m 
MAGIC. 
iCatural square. 
2 
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6 
7 
8 
9 
Magic square. 
2 
7 
6 
9 
5 
1 
4 
3 
8 
Magic sqiiares seem to have been so called, 
from their being used in the constniction of 
talismans. 
Take another instance ; 
Natural square; 
Magic square. 
f 
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5 
6 
7 
8 
9 
10 
11 
12 
13 
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16 
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21 
22 
1 S 
24 
26 
16 
14 
8 
2 
25 
3 
22 
20 
11 
9 
15 
6 
4 
I CO 
1 ©>1 
17 
24 
18 
12 
10 
1 
1 
6 
21 
19 
13 
where every row and diagonal in the magic 
square makes just the sum 66, being the same 
as the two diagonals of the natural square. 
It is probable that these magic squares 
w'ere so called, both because of this proper- 
ty in them, viz. tliat the ranks in every di- 
rection make the same sum, appeared ex- 
tremely surprising, especially in the more 
ignorant ages, when mathematics passed for 
magic, and because also of the superstitions 
opeiations they were employed in, as the 
construction of talismans, &c. ; for, ac- 
cording to the childish philosophy of those 
days, which ascribed virtues to numbers, 
what might not be expected from numbers 
so seemingly wonderful .? The magic square 
w-as held in great veneration among the 
Egyptians, and the Pythagoreans their dis- 
ciples, who, to add more efficacy and virtue 
to this square, dedicated it to the then 
known seven planets divers ways, and en- 
graved it upon a plate of the metal that was 
esteemed in sympathy with the planet. The 
square, thus dedicated, was inclosed by a re- 
gular polygon, inscribed in a circle, M'hich 
W'as divided into as many equal parts as 
there were units in the side of the square ; 
with the names of the angels of tlie planet’ 
and the signs of the zodiac written upon the 
void spaces between the polygon and the 
circumference of tlie circumscribed circle. 
Such a talisman or metal they vainly ima- 
gined would, upon occasion, befriend the 
person who carried it about him. To Sa- 
turn they attributed the square of 9 places 
or cells, the side being 3, and the sum of the 
numbers in every row 15 ; to Jupiter the 
square of 16 places, the side being 4, and 
the amount of each row 34 : to Blars the 
square of 25 places, the side being 5, and the 
amount of each row 65 : to the sun the 
square with 36 places, the side being 6, and 
the sum of each row 111 : to Venus the 
square of 49 places, thej side being 7, and 
the amount of each roiy 175 : to Blercury 
the square with 64 plqces, the side being 8, 
and the sum of each row’ 260 : and to the 
moon the square of 81 places, the side being 
9, and the amount of each row 369. Finally, 
they attributed to imperfect matter, the 
square w'ith 4 divisions, having 2 for its 
side ; and to God the square of only one 
cell, the side of which is also an unit, which 
multiplied by itself undergoes no change. 
To form a magic square of an odd number 
of terms in the arithmetic progression 
1, 2, 3, 4, &c. Place the least term 1 in 
the cell immediately under the middle or 
central one ; and the rest of the terms, in 
their natural order, in a descending diagonal 
direction, till they run off either at the 
bottom, or on the side : when the number 
runs off at the bottom, carry it to the up- 
permost cell, that is not occupied, of the 
same column that it would have fallen in 
below, and then proceed descending diago- 
nalwise again as far as you can, or till the 
numbers either run off at bottom or side, 
or are interrupted by coming at a cell al- 
ready filled : now when any number runs 
off at the right-hand side, then bring it to the 
furthest cell on the left-hand of the same 
row or line it would have fallen in towards 
tlie right-hand : and when the progress 
diagonal wise is interrupted by meeting with 
a cell already occupied by some other num- 
ber, then descend diagonally to the left 
from this cell till an empty one is met w'ith, 
where enter it ; and thence proceed as 
before. Thus, 
To make a magic square of the 49 num- 
22 
47 
16 
41 
10 
35 
4 
5 
23 
48 
17 
42 
11 
29 
30 
6 
24 
49 
18 
36 
12 
13 
31 
7 
25 
43 
19 
37 
38 
14 
32 
1 
26 
44 
20 
21 
39 
8 
33 
2 
27 
45 
46 
15 
40 
9 
34 
3 
28 
