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COLLEGE. CFTHEGAPIBNZA. AT ROME---AN 
ILLWTRATION OF THE/ VALUE/ OF A VERTICAL 
AND HORIZONTAL DIVISION OF A FACADE TO AS¬ 
SIST THE BYE TO AN APPREHENSION OF THE/ 
NUMBBB ORi NUMBERS OF WHICH IT IS THE 
EXPRESSION. IN THIS CASE 21 THE PRODUCT 
OF ,3 AND 7 
relation with one another. For example, an 
important conjunction occurs in 12, for of a 
series of twos it is the sixth, of threes the 
fourth, of fours the third, and of sixes the 
second. It stands to 8 in the ratio of 3:2, 
and to 9 of 4 : 3. It is related to 7 through 
being the product of 3 and 4, of which num¬ 
bers 7 is the sum. 11 and 13 are not con¬ 
junctive numbers. 14 is so in the series of 
twos, fours, and sevens; 15 is so in the 
series of fives and threes. The next con¬ 
junction of 3 and 4 and their first multiples 
after 12 is in 24, and the next following in 
36, which numbers are respectively the two 
and three of a series of twelves, each end 
being but a new beginning. 
It will be seen that this discovering of 
numerical conjunctions consists merely of 
resolving numbers into their prime factors, 
and that a conjunctive number is a com¬ 
mon multiple; but by naming it so, to 
dismiss the entire subject as known and 
exhausted is to miss a sense of the wonder, 
beauty, and rhythm of it all, a mental im¬ 
pression analogous to that made upon the 
eye by the swift glancing balls of a juggler, 
the evolutions of drilling troops, or the in¬ 
tricate figures of a dance, for these things 
are number, concrete and animate in time 
and space. 
The truths of number are of all truths 
the most interior, abstract, and difficult of 
apprehension, and knowledge becoming clear, 
definite and certain, to the extent that it can 
be made to enter the mind through the 
channels of physical sense, it is well to 
accustom oneself to conceiving of number 
graphically, by means of geometrical sym¬ 
bols rather than in terms of the familiar 
Arabic notation. This, though admirable 
for purposes of computation, is of too 
condensed and arbitrary a character to reveal 
the properties of individual numbers. To 
state, tor example, that 4 is the first square, 
and 8 the first cube conveys but a vague 
idea to most persons, but if 4 be represented 
as a square enclosing four smaller squares, 
and 8 as a cube containing eight smaller 
cubes, the idea is apprehended immediately 
and without effort. 3 is, of course, the 
triangle ; the irregular and vital beauty of 
the number 5 appears clearly in the hep- 
lalpha, or five-pointed star, the faultless 
symmetry of 6, its relation to 3 and to 2, and 
its equal division of the circle are portrayed 
in the familiar hexagram known as the Shield 
of David. 7 when represented as a compact 
group of circles reveals itself as a number of 
singular beauty and perfection, worthy of the 
important place accorded to it in all mystical 
philosophies. It is a curious fact that when 
asked to think of any number less than 10, 
most persons will choose 7. 
Every form of art, though primarily a 
vehicle for the expression and transmission 
of particular ideas and emotions, has sub¬ 
sidiary offices, just as a musical tone has 
harmonies which render it more sweet. 
Painting reveals the nature of color; music 
of sound in wood, in brass, and in stretched 
strings ; architecture shows forth the quali¬ 
ties of light, and the strength and beauty 
263 
