The Three Right Angles of the Balance
Real, semireal and potential angles, and how a weight's potentia depends on a right angle
Leonardo sets out the nature of the three angles — real, semireal and potential — which are always right angles. The first degree of a weight's potentia over its support occurs when the line of that potentia meets the line of resistance at a right angle. Worked figures track how a value of 16 has a potentia of 4 at f and of 16 at c, and argue that weight m cannot descend unless n rises, which the proportion of the potential arm to the real arm makes impossible. Angles a b c, b c d and f a g exemplify the real, semireal and potential kinds.
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The three angles are always right
The nature of the 3 angles, namely real, semireal and potential, is that they are always right. Angle a b c is of real potentia, b c d of semireal potentia (d c being cord and b c potentia), and f a g potential, its only real line being the cord g n.
Potentia is first felt at a right angle
The first degree of the potentia of weights upon their supports occurs when the line of that potentia joins the line of its resistance at a right angle. This right-angle condition marks the maximum of a support's resistance.
16 has potentia 4 at f and 16 at c
The 4 of f g pulled along d f would resist as 1 against the weight l, so one must set 16, which diminishing by three-quarters leaves 4 at f and 16 at c against 4 at l. The same scaling recurs in the lower figures, where a 4 is potent as 1 at h and as 4 at d, and as 1 at m and 4 at n.
Weight m cannot descend unless n rises
Here the weight m will not go down unless n rises, which is impossible because of the proportion of the potential arm to the real arm, which are alike as to weights. The balance therefore holds.