By L. I. Sedov, J. R. M. Radok
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Additional resources for A course in continuum mechanics, vol. 1: Basic equations and analytical techniques
2 Concerning the natural motion of falling bodies, Aristotle maintained in Book I of the Treatise on the Heavens that the “relation which weights have to each other is reproduced inversely in their durations of fall. If a weight falls from a certain height in so much time, a weight which is twice as great will fall from the same height in half the time. ” In his Physics (Part V), Aristotle remarked on the acceleration of falling heavy bodies. A body is attracted towards its natural place by means of its heaviness.
Suppose that there is, in the fluid, another solid RSQY which is made of the fluid and is equal and similar to BHTC, that part of the body EHTF which is immersed in the fluid. The portions of the fluid which are contained by the surface XO in the first pyramid and the surface OP in the second pyramid are equally placed and continuous with each other. But they are not equally compressed. For the portions of the fluid contained in XO are compressed by the body EHTF and also by the fluid contained by the surfaces LM, XO and those of the pyramid.
He sets out to determine the relation between γ and θ. The weight α on the plane μ has the form of a sphere with centre ε. Pappus reduces the investigation of the equilibrium of this sphere on the inclined plane to the following problem. A balance supported at λ carries the weight α at ε and the weight β which is necessary to keep it in equilibrium at η—the end of the horizontal radius εη. The law of the angular lever, which Pappus borrows from Archimedes’ Πε ζυγν or from Hero’s Mechanics, provides the relation On the horizontal plane where the power necessary to move α is γ, the power necessary to move along β will be Pappus then assumes that the power θ that is able to move the weight α on the inclined plane μ will be the sum of the powers δ and γ, that is Fig.
A course in continuum mechanics, vol. 1: Basic equations and analytical techniques by L. I. Sedov, J. R. M. Radok