On 'nothing', the arithmetical zero, and Vespucci's geometry book
Leonardo's discourse on nothingness in time and nature, tied to the zero of arithmetic
The leaf carries Leonardo's most sustained meditation on 'nothing' (nulla): it exists only in time, between past and future, and among words for impossible things, but has no place in nature, since where nothing were, a vacuum would be. He binds the idea to mathematics, noting that this nothing has its part equal to the whole and is represented by the tenth character of the arithmeticians, the zero, which behaves alike in division and multiplication, in adding and subtracting. Among the arguments sit a note that every drop of water in watered silk makes its own wave when colour is thrown on it, and a personal memorandum that Vespucci means to give him a book of geometry. Geometric figures with numbers and a plumb-line sketch accompany the text.
On this page
The 'nothing' that resides between past and future
The nothing near us contains in itself all the things that have no being; in respect to time it resides between the past and the future and possesses nothing of the present, and in respect to nature it has no place. Its part is equal to the whole and the divisible to the indivisible.
Nothing as the zero, the tenth character of the arithmeticians
This nothing has its part equal to the whole and the whole to the part, and produces the same sum in its division as in its multiplication, and in adding as much as in subtracting, as is shown among the arithmeticians by its tenth character, which represents this nothing. Every continuous quantity is intellectually divisible to infinity.
Vespucci to give Leonardo a book of geometry
Amid the notes on the upper sheet stands a brief memorandum: Vespucci wants to give me a book of geometry. It follows an observation that every drop of water in watered silk makes its own wave, and that colour thrown upon it behaves in the manner of water.