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 m............