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How Did the 19th Century Artist Jules Bourgoin Construct Islamic
Patterns? Alan D. Adams, Holland, New York, 2015.
It is generally agreed that it cannot be determined with
certainty how most Islamic Geometric designs were drawn by the
original artists. The compass and straight edge method of their
construction is not generally clear by inspection of the final
product.
It is surprising that it is also not very clear how the artists
who collected and cataloged these in the 19th century constructed
their patterns. Ernst Herzfeld, James Wild and Jules Bourgoin
published drawings but it is remarkably difficult to work backwards
from their layouts to see how they define proportions and
construction. The evidence does exist in their publications, but it
is not always obvious.
The best known English language catalog of Islamic pattern,
mostly due to a Dover publication Arabic Geometrical Pattern &
Design, 1973,1 is Bourgoins collection from, Les Elements de l'Art
Arabe Trait des Entrelacs of 1879.2 This collection of over 200
patterns covers many of the basic types of the art. It has probably
started thousands down the road of learning the art.
It is frequently said that the text of Les lments de l'Art Arabe
Trait des Entrelacs does not teach much about how most of the
patterns are drawn. The text was not even included in the Dover
publication. The basic layout circles of the patterns appear in the
plates but it is not clear how the sizes or spacings of these
layout elements are determined. The information is in the text of
the original publication and earlier work by
Bourgoin and it is possible to see how he laid out most of his
patterns.
Bourgoins Trait des Entrelacs is in fact his third publication
on the art of the Arabs. The first major publication is Les Arts
Arabes; Architecture, Mensuirie, Bronzes, Plafonds, Revtements,
Marbres, Pavements, Vitraux, etc. Le Trait Gnral de lArt Arabe of
1867, 1873.3 This publication certainly does contain enough
information in some of the drawings to determine exactly how he
constructed his patterns. He uses a general and common method which
leads to the best symmetry patterns. The layouts for the classic
parallel arm 10 point and twelve point stars appear in the early
chapters and sufficient evidence appears in the drawings to define
the exact method used for layout.4
Bourgoin gives a complete course on the geometry needed to draw
the figures in the 1867 publication. He introduces the divisions of
the circle, the Regular Polygons and Derived Polygons followed by
the regular and Archimedean tilings he will use later. Finally he
shows the complete layout of the ten point star in Deuxime Partie,
Part Two; The Interlacing Line.
A set of divided circles are drawn inside a grid of 72 rhombi
(rhombuses). The
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divisions required to draw the decagon are drawn, the radii. The
inter-radii, to divide the star into 20 parts are also drawn. He
does not include any construction of the rhombus or pentagons used
to do these divisions. Bourgoin always assumes that angles are
measured.
There is a single extra layout line on this drawing, drawn as a
dotted line. It is indicated in pink.
This is the only layout line required to complete this pattern,
beyond the divided circle. It connects two 10 fold divisions,
radii, of the circle, divisions 1 and 4.
Where that line crosses the inter-radii, the 20 fold division, a
layout circle is drawn, shown in red. Inside that circle, a star
polygon is drawn by connecting the vertices, radii, 1 to 5, in
blue. To be confusing, mathematicians call this 0 to 4, a 10/4 star
polygon.
Extending the star polygon to intersect the decagon drawn inside
the circles completes this star. Where the pattern lines meet the
edge of the circle, lines are extended until they intersect a line
from a neighboring star, where they terminate. These rules and a
single layout line completely define the star. The text description
is sketchy, but consistent.
Bourgoins layout is a short cut and it is only general for
parallel sided, even number stars. The general case appears
below
The two points used by Bourgoin are defined by a small minor
layout circle. It is drawn at the intersection of the inter-radii.
The radius of this minor circle is defined by the line
perpendicular to the radius from the major circle, to the point
indicated in black. If the correct tiling polygon is drawn, in
blue, this is easy to draw.
If the star polygon in the center is extended out, it defines a
new star polygon inside the minor layout circle, a perfect five
point star.
This completely defines the pattern, and it is completely
general for 10 point symmetry with any star polygon in the center,
not just the 10/4 polygon.
The figure on the next page shows the result for a different
star polygon, resulting in a tapered 10 point star. Technically,
this is a 20/7 star, drawn as a ten point star. The minor star is
in turn now drawn from a 10/7 star polygon.
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There is good evidence to say that Bourgoin understood this
completely. A layout for a 12 point pattern in his third
publication Prcis de l'art arabe of 1892,5 Plate 94 of part III
shown at left, shows the correct and complete method.
The exact layout is drawn in full. The minor layout circle, in
red, lies on the tiling boundary, drawn in blue, at the
inter-radius. This minor layout circle defines the required second
circle to draw the star polygon. No further layout is required to
complete this pattern.
Many but not all of Bourgoins star rosette patterns can be drawn
without any additional layout rules.
The results for the smaller star are not predictable with this
method.
The figure in the center of the layout will always be a regular
star polygon. The figure in the smaller, minor layout circle is
unpredictable. The five point star at
left for the twelve fold figure is irregular. All rays have the
same length, but the angles are not equal. Angles are only equal
for six and ten fold stars. Using this layout method gives a minor
star with the least possible distortion.
It is entirely possible that Bourgoin discovered this
independently, but he is not the first person to understand this
correctly. A completely correct description appears as a sketch
with in the unpublished notebooks of James William Wild from about
1845.
Wild served as recording architect in 1842 travels with Karl
Richard Lepsius and then stayed on in Egypt to study Arabic
architecture. Wild made extensive written and sketched records of
Mosque construction, decoration and residential decorative
pattern.6 His material was later used for the four Arabic plates of
his brother in law Owen Jones famous Grammar of Ornament of 1856.
After serving as curator at Sir John
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Soanes Museum, he left his collection of notes to various
libraries and these notes are now at the Victoria and Albert
Museum.7
Figure 1. James William Wilds Notebooks. Victoria and Albert
Museum, London. 2011EP3581
The text in Wilds notebook reads: A Star of 12 points inscribed
within 12 gons which touch each other in four points. The
constructive lines are squares. The small circle at A shows the
manner of setting out the thickness of the 12 petals so that
the
little stars B left by the intersections of the figure may have
equal rays.
Wilds construction is exactly the same construction shown above
from Bourgoins later 1892 publication.
Ernst Herzfeld was another later major contributor to the
recording of the monuments of the near east. He published
principally on the monuments and architecture of the area but he
did include carefully drawn
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depictions of their geometric ornament. It is clear from his
surviving preliminary sketches that he used the same method of
construction as Wild and Bourgoin.
Bourgoin Pattern Instructions from Les lments de l'Art Arabe
It is interesting that Bourgoin did not use this general and
precise method in many of his patterns where it would have given
the best symmetry result. There are text notes for each of the
plates in Les lments de l'Art Arabe. They are brief and need the to
be read together with the layout lines sketched in the plates to
read sensibly, but they are clear in most cases. A classic,
extremely common star serves as an example. Plate 48 is the classic
8 point star rosette. From page 19:
PL 48 Vertices and the center: 1st with a radius equal to half
of the side of the square, describe a regular octagon on the
tangent circumference; 2nd with a radius almost arbitrary
(according to the proportion that we want to give the arms of the
rosette; Here radius equal to half the side of inscribed square is
used) describe a concentric circumference and construct the
diagonal 6 into 6 divisions; a star is thus obtained where long
sides, extended to meet the sides of the octagon, determine the
rosette mesh. Extended sides of the octagon determine small
octagons that separate rosettes.
Following Bourgoins text instructions with an eye on his plate
gives exactly the figure he has drawn in plate 48. On the left; 1st
with a radius equal to half of the side of the square, describe a
regular octagon on the tangent circumference. The tangent
circumference is the inscribed circle of the square tiling polygon.
The radius of that circle is of a side. On the right; 2nd with
a
radius almost arbitrary (according to the proportion that we
want to give the arms of the rosette; Here radius equal to half the
side of inscribed square is used) describe a concentric
circumference. An inscribed square is drawn in blue and it
inscribed circle is drawn in turn. construct the diagonal 6 into 6
divisions; a star is thus obtained where long sides, extended to
meet the sides of the octagon, determine the rosette mesh. Extended
sides of the octagon determine small octagons that separate
rosettes. The term 6 into 6 divisions sounds odd but it simply
means the construction of the star
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polygon by connecting each sixth intersections of the divisions
of the pattern at the inscribed circle. Note that Bourgoin also
counts from zero, 0 to 6.
Extending the sides of the layout octagon forms the sides of the
small octagons of the pattern and it is complete. It is not the
best symmetry pattern. If he had used the same layout which he used
for his 12 point
star, he would have used the inner circle shown in the figure to
the right. The small layout circle at the right of the layout
should define equal length arms for the small 5 point star. This is
doomed to be a poor symmetry star due to the 8/4 fold symmetry of
the pattern. Even so, Bourgoins layout could have been more
symmetric if he had used the layout method he had used for 10 and
12 stars.
Later 12 point star rosette pattern constructions use similar
arbitrary radii. This is particularly surprising since he had used
the best construction in his earlier or contemporary publication,
shown above.
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The pattern which should show perfect symmetry in all its
elements is the ten point rosette tiling. The layout described by
Bourgoin in Les lments de l'Art Arabe is correct, but it is
completely unrelated to the layout shown from his earlier work
above. It is rigorously correct, but rather strange. It teaches no
general lesson.
As a final impression, Bourgoins Les lments de l'Art Arabe is an
inconsistent collection of constructions. Some are geometrically
correct but not general, some are unsuccessful with poor
proportions and some are simply trial and error. Almost all of them
rely on construction of angles with a protractor and are therefore
unrelated to any possible historical method. It is safe to say that
the constructions described do work to give the patterns shown.
They do not teach anything useful to approach new patterns or
understand the structure of those presented.
References and Notes
Note: The translations from the French originals are mine. I do
not read French, these were laboriously translated and doubtless
contain errors. Geometry, however, is universal. I believe that the
sense is correct.
Note on copyright: The last copyright on Bourgoins works expired
in 1978. Born December 12, 1838 died February 4, 1908. James
William Wilds notebook extract is copyright to Victoria and Albert
Museum, used under their conditions; Content in which the V&A
owns copyright (or related rights) may be downloaded and used free
of charge but subject always to these Terms of Use. The permission
granted by these Terms of Use is for "non-commercial" use of the
Content only (meaning any use that is not intended for or directed
towards commercial advantage or private monetary compensation).
http://www.vam.ac.uk/content/articles/t/terms-and-conditions/
1) Bourgoin, Jules. Arabic Geometrical Pattern & Design,
Dover Publications, 1973.
2) Bourgoin, J. Les lments de l'Art Arabe Trait des Entrelacs,
Librairie de Firmin-Didot et Cie, Paris, 1879.
3) Bourgoin, J. Les Arts Arabes; Architecture, Mensuirie,
Bronzes, Plafonds, Revtements, Marbres, Pavements, Vitraux, etc.
Avec une table descriptive et explicative, et le Trait Gnral de
lArt Arabe, V. A. Morel et Cie, Paris, 1867, 1873. p 25. Originally
issued in 40 parts, explaining the publication dates.
5) Page 25 Ref 3.
5) Bourgoin, J. Prcis de l'art arabe et matriaux pour servir
l'histoire, la thorie et la technique des arts de l'Orient
musulman, (Summary of Arab Art.) Ernest Leroux, Paris, 1892.
6) The Art Journal: New Series, 1893 J.S. Virtue London, p 120 -
121. Obituary. Stanley Lane-Poole Art of the Saracens in Egypt
Chapman and Hall, London, 1886. p 115 and other sources mention
Wilds stay.
7) Notebooks of James William Wild, Victoria and Albert Museum,
Accession number 2011EP3581
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