was euclid right in defining number to be a collection of unities of the same kind? when newton says that number is an abstract relation of one quantity to another of the same kind, does he not understand by that the use of numbers in arithmetic and geometry? wolfe says, number is that which has the same relation with unity as one right line has with another. is not this rather a property attributed to a number, than a definition? if i dared, i would simply define numbers the idea of several unities.

i see white — i have a sensation, an idea of white. it signifies not whether these two things are or are not of the same species; i can reckon two ideas. i see four men and four horses — i have the idea of eight; in like manner, three stones and six trees will give me the idea of nine.

that i add, multiply, subtract, and divide these, are operations of the faculty of thought which i have received from the master of nature; but they are not properties inherent to number. i can square three and cube it, but there is not certainly in nature any number which can be squared or cubed. i very well conceive what an odd or even number is, but i can never conceive either a perfect or an imperfect one.

numbers can have nothing by themselves. what properties, what virtue, can ten flints, ten trees, ten ideas, possess because they are ten? what superiority will one number divisible in three even parts have over another divisible in two?

pythagoras was the first, it is said, who discovered divine virtue in numbers. i doubt whether he was the first; for he had travelled in egypt, babylon, and india, and must have related much of their arts and knowledge. the indians particularly, the inventors of the combined and complicated game of chess, and of ciphers, so convenient that the arabs learned of them, through whom they have been communicated to us after so many ages — these same indians, i say, joined strange chimeras to their sciences. the chald?ans had still more, and the egyptians more still. we know that self-delusion is in our nature. happy is he who can preserve himself from it! happy is he who, after having some access of this fever of the mind, can recover tolerable health.

porphyrius, in the “life of pythagoras,” says that the number 2 is fatal. we might say, on the contrary, that it is the most favorable of all. woe to him that is always single! woe to nature, if the human species and that of animals were not often two and two!

if 2 was of bad augury, 3, by way of recompense, was admirable, and 4 was divine; but the pythagoreans and their imitators forgot that this mysterious 4, so divine, was composed of twice that diabolical number 2! six had its merit, because the first statuaries divided their figures into six modules. we have seen that, according to the chald?ans, god created the world in six gahambars; but 7 was the most marvellous number; for there were at first but seven planets, each planet had its heaven, and that made seven heavens, without anyone knowing what was meant by the word heaven. all asia reckoned seven days for a week. we divide the life of man into seven ages. how many reasons have we in favor of this number!

the jews in time collected some scraps of this philosophy. it passed among the first christians of alexandria with the dogmas of plato. it is principally displayed in the “apocalypse of cerinthus,” attributed to john the apostle.

we see a striking example of it in the number of the beast: “that no man might buy or sell, save he that had the mark, or the name of the beast, or the number of his name. here is wisdom. let him that hath understanding count the number of the beast: for it is the number of a man; and his number is six hundred three score and six.”

we know what great pains all the great scholars have taken to divine the solution of this enigma. this number, composed of three times two at each figure, does it signify three times fatal to the third power? there were two beasts, and we know not yet of which the author would speak.

we have seen that bossuet, less happy in arithmetic than in funeral orations, has demonstrated that diocletian is the beast, because we find the roman figures 666 in the letters of his name, by cutting off those which would spoil this operation. but in making use of roman figures, he does not remember that the apocalypse was written in greek. an eloquent man may fall into this mistake. the power of numbers was much more respected among us when we knew nothing about them.

you may observe, my dear reader, in the article on “figure,” some fine allegories that augustine, bishop of hippo, extracted from numbers.

this taste subsisted so long, that it triumphed at the council of trent. we preserve its mysteries, called “sacraments” in the latin church, because the dominicans, with soto at their head, allege that there are seven things which contribute to life, seven planets, seven virtues, seven mortal sins, six days of creation and one of repose, which make seven; further, seven plagues of egypt, seven beatitudes; but unfortunately the fathers forget that exodus reckons ten plagues, and that the beatitudes are to the number of eight in st. matthew and four in st. luke. but scholars have overcome this difficulty; by retrenching from st. matthew the four beatitudes of st. luke, there remain six, and add unity to these six, and you will have seven. consult fra paolo sarpi, in the second book of his history of the county of trent.