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J J O'Connor and E F Robertson – University of St Andrew, Biography

After returning to Nürnberg in 1521, Dürer's health became still worse.

He did not slacken his work on either mathematics or painting but most of his effort went into his work Treatise on proportion.

Although it was completed in 1523, Dürer realised that it required mathematical knowledge which went well beyond what any reader could be expected to have, so he decided to write a more elementary text.

He published this more elementary treatise, in four books, in 1525 publishing the work through his own publishing company.

 

The treatise, Unterweisung der Messung mit dem Zirkel und Richtscheit, was the first mathematics book published in German (if one discounts an earlier commercial arithmetic book) and places Dürer as one of the most important of the Renaissance mathematicians….

Book 1 - The first of the four books describes the construction of a large number of curves, including the Spiral of Archimedes, the Equiangular or Logarithmic Spiral, the Conchoid, Dürer's Shell Curves, the Epicycloid, the Epitrochoid, the Hypocycloid, the Hypotrochoid, and the Limaçon of Pascal (although of course Dürer did not use that name!).

 

Book 2 - In the second book he gave exact and approximate methods to construct regular polygons. Dürer also gave approximate methods to square the circle using ruler and compass constructions in this book. A method to obtain a good approximation to the trisector of an angle by Euclidean construction is also given.

Book 3 -  considers pyramids, cylinders and other solid bodies. The second part of this book studies sundials and other astronomical instruments.

Book 4 -  The final book studies the five Platonic solids as well as the semi-regular Archimedean solids. Also in this book is Dürer's theory of shadows and an introduction to the theory of perspective.