On the Nature of Force; Weight of a Beam Between Two Walls
Leonardo's definition of force, then how a leaning beam's weight divides between its two supports.
The page opens with Leonardo's celebrated definition of force as a spiritual, incorporeal and invisible power of brief life, born in bodies driven from their natural rest by accidental violence. A triangular diagram of a stick inclined between two walls accompanies a calculation of how a beam of eight pounds and four braccia distributes its weight to the wall a c and to the point e. A further passage, illustrated by a horizontal line with a small circle, reasons geometrically and arithmetically that a long body divides its load between its two contacts f e when level, throws it all onto the lower end g e when vertical, and shares it proportionally (as a e) in intermediate positions.
On this page
What force is
Leonardo defines force as a spiritual power, incorporeal and invisible, caused with brief life in bodies that accidental violence has driven out of their natural being and rest. It is spiritual because it holds active life, incorporeal because the body in which it is born grows neither in weight nor form, and short-lived because it always strives to overcome its cause and, once that is overcome, destroys itself.
Weight a leaning beam gives to wall a c and to point e
To find how much of an eight-pound, four-braccia stick weighs on the wall a c and how much on the point e, halve the base d e of the triangle a c e; the portion the upper part of the stick occupies stays on the wall a c, the rest goes to e. A body whose length exceeds its breadth and depth throws the greater share of its heaviness onto the lower part that falls below its horizon.
Sharing the load between two ends (f e, g e, a e)
A long body gives equal load to its two contacts f e when they are equidistant from the centre, but when vertical the lower end g e receives everything and the upper nothing; between the two cases the load is shared. For a weight of 4 braccia and 8 pounds hung above point c, the mean of 4 and 8 is 6, so e bears 6 and c a bears 2, confirmed by dividing the triangle's base at d.
