Theory of the balance: arms, appendicles and centres of gravity
Real versus potential arms, the angles at their junctions, and the mathematical, natural and magnitude centres
In closely reasoned notes Leonardo analyses the balance (bilancia), distinguishing its 'real' arms and appendicles - the material, palpable parts - from 'potential' ones, invisible lines running from the centre of the balance to the right angle of each junction. He examines the acute and obtuse angles formed where an appendicle meets an arm, observing that a straight line joined to a curved one makes an obtuse angle, and that of the acute junctions the more acute sustains the lesser weight. A further set of definitions separates the mathematical (accidental) centre of gravity, the natural centre that divides a body into two equal weights, and the centre of magnitude that divides it into two equal lengths - all three coinciding in bodies of uniform quality.
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Real and potential arms and appendicles of the balance
Each arm of the balance is double: one part is called 'real' and the other 'potential'; the appendicles of the weights are double in the same way. The real arms and appendicles are material and palpable, while the potential ones are invisible and impalpable, their limits running from the centre of the balance to the right angle of their junction, which is always right-angled.
Mathematical, natural, and magnitude centres of gravity
The mathematical centre is the centre of the accidental gravity of suspended bodies; the natural centre divides a body's gravity into two equal weights (having place only at the centre of the world); and the centre of magnitude divides a body into two equal lengths. In bodies of uniform quality all three fall in one and the same place.
Angles at the junction of arm and appendicle
The angles at the common appendicle are obtuse, being composed of a straight line joined to a curved one; those made by the real appendicle with the real arm are acute, and of these the more acute sustains the lesser weight.
