Archimedes

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:—

1. 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

Papadopoulos Kerameus at Constantinople. This proved to contain writings of Archimedes copied in a good hand of the tenth century. An attempt had been made (fortunately with only partial success) to wash out the old writing, and then the parchment was used again to write a Euchologion upon. However, on most of the leaves the earlier writing remains more or less legible. The important fact about the MS. is that it contains, besides substantial portions of the treatises previously known, (1) a considerable portion of the work, in two books, On Floating Bodies, which was formerly supposed to have been lost in Greek and only to have survived in the translation by Wilhelm of Mörbeke, and (2) most precious of all, the greater part of the book called The Method, treating of Mechanical Problems and addressed to Eratosthenes. The important treatise so happily recovered is now included in Heiberg’s new (second) edition of the Greek text of Archimedes (Teubner, 1910-15), and some account of it will be given in the next chapter.

The order in which the treatises appear in the MSS. was not the order of composition; but from the various prefaces and from internal evidence