Squaring a quadrilateral by equal removals from the diagonal
Finding the side of the equal square when two spaces about the diagonal are made equal
A continuation of the quadrature studies on the recto, this sheet works out how to find the side of a square equal to a given quadrilateral. Leonardo argues that when the two spaces o p and c n about the diagonal are equal and the line o n through their ends also touches the corner g of the quadrilateral, then c n (or o p) is the side of the required square. The proof completes the quadrilateral into o m h n, uses the diagonal o n to halve it, and removes equal parts from each side. A lettered rectangle with diagonals occupies the centre of the sheet.
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The side of the square from equal spaces about the diagonal
Leonardo states that a n is similar to m o and that b o and b n are similar. When the spaces o p and c n are equal and the line o n through their ends also touches the corner g of the quadrilateral to be squared, then c n (or equally o p) is a side of the sought square.
Proof by removing equal parts
He completes the quadrilateral along o m into m n, forming o m h n, which the line o n divides into two equal parts. Since removing equal parts from equals leaves equals, he takes Z x from one side and S v from the other, leaving X t equal between them.