Eliae Vineti ... de logistica libri tres

...hundred and eighty-nine, and three hundred and sixty-seven, if you are to compose them: seven and nine, which are in the first position—to which the circle adds nothing—make sixteen. This number is designated by two signs thus: 16.

Example

990

789
367

Therefore, of these signs, the former, 6, is to be marked under the line in the same perpendicular column. The other, 1, should be marked in the second position immediately. But because it would thus occupy the place of the digits that will be found in it, its notation is deferred until those are collected, to which it may be added in this way: nine, 8, and 6 of the second position make twenty-three. Now to those, one must add that 1 reserved from the previous position, and they will become twenty-four. This number, because it is marked with two signs thus, 24, has its first part 4 to be marked underneath; the other is to be reserved for the third position. This one has 9 and 7, which make sixteen, and 3, which makes nineteen, to which those two reserved from the second position must be added; and it will become 21, a number also of two signs. The former of which will hold the third position, the latter the fourth. Thus, in the last position, there is no reason why you should not mark down immediately whatever results from the composition of the digits.

Example

990

789
367

2146