Canal gradients and a series of balance-beam schemes
The fall of Milan's canals per mile, many weighted balance diagrams, arithmetic, and a wing study
The right-hand page opens with a note on hydraulic gradient: Leonardo observes that the canals leaving Milan fall about one braccio per mile, that an 'ounce' per mile suffices for the surface movement of water, and that over 400 miles such a fall would (by the curvature of the world) make the water run backward. The lower two-thirds of the sheet is filled with rows of balance-beam schemes, each arc labelled with small pan-weights and numeric ratios, together with an arithmetic calculation on the lower margin. Small figures of a pyramid hung from a balance and a rectangle set on a triangle carry letter- and number-labels. A broad, ribbed, sail-like winged apparatus is drawn at the top centre; it is not described in the accompanying text.
On this page
Rows of balance-beam schemes with weights
The lower half of the sheet carries a series of small balance diagrams, each an arc or beam hung with pan-weights and annotated with numeric ratios such as 2:2, 3:1 and 1:3½. One figure shows a pyramid hung from a balance with the labels c, a, d, b. The schemes explore how weights placed at differing arms bring a beam to equilibrium.
Fall of the Milanese canals per mile
Leonardo notes that the canals from Milan drop about one braccio per mile, and that an 'ounce' of fall per mile is enough for the surface movement of the water. He adds that if one braccio of fall were given for every mile, then over 400 miles the rule would make the water flow backward, because of the curvature of the world.
Arithmetic calculation and numeric ratios
A worked multiplication is written on the lower margin, alongside the many numeric ratios that label the balance schemes. The figures include a rectangle set on a triangle marked 4-2. The numbers set out the proportional weightings the balance diagrams test.
Winged, sail-like apparatus
At the top centre a broad, ribbed, sail-like wing is drawn, surmounted by a burst or rosette-like finial. The membrane is stretched over radiating ribs in the manner of a wing study. No transcribed text accompanies this drawing.