Archimedes’ “On the Equilibrium of Planes”, Prop 4

 

by Corry Shores
[Search Blog Here. Index-tags are found on the bottom of the left column.]

[Central Entry Directory]

[Mathematics, Calculus, Geometry, Entry Directory]

[Archimedes Entry Directory]

[“On the Equilibrium of Planes”, Entry Directory]

 

Archimedes

On the Equilibrium of Planes

or

The Centres of Gravity of Planes,

Book I

Proposition 4

[The following is quotation]

 

Proposition 4

P4. If two equal weights have not the same centre of gravity, the centre of gravity of both taken together is at the middle point of the line joining their centres of gravity.

[Proved from Prop. 3 by reductio ad absurdum. Archimedes assumes that the centre of gravity of both together is on the straight line joining the centres of gravity of each, saying that this had been proved before. The allusion is no doubt to the lost treatise On levers]

 

 

 

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