scale-beam

Now since cylinder, cone, and spherical segment are filled up with such circles, the cylinder in its present position [will be in equilibrium at $\alpha$] with the cone + the spherical segment if they are transferred and attached to the scale-beam at $\theta$.

Geometrical Solutions Derived from Mechanics; a Treatise of Archimedes 280? BC-211? BC Archimedes

Therefore also the segment of the right conoid in its present position will be in equilibrium at the point $\alpha$ with the cone if it is transferred and so arranged on the scale-beam at $\theta$ that

Geometrical Solutions Derived from Mechanics; a Treatise of Archimedes 280? BC-211? BC Archimedes

Then if cylinder, spheroid and cone are filled with such circles, the cylinder in its present position will be in equilibrium at the point $\alpha$ with the spheroid $+$ the cone if they are transferred and so arranged on the scale-beam at the point $\alpha$ that $\theta$ is the center of gravity of both.

Geometrical Solutions Derived from Mechanics; a Treatise of Archimedes 280? BC-211? BC Archimedes

In the same way it can be shown that if another straight line be drawn in the parallelogram $\epsilon\gamma \ | \beta\gamma$ the circle formed in the cylinder, will in its present position be in equilibrium at the point $\alpha$ with that formed in the segment of the right conoid if the latter is so transferred to $\theta$ on the scale-beam that $\theta$ is its center of gravity.

Geometrical Solutions Derived from Mechanics; a Treatise of Archimedes 280? BC-211? BC Archimedes

Think of $\gamma\theta$ as a scale-beam with the center at $\kappa$ and let $\mu\xi$ be any straight line whatever $\ |

Geometrical Solutions Derived from Mechanics; a Treatise of Archimedes 280? BC-211? BC Archimedes

Now imagine $\delta\theta$ to be a scale-beam with its center at $\alpha$; let the base of the segment be the circle on the diameter $\beta\gamma$ perpendicular to

Geometrical Solutions Derived from Mechanics; a Treatise of Archimedes 280? BC-211? BC Archimedes

Therefore also the segment of the right conoid in its present position will be in equilibrium at the point $\alpha$ with the cone if it is transferred and so arranged on the scale-beam at $\theta$ that

Geometrical Solutions Derived from Mechanics; a Treatise of Archimedes 280? BC-211? BC Archimedes

Now since cylinder, cone, and spherical segment are filled up with such circles, the cylinder in its present position [will be in equilibrium at $\alpha$] with the cone + the spherical segment if they are transferred and attached to the scale-beam at $\theta$.

Geometrical Solutions Derived from Mechanics; a Treatise of Archimedes 280? BC-211? BC Archimedes

Therefore if the segment and the cone are filled up with circles, all circles in the segment will be in their present positions in equilibrium at the point $\alpha$ with all circles of the cone if the latter are transferred and so arranged on the scale-beam at the point $\theta$ that $\theta$ is their center of gravity.

Geometrical Solutions Derived from Mechanics; a Treatise of Archimedes 280? BC-211? BC Archimedes

Therefore if cylinder, sphere and cone are filled up with such circles then the cylinder in its present position will be in equilibrium at the point $\alpha$ with the sphere and the cone together, if they are transferred and so arranged on the scale-beam at the point $\theta$ that $\theta$ is the center of gravity of both.

Geometrical Solutions Derived from Mechanics; a Treatise of Archimedes 280? BC-211? BC Archimedes