A Body Falling While the Cosmos Turns Once in 24 Hours
Why the fall stays straight though the elements revolve; the stone dropped from a tower
Folio 55r continues the thought-experiment of the previous page: a heavy body falling from the sphere of fire while the whole cosmos rotates once every 24 hours. Using a top-right diagram of concentric arcs lettered a, b, c, d, m, Leonardo argues that although the body traces a helical curve it never leaves the straight line running from its starting point to the centre of the world, so its motion is 'composite' of straight and curved. He closes with the everyday case that gives the abstraction bite: a stone thrown from a tower does not strike the tower's side before it reaches the ground.
On this page
Why a falling body keeps a straight path though the earth turns
The heavy body b, moving from a toward the world's centre m, makes a helical descent yet never strays from the straight line joining its start to the centre. As it descends from a to b to d, the point a rotates round to c, so the body is always found on the straight line from the current centre-point to m. After 24 hours it reaches earth beneath its starting place, and the motion is composite.
The stone thrown from the tower
If a body descends from the highest to the lowest of the elements in 24 hours its motion is composite of straight and curved. It never leaves the shortest line from start to the centre, coming to rest at the point directly below where it began. From this it follows that a stone dropped from a tower does not strike the tower's side before it hits the ground.
A full revolution of the elements in twenty-four hours
The falling body is imagined dropping from the sphere of fire while the elements complete one whole revolution about the centre of the world every 24 hours. This rotating cosmos is the frame within which the straight-versus-curved descent is analysed.
