Weights, Balances and the Material Pivot
Folio 1r: statics of the balance, its moment, and why ice floats
This page is filled with diagrams of balances, weights on inclined planes and pulleys accompanied by propositions on statics. Leonardo argues that the swinging (ventilazione) of a balance depends on the thickness and length of its material pole, that a circular balance never oscillates, and that the heavier part of a body guides the lighter. A closing note asks why ice, though denser than water, floats, answering that it expands as it forms; the name 'Antonio' is jotted in an adjacent space.
On this page
Why a balance swings: the material pole
The smaller the thickness of the balance's pole, the smaller the moment of its swing; the longer the balance, the smaller the moment, since the pole becomes proportionally more slender. If the mathematical centre alone were the pole, the balance would never oscillate at all.
The circular balance never oscillates
In the round or circular balance no swinging occurs, because its parts are always equal around the pole. The centre of the pole always lies by a perpendicular line above the point where its support touches it.
Density, weight and floating ice
A body that condenses more becomes heavier, like the air in wind-balls. Leonardo then asks why ice, denser than water, floats upon it, and answers that ice grows (expands) as it forms.
Beam length and the moment of the balance
The moment of a balance is treated proportionally: two beams whose poles are of the same thickness differ in moment because the longer beam makes its pole relatively more slender. The light thing always rests above the heavy when both are free.
The name 'Antonio' jotted beside the figures
In a space adjacent to the mechanical diagrams the single name 'Antonio' is written, a memorandum unrelated to the surrounding propositions on statics.