Proposition II states no new fact. Essentially it means that if a sphere, cylinder, and cone (always circular) have the same radius, $r$, and the altitude of the cone is $r$ and that of the cylinder $2r$, then the volumes will be as $4 : 1 : 6$, which is true, since they are respectively $\frac{4}{3}\pi r^3$, $\frac{1}{3}\pi r^3$, and $2\pi r^3$. The interesting thing, however, is the method pursued, the derivation of geometric truths from principles of mechanics. There is, too, in every sentence, a little suggestion of Cavalieri, an anticipation by nearly two thousand years of the work of the greatest immediate precursor of Newton. And the geometric imagination that Archimedes shows in the last sentence is also noteworthy as one of the interesting features of this work: ``After I had thus perceived that a sphere is four times as large as the cone. . . it occurred to me that the surface of a sphere is four times as great as its largest circle, in which I proceeded from the idea that just as a circle is equal to a triangle whose base is the periphery of the circle, and whose altitude is equal to its radius, so a sphere is equal to a cone whose base is the same as the surface of the sphere and whose altitude is equal to the radius of the sphere.'' As a bit of generalization this throws a good deal of light on the workings of Archimedes's mind. In proposition III he considers the volume of a spheroid, which he had already treated more fully in one of his letters to Dositheos,\footnote{\selectlanguage{greek} Per\`i kwnoeide\~wn kai sfairoeide\~wn.} and which contains nothing new from a mathematical standpoint. Indeed it is the method rather than the conclusion that is interesting in such of the subsequent propositions as relate to mensuration. Proposition V deals with the center of gravity of a segment of a conoid, and proposition VI with the center of gravity of a hemisphere, thus carrying into solid geometry the work of Archimedes on the equilibrium of planes and on their centers of gravity.\footnote{\selectlanguage{greek} 'Epip\'edwn \`isorropi\~wn \^h k\'entra bar\~wn \'epip\'edwn.} The general method is that already known in the treatise mentioned, and this is followed through proposition X.