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.
QA31.E8 B6 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 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 (1575-1660), 1647. *The key of the mathematicks new forged and filed: together with a Treatise of
the resolution of all kinds of affected aequations in numbers. With 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,
by Will. Oughtred*.
[There are no copies of this work listed in WorldCat (or OCLC the Online Computer Library Caltagoue), yet there are two copies at American University. Only one has the portrait of Oughtred.]QA33
.O96 1647

- This is the first English edition of Oughtred's
*Clavis mathematicae*(1637), a work which influenced the young Newton.

Rene Descartes (1596-1650), 1649. *Philosophiae naturalis principia mathematica*.
Lugduni Batavorum : Ex Officina Ioannis Maire, 1649.
QA551 .D44 1649

- Bound together here with one of the most important philosophical works of Descartes is the first Latin translation of his Geometrie, the second appendix of his Discourse de la Methode (1637). This work contains commentary by Florimond de Beaune (1601-1652) and Frans van Schooten (1615-1660). It was interesting to compare the bulk of the commentaries in this work with those in the second Latin edition (which we saw later at the Naval Observatory Library).

Diophantus of Alexandria, 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 epistolis*, Tolosae: B. Bosc, 1670.
AU: LIB Special Collections Rare:
QA33.D24 B1 1670 .

- This work contains the first printed statement of Fermat's Last Theorem. Fermat read the 1620 edition of Diophantus and wrote his famous comments in that work, no doubtless lost. This edition edited by Fermat's son Samuel.

Newton, Isaac (1642-1727), 1769.*
Universal arithmetick: or, A treatise of
arithmetical composition and resolution. Written in Latin by Sir Isaac Newton.
Translated by the late Mr. Ralphson; and rev. and cor. by Mr. Cunn. To which is
added, a treatise upon the measures of ratios, by James Maguire, A.M. The whole
illustrated and explained, in a series of notes, by the Rev. Theaker Wilder*,
London, Printed for W. Johnston, 1769. AU: LIB Special Collections Martin:
QA35 .N564 .

- Newton's most widely read work.

Maria Gaetana Agnesi (1718-1799), 1801*
Analytical institutions in four books:
originally written in Italian / By Donna Maria Gaetana Agnesi ... Tr. into
English by the late Rev. John Colson ... Now first printed, from the
translator’s manuscript, under the inspection of the Rev. John Hellins*,
London : Printed by Taylor and Wilks, 1801. AU: LIB Special Collections:
QA35 .A2.

- A wonderful work. It should be reprinted. For details see my "Agnesi vs. Euler: Out with the old, in with the new."

L'Hospital, Guillaume (1661-1704), 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: Printed for William Innys, 1730. AU: LIB
Special Collections Martin:
QA302 .S877 1730

- This is an English translation of the first calculus book. It is a double translation: From French to English and from Leibnizian notation to Newtonian.

Playfair, John (1748-181), *1814
Elements of geometry: containing the first six
books of Euclid, with a supplement on the properties of the circle, the
intersections of planes, and the geometry of solids / by John Playfair*, 2d
American ed. with improvements. Boston, Printed by T. B. Wait and Sons for
F. Nichols, 1814. AU: LIB Special Collections Martin:
QA451 .P6 1814

- A famous geometry book that appeared in many editions.

J.-L. (Jean-Louis) 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*.
QA303 .B752 1828

- 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.

Bézout, Etienne (1730-1783), 1836*.
First principles of the differential and
integral calculus, or The doctrine of fluxions, taken chiefly from the
mathematics of Bézout, and translated from the French for the use of the
students of the university at Cambridge, New England*, Boston, Hilliard, Gray
& co., 1836. AU: LIB Special Collections Martin:
QA303 .B57 1836

- An interesting calculus book.

Euclid, edited by
Byrne, Oliver (1810-1880), 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.

- The entire text is on the web. The AU library has a dozen books by Byrne. This one is expensive as the publisher has become famous for excellent printing.

Carroll, Lewis, (1832-1898), 1879. *Euclid and his modern rivals*,
London, Macmillan and Co., 1879.
QA28 .D6

- This work has been reprinted by Dover. Carroll's monogram is on the half-title.

S. C. (Sylvester Clark) Gould (1840-1909), 1888.*Bibliography on the polemic problem, What is the value of*
π, Manchester, N.H., 1888.
466 .G697 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.
QA467 .F96 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.
Individuals interested in this topic should consult
*Mathematical Cranks*(1994) and*The Trisectors*(1994), both by Underwood Dudley.

The American University is part of the Washington Research Library Consortium. You can search for books in the entire Consortium or just at American University via http://www.library.american.edu/ . 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