The Arithmetic of Beauty 
THE ARITHMETIC OF BEAUTY. 1 
A LTHOUGH architecture is based pri¬ 
marily upon geometry, it is possible to 
express all spatial relations numerically, for 
arithmetic and not geometry is the universal 
science ot quantity. The relation ot masses 
one to another, of voids to solids, and of 
heights and lengths to widths form ratios ; 
and when such ratios are simple and har¬ 
monious, architecture may be said to “aspire 
towards the condition of music.” I he 
trained eye, and not 
an arithmetical for- 
m u 1 a determines 
what is, and what is 
not beautiful pro¬ 
portion. Neverthe¬ 
less the fact that 
the eye instinctively 
rejects certain pro¬ 
portions as unpleas¬ 
ing, and accepts 
others as satisfactory 
is an indication of 
the existence of laws 
of number, not un¬ 
like those which 
govern musical harmony. 'I'he secret of the 
deep reasonableness of such selection by the 
senses lies hidden in the very nature of 
number itself, for number is the invisible 
thread on which the worlds are strung,—the 
universe abstractly symbolized. 
Number is the within of all things,—the 
“ first form of Brahman.” It is the measure 
of time and space; it lurks in the heart beat 
and is blazoned upon the starred canopy of 
night. Substance, in a state of vibration, 
that is, conditioned by number, ceaselessly 
undergoes the myriad transmutations which 
produce phenomenal life, becoming in turn 
sound, heat, light, and electricity. Elements 
separate and combine chemically according to 
numerical ratios. “ Moon, plant, gas, crystal 
are concrete geometry and number.” To 
the Pythagoreans, and the ancient Egyptians, 
from whom the former perhaps derived their 
philosophy, numbers were possessed of sex, 
odd numbers being conceived of as masculine, 
i Concluding Mr. Bragdon’s series of articles entitled:—“The 
Beautiful Necessity : being Essays upon Architectural Esthetics,’’ begun 
in the January number of House and Garden. 
or generating, and even numbers as feminine 
on account of their infinite divisibility. 
H armonious combinations were those involv- 
ing the marriage of a masculine and a feminine 
number,—an odd number and an even. 
Number proceeds from unity towards in¬ 
finity and returns again to unity as the soul, 
defined by Pythagoras as a self-moving num¬ 
ber, goes forth from, and returns to God. 
These two acts, one of projection, and the 
other of recall,—these two forces, centrifugal 
and centripetal, — are symbolized in the opera¬ 
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BALATZO G1EAUD. AT EQME/-■ 26; 4X7— 
tions of addition and subtraction. Within 
them is embraced the whole of computation; 
but because every number, every aggregation 
of units, is also a new unit capable of being 
added or subtracted, there are also the opera¬ 
tions of multiplication and division, which 
consist in the one case of the addition of sev¬ 
eral equal numbers together, and in the other 
of the subtraction of several equal numbers 
from a greater until that be exhausted. 
The progression and retrogression of 
numbers in groups expressed by the multi¬ 
plication table gives rise to what may be 
termed “ numerical conjunctions,” to coin a 
phrase. These are analogous to astronom¬ 
ic a 1 conjunctions. 
The planets, revolving 
around the sun at 
different rates of speed, 
and in widely separated 
orbits at certain times 
come into line with each 
other and with the sun. 
T hey are then said to 
be in conjunction. Similarly, numbers, ad¬ 
vancing towards infinity singly and in groups 
(expressed by the multiplication table), at 
certain stages of their progression come into 
THE. NUME/RICAL BASIS OF TEE 
THE/ TUSCAN. DORIC. AND IONIC ORDL&S 
ACCORDING TO VIGNOLE-^ PROPORTION! 
DETERMINED BY THE NUMBER/5 3. 4. AND 
THE1IB CONJUNCTIVE NUMBER,, 12«-* 
262 
