Which prop best supports a loaded beam; lever forces
Comparing props a p and a q, lever and counter-lever, and line intersections
On folio 99r Leonardo studies how to support a weight n at the end a of a beam a b that is too weak to resist it, comparing two possible props, a p and a q, to find which is of greater effectiveness. A longer note works through the mechanics of pulling the weight s along different lines (n a, a m, f a, e a), tracing how the effort changes as the lever and counter-lever lengths vary and concluding that along line e a the load would in effect become infinite. A third passage, beside a column of figures down the right margin, treats the intersection of two straight lines at right angles as a true point and how the 'contact' grows when the four enclosing angles become unequal. The facing leaf, folio 102v, is blank.
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Choosing a prop for a beam too weak for its load
Leonardo wishes to hold the weight n at the end a of a beam a b that is not strong enough to resist it, and considers giving it either the prop a p or the prop a q, asking which will be of greater power.
Lever and counter-lever: effort along different lines
Pulling the weight s along line n a costs about as much power as the weight's resistance, since the lever a e and the counter-lever a e are one and the same line. Pulled along a m the mover gains 1/12 of effort, along f a it gains a quarter more than along n a, and along e a no force could ever lift it, the lever being divisible to infinity so that the load in effect becomes infinite.
Intersection of two lines at right angles as a true point
The crossing of two straight lines among four right angles is made at a true point; it occupies a space greater than a point in proportion as, of the four angles enclosing it, the two opposite ones differ more from the other two. Thus the intersection a is made at a point, while the intersection r is made in a greater contact than a point.