A Balance Hung at Its Centre of Gravity Stays Still
Folio 2v: equilibrium of equal weights at the ends of a wheel's diameter
Leonardo argues that a balance suspended exactly at its centre of gravity would remain motionless in any oblique position, as happens with the round balance. He then treats two equal weights a and c fixed at the ends of a wheel's diameter: an imagined adversary claims a will descend by the straighter path a d while c rises, but Leonardo answers that since the weights, arms b a and b c, and the arcs a d and c e with their chords and sagittae are all equal, there is no cause of motion, as experience confirms. A framed, fan-ribbed structure with many radiating cords is drawn at the foot of the page but is not transcribed in the bundle.
On this page
A balance suspended at its centre of gravity stays still
If it were possible to suspend the balance at the centre of its gravity, it would always remain still without any swinging, in whatever oblique position it were placed. This is what is seen to happen with the round balance.
Equal weights on a wheel's diameter do not self-return
Two equal weights a and c fixed at the ends of the wheel's diameter, once drawn from the position of equality, will never return to it by themselves. An adversary claims a descends by the straighter path a d while c rises along c e, but this is impossible, since equal things do not overcome one another.
Equal arms, arcs, chords and sagittae yield no motion
Because the weights a and c are equal, the balance arms b a and b c are equal, and the arcs of motion a d and c e are equal together with their chords and sagittae, there is no cause of motion. Leonardo says experience already confirms this equilibrium.