Balancing Pyramids: Centers of Gravity on a Beam
Which wedges count in equilibrium; the center of gravity at a quarter of the length
Two labeled diagrams work out the equilibrium of pyramids and wedges hung on a balance. Leonardo argues that 4 of the wedges may be ignored because their center of gravity falls below the balance's suspension point, at one-quarter of the pyramid's length from the base, while the balance beam a c measures three-quarters of the pyramid's length. Faint offset sketches of perspective boxes and pyramids also appear on the sheet but are not transcribed.
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Which wedges count in the balance
There are 4 wedges (bisconi) at a of which no account is taken in equilibrium, because the center of their gravity falls below the suspension-point f, at one-quarter of the pyramid's length toward the base. Account is instead taken of the two pyramids at g and aa, whose center is r, standing against the 4 pyramids.
Center of gravity at one-quarter from the base
The balance a c is three-quarters of the pyramid's length, so the line b S falls at one-quarter of the length toward the base. Four wedges are removed because they stand in the position of equality.
Proportional division of the pyramid's length
The reasoning divides the pyramid's length into a three-quarter beam segment and a quarter toward the base, locating the center of gravity by the letter points b, S and the pyramid's base. The quarter and three-quarter divisions are the geometric heart of the equilibrium argument.