Trattato Della Pittura  (A Treastie on Painting) is a collection of papers written by Leonardo da Vinci that was assembled by Francisco Melzi, one of da Vinci's former students ("Elmer Belt Library of Vinciana"). Historians estimate that the manuscripts in Trattato Della Pittura  were written from 1469 up until da Vinci's death in 1519. Notably, the treastie was formally published even after Melzi's death (who passed away in 1570) under the title On Painting. The title was changed to Trattato Della Pittura in 1817 when it was re-published in its modern form. 

The work discusses human emotion, structures, and objects from a scientific perspective as to educate painters how to capture realsim in their art. A section of the book titled "VII. Botany for Painters and Elements of Landscape Painting" outlines da Vinci's observations on the anatomy of trees and how lighting and shade interact with leaves. Da Vinci included diagrams of leaves in different conformations and labeled which parts would be in shade, reflected light, or transmitted light relative to the sun's location. 

Throughout the section, da Vinvi proposes mathematical formulas to model the thickness of branches and the angle they form from their parent branch. A majority of the entries are dedicated to elucidating branch geometery throughout its development. Da Vinci suggests that new shoots grow closer together and outwards and will sink down with age, especially if they bear fruit. There are four "modes" of tree growth that outline differences in branch formation and size across tree specifies. Da Vinci exemplified these differences through the examples of an elm and walnut tree (da Vinci 456). 

The book also illustrates da Vinci's proposed hypotheses on plant development which account for observations he recorded. For example, da Vinci suggests that the lower shoots on trees grow more quickly than ones higher up the trunk because "the sap, which nourishes them, is heavy and tends more downwards than upwards" (da Vinci 405). He also reasons that leaves formed on the youngest branch will grow in an opposite direction of the previous branch so that the leaves layer eachother to "serve as a nourishing breast for the shoot or fruit that grows the following year" (416). Da Vinci states that this method of leaf development is favorable for collecting rain water and allowing new branches to receive sunlight. 

Themes of the importance of sap are consistent throughout the work. Da Vinci believed that tree sap was responsible for providing branches and leaves with nourishment. Da Vinci suggested that tree branches tend to grow more densely in the south direction because the sun will draw sap to the sourthern surface. While modern knowledge of photosynthesis refutes some of da Vinci's claims, many of his obersvations on plant structure and peices of advice on illustrating shading and lighting have influenced generations of artists. 

Sources

Da Vinci, Leonardo. Trattato Della Pittura. Vol. I: VIII, 393-481. www.secretofthevine.com/library/volume_one/aor/dv/0431.htm.

“Elmer Belt Library of Vinciana.” Elmer Belt Library of Vinciana UCLA Library, www.library.ucla.edu/special-collections/discover-collections/collecting....

Image is a re-modeled sketch from da Vinci's notebook on how light accesses leaves (da Vinci 470).