Stretching a rectangle sideways to find its lost length
Reducing an oblong to a square, then rebuilding it to a set length (props. 8-9)
The page continues Leonardo's series on the "inversion of the measures of a rectangle." One proposition (9) stretches the oblong a b c d in the direction of its breadth to a given distance o i and asks by how much its length shortens; another, the converse of the eighth, rebuilds the smaller rectangle a d f g from a square. Both constructions reduce the figure to an equilateral square by the fifth proposition and rebuild it by the sixth. Two semicircle diagrams with inscribed squares and rectangles are drawn across the middle of the sheet.
On this page
Converse of the eighth: rebuilding rectangle a d f g
Placing the rectangle a c h i, Leonardo makes from it the equilateral square K l a s by the fifth proposition, then by the sixth makes from that square the smaller rectangle a d f g reduced to the required length. This is stated as the converse of the eighth proposition.
Stretching rectangle a b c d to the length o i
The oblong a b c d is to be stretched in the direction of its breadth to the given length o i, and its shortening is sought. Leonardo reduces it to the equilateral square b e o t by the fifth proposition, then by the sixth rebuilds the long rectangle o f i K, finding a b c d lowered by the amount c to f and lengthened by the whole of o i.