'Experience never errs': friction at a weighing pivot
The maxim on experience, deflected motion, and fraction sums for pivot friction
The double-page spread opens with Leonardo's celebrated methodological maxim that 'experience never errs; only our judgements err' when we expect from it effects not present in our experiments. A lettered diagram then shows how a moving body travels straight toward the center unless a resistance deflects it onto a new path defined by necessity. The bulk of the sheet works through numerical examples of the friction ('confregazione') at the pivot or pin of a weighing device, computing how much extra weight a counterpoise needs to make up the quarter of its force lost to friction, and how this changes when the arm is doubled. A version of the maxim recurs at the foot of the right-hand page, reproaching those who blame innocent experience for their own ignorance.
On this page
'Experience never errs; only our judgements err'
Leonardo declares that experience never fails; only our judgements do, when they promise themselves from it an effect not present in our experiments. Given a principle, whatever follows from it is a true consequence unless it is impeded; and if some impediment follows, the resulting effect shares in the impediment in proportion as that impediment is more or less powerful than the principle.
A moving body deflected from its straight path by resistance
Let the line a b be the motion of a body impeded only by uniform air: its motion runs straight toward the center. But if it must move along the line c d e and meets the impediment e f, it then follows a second motion g h, which participates in the impediment the more, the more powerful the impediment is than the original principle.
Friction at the pivot consumes a quarter of the weight
A pole a weighing 2 libbre with a weight b attached makes 4 libbre, and this produces a friction at the pin able to resist a quarter of any weight sustained there. Leonardo tracks how weights placed at d, c and f must be increased to make up the quarter of force each loses to the friction of the pin.
Counterpoise on a doubled arm over the friction pivot
When the counterpoise arm is double that of the friction, the counterpoise is half the opposing force, so 3/16 is set against 3/8; because these 3/16 lack a quarter of their power to their own friction, another sixteenth is added, giving 4/16, and so on. Half of the counterpoise, he finds, always remains to be recovered, remedied only by loading the pole further.
Reproach to those who blame experience
Men wrongly complain of experience, accusing it with bitter reproaches of being fallacious. Leonardo tells them to leave experience alone and turn their lament instead against their own ignorance, which drives them with vain and foolish desires to promise themselves things not in its power.
