The Geometry of Piero della Francesca

Conclusion

Piero’s books are a mass of detail—detailed arithmetic, detailed instructions. In the case ofDe Prospectiva Pingendi, though, we have another medium, the paintings, to reveal what it is really about. We see that a simplistic reading would completely miss the point. With the mathematical treatises we are not so fortunate—there is no other medium. If we want to know the real meaning, we have to construct it from the treatises alone by getting behind the superficial details and discovering the mathematical thought. Beneath the surface, the thought is surprisingly deep. Piero was a real mathematician—one can say it without apology.

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References

  1. [1]

    M.A. Lavin, “The Piero Project,” inPiero della Francesca and His Legacy, ed. by M.A. Lavin, University Press of New England, Hanover, NH (1995), 315–523.

    Google Scholar 

  2. [2]

    G. Vasari, LeOpere, ed. G. Milanesi, vol. 2, Florence (1878), 490.

    Google Scholar 

  3. [3]

    Piero della Francesca, DeProspectiva Pingendi, ed. G. Nicco Fasola, 2 vols., Florence (1942).

  4. [4]

    Piero della Francesca,Trattato d’Abaco, ed. G. Arrighi, Pisa (1970).

  5. [5]

    Piero della Francesca,L’opéra “De corporibus regularibus” di Pietro Franceschi detto della Francesca usurpata da Fra Luca Pacioli, ed. G. Mancini, Rome, (1916).

  6. [6]

    M. Clagett,Archimedes in the Middle Ages, University of Wisconsin Press, 1971.

  7. [7]

    T.L. Heath,The Thirteen Books of Euclid’s Elements, Cambridge University Press (1908), 97.

  8. [8]

    T.L. Heath,The Works of Archimedes, Cambridge University Press (1897), xxix.

  9. [9]

    M. Clagett, op. cit. vol 3, pp. 383-415.

  10. [10]

    P. Grendler, “What Piero Learned in School: Fifteenth-Century Vernacular Education,” inPiero della Francesca and His Legacy, ed. M.A. Lavin, University Press of New England (1995), 161–176.

  11. [11]

    Leon Battista Albert!,On Painting, ed. Martin Kemp, trans. Cecil Grayson, London-New York (1991).

    Google Scholar 

  12. [12]

    M. Kemp, “Piero and the Idiots: The EarlyFortuna of His Theories of Perspective,” inPiero della Francesca and His Legacy, ed. M.A. Lavin, University Press of New England (1995), 199–212.

  13. [13]

    J.V. Field, “A Mathematician’s Art,” inPiero della Francesca and His Legacy, ed. M.A. Lavin, University Press of New England (1995), 177–198.

  14. [14]

    J. Elkins, “Piero della Francesca and the Renaissance Proof of Linear Perspective,”Art Bulletin 69 (1987), 220–230.

    Article  Google Scholar 

  15. [15]

    M.D. Davis,Piero della Francesca’s Mathematical Treatises, Longo Editore, Ravenna (1971).

  16. [16]

    S.A. Jayawardene, ‘The Trattato d’abaco’ of Piero della Francesca,” inCultural Aspects of the Italian Renaissance, Essays in Honour of Paul Oskar Kristeller, ed C. Clough, Manchester (1976).

  17. [17]

    L. Pacioli,Summa Arithmetica, Venice (1494) Book II, fol. 72r, Problem 36.

  18. [18]

    L. Pacioli, DeDivina Proportione, Venice (1509).

  19. [19]

    J.J. Sylvester, “On Staudt’s Theorems Concerning the Contents of Polygons and Polyhedrons, with a Note on a New and Resembling Class of Theorems,’Philosophical Magazine IV (1852), 335–345.

  20. [20]

    T.L. Heath,The Method of Archimedes, Recently Discovered by Heiberg, Cambridge University Press (1912).

  21. [21]

    P.R. Cromwell, “Kepler’s Work on Polyhedra”,The Mathematical Intelligencer Vol. 17, No. 3, New York (1995), 23–33.

    Article  MATH  MathSciNet  Google Scholar 

  22. [22]

    Nicolo Tartaglia,Trattato Generate di Numeri e Misure, Venice (1559).

  23. [23]

    Nicolo Tartaglia, op. cit., Part IV Book 2, and Part V Book 2.

  24. [24]

    Nicolo Tartaglia, op. cit., Part I Book 13, fol. 107r.

  25. [25]

    In this paragraph I paraphrase arguments culled from 18th century sources by Gino Arrighi and quoted by him in the introduction to Ref. [4].

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Correspondence to Mark A. Peterson.

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Peterson, M.A. The Geometry of Piero della Francesca. The Mathematical Intelligencer 19, 33–40 (1997). https://doi.org/10.1007/BF03025346

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Keywords

  • Mathematical Intelligencer
  • Fifteenth Century
  • Regular Polyhedron
  • Archimedean Solid
  • Pythagoras Theorem