Mathematical Treasures at the Bertrand Library

The following letter was sent by Ed Sandifer to the mathematics faculty following his visit to Bucknell in March 2007.  We are grateful for his permission to reproduce his letter here.

I found six important items in Special Collections of the Bucknell University Library:

       The Assistant Curator, Ms. Williard, was extremely helpful, and I got the impression that, if the Department wanted to prepare an exhibit of these works, the staff at Special Collections would be willing and able to help.

       There are a few basic rules and courtesies of using Special Collections everywhere. Many archives have additional rules, and you should make sure you know them, too. (Library of Congress Special Collections sometimes assigns you an assistant who wears cotton gloves and turns the pages for you. You look at the book through the glass of a display case. Some other collections will issue you a library card and let you check out and take home a copy of the very same book.)

       Rules:

1. Wash your hands before you enter the Archives. If you can’t do that, ask the Librarian where you can do that.
2. Take in as little as you can, usually a pad of paper or a computer, and a pencil.
3. Never a pen. Never even take one out of your pocket. Better yet, leave it at home. Pens can leak and permanently damage irreplaceable objects.
4. Never make copies without permission.

       These rules are to protect the collections, not to restrict access.

1. Mr. Blundevil His Exercises

       This is the treasure of the collection. It is a beautifully bound volume of over 700 pages that covers the complete curriculum of mathematics of the time, starting with numeration, addition, subtraction, etc., and ending with the most difficult mathematics taught at the time (note that this was two years before Descartes published his Geométrie, the mathematics of navigation, calculation of dates and astronomical cycles (mostly forgotten things like the epact and the golden year), and the operation of the “Mathematical Ievvell,” the Astrolabe.
       Note that, at the time, the letters I and J were regarded as the same letter, as were U and V, and that a W was literally a double-u or a double-v. So, “Ievvell” was how Mr. Blundevil spelled “Jewell.”
       The book is full of fascinating details like this.

       This is quite a valuable book because it has three movable “volvelles,” kind of circular paper calculators on pages 315, 720 and 744. Many books of the time are supposed to have volvelles in them, but almost always, all of them are missing, as they are very fragile. This book has all of its volvelles, as well as all of its plates, and since it is in such good collection, it is really quite valuable. I would suggest that, if you want to try to understand these volvelles, you ask the folks in Special Collections to help you make a facsimile.
       The style of the parts of the book that I read are very much like a Catechism. In one type face, the Tutor asks “What is arithmetic?” Then in Gothic type face, we get the answer. This style was quite popular at the time.
       There are several wonderful illustrations and a few fold-out plates, e.g. those on pages 692, 694 and 799.
       Inside the back cover, there is an advertisement for a mathematics tutor named Robert Hartwell.
       Around page 3, there is a curious white residue near the edge of the pages. I’ve never seen such before. It might be an interesting project for someone to figure out what it is.
       There are also a great number of hand notations made in ink in the margins of the book. Somebody a long time ago read the book carefully. Since then, the book has been trimmed and re-bound.

2. Montucla – Histoire des Mathématiques

       This was one of the first modern histories of mathematics and it is very well known. It was published in two volumes in 1758, and republished later in the century in as many as four volumes.
       Your copy once belonged to the Author himself, who made corrections and changes for a later edition. See, for example, pages 85 and 88.
       The book is in French.
       On page 49 we see the story of how the Phoenicians developed the number system used by the Greeks, but based on the Hebrew alphabet instead of the Greek. To represent numbers up to 999, they used the first nine letters of the Hebrew alphabet to represent values 1 to 9, the next nine letters to represent the “decades” 10, 20, ... 90, and the rest of the letters to represent hundreds. With the modern 26-letter English alphabet, we could only represent numbers up to 899 using this system.
       There are lots of wonderful plates, especially at the end of Volume 2, Huygens’ isochronal pendulum, Roberval’s quadrature of they cycloid, Descartes’ mechanical constructions of rational functions, Descartes’ explanation of the rainbow, and lots of others. The book gets as far as Newton, Gregory, Huygens, Halley, Bernoulli (probably Jakob) and, my favorite, Jakob Hermann, Euler’s cousin, 15 years older than Euler.

3. Opere di Galilei     1656    two volumes

       I didn’t look at this book. The contents were collected after Galileo’s death, and I expect that this wasn’t published in Italy because Galileo wasn’t a hero in Italy; he was almost a heretic.

4. Chronology of Antient Kingdoms – Isaac Newton

       Newton died in 1727. His estate was “frozen” for a while as auditors made sure that he had done his job as Warden of the Mint honestly (he had). One of his heirs, John Conduitt, wanted to get some income from Newton’s fame, so he gathered together one of Newton’s favorite projects, the Chronology, and published it just a year after Newton died. Newton died a hero, and the book was very popular.

       You have what seems to be a first edition.

5. Antiquae Musicae Auctores Septem

       This translates as “The ancient music of seven authors” and describes the music theory of the ancients, including Euclid and Nichomachus, though heavily edited by the man who published these two volumes, Marco Meibomius.
       The book is dedicated to Queen Christina of Sweden, the subject of a classic movie and philosophy student of Descartes.
       It is in parallel Greek and Latin.
       Page numbers start again at page 1 with every new author, so things are a little hard to find.
       I particularly liked the Euclid. We all know of Euclid’s Elements. A few other of his works survive, Optics and Data are the best known. The Music is very rare and quite obscure. There are a few theorems around page 25, and some anachronistic music notation around page 65. Meibomius was trying to explain Euclid using a notation that Euclid would not have known.
       I have never heard of this book before, and I suspect that it is quite a treasure, though because it doesn’t have many illustrations, it is likely that the collectors haven’t made it an extremely valuable book.

6. Encyclopédie – 39 volumes, mostly by Diderot and d’Alembert

       This was the Great Project of the European Enlightenment. It covered everything that was important, all laid out in a style and philosophy consistent with the Enlightenment. Only now is it being translated into English.
       It has wonderful essays on calculus, differentiation, and a number of other mathematical topics. I didn’t look at your copy, but I own a couple of the volumes myself.

      I hope all this is interesting to you, and that you can find a way to use these wonderful volumes. I would urge you to be especially careful when handling Mr. Blundevil and Antiquae Musicae. Your Archivists will be delighted to help you.

Ed Sandifer
March 2, 2007