For instance, take the results of the following table:—
| 37 | multiplied by | 3 | gives | 111, | and | 3 | times | 1 = | 3 |
| 37 | ,, | 6 | ,, | 222, | ,, | 3 | ,, | 2 = | 6 |
| 37 | ,, | 9 | ,, | 333, | ,, | 3 | ,, | 3 = | 9 |
| 37 | ,, | 12 | ,, | 333, | ,, | 3 | ,, | 3 = | 9 |
| 37 | ,, | 15 | ,, | 444, | ,, | 3 | ,, | 4 = | 12 |
| 37 | ,, | 18 | ,, | 555, | ,, | 3 | ,, | 5 = | 15 |
| 37 | ,, | 18 | ,, | 666, | ,, | 3 | ,, | 6 = | 18 |
| 37 | ,, | 21 | ,, | 777, | ,, | 3 | ,, | 7 = | 21 |
| 37 | ,, | 24 | ,, | 888, | ,, | 3 | ,, | 8 = | 24 |
| 37 | ,, | 27 | ,, | 999, | ,, | 3 | ,, | 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 Traite 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 400 figures.” Paris,
