Jan Hudde’s Second Letter: On Maxima and Minima - Further Reading - References

Daniel J. Curtin (Northern Kentucky University)

Further Reading

Information about Hudde’s life and a detailed explanation of the contents of the second letter are in [Curtin], which uses the examples that appear in the original. Jeff Suzuki’s nice article [Suzuki] also covers these ideas and puts them in a broader context. I know of only one translation of the second letter, which is into Dutch [Grootendorst]; the notes are useful even to those of us whose Dutch is minimal indeed.


[Curtin] D. J. Curtin, “Jan Hudde and the Quotient Rule before Newton and Leibniz,” College Mathematics Journal, 36 (4) (2005), 262-272.

[Descartes] René Descartes, Geometria, with notes by Florimond de Beaune and Frans van Schooten, Fridericus Knoch, Frankfurt am Main, 1695. A complete photocopy is available at Gallica (Bibliothèque Nationale de France): http://gallica.bnf.fr/ark:/12148/bpt6k57484n. For Hudde’s Second Letter, see pages 507–516 (Screens 523–532). Photo images of a 1683 edition of the text, published in Amsterdam, are available at e-rara (ETH-Bibliothek, Zürich): http://dx.doi.org/10.3931/e-rara-24189. Images (pages) 507–516 contain Hudde’s Second Letter.

[Grootendorst] A. W. Grootendorst, “Johan Hudde’s ‘Epistola secunda de maximis et minimis’.” Text, translation, commentary (Dutch), Nieuw Archief voor Wiskunde, vol. 5 (1987), series 4, 303-334.

[Schooten] Frans van Schooten, Exercitationum Matematicorum, Elsevier, Batavia, 1657.

[Suzuki] Jeff Suzuki, “The Lost Calculus (1637-1670): Tangency and Optimization Without Limits,” Mathematics Magazine, vol. 78, (2005), 339-353.


The author wishes to express his gratitude to the reviewer who greatly improved the translation, correcting several errors and suggesting many improvements. Any remaining errors are, however, the author’s own!