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The Mind of Leonardo
IV.4C
 
IV.4C
Branching forms
 
  [IV.4C  Branching forms]    
 
     

According to Leonardo, the overall diameter of the branches grown from a trunk in a year is equal to the diameter of the trunk from which they depart. The same holds true for the secondary branches growing in the following year. This implies the existence of a precise proportional ratio between the various orders of ramification. By analogy, Leonardo extends this law to the relationship of the flow capacity of a river to that of the branches into which it divides, and to the ramifications of the vessels of the heart and the bronchial tubes.

“All of the branches of a tree, regardless of its height, when added together are equal to the size of their trunk. All of the ramifications of water, regardless of their length, being of equal motion are equal to the size of the river from which they branch off.”

(Leonardo da Vinci, Ms. I, 12v)

“All of the air that enters the windpipe is of equal quantity in all of the degrees that are generated by its ramification, like the branches born each year from plants, which each year, considering all of these branches joined together, are equal to the size of the stalk of the plant.”

(Leonardo da Vinci, Royal Collection, Windsor, 19064v)

“Always the ramifications of the veins are the greater when they branch off from the larger trunks, that is, the main ramifications, and the same is true of the ramifications of these ramifications, up to the end.”

(Leonardo da Vinci, Royal Collection, Windsor, 19074r)


 
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