Eliae Vineti ... de logistica libri tres

...the costs of buildings are consummated. And in Columella, in the fifth book, where he writes thus about the measurement of a hexagonal field: "Since there are six sides: which, consummated, result in two thousand." And a little later, about the planting of seeds: "And in the same order you will consummate the number of seeds." The same also is meant by his verbal form among the same ancients, as in those of the jurist Pomponius, which are extant in the thirty-sixth law of the title on the edict of buildings, in the twenty-first book of Justinian’s Digest. "But if, with the price of individual slaves established, all have been sold for as much as resulted from the consummation of the individuals." This seems to be the primary and proper meaning of consummating, from which the other, meaning to finish or complete, has been transferred.

But when you wish to compose numbers, you will describe them such that their first digits, those which lie to the right, form a perpendicular line. Thus, the second, third, fourth, and others of other positions, if there are many, are to be established. For in this matter, the ratio of positions must be observed first. If these are confused, you achieve nothing. Those being marked in this way, a straight line is to be placed underneath. Starting the composition from the right, the digits of each position are to be joined, and in that same position, they are to be marked under the line. From this, what is called the "sum" is effected. But the matter will be captured more easily through examples. Let there be two numbers to be joined: thirty-one days of the month of January and twenty-eight of February. You will mark these above a straight line. Then you will compose the digits of the first position, 1 and 8. These make nine, which you will mark as 9 under them, below the line. Then, 2 and 3, unless you prefer to begin from the upper, saying three and two: they make five. This digit 5 you will also place under their own positions.

Observation of the ratio of positions first

Example