(www.counton.org/explorer/)
Matthaus Roriczer 1485-1521 Catedral de Ratisbona
Geometria práctica del Gótico "
ein Buchlein der Fialen Gerechtigkeit" ( "Opúsculo
sobre la correcta forma de hacer pináculos")
y la " Geometria deutsch"
Los canteros medievales construyeron las catedrales
góticas con unas curiosas matemáticas
que no precisaban del numero pí para los cálculos
necesarios.
Cálculo de la longitud necesaria de hierro
para formar un círculo.
El método coincide con el que aprendió
Miquel Ramis de un herrero mallorquin que evidentemente
no supo nunca de la existencia de Roritzer. Esto dice
mucho de la pervivencia de la transmisión oral
de conocimientos, puesto que como veremos seguidamente,
el método se mucho más anterior a Roritzer.
Se divide el diametro en 7 partes iguales, obteniendo
un módulo D/7 que se coloca en el exterior.
Se repite dos veces más el círculo y
la distancia total es la longitud del hierro que necesitamos
para fabricar un círculo de este diámetro.
En realidad, como hizo notar uno de nuestros alumnos,
Martino Janosevich, es una manera indirecta pero precisa
de obtener el número 3,1428 que habitualmente
utilizamos para calcular este perímetro: La
relación entre el diámetro compuesto
de 3 círculos+1 módulo y la nueva distancia
obtenida es precisamente de 3,1428 (1)
En realidad, nuestro herrero estába utilizando
el método de Arquimedes.
y de repente, encontramos una prueba irrefutable que
conecta un taller de herrería en Mallorca en
el siglo XXI con la Grecia clásica. Homérico!!
The mediaeval masons, who were called
"free masons", were not bound to a guild
in any specific city and wandered from place to place
where churches were erected and stone masons were
needed. Thus, these masons were "free" and
had the character of an international society. They
were nevertheless regionally organized. Only in Germany
had an orgarization been fully developed. The representatives
of nearly all lodges of Germany held a common session
in Regensburg in 1459. This document refers to the
secrets of free masonry Paragraph thirteen says :
"Also no workman, nor master, nor parlier, nor
journeyman shall teach anyone, whatever he may be
called, not being one of our handcraft and never having
done mason work, how to take the elevation from the
ground plan" It was the master's duty to keep
the book of the lodge and to have it read to the masons
every year. What's the secret of how to take the elevation
from the ground plan ? Matthaus Roriczer, only one
generaton after the great session of Regensburg, published
the secret in a small booklet with the consent of
the bishop of Regensburg in 1486. He teaches it by
means of a single square. From this figure Roriczer
derives all proportions of his edifice, in this case
a pinnacle, inasmuch as its dimensions are related
to one another as the sides of a sequence of squaret,
the areas of which diminish (or increase) in geometrical
progression. However the modern scholars of the nineteenth
century who read Roriczer's booklet did not recognized
that it revealed the secret of the mason and that
it illustrated a general mcethod. It is clear that
Roriczer's rule is the special case of a general method.
In recent years many scholars have searched for the
geometric system(s) by which the building was designed.
But they have become mired in dispute, although nearly
every one believes geometrical patterns were used
and therefore ought to be possible of recovery. On
the latter point, some of us are more skeptical of
"success" than others. In a paper on the
geometrical proportion of the Pantheon in ancient
Rome (July, A.I.J. 1986) I reported the geometrical
rule which determines the wall thickness of the Pantheon.
This can be done by the following procedure: first,
draw the circle incribed in the basic square, then
draw to the smaller square inscribed in this circle.
Consequently, a cloister-like discrepancy results
between the smaller circle and the basic circle. This
discrepancy is((2-?<2>)/4)S (S=span). This figure
(two squares) is the same as that of Roriczer in which
the smaller square is rotated by 45 degrees. So I
have applied the Pantheon Rule to the Gothic Cathedrals:
Chartres, Reims and Amiens, and examined the cogency
of the rule in the present paper. These Cathedrals
have proved to use design techniques as follows: 1.
The thickness of buttress is determined by my Pantheon
Rule. It seems that the thickness of the walls and
piers are governed by the same rule. 2. The first
great unit (=a) derives from 16-divided-squares of
the basic square. 3. The second great unit (=l) derives
from 9-divided-squares of the outer square which is
produced by drawing the cloisterlike discrepancy outside
the basic square. 4. The third great unit ( = a',
l') derives from the law of diminishing ?a or ?l (the
said discrepancy) from a or l. 5. The fourth great
unit (=b) derives from the function of a and (or)
l. 6. The diversity of Chartres, Reims and Amiens
derives from combinations of these great units: a,
l, b, a', l' and b'.
http://ci.nii.ac.jp/naid/110001020908/
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Como pasar un area cuadrada a un area triangular
:
Un cuadrado le dividimos el lado DC en dos
segmentos iguales DE y EC. Prolongamos el
lado hasta un segmento BD : el nuevo segmento
BC es el lado del triángulo equilátero. |
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Construcción geométrica de
"Geometría Deutsch" mostrando
una sección horizontal de un pináculo.
( Img: www.emis.de/journals/NNJ/RHF-fig09.html) |
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Como localizar el centro de una porción
de círculo.
( Img:www.hs-augsburg.de/~harsch/germanica/Chronologie/15Jh/Roriczer/ror_g04r.html) |
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La Geometría es una rama de las matemáticas
pero puede ser tambien usada como una herramienta que
es especialmente útil para diseñar desde
una catedral hasta un coche. Esto era especialmente
cierto para los masones que construyeron las maravillosas
catedrales e iglesias por todo Europa.
Su geometría práctica, la "geometría
fabrorum", se mantuvo en secreto dentro de las
logias, que fueron precursoras de los sindicatos y del
colegio de Arquitectos. Algunas de estas fórmulas
son perfectamente precisas, otras son aproximaciones,
pero perfectamente adecuadas para un uso práctico.
Probablemente muchas de estas construcciones se han
perdido en el secreto que rodeaba las logias. Esta construcción
nos llega gracias al Mason Mathius (Mathew) Roriczer,
famoso por una construcción aproximativa de pinaculos
( torretas ornamentales que se utilizan en la arquitectura
gótica para decorar un techo o contrafuerte o
incluso dentro de una iglesia.).
Un ejemplo de la Geometría práctica del gótico:
el Büchlein der Fialen gerechtigkeit y la Geometria
Deutsch de Matthäus Roriczer
Albert Presas i Puig
Max Planck Institut für Wissenschaftsgeschichte
El Quadrivium medieval y posteriores clasificaciones
del saber distinguían entre una geometría teórica y
una práctica. La geometría teórica que obtenía sus conocimientos
sola mentis speculatione, consistía exclusivamente
en el estudio de los Elementos de Euclides, accesibles
en latín con sus demostraciones desde el siglo XII.
La geometría práctica se entendía como ars bene
metiendi y se identificaba con la agrimensura y
el uso de determinados instrumentos. Algunos textos
dedicados a la geometría práctica eran concebidos como
una serie de reglas para el correcto uso de tales instrumentos.
En este artículo se presenta la geometría utilizada
por los maestros albañiles del gótico tardío. Para ello
se comentan dos cuadernos de Matthäus Roriczer, mostrando
sus características esenciales comparándolas con la
tradición teórica.
Geometría, Matemáticas, Técnica, Alemania, Siglo XV.
© Sociedad Española de Historia de las Ciencias
y de las Técnicas
Matthaüs Roriczer
Matthaus (aka Matthew) Roriczer was born in Regensburg
around the year 1430. He came from a family of masons.
His grandfather, Wenzel was a student of Heinrich Parler
in Prague, who had earlier made proposals for Milan
Cathdral in the throes of its 'geometrical problem.'
His father Konrad (ca.1410/15 - 1475) was a cathedral
master builder. Roriczer served as a master of the choir
building of St. Lorenz in Nuremberg, working with father
Konrad. In Nuremberg, it receives 1463 the championship
and the civil right. Later he worked with Hans Böblinger
on a church in Eßlingen.
Roriczer is later summoned by bishop Wilhelm from Reichenau
to Eichstätt where his father Konrad was the cathedral
master builder. At Eichstätt, Roriczer was invited
to give an expert opinion over the on vault of a church
in Munich.
As successor of its father, who had died 1475, he takes
over as cathedral master builder to Regensburg around
1475/80. Also, whilst building the cathedral, he operates
the first book printing bureau of the city of Regensberg.
In 1459 masons met at Regensburg, Germany to standardize
the statutes of their lodges. One of their decisions
was that no one should reveal to the outside world the
art of taking an elevation from a plan. That Regensburg
Convention stated that, "no workman, nor master,
nor journeyman shall teach anyone, whatever he may be
called, not being one of our handicraft and never having
done mason work, how to take the elevation from the
ground plan."
He published in 1486 "Das Büchlein von der
fialen gerechtikait", dedicated to bishop Wilhelm.
Roriczer in Regensburg died sometime between 1492 and
1495.
http://www.designspeculum.com/TEDS/roriczer.html (
transcripción de todas las páginas y dibujos)
Notas:
1.- Haciendo la regla de 3: Si 7 módulos son
1; entonces 8 módulos serán X . X= 8x1/7=1,1428
. Ver renaldini |