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.

Luca Paccioli (d. ca. 1514). 1523.
Summa de arithmetica, geometria: proportioni: et proportionalita.
Nouamente impressa in Toscolano, <1523>

Johann Kepler (15711630). 1615.
Nova stereometria doliorvm vinariorvm, in primis Austriaci,
figurae omnium aptissimae; et usus in eo virgae cubicae
compendiosissimus & plane singularis. Accessit
stereometriae Archimedeae supplementum.
Lincii, excudebat J. Plancvs, sumptibus authoris, 1615.
This is Kepler's magnificent contribution to the protocalculus.
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 maxmin promblem). Then
Kepler gets carried away and finds the volumes of lots of curious
solids of revolution.

Claude Perrault (16131688). 1676.
Memoires pour servir a l'histoire naturelle des animaux
Paris : De l'Imprimerie royale, 1676. First published anonymously by the Academie des sciences, Paris in 2 parts in 1671 and 1676.
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.

Gottfried Wilhelm, Freiherr von Leibniz (16461716). 1864.
G. G. L. De geometria reconditaet analysi indivisibilium atque
infinitorum, addenda his quae dicta sunt in Actis a. 1864,
maji p. 233; octob. p. 264; decemb. p. 586.
Detached from Acta eruditorum mensis junii a. MDCLXXXVI, Lipsiae, 1686, p. 292300. 20 cm.
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.

Euclid.
Eukleidou ta sozomena = Euclidis quae supersunt omnia / ex
recensione Davidis Gregorii, M.D., Astronomiae Professoris
Saviliani, & R.S.S.
Uniform Title: Works. Latin & Greek
Oxoniae : E Theatro Sheldoniano, 1703.
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, 16591708 is the first collected edition of the works
of Euclid.

Apollonius, of Perga.
Apollonii Pergaei Conicorum libri octo, et Sereni Antissensis
De sectione cylindri & coni libri duo.
Uniform Title: Konika. Latin & Greek.
Oxoniae, e Theatro Sheldoniano, 1710.
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.

Montmort, Pierre Remond de.
Title: Letter
Imprint: 1718.
Physical Description:
2 items.
Summary: A.L.S. (1718 Mar. 27) to Newton concerning the problem of
trajectories set by the Bernouillis, in French, Latin, and
English, and A.L. (1718 Dec. 18) to Taylor concerning other
scientists that Taylor should know, in French.
Added Entry: Newton, Isaac, Sir, 16421727.
Taylor, Brook, 16851731.
Burndy Library, donor.
To see a manuscript in Newton's hand was a rare first for all of us.

Gaspard Monge (17461818). 1798 or 1799
Title: Geometrie descriptive : lecons donnees aux ecoles normales,
l'an 3 de la Republique / par Gaspard Monge ...
Paris : Baudouin ..., an 7 <1798 or 1799>
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.

Carl Friedrich Gauss, Carl Friedrich (17771855).
Disquisitiones arithmeticae
Lipsiae : In commiss. apud Gerh. Fleischer, jun., 1801.
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.

Farkas Bolyai (17751856).
Tentamen juventutem studiosam in elementa matheseos purae,
elementaris ac sublimioris, methodo intuitiva, evidentiaque
huic propria, introducendi : cum appendice triplici /
auctore professore matheseos et physices chemiaeque publi.
ordinario.
Maros Vasarhelyini, 1832 : Typis Collegii Reformatorum per
Josephum et Simeonem Kali de fels"o Vist., <18321833>
Appendix: scientiam spatii absolute veram exhibens / auctore
Johanne Bolyai: t. 1, 28 p. following p. 502.

Sir William Rowan Hamilton (18051865).
Lectures on quaternions : containing a systematic statement of
a new mathematical method, of which the principles were
communicated in 1843 to the Royal Irish Academy, and which
has since formed the subject of successive courses of
lectures, delivered in 1848 and subsequent years, in the
halls of Trinity College, Dublin : with numerous
illustrative diagrams, and with some geometrical and
physical applications / by Sir William Rowan Hamilton ...
Hodges and Smith ... ; London : Whittaker & Co. ... ;
Cambridge : Macmillan & Co., 1853.
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