ARITHMOS XXXXIII  --- Analytic Geometry

At our previous meeting at the Yale Babylonian Collection,

ARITHMOS, YBC 7289, ORESME and Laplace

it was decided to devote our next meeting, November 10-11, 2012, to early work on analytic geometry. Since an earlier meeting discussed some of Descarte's work (1637), we will move on to one of his commentators, Jan de Witt.

The Geometrie has been published in two Latin editions, 1649, and 1659-1661. All three of these volumes are freely available from .
The 1661 volume contains the following works by de Witt:

    Elementa linearum curvarum. Liber primus. Pp. [153]-242.

    Elementa linearum curvarum. Liber secundus. Pp. 243-340.  

Both of these have been translated by Albertus W. Grootendorst:

Jan de Witt’s Elementa Curvarum Linearum. Liber Primus. (Springer, June 16, 2000, ISBN 978-0-387-98748-4).

Jan de Witt’s Elementa Curvarum Linearum. Liber Secundus. (Springer, 2010, ISBN 978-0-85729-141-7).

The Introduction  to Grootendorst's English translation of de Witt's Liber secundus is available on line, and the ARITHMOS fellows should peruse it.

The chosen readings were all from  the  Liber secundus (page numbers refer to the 1661 edition which are reproduced in Grootendorst's translation):
Our next meeting is scheduled for February 2-3, 2013 with March 2-3 as the snow dates. We plan to reading some of the Geométrié of Descartes.


Boyer, Carl B., History of Analytic Geometry, Dover.

Rowen, Herbert H., John de Witt, Grand Pensionary of Holland, 1625-1672. Princeton University Press, 1978.

Ruane, P. N., Review of the English edition of the Secundus. MAA Reviews.

Serfati, M., "Chapter 1: René Descartes, Géométrie, Latin edition (1649), French edition (1637)". In I. Grattan-Guinness and Roger Cooke, editors, Landmark writings in Western mathematics 1640-1940, pp. 1-22. Elsevier. ISBN 0-444-50871-6. This whole chapter is on line.

Swetz, Frank J.  and Katz, Victor J., "Jan de Witt's Elements of Curves," Loci: Convergence. Contains five images of the Secundus with commentary.

October 10, 2012. Fred Rickey