Venn diagrams have turned out to be visual tools that are enormously popular, but diagrams to help visualize relationships between classes or concepts in logic had existed prior to those of John Venn. The use of diagrams to demonstrate valid logical arguments has been found in the works of a few early Aristotelian scholars and appeared in the works of the famed mathematicians Gottfried Wilhelm Leibniz and Leonhard Euler. In a 1686 fragment (which remained unpublished for over 200 years), the universal genius Leibniz illustrated all of Aristotle’s valid syllogisms through circle drawings. In 1761, the much-admired master mathematician Euler used almost identical diagrams to explain the same logical syllogisms. One hundred and twenty years later, John Venn ingeniously altered what he called “Euler circles” to become the familiar diagrams attached to Venn’s name. This paper explores the history of the Venn diagram and its predecessors.


Venn Diagram Line Diagram Diagrammatic Method Puzzle Piece Eulerian Diagram 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Aristotle. (1619). Aristotelis Stagiritae Peripateticorum Principis Organum (Paris ed.), translated by Julius Pacius a Beriga with commentary. Sebastianum Chappelet.
  2. Bullynck, M. (2013). Erhard Weigel’s contributions to the formation of symbolic logic. History and Philosophy of Logic, 34(1), 25–34.zbMATHMathSciNetCrossRefGoogle Scholar
  3. Dalton, O. M. (1925). A portable dial in the form of a book, with figures derived from Raymond Lul. Archaeologia, 74, 89–102.CrossRefGoogle Scholar
  4. Dunham, W. (1990). Journey through Genius. New York: Penguin.zbMATHGoogle Scholar
  5. Euler, L. (1770). Lettres a une Princesse D’Allemagne sur divers sujets de physique et de philosophie, Tome second. Mietau et Leipsic: Chez Steidel et compagnie.
  6. Euler, L. (1802). Letters of Euler on different subjects in physics and philosophy addressed to a German Princess (CI–CVIII) (2nd ed.), translated by Henry Hunter. London: Murray and Highley.Google Scholar
  7. Gardner, M. (1958). Logic machines and diagrams. New York: McGraw-Hill.zbMATHGoogle Scholar
  8. Hamilton, S. W. (1874). Lectures on metaphysics and logic, Vol. III: Lectures on logic, Vol. I (3rd ed.). Edinburgh and London: William Blackwood and Sons.Google Scholar
  9. Lambert, J. H. (1764). Neues Organon (Vol. 1, pp. 128–133). Leipzig.Google Scholar
  10. Leibniz, G. W. (1903). De Formae Logicae Comprobatione per Linearum Ductus, Phil., VII, B, IV, 1–10. Opuscules et fragments inédits de Leibniz, extraits des ms. de la Bibliothèque royale de Hanovre par Louis Couturat. Paris, pp. 292–331. Bibliothèque Nationale in Paris Gallica,
  11. Leibniz, G. (1966). Logical papers. Translated and edited by G. H. R. Parkinson. Oxford: Clarendon Press.Google Scholar
  12. Llull, R. (1609). Opera ea quae ad adinventam ab ipso artem universalem scientiarum. Sumptibus Lazarus Zetzne Bibliopola. Google Books: Bavarian State Library, p. 109.
  13. Nubiola, J. (1993). Juan Luis Vives y Charles S. Peirce. Anuario Filosófico, 26, 155–164.Google Scholar
  14. Sales, T. (2011). Llull as computer scientist, or Why Llull was one of us. In A. Fidora & C. Sierra (Eds.), Ramon Llull: From the Ars Magna to Artificial Intelligence (pp. 25–38). Barcelona, Spain: Artificial Intelligence Research Institute.
  15. Sholz, H. (1961). Abriss der Geschichte der Logik (Concise History of Logic), translated by Kurt F. Leidecker. Philosophical Library, New York (Original work published 1931).Google Scholar
  16. Venn, J. (1880). On the diagrammatic and mechanical representations of propositions and reasonings. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 9(59), 1–18.CrossRefGoogle Scholar
  17. Venn, J. (1881). Symbolic logic. London: Macmillan and Co. Forgotten Books 2012 reprint.Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.New Jersey City UniversityJersey CityUSA

Personalised recommendations