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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): 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): 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!

Daniel J. Curtin (Northern Kentucky University), "Jan Hudde’s Second Letter: On Maxima and Minima - Further Reading - References," Convergence (June 2015)