Double-proportion balance and centres of solid figures
Equilibrium of 2-to-4 arms; true centres of a truncated pyramid and a triangular rod
Also headed 'Tested by experiment', the top of the page repeats the double-proportion balance (arms 2 and 4): the short arm leaves 3 on the long side, so a 6 hung at its midpoint stands equal to the opposite 3. Below, short notes turn to the centres of gravity of solid shapes, marking point a as the 'true centre' of a suspended truncated pyramid and labelling a triangular rod 4 4. Several small sketches at the foot show suspended wedge-like beams and truncated-pyramid bodies, accompanied by a further brief untranscribed label.
On this page
Balancing arms 2 and 4 with a midpoint weight
With arms in double proportion (2 and 4), the 2 takes from the 4 a weight subdouble to itself, one, so that 4 remains 3 and 2 becomes nothing. Because the shorter arm is subdouble the other, a 6 hung at its midpoint stands equal to the 3 at the opposite midpoint.
True centre of a suspended truncated pyramid
A suspended truncated pyramid is marked with point a, identified as its true centre. A companion triangular rod is labelled 4 4, and a further truncated pyramid is shown suspended without accompanying text.