Rules of Tree Branching: Angles, Thickness, Leaf-Scars
Propositions 7-11 on how boughs fork, twist, and record their fallen leaves
A page of the Treatise on Painting continuing Leonardo's numbered rules (seventh through eleventh) for the ramification of plants. He states that where two branchlets rejoin, their combined thickness reconstitutes the parent branch, because the sap of the thicker bough divides among its offshoots, and that a fork bends most sharply when its branches are of equal size. A closing note (824) adds that the scar where a leaf detaches keeps growing in the same proportion as the branch until the bark bursts with age. Two small pen diagrams of forked branches, lettered a-b-c-d-e-f-o-p and a-c-d / n-o-a, accompany the rules.
On this page
A bough's thickness equals the sum of its offshoots (rule 8)
Every fork, taken together, recomposes the thickness of the branch it springs from. Leonardo letters this: a b joined make e, c d joined make f, and e f joined make the thickness of the first branch o p; so o p equals all the thicknesses a b c d, because the sap of the thickest bough divides among its branches.
A fork twists most when its branches are equal (rules 9-10)
The main boughs carry as many twists as there are branchings that do not meet one another. The twist bends most where the two branches are of most uniform thickness: branch a c d, whose limbs a c and b c are equal, is more bent than n o a above it, whose limbs are more unequal.
Each fallen leaf leaves a lasting scar (rule 11 / §824)
The attachment of the leaf always leaves a trace beneath its branch, growing along with the branch until the bark cracks and bursts through the tree's old age. The margin from which the leaf detaches enlarges in the same proportion as the branch and stays visible until age splits the bark.