MoMath + Wolfram

Funding for this project generously provided by Overdeck Family Foundation


Cardano's Ars Magna

Algebraic solutions to cubic and quartic equations

Gerolamo Cardano's Ars Magna (The Great Art) was first published in Nuremberg, Germany, in 1545. It is considered one of the outstanding scientific treatises of the early Renaissance.

Cardano's Ars Magna

While solutions to cubic equation had been discovered by Niccolò Tartaglia in 1535 and by Scipione del Ferro previously, neither result had been published. In Ars Magna, Cardano first published algebraic solutions not only to the cubic but also to the quartic equation, crediting del Ferro as the first to solve the cubic equation and stating that the solution presented used del Ferro's method. The forty chapters of Ars Magna also introduced the concepts of multiple roots and complex numbers for the first time.

Artifact dimensions

7.3 in. × 10.7 in.

Artifact origin

Nuremberg, Germany

Current artifact location

Linda Hall Library of Science, Engineering & Technology

Catalog number

QA35.C35 1545


Algebra timeline Babylonian Metric Algebra Problems Tablet Berlin Pythagorean Theorem Papyrus Rhind Papyrus Al-Khwārizmī's Al-Jabr Khayyam's Al-jabr Cardano's Ars Magna Recorde's Whetstone of Witte Faulhaber's Academia Algebrae Wallis's Treatise of Algebra Emerson's Treatise of Algebra Hermes's Suitcase of Göttingen

Interactive Content

Computational Explanation

Other Resources

Additional Reading

  • Cardano, G. Ars Magna or The Rules of Algebra. New York: Dover, 1993.
  • Smith, D. A Source Book in Mathematics, Vol. 1. New York: Dover, pp. 295–297, 1959.
  • Witmer, T. (trans.). Ars Magna or The Rules of Algebra. Cambridge, MA: MIT Press, 1968.

Image Credits

Linda Hall Library of Science, Engineering & Technology, Kansas City, Missouri