Equilibrium of a triangular figure divided about its axis
Two suspended triangles and a proof on the centre of balance
At the top of the leaf two triangular figures hang from horizontal bars, lettered so their balance can be studied. The accompanying proof argues that if one angle of a planar 'pyramid' (triangle) lies perpendicularly below the middle of its side, the weight of the figure is divided equally and rests in equilibrium. Leonardo shows that the line b e halves the triangle into four equal sub-triangles, two on each side, which must therefore balance.
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Why the halving line puts the figure in equilibrium
If one angle of any planar pyramid (triangle) falls perpendicularly beneath the middle of its side, its weight is equally divided and rests in balance. Taking the base angle beneath the mid-side as e and the mid-side as b, the line b e splits the figure into four equal sub-triangles, two on the right and two on the left, which must stand in equilibrium.
Suspended triangles lettered for the demonstration
Two triangular figures are drawn hanging from horizontal supports, the right one lettered a-c-b-d and the left one a-b-d-c-f-e. The lettering fixes the vertices, the mid-side point b, and the interior sub-triangles a b d and d b e used in the equality argument.