The centre of a suspended body lies below its support
Balance-beam diagrams and the fifteenth conclusion on centres of gravity
A page of statics whose opening proposition states that the centre of any suspended body comes to rest beneath the centre of its support. The lettered balance-beam diagrams, marked with lengths in braccia, are argued to be constrained by necessity, invoking the fifteenth conclusion that each weight's centre falls below its point of support. A page number at the top corner and a small inventory tab pasted at the left edge carry further, untranscribed markings.
On this page
A hanging body settles below its support
The governing proposition: the centre of any suspended body will come to rest below the centre of its support. This principle organises the several balance diagrams drawn on the sheet.
Why the beam cannot hang level: the fifteenth conclusion
Reasoning from experience and from 'reason, the rudder of nature', the note argues that if a b were of equal height, with a c d and b d each 8 braccia long, the perpendicular m n would strike at h rather than n. All the weight g h would then hang at end e and f would be unloaded, contradicting the fifteenth conclusion that each weight's centre falls beneath its support.
Cord tied at the middle of weight c e
For m n to stay level it is necessary that the weight c e be tied at its middle by the cord n d, so that e behaves as if supported by b and c as if supported by a, the perpendicular running from the pole of the balance to the middle of the weight at point d.
Beam arms measured in braccia
The lettered figures are marked with proportional lengths, arms of 8 braccia and divisions labelled 4, used to test whether the beam can rest level.