DESCRIPTION OF THE PLATES

PLATE LI.Band at Springing of Arch at the Entrance to one of the Halls.

PLATE LI.

Band at Springing of Arch at the Entrance to one of the Halls.

In the art of the Arabs the inspiration is completely independent of 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 detailof 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 hisL’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

PLATE LII.Panelling of a Recess.

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, ormosaics. 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 beentirelygeometric.

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

PLATE LIII.Blank Window.

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 theplanwhich 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.

1 GREEK, RECTILINEAR.1´ GREEK, CURVILINEAR.2 CHINESE, RECTILINEAR.2´ GREEK, CURVILINEAR.3 and 4, GREEK, ALTERNATINGPATTERN.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.

PLATE LIV.Ornaments on the Walls, House of Sanchez.

PLATE LIV.

Ornaments on the Walls, House of Sanchez.

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.

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.

PLATE LV.Ornament in panels on the Walls.

PLATE LV.

Ornament in panels on the Walls.

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.

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.

1, 1´, DAMASCENE.2, 2´, 2´´, 2´´´, ARABIAN.3, 3´, ARABIAN.4, 4´, 4´´, DAMASCENE (ANALOGOUSTO 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.

PLATE LVI. Ornament in spandrils of arches.

1, 2, 3, GREEK.4 EGYPTIAN.5 STYLE “LABROUSTE.”5´ BYZANTINE.6 GREEK.7, 7´, GREEK.8, 9, 10, 10´, 11, 11´,GREEK (PARTHENON).

Arabian Construction.1, 1´, ONE SPIRAL.2, 2´, TWO SPIRALS.3, 3´, THREE SPIRALS.4 CROSS QUARTERLY INDICATING POSITIONS ESSENTIAL TO THEmotifNUMBER 3.5, 6, 7, 8, REPETITIONS OFmotifNUMBER 3 VARIOUSLY TREATED.9, 10, 11, 12, 13, 14, ARRANGEMENTS BY ALTERNATING TREATMENT OFmotifNUMBER 3.THESE ARRANGEMENTS AFFORD EXCELLENT EXAMPLES OF THE ENDLESS DIVERSITYOF GEOMETRIC FORMS.

PLATE LVII.Centre Ornament of the Window.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.

PLATE LVII.

Centre Ornament of the Window.

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.

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.

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.

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.

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.

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.

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.

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.

PLATE LX.The beautiful Mosaic in the centre of this plate is part of the Dado.

PLATE LX.

The beautiful Mosaic in the centre of this plate is part of the Dado.

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.

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.

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.

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.

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.

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.

PLATE LXIII.Mosaics in the Baths.

PLATE LXIII.

Mosaics in the Baths.

PLATE LXIV.Mosaic from the portico of the Generalife.

PLATE LXIV.

Mosaic from the portico of the Generalife.

1, 2, 3, VARIATIONS ON A CHINESEmotif.4, 5, 6, VARIATIONS ON AmotifHISPANO-ARABIAN.7, 8, 9, VARIATIONS ON Amotif, SYRO-ARABIAN.10, 11, 12, VARIATIONS ON Amotif, GALLO-ROMAN.

PLATE LXV.Ornaments in Panels.

PLATE LXV.

Ornaments in Panels.

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.

PLATE LXVI.Ornaments over Arches at one of the Entrances.

PLATE LXVI.

Ornaments over Arches at one of the Entrances.

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.

Egypto-Arabian Knot, or Net-work.

Indo-Syro-Arabian Knot, or Net-work.1 SQUARES AND OCTAGONS.2 DERIVED FROM SQUARES.3 DERIVED FROM THE SQUARE: FROM THE CENTREA DODECAGON AND OTHER FIGURES ARE FORMEDBY SUB-DIVISION.4 DERIVED FROM THE SQUARE: THE ANGLES BEINGDIVIDED, THE RESULTING RAYS DETERMINETHE FIGURES BY INTERSECTION.5 ANALOGOUS TO FIGURE 2.6 TRIGONOMETRICAL.7 HEXAGONAL.

Indo-Syro-Arabian Knot, or Net-work.

PLATE LXVII.Ornaments on the Walls.

PLATE LXVII.

Ornaments on the Walls.

1, 1’, BRICK FACINGS FROM ROSETTA.2, 3, 4, ARABIAN.5 JAPANESE.6 GRECO-ASSYRIAN.7 ARABIAN.8 CHINESE.

1 ARABIAN.2 ORNAMENTED BRICK, ROSETTA.3, 4, 5, 6, FOUR ANALOGOUSmotifs, RESPECTIVELY CHINESE, ARABIAN (bis) AND GRECO-ASSYRIAN. 7 ARABIAN. 8 GRECO-EGYPTIAN.

PLATE LXVIII.Ornaments in Panels on the Walls.

PLATE LXVIII.

Ornaments in Panels on the Walls.

1 ARABIAN (DAMASCUS).2 CEILING, LOUIS XIII.3, 4, 5, ARABIAN (DAMASCUS)?6 INDIAN.

1, 2, 3, 4, 5, 6, 7, 8, ARABIAN.

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.

PLATE LXIX.Small Panel in Jamb of a Window.

PLATE LXIX.

Small Panel in Jamb of a Window.

1 PERSIAN. 2 ARABIAN CEILING, FROM CAIRO. 3 CEILING, PAINTED BY DUBAN.4 BYZANTINE. 5 CHINESE. 6 POMPEIAN.

PLATE LXX.Small Panel in Jamb of a Window.

PLATE LXX.

Small Panel in Jamb of a Window.

1, 2, LACE-WORK. 3, 3’, EGYPTIAN. 4, 4’, EGYPTIAN. 5, 6, EGYPTIAN.

1, 2, 3, ANGLO-SAXON. 4 EGYPTIAN. STRANGELY ANALOGOUS TO NUMBER 3.5, 6, 7, ANGLO-SAXON. 8 EGYPTIAN.

1 ARABIAN.2 ITALIAN.3 RENAISSANCE.4 ARABIAN.5 ARABIAN.6 ARABIAN.

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.

PLATE LXXI.Panel in the Upper Chamber of the House of Sanchez.

PLATE LXXI.

Panel in the Upper Chamber of the House of Sanchez.

1, 2, 3, “PALMETTES” FROM THE PROWS OFdahabiehs(NILE BOATS)4, 5, 6, 7, 8, GREEK, FROM EXAMPLES AT ATHENS.

1, 2, 3, “PALMETTES” FROM THE PROWS OFdahabiehs(NILE BOATS)

4, 5, 6, 7, 8, GREEK, FROM EXAMPLES AT ATHENS.

1-9. THIS PLATE IS DEVOTED TO CURVILINEAR FIGURES, CHIEFLY FROM ATHENS.FIGURE 7 IS FROM A MURAL DECORATION AT POMPEII.

HEXAGONAL FAMILY

1 PLAN, TRIANGULAR. TO DESCRIBE THE HEXAGON.

2 PLAN, TRIANGULAR. LARGE AND SMALLER HEXAGONS.

3 PLAN, TRIANGULAR. CURVILINEAL TRANSFORMATION OF THE PRECEDING FIGURE.

4 TRIANGLES CURTAILED; OR, TERNARY HEXAGONS INTERSECTED.

PLATE LXXII.Spandril from Niche of Doorway at one of the Entrances.

PLATE LXXII.

Spandril from Niche of Doorway at one of the Entrances.

5 INTERSECTIONS IN COMPARTMENTS. FIVE FIGURES—LARGE AND SMALLER HEXAGON; HEXAGON OF UNEQUAL LENGTH; DOVE-TAILED HEXAGON; HEXAGONAL STAR; TRIANGLE.

6 HEXAGONS INTERSECTED CIRCULARLY BY THE SIX POINTS, THE APICES UNITED BY A TRIANGLE. FOUR FIGURES—STAR, PENTAGON, TRIANGLE, LOZENGE.

7 HEXAGONS, INTERSECTED BY THE APICES. THREE FIGURES—STAR, LOZENGE, DODECAGON.

8 TRIANGULAR PLAN. FROM THE APICES OF THE TRIANGLES OF DIVISION DRAW HEXAGONAL STARS. THE PLAN IS INTERSECTED BY DETACHED HEXAGONS ENCLOSING THE STARS.

9 TRIANGLES ENCLOSED, AND LEAVING HEXAGONAL STARS, THE STARS BEING JOINED BY ZIG-ZAG BANDS.

10 HEXAGONAL STAR, OF WHICH A SIDE FROM EACH APEX IS EXTENDED IN REVOLVING; THREE STARS THUS REVOLVED ARE JOINED BY A BAND.

11 BANDS ENVELOPING A HEXAGON.

12 RECTANGLES INTERSECTING REGULARLY BY THREES, AND INTERLACED BY THEIR SMALLER SIDES, THEIR EXTREMITIES, PENETRATING, FORMING THREE PAIRS OF PENTAGONS.

PLATE LXXIII.Lintel of a Doorway.

PLATE LXXIII.

Lintel of a Doorway.

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.

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.

16 FIGURE ANALOGOUS TO FIGURE 8.q.v.

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.

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