The Fourth Demonstration: A Square of 12 Split into 48 and 96
A line divided 4 + 8 = 12 and its square dissected into rectangles of 48 and 96 (= 144).
The Fourth demonstration divides a line into 4 + 8 = 12 and draws the square built on it. The square is cut into two rectangles labelled 48 and 96, whose sum is 144, the square of 12. A side calculation restates the multiplication (12 x 4 = 48, 12 x 8 = 96), confirming the dissection arithmetically. The sheet is a cleaner, simpler instance of the same Euclidean squaring of a divided line.
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The line divided 4 + 8 = 12
A segment is divided into 4 and 8, whose sum is 12 – the side of the square drawn below. The division fixes the two parts whose products build the square.
Square split into two rectangles, 48 and 96
The square on the line 12 is divided into two rectangles labelled 48 and 96 (that is, 12 x 4 and 12 x 8), which together make 144. The figure shows the square of the whole line as the sum of the rectangles on its parts.