se times, on the hypothesis of rays issuing from the eye
to the object, instead of passing, as we consider them to do, from the
object to the eye. It is, however, on the excellencies of his Elements
of Geometry that the durable reputation of Euclid depends; and though
the hypercriticism of modern mathematicians has perhaps successfully
maintained such objections against them as that they might have been
more precise in their axioms, that they sometimes assume what might be
proved, that they are occasionally redundant, and their arrangement
sometimes imperfect, yet they still maintain their ground as a model of
extreme accuracy, of perspicuity, and as a standard of exact
demonstration. They were employed universally by the Greeks, and, in
subsequent ages, were translated and preserved by the Arabs.

[Sidenote: The writings and works of Archimedes.]

Great as is the fame of Euclid, it is eclipsed by that of Archimedes the
Syracusan, born B.C. 287, whose connection with Egyptian science is not
alone testified by tradition, but also by such facts as his acknowledged
friendship with Conon of Alexandria, and his invention of the screw
still bearing his name, intended for raising the waters of the Nile.
Among his mathematical works, the most interesting, perhaps, in his own
estimation, as we may judge from the incident that he directed the
diagram thereof to be engraved on his tombstone, was his demonstration
that the solid content of a sphere is two-thirds that of its
circumscribing cylinder. It was by this mark that Cicero, when Quaestor
of Sicily, discovered the tomb of Archimedes grown over with weeds. This
theorem was, however, only one of a large number of a like kind, which
he treated of in his two books on the sphere and cylinder in an equally
masterly manner, and with equal success. His position as a geometer is
perhaps better understood from the assertion made respecting him by a
modern mathematician, that he came as near to the discovery of the
Differential Calculus as can be done without the aid of algebraic
transformations. Among the special problems he treated of may be
mentioned the quadrature of the circle, his determination of the ratio
of the circumference to the diameter being between: 3.1428 and 3.1408,
the true value, as is now known, being 3.1416 nearly. He also wrote on
Conoids and Spheroids, and upon that spiral still passing under his
name, the genesis of which had been suggested to him by Conon. In hi