Beam balanced by six counterweights
Statics of a 60-pound beam held level by ranked counterweights, with lever geometry
The sheet works out how a beam (trave) weighing 60 pounds is held level by a rank of counterweights hung from cords. Leonardo asks the reader to build the figure first simply, with six counterweights and no semicircles, then to derive a general rule; a second beam shows how many weights are needed to raise its head when pulled by the cords o q and r q. He treats the line y r, drawn from centre 5, as the geometric demonstrator of all the imagined levers, and jots references to the Chronicle, the Bible and Master Luca's Arithmetic in the lower corner.
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Beam held level by six counterweights
Make the figure first in simple form, with only six counterweights and no semicircles. Set down how much each counterweight must weigh to stay level with the 60-pound beam, and how much each would weigh to serve alone as its counterweight, then form the general rule with the semicircles below.
The line y r as demonstrator of the levers
The line y r is produced from the centre 5 and demonstrates all the levers imagined between the pulling cords and the foot of the beam — the levers a r, n r, m r, o r, p r and q r. A single circular line between a and r is said to suffice for the office of all six figures.
How many weights raise the beam's head
To raise the head of the beam with cord o q, see how many times n S goes into the length S q — four times — so four weights at n o balance the head. With cord r q, the line from the beam's right angle goes twice into the length, so two weights at r balance the upper end.
References jotted in the corner
A short list of sources noted in the lower-left corner: in the Chronicle, in the Bible, and in the Arithmetic of Master Luca.