Book on Painting: Whether Painting Is a Science
Opening of the Trattato — the geometer's point and the arithmetic zero as first principles
This folio transmits the title and opening chapter of Leonardo's Book on Painting, compiled by Francesco Melzi and headed as the work of the Florentine painter and sculptor. Chapter 1 asks whether painting is a science, defining science as mental discourse grounded in ultimate principles and taking geometry as its model: surface reduces to line, line to the indivisible point. Leonardo argues the point has no material substance, then turns to arithmetic, invoking the zero (the 'tenth figure') to illustrate a quantity that is nothing yet governs number. The scanned leaf itself appears blank; the reading is grounded in the accompanying transcription.
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Is painting a science?
The treatise opens by asking whether painting deserves the name of science. Leonardo defines science as the mental discourse that arises from its ultimate first principles, insisting that no inquiry counts as true knowledge unless it rests on such foundations.
The point as the first principle of geometry
Taking geometry as the model of a true science of continuous quantity, Leonardo traces the surface of bodies back to the line that bounds it, and the line back to the point. The point is that than which nothing can be smaller, and it has no share in the material substance of the surface; even all the points of the universe united could compose no part of a surface.
The zero, tenth figure of arithmetic
To show how a part can be said to equal its whole, Leonardo appeals to the zero, or nought, calling it the tenth figure of arithmetic. In itself it is worth nothing, yet it stands as proof in his argument about quantity and the composition of wholes from points.