Experiment of the Balance: Rest About the Fulcrum
An equal-armed beam stays wherever the hand leaves it, like a circle about its pole
The heading announces an "experiment of the balance": an equal-armed beam remains wherever it is left, just as a circle turns about its own pole. Four diagrams show the beam and its inscribed rhombus tilted at various obliquities about the fulcrum, while a small central sketch shows a rod standing upright within a vessel. Leonardo argues that the central line b d divides the figure into two triangles, b c d and d b e, that are similar and equal in figure and in weight, so the arms stay balanced at any tilt. He concludes the balance has no motion when its mathematical centre lies amid equal opposing weights.
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An equal-armed balance rests wherever it is left
The balance remains in whatever position the hand of man leaves it, like a circle about its pole. When its pivot is placed near the mathematical point that is its centre of gravity, the equal arms hold any obliquity indifferently.
Central line b d divides the beam into two equal triangles
The line b d, at whose middle the mathematical centre lies, splits the beam into triangles b c d and d b e, similar and equal in figure and weight. The upper angle c is as far from the central line as angle e, as the line e p shows, so their differing position does not alter the weights.
No motion when the mathematical centre lies among equal weights
Because it does no harm for one weight (angle c) to sit higher than the other (angle e), Leonardo concludes that such a balance will have no motion, its mathematical centre standing in the midst of all the opposing weights that are equal to one another.