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 (18351918) was an inveterate problem solver and book
collector. He founded two early mathematics periodicals, The Mathematical
Visitor (18781894) and The Mathematical Magazine (18821884). 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: 2234.
What follows is a list of books that we will look at and a few
comments about them.

Euclid (fl. ca. 300 BC). 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 Iohn Daye, 1570.
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).

William Oughtred (15751660). 1637.
The Key to the Mathematik.
[There are no copies of this work listed in OCLC (Online Computer Library Caltagoue), yet there are two copies at American University, neither of which is in their computer catalogue. Only one has the portrait of Oughtred.]
This is the first English edition of Oughtred's Clavis Mathematicae (1637), a work which influenced the young Newton.
 Robert Record (1510?1558). 1668.
Record's arithmetick, or, The ground of arts : teaching the perfect work
and practice of arithmetick, both in whole numbers and fractions, after a
more easie and exact form then in former time hath been set forth.
AU Special Collections Martin: QA33 .R31 1668.
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.
 Pierre de Fermat (16011665). 1670.
Diophanti Alexandrini Arithmeticorum libri sex, et De numeris
multangulis liber unus ; cum commentariis C. G. Bacheti v. c. &
obseruationibus d. P. de Fermat ... Accessit Doctrinae analyticae inuentum
nouum, collectum ex varijs eiusdem d. de Fermat episto,
AU Special Collections Martin: QA33.D24 B1 1670.
Everyone today has heard of Fermat's Last Theorem. We shall see in this work
the original statement of the problem.
 Edmund Stone. 1730.
The method of fluxions both direct and inverse: the former being a
translation from the celebrated Marquis De L'Hospital's Analyse des
infinements petits and the latter supply'd by the translator, E. Stone,
London 1730. AU Special Collections Martin QA302 .S877 1730.
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.
 The Mathematical correspondent. NewYork : Sage and Clough, 1804.
AU Special Collections Martin QA1 .M426
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.
 Charles Hutton, (17371823). 1822.
A course of mathematics for the use of academies, as well as private
tuition. . . . To which is added as Elementary essay on
descriptive geometry. By Robert Adrain. New York, 1822.
AU Special Collections Martin QA37 .H99 1822.
This work was widely used as a textbook in England and the United States.
This edition was edited by Robert Adrain (17751843) the most important American
mathematician in the early nineteenth century. The section on descriptive
geometry was likely plagiarized from Claude Crozet.

J.L. (JeanLouis) Boucharlat (d. 1848). 1828.
An elementary treatise on the differential and integral calculus
Cambridge : W. P. Grant, 1828.
Translation of Elemens de calcul differentiel et de calcul integral.
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 nineteenthcentury.

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,
London, W. Pickering, 1847. AU Special Collections Martin QA451 .B9.
The entire text of this wonderful book is available on the web at
http://www.math.ubc.ca/people/faculty/cass/Euclid/byrne.html
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.
 Charles
Davies (17981876). 1850.
Elements of geometry and trigonometry: translated from the French of A.M.
Legendre by Daniel Brewster: revised and adapted to the course of
mathematical instruction in the United States, New York, 1848. AU
Special Collections Martin QA529 .D24 1848.
Probably the most famous of geometry textbooks. It is a translation of
Legendre.
 Charles
Davies (17981876). 1850.
Elementary algebra: embracing the first principles of the science,
New York 1845. AU Special Collections Martin QA152 .D257 1850
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.
 Francis
H. Smith (18121890). 1874.
An elementary treatise on analytical geometry, translated from the
French of J.B. Biot, for the use of the cadets of the Virginia Military
Institute, at Lexington, Va., and adapted to the present state of
mathematical instruction in the colleges of the United States. AU
Special Collections Martin. QA551 .B63 1874.
In discussing the equations of straight lines, early nineteenth century
French and American texts found the slopeintercept 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 Coordinate 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.

Carroll, Lewis, (18321898). 1879.
Euclid and his modern rivals,
London, Macmillan and Co., 1879.
This work has been reprinted by Dover.

S. C. (Sylvester Clark) Gould (18401909). 1888.
Bibliography on the polemic problem, What is the value of ... , Manchester, N.H., 1888.
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.

Rufus Fuller, 1893.
A double discovery. The square of the circle.
Boston, MA, Printed for the author, 1893.
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 fredrickey@usma.edu
July 8, 2002.