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Mathematical Treasures - De Divina Proportione, by Luca Pacioli

Frank J. Swetz and Victor J. Katz

This is the Tree of Proportions and Proportionality from the De Divina Proportione of Luca Pacioli (1445 - 1509), published in 1509.  Some of the terms in Pacioli's tree are familiar today and some are taken from the study of proportions by Nicomachus in his Arithmetic, but the meanings of some other terms are not generally known.  It would be a worthwhile project to go through the tree and decipher the meanings of all of the terms in it.


One image from De Divina Proportione of a stellated dodecahedron. This was a woodcut print of an illustration by Leonardo Da Vinci.

  • Another "mathematical treasure" in Convergence provides additional information about Pacioli’s Divina proportione, along with two images from the copy housed at the University of Oklahoma Library.
  • Another article in Convergence displays illustrations of the Platonic solids, prepared for De Divina Proportione by Leonardo da Vinci.

Index to Mathematical Treasures

Frank J. Swetz and Victor J. Katz, "Mathematical Treasures - De Divina Proportione, by Luca Pacioli," Convergence (January 2011)

Mathematical Treasures from the Smith and Plimpton Collections at Columbia University