Leonardo da Vinci defends his studies and his notebooks and sets up rules as to how to interpret what he wrote. Leonardo doesn’t hesitate to deride a trained mathematician or scholars. Leonardo was not revered through formal education, and discusses his opinions of true science, education, and knowledge.

Leonardo provides the reader a background on his works, stating that his studies and efforts are not to challenge the great theorists that came before him. He also makes a point of ridiculing the past geniuses however. “…alleging that my proofs are contrary to the authority of certain men held in great reverence by their inexperienced judgments, not considering that my works are the issue of simple and plain experience.”

Leonardo attacks the naysayers of his abilities despite his inexperience in classical mathematics and Latin. Leonardo insists that the readers must acknowledge his laborious and countless studies. “I am fully aware that the fact of my not being a man of letters may cause certain presumptuous persons to think that… I am a man without learning. Foolish folk! … They do not know that my subjects require for their exposition experience rather than the words of others.” Leonardo has experienced his studies and analyses. He did not sit in a classroom and listen to the work and findings of others. He found his own.

Leonardo ridicules the conventions of classical education, claming the formality and uniformity hinders self-exploration and enlightenment. “They strut about puffed up and pompous, decked out and adorned not with their own labours, but by those of others.”

Leonardo writes a disclaimer for those reading his work: “Let no man who is not a mathematician read the elements of my work.” I like this comment. I often feel as when I am writing a technical paper the reader must be aware of the subject. If not, the writer must first inform the reader, then address and discuss the critical points. Leonardo didn’t have time to do this – he studied life and kept a notebook. By declaring that only math-knowledgeable peoples read his mathematical statements ensures Leonardo that the reader will try to understand and admire the studies of da Vinci.

Leonardo states that sciences that do not go through any of the five senses are vain and full of errors. If you can neither see nor feel such scientific conclusions, the results will stir constant debate. “…such as the nature of God and soul and the like, about which there are endless disputes and controversies.” Leonardo spent most of his time experiencing his studies. “All true sciences are the result of Experience which has passed through our senses, thus silencing the tongues of litigants.”

Leonardo demands that one must show experience to convince one of scientific discovery and knowledge. Leonardo spent most of these notebooks defending his background and work. Leonardo believed the way to learn was to live and study, and never be satisfied.

Leonardo explains the phenomenon of perspective and the workings of the eye in these selected notebooks. Leonardo uses the idea of a pyramid to which he drives all the lines of perspective and what the eye sees.

Leonardo, like at many other points in his notebooks, states the obvious. But then again, what is obvious now, was not obvious during the Renaissance, and Leonardo putting words to these observations on nature and humans, and Leonardo’s directions on painting were revolutionary in thought. But then again, they are obvious. “Among objects of equal size that which is most remote from the eye will look smallest,” is simply why the stop sign keeps getting larger and larger as the occupant of the automobile proceeds towards it. Leonardo states that when a person has in view similar objects at similar distances, the viewer will first recognize the brightest object.

Einstein would have doubted this assertion no doubt that light passes through air in a straight path. Before making this statement, Leonardo references Euclidean geometry and the assumption that the universe lies in x-y-z space. “…to assert that every ray passing through air of equal density travels in a straight line from its cause to the object or place where it strikes.” This statement still explains light traveling through air in the microspective view, what we see in our day-to-day lives, in computer clusters and classrooms and kitchens.

Leonardo amazed me quite simply with his explanation and depiction of the inner-workings of the eye. I cannot even fathom how many hours he studied the workings of the eye, and more amazing, without any technology. I wonder if he had any idea our eyes initially see everything inverted, and what the man would state on that fact.

I had a hard time picturing a few of the perspective “laws” that Leonardo states. First, his statement that an object farthest away will appear lightest, which I think goes against the thought that the objects farther away are darkened in the shadows. Maybe Leonardo is intending to mean a different aspect, as he states, “Of several bodies of equal size and tone, that which is farthest will appear lightest and smallest.” Second, his statements on the “luminous atmosphere” and the application of blue to a dark object is not all too clear with me. Leonardo maybe is stating the idea that air and atmosphere are blue, in conception and reality, thus applying blue in a painting, will describe a rich atmosphere between the viewer and the object.

Perspective is the foundation to painting, or as Leonardo states, “the bridle and rudder.” It is with perspective that a whole painting follows. Leonardo in all his works has established and maintained perspective. He has introduced spectacular settings, foregrounds, and backgrounds, utilizing perspective to keep the painting real in space. “Painting is based upon perspective.”