The 'Mistress' Balance and Tests of Springs and the Screw
Weighing the power of the screw, and whether length, thickness or width doubles a spring's strength
Leonardo opens with the 'Maesstra' (the Mistress or master-instrument), a beam balance he has built to reveal its secrets, showing how a pound placed at n stays equal with a load placed at f. Below, a screw-and-nut apparatus (a being the 'mother' or nut) is offered as a way to weigh and test the power of the screw, and a small figure asks how far and along what line a spring will fling the weight n. Two curved springs each labelled 'dupla' (double) accompany refutations of common beliefs: that a spring of doubled length has double the power, or that one of doubled thickness has doubled strength. He closes by posing the open question of whether doubling a spring's width, at equal length and thickness, leaves its power unchanged.
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The 'Maesstra': a balance revealing when loads at n and f are equal
'Maesstra' (Mistress). Leonardo says he has built himself the master-instrument, which faithfully shows its secrets and makes him understand how every pound placed at n stands equal with a load placed at f, for the reason he showed 'in the 5th of the ninth.'
Weighing and testing the power of the screw
A way of weighing and experimenting on the power of the screw, where a is its 'mother' (the nut); by this method one can grasp its nature in fine detail and prove it 'double and single.' Letters a, l, q, m, n, r, f mark the apparatus.
How far the spring flings the weight n
A marginal note beside the figure poses the problem: n — how far the spring will fling the weight n, and along what line.
Refuted: that doubling a spring's length doubles its power
Many have believed that springs of equal thickness and width are of double power to one another when their length is doubled, each making the same quality of curvature. But, Leonardo insists, here is a great deception. One of the arcs is marked 'dupla' (double).
Doubled thickness, and the open question of doubled width
Others believe that springs of equal length and width but doubled thickness are of doubled strength at equal curvature; these too are in great error. It is then asked whether springs of equal thickness and length but doubled width are of equal power at equal bending.