material; his objective is always something new, some definite addition to the sum of knowledge. Confirmation of this is found in the introductory letters prefixed to most of his treatises. In them we see the directness, simplicity and humanity of the man. There is full and generous recognition of the work of predecessors and contemporaries; his estimate of the relation of his own discoveries to theirs is obviously just and free from any shade of egoism. His manner is to state what particular discoveries made by his predecessors had suggested to him the possibility of extending them in new directions; thus he says that, in connexion with the efforts of earlier geometers to square the circle, it occurred to him that no one had tried to square a parabolic segment; he accordingly attempted the problem and finally solved it. Similarly he describes his discoveries about the volumes and surfaces of spheres and cylinders as supplementing the theorems of Eudoxus about the pyramid, the cone and the cylinder. He does not hesitate to say that certain problems baffled him for a long time; in one place he positively insists, for the purpose of pointing a moral, on specifying two propositions which he had enunciated but which on further investigation proved to be wrong.

The ordinary MSS. of the Greek text of Archimedes give his works in the following order:—

On the Sphere and Cylinder (two books). 2. Measurement of a Circle. 3. On Conoids and Spheroids. 4. On Spirals. 5. On Plane Equilibriums (two books). 6. The Sandreckoner. 7. Quadrature of a Parabola.

A most important addition to this list has been made in recent years through an extraordinary piece of good fortune. In 1906 J. L. Heiberg, the most recent editor of the text of Archimedes, discovered a palimpsest of mathematical content in the “Jerusalemic Library” of one