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Show I THE MAGICAL SQUARE. Am Arithmetical Faille Hold la Vonera-tlon Vonera-tlon br th Kcjrptmna. It will ho soon that In tho natnral quro tho nurolors 'from 1 to 40 run In arithmetical progression. In tho mar;-leal mar;-leal nquaro tho numbers aro disposed In parallel and equal rankB, bo that tho urn In each row, takon either porpon-dlcularly, porpon-dlcularly, horliontally or diagonally, are equal to ono another L o., 170. Theeo magical squaro can, however, bo wuoh extended, write Thomas Eathln in tho "leda Moroury, and show still moro curious results: NATCnL SQUARE. !1 9 Z 4 B S 1 S 0 10 11 IS 13 H IS 18 IT IS IB S3 21 I ti 33 vi sa st n n m :i a rj si . f M 87 SS 33 10 il 43 43 41 48 47 43 49 MAQICAI. agCAItE. I M 47 10 41 10 35 4 ' B t3 41 17 iU II w 4 f mm Mfc S) "M 49 18 30 V4 i 13 31 7 SB 43 19 37 f 33 II a I M 41 SO SI SO 8 S3 0 27 4.1 4) IB 40 0 34 3 SS Tho magic squaro was hold In great veneration among the Egyptians and dedicated to the thonsovon known plan-otfl plan-otfl In various ways. To Saturn they attributed at-tributed tho squaro of nlno plaoes, tho side bolnp throe and Uio sum of tho numbora In evory row being flttosn. To Vonus thoy attributed tho square I hae given. Finally, tboy attributed to (iod tho squaro of only on cell, tbo aldo of which Is only a unit, which, multiplied by Itself, undergoes ro ohango. Tbo ancient) having used theso maglo squares for various purpose, they bo-came bo-came a subject of consideration among mathematicians; no; becauoo they Imagined Im-agined that they would be of any solid use or advantage, but rather as a kind of play in which tho dltQculty makes tho merit. If your young readers want a Uttlo recreation In the combination of flgurss, lot thorn mako a largo square in which there aro 230 smaller squares, and place in those smaller squares all tho numbers from 1 to 234 In such u mannor as will answer tho following conditions: 1. Tho sum of tho sixteen numbers in each column or row, vertical verti-cal or horizontal, to b 2,0U). 2. Kvery half column, vortical or horizontal, makes 1,039, or ono-h&lf' tint, sum of 2,050. 3. Half a diagonal aocondlng addod to halt a diagonal ,dcacondlng makos alf.6 tho same sum d,X30, taking thoso half diagonals from tbo ends of any Bldos of tho squares to tho middle of it, and so reckoning thon cither upward or downward, or sideways from right to loft, or from loft to right. 4. The sanio with all tho parallols to the half dlagotials, as many as can bo drawn tn the great squaro; for any two of thum bolng directed upward anil downward, from tho plaoo whero thoy begin to that whero thoy end, tholr t.ums will mako tho same, 2,056, 8. If aoquaro hole equal in breadth to four of tho llttlo squares bo cut In u pper, through which iiny of tho 10 llttlo squares In tho groat squaro may bo soon, and ttio popor bo laid upon thiJ great squaro, tho sum of all tho 10 num-lors num-lors soon through tho holo Is always equal to 2,030, tbo sum JL tho 10 num-bors num-bors in any horizontal or vortical column. I am not prepared to say whother thnrols more, than ono corroct way of placing tho numbers which will fulfill tho above conditions, but can asicrt that if a thousand pooplo now com-menco com-menco to arrange the figures thoy may work all tholr lives, and each of thom form a squaro a minute, and although evory combination may be dlftorent, thoy will not have complotod ono-mllllonth ono-mllllonth part of the wrong combinations combina-tions which can be made. I'orhaps this Is a sufficient rofutatlon of tho frequent assortlon that thero Is no rule for tho formation of theso majlcal squares. |