Dividing a line: the gnomon and the square of the whole
Segment a 6 c 6 b 4 d and a square decomposed into 36, 24, 24, 16 summing to 100
Headed 'sixth', the page demonstrates the square on a divided line in the manner of Euclid's second book. A segment is marked a c b and then a 6 c 6 b 4 d with the total 10; the right column raises a square on part of the line and takes it gradually apart, while a gnomon is set equal to a rectangle with the figures 8, 8, 4. The final figure decomposes the square into the four regions 36, 24, 24, 16, and the margin verifies 64 + 36 = 100. The letters a, c, b, d mark the points of division.
On this page
Line divided a 6 c 6 b 4 d, total 10
A segment is divided and labelled a 6 c 6 b 4 d, the parts totalling 10. It is the base line whose square is decomposed in the figures below.
Gnomon equal to a rectangle
A gnomon is set equal to a rectangle, carrying the figures 8, 8, 4. The equivalence is the Book II relation between the gnomon and the rectangle on the parts of the line.
Square of the whole decomposed: 36 + 24 + 24 + 16 = 100
The square on the whole line is broken into the four regions 36, 24, 24, 16, alongside the figures 64 and 100. It exhibits numerically the square of the divided line.
Margin check 64 + 36 = 100
The left margin lists 16, 4, 64, 36 and 100, verifying that the partial squares 64 and 36 add to the square of the whole, 100.