Balance puzzles and the centre of gravity of a quadrilateral
Four equilibrium problems, closing with how to locate a figure's centroid
The right-hand column carries four balance diagrams — beams with shaded, wedge-shaped weight distributions and hanging pans marked with a plus — each posed as a question about equilibrium: what weight must stand at m to match n, on which arm weight should be added, and where to place ten pounds against a ten-pound load. The final note gives a method for finding the centre of gravity of a quadrilateral a b c d by detaching the triangle a b D, taking its centroid at one third, and combining it with the centroid of the remaining figure on a balance. Leonardo treats the geometric figures themselves as weights to be weighed against one another.
On this page
What weight at m balances n
A beam bearing the mark 8, with ends m and n, is posed as a puzzle: what weight must stand at m to stand equal with n. It opens a set of equilibrium questions left for the reader to work out.
Placing ten pounds against a ten-pound load
Given the weight n of 10 pounds, the problem asks what weight to set on the opposite arm of the balance, and in what position the 10 pounds of m must be placed for the beam to hang level.
Centroid of a quadrilateral by decomposition
To find the centre of gravity of the quadrilateral a b c d, Leonardo detaches the triangle a b D and takes its centre at one third, then takes the centre of the remaining figure a D c d at the middle of its length, and sets each on the balance in its fitting place.