Studies of the Balance: Natural and Accidental Figures
Equal weights at equal distances, and true versus false positions of the beam
A page of balance (bilancia) studies argues that a beam carrying equal weights oppositely applied at equal distances from the fulcrum can rest with its ends at different heights without abandoning its natural tendency to equilibrium. Several diagrams are labelled 'natural,' 'false,' and 'accidental' figures, with lettered points (b, a, d, c; f, e, g, h) and the recurring values 4 and 8 marking the arms and weights. Further pairs at the foot contrast a 'natural' figure of two parallels with an 'accidental' one having a single parallel.
On this page
Equal weights at equal distances may rest at any height
A balance with equal weights applied oppositely at equal distances from the pole can hold its extremities at various heights without forgoing its natural desire for equilibrium. The claim heads the study at the upper right.
Natural, false and accidental figures of the balance
The beam diagrams are captioned 'natural figure' with points b 4 a and d 4 c, a 'false figure' said to stand below for the natural one, and an 'accidental figure' with points f 4 e and 8 g 4 h.
Natural figure of two parallels versus accidental with one
The lowest pair is labelled 'natural, of 2 parallels' and 'accidental, with a single parallel,' contrasting the geometric arrangement of the beams.
