Rods, Cords and the Balance of Equal Arms
A postulate on centres of gravity, and three weights on a triangular balance
A postulate opens the page: by 'rods' and 'cords' Leonardo means long bodies of uniform thickness and weight, whose centre of gravity always lies at the middle of their length and thickness at any inclination. He states that a two-armed balance with equal arms always returns to the level position, while a balance of three equal arms meeting at three equal obtuse angles rests in any position it is turned to. A second block, keyed to six figures, works out where three weights — greatest, least and middling — settle relative to the fulcrum of a triangular balance. Geometry diagrams with a large arc and weighted balance-arms fill the right half of the sheet, and a spiralling shell is drawn in reddish ink near the centre (a drawn element not covered by the transcription).
On this page
Postulate: rods, cords and their centre of gravity
Leonardo defines 'rods' (and likewise 'cords') as long bodies of uniform thickness and weight. He posits that the centre of gravity of such a rod always lies at the middle of its length and thickness, whatever its degree of inclination.
Stability of two- and three-armed balances
A balance of two equal arms always stands at equal height and, however displaced, returns to the position of equality. A balance of three equal arms enclosing three equal obtuse angles rests in every position it is turned to about its centre, and the same holds for any number of arms equal in quality and distance.
Placing three weights on the triangular balance
Keyed to six figures, Leonardo works out where a greatest, a middling and a least weight settle on a triangular balance. If the middle weight is less than double the least, the greatest interposes between the least and the fulcrum; if it reaches or exceeds double, the least falls between the fulcrum and the greatest; and the heaviest with the lightest together counterpoise the middling gravity.
Arc and weighted balance-arm constructions
The right half of the sheet carries geometric constructions: a large circular arc, gridded scales and balance-arms hung with boxed weights lettered in the diagrams. These lay out the geometry underlying the weight problems set in the text.