On Equilibrium (-1799)

"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, "On the Equilibrium of Planes" Vol. I, 3rd century BC)

"Two magnitudes whether commensurable or incommensurable, balance at distances reciprocally proportional to the magnitudes." (Archimedes, "On the Equilibrium of Planes" Vol. I, 3rd century BC)

"Inequality is the cause of all local movements. There is no rest without equality." (Leonardo da Vinci, Codex Atlanticus, 1478)

"There must be a double method for solving mechanical problems: one is the direct method founded on the laws of equilibrium or of motion; but the other one is by knowing which formula must provide a maximum or a minimum. The former way proceeds by efficient causes: both ways lead to the same solution, and it is such a harmony which convinces us of the truth of the solution, even if each method has to be separately founded on indubitable principles. But is often very difficult to discover the formula which must be a maximum or minimum, and by which the quantity of action is represented.” (Leonhard Euler, “Specimen de usu observationum in mathesi pura", Novi Commentarii academiae scientiarum Petropolitanae 6, 1756/57)

"Statics is the science of the equilibrium of forces. In general, force or power is the cause, whatever it may be, which induces or tends to impart motion to the body to which it is applied. The force or power must be measured by the quantity of motion produced or to be produced. In the state of equilibrium, the force has no apparent action. It produces only a tendency for motion in the body it is applied to. But it must be measured by the effect it would produce if it were not impeded. By taking any force or its effect as unity, the relation of every other force is only a ratio, a mathematical quantity, which can be represented by some numbers or lines. It is in this fashion that forces must be treated in mechanics." (Joseph-Louis de Lagrange, "Mechanique Analytique", 1788)