The true arm of a balance: where cord and lever meet at a right angle
A weight at m balances a weight (8) hung over pulley p about fulcrum a; the drop-perpendicular n marks the true arm.
On this recto Leonardo analyses a balance whose horizontal arm is pivoted at a, with a weight hung at m and a second weight (8) carried by a cord that runs over a pulley p. He argues that the 'true' end of an arm lies where the straight line of the arm meets the pull of the cord at a right angle, and marks that perpendicular n as the effective, or 'virtual', arm. A semicircle drawn about the pivot lets him compare how the length of this true arm changes as the cord's direction shifts. He adds that whatever force is lost at the loaded end reappears at the pivot along the true arm af.
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The virtual arm is the perpendicular from the pivot to the cord
Leonardo defines the true end of a balance arm as the point where the straight line of the arm joins the straightness of the cord pulled taut by the weight, forming a right angle. This is seen at S with ma, and likewise pn with na, which he names the virtual arm. He adds that whatever is lacking of the true weight hung at f is regained at the pivot along the true arm af.
Weights m and 8 balanced across the fulcrum a
The upper diagram shows a horizontal balance arm with a semicircle drawn about the left-hand pivot a. A weight hangs at m while a cord from the far end runs over a pulley p to suspend the weight labelled 8, with a second load (S / 4) at the right. The perpendicular n dropped from a to the cord fixes the true, working length of the arm.