DESCRIPTION OF THE PLATES
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.
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.
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.
14
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.
18 DODECAGONS INTERSECTED BY EACH OTHER, WHICH ARE OBTAINED BY SUB-DIVISION OF THE ANGLES OF THE TRIANGLES INTO FOUR EQUAL PARTS.
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.
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.
21 DISTRIBUTION PROCEEDING FROM HEXAGONS AND TRIANGLES.
22 SIX-POINTED STARS AND HEXAGONS, FROM WHICH PROCEED BAND-WORK AND LOZENGES.
23 HEXAGONS, TRIANGLES, AND SIX-POINTED STARS.
24 SUBJECT SIMILAR TO NUMBER 21.
PLATE LXXIV.
Capital of Columns.
25 LARGE HEXAGONS CROSSED AND CUT BY FIGURES QUARTERED BY EIGHT SIDES; HORIZONTAL AND VERTICAL BANDS PROCEEDING FROM SIX-POINTED STARS.
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.
27 EACH SIX-POINTED STAR IS SURROUNDED BY A ROSETTE OF SIX HEXAGONS, WHICH, IN THEIR TURN, DISTRIBUTE THEIR LINES TO FORM LARGER HEXAGONS.
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.
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.
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.
31 SUBJECT ANALOGOUS TO NUMBERS 28, 29.
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.
PLATE LXXV.
Capital of Columns.
33 HEXAGONAL AND OCTAGONAL DISTRIBUTION.
34 HEXAGONAL DISTRIBUTION. PENTAGONAL STARS AND HEXAGONS.
35 HEXAGONAL STAR INSCRIBING A SECOND SIX-POINTED STAR. THE INTERSECTIONS GIVE LOZENGES AND HEXAGONS.
36 SQUARE PLAN. DIVIDE OPPOSITE LINES INTO THREE, AND BY THE CENTRE OF THE SQUARE CARRY TWO CROSS LINES.
PLATE LXXVI.
Capital of Columns.
37 TRIANGULAR PLAN. HEXAGONAL STAR AND HEXAGONAL ROSETTE ENCLOSED BY REGULAR HEXAGON.
38 HEXAGONAL, SQUARE, AND TRIANGULAR PLAN. HEXAGONAL DISTRIBUTION. DODECAGON STAR IN CENTRES.
39 TRIANGULAR PLAN. HEXAGONAL DISPOSITION.
40 TRIANGULAR PLAN. HEXAGONS AND TRIANGLES; INTERSECTED HEXAGONS; HEXAGONAL CURVILINEAR ROSETTES.
PLATE LXXVII.
SEVILLE.
Socle of the Entrance Arch to the Antechapel.
41 TRIANGULAR PLAN. DODECAGONAL STARS; HEXAGONAL STARS ENCLOSED BY REGULAR HEXAGON.
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.
43 CURVILINEAL TRANSFORMATION OF FIGURE 42.
44 OCTAGONAL STARS; INTERSECTING LOZENGES, SQUARES, TRILATERALS.
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.
46 SQUARE PLAN. FROM THE CENTRE A CIRCUMFERENCE, AND BY DIAGONALS A STARRED OCTAGON.
47 CURVILINEAR AND UNDULATING OCTAGONS AND PENTAGONS.
48 DISTRIBUTION OF STARRED AND REGULAR OCTAGONS, WITH STARRED PENTAGONS.
49 OCTAGONAL ROSETTES FOLLOWING ISOCELES TRIANGLE WITH PENTAGONAL STARS AND REGULAR OCTAGONS INTERCALARY.
50 DESCRIBE CIRCUMFERENCES AS SHOWN IN PLAN, IN WHICH ARE CARRIED DIAGONALS. FROM THE CENTRE INSCRIBE A SQUARE. THE INTERSECTIONS OF THE LINES OF THE STAR COMPLETE THE FIGURE.
51 DESCRIBE CIRCUMFERENCES EQUAL AND TANGENT, AND DIVIDE INTO SIXTEEN EQUAL PARTS. BY THE ANGLES OF DIVISION DESCRIBE A PENTAGON STARRED. BY THE CENTRE OF THE SQUARE AN OCTAGON STARRED, FROM WHICH EMANATES AN OCTAGON ROSETTE. HEXAGONS REGULAR AND STARRED.
52 DIVIDE TANGENT CIRCUMFERENCES INTO SIXTEEN EQUAL PARTS. SIMILAR DISPOSITION TO FIGURE NUMBER 49, BUT WITH DIFFERENT TREATMENT.
53 DESCRIBE CIRCUMFERENCES AS IN PLAN; INSCRIBE THEREIN BY THE DIAGONALS A STAR, THE SIDES OF WHICH, PROLONGED AND INTERSECTED BY THE OCTAGONAL STAR, DETERMINE THE ROSETTES.
54 DIVIDE CIRCUMFERENCES AS IN PLAN INTO THIRTY-TWO EQUAL PARTS. FROM THE CENTRE OF THE SQUARE INSCRIBE A STAR OF SIXTEEN POINTS, THE PROLONGATION OF ITS LINES FORMING THE ROSETTE OF SIXTEEN.
55 DESCRIBE CIRCUMFERENCES AS IN PLAN. FROM THE CENTRE OF THE PLAN BY RADIATING LINES INSCRIBE A STARRED OCTAGON; THE PROLONGATION AND MEETING OF ITS LINES IN REPETITION COMPLETE THE FIGURE.
56 DESCRIBE CIRCUMFERENCES AS IN PLAN. IN THE CENTRE OF FOUR EQUAL SQUARES TRACE AN OCTAGONAL ROSETTE, AFTER HAVING TAKEN IN THE LARGE ROSETTE OF SIXTEEN POINTS, WHICH LENDS ITS LINES TO THE FORMATION OF EIGHT SURROUNDING CRUCIFORM FIGURES.
PLATE LXXVIII.
SEVILLE.
Socle of the Entrance Arch to the Chapel.
57 FROM THE CENTRE OF FOUR EQUAL SQUARES DESCRIBE CIRCUMFERENCES AS IN PLAN. INSCRIBE THEREIN THE STARRED OCTAGON, THE PROLONGED SIDES OF WHICH DETERMINE THE QUADRILATERAL ROSETTE.
58 THE SQUARE OF DISTRIBUTION IS A RECTANGLE LENGTHENED, FROM WHICH OCTAGONS ARE TRACED. TERNARY STARS, YET WITH SIX POINTS, AND PAIRED STARS WITH FIVE POINTS FILL IN THE RECTANGLE.
59 DESIGN OF FOUR FIGURES. AN OCTAGON, A HEXAGON PAIRED, A STARRED PENTAGON, AND A STARRED HEXAGON.
60 ANALOGOUS TO NUMBER 58, WITH CLOSER DEVELOPMENT.
61 A STARRED OCTAGON, THE PROLONGED LINES OF WHICH FORM AN OCTAGONAL ROSETTE, SEPARATED BY A REGULAR HEXAGON.
62 DIVIDE CIRCUMFERENCES AS IN PLAN INTO SIXTEEN EQUAL PARTS. THE DIAGONALS WILL GIVE A STAR OF SIXTEEN POINTS, THE LINES OF WHICH, EXTENDED, FORM A ROSETTE OF SIXTEEN POINTS WITHIN A SQUARE. THE ANGLES OF THE SQUARE INTERSECT REGULAR HEXAGONS.
63 DESCRIBE THE CIRCUMFERENCES AS IN THE PLAN. INSCRIBE FROM A CENTRE A STARRED OCTAGON ENCLOSED WITHIN A REGULAR OCTAGON, A STARRED HEXAGON WITHIN ALTERNATE HEXAGONS, AND A CRUCIFORM FIGURE WITHIN A FOUR-POINTED STAR.
63’ DESCRIBE CIRCUMFERENCES AS IN THE PLAN, AND FROM A CENTRE INSCRIBE A STARRED OCTAGON; FROM THE EXTENDED LINES IS FORMED A CRUCIFORM FIGURE. FROM OTHER CENTRES INSCRIBE STARRED AND REGULAR HEXAGONS.
PLATE LXXIX. SEVILLE.
Detail of the Tiles of the Altar.
64 DESCRIBE CIRCUMFERENCES AS IN THE PLAN. FROM A CENTRE INSCRIBE A STARRED OCTAGON OF WHICH THE SIDES ARE PROLONGED. BY THESE PROLONGATIONS, AND BY OCTAGONAL FIGURES IN PAIRS, THE TRACING IS COMPLETE.
65 DIVIDE CIRCUMFERENCES AS IN THE PLAN INTO TWENTY-FOUR EQUAL PARTS, AND INSCRIBE FROM A CENTRE A STARRED DODECAGON, THE EXTENDED LINES OF WHICH DETERMINE THE INTERSECTING LINES OF THE ROSETTE.
66 DESCRIBE CIRCUMFERENCES AS IN THE PLAN. FROM A CENTRE INSCRIBE A STARRED DODECAGON ANALOGOUS TO NUMBER 65.
67 TRIANGULAR PLAN. DESCRIBE CIRCUMFERENCES AS IN THE PLAN. FROM A CENTRE INSCRIBE A STARRED DODECAGON, THE EXTENDED LINES OF WHICH FORM THE UNEQUAL LIMBS OF A ROSETTE, AND A CRUCIFORM FIGURE WITHIN A SQUARE.
PLATE LXXX.
SEVILLE.
Socle in the Interior of the Chapel.
68 DIVIDE AS IN THE PLAN. INSCRIBE A STARRED DODECAGON, THE SIDES OF WHICH PROLONGED INSCRIBE THE LINES OF THE ROSETTE. FOUR ROSETTES PENETRATE EACH OTHER, AND ARE EACH INVADED BY A STAR HAVING TRIANGULAR WEBS.
69 FROM A CENTRE AS IN THE PLAN DESCRIBE A STARRED DODECAGON, THE SIDES OF WHICH PROLONGED FORM THE LINES OF THE ROSETTE. THE ROSETTE, BY EXTENDING LINES, IS SURROUNDED BY TWELVE HEXAGONS.
70 DIVIDE AS IN THE PLAN. DESIGN ANALOGOUS TO NUMBER 69. BY EXTENSION OF LINES OF THE ROSETTE HEXAGONS ARE GROUPED.
71 DIVIDE AS IN PLAN. DESIGN ANALOGOUS TO NUMBER 70.
PLATE LXXXI.
SEVILLE.
Socle in the Interior of the Chapel.
72 DIVIDE AS IN PLAN. THE CIRCUMFERENCES DIVIDED INTO TWENTY-FOUR EQUAL PARTS DETERMINE THE ROSETTE, THE EXTENDED LINES OF WHICH DESCRIBE THE STARRED PENTAGON.
73 CURVILINEAR TRANSFORMATION OF NUMBER 72 BY THE SUBSTITUTION OF ARCS FOR RECTILINEAL FEATURES.
74 DIVIDE THE CIRCUMFERENCES INTO TWENTY-FOUR EQUAL PARTS. INSCRIBE THE STARRED DODECAGON, THE EXTENDED LINES OF WHICH DESCRIBE THE ROSETTE.
75 DESCRIBE THREE CONCENTRIC CIRCUMFERENCES AS IN PLAN. THE ROSETTE BECOMES ENTIRE BY LINES EXTENDED FROM THE STARRED DODECAGON. CROSSED LINES FROM THE ROSETTE DETERMINE THE SQUARE.
76 TRANSFORMATION OF NUMBER 75. ROSETTE IDENTICAL. IN THE CENTRE OF A SQUARE DESCRIBE AN OCTAGON, THE PROLONGED SIDES OF WHICH INVADE THE SQUARE WHICH FIGURES AROUND THE ROSETTE.
77 DIVIDE AS IN PLAN. FROM A CENTRE TRACE A STARRED HEXAGON, THE EXTENDED LINES OF WHICH CUT THE PROLONGED LINES OF THE ROSETTE.
78 DESCRIBE CIRCUMFERENCES AS IN PLAN. FROM A CENTRE TRACE A STARRED DODECAGON. THUS ARE DETERMINED ROSETTES PLACED END TO END, EACH IN A REGULAR HEXAGON.
79 DESCRIBE CIRCUMFERENCES AS IN PLAN. THE ROSETTE IS DETERMINED BY THE STARRED DODECAGON. THIS DESIGN IS MOST DIVERSIFIED, AND CAPABLE OF EXHAUSTIVE FORMS OF ORNAMENT.
80 FROM A CENTRE DRAW A STARRED DODECAGON, WHICH DETERMINES THE ROSETTE, THE CROSSED LINES AT THE POINTS OF THE ROSETTE DETERMINING THE MANY REGULAR HEXAGONS AND tricèles.
81 HEXAGONAL DISTRIBUTION. FROM A CENTRE DRAW A STARRED DODECAGON DETERMINING THE ROSETTE, THE ALTERNATELY CROSSED LINES OF WHICH FORM A tricèle, WITHIN A SECOND CIRCUMFERENCE, AS IN THE PLAN, DRAW A STARRED HEXAGON, THE EXTENDED LINES FORMING SIX REGULAR HEXAGONS.
82 FROM A CENTRE A STARRED DODECAGON. THE LINES EXTENDED FORM AN OUTER STARRED DODECAGON, AND BY CROSSING DESCRIBES A STARRED HEXAGON AND A LOZENGE, WITHIN WHICH IS A CRUCIFORM FIGURE.
82’ THE RADIUS OF THE CIRCUMFERENCE IS EQUAL TO A THIRD OF THE HEIGHT OF THE TRIANGLE, AND THE SQUARE MAKES A STAR OF FOUR POINTS AT EACH ANGLE.
83 DRAW CIRCUMFERENCES AND DIVIDE AS IN PLAN. THE STARRED DODECAGON DETERMINED BY INTERTWINED SQUARES. THE LINES OF THE DODECAGON, EXTENDED AT INTERVALS, FORM A STAR OF FOUR POINTS.
84 DESCRIBE CIRCUMFERENCES AS IN PLAN. FROM A CENTRE AN INNER AND OUTER STARRED DODECAGON, THE LINES OF WHICH EXTENDED FORM A STARRED AND REGULAR HEXAGON, INCLUDING A STARRED OCTAGON WHICH MERGES INTO A CRUCIFORM FIGURE.
85 TRACE THE NET-WORK OF THE DODECAGON, THE HEXAGON, AND THE FOUR-POINTED STARS. FOLLOW DIAGONALS AS IN PLAN.
86 DRAW CIRCUMFERENCES AS IN PLAN. FROM A CENTRE AN INNER AND OUTER STARRED DODECAGON. EXTENDED LINES OF THE INNER DODECAGON FORM SIX SQUARES WHICH INVADE A REGULAR DODECAGON.
PLATE LXXXII. Mosaics from Various Halls.
87 SQUARE PLAN. AN INNER AND OUTER STARRED DODECAGON, AND A REGULAR DODECAGON BY DIAGONALS.
88 SQUARE PLAN. DESCRIBE CIRCUMFERENCES AND DIVIDE THEM INTO TWENTY-FOUR EQUAL PARTS, AND DRAW THE DIAGONALS OF EIGHT IN EIGHT DIVISIONS. THE REST FOLLOWS.
89: NET-WORK OF THE DODECAGON AND THE TRIANGLE ASSEMBLED. BY EXTENDED LINES OF THE STARRED DODECAGON AN IRREGULAR POLYGON, AND A ROSETTE OF TWELVE LIMBS ARE FORMED.
90: ISOCELES PLAN. A CIRCUMFERENCE IS DRAWN IN A SQUARE AND DIVIDED INTO TWENTY-FOUR EQUAL PARTS. A CIRCUMFERENCE, CONCENTRIC TO THE FIRST, COMPLETES THE ROSETTE BY MEANS OF DIAGONALS. THE SMALL HEXAGON AND THE OCTAGON ARE TRACED.
91: DESCRIBE CIRCUMFERENCE AND DIVIDE INTO TWENTY-FOUR EQUAL PARTS. THE REGULAR DODECAGON IS DRAWN. THE INNER AND OUTER STARRED DODECAGONS ARE DESCRIBED BY RADIATING LINES.
92: NET-WORK OF THE HEXAGON AND THE TRIANGLE. THE ROSETTE OF TWELVE POINTS SPRINGING FROM A STARRED DODECAGON IS ENCLOSED BY A HEXAGON, TRELLISED, FROM WHICH THE tricèles ARE DRAWN.
93: OF SIMILAR INTENTION TO NUMBER 92, BUT AN IRREGULAR HEXAGON RECEIVES INTERCALARY LOZENGES.
94: TRIANGULAR PLAN. TRACED BY TRELLISED NET-WORK. THE HEXAGON ENVELOPED IN SPIRALS.
95: TRIANGULAR PLAN. HEXAGON ENVELOPED IN SPIRALS. ANALOGOUS TO NUMBER 94.
96: NET-WORK OF THE OCTAGON, HEXAGON, AND CIRCLE, ASSEMBLED. FROM THE STARRED OCTAGONS A CURVILINEAL ROSETTE.
97: SQUARE PLAN. STARS AND ROSETTES. DESCRIBE CIRCUMFERENCES AS INDICATED. THE OCTAGONAL STARS RECEIVE THE EXTENDED LINES OF THE HEXAGONAL AND PENTAGONAL STARS. THE REST FOLLOWS.
98: DIVIDE CIRCUMFERENCES AS IN THE PLAN. FROM THE CENTRE OF THE HEXAGONAL ROSETTE DESCRIBE A CIRCUMFERENCE TANGENT TO THE FIRST, AND DIVIDE INTO TWELVE PARTS. BY THE AID OF THE PENTAGON COMPRISED COMPLETE THE ROSETTE; THEN, DEPENDING ON THE PENTAGON—WHICH, THOUGH IRREGULAR, RULES ALL—TRACE THE PENTAGONAL FIGURE WHICH STANDS ON THE POINTS OF THE ROSETTES.
PLATE LXXXIII.
Mosaics from Various Halls.
99 ISOCELES PLAN. DIVIDE THE SPACE SURROUNDING THE ACUTE APICES OF THE LOZENGE INTO TWENTY EQUAL PARTS, AND OF THE OBTUSE APICES INTO SIXTEEN. IN THE ONE DRAW A STARRED DECAGONAL, AND IN THE OTHER A STARRED OCTAGONAL ROSETTE. THE ADJUSTMENT OF TWO TYPES SO DIFFERENT IS NOT CONSIDERED SUCCESSFUL.
100 DIAGRAM OF THE DODECAGON, HEXAGON AND SQUARE. IN THE CENTRE OF THE SQUARE A REGULAR OCTAGON, WHICH IS SUPREME. THEN FROM THE STARRED DODECAGON INSCRIBE A ROSETTE OF TWELVE POINTS; LASTLY, FROM THE STARRED HEXAGON INSCRIBE A ROSETTE OF SIX POINTS.
101 DIVIDE THE CIRCUMFERENCES AS IN THE PLAN, THE ONE INTO TWENTY-FOUR AND THE OTHER INTO TWELVE EQUAL PARTS. FOR THE REST, THE CENTRES BEING INDICATED, IT IS EASY TO TRACE THE ARCS, AND SO COMPLETE THE FIGURE.
102 THE LOZENGE AND TRELLISED ROSETTE EMANATING FROM STARRED HEXAGON, ALTERNATING ROW BY ROW WITH DODECAGONAL ROSETTE SPRINGING FROM STARRED DODECAGON.
PLATE LXXXIV.
Part of Ceiling of a Portico.
103 DESCRIBE THE CIRCUMFERENCES AS IN PLAN. BY THE POINTS OF THE STARRED HEXAGON DESCRIBE A REGULAR HEXAGON. BY LINES EXTENDED FROM THE STARRED HEXAGON THE TWELVE-POINTED ROSETTE IS FORMED, CONSTRUCTING AT THE SAME TIME THE STARRED DODECAGON.
104 DESIGN ANALOGOUS TO NUMBER 103, BUT WITH CHANGE OF motif.
105 SQUARE PLAN. DIVIDE AS INDICATED AND INSCRIBE A STARRED DODECAGON, THE EXTENDED LINES OF WHICH FORM AN OUTER STAR ALSO OF TWELVE POINTS; THE STARRED OCTAGON IS CONSTITUTED BY POINTS PROLONGED FROM THE DODECAGON.
106 SQUARE PLAN. SIMILAR GROUND-WORK TO THAT OF NUMBER 105. THE DODECAGONAL AND OCTAGONAL ROSETTES ARE DESCRIBED BY CONCENTRIC CIRCUMFERENCES.
107 SQUARE PLAN. SIMILAR GROUND-WORK TO NUMBERS 105 AND 106. THE TREATMENT CONSIDERABLY CHANGED.
108 SQUARE PLAN. SUB-DIVIDE AS INDICATED. INSCRIBE THE PENTAGON, THE EXTENDED LINES OF WHICH ESTABLISH THE OCTAGONAL STAR AND ROSETTE, AS WELL AS THE DODECAGONAL ROSETTE AND STAR.
109 SQUARE PLAN. DIVIDE AS INDICATED. THE FLOWER-WORK WHICH ACCOMPANIES THE IRREGULAR OCTAGON, THOUGH INDEPENDENT OF GEOMETRIC CONSTRUCTION, IS YET WITHIN THE PROPULSION OF THE LINES.
110 GROUND-WORK ANALOGOUS TO NUMBER 108, BUT ON A TRIANGULAR PLAN. THE EXTENDED LINES OF THE PENTAGON GOVERN THE ENNEAGONAL AND DODECAGONAL STAR AND ROSETTE.
111 CURVILINEAR TRANSFORMATION OF NUMBER 110.
112 TRIANGULAR PLAN. DISTRIBUTION OF ENNEAGONAL AND DODECAGONAL STARS AND ROSETTES. [THE DODECAGON ONLY PARTIALLY DISPLAYED.]
113 TRIANGULAR PLAN. SIMILAR CONSTRUCTION TO NUMBER 112. THE DODECAGONAL STAR, ROSETTE, AND OUTER STAR, WHICH ARE IN THE DIAGRAM NUMBER 112 ONLY PARTIALLY SEEN, ARE HERE DISPLAYED.
114 TRIANGULAR PLAN. FROM A CENTRE AS IN PLAN DESCRIBE CIRCUMFERENCES, WHICH RULE THE DODECAGONAL STAR, ROSETTE, AND OUTER STAR. MANY OF THE FIGURES ARE DRAWN INDEPENDENTLY, THOUGH GOVERNED BY DIVISIONS.
115 DIVIDE AS IN PLAN. INSCRIBE A DECAGONAL ROSETTE, FROM THE PROLONGED LINES OF WHICH PROCEED THE PENTAGONAL STAR, THE REGULAR OCTAGON, AND OTHER FIGURES.
116 DIVIDE AS IN PLAN. TWO DIFFERENT ROSETTES, ONE OF TWELVE AND THE OTHER OF FIFTEEN POINTS. [THE DODECAGONAL ROSETTE IS, HOWEVER, ONLY PARTIALLY SHOWN HERE.]
117 DESCRIBE CIRCUMFERENCES AND TRACE ROSETTE OF SIXTEEN POINTS. THE LINES EXTENDED WILL COMPLETE THE FIGURE.
118 CURVILINEAR TRANSFORMATION OF NUMBER 117.
119 DIVIDE AS INDICATED, AND THE RESULTING ROSETTE OF SIXTEEN POINTS, WHICH WOULD NATURALLY BE RECTILINEAR, MAY BE EASILY TRANSFORMED TO CURVILINEAR; WHILE THE PENTAGONAL STARS, TREATED IN UNDULATING FORM, BECOME FLOWER-WORK OR FOLIAGE.
120 SAME GROUND-WORK AS NUMBER 119. BUT HERE THE ROSETTE IS STARRED, END ON END, ABOUT THE POINTS.
121 SUB-DIVIDE AS IN PLAN. THE CIRCUMFERENCE GOVERNING THE HEPTAGON IS DIVIDED INTO EQUAL PARTS; BY PROLONGING THE SIDES OF THE HEPTAGON THE ROSETTE OF SIXTEEN POINTS IS INSCRIBED.
122 CIRCUMFERENCES TANGENT TO THOSE OF THE PENTAGON INSCRIBE THE ROSETTE OF SIXTEEN POINTS.
123 TRANSFORMATION OF THE RECTILINEAL ROSETTE NUMBER 122. THE FIGURES IN OTHER RESPECTS IDENTICAL.
124 DIVIDE AS INDICATED. THE EXTENDED LINES OF THE HEXAGON INSCRIBE THE ROSETTE OF EIGHTEEN POINTS AND THAT OF NINE POINTS. THE REST IS BUT A MATTER OF ADJUSTMENT.
125 DESIGN ANALOGOUS TO NUMBER 124. IN THIS ARRANGEMENT, TWO SIDES OF THE HEPTAGON PROLONGED DETERMINE THE ROSETTE OF EIGHTEEN AND THAT OF TWELVE POINTS.
126 SQUARE PLAN. DIVIDE AS INDICATED. INSCRIBE A ROSETTE OF TWENTY POINTS (THE HALF OF WHICH IS SHOWN IN THE DIAGRAM). IN A TANGENT CIRCUMFERENCE INSCRIBE THE ROSETTE OF TWELVE POINTS. THE REST FOLLOWS.
127 DISTRIBUTION OF THE DODECAGON, HEXAGON, AND SQUARE ASSEMBLED. BY THE MIDDLE POINTS OF THE SIDES OF THE DODECAGON INSCRIBE A STAR AND A ROSETTE OF TWENTY-FOUR POINTS. WITHIN THE HEXAGON INSCRIBE TWO TRIANGLES FROM A TANGENT CIRCUMFERENCE. A LOZENGE IS INSCRIBED BETWEEN OPPOSITE SIDES OF THE SQUARE. LASTLY, BY tricèles révolvés, ALL THE PROLONGED LINES ARE RECONCILED.
128 DISTRIBUTION OF THE DODECAGON, HEXAGON, AND SQUARE ASSEMBLED. IN THE DODECAGON INSCRIBE A ROSETTE OF TWENTY-FOUR POINTS; IN THE HEXAGON A ROSETTE OF TWELVE POINTS; AND, LASTLY, IN THE SQUARE A ROSETTE OF EIGHT POINTS. A LITTLE PENTAGONAL STAR RECONCILES THE PROLONGED LINES.
129 SUB-DIVIDE AS IN PLAN. DODECAGON, HEXAGON, AND SQUARE ASSEMBLED. IN THE DODECAGON A ROSETTE OF TWELVE POINTS. IN THE TANGENT CIRCUMFERENCE SIX HEXAGONS. THE SQUARE GOVERNS THE PROLONGED LINES.
130 THE ROSETTES ARE AS IN NUMBER 129. THE SMALLER HEXAGONS GOVERN THE PRINCIPAL FIGURES.
131 SQUARE PLAN; DISTRIBUTION FOLLOWS THE NET-WORK OF THE OCTAGON AND SQUARE. THE ROSETTE IS LINKED BY THE SMALLER OCTAGONS.
132 ANALOGOUS TO NUMBER 131.
133 OCTAGONS AND SQUARES ASSEMBLED. THE OCTAGONAL ROSETTE GOVERNS.
134 SUB-DIVIDE AS INDICATED. DESCRIBE A CIRCLE IN WHICH IS INSCRIBED A STAR WITH SIDES PROLONGED, DETERMINING AN OCTAGONAL ROSETTE. BY CONCENTRIC CIRCLES, SOMEWHAT ARBITRARY, THE ROSETTE OF SIXTEEN POINTS IS DETERMINED.
135 SUB-DIVIDE AS IN PLAN. IN A CIRCLE IS INSCRIBED AN OCTAGONAL ROSETTE, AND TAKE A TANGENT CIRCUMFERENCE IN WHICH TO INSCRIBE THE ROSETTE OF SIXTEEN POINTS. THE REST FOLLOWS.
136 DISTRIBUTION OF THE OCTAGON AND SQUARE. A CONCENTRIC CIRCLE CONTAINS ARCS COMPOSING A CURVILINEAR ROSETTE, WITHIN WHICH IS A ROSETTE OF FIVE POINTS. IN THE CENTRE OF THE SQUARE PLAN A CURVILINEAR ROSETTE ENCLOSING AN OCTAGONAL ROSETTE WITH SIDES PROLONGED, BRINGING INTO ACCORD THE PENTAGONAL ROSETTES.
137 SUB-DIVIDE THE MAIN CIRCLE INTO THIRTY-TWO EQUAL PARTS, AND INSCRIBE THE ROSETTE OF SIXTEEN POINTS. OTHER CIRCLES ARE INSCRIBED, EACH CONTAINING A PERFECT OCTAGON.
138 NET-WORK OF OCTAGON AND SQUARE. INSCRIBE A ROSETTE OF EIGHT POINTS, AND IN A CIRCUMFERENCE TANGENT INSCRIBE A ROSETTE OF TWENTY-FOUR POINTS. THE ROSETTES ARE BROUGHT INTO ACCORD BY THE HEXAGONS.
139 IN A CIRCUMFERENCE INDICATED IN THE SQUARE PLAN INSCRIBE THE OCTAGONAL ROSETTE. EXTENDED SIDES DETERMINE THE PERFECT OCTAGONS.
140 SQUARE PLAN. OCTAGONAL AND SQUARE DISTRIBUTION. TWO ROSETTES, ONE OF SIXTEEN AND ONE OF EIGHT POINTS. THE DIAGONALS FROM THE ANGLES OF THE PENTAGON COMPLETE THE ROSETTE OF SIXTEEN POINTS, AND THE EXTENDED SIDES OF THE PENTAGON DETERMINE THE OCTAGONAL ROSETTE.
141 SQUARE PLAN. NET-WORK OF THE OCTAGON AND SQUARE ASSEMBLED. DESCRIBE CIRCUMFERENCES AS IN THE PLAN. IN JOINING THE POINTS OF DIVISION, THERE IS ON THE ONE PART THE HEXAGON, AND ON THE OTHER PART THE ROSETTE OF SIXTEEN POINTS. THE tricèle révolvé ASSISTS IN ELUCIDATING THE NET-WORK.
142 CURVILINEAR NET-WORK COMPOSED OF STARS OF FIVE, SIX, AND EIGHT POINTS. DESCRIBE THE CIRCUMFERENCES AS IN THE PLAN. ONE CIRCLE DESCRIBES THE STAR OF FIVE POINTS; ANOTHER CIRCLE INSCRIBES A CURVILINEAR IRREGULAR HEXAGON; STILL ANOTHER CIRCLE INSCRIBES A STAR OF EIGHT POINTS, AND THE LAST CIRCLE A STAR OF SIX POINTS.
143 SUB-DIVIDE AS INDICATED. THE PROLONGED LINES OF THE PENTAGONAL STAR DETERMINE THE DECAGONAL STAR AND ROSETTE.
144 DIVIDE AS IN THE PLAN. BY TANGENT CIRCUMFERENCES INSCRIBE THE ROSETTES. BY SIDES EXTENDED THE REST FOLLOWS.
145 OCTAGONAL, DECAGONAL, AND DODECAGONAL STARS AND ROSETTES. BY SIDES PROLONGED THE REST FOLLOWS.
146 OCTAGONAL, DECAGONAL, AND DODECAGONAL STARS AND ROSETTES. BY EXTENDED LINES AND THE ADJUSTMENT OF THE REGULAR OCTAGONS THE DIAGRAM IS COMPLETED.
147 IN A CIRCUMFERENCE AS INDICATED INSCRIBE A STAR OF NINE POINTS, AND BY SIDES PROLONGED A ROSETTE OF NINE POINTS; IN A SECOND A STAR AND ROSETTE OF TWELVE POINTS; AND IN A THIRD CIRCUMFERENCE A STAR AND ROSETTE OF TEN POINTS. THE REST FOLLOWS BY EXTENSION.
148 THE CENTRAL CIRCUMFERENCE DIVIDED INTO THIRTY-TWO EQUAL PARTS PRODUCES A STAR AND ROSETTE OF SIXTEEN POINTS. DIVIDE OTHER CIRCUMFERENCES TO PRODUCE STARS AND ROSETTES OF TWELVE AND TEN POINTS. THE REST FOLLOWS.
149 CIRCUMFERENCES DIVIDED AS INDICATED. INSCRIBE STARS OF NINE, TEN, AND TWELVE POINTS.
150 NET-WORK ANALOGOUS TO NUMBER 148. THE LINES OF THE HEPTAGON, EXTENDED, JOIN THE LINES OF THE ROSETTES.
151 THIS EXAMPLE EXHIBITS THE MARVELLOUS INGENUITY OF THE ARABIAN DESIGNER IN COMPOSITION, ROSETTES OF FIVE, SIX, SEVEN, AND EIGHT POINTS BEING ADJUSTED. THE DESIGN IS EVIDENTLY THE PRODUCTION OF AN ART-WORKMAN. IF THE NET-WORK IS NOT ACTUALLY PERFECT, IT APPROACHES PERFECTION SO NEARLY THAT IT MAY BE CONSIDERED EXACT.
152 ISOCELES OR LOZENGE PLAN. THE ROSETTE OF FOURTEEN POINTS RESULT FROM THE EXTENDED LINES OF THE HEPTAGONS.
153 ANALOGOUS TO NUMBER 152, BUT WITH DIAGONALS SOMEWHAT DIFFERENTLY TREATED.
154 ROSETTE OF FOURTEEN POINTS GOVERNED BY HEPTAGONS.
155 ROSETTE OF FOURTEEN POINTS FROM EXTENDED LINES OF THE HEPTAGONS. THE REST FOLLOWS.
156 PENTAGONAL ADJUSTMENT. A CIRCUMFERENCE TANGENT TO THOSE OF THE PENTAGON INSCRIBES A STARRED ROSETTE OF FOURTEEN POINTS.
157 BY A CONCENTRIC CIRCUMFERENCE IS INSCRIBED THE ROSETTE OF FOURTEEN POINTS. THE PENTAGON WHICH GOVERNS HAS ONE OF ITS SIDES EXTENDED TO GREATER LENGTH THAN THE SIX OTHERS.
158 BY THE AID OF A CIRCUMFERENCE, INDICATED, IS INSCRIBED THE HEPTAGONAL STAR FROM WHICH THE OTHER FIGURES PROCEED.
159 DECAGONAL STARS AND ROSETTES, WITH INTERCALARY PENTAGONS. ALSO WITH INTERCALARY MESHES, WHICH ARE EQUAL TO THOSE OF THE ROSETTES.
160 ANALOGOUS TO NUMBER 159.
161 SUB-DIVIDE THE SPACE SURROUNDING THE ISOCELES TRIANGLE AS INDICATED. THE CIRCUMFERENCES BEING DESCRIBED. THE DIAGONALS EXTENDED COMPLETE THE FIGURE.
162 PLAN AND CIRCUMFERENCES THE SAME AS NUMBER 161. THE AID OF A CONCENTRIC CIRCUMFERENCE IS CALLED IN TO FORM THE ROSETTE OF TEN POINTS. THE REST FOLLOWS.
163 DESCRIBE EQUAL AND TANGENT CIRCUMFERENCES TO FORM A STAR OF TEN POINTS, AND TAKE THE DIAGONALS OF SIX IN SIX DIVISIONS.
164 DESCRIBE CIRCUMFERENCES AS INDICATED, AND TAKE THE DIAGONALS OF SIX IN SIX DIVISIONS. DRAW A HORIZONTAL LINE AT THE HIGHER LINE OF THE LITTLE PENTAGON, AND REPEAT THE CONSTRUCTION BELOW THE LINE.
165 DIVIDE CIRCUMFERENCES AND DRAW PARALLEL LINES AS INDICATED. TAKE THE DIAGONALS OF SIX IN SIX DIVISIONS, AND THE REST FOLLOWS.
166 DESCRIBE CIRCUMFERENCES EQUAL AND TANGENT, AND TAKE THE DIAGONALS OF FOUR IN FOUR DIVISIONS; THEN IN THE CONCENTRIC CIRCUMFERENCES TAKE THE DIAGONALS OF SIX IN SIX DIVISIONS.
167 SUB-DIVIDE AS IN PLAN. INSCRIBE THE ROSETTE OF TEN POINTS; THE LITTLE PENTAGONS AND LOZENGES FOLLOW, AND THE REST FOLLOWS.
168 ANALOGOUS TO NUMBER 167, BUT IN PLACE OF THE ROSETTE STARS ARE FORMED.
169 CURVILINEAR TRANSFORMATION OF NUMBERS 167 AND 168. THE POINTS OF CENTRAL DISTRIBUTION ARE MARKED BY MINUTE CROSSES.
170 SIMILAR GROUND WORK TO THE THREE FOREGOING DIAGRAMS. THE LITTLE PENTAGONS GOVERN THE DESIGN.
171 DESCRIBE THE CIRCUMFERENCES AS IN PLAN, AND INSCRIBE THE DECAGONAL STAR. THE SMALL DECAGONS IN THE CENTRE OF THE TRIANGLES OF THE PLAN, BY EXTENDED LINES, FORM THE ROSETTE.
172 DIVIDE AS IN PLAN. UPON THE LESSER SIDE TRACE AN ISOCELES TRIANGLE. BY THE APEX OF THE TRIANGLE TRACE A CIRCUMFERENCE, IN WHICH TAKE THE DIAGONALS OF THREE IN THREE DIVISIONS.
173 LOZENGE PLAN, WITH COMBINING LINES. THE LOZENGE IS IMAGINARY, AND DOES NOT INDICATE THE RADII IN EXTENSION ONE WITH THE OTHER, BUT ONLY THE ORDER OF SUB-DIVISION OF THE PENTAGONAL AND DECAGONAL ROSETTES.
174 SUB-DIVIDE AS IN PLAN THE SPACE SURROUNDING A POINT INTO TWENTY EQUAL PARTS. AT THE MEETING OF THE HORIZONTAL WITH THE VERTICAL LINE DRAW A CONCENTRIC CIRCUMFERENCE IN WHICH IS INSCRIBED THE STARRED DECAGONAL ROSETTE. THE SMALL PENTAGON IS DOMINANT.
174 SAME GROUND-WORK AS NUMBER 172, BUT WITH A GREATER INTERVAL BETWEEN THE ROSETTES. ONE OF THE ROSETTES, INSTEAD OF BEING RECTILINEAR, IS CURVILINEAR.
175 SUB-DIVIDE AS INDICATED. DESCRIBE CIRCUMFERENCES EQUAL AND TANGENT, AND TAKE THE DIAGONALS OF FOUR IN FOUR DIVISIONS. LASTLY, THE ROSETTES ARE EFFECTED.
175’ DRAW CIRCUMFERENCES AND SUB-DIVIDE AS IN PLAN. TAKE THE DIAGONALS OF FOUR IN FOUR DIVISIONS, WHICH, PROLONGED, COMPLETE THE DESIGN.
176 DESCRIBE CIRCUMFERENCES AND TAKE A PERPENDICULAR LINE TO THE BORDER OF THE RADIUS; TAKE THE DIAGONALS OF FOUR IN FOUR DIVISIONS, WHICH PROLONGED, COMPLETE THE FIGURE.
176’ RECTANGLE PLAN OF DIAGONAL SYMMETRY. TAKE THE DIAGONALS OF FOUR IN FOUR DIVISIONS. THEN BY A CONCENTRIC CIRCUMFERENCE. SET OUT THE ROSETTE. THERE ARE, IN FACT, THREE ROSETTES OF TEN POINTS EQUAL AND TANGENT.
177 LOZENGE PLAN, WITH COMBINING LINES A CONCENTRIC CIRCUMFERENCE DESCRIBES A STAR THE ROSETTE IS THEN DRAWN. THEN GRADUALLY, BY THE AID OF THE PENTAGONAL ADJUSTMENT, THE NET-WORK IS DESCRIBED.
178 LOZENGE PLAN, WHERE THE GREAT AXIS IS THREE TIMES THAT OF THE LESSER AXIS. SUB-DIVIDE AS IN PLAN. TRACE CIRCUMFERENCES EQUAL AND TANGENT, IN WHICH ARE INSCRIBED REGULAR PENTAGONS. THE REST IS EASILY FOLLOWED. THE NET-WORK IS COMPOSED OF FIVE SERIES OF LINES.
FINIS.
