SAPIENTIA. They are all either augmented or diminished.
HADRIAN. And that “evenly even” number of which you spoke?
SAPIENTIA. That is one which can be divided into two equal parts, and these parts again into two equal parts, and so on in succession until we come to indivisible unity: 8 and 16 and all numbers obtained by doubling them are examples.
HADRIAN. Continue. We have not heard yet of the “evenly uneven” number.
SAPIENTIA. One which can be divided by two, but the parts of which after that are indivisible: 10 is such a number, and all others obtained by doubling odd numbers. They differ from the “evenly even” numbers because in them only the minor term can be divided, whereas in the “evenly even” the major term is also capable of division. In the first type, too, all the parts are evenly even in name and in quantity, whereas in the second type when the division is even the quotient is uneven, and vice versa.
HADRIAN. I am not familiar with these terms, and divisors and quotients alike mean nothing to me.[10]
SAPIENTIA. When numbers of any magnitude are set down in order, the first set down is called the “minor term” and the last the “major.” When, in making a division, we say by how many the number is to be divided, we give the “divisor,” but when we enumerate how many there are in each of the parts we set forth the “quotient.”
HADRIAN. And the “unevenly even” numbers?
SAPIENTIA. They, like the “evenly even,” can be halved, not only once, but sometimes twice, thrice, and even four times, but not down to indivisible unity.
HADRIAN. Little did I think that a simple question as to the age of these children could give rise to such an intricate and unprofitable dissertation.