Inclined-plane motion, bending beams, and hurled bodies
Weight n falls faster as line a b enters line a c; squaring a tree trunk
This richly illustrated page gathers short propositions on motion and the strength of materials. A right-triangle diagram of an inclined plane (vertices a, b, c, with balls m and n and the word pruova) states that weight n falls as much faster than weight m as line a b enters into line a c. Leonardo then treats the bending of wood, no body bends without shortening, the middle bends most easily, and a longer piece bends with less force, and, with a square-in-circle sketch, notes that squaring a tree trunk into the largest beam costs a quarter of its thickness, weight, and strength. Further notes, illustrated by a bladder and a knife stuck in a board, observe that a body hurled too hard travels less far and that something moved beyond its nature springs furiously back. A maxim added later urges that details answer to the parts and the parts to the whole.
On this page
Motion on an inclined plane (a, b, c)
In the right-triangle diagram (upper vertex a, right angle b, lower vertex c) a ball m sits at c and a ball n at b. Weight n will fall as much faster than weight m as line a b enters into line a c. The word pruova (proof) is written along the hypotenuse.
On the bending of wood
No body can be bent without decreasing its length. In a body of consistent width the part farthest from the ends bends most easily, and of two equally heavy pieces the longer bends with less force. He reminds himself to prove it by experience with a thin wood over two supports.
Squaring a tree trunk loses a quarter
To square a tree trunk into the largest possible square beam, you diminish it by one-fourth of its thickness, weight, and strength. An irregular square inscribed in a circle shows the beam's cross-section taken from the trunk.
A body hurled too hard travels less far
Something hurled through the air by a power greater than suits its lightness travels a shorter path than if moved by a lesser power. Make a bundle or a bladder: thrown slowly it goes far, thrown hard it goes only a short way.
A knife sprung back beyond its place
Something moved beyond its nature returns furiously beyond its nature. A knife stuck into a board, pulled and released, passes beyond the place where it stood before it was moved.