M A G
361
J'deways to the middle, and back to the same side again. N. B.
. u e set of these half-diagonals and their parallels may be drawn1,1 the same square upward and downward. Another such setin ay be drawn from any of the other three sides.
. The four corner-numbers in the great Square, added to the•our central numbers therein, make 1028; equal to the half-sum, any vertical or horizontal column which contains 16 numbers;ai 'd equal to half a diagonal or its parallel.
, 0 - If a square hole (equal in breadth to four of the little squares)y e r -ut in a paper, through which any of the 16 little squares in the8 ^ c at square may be seen, and the paper be laid on the greatWare, the sum of all the 16 numbers, seen through the whole,“equal to the sum of the 16 numbers in any horizontal or verti-Ca ‘ column, viz. to 2056.
^ he magic circle of circles, (Plate CLIII. fig. 2 ,) is composed ofSl “nes of numbers from 12 to 75 inclusive, divided into eight con-entric circular spaces, and ranged in eight radii of numbers, with the! ""'her 12 in the centre ; which number, like the centre, is com-l^crn to all these circular spaces, and to all the radii. The num-c ® rs a 'e so placed, that the sum of all those in either of the con--entric circular spaces above-mentioned, together with the centralc , l ""her 12, make 360 ; equal to the number of degrees in a cir-Ci 1 he numbers in each radius also, together with the centralJUuher 12 , make just 360. The numbers in half of any of theove circular spaces, taken either above or below the double ho-^"Ui line, with half the central number 12, make ISO; equalPie number of degrees in a semicircle. Jf any four adjoiningcii -" 1 i ls Isken, .as if in a square, in the radial divisions of thesen of these, with half the central number,moreover, included, four sets of other cir-
"'Ij'ular spaces, the sum, e 180. There are, n
W iT s P accs > bounded by circles which are eccentric with respectcommon centre ; each of these sets containing five species.]y e centres of the circles which bound them are at A, B, C, andthy ^ sct: " hose centre is at A is bounded by dotted lines;H,, Sfet "'hose centre is at C is bounded by lines of short uncon-c ' e< I strokes ; and the set round D is bounded by lines of uu-Iii longer strokes, to distinguish them from one another.
b '^"ingthis figure by hand, the set of concentric circles shouldcl es ‘ awilw hh black ink, and the four different sets of eccentric tir-W * oul hinds of ink of different colours; as blue, red, yel-T|,’ a,K ' green, for distinguishing them readily from one another.CQn S ? S( r ls eccentric circular spaces intersect those of thee ac 3 eiltl '‘ c 5 and e'ach other; and yet the numbers contained in20 '■he eccentiic spaces, taken all around through any of thecent • are eccei 'b'h', make the same sum as those in the con-I'hgp 1 ? namely 360, when the central number 12 is added.' v 'th'| , ves also, taken above or below the double horizontal line,tl 0); Vi ^ the cenlral number, make 180. Observe, that there isci rt , ," e of the numbers but what belongs at least to two of theth e ,. , ar spaces, some to three, some to fotir, some to five ; and yetin jL are a 'l so placed as never to break the required number 5Gobrj n ^ ,°f ihe 28 circular spaces within the primitive circle. Toare t ?.. lcs e matters in .view, all the numbers as above mentionedbotjj r| n out ’ :ll 'd pheed in separate columns as they stand around‘diio- concentric and eccentiic circular spaces, always begin-Set^a'i 1 the outermost and,ending with the innermost of eachClr cunf a ' 30 l ' le numbers as they stand in the eight radii, from thebniq ,, 1 |ccnce to the centre; the common central number 12a P' a ced the lowest in each column.
1- In the eight concentric circular spaces.
H
72
23
65
21
67
12
74
30
4]
46
57
63
16
70
18
68
27
61
36
3!)
40 '
37
51
28
58
47
32
54
34
52
43
45
40
55
33
53
35.
44
42
31
48
.38
50
36
59
29
73
24
71
17
69
19
60
26
12
1 5
(H
22
66
2(3
75
13
12
12
12
' 12
12
12
12
00 j 360V °L. IH— No>
360
30.
360 ,
3G0 .
360
360
.
360
MAG
2 . In the eight radii.
14
25
30
41
4'6 '
57
62
73
72
63
56
47
40
31'
24
15
23
16
39
32
DO
48
71
■ 64
65
70
49
54
33
33
17
<22 -
' 21
18
37
34
53
50
69
66
67
68
51
52
35
36
19
20
12
27
28
43
44
59
60
75
74
61
58
45
42'
29
26
13
12
12
12
12
12
12
12
12
360
360
360
360
360
360
360
360
i. £
14
72
23
65
21
o
63
16
70
18
63
39
49
37
51
28
54
34
52
43
45
o 2
33
53
35
44
42
<D "S
48
38
50
36
59
J! 3
24
71
17
69
19
73
15
64 .
22
66
. In the
cular sf
is at A.
12
12
12
YZ
12
360
360
360
360
,360
• 03
30
56
39
49
37
^ G
47
32
54
34
52
.2 u
s—
55
33
53
35
44
38
50
36
59
29
17
69
19
60
26
03 £
64
22
60
20
75
V
> ft
72
23
65
21 -
67
v *-* ft
25
63
10
70
18
03 Cm£
12
12
12
12
12
~ w
360
360
300
360
360
i £
46
40
55
33
53
° G
31
48
38
50
36
•E «
71
17
69
19
60
"c ft,
22
66
20
75
13
03 O
O _G
65
21
' 67
12
74
<D *
03 ^
16
70
18'
6 S
27
(V) C/5
56
39
49
37
51
« £
41
47
32
54
34 '
■1 1*^3
12
12
12
12
12
a
’I 3.S3
360
360
360
360
300
4 £
62
24
71
17
69
o £
15
64
22
66
20
23 '
65
21
67
12
1 S
70
18
68
27
01
U 2
49
37
51
28
58
ft
32
54
34
52
43
03
> <U
40
55
33
53
35
<13 2- •
57
12
31
12
48
12
38
12
50
12
. 0.12
360
360
360
360
360
<o
If, now, we take any four numbers, as in a squareform, either from No. 1 , No. 2 . (as we suppose fromNo. 1 .) as in the margin, and add half the central 03 'number 12 to them, the sum will he 180; equal to 0half the number in any circular space taken above or below thedouble horizontal line, and equal to the number of degrees in asemicircle. Thus 14, 72, 25, 03, and 6 , make 180.
4 Z
MAGISTERY,