A square inscribed in a right triangle
The excess parts of the legs, multiplied, give a rectangle equal to the square
This spread sets out a plane-geometry theorem in words and lettered figures. Leonardo proves that when a square is inscribed at the right angle of a right triangle with its opposite corner touching the hypotenuse, the parts by which the triangle's legs exceed the square's sides, multiplied one by the other, yield a rectangle equal in area to the square. A second, shorter note poses the related problem of stretching a given quadrilateral to a given length and asking how much its width must shrink. The figures are lettered a b c, a c and d e b f.
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Square inscribed at the right angle of a triangle
Let a b c be the right angle of the right triangle and a c its hypotenuse; d e b f is the square inscribed so that its angle d b f coincides with the triangle's right angle while the opposite corner touches a c. The legs' excesses d a and f c, multiplied one by the other, form a rectangle equal in area to the square d e b f, its width a d and its length f c.
Stretching a quadrilateral to a given length
A brief problem asks to extend the length of a given quadrilateral to match the length of a given line, and then to determine by how much its width must contract. It treats the inverse relation between length and breadth at constant area.