living nature. The Arab artist proceeds from within to the exterior; he
sets himself problems, and transfers them by means of the compass and
rule. The decorative impulse of Arab art consists of geometrical
diagrams either carved into relief, or inlaid, or simply laid flat.
Since the inspiration is dry, and purely abstract, the artistic
development is slight and unimportant; and, since the motive is
restricted, Arab decorative art has remained simple, but still of an
incomparable elegance, because the harmony between inspiration and
execution is perfect. By their creed Mohammedan artists were forbidden
to represent living forms, yet they adopted the principles they found in
Nature, and developed them with absolute fidelity. Thus, as I showed in
dealing with the architecture of the Alhambra, in surface decoration by
the Moors the lines flow from a parent stem; every ornament, however
distant, can be traced to its branch and root. In all cases we find the
lines radiating from a parent stem, as we may see exemplified in Nature
by the human hand, or in a leaf. We are never offended, as in modern
practice, by the random introduction of an ornament set down without a
reason for its existence. However irregular the expanse they have to
decorate, they always commence by dividing the field into equal areas,
and round these main lines they fill in their details, which invariably
return to their parent stem, a system which proves them to have been
absolute masters of space.
In the introduction to my volume on the Alhambra, I emphasised this
fact, that the Moors ever had regard to the first principle of
architecture--to decorate construction, never to construct decoration.
In Arabian architecture, not only does the decoration arise naturally
out of the construction, but the constructive idea is carried out in
every detail of the ornamentation of the surfaces. A superfluous or
useless ornament is never found in Moorish decoration; every ornament
arises naturally and inevitably from the parent design. The general
forms were first laid down; they were subdivided by general lines; the
interstices were then filled in with ornament, to be again subdivided
and enriched for closer inspection. The principle was carried out with
the greatest refinement, and the harmony and beauty of all Moorish
ornamentation is derived from its observance. The highest distinction
was thereby obtained; the detail never interfering with the general
form. Seen at a distance, the main lines strike the eye; on nearer
approach, the ornamentation comes into the composition; and a minute
inspection reveals the detail on the surface of the ornaments
themselves.
Monsieur A. Rhone, in his _L’Egypte à Petites Journées_, holds that,
“seeing the marvellous resources which the Arabs have found in geometry
for decorating surfaces, one regrets less for art that the laws of
Islamism have forbidden them, as an idolatrous act, to introduce
representations of animated forms. Although these laws were not so
strictly observed as is generally believed, who knows, if in turning the
Arabian artists away from sculpture and statuary, they have not been the
means of preserving this special and almost transcendant aptitude that
the Semites have for all subtle combinations, and especially for those
of geometrical numbers, lines, and figures?”
Although the principles of Moorish art are so rigid and severe, the
Arabs have not remained exempt from exterior influence, but have adapted
and incorporated foreign feeling into their art, and modified it to
their purpose. A note by the late Owen Jones greatly emphasises this
fact. He says:--“When the Mohammedan religion and civilisation
[Illustration: PLATE LII.
Panelling of a Recess.]
rose with such astonishing rapidity in the East, the Arabs, in their
mosques, made use of the materials which they found ready to their hands
in the ruins of old Roman buildings which they purposely destroyed; they
took columns with their Corinthian capitals, etc., and adapted them to
the arrangement required for their own temples. In their subsequent
works they did not, as we should have done, continue to copy and
reproduce the models which were at first so convenient to them; but,
applying to them their own peculiar feelings, they gradually departed
from the original model, to such an extent at last, that but for the
intermediate steps we should be unable to discover the least analogy
between them. Yet by this process the capitals of their columns can be
traced back to the Corinthian order which they, in the first instance,
found so abundantly for their use.”
Arab art must ever remain distinct from every other school and style,
because the essential foundation of it is fixed and limited. Now, those
who resign themselves to a style of art reduce themselves to formulas,
to copies, or to diagrams. Greco-Roman art has its formulas of ordinance
and propositions; Chino-Japanese art has its characteristic copies; and
Syro-Arabian art its abstract and geometrical diagrams. The general
elements of Arabian art, as applied to architecture and decoration,
consist of stalactites, intertwinings, and ornaments. Stalactites, which
are at the same time ornaments and members of architecture, are employed
in corbelling, in coving, and in pendentives, and are modelled and
superposed by tapia, or cut in wood and placed side by side, or opened
into hollows by superficial casings in wire and tressing. The
intertwinings which embellish the surfaces are carved and trimmed in
splitboards of carpentry, or laid in compartments, or carved in open
work, or engraved in stone, wood, and metal; or set in filigree,
vignettes, or mosaics. The ornaments, which divide themselves into
decoration by embroidery or embellishment in sections, reduce themselves
to a small number of elements, or flower-work cut flat in outline. The
outlines, complete in the boundary which limits them, are quite
characteristic. They do not resemble in any way, except in so far as the
unalterable laws of geometry decree, the outline drawn by Europeans, nor
the cursive traits used by the Chinese and Japanese. All Arab ornament
is by involution of lines; in short, it may be said to be _entirely_
geometric.
The art of the Mohammedan, so powerful in appeal to the imagination, not
only by beauty and grace, but by the doctrine of the Koran inscribed in
their temples on every side in ornamented characters,--so admirably
traced that they appear to form part of a perfected design proclaiming
the power of Allah, and impressing upon the believer respect for the
laws and the love of virtue;--produces an effect little short of
magical. Still does that art accompany its religion in a lingering
death. Crushed by the rapid strides which surrounding nations have made
in the progress of civilization, and which have outrun and ruined it,
yet do a few bright emanations appear, to show that as in religion they
are faithful to their creed, so in art do their crumbling monuments
preserve their shattered remains on which the observer still may see, in
deep characters, the chronicles of the times.
In the illustrations which accompany these brief notes, the Arab’s
mastery of line in the composition of design may be studied, and its
mystery revealed; but to reduce these geometrical intertwinings to their
original elements demands patience, application, and very much time. At
first sight these diagrams may appear monotonous, but each is
constructed on a particular theme. Most of them spread
[Illustration: PLATE LIII.
Blank Window.]
throughout the Orient, and may be more particularly studied in the
Moorish monuments in Spain, where they are employed indifferently in
carvings, in mosaic and inlaid work, in application to chased bronze,
and in compartments of decoration and embroidery. The infinite variety
the artists are able to introduce while working on strict rules, which
admit of no exception, is the result of instinct perfected by centuries
of practice. That in their work was something to be learned, as well as
to be felt, is evident from the Moorish poet’s exhortation to us to
attentively contemplate the adornments of their palaces, and thereby
reap the benefit of a commentary on decoration. It is, then, for the
benefit of students who would know something more of Arabian
ornamentation than can be derived from the sensation produced by broad
effects, and for lovers of the fine arts who would understand the
inwardness of Moorish refinement and reduce its mysteries to their
primary bases, that the accompanying diagrams have been reproduced.
At foot of each diagram is added a short explanatory note; but it is
expedient for the student to give consideration to the _plan_ which is,
in every case, set out in dotted lines. By this means, he will discover,
if he approaches his subject with a free mind, that his task will offer
less difficulty than would appear at the outset. To minutely describe
the construction of each diagram, and, at the same time comply with the
stringent rules of geometry, would occupy much too great a space; nor
would the result, perhaps, be proportioned to the labour.
[Illustration:
1 GREEK, RECTILINEAR.
1’ GREEK, CURVILINEAR.
2 CHINESE, RECTILINEAR.
2’ GREEK, CURVILINEAR.
3 and 4, GREEK, ALTERNATING
PATTERN.
5, 6, 7, 8, 9, 10, GREEK, INTERCALARY PATTERNS.
11 CHINESE.
12 ASSYRIAN.
13 POMPEIAN.
14 GREEK.
15 GREEK.
16 GREEK.
17 CHINESE, ALTERNATING PATTERN.
18 GREEK, ALTERNATING PATTERN.
19 CHINESE.
20 CHINESE.
21 ARABIAN.
22 CHINESE.
23 GREEK.
24 RENAISSANCE.
25 ARABIAN.
26 CHINESE.
27 CHINESE.
28 PERSIAN.
29 POMPEIAN.
30 CHINESE.
31 CHINESE.
32 GREEK.]
[Illustration: PLATE LIV.
Ornaments on the Walls, House of Sanchez.]
[Illustration:
1, 2, 3, 4, GREEK AND ALBANIAN.
5, 6, 7, 8, RENAISSANCE.
9, 10, 11, 12, 13, 14, ITALIAN.
15, 16, GALLO-ROMAN.
17, 18, 19, ITALIAN.
20 ITALIAN.
21, 22, ITALIAN FAÏENCE.
23 PONDICHERY.
24 ARABIAN.
25, 26, GREEK.]
[Illustration:
1, 2, 3, 4, 5, 6, 7, 8, 10, ARABIAN.
9 CHINESE.
11 RENAISSANCE.
12 GREEK.
13 ARABIAN.
14 ARABIAN.
15 GREEK, ALTERNATING PATTERN.
16 GREEK.
17 MEXICAN AND ARABIAN.
18 GREEK.
19 ARABIAN.
20 AMERICAN, ANCIENT POTTERY.
21, 22, ARABIAN.]
[Illustration: PLATE LV.
Ornament in panels on the Walls.]
[Illustration:
1, 2, EGYPTIAN.
3 EGYPTIAN NECKLACE.
4 ASSYRIAN.
5 POMPEIAN.
6 ITALIAN.
7 EGYPTIAN.
8 FRIEZE. 18TH CENTURY.
9 GREEK.
10 UNCERTAIN.
11 ARABIAN.
12 FRIEZE. 18TH CENTURY.]
[Illustration:
1, 2, 3, 4, FROM PAINTED VASES.
5 GREEK.
6 ORIENTAL FILIGREE.
7, 8, GREEK.
9 PERSIAN.
10 GREEK.
11 CHINESE.
12 ORIENTAL FILIGREE.
13 INDIAN.
14, 15, PERSIAN.
16 ARABIAN.
17 GREEK.
18 PERSIAN.
19 ORIENTAL CHASING.
20 ARABIAN.
21 PERSIAN.
22 TURKISH.
23 GREEK.
24 PASSEMENTERIE.
25 NEAPOLITAN.]
[Illustration:
1, 1´, DAMASCENE.
2, 2´, 2´´, 2´´´, ARABIAN.
3, 3´, ARABIAN.
4, 4´, 4´´, DAMASCENE (ANALOGOUS TO FIGS. 1´, 2´´´, 3´).
5, 5´, ARABIAN.
6, 6´, ARABIAN.
7, 8, 9, ARABIAN.
10, 10´, 11, 11’, CHINESE.
12, 12´, GREEK.
13, 14, PERSIAN.
15, 16, ANGLO-SAXON.]
[Illustration: Ornament in spandrils of arches.]
[Illustration:
1, 2, 3, GREEK.
4 EGYPTIAN.
5 STYLE “LABROUSTE.”
5´ BYZANTINE.
6 GREEK.
7, 7´, GREEK.
8, 9, 10, 10´, 11, 11´,
GREEK (PARTHENON).]
[Illustration:
_Arabian Construction._
1, 1´, ONE SPIRAL.
2, 2´, TWO SPIRALS.
3, 3´, THREE SPIRALS.
4 CROSS QUARTERLY INDICATING POSITIONS ESSENTIAL TO THE _motif_ NUMBER 3.
5, 6, 7, 8, REPETITIONS OF _motif_ NUMBER 3 VARIOUSLY TREATED.
9, 10, 11, 12, 13, 14, ARRANGEMENTS BY ALTERNATING TREATMENT
OF _motif_ NUMBER 3.
THESE ARRANGEMENTS AFFORD EXCELLENT EXAMPLES OF THE ENDLESS DIVERSITY
OF GEOMETRIC FORMS.]
[Illustration: PLATE LVII.
Centre Ornament of the Window.
Dado. Dado.
Pilaster. Pilasters.
Mosaic Dado in a window.
The recess or divan containing these beautiful Mosaics was, doubtless,
the throne of the Moorish kings. The Mosaics are as perfect as when
originally executed, and seem, indeed, to be imperishable. They are
formed of baked clay squeezed into moulds of the different figures,
glazed on the surface.]
[Illustration: PLATE LVIII.
Mosaic Dados on pillars between windows.
The Mosaic Dados on the pillars present a great variety in their
patterns, although the component parts are in each the same.]
[Illustration: PLATE LIX.
Mosaic Dados on pillars between windows.
These Mosaics, though in appearance so different from those of the
preceding plate, will be found on examination to be composed of the same
pieces differently combined.]
[Illustration: PLATE LX.
Lining of one of Pilaster.
the columns.
Dado. Dado. Dado.
The beautiful Mosaic in the centre of this plate is part of the Dado.]
[Illustration: PLATE LXI.
Pavement of the Hall of the Baths.
Mosaic Dado round the internal walls of the Mosque.
Mosaics from the Mosque and the Hall of the Baths. The Mosaic Dados
round the walls of the Mosque appear to be the only portions of the
ancient private Mosque attached to the Palace which have been
preserved intact in their original situation. The motto of the
Kings of Granada, “_There is no conqueror but God_,” was replaced
by “_Nec plus ultra_” of Charles V., when the Mosque was converted
by him into a chapel. The beautiful Mosaic at the top of the plate
is placed round the fountain of the Chamber of Repose of the Baths.]
[Illustration: PLATE LXII.
Azulejos. Painted Tiles.
On the floor of one of the alcoves of the Hall of Justice are to be seen
the painted tiles delineated in the centre of this plate.]
[Illustration: PLATE LXIII.
Mosaics in the Baths.]
[Illustration: PLATE LXIV.
Mosaic from the portico of the Generalife.]
[Illustration: 1, 2, 3, VARIATIONS ON A CHINESE _motif_.
4, 5, 6, VARIATIONS ON A _motif_ HISPANO-ARABIAN.
7, 8, 9, VARIATIONS ON A _motif_, SYRO-ARABIAN.
10, 11, 12, VARIATIONS ON A _motif_, GALLO-ROMAN.]
[Illustration: PLATE LXV.
Ornaments in Panels.]
[Illustration: 1 SIMPLE PLAIT, UNDULATED.
2 DOUBLE PLAIT.
3 SIMPLE PLAIT, INTERSECTED.
4 PLAIT, FROM A GREEK VASE.
5 REDOUBLED PLAIT, GREEK.
6 INFLECTED PLAIT, GREEK.
7 INFLECTED PLAIT, GREEK.
8 QUADRUPLED PLAITS, INTERLACED, SICILIAN.
9 SICILIAN.
10 TRIPLE PLAIT, GREEK.
11 TRIPLE PLAIT, GREEK.
12 DIVERSIFIED PLAIT, NEAPOLITAN.
13 GREEK.
14 GREEK.
15 ARABIAN.
16 PERSIAN (THREE PLAITS, INTERSECTED).
17 GREEK.]
[Illustration: PLATE LXVI.
Ornaments over Arches at one of the Entrances.]
[Illustration: _Egypto-Arabian Knot, or Net-work._
1 DERIVED FROM THE PENTAGON.
2 VARIETY OF PROCEEDING.
3, 4, TRIGONOMETRICAL.
5 OCTAGONAL.
6 HEPTAGONAL.
7 QUADRILATERAL.
8 OCTAGONAL.]
[Illustration: _Indo-Syro-Arabian Knot, or Net-work._
1 SQUARES AND OCTAGONS.
2 DERIVED FROM SQUARES.
3 DERIVED FROM THE SQUARE: FROM THE CENTRE A DODECAGON AND OTHER FIGURES
ARE FORMED BY SUB-DIVISION.
4 DERIVED FROM THE SQUARE: THE ANGLES BEING DIVIDED, THE RESULTING RAYS
DETERMINE THE FIGURES BY INTERSECTION.
5 ANALOGOUS TO FIGURE 2.
6 TRIGONOMETRICAL.
7 HEXAGONAL.]
[Illustration: PLATE LXVII.
Ornaments on the Walls.]
[Illustration: 1, 1’, BRICK FACINGS FROM ROSETTA.
2, 3, 4, ARABIAN.
5 JAPANESE.
6 GRECO-ASSYRIAN.
7 ARABIAN.
8 CHINESE.]
[Illustration: 1 ARABIAN.
2 ORNAMENTED BRICK, ROSETTA.
3, 4, 5, 6, FOUR ANALOGOUS _motifs_, RESPECTIVELY CHINESE, ARABIAN
(_bis_) AND GRECO-ASSYRIAN.
7 ARABIAN.
8 GRECO-EGYPTIAN.]
[Illustration: PLATE LXVIII.
Ornaments in Panels on the Walls.]
[Illustration: 1 ARABIAN (DAMASCUS).
2 CEILING, LOUIS XIII.
3, 4, 5, ARABIAN (DAMASCUS)?
6 INDIAN.]
[Illustration: 1, 2, 3, 4, 5, 6, 7, 8, ARABIAN.]
[Illustration: 1 INCRUSTATION ON POTTERY, FROM OIRON.
2 RENAISSANCE.
3 MEXICAN.
4 CHINESE.
5 EGYPTIAN.
6 ARABIAN.
7, 8, 9, EARLY TILES, FROM DAMASCUS, ROME, AND FLORENCE RESPECTIVELY.
10 ITALIAN.
11, 11’, EGYPTIAN.
12 ITALIAN.]
[Illustration: PLATE LXIX.
Small Panel in Jamb of a Window.]
[Illustration: 1 PERSIAN.
2 ARABIAN CEILING, FROM CAIRO.
3 CEILING, PAINTED BY DUBAN.
4 BYZANTINE.
5 CHINESE.
6 POMPEIAN.]
[Illustration: PLATE LXX.
Small Panel in Jamb of a Window.]
[Illustration: 1, 2, LACE-WORK.
3, 3’, EGYPTIAN.
4, 4’, EGYPTIAN.
5, 6, EGYPTIAN.]
[Illustration: 1, 2, 3, ANGLO-SAXON.
4 EGYPTIAN. STRANGELY ANALOGOUS TO NUMBER 3.
5, 6, 7, ANGLO-SAXON.
8 EGYPTIAN.]
[Illustration: 1 ARABIAN.
2 ITALIAN.
3 RENAISSANCE.
4 ARABIAN.
5 ARABIAN.
6 ARABIAN.]
[Illustration: 1, 2, 3, FROM THE CHURCH OF ST. CROIX, JERUSALEM.
4 SICILIAN.
5, 6, 7, 8, ARABIAN.
9, 10, CHISELLINGS ON STONE, JERUSALEM.
11 MARBLE CHASING, JERUSALEM.
12, 13, ARABIAN CHASINGS, ON COPPER.]
[Illustration: PLATE LXXI.
Panel in the Upper Chamber of the House of Sanchez.]
[Illustration: 1, 2, 3, “PALMETTES” FROM THE PROWS OF _dahabiehs_ (NILE
BOATS)
4, 5, 6, 7, 8, GREEK, FROM EXAMPLES AT ATHENS.]
[Illustration: 1-9. THIS PLATE IS DEVOTED TO CURVILINEAR FIGURES,
CHIEFLY FROM ATHENS.
FIGURE 7 IS FROM A MURAL DECORATION AT POMPEII.]
DESCRIPTION OF THE PLATES
HEXAGONAL FAMILY
[Illustration: 1 PLAN, TRIANGULAR. TO DESCRIBE THE HEXAGON.]
[Illustration: 2 PLAN, TRIANGULAR. LARGE AND SMALLER HEXAGONS.]
[Illustration: 3 PLAN, TRIANGULAR. CURVILINEAL TRANSFORMATION OF THE
PRECEDING FIGURE.]
[Illustration: 4 TRIANGLES CURTAILED; OR, TERNARY HEXAGONS
INTERSECTED.]
[Illustration: PLATE LXXII.
Spandril from Niche of Doorway at one of the Entrances.]
[Illustration: 5 INTERSECTIONS IN COMPARTMENTS. FIVE FIGURES--LARGE AND
SMALLER HEXAGON; HEXAGON OF UNEQUAL LENGTH; DOVE-TAILED HEXAGON;
HEXAGONAL STAR; TRIANGLE.]
[Illustration: 6 HEXAGONS INTERSECTED CIRCULARLY BY THE SIX POINTS, THE
APICES UNITED BY A TRIANGLE. FOUR FIGURES--STAR, PENTAGON, TRIANGLE,
LOZENGE.]
[Illustration: 7 HEXAGONS, INTERSECTED BY THE APICES. THREE
FIGURES--STAR, LOZENGE, DODECAGON.]
[Illustration: 8 TRIANGULAR PLAN. FROM THE APICES OF THE TRIANGLES OF
DIVISION DRAW HEXAGONAL STARS. THE PLAN IS INTERSECTED BY DETACHED
HEXAGONS ENCLOSING THE STARS.]
[Illustration: 9 TRIANGLES ENCLOSED, AND LEAVING HEXAGONAL STARS, THE
STARS BEING JOINED BY ZIG-ZAG BANDS.]
[Illustration: 10 HEXAGONAL STAR, OF WHICH A SIDE FROM EACH APEX IS
EXTENDED IN REVOLVING; THREE STARS THUS REVOLVED ARE JOINED BY A BAND.]
[Illustration: 11 BANDS ENVELOPING A HEXAGON.]
[Illustration: 12 RECTANGLES INTERSECTING REGULARLY BY THREES, AND
INTERLACED BY THEIR SMALLER SIDES, THEIR EXTREMITIES, PENETRATING,
FORMING THREE PAIRS OF PENTAGONS.]
[Illustration: PLATE LXXIII.
Lintel of a Doorway.]
[Illustration: 13 FROM THE APICES OF TRIANGLES OF DIVISION DESCRIBE
CIRCUMFERENCES; DIVIDE THE CIRCUMFERENCES IN TWELVE EQUAL PARTS, AND
TAKE THE DIAGONALS OF FIVE IN FIVE DIVISIONS; THUS STARS OF SIX POINTS
ARE OBTAINED. THESE STARS CONTAIN IN THE ENCLOSURE A HEXAGON OF TERNARY
SYMMETRY, WITH ANGLES ALTERNATELY RIGHT AND OBTUSE.]
[Illustration: 14]
[Illustration: 15 FROM THE APICES OF THE TRIANGLES OF DIVISION DESCRIBE
A CIRCUMFERENCE. WITH A RADIUS EQUAL TO THAT OF THE TRIANGLE. INSCRIBE A
DODECAGON; THEN TAKE THE DIAGONALS OF THREE IN THREE DIVISIONS FROM THE
OTHER DIAGONALS WHICH FORM THE SQUARES.]
[Illustration: 16 FIGURE ANALOGOUS TO FIGURE 8. _q.v._]
[Illustration: 17 FROM THE APICES OF THE TRIANGLES OF DIVISION DESCRIBE
CIRCUMFERENCES HAVING A RADIUS EQUAL TO ONE-THIRD OF A SIDE; SUB-DIVIDE
THEM INTO TWELVE EQUAL PARTS, THEN TAKE THE DIAGONALS OF THREE IN THREE
DIVISIONS. THE RADIUS OF THE CIRCUMFERENCES WOULD BE SMALLER OR LARGER
THAN THE ONE-THIRD OF THE SIDE; AND THEN, BY MEANS OF AN ADJUSTMENT, THE
SQUARES BETWEEN THE APICES WOULD HAVE A SIDE EQUAL TO THAT OF THE
STARS.]
[Illustration: 18 DODECAGONS INTERSECTED BY EACH OTHER, WHICH ARE
OBTAINED BY SUB-DIVISION OF THE ANGLES OF THE TRIANGLES INTO FOUR EQUAL
PARTS.]
[Illustration: 19 DODECAGONS CONTAINING SIX-POINTED STARS SUB-DIVIDED BY
BANDS. THE RADIUS OF THE DODECAGONS IS EQUAL TO HALF A SIDE OF THE
TRIANGLES OF DIVISION.]
[Illustration: 20 FROM THE APICES OF THE TRIANGLES DESCRIBE A
CIRCUMFERENCE, WITH ITS RADIUS EQUAL TO HALF A SIDE OF THE TRIANGLES.
THE SIX-POINTED STARS AND BANDS WHICH ARE DERIVED FROM THEM COULD BE OF
DIFFERENT PROPORTIONS.]
[Illustration: 21 DISTRIBUTION PROCEEDING FROM HEXAGONS AND TRIANGLES.]
[Illustration: 22 SIX-POINTED STARS AND HEXAGONS, FROM WHICH PROCEED
BAND-WORK AND LOZENGES.]
[Illustration: 23 HEXAGONS, TRIANGLES, AND SIX-POINTED STARS.]
[Illustration: 24 SUBJECT SIMILAR TO NUMBER 21.]
[Illustration: PLATE LXXIV.
Capital of Columns.]
[Illustration: 25 LARGE HEXAGONS CROSSED AND CUT BY FIGURES QUARTERED BY
EIGHT SIDES; HORIZONTAL AND VERTICAL BANDS PROCEEDING FROM SIX-POINTED
STARS.]
[Illustration: 26 FROM THE APICES OF THE TRIANGLES OF DIVISION DESCRIBE
THE CIRCUMFERENCES, AND DIVIDE THEM INTO TWELVE EQUAL PARTS. BY THE
POINTS OF THE STAR THUS MADE, DESCRIBE SIX HALF-CIRCLES, IN EACH CASE
FORMING A ROSETTE. SMALL INTERCALARY CIRCLES UNITE THE ROSETTES.]
[Illustration: 27 EACH SIX-POINTED STAR IS SURROUNDED BY A ROSETTE OF
SIX HEXAGONS, WHICH, IN THEIR TURN, DISTRIBUTE THEIR LINES TO FORM
LARGER HEXAGONS.]
[Illustration: 28 EACH SIX-POINTED STAR IS SURROUNDED BY A ROSETTE OF
SIX HEXAGONS, WHICH ARE SUPPLEMENTED BY PERPENDICULAR LINES, WHICH, BY
INTERSECTING OCTAGONS THEMSELVES, ARE THE MEANS OF COMPLETING SMALL
HEXAGONS.]
[Illustration: 29 FROM THE UPPER ANGLES OF THE SQUARES OF DIVISION TRACE
STARS SIX-POINTED, ROTATING ALTERNATELY AS SHOWN IN DIAGRAM. THE
JUNCTION OF THE LINES OF DIVISION DETERMINE THE POINTS OF THE FIGURE.]
[Illustration: 30 ALTERNATING DISPOSITIONS OF SIX-POINTED STAR, WITH
EXTERIOR ROSETTE OF SIX HEXAGONS. THE ANGLES OF THE SQUARE BEING DIVIDED
INTO THREE EQUAL PARTS BY A FIRST AND SECOND RADIUS, A CIRCUMFERENCE IS
MADE, WITHIN WHICH IS INSCRIBED THE STAR OF SIX POINTS. THE REST
FOLLOWS.]
[Illustration: 31 SUBJECT ANALOGOUS TO NUMBERS 28, 29.]
[Illustration: 32 ALTERNATING DISPOSITION OF SIX-POINTED STAR,
SURROUNDED BY SIX HEXAGONS. SUB-DIVIDE THE ANGLES OF THE SQUARE INTO
THREE EQUAL PARTS. THE CONJUNCTION OF THE RADII WITH THEM, AND WITH THE
MEDIALS OF THE SQUARE, MAKE THE FIGURE. IN THE CENTRE OF THE SQUARE A
LINEAL SUBJECT, ALTERNATING.]
[Illustration: PLATE LXXV.
Capital of Columns.]
[Illustration: 33 HEXAGONAL AND OCTAGONAL DISTRIBUTION.]
[Illustration: 34 HEXAGONAL DISTRIBUTION. PENTAGONAL STARS AND
HEXAGONS.]
[Illustration: 35 HEXAGONAL STAR INSCRIBING A SECOND SIX-POINTED STAR.
THE INTERSECTIONS GIVE LOZENGES AND HEXAGONS.]
[Illustration: 36 SQUARE PLAN. DIVIDE OPPOSITE LINES INTO THREE, AND BY
THE CENTRE OF THE SQUARE CARRY TWO CROSS LINES.]
[Illustration: PLATE LXXVI.
Capital of Columns.]
[Illustration: 37 TRIANGULAR PLAN. HEXAGONAL STAR AND HEXAGONAL ROSETTE
ENCLOSED BY REGULAR HEXAGON.]
[Illustration: 38 HEXAGONAL, SQUARE, AND TRIANGULAR PLAN. HEXAGONAL
DISTRIBUTION. DODECAGON STAR IN CENTRES.]
[Illustration: 39 TRIANGULAR PLAN. HEXAGONAL DISPOSITION.]
[Illustration: 40 TRIANGULAR PLAN. HEXAGONS AND TRIANGLES; INTERSECTED
HEXAGONS; HEXAGONAL CURVILINEAR ROSETTES.]
[Illustration: PLATE LXXVII.
SEVILLE.
Socle of the Entrance Arch to the Antechapel.]
[Illustration: 41 TRIANGULAR PLAN. DODECAGONAL STARS; HEXAGONAL STARS
ENCLOSED BY REGULAR HEXAGON.]
[Illustration: 42 SQUARE PLAN. FROM THE CENTRE DESCRIBE A CIRCUMFERENCE;
DIVIDE CIRCUMFERENCE INTO EIGHT EQUAL PARTS, STARRED OCTAGONS ARE THUS
OBTAINED, THE PROLONGED SIDES OF WHICH DETERMINE QUADRILATERAL STARS.]
[Illustration: 43 CURVILINEAL TRANSFORMATION OF FIGURE 42.]
[Illustration: 44 OCTAGONAL STARS; INTERSECTING LOZENGES, SQUARES,
TRILATERALS.]
[Illustration: 45 DIVIDE THE SQUARE INTO FOUR EQUAL PARTS. THE MEETING
OF THE FIRST LINE WITH THE MEDIAN OF THE SQUARE GIVES THE RADIUS OF A
CIRCUMFERENCE. THE DIAGONAL LINES GIVE AN OCTAGONAL STAR.]
[Illustration: 46 SQUARE PLAN. FROM THE CENTRE A CIRCUMFERENCE, AND BY
DIAGONALS A STARRED OCTAGON.]
[Illustration: 47 CURVILINEAR AND UNDULATING OCTAGONS AND PENTAGONS.]
[Illustration: 48 DISTRIBUTION OF STARRED AND REGULAR OCTAGONS, WITH
STARRED PENTAGONS.]
[Illustration: 49 OCTAGONAL ROSETTES FOLLOWING ISOCELES TRIANGLE WITH
PENTAGONAL STARS AND REGULAR OCTAGONS INTERCALARY.]