BOOK I.

you join: and note the sum of thirty-six thousand six hundred and five under the other. If you then compose the remaining five: and place the sum of these, forty-four thousand five hundred and two, under the sums of the others. And, if you finally combine those three sums: from which the sum of all is effected, 115210.

It happens, however, for the most part, that some of those to be composed are smaller than others: and in the final places, a digit is found to which there is lacking another with which it can be composed in that place: which, nevertheless, it is necessary to add to the sum under the line, as it is alone. As in this example. The digits of the first place make 21, a number of two digits. The prior of these, 1, is to be noted immediately under the line, the digits themselves having been joined: the other is to be reserved. But in the second place, the lowest number has nothing: but the upper ones, 1 and 6, which become seven. To which 7, the two reserved from the previous place must be added: and 9 will be made, to be noted under the line. The third place follows, and the fourth: in which neither the middle nor the lowest have anything: but only the highest is there, which in that place has five, and