Rare Books at the University of Michigan
The University of Michigan
Library started with 3707 volumes (purchased for $5000), including Audubon's
"The Birds of America" (1827-38). It offered little mathematics and grew slowly.
A major improvement came in 1881 when a complete run of Crelle's Journal was
donated. Two faculty made important contributions to the mathematics collection.
Alexander Ziwet, who was on the faculty from 1898 to 1925, worked to improve the
library and contributed a large collection of his own books. Louis C. Karpinski,
on the faculty from 1904 to 1948, gathered many rare volumes for the mathematics
collection. Another important influence occurred in 1964 when Mathematical
Reviews moved to Ann Arbor. Today the mathematics collection at the University
of Michigan is one of the best in the world. The collection of rare mathematics
books is outstanding.
The titles listed below in chronological order were selected by V. Frederick
Rickey, of Bowling Green State University, to show to a history of mathematics
course taught at Michigan State University by Dan Chazan on March 11, 1996. We
would like to thank Peggy Daub, Head of Special Collections and curator of the
mathematics collection at the library for her assistance.
- Euclid
1482 Elementa geometrie
Published in Venice by Erhard
Ratdolt. Uncatalogued.
This magnificent volume is the first printed
Euclid. It is an "incunabula," i.e., printed before 1500 "in the cradle of"
printing. Note the many diagrams in the margins; this was a great innovation and
very well done. The first pages are very worn and then it is clean thereafter;
this indicates the difficulty of Euclid. This work is hard for us to read
because of the many abbreviations used by the printer (they are a holdover from
the manuscript tradition). See Harrison D. Horblit, "One hundred books famous in
science" (1964) for a reproduction of the title page.
- Record, Robert, 1510?-1558.
1557
The whetstone of witte, whiche is
the seconde parte of arithmetike: containyng the extraction of rootes: the
cossike practise, with the rule of equation: and the woorkes of surde nombers.
Special Collection QA33 .R3
It is in this work that the equals
sign was first introduced, "bicause noe .2. thynges, can be moare equalle." Vera
Sanford gives a nice description of this work in the Mathematics Teacher 50
(1957), 258- 266; reprinted in Frank Swetz, "From Five Fingers to Infinity."
This book of Record has been reprinted in 1969 by Da Capo Press as volume 142 in
"The English Experience. Its record in early printed books published in
facsimile," so it is not something that one needs to read, or even should read,
in a rare book room. This series contains a number of mathematica works of
interest.
- Euclid.
<1570>
The Elements of geometrie of the most
auncient philosopher Euclide of Megara faithfully (now first) translated into
the Englishe toung by H. Billingsley, citizen of London; whereunto are annexed
certaine scholies, annotations, and inventions, of the best mathematiciens,
both of time past and in this our age; with a very fruitfull praeface made by
M.I. Dee, specifying the chief mathematicall scieces, what they are, and
whereunto commodious; where, also are disclosed certaine new secrets
mathematicall and mechanicall, untill these our daies, greatly missed. London,
Imprinted by I. Daye <1570>
Special Collection QA31.E88 S732 1570
The first edition of Euclid to appear in English is a magnificent
volume (or two, as it is sometimes bound). Most impressive is book XI with it's
fold up diagrams, one of which is pictured in Katz's A History of
Mathematics, p. 356 (you can make a nice overhead from it). The long preface
to the work has been republished with an informative introduction by Allen G.
Debus, "John Dee. The Mathematical Preface to the Elements of Geometrie of
Euclid of Megara(1570)," Science History Publications, 1975. It includes a nice
portrait of Dee that will make a fine overhead.
- Descartes, Rene, 1596-1650.
1637
Discours de la methode pour bien
conduire sa raison et chercher la verite dans les sciences. Plus La
dioptriqve. Les meteores. Et la geometrie. Qui sont des essais de cete
methode. Par Rene Descartes.
Special Collection Q 155 .D44
An
English translation of the appendix on geometry by D. E. Smith and M. L. Latham
is available from Dover Publications (since a facsimilie of the original French
is included, this is a useful source of overheads). One topic I use from this is
the geometric solution of quadratic equations. Our use of "x," "y," and "z," for
variables and consonants for constants comes from this work of Descartes. So
does our exponential notation. The appendix on optics is also of interested
because of its work on the conics. See "Discourse on Method, Optics, Geometry,
and Meteorology," translated by Paul J. Olscamp (former president of Bowling
Green State University), for the only English translation of the whole work.
- Schooten, Frans van, 1650-1660.
<1646>
Francisci a Schooten
... De organica conicarum sectionum in plano descriptione, tractatus.
Geometris, opticis; praesertim vero gnominicis & mechanicis utilis. Cui
subnexa est appendix, de cubicarum aequationum resolutione.
Special
Collection QB 215 .F76
For reproductions of some of these neat
diagrams see Jan van Maanen, "Alluvial deposits, conic sections, and improper
glasses," in Learn from The Masters, MAA, 1995 or Phil Jones in the 18th NCTM
Yearbook.
- Gregorius a Sancto Vincentio, 1584-1667.
1647
Problema austriacum
plus ultra quadratura circuli
Special Collection QA467 .G82
The
title above comes from the frontispiece of this volume which contains the most
fantastic allegory in the entire history of mathematics (the title page reads
"Opus geometricum quadraturae circuli et sectionum coni"). It shows Archimedes
drawing the diagram for his proof of the area of a circle, behind which are the
Pillars of Hercules which the ancient geometers were not able to get beyond. But
Gregorius did as the putto holding the square frame which focuses the sunbeam
into a circle on the ground illustrate --- he squared the circle. That incorrect
result ruined his reputation, but many important mathematicians read this book.
My favorite result in the book is the conncection between the natural logarithm
and the rectangular hyperbola which is used as our definition of the logarithm.
- Oughtred, William, 1575-1660.
1647
The key of the mathematicks new
forged and filed: together with a treatise of the resolution of all kinde of
affected aequations in numbers. VVith the rule of compound usury; and
demonstration of the rule of false position. And a most easie art of
delineating all manner of plaine sun-dyalls Geometrically taught
Special
Collection QA 33 .O93 E5
The first edition of the "Clavis
mathematicae" appeared in 1631. Its 88 pages contained the essentials of
arithmetic and algebra using an abundance of novel symbolism. "The exposition
was severely brief, yet accurate. He did not believe in conducting the reader
along level paths or along slight inclines. He was a guide for
mountain-climbers, and woe unto him who lacked nerve." So wrote Florian Cajori
in "William Oughtred. A Great Seventeent-Century Teacher of Mathematics,"
(1916), which gives a nice outline of the contents of this book. Interestingly
this was one of the books that Newton read as an undergraduate (on his own, not
as a textbook); John Wallis also learned algebra from it. This copy lacks the
frontispiece portrait of Oughtred which some copies of the 1637 edition contain.
- Diophantus, of Alexandria.
1670
Diophantus Alexandrini
Arithmeticorvm libri sex, et De nvmeris mvltangvlis liber vnvs.
Special
Collection QA 31 .D593 1670
This work, edited by Fermat's son Samuel,
contains Fermat's famous marginal annotations on Fermat. A reproduction of the
page containing the first printed statement of Fermat's Last Theorem appears in
the first issue of "Math Horizons."
- Wallis, John, 1616-1703.
1685
A treatise of algebra, both
historical and practical. Shewing the original, progress, and advancement
thereof, from time to time; and by what steps it hath attained to the heighth
at which it now is. With some additional treatises, I. Of the Cono-cuneus ...
II. Of angular sections; and other things relating thereunto, and to
trigonometry. III. Of the angle of contact ... IV. Of combinations,
alternations, and aliquot parts.
Special Collection QA 33 .W214
There are lots of interesting mathematical results here: The book
contains the first statement of Newton's general binomial theorem (Ch. XCI). He
says clearly that geometric series are sometimes finite (i.e., convergent) and
sometimes not (Ch. XCVI). This work is loaded with historical comments, not all
of which are accurate. See J. F. Scott, "John Wallis as a historian of
mathematics," Annals of Science, 1 (1936),335-357. This copy lacks the
frontispiece portrait of Wallis.
- L'Hospital, marquis de (Guillaume Francois Antoine), 1661-1704.
1696
Analyse des infiniment petits, pour l'intelligence des lignes courbes.
Special Collection QA302 .L691
This lovely book was the first
calculus book ever published --- just 300 years ago. L'hospital's rule, which
was discovered by Johann Bernoulli, was published here for the first time. See
Dirk J. Struik's "A Source Book in Mathematics, 1200-1800" for a translation of
that portion of the work. I think the original proof is much more informative to
students than the usual proof involving Cauchy's mean value theorem. The best
evaluation of the work of L'Hospital is in J. Coolidge's "Great Amateurs of
Mathematics." The title page is reproduced in a paper by Carl Boyer in the
Mathematics Teacher 39(1946), 159-167; reprinted in "Swetz's From Five Fingers
to Infinity."
- Euclid.
1703
Eukleidou ta sozomena. Euclidis quae supersunt omnia.
Special Collection QA 31 .E84 1703
This work, which is edited by
David Gregory, is the first collected works of Euclid. The text is in Latin and
Greek. The work was published at the Sheldonian Theater (which is pictured as
the printers device on the title page), a building designed by Christopher Wren,
a man who would have been much better known as a mathematician had it not been
for the fire of London in 1666. The reason for choosing this work is its
wonderful frontispiece. A very similar frontispiece appeared in a 1710 edition
of Apollonius.
- Cocker, Edward, 1631-1675.
1710
Cocker's Arithmetick: being a
plain and familiar method ... Edition: The eight and twentieth ed., carefully
corrected, with additions. Licensed Sept. 3, 1677. Roger L'Estrange.
Published: London, E. Tracey, 1710.
Special Collection QA33 .C65 1710
- Cowley, John Lodge.
[1758?]
An appendix to the Elements of Euclid,
in seven books. Containing forty-two moveable schemes for forming the various
kinds of solids, and their sections, by which the doctrine of solids in the
eleventh, twelfth, and fifteenth books of Euclid is illustrated, and rendered
more easy to learners than heretofore ...
Special Collection QA31.E88S76
C87 176-
According to information in the 18th NCTM Yearbook by Lao
Genevra Simons, this is probably the 176? edition of the work. Plate XI, The
Exoctoedron or Canted Cube, is shown both flat and folded up into a solid. One
plate on the conics is also illustrated.
- Maseres, Francis, 1731-1824.
1758
A dissertation on the use of the
negative sign in algebra: containing a demonstration of the rules usually
given concerning it; and shewing how quadratic and cubic equations may be
explained, without the consideration of negative roots. To which is added, as
an appendix, Mr. Machin's Quadrature of the Circle. By Francis Maseres.
Special Collection QA 212 .M39
Maseres wrote many books and
included translations of lots of interesting thigs. He is an individual
deserving of scholarly study.
- Dilworth, Thomas 1773
The Schoolmaster's Assistant: Being a
Compendium of Arithmetic Both Practical and Theoretical. The Seventeenth
Edition.
Special Collection
This was the first arithmetic
published in the United States. The title page of this copy is reproduced on p.
15 of "A History of Mathematics Education in the United States and Canada," NCTM
Yearbook #32 (1970). Dilworth was the most popular eighteenth-century arithmetic
in the U.S.
- Gregory, Olinthus, 1774-1841.
1834
Mathematics for practical men:
being a common-place book of ... pure and mixed mathematics, with their
application; especially to the pursuits of surveyors, architects ... and civil
engineers. With numerous engravings. By Olinthus Gregory. Edition: 1st
American from the 2d London ed., cor. and improved
GRAD (at Buhr) Ask at
any library QA37 .G823 1834
On September 25, 1841, instruction began
at the University of Michigan with seven students in classes taught by two
professors: the Reverend George P. Williams for mathematics and science, and the
Reverend Joseph Whiting for Greek and Latin. Textbooks included this work, the
following two items, as well as Davies's "Arithmetic," "Surveying," and
"Descriptive Geometry," and Bridges's "Conic Sections." [Source: NCTM Yearbook
#32, p. 29 in an article by Phillip S. Jones, professor emeritus at the
university, and "Mathematics at the University of Michigan" by Wilfred Kaplan,
in "A Century of Mathematics in America, Part III, edited by Peter Duren et
alia, AMS 1989.]
- Legendre, A. M. (Adrien Marie), 1752-1833.
1836
Elements of
geometry and trigonometry.
GRAD (at Buhr) Ask at any library QA529 .L315
1836
- Davies, Charles, 1798-1876.
1838
Elements of algebra: tr. from the
French of M. Bourdon. Revised and adapted to the course of mathematical
instruction in the U.S., by Charles Davies.
GRAD (at Buhr) Ask at any
library QA154 .D25 1838
Louis Pierre Marie Bourdon (1779-1854) wrote a
treatise on algebra that quickly became very popular in France. This is an
abridged translation. Although rule based, this is a much more serious first
algebra course than any we have today.
- Byrne, Oliver.
1847
The first six books of the elements of Euclid,
in which coloured diagrams and symbols are used instead of letters for the
greater ease of learners.
Special Collection QA451 .B995
If you have comments, send email to V. Frederick Rickey at rickey@math.bgsu.edu
The URL of this web document is
http://www.bgsu.edu/~vrickey/info-on-me/rare-AnnArbor.html