Studies of the bent lever and its lifting forces
On motion and friction; the bent versus the straight counter-lever
Folio 63v studies the counter-lever (contralieva) under the headings 'On motion and friction' and 'On the straight counter-lever.' Two large crane-arms at the top compare a straight arm carrying weights (10, 01) with a bent arm sweeping through arcs; the bent counter-lever S n m o p exerts a different effort at each distance from its center (lines S t, m t, n t, o t, p t), and as the weight at X rises it grows lighter, losing 1/10 by the time the tip reaches b. Leonardo tells himself to draw the figure henceforth only with the line p X b and to drop the superfluous curves. Lower diagrams ask which shaft or point costs more effort to raise or push, resolving each by the way its motion rises or declines.
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Bent versus straight counter-lever
The bent counter-lever S n m o p exerts as many different efforts in lifting as it has distances from its center, shown by the lines S t, m t, n t, o t, p t. As the weight hung at X rises it becomes lighter, so that when the tip reaches b the weight is diminished by 1/10, whence a feels 5 1/2 and b 4 1/2.
Simplify the figure to the line p X b
Leonardo instructs himself to draw this figure from now on only with the line p X b, removing the curved lines o c, m d, n e as superfluous; the line b S is that of the motion S and b X p that of the motion of p.
Which shaft costs more effort
He asks whether the bent lever labours more to raise the shaft a b or the shaft c d, answering that c d costs more because it is thrust toward its pivot; a later note finds pulling and pushing equal, since each must climb the bent lever.
Easiest point to push: a, b or c
Of the points a, b, c he asks which is pushed most easily, concluding c is easiest and a hardest, because the motion of a rises along a S while the motion of c declines along c n.