Euclid's Staff and the Impact of a Ball on Fresh Earth
A rod for measuring a wall's height and width; the dent left by a struck ball
A lettered drawing (a, d, c, b) accompanies a note that if a ball is beaten onto a slab of fresh earth the impression a b is found much greater than d c. A second drawing (a, S, n, c) presents 'Euclid's staff', a rod ten braccia long fitted with crosses: holding the eye at c and enlarging or shrinking the crosses until they span a wall, one reads its height and width by proportion. A faint plan is drawn across the upper half of the sheet, and further faint matter is present but was not transcribed.
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Euclid's staff: measuring a wall by proportion
The rod a–S–n–c is ten braccia long and carries crosses that are grown or shrunk until they occupy the whole height and width of the wall, the eye held at point c. Since the staff's length is known, one reads what fraction of the ten braccia the cross covers: as much as a b enters into c, so much S c enters into c n.
A ball beaten onto a slab of fresh earth
If you beat a ball onto a slab of fresh earth, as shown in the drawing, you will find the impression a b to be much greater than d c. The note breaks off before giving the reason.
The ten-braccio measuring rod
The instrument is a rod ('bacolo') ten braccia long, first fixed firmly, with crosses at the ends of its rods that are adjusted along the handle. Knowing the aggregate length, the observer converts the crosses' widths into the wall's dimensions by direct proportion.