Costing the Excavation of the Fortress Ditch
A rule of three on price per canna, from 9,472 to 29,600 ducats, for a ditch 640 braccia long
This page works out the cost of digging a fortress ditch 160 canne (640 braccia) long, 16 braccia deep and 17 braccia wide, totaling 1,326,080 square braccia. At 64 soldi the square canna that comes to 9,472 gold ducats for the earth alone, without walls or foundations; because the lower rock must be cut in three descending shifts of men, the rate rises to 15 lire the canna. A rule of three then rescales the price, so that at 200 soldi the canna the same work reaches exactly 29,600 ducats. A small square with a diagonal and a faint hatched plan accompany the sums.
On this page
Dimensions of the ditch and three shifts of diggers
The ditch is 160 canne (640 braccia) long, 16 braccia deep and 17 braccia wide top to bottom, making 1,326,080 square braccia, priced at 64 soldi the square canna for 9,472 ducats. Where the ground is rock rather than earth the rate climbs from 5 to 15 lire the canna, because the cut must be taken in three shifts of men, each working 5 braccia lower than the one above. The figure is given for the excavation alone, apart from masonry.
Rule of three: 64 versus 200 soldi the canna
Because 10 is midway between 5 and 15, the square canna is set at 10 lire for a ditch 15 braccia deep. A proportion is then set up: if the excavation costs 9,472 ducats at 64 soldi the canna, at 200 soldi the canna it will reach exactly 29,600 ducats. It is a straightforward rescaling of one price against another.
A fortress ditch, apart from its walls and foundations
The cost given covers digging the ditch only, expressly without the walls or the foundations of the fortress. The ditch belongs to a defensive work whose masonry would be costed separately. A faint hatched plan is drawn at the lower left of the sheet.