The Book of Painting: Whether Painting Is a Science
The treatise's opening: defining science from first principles - the point, line, surface, and the zero of arithmetic.
This opening leaf of Leonardo's Book of Painting asks whether painting is a science, defining science as mental discourse that proceeds from its ultimate principles. Taking geometry as his model, he traces the surface of bodies down to the line and then to the point, which he calls the first principle of geometry - a thing so minimal that nothing in nature or the mind can give rise to it. He argues that points have no material substance, so that even a thousand of them, could they be joined, would compose no part of a surface. The passage closes by invoking the zero, the tenth figure of arithmetic, as proof that a part may be said to equal its whole, the argument continuing onto the following page.
On this page
Painting defended as a science
Leonardo opens the treatise by asking whether painting is a science, and defines science (scienzia) as mental discourse originating in its ultimate principles. He sets up geometry as the exemplary true science against which painting's own claim will be tested.
From surface to line to the point
Geometry begins from the surface of bodies, finds its origin in the line that bounds that surface, and the line in turn ends in the point. The point is the first principle of geometry, that than which nothing smaller can exist, and it possesses no material substance of its own; not even all the points of the universe, if united, would compose part of a surface.
The zero invoked as proof
To argue that a part can be equal to its whole, Leonardo turns to the zero - the tenth figure of arithmetic - which is nothing in itself. The sentence breaks off at the foot of the page, the demonstration carrying over to the verso.