This is the
talk page for discussing improvements to the
Archimedes Palimpsest article. This is not a forum for general discussion of the article's subject. |
Article policies
|
Find sources: Google ( books · news · scholar · free images · WP refs) · FENS · JSTOR · TWL |
![]() | This article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||||||||||||||||||||||||||||||||||||||
|
According to the Wikipedia entry for Archimedes , the original mathematical treatise, later erased by 13th century religious writers, had been previously penned, in the 10th century AD, i.e. the very era when the scholar Suidas lived. Perhaps Suidas wrote the original mathematical treatise ? 24.143.92.97 ( talk) 04:27, 25 February 2012 (UTC)
To say that it was "discovered" in 1906 makes it sound as if no one knew of its existence before then. It is true that it was not generally known among either mathematicians or historians, but, if I understand correctly, neither was it something that had not been mentioned in print. Heiberg's translation was what made its contents well known, but its existence was hardly a secret. Michael Hardy 18:46 Apr 25, 2003 (UTC)
Yep, the second external link (my isisletter "Did Isaac Barrow read it?") contains an accurate chronology of the discovery compiled from various sources Arivero 15:28, 14 June 2006 (UTC).
I have read that the gold illumination was forged in the 10th century, not the twentieth. Can someone confirm this? — Muckapædia 5h38, 7e Août 2006 (EST)
I removed this because I don't understand the amusement, and the "a theorem behind" phrase. AxelBoldt 22:37, 29 March 2007 (UTC)
The article states: "Essentially then, the method consists in dividing the two areas or volumes in infinitely many stripes of infinitesimal width, and "weighing" the stripes of the first figure against those of the second". Really? So you think Archimedes actually succeeded in dividing the areas/volumes into infinitely many stripes of infinitesimal width? Wow. I am amazed at how stupid you are. Archimedes' method was one of approximation. It is very similar to natural integration by approximation (no trial and error involved). However, that Archimedes used infinitesimals is highly unlikely. Infinitesimal is an ill-defined concept that Archimedes knew nothing about. The term infinitesimal was only coined in the 16 or 17th century. Yet another factually incorrect article by Wikipedia Sysops/Administrators. 70.120.182.243 16:58, 4 July 2007 (UTC)
I don't think he used that word in this text. Nonetheless he used infinitesimals in this text. As for how he did it, just read this page; that tells you how. And he said in this text that these are not complete proofs. I think it was elsewhere that he in effect rejected any attempt to take infinitesimals literally, by stating a sort of Archimedean axiom, as we would now call it. Michael Hardy 02:32, 11 July 2007 (UTC)
Modern integral calculus relies on the fundamental theorem of calculus, which says you can find an integral if you can find an antiderivative. Michael Hardy 17:49, 15 July 2007 (UTC)
There are some specific contexts where it's not vague at all. See non-standard analysis. It's hardly true that it's rarely used in the present day. And as one with much experience teaching calculus, I think it ought to be used a lot more than it is in such freshman-level courses. Michael Hardy 11:45, 16 July 2007 (UTC)
This beautiful article is still lacking of any mention to the strong criticism raised by many historicians on the Palimpsest's operation (to quote one issue, some people think that the analysis on the poor remains of the Stomachion is a series of uncontrolled guesses, where the logic implication has been replaced by "then why not" or "so it could also be that" &c.)-- pm a 11:43, 5 December 2010 (UTC)
The link on Palimpsest seems to be broken.
Greek writing of the photo appears in the Middle Byzantine style, maybe not so much prior to the religious text that has replaced it. Am I wrong? — Preceding unsigned comment added by 84.222.77.231 ( talk) 15:45, 26 June 2011 (UTC) Perhaps Komnenos or Angelus period ?
1229 is the thirteenth century, not the twelfth 68.49.247.221 ( talk) 20:27, 6 July 2012 (UTC)
The following sentence:
In Heiberg's time, much attention was paid to Archimedes' brilliant use of infinitesimals to solve problems about areas, volumes, and centers of gravity.
Has been changed to:
In Heiberg's time, much attention was paid to Archimedes' brilliant use of the method of exhaustion to solve problems about areas, volumes, and centers of gravity.
Archimedes knew nothing about infinitesimals. — Preceding unsigned comment added by 197.64.207.71 ( talk) 07:47, 25 June 2013 (UTC)
Hello fellow Wikipedians,
I have just modified one external link on Archimedes Palimpsest. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
When you have finished reviewing my changes, please set the checked parameter below to true or failed to let others know (documentation at {{
Sourcecheck}}
).
This message was posted before February 2018.
After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than
regular verification using the archive tool instructions below. Editors
have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the
RfC before doing mass systematic removals. This message is updated dynamically through the template {{
source check}}
(last update: 5 June 2024).
Cheers.— InternetArchiveBot ( Report bug) 07:52, 17 October 2016 (UTC)
It seems wrong to me that this section should be much larger that the \\{{main\\}} that it points to. It also reads very oddly. Snori ( talk) 07:55, 10 February 2017 (UTC)
Hello fellow Wikipedians,
I have just modified one external link on Archimedes Palimpsest. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
This message was posted before February 2018.
After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than
regular verification using the archive tool instructions below. Editors
have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the
RfC before doing mass systematic removals. This message is updated dynamically through the template {{
source check}}
(last update: 5 June 2024).
Cheers.— InternetArchiveBot ( Report bug) 10:22, 7 December 2017 (UTC)
I've removed the following speculation "This almost certainly refers to
Rick Adams because of a blogpost by
Michael Shermer where he describes seeing it at a birthday party for
James Randi in the collector's home in Falls Church, Virginia, where Adams (a benefactor and treasurer of the
James Randi Educational Foundation) is known to live.
[1]"
The source given does not name the person owning the palimpsest, even supposing it is
reliable, so any assumption as to their identity is speculative (and, for WP,
original research). Also, as Rick Adams is still alive, it contravenes our
guidelines on information about living persons.
Moonraker12 (
talk)
22:55, 18 December 2018 (UTC)
I've tagged the following assertion "Archimedes often used what are now called Riemann sums" as dubious; there's no source given to back this up (in fact, the whole section is unsourced); so, did Archimedes really work out a method that wasn't re-discovered until the 19th century, and if he did, shouldn't we be calling them Archimedean sums? Moonraker12 ( talk) 23:00, 18 December 2018 (UTC)
The article currently asserts that:
Unable to sell the book privately, in 1998 the businessman's daughter risked a public auction in New York contested by the Greek church; the U.S. court ruled for the auction, and the manuscript was purchased by Jeff Bezos. [1]
However, the given source for this claim asserts merely that:
The identity of the purchases remains secret, although Finch allowed that he is a private American involved in the high-tech industry—specifically not Bill Gates. (The German magazine Der Spiegel reports that the palimpsest’s owner is most likely Jeff Bezos, founder and CEO of the online retailer Amazon.com.)
https://archive.org/details/eurekamanlifeleg0000hirs_c0p0/page/186/mode/2up
This appears to be referring to https://www.spiegel.de/international/world/revolutionary-authentic-stolen-the-story-of-the-archimedes-manuscript-a-490219.html
Typometer ( talk) 21:58, 8 March 2023 (UTC)
References
I find this paragraph in this article:
Archimedes used exhaustion to prove his theorems. This involved approximating the figure whose area he wanted to compute into sections of known area, which provide upper and lower bounds for the area of the figure. He then proved that the two bounds become equal when the subdivision becomes arbitrarily fine. These proofs, still considered to be rigorous and correct, used geometry with rare brilliance. Later writers often criticized Archimedes for not explaining how he arrived at his results in the first place. This explanation is contained in The Method.
Is there some reason to think this is true? A line parallel to the axis of a parabola, drawn through the midpoint of a chord of the parabola, intersects the parabola, so that that point of intersection is one vertex of a triangle whose other vertices are the endpoints of the chord. Archimedes said the area bounded by that chord and the curve has 4/3 the area of that triangle. To show that he looked at the two other chords that are the other two sides of the triangle. With each of those two chords, he constructed a triangle in the same way. He showed that each of those two triangle has 1/8 the area of the first triangle, so that the sum of those two areas is 1/4 the first area. Then he iterated the process, getting The argument in the Palimpsest for the area bounded by the curve and the chord is radically different from that. It does not appear to explain in any way how he found that argument.
Moreover, is there some reason to think somebody criticized him for not explaining how he arrived at that result? That should be cited. And I doubt it can be. Michael Hardy ( talk) 18:39, 3 August 2023 (UTC)
This is the
talk page for discussing improvements to the
Archimedes Palimpsest article. This is not a forum for general discussion of the article's subject. |
Article policies
|
Find sources: Google ( books · news · scholar · free images · WP refs) · FENS · JSTOR · TWL |
![]() | This article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||||||||||||||||||||||||||||||||||||||
|
According to the Wikipedia entry for Archimedes , the original mathematical treatise, later erased by 13th century religious writers, had been previously penned, in the 10th century AD, i.e. the very era when the scholar Suidas lived. Perhaps Suidas wrote the original mathematical treatise ? 24.143.92.97 ( talk) 04:27, 25 February 2012 (UTC)
To say that it was "discovered" in 1906 makes it sound as if no one knew of its existence before then. It is true that it was not generally known among either mathematicians or historians, but, if I understand correctly, neither was it something that had not been mentioned in print. Heiberg's translation was what made its contents well known, but its existence was hardly a secret. Michael Hardy 18:46 Apr 25, 2003 (UTC)
Yep, the second external link (my isisletter "Did Isaac Barrow read it?") contains an accurate chronology of the discovery compiled from various sources Arivero 15:28, 14 June 2006 (UTC).
I have read that the gold illumination was forged in the 10th century, not the twentieth. Can someone confirm this? — Muckapædia 5h38, 7e Août 2006 (EST)
I removed this because I don't understand the amusement, and the "a theorem behind" phrase. AxelBoldt 22:37, 29 March 2007 (UTC)
The article states: "Essentially then, the method consists in dividing the two areas or volumes in infinitely many stripes of infinitesimal width, and "weighing" the stripes of the first figure against those of the second". Really? So you think Archimedes actually succeeded in dividing the areas/volumes into infinitely many stripes of infinitesimal width? Wow. I am amazed at how stupid you are. Archimedes' method was one of approximation. It is very similar to natural integration by approximation (no trial and error involved). However, that Archimedes used infinitesimals is highly unlikely. Infinitesimal is an ill-defined concept that Archimedes knew nothing about. The term infinitesimal was only coined in the 16 or 17th century. Yet another factually incorrect article by Wikipedia Sysops/Administrators. 70.120.182.243 16:58, 4 July 2007 (UTC)
I don't think he used that word in this text. Nonetheless he used infinitesimals in this text. As for how he did it, just read this page; that tells you how. And he said in this text that these are not complete proofs. I think it was elsewhere that he in effect rejected any attempt to take infinitesimals literally, by stating a sort of Archimedean axiom, as we would now call it. Michael Hardy 02:32, 11 July 2007 (UTC)
Modern integral calculus relies on the fundamental theorem of calculus, which says you can find an integral if you can find an antiderivative. Michael Hardy 17:49, 15 July 2007 (UTC)
There are some specific contexts where it's not vague at all. See non-standard analysis. It's hardly true that it's rarely used in the present day. And as one with much experience teaching calculus, I think it ought to be used a lot more than it is in such freshman-level courses. Michael Hardy 11:45, 16 July 2007 (UTC)
This beautiful article is still lacking of any mention to the strong criticism raised by many historicians on the Palimpsest's operation (to quote one issue, some people think that the analysis on the poor remains of the Stomachion is a series of uncontrolled guesses, where the logic implication has been replaced by "then why not" or "so it could also be that" &c.)-- pm a 11:43, 5 December 2010 (UTC)
The link on Palimpsest seems to be broken.
Greek writing of the photo appears in the Middle Byzantine style, maybe not so much prior to the religious text that has replaced it. Am I wrong? — Preceding unsigned comment added by 84.222.77.231 ( talk) 15:45, 26 June 2011 (UTC) Perhaps Komnenos or Angelus period ?
1229 is the thirteenth century, not the twelfth 68.49.247.221 ( talk) 20:27, 6 July 2012 (UTC)
The following sentence:
In Heiberg's time, much attention was paid to Archimedes' brilliant use of infinitesimals to solve problems about areas, volumes, and centers of gravity.
Has been changed to:
In Heiberg's time, much attention was paid to Archimedes' brilliant use of the method of exhaustion to solve problems about areas, volumes, and centers of gravity.
Archimedes knew nothing about infinitesimals. — Preceding unsigned comment added by 197.64.207.71 ( talk) 07:47, 25 June 2013 (UTC)
Hello fellow Wikipedians,
I have just modified one external link on Archimedes Palimpsest. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
When you have finished reviewing my changes, please set the checked parameter below to true or failed to let others know (documentation at {{
Sourcecheck}}
).
This message was posted before February 2018.
After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than
regular verification using the archive tool instructions below. Editors
have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the
RfC before doing mass systematic removals. This message is updated dynamically through the template {{
source check}}
(last update: 5 June 2024).
Cheers.— InternetArchiveBot ( Report bug) 07:52, 17 October 2016 (UTC)
It seems wrong to me that this section should be much larger that the \\{{main\\}} that it points to. It also reads very oddly. Snori ( talk) 07:55, 10 February 2017 (UTC)
Hello fellow Wikipedians,
I have just modified one external link on Archimedes Palimpsest. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
This message was posted before February 2018.
After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than
regular verification using the archive tool instructions below. Editors
have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the
RfC before doing mass systematic removals. This message is updated dynamically through the template {{
source check}}
(last update: 5 June 2024).
Cheers.— InternetArchiveBot ( Report bug) 10:22, 7 December 2017 (UTC)
I've removed the following speculation "This almost certainly refers to
Rick Adams because of a blogpost by
Michael Shermer where he describes seeing it at a birthday party for
James Randi in the collector's home in Falls Church, Virginia, where Adams (a benefactor and treasurer of the
James Randi Educational Foundation) is known to live.
[1]"
The source given does not name the person owning the palimpsest, even supposing it is
reliable, so any assumption as to their identity is speculative (and, for WP,
original research). Also, as Rick Adams is still alive, it contravenes our
guidelines on information about living persons.
Moonraker12 (
talk)
22:55, 18 December 2018 (UTC)
I've tagged the following assertion "Archimedes often used what are now called Riemann sums" as dubious; there's no source given to back this up (in fact, the whole section is unsourced); so, did Archimedes really work out a method that wasn't re-discovered until the 19th century, and if he did, shouldn't we be calling them Archimedean sums? Moonraker12 ( talk) 23:00, 18 December 2018 (UTC)
The article currently asserts that:
Unable to sell the book privately, in 1998 the businessman's daughter risked a public auction in New York contested by the Greek church; the U.S. court ruled for the auction, and the manuscript was purchased by Jeff Bezos. [1]
However, the given source for this claim asserts merely that:
The identity of the purchases remains secret, although Finch allowed that he is a private American involved in the high-tech industry—specifically not Bill Gates. (The German magazine Der Spiegel reports that the palimpsest’s owner is most likely Jeff Bezos, founder and CEO of the online retailer Amazon.com.)
https://archive.org/details/eurekamanlifeleg0000hirs_c0p0/page/186/mode/2up
This appears to be referring to https://www.spiegel.de/international/world/revolutionary-authentic-stolen-the-story-of-the-archimedes-manuscript-a-490219.html
Typometer ( talk) 21:58, 8 March 2023 (UTC)
References
I find this paragraph in this article:
Archimedes used exhaustion to prove his theorems. This involved approximating the figure whose area he wanted to compute into sections of known area, which provide upper and lower bounds for the area of the figure. He then proved that the two bounds become equal when the subdivision becomes arbitrarily fine. These proofs, still considered to be rigorous and correct, used geometry with rare brilliance. Later writers often criticized Archimedes for not explaining how he arrived at his results in the first place. This explanation is contained in The Method.
Is there some reason to think this is true? A line parallel to the axis of a parabola, drawn through the midpoint of a chord of the parabola, intersects the parabola, so that that point of intersection is one vertex of a triangle whose other vertices are the endpoints of the chord. Archimedes said the area bounded by that chord and the curve has 4/3 the area of that triangle. To show that he looked at the two other chords that are the other two sides of the triangle. With each of those two chords, he constructed a triangle in the same way. He showed that each of those two triangle has 1/8 the area of the first triangle, so that the sum of those two areas is 1/4 the first area. Then he iterated the process, getting The argument in the Palimpsest for the area bounded by the curve and the chord is radically different from that. It does not appear to explain in any way how he found that argument.
Moreover, is there some reason to think somebody criticized him for not explaining how he arrived at that result? That should be cited. And I doubt it can be. Michael Hardy ( talk) 18:39, 3 August 2023 (UTC)