Conception: the circumscribed is smaller than the circumscribing
A geometric axiom tested against the surfaces of a cylinder and the water around it
Headed "Conception," the note lays down an axiom: the circumscribed figure is always smaller than the one that circumscribes it, and two surfaces laid exactly upon one another, neither exceeding the other, are equal. Leonardo then tests this against a cylinder clothed by the water or air around it, arguing against an opponent that the cylinder's boundary belongs to the cylinder's own substance and the water's boundary to the water's. There are therefore two distinct surfaces, one circumscribing the other and so greater. The sheet is filled with continuous mirror-script prose and bears no diagrams.
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The circumscribed is always smaller than the circumscribing
The opening axiom states that a circumscribed figure is always smaller than the figure that circumscribes it. It adds that two surfaces laid one upon the other, neither exceeding the other nor exceeded by it, are without doubt equal.
The cylinder clothed by water: two boundaries, not one
Against an opponent who claims the surface of a cylinder and of the water clothing it are one and the same, Leonardo answers that the cylinder's boundary is of the cylinder's own substance and the water's boundary of the water's. Hence there are two surfaces circumscribing one another, and by the first conception one is greater than the other.
