Реферат: Albrecht Durer
Реферат: Albrecht Durer
Born: 21 May 1471 in Imperial Free City of Nürnberg (now in
Died: 6 April 1528 in Imperial Free City of Nürnberg (now in
Albrecht Dürer was the third son of Albrecht Dürer and
Barbara Holfer. He was one of their eighteen children. The Dürer family
came from Hungary, Albrecht Dürer senior being born there, and at this
time the family name was Ajtos. The name Ajtos means "door" in Hungarian
and when Dürer senior and his brothers came to Germany they chose the name
Türer which sounds like the German "Tür" meaning door. The
name changed to Dürer but Albrecht Dürer senior always signed himself
Türer rather than Dürer.
Here are portraits of his father and mother.
Albrecht Dürer senior was a jeweller who had served his
apprenticeship with Hieronymus Holfer, and then married Holfer's daughter.
Albrecht Dürer junior wrote about his father and his upbringing (see for
My father suffered much and toiled painfully all his life, for he
had no resources other than the proceeds of his trade from which to support
himself and his wife and family. He led an honest, God-fearing life. His
character was gentle and patient. He was friendly towards all and full of
gratitude to his Maker. He cared little for society and nothing for worldly
amusements. A man of very few words and deeply pious, he paid great attention
to the religious education of his children. His most earnest hope was that the
high principles he instilled into their minds would render them ever more
worthy of divine protection and the sympathy of mankind. He told us every day
that we must love God and be honourable in our dealings with our neighbours.
As a young boy Dürer was educated at the Lateinschule in St
Lorenz and he also worked in his father's workshop learning the trade of a
goldsmith and jeweller. By the age of 13 he was already a skilled painter as
seen from a self portrait which he painted at that time. This was the first of
many self-portraits which Dürer painted and they provide a wonderful
record. Here is our collection of such self-portraits.
In 1486 Dürer became an apprentice painter and woodcut
designer to Michael Wolgemut, the leading producer of altarpieces. After an
apprenticeship of four years, Dürer had learnt all he could from Wolgemut
and had reached a level of artistic quality exceeding that of his famous
teacher. Wolgemut advised Dürer to travel to widen his experience and meet
other artists. Following Wolgemut's advice, Dürer delayed visiting Italy
(which Wolgemut himself never visited), where there were very different
artistic styles, until he had fully developed his own style and learnt more
techniques from other German artists.
Here is a portrait of Wolgemut.
Dürer travelled first to Nördlingen, where he met
artists of the Swabian school. The Swabian style had been influenced by Dutch
artistic design which Dürer had not met before. His next visit was to Ulm
where he met more artists of the Swabian school. Dürer:-
... participated with keen enjoyment in the discussions among
artists of his own age, in the low-ceilinged taverns, over foaming mugs of
beer. These youthful enthusiasts, in common with those of all nations
throughout history, were bent on rejuvenation of the art of the world. They
were delighted with Dürer's drawings, with his first engravings and the
small pictures he had already painted, independently of Wolgemut's directions
Leaving Ulm, Dürer made his way to Constance which charmed
him with its fairyland appearance. Basel was the next town which Dürer
visited, and he found it quite similar to his home town of Nürnberg.
Finally Dürer returned home, making visits to Colmar and Strasbourg on the
It had been a long journey of great importance to Dürer which
had taken nearly four years, but after he returned to Nürnberg in 1494 he
felt disappointed that he had not visited Italy. He had also become convinced
... the new art must be based upon science - in particular, upon
mathematics, as the most exact, logical, and graphically constructive of the
Italy was not only a country with new ideas to offer Dürer in
art, but it was also leading the world at this time in the revival of
mathematics. Before setting out for Italy, however, Dürer married Agnes
Frey, the daughter of a learned man Hans Frey who had made quite a lot of money
through making jewellery, musical instruments, and mechanical devices.
Here are portraits of Agnes.
The marriage seems to have been more the idea of the parents of
Agnes and Albrecht, and the pair were married on 7 July 1494. It was a marriage
which helped raise Dürer's status in Nürnberg, as well as provide him
with money which helped him set up his own studio.
Before the end of 1494, Dürer was on his travels again,
leaving Agnes behind in Nürnberg. First he visited Augsburg where he met
strong Italian artistic influences for the first time. Travelling through the
Tyrol, he reached Trento and his first view of Italy.
Here is one of his paintings of Trento.
He travelled on to Verona before reaching Venice which was his
main objective. In Venice, Dürer, as he had done throughout his journeys,
sketched scenes, visited galleries and churches, and met with the local
artists. One of the artists that he met in Venice, Giovanni Bellini, had an
important influence on Dürer for:-
... everything that [Venice] could teach him was to be found in
Giovanni's paintings. He cultivated the artist's society, therefore, with a
devotion both impassioned and deferential, retaining throughout his life, with
his whole heart and soul, unbounded feelings of gratitude to the man whose
pictures had unveiled so wonderful a world to him.
Dürer returned to Nürnberg in 1495, and although he does
not seem to have met with any of the major Italian mathematicians on his
journeys, he did meet Jacopo de Barbari who told him of the mathematical work
of Pacioli and its importance to the theory of beauty and art. Nor did
Dürer meet with Leonardo da Vinci while in Italy, but he learnt of the
importance which that artist placed in mathematics. Back in Nürnberg,
Dürer began a serious study of mathematics. He read Euclid's Elements and
the important treatise De architectura (On Architecture) by Vitruvius (1st century
BC), the famous Roman architect and engineer. He also became familiar with the
work of Alberti and Pacioli on mathematics and art, in particular work on
It was not only this scientific approach to art that influenced
Dürer as he began his artistic career in Nürnberg, but he also
benefited from seeing different artistic styles and the different scenery which
he had viewed:-
The variety of regions through which Dürer had passed in the
course of his travels and the care he had taken with the drawings and
water-colours he had made of the most attractive or unfamiliar of them had
provided him with a great range of pictorial motives emanating from the most
In 1495 Dürer was still not well known as an artist in the
highest circles but news of his skill reached Frederick the Wise, Elector of
Saxony, and Dürer was commissioned to paint his portrait. Frederick liked
his portrait which Dürer painted in April 1496 when Frederick had visited
Nürnberg. Despite Frederick's attempts to persuade Dürer to move to
Weimar and become Court painter, the artist did not wish to leave
Nürnberg. He was deeply attached to Nürnberg, painting these views
of the city in 1497.
From about 1500 Dürer's art showed the influence of the
mathematical theory of proportion which he continued to spend so much time
studying. It is claimed that his self-portrait in a wig made in 1500 has the
dimensions of the head constructed proportionally. For the engraving Adam and
Eve made in 1504, Dürer described the intricate ruler and compass
constructions which he made to construct the figures. It was not only the
mathematical theory of proportion which influenced Dürer's art at this
period, but also his mastery of perspective through his study of geometry. This
is most clearly seen in his woodcuts Life of the Virgin made between 1502 and
During the ten years after 1496 Dürer went from a relatively
unknown artist to someone with a wide reputation as both an artist and a
mathematician. His personal circumstances had changed greatly. His father had
died in 1502 and Dürer was left to care for his invalid, and nearly blind,
mother. He had set up his own printing press while he, or often his wife, sold
his works to buyers at local fairs. It was a difficult life and one in which Dürer's
health began to suffer. In fact he would never regain full health during the
rest of his life.
From 1505 to 1507 Dürer made a second visit to Italy,
spending much time again in Venice. It was a very different visit from his
first, with Dürer now more interested in his international fame than in
learning about art. He was so conscious of his fame, and the threat he
perceived that he might hold to the local artists, that:-
... he refused invitations to dinner in case someone should try to
It was not about art that Dürer now wished to learn from the
Italians, but rather about mathematics. He visited Bologna to meet with
Pacioli whom he considered held the mathematical secrets of art. He also
visited Jacopo de Barbari and the great efforts which Dürer made to meet
de Barbari shows the importance which Dürer more and more attached to
mathematical knowledge. Dürer returned to Nürnberg from this second
visit to Italy feeling that he must delve yet more deeply into the study of
In about 1508 Dürer began to collect material for a major
work on mathematics and its applications to the arts. This work would never be
finished but Dürer did use parts of the material in later published work.
He continued to produce art of outstanding quality, and he produced one of his
most famous engravings Melancholia in 1514. It contains the first magic
square to be seen in Europe, cleverly including the date 1514 as two entries in
the middle of the bottom row. Also of mathematical interest in Melancholia is
the polyhedron in the picture. The faces of the polyhedron appear to consist of
two equilateral triangles and six somewhat irregular pentagons. An interesting
reconstruction of the polyhedron is given in , see also for further details.
Dürer worked for Maximilian I, the Holy Roman emperor, from
about 1512. Maximilian, however, had little in the way of wealth to pay for
Dürer's work and he asked the councillors of Nürnberg to exempt
Dürer from taxes as compensation. He then asked the councillors to pay
Dürer a pension on his behalf, which certainly did not please them. From
about 1515 the councillors tried to avoid paying this pension. Dürer met
Maximilian personally for the first time in 1518 and, probably from one sitting
in Augsburg, painted Maximilian's portrait. The following year Maximilian died
and this was the final excuse for the councillors to refuse to make any further
payment, saying that the new emperor Charles would have to agree to the
Although Dürer was fairly well off by this time and the
pension was not necessary for him, it was more a matter of prestige to have his
pension restored. He set off for Antwerp on 15 July 1520 with his wife and
their maid to visit the Emperor Charles V. Passing through Aachen, Dürer sketched
the cathedral at Aachen.
Dürer had a second reason for this visit to the Netherlands,
for he believed that Maximilian's daughter had a book by Jacopo de Barbari on
applications of mathematics to art, and Dürer had long sought the truths
which he believed this work contained. On meeting Maximilian's daughter he
offered her the portrait of her father which he had painted, but was distressed
to find that she did not want the portrait. She had already given the book by
Jacopo de Barbari to another artist so Dürer's quest was in vain. He did
persuade Charles V to restore his pension, however, which was formally agreed
on 12 November 1520.
After returning to Nürnberg, 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.
This treatise, Unterweisung der Messung mit dem Zirkel und
Richtscheit, is 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. Dürer's sources
for this work are discussed in  where three main sources are suggested (i)
the practical recipes of craftsmen, (ii) classical mathematics from printed
works and manuscripts, and (iii) the manuals of Italian artists. The article
 gives many details of the mathematics contained in the treatise.
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!). Details about
Dürer's descriptions of the curves, in particular one he calls a
"muschellini", is given in.
In the second book he gave exact and approximate methods to
construct regular polygons. Dürer's constructions of regular polygons with
5, 7, 9, 11 and 13 sides is discussed in . 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 three considers pyramids, cylinders and other solid bodies.
The second part of this book studies sundials and other astronomical
instruments. 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.
In 1527 Dürer published another work, this time on
fortifications. There were strong reasons why he produced a work on fortifications
at this time, for the people of Germany were in fear of an invasion by the
Turks. Many cities, including Nürnberg, would improve their fortifications
using the methods set out by Dürer in this book. Dürer's final
masterpiece was his Treatise on proportion which was at the proof stage at the
time of his death.
Descriptive geometry originated with Dürer in this work
although it was only put on a sound mathematical basis in later work of Monge.
One of the methods of overcoming the problems of projection, and describing the
movement of bodies in space, is descriptive geometry. Dürer's remarkable
achievement was through applying mathematics to art, he developed such
fundamentally new and important ideas within mathematics itself.
J J O'Connor and E F Robertson
подготовки данной работы были использованы материалы с сайта http://www-history.mcs.st-andrews.ac.uk/