Beam, potential lever, and divisibility to infinity
Notes on breaking an arched cord, the potential lever, and continuous quantity divisible without end
The verso continues Leonardo's mechanics of beams, cords and pulleys, with sketches of triangles, arcs, levers and a spiral of concentric circles. He treats a uniform beam hung by two hangers, asks what weight would break an arched cord of known resistance, and develops his notion of the 'potential lever' — force exists wherever the potential lever does, and grows as the lever shrinks. Further notes argue, in the language of act and potency, that a continuous quantity is divisible to infinity yet can be recomposed by the same degrees, and that the centre of moving matter is driven from the centre of the wheel. The writing is in mirror script across the sheet, some of it inverted.
On this page
The potential lever and the birth of force
Leonardo ties force to the 'potential lever': wherever the potential lever exists, the force too exists, and the force is of greater excellence the smaller that lever is. Force is born together with the potential lever and dies when the lever is lacking.
Breaking an arched cord of known resistance
Given the resistance of a straight cord, Leonardo asks what weight will break his arched cord 'at the site of equality.' He adds that the lever is never consumed by any power.
Continuous quantity divisible to infinity
Invoking the proposition that every continuous quantity is potentially divisible to infinity, Leonardo distinguishes act from potency: what is divisible in act is also divisible in potency, but not everything divisible in potency is divisible in act. Divisions carried toward infinity can be reversed, the parts rejoining by the same degrees in which they were divided.
The centre of moving matter driven from the wheel's centre
A note beside a helical line, written with the sheet inverted, states that the centre of the matter that moves is always moved from the centre of the wheel.