Albrecht_Durer_Self-Portrait.jpg

Self-Portrait Painting at age 26, during the year 1498; he lived from 1471-1528.


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August 22, 2016 Update: Good News; The entire original manuscript: "The Four Books on Measurement" (180 pages) by Albrecht Durer:

written in "Olde" German, hand-drawn, and hand-printed in 1525 in Nuremberg, is available free online at the Hathi Trust (one of the most important

libraries in the world!) for you to see and learn about this Renaissance Man, who contributed so much art and science to his and our world...

https://catalog.hathitrust.org/Record/100237681

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A good website to start learning about this Great Man in History:

1. http://www.albrecht-durer.org/

His contributions to Geometry are found in his manuscripts: The Four Books on Measurement

(from Wikipedia)

Four Books on Measurement

Dürer's work on geometry is called the Four Books on Measurement (Underweysung der Messung mit dem Zirckel und Richtscheyt or Instructions for Measuring with Compass and Ruler).[27] The first book focuses on linear geometry. Dürer's geometric constructions include helices, conchoids and epicycloids. He also draws on Apollonius, and Johannes Werner's 'Libellus super viginti duobus elementis conicis' of 1522.
The second book moves onto two dimensional geometry, i.e. the construction of regular polygons. Here Dürer favours the methods of Ptolemy over Euclid.
The third book applies these principles of geometry to architecture, engineering and typography.
In architecture Dürer cites Vitruvius but elaborates his own classical designs and columns. In typography, Dürer depicts the geometric construction of the Latin alphabet, relying on Italian precedent. However, his construction of the Gothic alphabet is based upon an entirely different modular system. The fourth book completes the progression of the first and second by moving to three-dimensional forms and the construction of polyhedra. Here Dürer discusses the five Platonic solids, as well as seven Archimedean semi-regular solids, as well as several of his own invention.
In all these, Dürer shows the objects as nets. Finally, Dürer discusses the Delian Problem and moves on to the 'construzione legittima', a method of depicting a cube in two dimensions through linear perspective. It was in Bologna that Dürer was taught (possibly by Luca Pacioli or Bramante) the principles of linear perspective, and evidently became familiar with the 'costruzione legittima' in a written description of these principles found only, at this time, in the unpublished treatise of Piero della Francesca. He was also familiar with the 'abbreviated construction' as described by Alberti and the geometrical construction of shadows, a technique of Leonardo da Vinci. Although Dürer made no innovations in these areas, he is notable as the first Northern European to treat matters of visual representation in a scientific way, and with understanding of Euclidean principles. In addition to these geometrical constructions, Dürer discusses in this last book of Underweysung der Messung an assortment of mechanisms for drawing in perspective from models and provides woodcut illustrations of these methods that are often reproduced in discussions of perspective.

His contributions to Human Anatomy are called: The Four Books on Human Proportion

Four Books on Human Proportion

Dürer's work on human proportions is called the Four Books on Human Proportion (Vier Bücher von Menschlicher Proportion) of 1528. The first book was mainly composed by 1512/13 and completed by 1523, showing five differently constructed types of both male and female figures, all parts of the body expressed in fractions of the total height. Dürer based these constructions on both Vitruvius and empirical observations of, "two to three hundred living persons,"[18] in his own words. The second book includes eight further types, broken down not into fractions but an Albertian system, which Dürer probably learned from Francesco di Giorgio's 'De harmonica mundi totius' of 1525. In the third book, Dürer gives principles by which the proportions of the figures can be modified, including the mathematical simulation of convex and concave mirrors; here Dürer also deals with human physiognomy. The fourth book is devoted to the theory of movement.
Appended to the last book, however, is a self-contained essay on aesthetics, which Dürer worked on between 1512 and 1528, and it is here that we learn of his theories concerning 'ideal beauty'. Dürer rejected Alberti's concept of an objective beauty, proposing a relativist notion of beauty based on variety. Nonetheless, Dürer still believed that truth was hidden within nature, and that there were rules which ordered beauty, even though he found it difficult to define the criteria for such a code. In 1512/13 his three criteria were function ('Nutz'), naïve approval ('Wohlgefallen') and the happy medium ('Mittelmass'). However, unlike Alberti and Leonardo, Dürer was most troubled by understanding not just the abstract notions of beauty but also as to how an artist can create beautiful images. Between 1512 and the final draft in 1528, Dürer's belief developed from an understanding of human creativity as spontaneous or inspired to a concept of 'selective inward synthesis'.[18] In other words, that an artist builds on a wealth of visual experiences in order to imagine beautiful things. Dürer's belief in the abilities of a single artist over inspiration prompted him to assert that "one man may sketch something with his pen on half a sheet of paper in one day, or may cut it into a tiny piece of wood with his little iron, and it turns out to be better and more artistic than another's work at which its author labours with the utmost diligence for a whole year."[28]

2. https://arxiv.org/ftp/arxiv/papers/1205/1205.0080.pdf

This is a 35 page commentary by G. H. Hughes in two sections: Part One is about Durer's Life
and Part Two include copies of Durer's actual hand-crafted text and hand-drawn Polygon Constructions, with a compass and unmarked straightedge,
which are from the above-mentioned Second Book on Measurement. The Calligraphy and Geometric Constructions are amazing. The author goes "bonkers"
at the conclusion, with unending obscure 'equations'... I just ignored them...