To find numbers with these mathematical relations is not very easy, except by actual trial with figures. If you take the base, haphazard, and perpendicular also, when you come to square them and add them together, the chances are very great that no root can be found to the number produced by the addition.
For example, take for the base, 2, for the perpendicular, 3. The sum of their squares is equal to 13, therefore, the third side is equal to the square root of thirteen. There is no such number really in existence, in the universe.
1st. Any fraction, squared, must on pure mathematical principles produce a fractional number.
2d. Two whole numbers added must produce a whole number. Therefore a right triangle, such that the base and perpendicular each squared and added together forms a whole number, cannot have a hypotenuse that can be found, unless it be in whole numbers.
We know that the squares of 9 and 16 have for their roots 3 and 4, therefore 13 can have no whole number root. As we have shown heretofore, that a whole number cannot have a fractional root, because no fractional number in existence can be squared so as to produce a whole number, it follows that 13 can have no numerical square root. The root thereof is forever hidden from man.
Our readers may wonder why we introduce this explanation here. The reason is this, that those who are not practical, or even theoretical mathematicians, may thereby understand the wonders connected with the word in its relations to the emblems from the Magic Test Book. That they may fully understand that the wonderful co-ordina-
