Finding the Center of a Suspended Body
A five-sixths calculation, and the rule of real before potential proofs
Under 'Of heaviness', Leonardo states that the center of gravity of a suspended body lies below the center of its support, then computes where the central line of a hung frame q r t S falls. Taking the shaft q r as 4 and t S as 2, and reasoning about which pendants carry which portions, he places the central line at five sixths of the space t S. A short figure of a body linked to a pulley is accompanied by his methodological rule: always put the real demonstrations before the potential ones, so the easier serves as a ladder to the harder. He closes by affirming that the arms of any balance are straight lines rising from the center of rotation and meeting the pendant at a right angle.
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The center of a suspended body lies below its support
The center of gravity of a suspended heavy body lies below the center of its support. This governs the whole demonstration of where the body's central line, and hence its center o, must fall.
Locating the central line at five sixths of the span
The central line o p of the heavy body q r t S arises at five sixths of the space t S. This is proved because the shaft q r is 4 and t S is 2, making 6; the two pendants p q and p r support all of q r (4) and half of t S (2), making 5, so the cord p S supports one, and the center of gravity o falls on the line o p.
A body on a pulley, and arms that meet the pendant at a right angle
A real figure of a body linked to a pulley is set opposite the third potential one. Leonardo adds his rule to put real demonstrations before potential ones. He affirms that the real or potential arms of any balance are straight lines rising from the center of rotation and ending in a right-angled junction with the pendant.