The Complete Works of Archimedes, Vol. 2

which follows immediately from Euclid IX, 35, because

In Volume III, p. 312, 10 ff., Eutocius cites Book II of the Conics of Apollonius; but unless a trace of an older recension of Apollonius is detected here too, it seems he was deceived, trusting his memory. For what he says: "On the hyperbola, the center of the figure, at which the diameters intersect one another, is outside," is nowhere read in Book II of the Conics. Rather, his words seem to be able to be referred to I, def. alt. 1, p. 42 (Halley ed.): "Let the bisection of the diameter of each of the hyperbola and the ellipse be called the center of the section." Yet this is true: that it can be understood from Conics II that the center of the hyperbola falls outside the figure (see, for example, II, 45: "To find the center of a given ellipse or hyperbola").

In this third volume, I have had no new collations of the Paris codices, with one or two exceptions. In the second index, I have mostly omitted the Latin interpretation, and altogether I have striven for brevity even more than in the first. Both for this reason, and because the first index was in the hands of the typesetters while I was preparing the second, a troublesome unevenness of the two indices arose. In the prolegomena, I had intended to treat the dialect of Archimedes, but since I wished to examine this question more deeply, and time was lacking as my Italian journey was imminent, I thought it better to defer the matter than to treat it now in an imperfect manner, which would displease me myself.