The Seventh Demonstration: Squaring 12 = 8 + 4 into 144
A smaller square joined to a larger one, with a note that the sixteen must be counted twice.
The Seventh of Leonardo's geometric-algebra demonstrations divides a line into 12 = 8 + 4 and squares it. A smaller square is joined to a larger one, the cells labelled 64, 32, 32 and 16, and a note explains that the value 4 stands for the two parts placed above, so that the 16 is to be counted twice. The parts recover the square of 12, which is 144, in the Euclidean manner of dissecting the square of a divided line.
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The line divided 12 = 8 + 4
A segment is divided into 12 = 8 + 4, the base quantities whose square the figure below will decompose. The whole and its two parts drive the whole demonstration.
Smaller square joined to the larger
A smaller square is set against a larger one, the cells carrying 64, 32, 32 and 16. Leonardo adds that the 4 stands for the two parts placed above, so that the 16 must be counted twice – the accounting device by which the dissection sums correctly to the square of the whole.