Painting Versus Poetry, and the Principles of Painting
No true science without mathematics; the paragone of painting and poetry; point, line, surface, and body.
The page completes the argument about the zero - the sign that is nothing in itself yet, by its position, multiplies a number tenfold without limit - before declaring that no human inquiry can be called true science unless it passes through mathematical demonstration. Leonardo then contrasts painting and poetry: poetry sets its subjects in the imagination through written words, whereas painting presents them directly to the eye, which receives their true likenesses as if they were natural. A further chapter names the first principles of the science of painting - the point, then the line, then the surface, and then the body clothed in that surface. Sciences that merely begin and end in the mind, he holds, lack the certainty that only experience can give.
On this page
The power of the zero
Leonardo completes his account of the zero, the figure that in itself is worth nothing yet, placed after a unit, makes it read as ten, and with each further zero multiplies the number tenfold without end. All the noughts of the universe, he notes, are equal to a single nought in their substance and worth.
No true science without mathematics
No human investigation, he asserts, may be called a true science unless it passes through mathematical demonstration. Sciences that begin and end in the mind are denied truth, for they admit no experience, without which nothing gives certainty of itself.
The difference between painting and poetry
As shadow is to the body that casts it, so imagination is to its effect, and so poetry stands to painting. Poetry lodges its subjects in the imagination by means of written letters, while painting presents them really before the eye, which receives their likenesses no differently than if they were natural.
The first principles of the science of painting
The first principle of the science of painting is the point; the second, the line; the third, the surface; and the fourth, the body that is clothed in that surface. This concerns what is to be represented, the sentence breaking off at the foot of the page.