some form of burning-mirror, e.g. a paraboloid of revolution, which would reflect to one point all rays falling on its concave surface in a direction parallel to its axis.
CHAPTER II.
GREEK GEOMETRY TO ARCHIMEDES.
In order to enable the reader to arrive at a correct understanding of the place of Archimedes and of the significance of his work it is necessary to pass in review the course of development of Greek geometry from its first beginnings down to the time of Euclid and Archimedes.
Greek authors from Herodotus downwards agree in saying that geometry was invented by the Egyptians and that it came into Greece from Egypt. One account says:—
“Geometry is said by many to have been invented among the Egyptians, its origin being due to the measurement of plots of land. This was necessary there because of the rising of the Nile, which obliterated the boundaries appertaining to separate owners. Nor is it marvellous that the discovery of this and the other sciences should have arisen from such