Curious Myths of the Middle Ages

For instance, the property of the number 9, discovered, I believe, by W. Green, who died in 1794, is inexplicable to any one but a mathematician. The property to which I allude is this, that when 9 is multiplied by 2, by 3, by 4, by 5, by 6, &c., it will be found that the digits composing the product, when added together, give 9. Thus: —

It will be noticed that 9 × 11 makes 99, the sum of the digits of which is 18 and not 9, but the sum of the digits 1 × 8 equals 9.

And so on to any extent.

M. de Maivan discovered another singular property of the same number. If the order of the digits expressing a number be changed, and this number be subtracted from the former, the remainder will be 9 or a multiple of 9, and, being a multiple, the sum of its digits will be 9.

For instance, take the number 21, reverse the digits, and you have 12; subtract 12 from 21, and the remainder is 9. Take 63, reverse the digits, and subtract 36 from 63; you have 27, a multiple of 9, and 2 + 7 = 9. Once more, the number 13 is the reverse of 31; the difference between these numbers is 18, or twice 9.

Again, the same property found in two numbers thus changed, is discovered in the same numbers raised to any power.

Take 21 and 12 again. The square of 21 is 441, and the square of 12 is 144; subtract 144 from 441, and the remainder is 297, a multiple of 9; besides, the digits expressing these powers added together give 9. The cube of 21 is 9261, and that of 12 is 1728; their difference is 7533, also a multiple of 9.

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 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: —

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 St. Louis, avec Atlas de 54 grandes Feuilles, comprenant 400 figures.” Paris, 1837. 2 vols. 8vo., the first of 593 pages, the second of 616. Price 36 fr.

I give three examples of magical squares: —

These nine ciphers are disposed in three horizontal lines; add the three ciphers of each line, and the sum is 15; add the three ciphers in each column, the sum is 15; add the three ciphers forming diagonals, and the sum is 15.

But the connection of certain numbers with the dogmas of religion was sufficient, besides their marvellous properties, to make superstition attach itself to them. Because there were thirteen at the table when the Last Supper was celebrated, and one of the number betrayed his Master, and then hung himself, it is looked upon through Christendom as unlucky to sit down thirteen at table, the consequence being that one of the number will die before the year is out. “When I see,” said Vouvenargues, “men of genius not daring to sit down thirteen at table, there is no error, ancient or modern, which astonishes me.”

Nine, having been consecrated by Buddhism, is regarded with great veneration by the Moguls and Chinese: the latter bow nine times on entering the presence of their Emperor.

Three is sacred among Brahminical and Christian people, because of the Trinity of the Godhead.

Pythagoras taught that each number had its own peculiar character, virtue, and properties.

“The unit, or the monad,” he says, “is the principle and the end of all; it is this sublime knot which binds together the chain of causes; it is the symbol of identity, of equality, of existence, of conservation, and of general harmony. Having no parts, the monad represents Divinity; it announces also order, peace, and tranquillity, which are founded on unity of sentiments; consequently One is a good principle.

“The number Two, or the dyad, the origin of contrasts, is the symbol of diversity, or inequality, of division and of separation. Two is accordingly an evil principle, a number of bad augury, characterizing disorder, confusion, and change.

“Three, or the triad, is the first of unequals; it is the number containing the most sublime mysteries, for everything is composed of three substances; it represents God, the soul of the world, the spirit of man.” This number, which plays so great a part in the traditions of Asia, and in the Platonic philosophy, is the image of the attributes of God.

“Four, or the tetrad, as the first mathematical power, is also one of the chief elements; it represents the generating virtue, whence come all combinations; it is the most perfect of numbers; it is the root of all things. It is holy by nature, since it constitutes the Divine essence, by recalling His unity, His power, His goodness, and His wisdom, the four perfections which especially characterize God. Consequently, Pythagoricians swear by the quaternary number, which gives the human soul its eternal nature.

“The number Five, or the pentad, has a peculiar force in sacred expiations; it is everything; it stops the power of poisons, and is redoubted by evil spirits.

“The number Six, or the hexad, is a fortunate number, and it derives its merit from the first sculptors having divided the face into six portions; but, according to the Chaldeans, the reason is, because God created the world in six days.

“Seven, or the heptad, is a number very powerful for good or for evil. It belongs especially to sacred things.

“The number Eight, or the octad, is the first cube, that is to say, squared in all senses, as a die, proceeding from its base two, an even number; so is man four-square, or perfect.

“The number Nine, or the ennead, being the multiple of three, should be regarded as sacred.

“Finally, Ten, or the decad, is the measure of all, since it contains all the numeric relations and harmonies. As the reunion of the four first numbers, it plays an eminent part, since all the branches of science, all nomenclatures, emanate from, and retire into it.”

It is hardly necessary for me here to do more than mention the peculiar character given to different numbers by Christianity. One is the numeral indicating the Unity of the Godhead; Two points to the hypostatic union; Three to the Blessed Trinity; Four to the Evangelists; Five to the Sacred Wounds; Six is the number of sin; Seven that of the gifts of the Spirit; Eight, that of the Beatitudes; Ten is the number of the commandments; Eleven speaks of the Apostles after the loss of Judas; Twelve, of the complete apostolic college.

I shall now point out certain numbers which have been regarded with superstition, and certain events connected with numbers which are of curious interest.

The number 14 has often been observed as having singularly influenced the life of Henry IV. and other French princes. Let us take the history of Henry.

On the 14th May, 1029, the first king of France named Henry was consecrated, and on the 14th May, 1610, the last Henry was assassinated.

Fourteen letters enter into the composition of the name of Henri de Bourbon, who was the 14th king bearing the titles of France and Navarre.

The 14th December, 1553, that is, 14 centuries, 14 decades, and 14 years after the birth of Christ, Henry IV. was born; the ciphers of the date 1553, when added together, giving the number 14.

The 14th May, 1554, Henry II. ordered the enlargement of the Rue de la Ferronnerie. The circumstance of this order not having been carried out, occasioned the murder of Henry IV. in that street, four times 14 years after.

The 14th May, 1552, was the date of the birth of Marguérite de Valois, first wife of Henry IV.

On the 14th May, 1588, the Parisians revolted against Henry III., at the instigation of the Duke of Guise.

On the 14th March, 1590, Henry IV. gained the battle of Ivry.

On the 14th May, 1590, Henry was repulsed from the Fauxbourgs of Paris.

On the 14th November, 1590, the Sixteen took oath to die rather than serve Henry.

On the 14th November, 1592, the Parliament registered the Papal Bull giving power to the legate to nominate a king to the exclusion of Henry.

On the 14th December, 1599, the Duke of Savoy was reconciled to Henry IV.

On the 14th September, 1606, the Dauphin, afterwards Louis XIII., was baptized.

On the 14th May, 1610, the king was stopped in the Rue de la Ferronnerie, by his carriage becoming locked with a cart, on account of the narrowness of the street. Ravaillac took advantage of the occasion for stabbing him.

Henry IV. lived four times 14 years, 14 weeks, and four times 14 days; that is to say, 56 years and 5 months.

On the 14th May, 1643, died Louis XIII., son of Henry IV.; not only on the same day of the same month as his father, but the date, 1643, when its ciphers are added together, gives the number 14, just as the ciphers of the date of the birth of his father gave 14.

Louis XIV. mounted the throne in 1643: 1 + 6 + 4 + 3 = 14.

He died in the year 1715: 1 + 7 + 1 + 5 = 14.

He lived 77 years, and 7 + 7 = 14.

Louis XV. mounted the throne in the same year; he died in 1774, which also bears the stamp of 14, the extremes being 14, and the sum of the means 7 + 7 making 14.

Louis XVI. had reigned 14 years when he convoked the States General, which was to bring about the Revolution.

The number of years between the assassination of Henry IV. and the dethronement of Louis XVI. is divisible by 14.