ARITHMOS XXXXIII --- Analytic Geometry

At our previous meeting at the Yale Babylonian Collection,

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

http://gallica.bnf.fr/ .

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):

- Pp. 243 - 248. This is the first work on equations of straight
lines but is far different than what we do today as de Witt dealt only
with positive line segments (and hence only the first quadrant is
considered). We read and discussed all of this material.

- Pp. 249 - 258. Discussion of the parabola. We read and discussed pages 249-250 and then got bogged down because terminology from the Liber primus was being used.
- We considered pp. 159 - 169 of the Liber primus. De Witt lays out numerous geometrical definitions which give his point of view. At first we had trouble with this terminology, but the "score card" on page 162 helped. The Liber primus was hard reading.

- Finally we the dealt with pages 255 - 257 of the Liber secundus, which dealt with parabolas.

- We had planned on reading pp. 263 - 265 and 304 - 318, but time ran out.

REFERENCES:

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

fred.rickey@me.com