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.

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. 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. 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. 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. 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. 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. 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. 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." 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. 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." 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. 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 wrote many books and included translations of lots of interesting thigs. He is an individual deserving of scholarly study. 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. 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.] 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.

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