Lengthening a compressed board without changing thickness
Diagrams of boards a b c and d e, solved by Euclid's first book
Rectangular diagrams at the right show a board to be lengthened, labelled with the points a, b and c, and a resulting lengthened board d e. The text poses the problem of how much a board narrowed into a given space extends when its thickness is unchanged. Leonardo solves it by reducing the board to a square (the fifth proposition of Euclid's first book), marking the compression within the square's height, and extending it to length d e by the seventh of the first.
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Diagrams of a board to be lengthened (a b c)
Rectangular figures show a board to be lengthened, labelled with the points a, b and c, and set up the geometry for the construction described alongside. A further figure records the board once lengthened, marked d e.
Extending a narrowed board by a Euclidean construction
The problem asks how much a board narrowed into a given space lengthens when its thickness stays constant. Leonardo takes the board a b, reduces it to a square by the fifth proposition of the first book, marks the space of compression in the square's height, and by the seventh of the first extends it to its due length, which is d e.