Partitioning the Hexagon Inscribed in Its Circle
A proof that similar figures keep the same proportion to their squares, with two circle-hexagon-square diagrams
A narrow strip of paper carries a geometrical demonstration headed 'On the partition of the hexagon from the circle that surrounds it', followed by 'conception'. Two diagrams at the right each set a hexagon and a square within a circle: a larger 'first' figure lettered b, c, a, e, d, and a smaller 'second' figure lettered o, m, n, q, p. Leonardo argues that, the two figures being similar, the portion n m o of the second stands to its square n o p q as the portion a c b of the first stands to its own square - proportion holding from similar part to similar part as from similar whole to similar whole.
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Partition of the hexagon within its circle
The sheet opens with the theme 'On the partition of the hexagon from the circle that surrounds it', followed by the word 'conception', introducing the construction of a hexagon and square set inside a circle.
First figure b c a e d and its square
The larger diagram encloses a hexagon and a square within a circle, lettered b, c, a, e, d and marked 'first'. The stated rule is that proportion runs from similar part to similar part just as from similar whole to similar whole.
Second figure o m n and the proportion of squares
A smaller similar figure, lettered o, m, n, q, p and marked 'second', follows. Being similar to the first, its portion n m o stands to its square n o p q in the same proportion as the portion a c b of the first figure stands to its square.