Rare Books in the Classroom

American University, Special Collections, August 12, 2002. 

The learning of mathematics can be enhanced by the introduction of historical materials, for it lets the student see so many things that would not otherwise occur in the classroom. On this visit to the Rare Book Room at American University, we will look at a number of items and will discuss how you teachers can use this experience to enliven your own classrooms.  

The heart of the mathematics collection in the Special Collections section of The American University Library is the Artemas Martin Collection of Mathematical Texts. Artemas Martin (1835-1918) was an inveterate problem solver and book collector. He founded two early mathematics periodicals, The Mathematical Visitor (1878-1894) and The Mathematical Magazine (1882-1884). For information about him see

Patricia R. Allaire and Antonella Cupillari, "Artemas Martin: An Amateur Mathematician of the Nineteenth Century and His Contribution to Mathematics," College Mathematics Journal, Volume 31, Number 1, Pages: 22-34.

What follows is a list of books that we will look at and a few comments about them. 

The first edition of Euclid to appear in English is a magnificent volume (or two, as it is bound at AU). Most impressive is book XI on solid geometry with it's fold up diagrams, one of which is pictured in Katz's A History of Mathematics, p. 365 (you can make a nice overhead from it).  This is the first English edition of Oughtred's Clavis Mathematicae (1637), a work which influenced the young Newton.

Record published an even more famous book entitled The Whetstone of Witte (1557) which has been reprinted as volume 142 of a series entitled The English Experience. Its Record in Early Printed Books Published in Facsimile. It is in this volume that the equals sign is first used. Right below it we find the first equations. The poem on the title pages describes the advantages of studying algebra. The title of the book is a trilingual pun: The Latin word for "whetstone" is "cos" which is similar to the Italian "coss", meaning thing. In the Cossike art the variable was called the thing. Of course you should remember that a whetstone is for sharpening knives, but Record implies that algebra can sharpen your wittes. 

Everyone today has heard of Fermat's Last Theorem. We shall see in this work the original statement of the problem. 

This is an English translation of the first calculus, that of L'Hospital (1696). But more than the words are translated. The differential notation of Leibniz has been replaced by the fluxional notation of Newton. 

This is the first mathematics periodical published in the United States. It was published under the editorship of George Baron, but only one volume and one additional number was ever published. Not surprisingly, it is primarily a problem journal. 

This work was widely used as a textbook in England and the United States. This edition was edited by Robert Adrain (1775-1843) the most important American mathematician in the early nineteenth century. The section on descriptive geometry was likely plagiarized from Claude Crozet.

Chosen as an example of the many calculus texts in the Martin Collection at AU. This one is important in that it was used as a textbook at the United States Military Academy at West Point. Being a translation, it shows the French influence on American mathematics early in the nineteenth-century.

The entire text of this wonderful book is available on the web at
High school students will enjoy looking at this and will learn a great deal. His method of presenting proofs is something that we should emulate on the blackboard. 

Probably the most famous of geometry textbooks. It is a translation of Legendre. 

Davies was the most prolific writer of mathematics textbooks in the nineteenth century. He wrote work at every level, from elementary arithmetics through college level texts. 

In discussing the equations of straight lines, early nineteenth century French and American texts found the slope-intercept form of the line and then spoke of the coefficient of x as "the tangent of the angle the line makes with the axis of x." This shows that the concept of slope had not yet crystalized. The first use of the letter "m" for slope that I have located is in A Treatise on Plane Co-ordinate Geometry (London, 1844) by Rev. Matthew O'Brien. The earliest use of the word "slope" that I am aware of is in the Mathematical Dictionary and Cyclopedia of Mathematical Science (New York, 1855) by Charles Davies and William G. Peck. 

This work has been reprinted by Dover. An interesting annotated bibliography dealing with the problem of squaring the circle. It contains both crazy things as well as important works. Such bibliographies are very useful to the historian of mathematics. This is an example of crank literature. The first clue is that the frontispiece is a picture of the author. The second is that the work is "Printed for the author." The third is that Diagram 16 claims that pi equals 3949/27889 exactly. Serious mathematicians don't do such things. Nonetheless, the book does have value as a curiosity. Students should be shown things like this as a simple exercise in sorting the wheat from the chaff in the vast mathematical literature.
The American University is part of the Washington Research Library Consortium and their catalog is available on the web. You will want to use the "Limits by Location" button so that you are just searching for books at American University.  Unfortunately there seems to be no way to search for all books in the Artemas Martin Collection.
If you have comments, send email to V. Frederick Rickey at   fred-rickey@usma.edu
July 8, 2002.