Squares on a line divided into 8 and 4 (Euclid II.7)
The square of 144 subdivided into a gnomon, with balance-beam parallelograms
The folio is headed 'Seventh, [book] second,' a reference to Euclid's Elements, and works a line divided into segments 8 and 4 (whole 12). The square on 12 (144) is drawn and subdivided into a smaller square (64), gnomon strips and rectangles, with a cancelled square at the top. At the foot, parallelograms are hung from the arms of a balance to display the equality of the areas, and side columns sum the parts to 160.
On this page
The whole square (144) subdivided into square and gnomon
The square on the line 12 is 144, subdivided using the parts 8 and 4 into a smaller square (64), two 32 strips and further pieces. The layout carries the labels 12 - 64 32 - 32 - 8 4.
Parallelograms suspended from a balance beam
At the foot the areas 64 16 and 48 48 16 are drawn as parallelograms hung from the arms of a balance to show their equality. The associated figures total 160.
Numeric columns summing the areas
Two columns tally the component areas: a left column 48, 48, 64 summing to 160, and a right column 99, 99, 16 summing to 208. The figures accompany the divided line marked 8 16 - 12 4.
Citation of 'the seventh of the second'
The page opens by naming its authority, the seventh proposition of the second book of Euclid's Elements. The demonstration that follows applies that proposition to the line divided into 8 and 4.