The number 37 has also somewhat remarkable properties; when multiplied by 3 or a multiple of 3 up to 27, it gives in the product three digits exactly similar. From the knowledge of this the multiplication of 37 is greatly facilitated, the method to be adopted being to multiply merely the first cipher of the multiplicand, by the first of the multiplier; it is then unnecessary to proceed with the multiplication, it being sufficient to write twice to the right hand the cipher obtained, so that the same digit will stand in the unit, tens, and hundreds places.
For instance, take the results of the following table:—
37 multiplied by 3 gives 111, and 3 times 1 = 3
37 multiplied by„ 6 gives„ 222, and„ 3 times„ 2 = 6
37 multiplied by„ 9 gives„ 333, and„ 3 times„ 3 = 9
37 multiplied by„ 12 gives„ 444, and„ 3 times„ 4 = 12
37 multiplied by„ 15 gives„ 555, and„ 3 times„ 5 = 15
37 multiplied by„ 18 gives„ 666, and„ 3 times„ 6 = 18
37 multiplied by„ 21 gives„ 777, and„ 3 times„ 7 = 21
37 multiplied by„ 24 gives„ 888, and„ 3 times„ 8 = 24
37 multiplied by„ 27 gives„ 999, and„ 3 times„ 9 = 27
The singular property of numbers the most different, when added, to produce the same sum, originated the use of magical squares for talismans. Although the reason may be accounted for mathematically, yet numerous authors have written concerning them, as though there were something “uncanny” about them. But the most remarkable and exhaustive treatise on the subject is that by a mathematician of Dijon, which is entitled, “Traité complet des Carrés magiques, pairs et impairs, simple et composés, à Bordures, Compartiments, Croix, Chassis, Équerres, Bandes détachées, &c.; suivi d'un Traité des Cubes magiques et d'un Essai sur les Cercles magiques; par M. Violle, Géomètre, Chevalier de S. Louis, avec Atlas de 54 grandes Feuilles, comprenant
