Survey of the River Adda for the Naviglio Canal
Meandering course of the Adda with distances, levels and cost estimates for cutting the canal from Trezzo to Brivio
Down the center of the sheet runs a long, winding drawing of the course of the river Adda, labelled at points a, b and c, surrounded on all sides by dense arithmetic. The notes survey and cost out a navigable canal (Naviglio) between the port of Trezzo and Brivio: total lengths of about six and a half miles, the depth of 57 braccia from the Naviglio's surface to that of the Adda at the mill of the Travaglia, and successive drops in level of 10 and 3 braccia. Leonardo proposes closing off the valley and the Tre Corni and reckons the excavation cost in thousands of ducats, converting miles into twelfths to check his figures. A separate memorandum at the upper right lists benefices and works and reminds him to speak 'first of the benefices, then of the works, then of the ingratitudes.'
On this page
Making the Adda navigable: the canal and the mill of the Travaglia
The plan is to cut a Naviglio alongside the winding Adda so that boats can pass between Trezzo and Brivio. At the mill of the Travaglia the drop from the surface of the canal to the surface of the river is given as 57 braccia, and Leonardo notes a 'perpetual mechanism, short as a lock-basin' to manage the descent. Closing off the valley and the Tre Corni is central to the scheme.
Surveyed distances from Trezzo to Brivio
The course is measured segment by segment: from Brivio to the mill of the Travaglia is 3 miles and 2/3 (8/12), and from that mill to the port of Trezzo is 2 miles and 2/5 (10/12). Added together the cutting of the Naviglio runs about 6 and 2/5 to 6 and 1/2 miles. The river drawing carries the letters a, b and c to key these distances.
Cost of the excavation and closing the valley
Leonardo estimates that he need excavate only half the cost of the embankment (costa), which will cost 3 thousand ducats. With 15 thousand ducats the valley and the Tre Corni can be sealed off, and below that the cutting of two miles is saved. The figures are worked repeatedly in the surrounding columns of arithmetic.
Reducing miles to twelfths to check the totals
To subtract 3 and 2/3 from 6 and 1/2 he converts the miles into twelfths (once): 6 times 12 makes 72, plus 6 makes 78; 36 plus 8 makes 44; 78 minus 44 leaves 34, which reduced back to miles gives 2 miles and 10/12, that is 5/6. Long multiplications by 4 and divisions by 3000 fill the margins as he multiplies lengths into hundreds and parts them into miles.