Duerer’s hand written manual on proportion

In Part I we learned that Dürer was desperate to learn new methods of perspective and how far he had gotten in this subject in late 1506.  He was on his way to Bologna, Italy to meet with a man to learn new perspective information.

Medieval and current Eichstatt today


A breach on the guarding of this mathematical knowledge occurred when Dürer was a young man regarding perspective which occurred in Eichstatt, 60 miles away from Nuremberg, in 1486-1488, at the behest of the Bishop of Eichstatt, who happened to be in charge of Willibald Pirkheimer’s education,  Dürer’s arch enemy.  At the same time, Albrecht had just been reapprenticed to Michael Wolgemut as illustrator for the Nuremberg Chronicles.  It is highly unlikely that this was coincidental, news travelled too fast.

Duerer’s portrait of Michael Wolgemut




In 1523, Dürer bought 10 books of the Bernhard Walter library that was not part of the purchase of his house and library in 1509, over which Pirkheimer apparently had control of until then. As we remember from the article about the Bizarre conspiracy About a Book, which totally involved Pirkheimer, Pirkheimer was keeping many secrets about books from 1480 onwards.

Which probably explains why Dürer didn’t publish his Manual on Measurement until he got his hands on these books in 1525. As early as January 1400, the French architect, Jean Mignot had declared that art without a scientific basis is nothing.  But this was not new; Plato and Socrates had based beauty on geometry, the golden mean, Pi, Phi, etc. It also turned out that Pirkheimer had purchased a great many manuscripts pertaining to ancient mathematics from the libraries of Regiomontanus, one of the world’s most famous astronomers and mathematicians, who was in Nuremberg 1476 and supposedly had bought books from Walters library, prior to Dürer buying his house and library in 1509.

Duerer’s Manual on Measurement

Pirkheimer, as we have seen in previous articles is a prime suspect of covering up truth, he never translated the Corvinus codexes brought to him by Cuspinian in 1480.


The illumination of King David from the Corvinus Library Codex 3

In the opening sentence of the manual, Dürer, in large letters credits Euclid as having provided the basis of geometry.  Dürer had bought a copy of Euclid’s book, which has an authentic note in his own handwriting that he had obtained it in Venice in 1507. It was the newly published translation by Bartolommeo Zamberti (Venice 1505), the first translation from the original Greek rather than the Arabic.

Zamberti’s Euclid

But Dürer had three sources that were available to him, published in Nuremberg, the exact year, at age 16, that he got reapprenticed to Michael Wolgemut for the Nuremberg Chronicles.  These sources were:

  1. Hans Schmuttermeyer,  Fialenbuechlein
  2. Matthis Roriczer, Puechlen von der filialen Gerichchtigkeit, Regensberg, 1486

The text describes the manner in which medieval masons used a “single dimensional unit” to produce a ground plan for a pinnacle that would be used in the construction of churches and cathedrals. At a time when there was no internationally agreed upon standard of measurement, medieval masons would define a square as a modular unit and then treat it in various ways, translating it or subdividing it, to give other relative measurements in a process called “constructive geometry” to create an effective local standard of measurement.  Schuttermeyer’s pamphlet spoke to the same issue.

3. Probably also published by Roriczer because of font, Geomatria deutsche, aus der geometry etliche nutzpalische stuck (Geometry in German, some useful things in geometry). Dürer used this for the construction of a pentagon but based it on Ptolemy, not Euclid.


Johann Tscherte Coat of arms done by Duerer

In 1522, Johann Tscherte, the same guy to whom Willibald Pirkheimer wrote a letter and trashed Agnes Dürerin as a total bitch for not selling Dürer ’s stuff to him after Dürer ’s death, which has dogged Agnes’ reputation for 500+ years, explained to Dürer  how to transform one geometrical figure into another with the same area.

Dürer was famous for his construction of letters and it has been traced that Hartmann Schedel, the author of the Nuremberg Chronicles, which was written 1486-1488, just as Dürer was working on the illustrations and so would know about Schedel’s text,  can be traced to an anonymous manuscript that begins with a copy of a letter by the Greek Scholar Johannes Laciaris (1445-1535) addressed to Piero de Medici.  What followed was detailed instructions on how to construct the Latin alphabet; for the Greek and Hebrew only drawings were provided but no text.


Duerer’s method for constructing Latin letters

Dürer used squares using a  1:10 ratio, while Pacioli, another famous mathematician, used a 1:9 ratio. Dürer states that his lettering method would also meet Pacioli’s 1:9 ratio, gives examples, but never explains why. Dürer ’s own text follows the Schedel manuscript more closely than Pacioli.


Luca Pacioli

When it came to perspective we know that a copy of Leon Battista Alberti’s De Pictura, written in 1435-1436, but not published until 1540 existed in Nuremberg in Regiomontanus’ library  (1476) to which Dürer had access and of course passed into the Bernhard Walthers library.  Regiomantanus had been in close contact with Alberti in Rome.


When Walthers died, because his famous wife had died in 1498, conflicting data says all of Walthers library passed to the city of Nuremberg and of course Willibald Pirkheimer was asked to prepare an inventory of the library.  It’s rather strange that Pirkheimer prepared TWO INVENTORIES, one NOT dated until 1512, after Dürer  had bought the Walthers house in 1509 and supposedly the library contents, and then again one dated from 1522. Both inventories list a copy of Alberti’s manuscript. Wherever we turn we always run into Pirkheimer supposedly being involved with suspect historical information, especially about books and pamphlets.

But all of this becomes suspect because Dürer goes to Venice in 1506-1507 and writes to Pirkheimer, who hides the authentic letters, so Pirkheimer has much detail to conceal the truth without anyone knowing he’s doing it.



More in Part III. Stay tuned.

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