Resources on Leibniz (under construction)
The archival situation of the works of Gottfried Wilhelm Leibniz is specific in comparison with many other mathematicians. Apart from the dissertation De arte combinatoria, written in his youth (1666), he never published a single treatise of mathematics during his lifetime. It is only with Gerhardt’s edition of the Mathematische Schriften (Leibniz 1849–1863), starting in the middle of the 19th century, that some of the hitherto unknown mathematical material was progressively discovered for the first time. Louis Couturat completed Gerhardt’s work in 1903 with his Opuscules et Fragments inédits, in which he gave access to many other unpublished mathematical works (Leibniz 1903). From this overall picture, one might get the impression that for a century or so, we have been in possession of a good overview of Leibniz’s unpublished work in mathematics, but this is far from true: in fact, to this day, more than half of Leibniz’s mathematical work still remains completely unpublished. Moreover, when one looks at the published half, typically the editions of Gerhardt and Couturat, one soon realises that they were not accomplished according to modern scientific standards. Hence the project, which did not arise until the beginning of the 20th century, to directly confront the difficulty and publish all of this material in chronological order and with all the variants. This is the origin of the so-called “Akademie Edition”, which now constitutes the standard for any rigorous access to the Leibniz texts (Leibniz 1923–). The main resources on Leibniz’s works are listed below, together with their online versions when available (more on the history of Leibniz’s editions here):
Akademie Edition
Leibniz, G. W. [1923–]: Gottfried Wilhelm Leibniz, Sämtliche Schriften und Briefe, herausgegeben von der Berlin-Brandenburgischen Akademie der Wissenschaften und der Akademie derWissenschaften zu Göttingen, Reihe 1–8, Darmstadt, Leipzig, Berlin, 1923–.
Preprint of the manuscripts edited in collaboration with the Mathesis team
Vol. I, General, political and historical correspondence
Vol. II, Philosophical correspondence
Vol. III, Mathematical, scientific and technical correspondence
Vol. IV, Political writings
Vol. V, Linguistic and historical writings (yet to be started)
Vol. VI, Philosophical writings
Vol. VII, Mathematical writings
Vol. VIII, Scientific, medical and technical writings
Gerhardt’s Editions
Leibniz, G. W. [1849–1863]: Leibnizens Mathematische Schriften, ed. C. I. Gerhardt, Berlin: A. Asher and Halle: H.W. Schmidt, 1849–1863.
Vol. I, Vol. II, Vol. III, Vol. IV, Vol. V, Vol. VI, Vol. VII.
Leibniz, G. W. [1875–1889]: Gottfried Wilhelm Leibniz, Die philosophischen Schriften, ed. C. Gerhardt, Halle; H. W. Schmidt, 1875–1889.
Vol. I, Vol. II, Vol. III, Vol. IV, Vol. V, Vol. VI, Vol. VII.
Other Editions
Leibniz, G. W. [1903]: Opuscules et Fragments inédits de Leibniz: extraits des manuscrits de la Bibliothèque royale de Hanovre, ed. Louis Couturat, Paris: Alcan, 1903. Available online.
Leibniz, G. W. [2018]: Mathesis universalis. Écrits sur la mathématique universelle, Paris: Vrin, textes introduits, traduits et annotés sous la direction de D. Rabouin.
Useful Web Resources
Mathesis Team’s Contributions
Arthur, T. W. and Rabouin, D. [2020]: “Leibniz’s syncategorematic infinitesimals II: their existence, their use and their role in the justification of Differential Calculus”, Archive for History of Exact Sciences (2020), vol. 74 (5), pp. 401-443.
Bella, S. [2021] « De l’intraitable à l’indéterminé : entre calcul et géométrie, réflexions leibniziennes autour de ⁰⁄₀ (1700-1706) », in Philosophia Scientiae, « Mathématiques et philosophie chez Leibniz à la lumière des manuscrits inédits », n. 25-2, juin 2021, p. 21-45.
Bella, S. [forthcoming 2021]: « /Magis morale quam mathematicum/, L’attestation volée*(mai 1705 – mars 1706) », Studia Leibnitiana.
Bella, S. [forthcoming 2021]: La (Re)construction française de l’analyse infinitésimale de Leibniz (1690-1706), Paris, éditions Garnier, collection Histoire et Philosophie des Sciences.
Brancato, M. [2017]: « The Young Leibniz and the Principle of Contradiction: Adoption and Use Between Philosophy and Mathematics » in A. Lalanne (ed.), Actes du colloque: Principia rationis. Les principes de la raison chez Leibniz (1646-1716), Lumières, Presses universitaires de Bordeaux, Bordeaux 2017.
Brancato, M. [2021]: « Leibniz’s Binary Algebra and its Role in the Expression and Classification of Numbers », in Philosophia Scientiae, « Mathématiques et philosophie chez Leibniz à la lumière des manuscrits inédits », n. 25-2, juin 2021, p. 71-94.
Crippa, D. (with P. Milici) [2019]: « A Relationship between the Tractrix and Logarithmic Curves with Mechanical Applications », The Mathematical Intelligencer (online first).
Crippa, D. [2019]: « One String Attached: Geometrical Exactness in Leibniz’s Parisian Manuscripts », in V. De Risi (ed.), Leibniz and the Structure of Sciences, Berlin, Springer 2019 pp. 203-252.
Debuiche, V. [2019]: « Expression and Analogy in Leibniz’s Philosophy » in L. Herrera (ed.), Äusserungen des Inneren. Beiträge zur Problemsgeschichte des Ausdrucks, Berlin, De Gruyter 2019, p. 65-83.
Debuiche, V. [2021]: Leibniz et l’expression, Presses Universitaires de Provence, Aix-en-Provence 2021.
Debuiche, V. and Rabouin, D. [2019]: « On the plurality of spaces in Leibniz” in Leibniz and the Structure of Sciences. Modern and New Essays on Logic, Mathematics, Epistemology, in V. De Risi (ed.) “Boston Studies in Philosophy and History of Science”, Berlin, Springer 2019, p. 171-201.
Debuiche, V. Rabouin, D. [2019]: « Unité et pluralité de l’espace chez Leibniz », Archiv für Geschichte der Philosophie, vol. 101, no. 3, 2019, pp. 345-375.
De Risi, V. [2018]: « Leibniz’s Geometry of Space and the Theory of Perspective », in Leibniz Lectures Leipzig, vol. 3, eds. F. Buchholz, M. Schlegel, Leipzig, Leipziger Universitätsverlag 2018, pp. 67-90.
De Risi, V. [2019]: « Analysis Situs, the Foundations of Mathematics and a Geometry of Space », in The Oxford Handbook of Leibniz, ed. M.R. Antognazza, Oxford, Oxford University Press 2019, pp. 247-58.
De Risi, V. [2019]: « Leibniz on the Continuity of Space », in V. De Risi (ed.) Leibniz and the Structure of Sciences. Modern and New Essays on Logic, Mathematics, Epistemology, Boston Studies in Philosophy and History of Science, Berlin, Springer 2019, p. 111-69.
De Risi, V. [2020]: « Has Euclid proven Elements I, 1? The early modern debate on intersections and continuity », in Reading Mathematics in the Early Modern Europe. Studies in the Production, Collection, and Use of Mathematical Books, ed. P. Beeley, Y. Nasifoglu, B. Wardhaugh, London, Routledge 2020, p. 12-32.
De Risi, V. [2021]: « Geometria delle figure e geometria dello spazio », in Perché studiare la logica, ed. E. Montuschi, P.D. Omodeo, Roma, Armando 2021, p. 16-49.
Rabouin, D. [2020]: « Exploring Leibniz’s Nachlass at the Niedersächsische Landesbibliothek in Hanover », European Mathematical Society Newsletter, issue 116, juin 2020, p. 17-23.
Rabouin, D. [2021]: « La logique comme ars inveniendi : un héritage leibnizien », in E. Haffner et D. Rabouin (ed.), L’épistémologie du dedans. Mélanges en l’honneur d’Hourya Benis-Sinaceur, Garnier 2021, p. 265-300.
Remaki, A. [2021]: « Exposants et tangentes chez Leibniz à Paris, entre formes et géométrie », in Philosophia Scientiae, « Mathématiques et philosophie chez Leibniz à la lumière des manuscrits inédits », n. 25-2, juin 2021, p. 95-132.
References
Bos, H. [1974]: « Differentials, Higher-Order Differentials and the Derivative in the Leibnizian Calculus », Archive for History of exact Sciences, 14, 1974, pp. 2-90.
Gouye, T. [1701]: « Nouvelle méthode pour déterminer aisément les rayons des développées dans toute sorte de courbe algébraïque. Par Monsieur Jacques B. Acta Eruditorum, Mensis Novembris anni 1700. Lipsiae », Mémoires de Trévoux, May-June 1701, pp. 422-430.
Grosholz E. and Yakira E. [1998]: « Leibniz’s Science of the Rational », Studia Leibnitiana Sonderhefte 26.
Hess, H-J. [1984]: « Zur Vorgeschichte der “Nova Methodus” (1676-1684) » in 300 Jahre Nova Methodus, Studia Leibnitiana, Sonderheft, 14, 1984, pp. 64-101.
Hermann, J. [1700]: Responsio ad Cl. V. B. Nieuwentiit Considerationes secundas circa calculi differientialis principia, Basilae, 1700.
L’Hospital, G. (de) [1696]: « Analyse des infiniment petits, pour l’intelligence des lignes courbes », Paris : De l’Imprimerie Royale.
Leibniz, G.W. [1689]: « Tentamen de motuum coelestium causis », Acta Eruditorum, February 1689, pp. 82-96.LEIBNIZ, G.W. [1701a]: « Extrait d’une lettre de Mr. de Leibnitz sur ce qu’il y a dans les Memoires de Janvier et de Fevrier touchant la generation de la glace, et touchant la Demonstration Cartesienne de l’existence de Dieu par le R. P. l’Amy Benedictin » , Mémoires de Trévoux, September-October 1701, pp. 200-220.
Leibniz, G.W. [1701b]: « Mémoire de Mr Leibnitz touchant son sentiment sur le Calcul différentiel », Mémoires de Trévoux, November-December 1701, pp. 270-271.
Leibniz, G.W. [1702]: « Extrait d’une lettre de M. Leibnitz à M. Varignon, contenant l’explication de ce qu’on a rapporté de luy dans les Memoires des mois de novembre et decembre derniers », Journal des Sçavans, 20 March 1702, pp. 183-186.
Leibniz, G.W., [1846]: Historia et Origo Calculi Differentialis a G.G. Leibnitio conscripta, Zur zweiten Säcularfeier des Leibnizischen Geburtstages sus den Handschriften der Könoglichen Bibliothek zu Hannover, herausgegeben von Re. C. I. Gerhardt, pp. 39-50.
Pasini, E. [1993]: Il Reale e l’Immaginario. La fondazione del calcolo infinitesimale nel pensiero di Leibniz, Edizioni Sonda, 1993.
Zacher, H. J. [1973]: Die Hauptschriften zur Dyadik von G. W. Leibniz, Frankfurt am Main : Vittorio Klostermann Verlag.