Show THE alon by tho egyptian it will be seen that in bunaro the ui abera from 1 to 49 run mn in arithmetical progression in tho the j may ical cal square the numbers are disposed in and equal ranks so t hantho turns sums in each row taken either gerpen per pen horizontally or diagonally diago hally t i are equal to i e 17 these magical macli extended eathine in the and ohof idill J jid ji d ys T J y t 1 B 4 5 C T i L i 8 0 10 11 12 13 U 15 1 17 18 19 50 91 5 23 itt 25 25 27 23 t so 30 31 sa 33 35 VI 37 sa 3 40 41 43 t B 43 44 13 40 47 43 49 i t 22 35 4 5 11 29 30 38 12 13 19 37 rm SQ 5 21 39 8 33 2 at 45 44 1 13 43 9 3 23 thematic square was bold in great veneration among tho egyptians and dedicated to tho then seven known planets in various ways to saturn they ai tha square of nino places the sidd being three and the som of the numbers in every row being fifteen to venus they attributed tho square I 1 have given finally they attributed bogod the square of only one cell abo side of which is only a unit which multiplied by itself undergoes no change the ancients having used these magic squares for serious purposes they bo came a subject of consideration among mathematicians noc because they imagined that they would be of any solids use or advantage but rather as a of play in w aich the difficulty makes the merit it your young readers latib a little recreation in the combination of figures let ko a urge square in which there are smaller squares and place in those smaller squares all the numbers from 1 to 25 iri such a manner as will answer thoa itol lowing conditions 1 the sum of the sixteen numbers in each column cal horizontal or tobe devory halt column vertical or horizontal makes lidah or one half the sum of 3 halt a diagonal ascending added to half a diagonal j t thaes also the same sum taking these halt diagonals from tha endom 0 of it and so nang them ther or downward or sideways from right to left or from left to righta 4 Tho Bamo wih all the parallels dt the halt diagonals as manyas many as cabbe drawn in the any two of them being directed upward and downward frodi the place where tuey begin to thai where end their sums ill malietha mali ethe same 5 if hole equal in breadth to four of the little squares be cut in a paper through which any of the 10 little quarts in iho great square may be been and tho paper be laid upon the great square tho sum of all ahti 16 numbers seen through tho holois always equal to 2056 abd tbd sum of tho ag numbers in any horizontal or column I 1 am not prepared to say whether there 13 more than one correct nay of placing tho numbers which will fulfill the above conditions but can aabert that it a thousand people now commence to arrange the figures they may world all their lives and each ol 01 them form a square a minute and although every combination may her different they faill not havo completed ane part of the tion can bo made perhaps ihas is a sufficient refutation 0 ahe frequent assertion that thoro is no rule tor the forma Uon of these magical solares sou ares |