Any cylinder having for its base the greatest of the circles in the sphere, and having its height equal to the diameter of the sphere, is one and a half times the sphere
The order is the one given in J.L. Heiberg's definitive edition, [Archimedes, ``Opera Omnia,'' with commentary by Eutocius, edited by I.L.~Heiberg and additional corrections by E.S.~Stamatis, B.G.~Teubner, Stuttgart, 1972]. The bracketed numbers represent the conjectured historical order in which the papers were written. Recent opinion is that ``Measurement of the Circle'' was an early work.
An excellent translation of this edition is
[Archim`ede, ``Oeuvres, 4 vol.,'' texte 'etabli et traduit
par C. Mugler, Les Belles Lettres, Paris, 1970--71].
Every mathematician knows that the only people who do history of math are the ones who can't do math, either because they're too old, or were just never good enough. So why spend time looking at the works of Archimedes when you should really be spending your time writing papers so you can finally get that job you always wanted? Here are my answers:
Much has been written about the life of Archimedes but few details are actually known. Even the one information about his family is conjectural. In ``The Sand Reckoner,'' there appears in the manuscripts the passage: ``Feid'ia d`e to~u >Ak'o'upatros,'' which make no sense. F.~Blass made the conjecture [Ast. Nach. #104 (1883), p. 255] that this is actually: ``Feid'ia d`e to~u >amo~u patr`os,'' which means ``our father Phidias.'' The reference is to the estimate given by Pheidias that the sun is 12 times larger than the moon, so this would imply that Archimedes' father was an astronomer.
Reviel Netz has proposed the theory that his name might be derived from
the Greek ``m~hdos'', which means cunning, so that combined with the usual
meaning of ``archi'', his name means
``master of cunning.'' This is confirmed in the Greek to French
dictionary [A.~Bailly, ``Abr'eg'e du dictionaire Grec
Francais, Hachette, Paris, 1901] which gives approximately
the same meaning based on the Greek words
``'arqw'' and ``m'hdomai''. This clearly implies that the name
Archimedes is a pseudonym, thus much less is known about him
than can be believed. Moreover, this is consistent with
the hypothesis that he wanted
to be remembered for his intellectual contribution.
Nevertheless, the cultural impact of Archimedes is impressive.
``The Great Seal of the State of California was adopted by the Constitutional Convention of 1849. The Roman goddess of wisdom, Minerva, has at her feet a grizzly bear and clusters of grapes representing wildlife and agricultural richness. A miner works near the busy Sacramento River, below the Sierra Nevada peaks. The Greek motto
Eurika(I have found it) refers to either the miner's discovery of gold or the expected entrance of California as a state of the Union. Near the upper edge of the seal are 31 stars representing the number of states with California's anticipated admission in 1850.''
The 1998 movie gave the first known mention of Archimedes' wife.
Thus, one of the character recounts the story that when Archimedes was stuck trying to analyze the contents of the golden wreath, his wife convinced him to relax by taking a bath, which led him to make his discovery about the principle of floating bodies.
The problem with this design is that it is completely contradictory to
the legacy of Archimedes. In the first place, the evidence as given in
Plutarch indicates exactly how Archimedes wanted to be remembered
``His discoveries were numerous and admirable; but he is said to have requested his friends and relations that, when he was dead, they would place over his tomb a sphere containing a cylinder inscribing it with the ratio which the containing solid bears to the contained.''
Latin translation by William of Moerbeke, ca. 1270 = Codex B of Heiberg.
The translations of William of Moerbeke were responsible for much of the retransmission of Greek works to Western Europe. Thus, Thomas Aquinas and other scholars of the 13th century, became acquainted with the works of Aristotle through his translation.
Latin translation by Jacobus Cremonensis, ca. 1458.
This manuscript was discovered in 1899 at the monastery of the Holy Sepulchre at Jerusalem. Mathematical symbols were recognized and the eminent Danish philologist J.L.~Heiberg, who had edited the works of Archimedes, Euclid, etc., was soon contacted. Heiberg went to Constantinople in 1906 to examine this document. What he found was a 10th--century palimpsest, a parchment containing works of Archimedes that, sometime between the 12th and 14th centuries, had been partially erased and overwritten by religious text. Heiberg managed to decipher the manuscript and found that it included a text of ``The Method,'' a work of Archimedes previously thought lost. (The story of the transmission of Archimedean manuscripts given in the book of Dijksterhuis reads like a chapter from ``The Maltese Falcon'').
The palimpset was soon lost once again, but reappeared recently and was sold at auction at Christie's by an unknown seller and bought by an unknown buyer for $2,000,000 on October 29, 1998, see the report of Fred Rickey, a mathematician at West Point. This gave scholars the opportunity to examine it for the first time in almost 100 years, as described by Fred Rickey:
``When we arrived Sunday afternoon, I asked where the manuscript was and headed right for it. It was in a glass case. One of the Christie's people came over right away to see if I needed help. I responded that I knew precisely what I was looking at and why it was important, but we struck up a nice conversation about the manuscript. The work was open to the page displayed on the cover of the catalogue. That I immediately noted this impressed the woman (I neglected to ask her name, but she knew a lot about the manuscript and I suspect it was Hope Mayo --- will check that out Thursday).
Soon someone was opening the case to put in a little sign about the manuscript and the woman asked if I would like to examine it more carefully while the case was open. Indeed I would, I said. She took it out of the case and placed it on a pair of foam covered wedges on the table. Got a real good look at. Was free to turn pages and examine it. Of course, my first interest was in the Method.
It was exceptionally difficult to read. I could see the Archimedian text where there was no overtext of the Euchologion, but it was very difficult for me to see much with my poor eyesight. The woman said several times that the light there was very poor, but I was not convinced. I could see that there were diagrams there, but could barely make them out. What I did not previously realize is that Heiberg could not make them out either and so the diagrams in the printed versions of the Method are by Heiberg.
The text is in poor condition. There are signs of fire damage and plenty of evidence of mold (now inert, I was told). There are holes in some pages, but, all in all, considering it is a millennium old, the vellum pages are easy to turn.
It was a real thrill to get to examine this manuscript and I look forward to being there for the sale. I certainly hope that it goes to a library or museum where scholars can examine it.''
Princeton University was going to make a bid to buy the manuscript, but backed out when the Greek Orthodox church made a claim that they were the rightful owners. In fact, they made an attempt to reclaim the palimpsest as indicated by the following press release from Christie's, October 29, 1998:
``Christie's is pleased to inform its clients that the Federal Court in New York last night denied a motion by the Greek Orthodox Patriarchate of Jerusalem to enjoin this afternoon's sale of the Archimedes Palimpsest. The judge ruled that under the applicable law our consignor has clear title to sell the manuscript, and the sale will take place as scheduled.''
Returning this document to the church is absurd. What would they do with it. Perhaps they wanted to overwrite it again... In any case, here is a description of the auction as given by Fred Rickey:
``The auction began promptly at 2 with a rereading of the press anouncement. It was announced as Lot 1, The Archimedes Palimpsest, and a photo of one leaf was shown on a screen. The auctioneer announced that he had a bid of 480,000. Immediately the bid was 500,000 and then it went up by increments of $50,000 to one million. The Christie's staff was on the phones with half a dozen potential buyers, but I only saw one of them bid. Three or four people in the room placed bids. I did not know any of them and it was even hard to tell who was bidding. At $1m the bids went up in increments of $100,000 until the bidding reached $1,800,000. There was some pause, then a (non-standard) bid of $1,850,000. Then 1.9m. Again the auctioneer took his time, looking carefully for more bids, giving the bidders time to think. Then a bid of $2,000,000 and another pause. One bidder said he was thinking, but the auctioneer said "we have to more on, there are more books to sell." Another pause, another call for bids. Then, with a crack of the hammer and the announcement "sold to the gentelman on my right" it was over. Ellapsed time: less than five minutes.
There was considerable bussle in the room. The person behind us identified the buyer as Simon Finch, a London dealer, who had bought many books during the morning portion of the sale.
I did not leave the room immediately, so missed an imprompt news conference by Felix de Marez Oyens, the Head of the Manuscript Department at Chrisite's. He revealed that Simon Finch had purchased the book for a private American, who was not Bill Gates.''
Recently, the Walters Museum in Baltimore, MD, managed to track down the anonymous buyer and managed to convince this person to loan the manuscript for exhibit from June 10 to September 5, 1999:
``International news of the manuscript's sale last October set of a chain of events that would result ultimately in the Palimpsest's temporary display at the Walters. Walters director Gary Vikan, a Byzantine scholar, was intrigued by the Palimpsest and, upon reading the news, charged Walters curator of manuscripts and rare books William Noel with a top-priority mission: to locate the manuscript and arrange for an exhibition. Noel's detective work revealed that a London book dealer who represents the privated collector is a friend and colleague of The Walters.
Realizing the importance of the Archimedes Palimpsest, the private collector, who wishes to remain anonymous, was already in search of a venue through which he could share his valuable new acquisition with the public. With one of the world's finest and largest manuscript collections, The Walters, he soon learned, would be an ideal partner in preparing the work for exhibition and interpreting its importance to museum visitors. `We are so privileged to be able to share the Palimpsest,' said Vikan.''
This image is how their web site portrays Archimedes:
In my opinion this exhibit would do much better to replace the display of the palimpsest, which can only be read by an extremely limited number of experts, by a translation of Archimedes works. This has an obvious implication about the character of the buyer, who has probably never tried to read or understand Archimedes, even in translation.
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