House £s? Garden 
THE/ BR/OLBTTA AT MANTUA J PALATZO UGUCCION1 AT FLORENCE/ 
PALAKZO BARTOUNI, FLORENCE PALAZZO TACCON1. BOLOGNA 
\i\RIOUJ PALACE FAQADE5- 3 U5ED AS A MULTIPLE/ 
Sometimes, as in the case ot the Venetian 
Ducal Palace the numbers involved are too 
great for counting, but other and different 
truths of number are celebrated; for 
example, the multiplication of the first 
arcade by 2 in the second, and this by 3 in 
the cusped arches, and by 4 in the quatre- 
foils above them. 
Seven is proverbially the perfect number. 
It is of a quantity sufficiently complex to 
stimulate the eye to resolve it, and yet so 
simple that it can be so resolved at a glance. 
As a center with two equal sides it is pos¬ 
sessed of symmetry, and as the sum of an odd 
and even number (3 and 4), it has vitality 
and variety. All these properties a work of 
architecture can variously reveal. Fifteen, u 
also, is a number of great perfection. It is 
possible to arrange the first 9 numbers in the 
form of a square so that the sum of each line, 
read across or up and down, will be 15. 
Thus : 
4 9 2 = is 
3 5 7 = 15 
8 1 6=15 
*5 15 15 
Its beauty is portrayed geometrically in the 
accompanying figure which expresses it, being 
THE BANQUETING HOULE. WHITEHALL 
21 - 
j 3X7 
15 triangles in groups of 5. Few arrange¬ 
ments of openings in a faqade better satisfy 
the eye than three superimposed groups of 
five. May not the secret of this satisfaction 
dwell in the intrinsic beauty of the number 
? This is a question which would 
__ be decided 
differently b y 
different per¬ 
sons, for the 
perception 
o f numerical 
beauty is 
largely intui¬ 
tive. 
In writing 
short, detached 
essays of this 
sort an author 
can represent 
his subject 
from one side 
only. If the 
present writer 
has seemed to insist on forcing some 
significance from everything he has brought 
to the reader’s attention, it is partly because 
he has been obliged, by the necessity of 
the case to write in that spirit. What 
he could not vivify he has been forced 
to omit. In conclusion, therefore, it is 
perhaps well that the reader be reminded 
that these are the byways, and not the 
highways of architecture into which he 
has been led,— that the highest beauty 
comes always, not from beautiful numbers, 
nor from likenesses to Nature’s eternal 
patterns of the world, but from utility, 
fitness, economy, and the perfect adap¬ 
tation of means to ends. This truth 
is usually exploited in the literature of 
architecture, to the exclusion, it has seemed 
to the writer, of every other. These 
essays have been attempted in the hope 
of being able to show that along with 
this truth there goes another: that in 
every good work of architecture, in addi¬ 
tion to its obvious and individual beauty, 
there dwells an esoteric and universal 
beauty, and that by taking more thought 
of this beauty, we may learn to build 
more worthily. 
Claude Bragdon. 
265 
