The law of the balance: arms, weights, and friction
Levers in inverse proportion, the rule of three for friction, and a sphere on an inclined plane
A crowded sheet of statics with many small balance and lever diagrams among sketched frame devices and a spring mechanism. Leonardo repeatedly formulates the law of the balance: the weights that keep the arms level are in the same proportion as the arms but inversely placed, so that multiplying and dividing arm lengths yields the weight to hang on each side. A separate figure sets up the counterweight of friction ('confregazione') and solves it by the rule of three, and a sphere resting on a plane is analysed for the weight it delivers to its point of contact and, when placed obliquely, along the line of descent.
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Weight a sphere delivers to its point of contact
Every sphere placed on any plane gives to its point of contact as much weight as twice the lesser part that projects beyond the straight line of that contact. The rule ties the load at the contact to how far the ball overhangs its support. It opens the sheet's study of how bodies press on their bearings.
Weights inversely proportional to the balance arms
The proportion of the weights that hold the arms of the balance level with the horizon is the same as that of the arms, but inverted. Multiply the lesser arm by the greater to find the weight for the lesser arm, and divide the greater arm by the lesser for its counterpart. Set the number of weights equal to the divisions of the arms that suspend them and exchange the positions.
The counterweight of friction
A figure marked 12, 3, 1, 4 is drawn to determine friction. If three units of friction give one, which must be balanced by the counterweight of that friction, what will four give? The proportional question sets friction against the load it resists.
The rule of three applied to the friction counterweight
Divide the number that sustains the counterweight by as many fours as the times it contains the arm of the friction. Once the counterweight is found by the rule of three, divide again by as many fours as the arm of the counterweight contains the arm of friction, and the result is the sought counterweight. Keep the numbers of arms and weights equal with opposite positions equal, and the arms will balance.
A sphere on an inclined plane
A sphere placed obliquely directs its weight toward two different aspects. One of these is along the line of the slope. The note begins to resolve the tendency of the ball into components on the inclined plane.
Frame device and spring mechanism sketches
Among the balance diagrams the sheet carries larger pen sketches of built mechanisms, including a tall trestle-like frame with a curved arm at upper right and a small strung device with a bent spring. They accompany the statics as applied illustrations. Further untranscribed labelling appears beside them.