The prove with the string of beads from "Beghinselen der Weeghconst"
On this page we will discuss Stevin's prove of the following law:
"Two bodies on two different, inclined planes are in balance if their weights are proportional
to the lengths of the two planes". Stevin was apparently so delighted with this really
beautiful and surprisingly simple proof, that he used the illustration to this proof as a vignette
on the title page of many of his books.
His proof goes thus: Let a string of beads be hanged around the triangle ABC with
horizontal base AC. The beads are all of equal weight and equidistant.
Let us neglect the weight of the string and let us assume
that the string can move freely around points S, T and V (see illustration).
Since the beads are equidistant, the number of beads on each inclined plane is proportional
to the length of the plane. Well, suppose the beads on each plane would NOT be in balance.
Then the string would start to move and very soon the beads would have moved exactly one
position. But since the beads are all alike in weight, we would have reached our initial
(supposedly unbalanced) state and therefore the string would continue to move indefinitely.
Well this is absurd and we conclude that our assumption that the beads are not in balance,
is wrong.
Now, if we remove the part of the string SV, the state of rest will be preserved since
this part exerts the same force on S as on V.
This concludes the prove.
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