ST A
S Q U (326
the 8 that precede the two last 8, and another with the 16means: the result will be four squares of 16 cells each, the num-bers of which '.'ill be equal when added together, either in bandsor diagonally ; for they will everywhere amount to the sum of130. It is therefore manifest, that if these squares be arrangedside bv side in any order, the square resulting from them must bemagicj and the sum in every direction 260. The followingis this magic arrangement of the square of 64 cells.
i
j 1
63
62
4
17
47
46
20
60
6
7
57
44
22
23
41
8
58
59
5
24
42
43
21
61
3
2
64
45
19
18
48
9
55 | 54
12
25
39
38
28
52
14
15
49
36
30
31
33
16
50
51
13
32
34
35
29
53
11
10
56
37
27
26
40
To arrange the square of 9, in this way, divide the progression*from 1 to 81 inclusively, into nine others, as 1, 10, 19....73; 2,11, 20....74; 3, 12, 21....75; 4, 13, 22....70, &c. and arrangeeach of these progressions magically in a square of 9 cells, markingthe first 1, the second II, the third III, &c. Hut it must be ob-served that in these difierent squares the sums of the bands andthose of the diagonals will be themselves in arithmetical progres-sion; viz. in the square I the sum will be 111, in the square IIll4, in the square III 117, and so on. If the nine squares be ar-ranged magically, the total must be magical; but the partialsquares cannot be transposed as in the preceding one of 64. Thesquare of 15 may be resolved into 25 squares of nine cells. If 25squares therefore of nine cells be arranged magically, filling them upwith the25 progressions which may be formed after this manner, 1,26,51....201 ; 2, 27, 52....202; 3,28, 53....203, &c. these squareswill have successively, and in order, for the sums of their bandsand their diagonals, 303, 306, 301), &c. to the last, which willamount to 375 in each of its bands and diagonals. By arrangingthese 25 squares magically in this manner, calling the first I, thesecond IF, &c. &c. a magic square will be had possessing all theproperties proposed.
To construct geometrical magic squares the same rules must befollowed as in the construction of other magic squares, (see Ma-gic Square, ) and this may be easily demonstrated from the pro-perty of logarithms. Without enlarging further upon this kind ofmagically arranged squares we shall coniine ourselves to givingtwo examples; the first is that of the 25 first terms of the geome-trical progression, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, &c. &c.and the second is that of the 16 first terms of the geometrical pro-gression 1,3, 9, 27, 81, 243, 729, 2187, &c. Instead of the sumof eaclt band being equal, as in the other squares, the product ofeach is the magic property in this kind. The product of eachband, in the fir-t example, whether vertical, horizontal, or dia-gonal, is 11529215046^6846976, and in the second example205891132094649. Thus, 65536 x 4194304 x 8 x 512 x 1024= 8388608 x 1 x 128 X 16384 = 1 x 64 x 4096 X 262144 X16777216 = 128 x 8192 x 521288 X 1048576 x 2 = 65536 x16 x 4096 x 1648576 x 250 =, &c. &c. &c.
65536
8338608
l
128
16384
4194304
16
64
8192
32768
8
32
4096
524288
2097152
512
2048
262144
1048576
4
1024
131072
16777216
2
256
.. A—..
1
4782969
1594323
27
177147
243
729
6561
2187
19683
59049
81
531441
9
3
14348907
Square Root. See Algebra, and Arithmetic .
Square Number, the product of a number multiplied in(d>itself. See Arithmetic, and Algebra . Thus 4, the productof 2, multiplied by 2 ;or 16, the product of 4 multiplied by 4, aresquare numbers.
Square-Rigged, an epithet applied to a ship whose yards arcvery long. It is also used in contradistinction to all vessels whosesails are extended by stays or lateen-yards, or by booms andgaffs; the usual situation of which is nearly in the plane of thekeel; and hence,
Square-Sail, is a sail extended to a yard which hangs parallelto the horizon, as distinguished from the other sails which are ex-tended by booms and stays placed obliquely.
SQUILACE, or SQUlLACI, an ancient town of Naples, inCalabria Ultra ; 30 miles S. of St. Severina, and 33 S. S. E, ofCosenza . Lon. 16. 40. E. Lat. 39. 3. N.
SQUILL, in botany. See Scilla.
SQUIRREL, in zoology. See Sciurus.
STABBING, inlaw. The offence of mortally stabbing ano-ther, though done upon sudden provocation, is punished as mur-der; the benefit of clergy being taken away from it by statute.See Murder.
STABLESTANT), in the forest-law, one of the four evidencesor presumptions, whereby a man is convinced to intend the steal-ing of the king’s deer in the forest: and this is when a man i 3found at his standing in the forest with a cross-bow bent, ready toshoot at any deer; or with a long bow, or else standing close by *tree with greyhounds in a leash ready to slip.
STACllVS, in botany, a genus of plants belonging to lb cclass didynamia, and order gymwospermia; natural order, Verti-ctllaUe. Upper lip of the corolla arched ; lower lip reflexed, a«othe larger intermediate laciua marginaled; stamina bent towardthe sides. 'There are twenty-four species.
STACKHOUSE, 'Thomas, a learned and pious English <lj'vine, who was many years curate of Kinchley, and afterwards vi-car of Beenham, in Berkshire . He first attracted the public a 1 'tention by bis Treatise on the Miseries of the Inferior Clerg)'*1722. lie acquired still greater fame by his New History of lh®Bible ; in 2 vols. folio; which lias been often reprinted, in 6 or °vols. 8vo. lie also wrote several oilier works; and died in 17-5^*
STALE, a town of Germany, in the late duchy of Bremen *22 miles \V of Hamburg, and 45 N. E. of Bremen . Lon. 9. I?*E. Lat. 53. 36. N.
STADIUM, an ancient Greek long measure, containing l^ 5geometrical paces, or 625 Roman feet, corresponding to our f llf 'long. The word is said to be formed from the Greek w ord c ar ! s ’a station, or to stand, because it is reported that Herein®'
having run a stadium at one breath, stood still at the end of jj*The Greeks usually measured distances by stadia, which they c al .'ed i-tfn.Sina-fA.as. Stadium also signified the course on which th®races were run. .
STAD1US, John, a learned mathematician, born at Loenho® >near Antwerp , in 1527. He became professor of history at L°vain, and afterwards of mathematics and history at Paris; wh®