Blows, levers, and turning a great screw
How an oblique fall weakens a blow, and how a screw lifts eighty thousand pounds
Notes with marginal diagrams continuing Leonardo's study of blows and weights. He shows that a wider hammer face penetrates lead less deeply, and that a weight falling along a more oblique line delivers a weaker blow, using a right triangle labeled a, b, m, n, S and a staff M-n-S treated as a lever. Two lower sketches turn to mechanics of the screw: a lever m raising an eighty-thousand-pound load, and a cross-section of screw m-n arguing that a single thread costs as much effort to turn as a hundred threads.
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Width of the striking face and depth of penetration
Of two hammers of equal weight falling from equal height, the one twice as wide penetrates only half as far into the lead. Breadth of the blow, not weight alone, governs how deep it drives.
An oblique fall gives a weaker blow (m n into m S)
Two equal weights falling from equal height deliver blows that differ as their fall-lines differ in obliquity. As many times as line m n enters into line m S, so many times weaker is the blow of weight b than that of weight a.
The staff M S striking as a lever at n
Holding M in the hand and striking with staff M S at point n, the blow loses effect as M n enters into n S, because the portion n S beyond the point acts as a lever. The longer the far arm, the less the blow tells.
Measuring the force to turn an 80,000-pound screw
A sketch of a lever driving a large screw threaded through a plank and attached to a load marked 80000. Leonardo proposes a method for measuring how much weight, placed on lever m, is needed to turn the screw bearing eighty thousand pounds.
One thread costs as much as a hundred
In the cross-section of screw m n, Leonardo argues that turning a single-threaded screw takes as much effort as a hundred-threaded one. A single thread supports the whole ten pounds, while ten threads each carry one pound of the same load.