Centre of Gravity of Two Joined Rods
Combining the centres of two rods on a balance beam, by the method of the 'Theory'
Two diagrams treat two rods joined end to end as a single body. In the first, n marks the centre of rod a b and m the centre of rod c f, and f is named as the centre of the whole combined weight. The second gives Leonardo's working method: bring each rod's centre onto the balance m n, divide the beam into as many parts as the rods weigh in pounds, then exchange the weight-ratios against the beam divisions inversely, as set out in the fourth proposition of his 'Theory'.
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Centres of the two rods a b and c f
The centre of rod a b is n and the centre of rod c f is m, and f is named as the centre of the whole weight of the two rods attached together. The upper diagram shows the two aligned rods with these labelled points.
Combined centre found on the balance m n
To find the combined centre of gravity, take the centre of each rod and refer it to the balance m n, divide the beam into as many parts as there are pounds in the two rods, then swap the weight-proportions against the beam-divisions inversely, following the fourth proposition of the 'Theory'.