by Corry Shores
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[“On the Equilibrium of Planes”, Entry Directory]
Archimedes
On the Equilibrium of Planes
or
The Centres of Gravity of Planes,
Book I
Proposition 3
[The following is quotation]
Proposition 3
P3. Unequal weights will balance at unequal distances, the greater weight being at the lesser distance.
Let A, B he two unequal weights (of which A is the greater) balancing about G at distances AC, BC respectively.
Then shall AC be less than BC. For, if not, take away from A the weight (A – B). The remainders will then incline | towards B [Post. 3]. But this is impossible, for (1) if AC = CB, the equal remainders will balance, or (2) if AC > CB, they will incline towards A at the greater distance [Post. 1].
Hence AC < CB.
Conversely, if the weights balance, and AC < CB, then A > B. (Heath 190-191)
From:
Archimedes. “On the Equilibrium of Planes or The Centres of Gravity of Planes, Book I”. In The Works of Archimedes. Ed. T.L. Heath. Cambridge UP, 1897. Obtained at
https://archive.org/details/worksofarchimede00arch
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