ORIGINAL QUERY:
Date: Mon, 03 Dec 2001 11:27:42 +0100
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Here is a research query from a Nexus Network Journal reader. It appears that the first pointed arch in Europe may have appeared in Sicily around 1130. In 1090 in Sicily there are no pointed arches; in 1130 there are. The first crusade dates from 1099. It may be logical to think that pointed arches were a result of the crusade.
Does anyone know what the first pointed arches were in Europe, and if there were any earlier than the Sicilian ones of 1130?
Comments
The so-called Maya's false vaults do not support and transmit loads to columns or walls, instead the loads runs vertically from the top of the walls to its base. In other words, the walls stands up in parallel arraignment and from its spring line starts gradually decreasing the span until it close horizontally with the capstones. To normalize the loads some wood-crossbeams were add to the walls intrados, so, at any moment the walls stones follows any sort of curvature, they simple overlaps in order to decrees the span. This explains why the spans between walls were very short (2.75m span at the spring line in the Inscriptions Temple, in Palenque, c. 602-692 AD).
Paul Gendrop, a friend of mine, acknowledges at least nine different sections of Mayan false vaults: The E-X building in Uaxactún, the structure 1 in Tikal, the frescoes temple in Tulum, the A-V building in Uaxactún, The Labná arch, The ball court in Copán, The secret crypt in Palenque, the house A in the Palenque's Palace, and the Governor's Palace in Uxmal (my favorite one). For more see: Paul Gendrop, Arte Prehispánico en Mesoamérica (México: Trillas, 1970).
1. pointed arches in Roman architecture: Cluny III (cca 1088)
www.owlnet.rice.edu/~hart205/Lectures/lecture33.htm
www.arch.ced.berkeley.edu/courses/arch170/past/95fall/euro.html
2. pointed arches in Morienval
www.newadvent.org/cathen/06665b.htm
(in which it is written, "The earliest structural pointed arch recorded in France is in the ambulatory of Morienval, referred to above, and is dated 1122."
It is extremely unlikely that it was the Crusades that imported pointed arches into Europe although it is true that the Crusades placed the relatively unsophisticated crusaders in contact with some sophisticated techniques in all areas of technology.
It is much more likely that it was trade and contact with Byzantium, the most cultured and advanced society of the time that was the source. Particularly as Byzantine culture was influenced by their contact with the architecture and civilisation of the Middle East - particularly Syria.
As far as the maths is concerned it seems that the setting out of a pointed arch can be done using rather simple geometry.The setting out of a pointed arch results from two givens.
1) that the arch height is constant (so that vaults of different widths will intersect at a constant height);
2) the springing of the arch is at right angles to the horizontal line between the base of the springings; i.e. the springing is vertical and not inclined given that:
1) The setting out of the arch would be done on a tracing floor;
2) The horizontal line of the base of the springing can be drawn at whatever angle but at the correct length of the distance between the springings. This distance could be either between the Intrados, that is the inner arc of the arch, or the extrados - the outer arc of the arch;
3) The mid point of the line can be established by intersecting arcs from each end of the line as long as each of the arcs has a radius longer than half of the line length;
4) The intersections of the arcs provide two positions along which a line can be sighted through two vertical staffs, one at each intersection. This line will be at right angles to the base line;
5)A third point can be established at the height of the arch by this sighting and by measurement;
6) The known width of the arch and the height can then be used to establish the line of one side of an equilateral triangle by forming a line between the point of the springing and the point of the arch height;
7) This line, subdivided in the same way as the base line, provides a line at right angles to, and from the mid point of, the side line of the triangle which, at the point at which it joins the base line, establishes the centre point of the radius of the arch. This is the only possible radius for an arc connecting the springing to the apex.
Where the radius lies beyond the distance between the springings the horizontal needs to be extended to the radius point but this would create no difficulty. Where the radius is less than the height of the arch (and less than half of the distance between the springings) the arch formed by the radius is half of a 'Moorish' arch, albeit turned 90°.
There is no indication of the setting out that I have suggested in any of the images of a tracing floor that I have examined but this has been entirely superficial. In any case it is possible that the setting out was done with chalk and that only the relevant and important lines were inscribed.
I have not been able to establish a simple means of geometrically dividing the arc into regular pieces but this may not have been necessary. On the other hand, the mass production of the voussoirs may have made life easier for the builders. In this case, the only stone that would have to be fitted would be the keystone.
For those who might be interested in theory about number and meaning I have just found a book called The Wise Master Builder by Nigel Hiscock, which deals with Platonic Geometry in Plans of Medieval Abbeys and Cathedrals.
I readers devono sapere che il vero arco, quello puro (esempio Cordoba, in Spagna), è una invenzione araba; quelli cosidetti romani sono ARCHIVOLTI, e NON archi. La differenza in shorts? L'arco è piano ed instabile,come una bicicletta, mentre l'archiVOLTO è spesso, come un'automobile a quattro ruote, che resta in equilibrio anche da ferma! Ecco perché un proverbio arabo recita: "l'Arco non dorme mai".
My answer: if Spain, South Italy, Greece etc, was and is Europe, and he means masonry block arches, the answer is yes. In fact, the mortar masonry pointed arches were imported by the Arabs. They were the owners of the Mediterranean Sea for at least 200 years, with strongholds or bases even in Provance (Fressineto) and Maunt Blanc, in the Alps!
Along the Italian peninsula they were acting as invited warriors and free lancing pirates : they burned even Saint Paul basilica in the surroundings of Rome! To day, in south Italy, we measure cultivated land in Arabic units, and I remember when grain was measured by volume by an homonym unit. When the Normans arrived in south Italy, (battle of Civitate/Fortore, therefore before crusades), the artisans, master builders, protomagisters etc were Arabic populations : King Ruggero II (Roger) stood up when El Idrisi was entering the throne room. Roger's nephew Frederik II (father from Germany, mamma from Palermo),spoke perfectly Arabic.
How they build before the Normans of Sicily?? By... the same methods. To-day the problem is to find examples, because Normans built churches where mosques existed (exp. San Giovanni degli Eremiti, Palermo): just to search for the bridges they left. (existing), and the problem is underlined and solved with signature.
From the "sophistic" point of view, million of pointed arches existed in antiquity, long before the Normans. Leaving out Arabic Spain (Europa!), we have many megalithic examples, in Greece, in Arpino (central Italy, home country of Cicero and Marcello Mastroianni). Not only, but all the entrance doors of the earth-mud-clay houses and "capanne" (huts) were and had to be of the pointed arch type, because this is and was the best natural form which match the statics and the pattern of the stresses transmitted in relation to that material.
The true problem is not that of the dates, numbers useful for bingo play; the reader should ask himself why the ancients build by pointed arches!
SECOND question, second reader: Does anyone know of any symbolism in the shape or mathematics that produces a pointed arch?
Answer: NO-
The pointed arch, derives from the laws of statics, which means geometry: As a concentrated load on a rope marks a cusp (a medallion along a necklace), so a concentrated load marks an inverted cusp along the "spinal column" of the arch. Hanging ropes develops tensile stresses, (and pull on the supports), and hard masonry arches develop compression stresses (and thrust on the supports). Numbers, and MODERN formulas are the same, for ropes and masonry arches; ( I mean, the basic, the 80%). An observer who turn upside down a post-card of the Brooklyn bridge, will obtain the profiles of a concrete arch bridge.
Bibliografia: two famous books, without a number, for everybody: Salvadori, Mario, Structure in Architecture (Princeton University Press) Torroja,de Miret, Edoardo, Philosophy of the Structures (original title: La racon y ser de los typos estructurales).
I'm fairly certain that earlier ones could be found in Spain a century or more before that, but at the moment I can't document them.