeant Buzfuz (talk) 10:34, 22 June 2024 (UTC)
 * It’s the lack of citations for the proofs that is my concern. As far as I can tell, those proofs are not found in the text being cited. Mr Serjeant Buzfuz (talk) 10:37, 22 June 2024 (UTC)

That's an essay that doesn't really summarize consensus of the math project. The style guide reads: "This is an encyclopedia, not a collection of mathematical texts; but we often want to include proofs to explain a theorem or definition. A downside of including proofs is that they may interrupt the flow of the article, whose goal is usually expository. Use your judgment; as a rule of thumb, include proofs when they expose or illuminate the concept or idea; don't include them when they serve only to establish the correctness of a result." Here it is clear that proofs aren't being gratuitously included. We are summarizing and explaining Archimedes' method. We include a detailed explanation and proof of just one of the propositions. Two more are only sketched. Tito Omburo (talk)

Proof is far from clear or easy to follow
The proof for the First proposition in the palimpsest is pathetic. It is by no means convincing and has large gaps in it. It is redundant to state that Archimedes had to show that point I is the center of gravity of the triangle. I counted 3 uses of the word "suffices". To my superior mind, this raises a bright red flag. Either fix the proof or just be honest enough to say that you don't know. May I suggest either of the illustrious Dr. Michael Hardy or Dr. Arthur Rubin, provide a sound and "easy to follow" proof? I will check back in several weeks and see if either has been able to accomplish the task. May the odds be ever in your favour. 166.249.134.226 (talk) 18:31, 17 June 2012 (UTC)

In the part of "the area of parabola"
"This type of method can be used to find the area of an arbitrary section of a parabola, and similar arguments can be used to find the integral of any power of x, although higher powers become complicated without algebra." that part of the text, this erroneous or incomplete, since neither arquimedes, nor any of the authors cited in the text say that, it would be good to cite that comment. to corroborate that information, or at least specify the types of buildings needed to reach what is this saying. — Preceding unsigned comment added by Sheldoniano (talk • contribs) 17:59, 23 October 2016 (UTC)

Added "Original research" tags
The five sections which explain Archimedes' propositions do not cite any sources. They read as if the editor has produced these proofs to illustrate how Archimedes' propositions work. For example, the first line in the section on the area of a parabola begins: "To explain Archimedes' method today, it is convenient to make use of a little bit of Cartesian geometry, although this of course was unavailable at the time." That sounds like a professor explaining it to a class. A similar reference to coordinate geometry is found in the first line of the section dealing with the volume of a sphere. The mathematical notation used in several of the sections is modern, not ancient Greek, and is clearly an attempt to explain Archimedes' work. Overall, this reads like a series of modern proofs to illustrate Archimedes' propositions, and is likely original research. Mr Serjeant Buzfuz (talk) 02:00, 24 August 2022 (UTC)


 * I added "Original research" tags back in 2022; they were deleted by an IP editor in 2023.  I"ve added the tag again, and this time I've listed this article at No Original Research Noticeboard. Mr Serjeant Buzfuz (talk) 22:21, 14 June 2024 (UTC)