I am very interested in rare books, so I was exceptionally thrilled to see the Archimedes Palimpsest this past weekend. It was on display at Christie's auction house in New York City and will be sold this Thursday. This text is invaluable to historians of mathematics because it contains the only known text of the Method of Archimedes and the only known Greek text of his work On Floating Bodies.
The October 27 Science Times section of the New York Times has an article about the Archimedes Palimpsest (with some nice pictures). This is the first thing that I have seen in the Times about it, except for a mention of the sale in a Christie's ad last week. The claim of the Greek government on the manuscript is mentioned there. Mathematicians quoted are Sherman Stein, who recently finished a book about Archimedes, and Chris Rorres, an amateur Archimedes scholar at Drexel. My wife, Joy, and I met some of his relatives when we went down to see the manuscript on Sunday, but I had never heard Rorres' name before, and was also surprised to hear that Stein is writing about Archimedes.
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.
I will now give a rather longish description of the make up of the manuscript. Before going down to Christie's, I purchased a copy of the catalogue and studied it carefully. It has a very careful technical description of the codex (a manuscript book), but I had difficulty comprehending it, so I made my own model of the book. Perhaps by describing it you will gain some feeling for what a superb scholarly accomplishment Heiberg gave us.
Today the codex consists of pages which are 195 mm tall and 150 mm wide. I made a model which is roughly half that size. Take four sheets of 8.5 by 11 paper and fold them along the long side. This will produce a little booklet (a quire) of 8 leaves (16 pages). On each of these pages two columns of text were written. A number of these quires (we don't know how many) were sewn together to form the original Archimedian manuscript in the 10th century. Later, probably in the 13th century, some monk, who did not value the mathematics, decided to use the precious velum of the manuscript (the book of Archimedes cost --- literally --- one sheep for each 4 leaves) to produce a Euchologion (a prayer book). He took the book apart and cut the pages where they were folded in the gutter of the book. This produces a number of 8.5 by 5.5 sheets (in my model). These were scrubbed clean (this is the etymology of the Greek word "palimpsest") so that a new text could be written on them. Fortunately for us, the scrubbing did not completely eradicate the original text. Now take four of the smaller sheets and fold them in half along the longer side to make a quire of the Euchologion.
That does not sound too complicated, but it gets worse. When the pages were scrubbed clean the original order was not preserved. The quire of the Euchologion where the Method begins consists of 4 sheets; two from the quire where the Method was originally and two from another quire. The Method began at the top of the second column of a sheet; this is now at the bottom of folio 46 of the Euchologion, with the text running from the edge of the book to the gutter. The bottom of this sheet was folded up to create folio 43. The bottom of the first column of the Method (in the original) is now on the back (verso) of f43 with the text running vertically from the gutter to the edge. The second column of text (originally the left column of the back of the sheet where the Method began) now starts at the bottom of folio 46v; read to the gutter and then turn to the recto of f43 and continue from gutter to edge. The third column of the original is at the top of f46v and continues on the top of f43. Whew, we have gotten through one page of the original manuscript of the Method. Next turn to folio 57 (remember the pages of the original were used in a random order) where the text is at the top and read from edge to gutter; then turn to the top of f64v and continue from gutter to edge (this page was folded the opposite way as the first). Well, that is probably enough of a description to have you hopelessly confused. I could not have written the above without my model in front of me (and I can't swear that I have it right even now).
Now that you have made a little booklet that is 5.5 inches tall and 4.25 wide you should write the Euchologion in it. This text will run horizontally across the pages (in one column); underneath that text is the Archimedes, with the lines now running vertically (and in two columns) --- depending on which page you are looking at you will have to turn the text either clockwise or counterclockwise to have the Archimedian text right side up (which way you turn it depends on which way the monk turned the original page). I actually wrote out several pages, using black ink for the Archimedian text and red for the Euchologion. It is a true mess, almost impossible to read.
Making this half scale model helped me a lot. Of course it helped me understand how the book was made, but more importantly it helped me understand how much work Heiberg had to do to decipher the palimpsest.
PS. Also on display at Christie's were the books for the Haskell F. Norman Library sale which will also take place Thursday. These were primarily works on psychology and medicine, but there was some mathematics, including several editions (but not a first) of Newton's Principia and Bolyai's Tentamen of 1829. I was especially pleased to examine a first edition of the Disquisitiones Arithmeticae of Gauss for I have read section VIII on regular polygons. I have previously seen copies on display but this was my first chance to look through one. Another treat was to see Phillip Jourdain's copy of Whitehead and Russell's Principia Mathematica. This was also a first edition.
Fred Rickey is professor of mathematics at the U. S. Military Academy at West Point.
MAA Online is edited by Fernando Q. Gouvêa (firstname.lastname@example.org). Last modified: Wed Oct 28 17:57:21 -0500 1998