Centre of gravity of a triangular prism; dragging a beam
The 'accidental' centre at one-third length, and where to tie a cord to drag a beam without turning
These notes locate the centre of gravity of an "equidistant pyramid" (a wedge-like triangular figure), which Leonardo places at one third of its length and calls the "accidental" centre, distinct from the true centre, because cutting the figure there leaves a longer piece weighing four-fifths of the shorter. Two further problems concern a beam m n dragged by a cord through a channel: at what point the cord should be tied so the beam moves most easily without turning, and what happens when it is pulled through a channel closed in several places.
On this page
The 'accidental' centre of gravity at one-third length
The third of the length of the equidistant pyramid is the centre of its accidental gravity. It is called accidental because it is not the true centre: dividing the figure at the third from the thicker side, the longer piece weighs 4/5 of the shorter.
Where to tie the cord to drag beam m n without turning
If beam m n is dragged by a cord meeting it at an angle, Leonardo asks at which point the cord should be tied to make the motion easiest. He supposes the beam runs through a channel, so that pulling cord c would not let it turn over, though pulling along its central line it would never turn.
Dragging the beam through a channel closed in several places
Beneath a further figure lettered a, b, c he sets the related task of defining what effect it will produce to drag the beam through a channel that is closed in several places.
