Dibner Library at the Smithsonian

The Dibner Lirary at the Smithsonian's National Museum of American History contains an extremely rich collection of rare mathematical works, so it was a real treat to visit this library. The items we saw were chosen because of their mathematical importance or because they had come up in discussions at the Institute. The works are listed in chronological order. This is Kepler's magnificent contribution to the proto-calculus. The work started when Kepler was buying wine for his (second) wedding celebration. He noted that the vinter measured the capacity of the barrell by puting a stick in the bung hole and measuring the distance to the far edge of the bottom (today it's a max-min promblem). Then Kepler gets carried away and finds the volumes of lots of curious solids of revolution. This work was chosen because of its magnificent frontispiece by Sebastien Le Clerc. It pictures King Louis XIV, his minister Colbert, and, between them Claude Perrault (among many other people). In the background is the Paris Observatory which Perrault designed. Perrault comes up in the history of mathematics because he posed the tractrix problem to Libniz. The frontispiece is reproduced in Bern Dibner, Heralds of Science, numer 84, a work which can be used to produce overheads for use in the history of mathematics class. It was a thrill to see this little paper, Leibniz's first paper on the integral calculus. The paper is a reaction to Craig's little book, which used the Leibnizian differential notation in England before any work using Newton's notation was published. But Craig made a mess of the calculus of Leibniz, so Leibniz showed how easy it was to prove the result of Barrow that Craig botched. This paper contains the first printed integral sign. This work was chosen for its wonderful frontispiece. It shows three Socratic philosophers who have been shipwrecked on the shores of Rhodes. When they come ashore they note some geometric diagrams in the sand and remember the words of Vitruvius: Fear not, for I see the footsteps of men. This work, edited by Gregory, David, 1659-1708 is the first collected edition of the works of Euclid. This work contains a very similar frontispiece to the 1703 Euclid except that the diagrams deal with the conics. We marveled at the skill of the engraver who was able to copy his work over so exactly, only altering the diagrams. To see a manuscript in Newton's hand was a rare first for all of us. Monge, one of the founders of the Ecole Polytechnique, is the father of Descriptive Geometry, a subject that has evolved today into engineering drawing. But in his day it was a military secret. There are many interesting plates in this volume. This famous work of Gauss is easily available in English translation, but it was neat to see the original. He begins by defining congruences for integers and ends with a detailed discussion of which regular polygons can be constructed. This work is noted for its difficulty.
Also on display were portraits of Euler, Kepler, Maclaurin, Tartaglia and Weierstrass. The Dibner Library has a large collection of portraits, but, unfortunately, they are not listed in the computer cataglog. The Smithsonian also has a collection of medals, some of which portray mathematicians. In the gallery outside the Dibner a show entitled "Science and the Artist's Book" was on display. Contemporary artists were asked to interpret a number of classical scientific books. Included was This magnificent volume is the first printed Euclid.

If you have comments, send email to V. Frederick Rickey at rickey@math.bgsu.edu