Equal Weights on Equal Slopes Stay Balanced
Weights on equal obliquities remain equal; the balance will not move
This page compares the weight of a body given by its position with the weight carried by the beam of a balance. Three linked figures develop the same law: two equal weights set on equal obliquities (a double inclined plane, then triangles carrying balls, then a circle with parallel chords) remain in balance and neither can make the other descend. Leonardo reasons that if there were motion the rising weight would face a greater obliquity than the descending one, so equal slopes keep equal weights at rest. He extends this to the balance, whose equal arms swing through similar, equal arcs whose weight-centres stay equally distant from the fulcrum.
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Equal weights on equal obliquities resist each other's descent
Two equal weights placed on equal obliquities stay equal and, in balance, resist one another's descent. This holds because, if there were motion, the obliquity would be greater in the weight that rises than in the one that descends.
A weight grows lighter as its supporting slope grows steeper
The weights o and m are equal on the equal obliquities a b and a c; but if m sits on the greater obliquity m n it becomes as much smaller as that slope becomes greater. So m never climbs slope m a nor does o descend slope o b, the obliquities being equal.
Similar, equal arcs keep weight-centres equally distant from the pivot
Equal weights e and h on the parallel equal obliquities a b c d cannot move the balance. Even if the arcs e f g h are not parallel, it suffices that they are similar and equal, so the centres of the weights moving along them stay always equally distant from the centre of the balance.