Right triangle with an inscribed square
A right triangle, an inscribed square, and a problem of reshaping a rectangle to a given length.
The left page (245v) sets out a geometrical proposition on a right triangle with a square inscribed in its right angle, arguing that the amounts by which the triangle's legs exceed the square's sides, multiplied together, yield a rectangle equal in area to the square. A right-triangle diagram with a shaded inner triangle and a small rectangle accompanies the argument. At the top of the right page (246r), in mirror script, a second problem asks how much a quadrilateral narrows in width when its length is stretched to a given line.
On this page
Excess legs of a right triangle over an inscribed square
The right triangle a b c shares its right angle with an inscribed square d e b f whose opposite corner touches the hypotenuse a c. The segments by which the triangle's legs exceed the square's sides are d a on one side and f c on the other. Multiplying d a by f c gives a rectangle equal in area to the square, with width a d and length f c.
Diagram of the triangle and square
Above the text a small rectangle is drawn, and below it a right triangle enclosing a shaded inner triangle, illustrating the square set into the right angle and the excess portions of the legs. The lettering keys the figure to the proposition.
Reshaping a quadrilateral to a given length
A short problem states the intention to extend the length of a given quadrilateral to match the length of a given line, then asks by how much its width is thereby reduced. It is written in mirror script at the head of the right leaf.