BOOK I.

in which is six; and the third, where you see three. And they signify in the first of these places, Simply, as they speak: in the second, Decuply: in the third, Centuply. That is to say, in the first place, they produce only what they have just been said to signify: in the second, ten times as much: in the third, a hundred times as much. For example, in the number twenty-three noted thus, 2 3, there are two marks and as many places. The triad is in the first, and the duad in the second. The triad there produces only three: but the duad in the later place signifies not two simply, but two tens: which are called twenty. 9 two places And in forty, which is noted thus, 40, there are two marks. Therefore, two places. The prior one is the mark of nothing, which, since it signifies no number—whence the name Nihil nothing was given to it—nevertheless, when placed before others (this can have no place in any number at the extreme end), by occupying a place and pushing others further away, it causes the mark of four in the second place to be found where it is worth ten times four, that is, forty. Similarly, in that number of days, 3 6 5, the five placed in the first place is nothing more or less than five days. But the six, which is in the second place, no longer denotes just six, which it would do if it stood alone or in the first place; rather, these six here represent sixty. And the three, which holds the third place, being increased in signification there by its position, produces three hundred: which are called three hundred in one word. Thus, the mark of the quaternary number placed in three places, 444, makes four hundred and forty-four: in the first of these places, four is worth four simply; but in the second, four decuply, that is forty; and in the third, four centu- ternary places