Quotes from book
On the Equilibrium of Planes

Name: On the Equilibrium of Planes
Author: Archimedes

ArchimedesOriginal title Περὶ ἐπιπέδων ἱσορροπιῶν

On the Equilibrium of Planes is a treatise by Archimedes in two volumes. The first book establishes the law of the lever, and locates the centre of gravity of the triangle and the trapezoid. According to Pappus of Alexandria, Archimedes' work on levers caused him to remark: "Give me a place to stand on, and I will move the Earth." . The second book, which contains ten propositions, examines the centres of gravity of parabolic segments.

“Equal weights at equal distances are in equilibrium and equal weights at unequal distances are not in equilibrium but incline towards the weight which is at the greater distance.”

Archimedes book On the Equilibrium of Planes

Book 1, Postulate 1.
On the Equilibrium of Planes

“It follows at once from the last proposition that the centre of gravity of any triangle is at the intersection of the lines drawn from any two angles to the middle points of the opposite sides respectively.”

Archimedes book On the Equilibrium of Planes

Book 1, Proposition 14.
On the Equilibrium of Planes

“The centre of gravity of any parallelogram lies on the straight line joining the middle points of opposite sides.”

Archimedes book On the Equilibrium of Planes

Book 1, Proposition 9.
On the Equilibrium of Planes

“In any triangle the centre of gravity lies on the straight line joining any angle to the middle point of the opposite side.”

Archimedes book On the Equilibrium of Planes

Book 1, Proposition 13.
On the Equilibrium of Planes