On Weights: The Balance Regaining Equality
Accidental weight against natural weight on unequal arms
Headed 'De pesi' (On weights), this page argues that a balance of equal arms and weights, once displaced from the position of equality, is compelled by necessity to regain it. Leonardo explains that the raised weight is more remote from the centre of revolution and so has a weaker support, whence it descends and lifts the opposite part. A second passage, 'On accidental weight against natural,' with a diagram of a balance whose arm is fixed to a wall projection (labelled b, a n c), shows that accidental weight loads the pole more than natural weight in proportion as the greater arm exceeds the lesser in length.
On this page
A displaced balance is compelled to regain equality
The balance of equal arms and weights, removed from the position of equality, makes its arms and weights unequal, whence necessity constrains it to regain the lost equality of arms and of weights. It is proved by the second proposition of this book.
Why the raised weight descends: a weaker support
The higher weight is more remote from the centre of revolution than the lower weight and therefore has a weaker support, so it descends more easily and raises up the opposite part of the weight joined to the end of the lesser arm.
Accidental weight equals natural weight through the arm ratio
The accidental weight placed on a balance against the natural weight is worth as much as that natural weight. The pole is loaded more by the accidental than by the natural weight in proportion as the greater arm n c exceeds the lesser arm n a in length.