John Wallis, 1616-1703

A special meeting of ARITHMOS will be held at the home of Fred Rickey (ask for directions: fred-rickey@usma.edu ) on May 17. Our purpose is twofold:

• To read some selections from A Treatise on Algebra (1685) by John Wallis.
• To bid goodbye to Amy Shell-Gellasch who is moving from West Point to Germany.

The schedule, which will be very relaxed, will be somewhat as follows:

• Noon. Lunch for early arrivals at a local restaurant.
• 2:00.  Informal conversation. Read some Wallis.
• 5:00.  More informal conversation, with wine.
• 6:00.  Dinner.
• Sometime:  Library tour.

The selection of texts has not yet been made [[ update: see list immediately below ]], but portions dealing with Newton's work on the Binomial Theorem are on the list. Your suggestions would be welcome.

I have been told that these do not print from your browser. Rather you should save them to your machine and then print them. When you do this, I suggest that you number them like I have below. Some of the pages have no page number and so it will be nice if we have a standard way of referring to them. I would like to thank Sheila H. Biles of the Special Collections and Archives Division of the United States Military Academy Library for preparing these images for us.

• Title page.
  • T.
• Table of contents
  • C1, C2, C3, C4, C5.
• Preface
  • P1, P2, P3, P4, P5, P6, P6a, P7, P8, P9.
  • This has a quick history of algebra. 
• Chapter XCI. The doctrine of Infinite Series, further prosecuted by Mr. Newton
  • Pp. 330, 331, 332, 333
  • This the important part as it contains the first announcement of Newton's Binomial Theorem for fractional exponents.
• Chapter XCVI. Of infinite progressions, geometrical
  • Pp. 347, 348, 349, 350, 351, 352, 353, 354, 355.

If you plan to attend, please email me and I will post you (send your snail address) a copy of the readings.

The work to be discussed is

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 now it is. With some additional treatises, I. Of the Cono-cuneus; being a Body representing in part a Conus, in part a Cuneus. II. Of Angular Sections; and other things relating thereunto, and to trigonometry. III. Of the angle of contact; with other things appertaining to the Composition of Magnitudes, the Inceptives of Magnitudes and the Composition of Motions, with the Results thereof. IV. Of combinations, alternations, and aliquot parts. By John Wallis. London, Printed by J. Playford, for R. Davis, 1685.

The English text is available on microfilm in Early English books, 1641-1700 : 402:29, 854:14, and so could be in your school's library.

The 1693 Latin text of the Treatise on Algebra is available on line. It contains a good deal of information not in the English text.

BIBLIOGRAPHY

The following are a few selected items relating to John Wallis and his Treatise on Algebra. Reading the DSB article by Scriba and the chapter of Oxford figures by Flood and Fauvel is encouraged before our meeting. The book by Scott remains the most comprehensive source. If you know other things that should be included, let me know (but this is not intended to be a comprehensive list of references related to Wallis).

Feingold, Mordechai, chapter 6, pp. 359-448 of The History of the University of Oxford, vol. IV, Seventeenth-century Oxford, Clarendon Press, Oxford, 1997,  contains "a full and broad account of the context of mathematical and scientific studies over this period at Oxford" according to Flood and Fauvel, 2000. I have not seen this, but have ordered a copy via ILL.

Flood, Raymond, Fauvel, John, "John Wallis," pp. 97-115 in Oxford figures, Oxford Univ. Press, Oxford, 2000.

Jesseph, Douglas M., Squaring the Circle: The War Between Hobbes and Wallis, University of Chicago Press, 1999.  Favorably reviewed by David Graves (Elmira College) on MAA Online. I have ordered a copy.

Scott, Joseph Frederick, "John Wallis as historian of mathematics," Annals of Science, 1 (1936), 335-357.

Scott, Joseph Frederick, "The Reverend John Wallis, F.R.S. (1616-1703)" Notes and Records of the Royal Society of London, Vol. 15. (Jul., 1960), pp. 57-67.   Available on JSTOR.

Scott, Joseph Frederick, The mathematical work of John Wallis, D.D., F.R.S. (1616--1703). Second edition. With a foreword by E. N. da C. Andrade. Chelsea Publishing Co., New York, 1981. xi + 240 pp. (1 plate). $14.95. ISBN 0-8284-0314-7. First edition was 1938.  MR 83m:01024.

Scriba, Christoph J., "The autobiography of John Wallis, F.R.S." Notes and Records of the Royal Society of London, Vol. 25, No. 1. (Jun., 1970), pp. 17-46.   Available on JSTOR.

Scriba, Christoph J., "Wallis, John," in the Dictionary of scientific biography, Vol. 14,  pp. 146-155, Scribner's, New York, 1976.

Stedall, Jacqueline A., "Of our own nation: John Wallis's account of mathematical learning in medieval England,", Historia Mathematica, 28 (2001), no. 2, pp. 73--122. MR 2002e:01012. A very scholarly treatment of some of the early historical chapters in the Algebra.

Posted May 1, 2003. Send comments to fred-rickey@usma.edu .